Finite Group Databasebeta

← #30546484

Subgroups — #30546484

Order 15616.

4782 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840597C211yesmaximal, characteristic, complemented
2C2×#16840561C211yesmaximal, characteristic, complemented
3C22×#14519798C211yesmaximal, characteristic, complemented
4#21459151C211yesmaximal, characteristic, complemented
5#21455138C214yesmaximal, complemented
6#21455124C214yesmaximal, complemented
7#21455113C211yesmaximal, characteristic, complemented
8#21455112C211yesmaximal, characteristic, complemented
9#21455108C211yesmaximal, characteristic, complemented
10#21455107C211yesmaximal, characteristic, complemented
11#21455092C211yesmaximal, characteristic, complemented
12#21455088C211yesmaximal, characteristic, complemented
13#21455087C211yesmaximal, characteristic, complemented
14#21455040C214yesmaximal, complemented
15#21455038C214yesmaximal, complemented
16#21454333C211yesmaximal, characteristic, complemented
17#416×D61C211yesmaximal, characteristic, complemented
18#408×D61C211yesmaximal, characteristic, complemented
19C61×#3009C211yesmaximal, characteristic, complemented
20#16840597—28no—
21#16840597—28no—
22C2×#14519824—21no—
23C2×#14519824C2211yescharacteristic
24C2×#14519824C2211yescharacteristic
25C2×#14519824C2212yescomplemented
26C2×#14519822—22no—
27C2×#14519822—21no—
28C2×#14519822C2211yescharacteristic
29C2×#14519822C2212yescomplemented
30C22×#11758226C2211yescharacteristic, complemented
31C22×#11758224—21no—
32C22×#11758224—22no—
33C22×#11758224C2211yescharacteristic
34C22×#11758224C2212yescomplemented
35C2×#41×D61—21no—
36C2×#41×D61C2211yescharacteristic
37C2×#41×D61C2211yescharacteristic
38C2×#41×D61C2212yescomplemented
39#16840561—28no—
40C2×#14519809C2212yescomplemented
41C2×#14519808C2211yescharacteristic, complemented
42C2×#14519805C2211yescharacteristic, complemented
43C2×#14519804C2212yescomplemented
44C2×#14519802C2211yescharacteristic, complemented
45C2×#14519800C2212yescomplemented
46C2×#14519798—28no—
47C2×#14519798C2214yescomplemented
48C2×#14519798C2214yescomplemented
49C2×#14519798C2212yescomplemented
50C22×#11758202C2211yescharacteristic, complemented
51C22×#11758190C2211yescharacteristic, complemented
52C22×#11758199C2211yescharacteristic, complemented
53C2×M16×D61C2211yescharacteristic, complemented
54C22×C8×D61C2211yescharacteristic, complemented
55#16840342C2214yescomplemented
56#16840337—21no—
57#16840336C2211yescharacteristic, complemented
58#16840331C2211yescharacteristic, complemented
59#16840330—21no—
60#16840326C2211yescharacteristic, complemented
61#16840323—22no—
62#16840313—21no—
63#16840311—21no—
64#16840275C2214yescomplemented
65#16840270—22no—
66#117×D61C2211yescharacteristic, complemented
67#16839922C2214yescomplemented
68#16839921C2214yescomplemented
69#16839921C2214yescomplemented
70#16839917C2214yescomplemented
71#16839916C2214yescomplemented
72#16839911C2214yescomplemented
73#16839909C2214yescomplemented
74#16839908C2214yescomplemented
75#16839908C2214yescomplemented
76#16839907C2214yescomplemented
77#16839903C2214yescomplemented
78#16839902C2214yescomplemented
79#16839897C2214yescomplemented
80#16839896C2214yescomplemented
81#16839772C2211yescharacteristic, complemented
82#16839770C2211yescharacteristic, complemented
83#16839767C2211yescharacteristic, complemented
84#16839760C2214yescomplemented
85#16839759C2211yescharacteristic, complemented
86#16839758C2211yescharacteristic, complemented
87#16839757C2212yescomplemented
88#16839756C2211yescharacteristic, complemented
89#16839755C2212yescomplemented
90#16839755C2214yescomplemented
91#103×D61C2212yescomplemented
92#102×D61C2212yescomplemented
93#16839730C2211yescharacteristic, complemented
94#16839729C2211yescharacteristic, complemented
95#16839728C2211yescharacteristic, complemented
96#16839727C2214yescomplemented
97C22⋊C8×D61C2214yescomplemented
98C2×H(5,𝔽2)×C61C2211yescharacteristic
99C2×#137×C61C2211yescharacteristic, complemented
100C22×SD16×C61C2211yescharacteristic, complemented
101C61×#536C2211yescharacteristic, complemented
102C61×#452C2214yescomplemented
103C61×#450C2214yescomplemented
104C61×#418C2211yescharacteristic, complemented
105C61×#416C2211yescharacteristic, complemented
106C61×#408C2211yescharacteristic, complemented
107#14519824—216no—
108#14519824—24no—
109#14519824—28no—
110#14519824—28no—
111#14519824—24no—
112#14519824—24no—
113#14519824—24no—
114#14519822—232no—
115#14519822—216no—
116#14519822—24no—
117#14519822—28no—
118#14519822—28no—
119#14519822—24no—
120C2×#11758226—21no—
121C2×#11758226—21no—
122C2×#11758226—24no—
123C2×#11758226—24no—
124C2×#11758226D411yescharacteristic
125C2×#11758226C2312yes—
126C2×#11758226C2312yes—
127C2×#11758226C2311yescharacteristic
128C2×#11758222—21no—
129C2×#11758222—22no—
130C2×#11758222—21no—
131C2×#11758222—22no—
132C2×#11758222C2312yes—
133C2×#11758222C2311yescharacteristic
134C2×#11758222C2312yes—
135C2×#11758222C2311yescharacteristic
136C2×#11758224—232no—
137C2×#11758224—216no—
138C2×#11758224—22no—
139C2×#11758224—21no—
140C2×#11758224—22no—
141C2×#11758224—22no—
142C2×#11758224—22no—
143C2×#11758224—21no—
144C2×#11758224—22no—
145C2×#11758224—28no—
146C2×#11758224—28no—
147C2×#11758224—21no—
148C2×#11758224—22no—
149C2×#11758224—21no—
150C2×#11758224—24no—
151C2×#11758224—22no—
152C2×#11758224—21no—
153C2×#11758224—22no—
154C2×#11758224D412yes—
155C2×#11758224D411yescharacteristic
156C2×#11758224D418yescomplemented
157C2×#11758224C2312yes—
158C2×#11758224C2312yes—
159C2×#11758224C2311yescharacteristic
160C2×#11758224C2312yes—
161C2×#11758224C2312yes—
162#41×D61—216no—
163#41×D61—28no—
164#41×D61—28no—
165#41×D61—24no—
166#41×D61—24no—
167#41×D61—24no—
168#41×D61D418yescomplemented
169C22×Dic122—21no—
170C22×Dic122—22no—
171C22×Dic122C2312yes—
172C22×Dic122C2311yescharacteristic
173C2×Q8×D61—21no—
174C2×Q8×D61D411yescharacteristic
175C2×Q8×D61C2312yes—
176C2×Q8×D61C2311yescharacteristic
177C22×D244—21no—
178C22×D244C2311yescharacteristic
179C22×C22⋊D61—21no—
180C22×C22⋊D61—22no—
181C22×C22⋊D61—22no—
182C22×C22⋊D61—22no—
183C22×C22⋊D61—22no—
184C2×D4×D61—21no—
185C2×D4×D61—22no—
186C2×D4×D61—21no—
187C2×D4×D61—22no—
188C2×D4×D61D412yes—
189C2×D4×D61D411yescharacteristic
190C2×D4×D61C2312yes—
191C2×D4×D61C2311yescharacteristic
192C23×Dic61—21no—
193C23×Dic61—22no—
194C22×C4×D61—21no—
195C22×C4×D61—22no—
196C22×C4×D61—21no—
197C22×C4×D61C2312yes—
198C22×C4×D61C2311yescharacteristic
199#14519809—28no—
200#14519808—24no—
201#14519805—24no—
202#14519804—28no—
203#14519802—24no—
204#14519800—28no—
205#14519798—216no—
206#14519798—216no—
207#14519798—28no—
208C2×#11758202—24no—
209C2×#11758202C2314yes—
210C2×#11758202C2312yes—
211C2×#11758190—24no—
212C2×#11758190C2314yes—
213C2×#11758190C2312yes—
214C2×#11758201C2312yes—
215C2×#11758201C2312yes—
216C2×D488C2312yes—
217C2×#11758199—24no—
218C2×#11758199C2314yes—
219C2×#11758199C2312yes—
220C2×#11758194C2311yescharacteristic
221C2×#11758189C2312yes—
222M16×D61—24no—
223C22×#92418C2311yescharacteristic
224C2×C8×D61—24no—
225C2×C8×D61C2312yes—
226C2×C8×D61C2312yes—
227C2×C8×D61C2312yes—
228#14519775—21no—
229#14519774—21no—
230#14519773—21no—
231#14519766—21no—
232#14519766—21no—
233#14519765—21no—
234#14519762—24no—
235#14519760—22no—
236#14519755—24no—
237#14519753C2314yes—
238#14519752—24no—
239#14519752C2314yes—
240#14519751C2314yes—
241#14519750—24no—
242#14519750—24no—
243#14519747—24no—
244#14519747—22no—
245#14519745—22no—
246#14519739—24no—
247#14519737—24no—
248#14519736C2311yescharacteristic
249#14519735C2312yes—
250#14519734—21no—
251#14519733—21no—
252C4⋊C4×D61C2312yes—
253C22⋊C4×D61—21no—
254C42×D61—21no—
255#14519702C2312yes—
256#14519702C2314yes—
257#14519701C2312yes—
258#14519700C2312yes—
259#14519700C2314yes—
260#14519699C2312yes—
261#14519698C2312yes—
262#14519698C2314yes—
263#14519697C2312yes—
264C22⋊#92418C2314yes—
265#14519689C2314yes—
266#14519689C2314yes—
267H(5,𝔽2)×C61—24no—
268H(5,𝔽2)×C61—24no—
269C2×#41×C61—21no—
270C2×#41×C61C2312yes—
271C2×#41×C61C2311yescharacteristic
272C2×#41×C61C2311yescharacteristic
273C22×Q8×C61C2311yescharacteristic
274C22×D4×C61—22no—
275C22×D4×C61—21no—
276C22×D4×C61C2312yes—
277C22×D4×C61C2311yescharacteristic
278#137×C61—24no—
279C2×Q16×C61C2312yes—
280C2×SD16×C61—24no—
281C2×SD16×C61C2314yes—
282C2×SD16×C61C2312yes—
283C2×M16×C61C2311yescharacteristic
284C22×C8×C61C2311yescharacteristic
285C4⋊Q8×C61—21no—
286#124×C61—21no—
287#123×C61—22no—
288C22⋊Q8×C61C2314yes—
289#117×C61C2311yescharacteristic
290#103×C61C2312yes—
291#102×C61C2312yes—
292#102×C61C2314yes—
293C22⋊C8×C61C2314yes—
294C24×C61—22no—
295C24×C61—21no—
296C23×D61—22no—
297C23×D61—21no—
298C23×D61—21no—
299C23×D61C2×D412yes—
300C23×D61C2×D411yescharacteristic
301#41×C61—28no—
302#41×C61—24no—
303#41×C61—24no—
304#41×C61—22no—
305#41×C61—22no—
306#41×C61—22no—
307#41×C61C2×D414yes—
308C2×Q8×C61—21no—
309C2×Q8×C61—22no—
310C2×Q8×C61—22no—
311C2×Q8×C61C2×D411yescharacteristic
312C2×Q8×C61C2412yes—
313C2×Q8×C61C2411yescharacteristic
314C2×D4×C61—216no—
315C2×D4×C61—28no—
316C2×D4×C61—22no—
317C2×D4×C61—21no—
318C2×D4×C61—24no—
319C2×D4×C61—24no—
320C2×D4×C61—22no—
321C2×D4×C61—21no—
322C2×D4×C61—22no—
323C2×D4×C61C2×D412yes—
324C2×D4×C61C2×D411yescharacteristic
325C2×D4×C61C2×D414yes—
326C2×D4×C61C2412yes—
327C2×D4×C61C2411yescharacteristic
328C22×C4×C61—22no—
329C22×C4×C61—21no—
330C22×C4×C61—21no—
331C22×C4×C61C2412yes—
332C22×C4×C61C2411yescharacteristic
333C2×C22⋊D61—216no—
334C2×C22⋊D61—216no—
335C2×C22⋊D61—216no—
336C2×C22⋊D61—216no—
337C2×C22⋊D61—22no—
338C2×C22⋊D61—21no—
339C2×C22⋊D61—28no—
340C2×C22⋊D61—22no—
341C2×C22⋊D61—22no—
342C2×C22⋊D61—21no—
343C2×C22⋊D61—22no—
344C2×C22⋊D61—22no—
345C2×C22⋊D61—24no—
346C2×C22⋊D61—22no—
347C2×C22⋊D61—21no—
348C2×C22⋊D61C2×D412yes—
349C2×C22⋊D61C2×D412yes—
350C2×C22⋊D61C2×D412yes—
351C22×Dic61—216no—
352C22×Dic61—22no—
353C22×Dic61—21no—
354C22×Dic61—28no—
355C22×Dic61—21no—
356C22×Dic61—22no—
357C22×Dic61—22no—
358C22×Dic61—22no—
359C22×Dic61—22no—
360C22×Dic61C2×D412yes—
361C22×Dic61C2×D411yescharacteristic
362#11758226—24no—
363#11758226—22no—
364#11758226—24no—
365#11758226—24no—
366#11758226—24no—
367#11758226—24no—
368#11758226—44no—
369#11758226—44no—
370#11758226C2×D414yes—
371Q8×D61—28no—
372Q8×D61—24no—
373Q8×D61—24no—
374Q8×D61—22no—
375Q8×D61—24no—
376Q8×D61C2×D414yes—
377#11758224—216no—
378#11758224—216no—
379#11758224—216no—
380#11758224—216no—
381#11758224—216no—
382#11758224—216no—
383#11758224—28no—
384#11758224—28no—
385#11758224—216no—
386#11758224—216no—
387#11758224—24no—
388#11758224—24no—
389#11758224—28no—
390#11758224—28no—
391#11758224—24no—
392#11758224—28no—
393#11758224—28no—
394#11758224—24no—
395#11758224—22no—
396#11758224—24no—
397#11758224—24no—
398#11758224—24no—
399#11758224C2×D418yes—
400#11758224C2×D414yes—
401#11758224C2×D418yes—
402D4×D61—216no—
403D4×D61—216no—
404D4×D61—28no—
405D4×D61—28no—
406D4×D61—28no—
407D4×D61—24no—
408D4×D61—24no—
409D4×D61—24no—
410D4×D61—22no—
411D4×D61C2×D414yes—
412#11758222—216no—
413#11758222—216no—
414#11758222—28no—
415#11758222—22no—
416#11758222—22no—
417#11758222—22no—
418#11758222—24no—
419#11758222—28no—
420#11758222—24no—
421#11758222—24no—
422#11758222—24no—
423#11758222C2×D414yes—
424C2×D244—21no—
425C2×D244—22no—
426C2×D244—22no—
427C2×D244—22no—
428C2×D244—22no—
429C2×D244—21no—
430C2×D244—24no—
431C2×D244—44no—
432C2×D244C2×D412yes—
433C2×D244C2×D411yescharacteristic
434C2×D244C2412yes—
435C2×D244C2411yescharacteristic
436C2×C4×D61—216no—
437C2×C4×D61—22no—
438C2×C4×D61—21no—
439C2×C4×D61—22no—
440C2×C4×D61—21no—
441C2×C4×D61—21no—
442C2×C4×D61—28no—
443C2×C4×D61—24no—
444C2×C4×D61—24no—
445C2×C4×D61—22no—
446C2×C4×D61—22no—
447C2×C4×D61—22no—
448C2×C4×D61—44no—
449C2×C4×D61C2×D412yes—
450C2×C4×D61C2×D412yes—
451C2×C4×D61C2×D411yescharacteristic
452C2×C4×D61C2×D411yescharacteristic
453C2×C4×D61C2×D414yes—
454C2×C4×D61C2×D414yes—
455C2×C4×D61C2412yes—
456C2×C4×D61C2411yescharacteristic
457C2×C4×D61C2411yescharacteristic
458C2×Dic122—28no—
459C2×Dic122—216no—
460C2×Dic122—22no—
461C2×Dic122—21no—
462C2×Dic122—22no—
463C2×Dic122—22no—
464C2×Dic122—21no—
465C2×Dic122—24no—
466C2×Dic122—24no—
467C2×Dic122C2×D412yes—
468C2×Dic122C2×D411yescharacteristic
469C2×Dic122C2×D414yes—
470C2×Dic122C2411yescharacteristic
471C2×Dic122C2412yes—
472Q16×C61—24no—
473SD16×C61—28no—
474SD16×C61—24no—
475M16×C61—22no—
476C2×C8×C61—22no—
477C2×C8×C61C2412yes—
478C2×C8×C61C2412yes—
479C4⋊C4×C61—24no—
480C4⋊C4×C61C2412yes—
481C22⋊C4×C61—21no—
482C22⋊C4×C61—24no—
483C42×C61—21no—
484C22⋊Dic61—21no—
485#11758202—24no—
486#11758202—28no—
487#11758201—24no—
488#11758201—24no—
489#11758199—28no—
490#11758199—24no—
491#11758198—22no—
492#11758198—24no—
493#11758198—24no—
494#11758198—24no—
495C4⋊Dic61C2412yes—
496#11758196—22no—
497#11758196—24no—
498C4×Dic61—21no—
499C4×Dic61—22no—
500#11758194—22no—
501C2×#92418—22no—
502C2×#92418C2412yes—
503C2×#92418C2412yes—
504D488—24no—
505#11758190—24no—
506#11758190—28no—
507#11758189—24no—
508C8×D61—24no—
509C8×D61—24no—
510C8×D61—24no—
511C23×C61—28no—
512C23×C61—21no—
513C23×C61—22no—
514C23×C61—24no—
515C23×C61—82no—
516C23×C61—84no—
517C23×C61C22×D412yes—
518C23×C61C22×D411yescharacteristic
519C22×D61—21no—
520C22×D61—28no—
521C22×D61—24no—
522C22×D61—24no—
523C22×D61—22no—
524C22×D61—42no—
525C22×D61—44no—
526C22×D61—42no—
527C22×D61—82no—
528C22×D61—84no—
529C22×D61—82no—
530C22×D61#12014yes—
531C22×D61C22×D412yes—
532C22×D61C22×D411yescharacteristic
533C22×D61C22×D411yescharacteristic
534Q8×C61—22no—
535Q8×C61—21no—
536Q8×C61—22no—
537Q8×C61—22no—
538Q8×C61—42no—
539Q8×C61C22×D412yes—
540D4×C61—28no—
541D4×C61—28no—
542D4×C61—24no—
543D4×C61—24no—
544D4×C61—22no—
545D4×C61—24no—
546D4×C61—22no—
547D4×C61—21no—
548D4×C61C22×D414yes—
549D4×C61C22×D412yes—
550C2×C4×C61—28no—
551C2×C4×C61—21no—
552C2×C4×C61—24no—
553C2×C4×C61—22no—
554C2×C4×C61—22no—
555C2×C4×C61—22no—
556C2×C4×C61—22no—
557C2×C4×C61—42no—
558C2×C4×C61C22×D412yes—
559C2×C4×C61C22×D411yescharacteristic
560C2×C4×C61C22×D412yes—
561C2×C4×C61C22×D412yes—
562C2×C4×C61C2511yescharacteristic
563C22⋊D61—28no—
564C22⋊D61—28no—
565C22⋊D61—28no—
566C22⋊D61—28no—
567C22⋊D61—24no—
568C22⋊D61—24no—
569C22⋊D61—24no—
570C22⋊D61—28no—
571C22⋊D61—28no—
572C22⋊D61—24no—
573C22⋊D61—24no—
574C22⋊D61—24no—
575C22⋊D61—84no—
576C2×Dic61—28no—
577C2×Dic61—28no—
578C2×Dic61—28no—
579C2×Dic61—24no—
580C2×Dic61—22no—
581C2×Dic61—21no—
582C2×Dic61—28no—
583C2×Dic61—24no—
584C2×Dic61—28no—
585C2×Dic61—24no—
586C2×Dic61—22no—
587C2×Dic61#12014yes—
588C2×Dic61C22×D412yes—
589C2×Dic61C22×D411yescharacteristic
590C2×Dic61C22×D411yescharacteristic
591D244—24no—
592D244—24no—
593D244—22no—
594D244—21no—
595D244—22no—
596D244—22no—
597D244—44no—
598D244—44no—
599D244—42no—
600D244—84no—
601D244C22×D412yes—
602C4×D61—28no—
603C4×D61—28no—
604C4×D61—24no—
605C4×D61—24no—
606C4×D61—24no—
607C4×D61—22no—
608C4×D61—22no—
609C4×D61—24no—
610C4×D61—24no—
611C4×D61—44no—
612C4×D61—44no—
613C4×D61—82no—
614C4×D61#12014yes—
615C4×D61#12014yes—
616C4×D61C22×D412yes—
617C4×D61C22×D412yes—
618C4×D61C22×D412yes—
619C4×D61C22×D412yes—
620Dic122—28no—
621Dic122—28no—
622Dic122—22no—
623Dic122—24no—
624Dic122—22no—
625Dic122—21no—
626Dic122—24no—
627Dic122—24no—
628Dic122C22×D412yes—
629Dic122C22×D414yes—
630C8×C61—22no—
631C8×C61—22no—
632#92418—22no—
633#92418—22no—
634#60366—611nomaximal, Sylow
635C22×C61—22no—
636C22×C61—24no—
637C22×C61—22no—
638C22×C61—22no—
639C22×C61—24no—
640C22×C61—42no—
641C22×C61—44no—
642C22×C61—84no—
643C22×C61—88no—
644C22×C61C2×#12012yes—
645C22×C61C23×D411yescharacteristic
646C2×D61—22no—
647C2×D61—22no—
648C2×D61—24no—
649C2×D61—22no—
650C2×D61—22no—
651C2×D61—44no—
652C2×D61—42no—
653C2×D61—44no—
654C2×D61—42no—
655C2×D61—84no—
656C2×D61—84no—
657C2×D61—88no—
658C2×D61—84no—
659C2×D61C2×#12012yes—
660C2×D61C2×#12012yes—
661C4×C61—22no—
662C4×C61—22no—
663C4×C61—42no—
664C4×C61—42no—
665C4×C61C2×#12012yes—
666C4×C61C23×D411yescharacteristic
667C4×C61C23×D411yescharacteristic
668Dic61—22no—
669Dic61—24no—
670Dic61—22no—
671Dic61—42no—
672Dic61C2×#12012yes—
673Dic61C2×#12012yes—
674C2×#585—611no—
675C2×#575—611no—
676C22×#135—611no—
677#3449—611no—
678#3013—614no—
679#3012—614no—
680#3011—611no—
681#3011—611no—
682#3010—611no—
683#3010—611no—
684#3009—611no—
685#3009D6111yescharacteristic, complemented
686#3008—611no—
687#3008—611no—
688#3002—614no—
689#3002—614no—
690#2896—611no—
691C2×#416—611no—
692C2×#408—611no—
693C2×C61—22no—
694C2×C61—42no—
695C2×C61—42no—
696C2×C61—44no—
697C2×C61C22×#12011yescharacteristic
698C2×C61#358412yes—
699D61—22no—
700D61—22no—
701D61—42no—
702D61—42no—
703D61—82no—
704#585—1228no—
705#585—1228no—
706C2×2−1+4—611no—
707C2×2−1+4—612no—
708C2×2−1+4—611no—
709C2×2−1+4—1221no—
710C2×H(5,𝔽2)—611no—
711C2×H(5,𝔽2)—612no—
712C2×H(5,𝔽2)—1222no—
713C2×H(5,𝔽2)—1221no—
714C2×H(5,𝔽2)C2×D6111yescharacteristic
715C22×#41—611no—
716C22×#41—611no—
717C22×#41—612no—
718C22×#41—611no—
719C22×#41—611no—
720C22×#41—612no—
721C22×#41—1222no—
722C22×#41—1221no—
723C22×#41—1221no—
724#575—1228no—
725C2×#137—611no—
726C2×#137—612no—
727C2×#137C2×D6111yescharacteristic, complemented
728C2×AGL(1,ℤ/8)—611no—
729C2×AGL(1,ℤ/8)—612no—
730C2×AGL(1,ℤ/8)—611no—
731C2×#135—612no—
732C2×#135—614no—
733C2×#135—612no—
734C2×#135—614no—
735C2×#135—1228no—
736C22×Q16—611no—
737C22×SD16—611no—
738C22×SD16C2×D6111yescharacteristic, complemented
739C22×D8—611no—
740C22×M16—611no—
741C23×C8—611no—
742#537—614no—
743#536—611no—
744#536—1221no—
745#536C2×D6111yescharacteristic, complemented
746#535—611no—
747#535—611no—
748#535—1221no—
749#534—1222no—
750#532—1221no—
751#532—1221no—
752#525—614no—
753#525—1222no—
754C2×#117—611no—
755#452—614no—
756#452—614no—
757#452—614no—
758#452C2×D6114yescomplemented
759#451—614no—
760#451—614no—
761#450—614no—
762#450C2×D6114yescomplemented
763#449—614no—
764#449—614no—
765#449—614no—
766#449—614no—
767#448—614no—
768#448—614no—
769#447—614no—
770#447—614no—
771#419—611no—
772#419—611no—
773#418—611no—
774#418C2×D6111yescharacteristic, complemented
775#417—614no—
776#416—611no—
777#416—611no—
778#416—611no—
779#416—612no—
780#416—612no—
781#416—614no—
782#416C2×D6111yescharacteristic, complemented
783C2×#103—612no—
784C2×#102—612no—
785#408—611no—
786#408—611no—
787#408—611no—
788#408—614no—
789#408C2×D6111yescharacteristic, complemented
790C2×C22⋊C8—614no—
791C61#6036611yescharacteristic, complemented, Sylow
7922−1+4—1228no—
7932−1+4—1224no—
7942−1+4—1224no—
7952−1+4—1224no—
7962−1+4—1228no—
7972−1+4—12216no—
7982−1+4—1224no—
799H(5,𝔽2)—24no—
800H(5,𝔽2)—24no—
801H(5,𝔽2)—1228no—
802H(5,𝔽2)—1228no—
803H(5,𝔽2)—1224no—
804H(5,𝔽2)—12216no—
805H(5,𝔽2)—12232no—
806H(5,𝔽2)—1224no—
807C2×#41—21no—
808C2×#41—611no—
809C2×#41—612no—
810C2×#41—611no—
811C2×#41—611no—
812C2×#41—612no—
813C2×#41—618no—
814C2×#41—611no—
815C2×#41—612no—
816C2×#41—612no—
817C2×#41—618no—
818C2×#41—611no—
819C2×#41—612no—
820C2×#41—612no—
821C2×#41—612no—
822C2×#41—612no—
823C2×#41—611no—
824C2×#41—612no—
825C2×#41—1221no—
826C2×#41—1222no—
827C2×#41—1222no—
828C2×#41—1221no—
829C2×#41—1221no—
830C2×#41—1221no—
831C2×#41—1222no—
832C2×#41—1222no—
833C2×#41—1221no—
834C2×#41—1222no—
835C2×#41—1224no—
836C2×#41—1221no—
837C2×#41—1221no—
838C2×#41—1224no—
839C2×#41—1224no—
840C2×#41—1224no—
841C2×#41—1224no—
842C2×#41—1224no—
843C2×#41—1222no—
844C2×#41—1222no—
845C2×#41—1222no—
846C2×#41—1222no—
847C2×#41—1221no—
848C2×#41—1228no—
849C2×#41—1228no—
850C2×#41—12216no—
851C2×#41—12232no—
852C2×#41—1228no—
853C2×#41—1228no—
854C2×#41—12216no—
855C2×#41—1222no—
856C2×#41—1221no—
857C2×#41C22×D6112yes—
858C2×#41C22×D6111yescharacteristic
859C2×#41C22×D6111yescharacteristic
860C22×Q8—611no—
861C22×Q8—611no—
862C22×Q8—612no—
863C22×Q8—611no—
864C22×Q8—612no—
865C22×Q8—1222no—
866C22×Q8—1221no—
867C22×Q8—1221no—
868C22×Q8C22×D6111yescharacteristic
869C22×D4—22no—
870C22×D4—21no—
871C22×D4—611no—
872C22×D4—612no—
873C22×D4—611no—
874C22×D4—612no—
875C22×D4—611no—
876C22×D4—1221no—
877C22×D4—1222no—
878C22×D4—1221no—
879C22×D4—1221no—
880C22×D4—1222no—
881C22×D4—1222no—
882C22×D4—1222no—
883C22×D4—1222no—
884C22×D4—1221no—
885C22×D4—1222no—
886C22×D4C22×D6112yes—
887C22×D4C22×D6111yescharacteristic
888C23×C4—611no—
889C23×C4—612no—
890C23×C4—1221no—
891C23×C4—1222no—
892C23×C4—1221no—
893C23×C4—1221no—
894C23×C4—1222no—
895#137—24no—
896#137—1228no—
897#137—1224no—
898AGL(1,ℤ/8)—1224no—
899AGL(1,ℤ/8)—1228no—
900AGL(1,ℤ/8)—1224no—
901#135—12216no—
902#135—12216no—
903#135—1228no—
904#135—1228no—
905C2×Q16—614no—
906C2×Q16—612no—
907C2×Q16—1224no—
908C2×Q16C22×D6112yes—
909C2×SD16—24no—
910C2×SD16—612no—
911C2×SD16—612no—
912C2×SD16—614no—
913C2×SD16—612no—
914C2×SD16—1224no—
915C2×SD16C22×D6114yes—
916C2×SD16C22×D6112yes—
917C2×D8—614no—
918C2×D8—612no—
919C2×D8—612no—
920C2×D8—1224no—
921C2×M16—611no—
922C2×M16—612no—
923C2×M16—1224no—
924C2×M16C22×D6111yescharacteristic
925C22×C8—611no—
926C22×C8—612no—
927C22×C8—612no—
928C22×C8—612no—
929C22×C8—1224no—
930C22×C8C22×D6111yescharacteristic
931C4⋊Q8—21no—
932C4⋊Q8—1221no—
933#127—1221no—
934#127—1221no—
935#124—21no—
936#124—1221no—
937#124—1221no—
938#124—1221no—
939#123—22no—
940#123—1224no—
941#123—1222no—
942C22⋊Q8—614no—
943C22⋊Q8—1224no—
944C22⋊Q8C22×D6114yes—
945#121—614no—
946#121—614no—
947#121—1224no—
948#121—1224no—
949#121—1224no—
950#120—1222no—
951#120—1224no—
952#120—1222no—
953C4×D4—1224no—
954C4×D4—1224no—
955#117—611no—
956#117—612no—
957#117—1221no—
958#117—1221no—
959#117C22×D6111yescharacteristic
960C2×C4⋊C4—612no—
961C2×C22⋊C4—1221no—
962C2×C42—1221no—
963#103—612no—
964#103—612no—
965#103—614no—
966#103—612no—
967#103—614no—
968#103C22×D6112yes—
969#102—612no—
970#102—614no—
971#102—612no—
972#102—612no—
973#102C22×D6112yes—
974#102C22×D6114yes—
975C22⋊C8—614no—
976C22⋊C8—614no—
977C22⋊C8—614no—
978C22⋊C8C22×D6114yes—
979C24—22no—
980C24—21no—
981C24—611no—
982C24—612no—
983C24—1221no—
984C24—1222no—
985C24—1221no—
986#41—28no—
987#41—24no—
988#41—24no—
989#41—22no—
990#41—22no—
991#41—22no—
992#41—614no—
993#41—614no—
994#41—618no—
995#41—618no—
996#41—614no—
997#41—1228no—
998#41—1224no—
999#41—1224no—
1000#41—1224no—
1001#41—1224no—
1002#41—12216no—
1003#41—12216no—
1004#41—1228no—
1005#41—1228no—
1006#41—1228no—
1007#41—1224no—
1008#41—1228no—
1009#41—1224no—
1010#41—1222no—
1011#41—1228no—
1012#41—1224no—
1013#41—1224no—
1014#41—1222no—
1015#41—1224no—
1016#41—1224no—
1017#41—1224no—
1018#41—1224no—
1019#41—1224no—
1020#41—1224no—
1021#41—12216no—
1022#41—12216no—
1023#41—12216no—
1024#41—12216no—
1025#41—12216no—
1026#41—12216no—
1027#41—12216no—
1028#41—12216no—
1029#41—1228no—
1030#41—1228no—
1031#41—1224no—
1032#41—1224no—
1033#41—1222no—
1034#41—1222no—
1035#41—1222no—
1036#41—2444no—
1037#41—2444no—
1038#41D4×D6114yes—
1039C2×Q8—21no—
1040C2×Q8—22no—
1041C2×Q8—22no—
1042C2×Q8—612no—
1043C2×Q8—611no—
1044C2×Q8—614no—
1045C2×Q8—614no—
1046C2×Q8—611no—
1047C2×Q8—612no—
1048C2×Q8—1221no—
1049C2×Q8—1222no—
1050C2×Q8—1224no—
1051C2×Q8—1224no—
1052C2×Q8—12216no—
1053C2×Q8—1228no—
1054C2×Q8—1224no—
1055C2×Q8—1222no—
1056C2×Q8—1224no—
1057C2×Q8—1228no—
1058C2×Q8—1224no—
1059C2×Q8—1222no—
1060C2×Q8—1221no—
1061C2×Q8—1222no—
1062C2×Q8D4×D6111yescharacteristic
1063C2×Q8C23×D6112yes—
1064C2×Q8C23×D6111yescharacteristic
1065C2×D4—216no—
1066C2×D4—28no—
1067C2×D4—22no—
1068C2×D4—21no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—22no—
1072C2×D4—21no—
1073C2×D4—22no—
1074C2×D4—614no—
1075C2×D4—612no—
1076C2×D4—612no—
1077C2×D4—612no—
1078C2×D4—612no—
1079C2×D4—611no—
1080C2×D4—611no—
1081C2×D4—612no—
1082C2×D4—1221no—
1083C2×D4—1224no—
1084C2×D4—1222no—
1085C2×D4—1222no—
1086C2×D4—1224no—
1087C2×D4—1222no—
1088C2×D4—1221no—
1089C2×D4—1222no—
1090C2×D4—1224no—
1091C2×D4—1228no—
1092C2×D4—1228no—
1093C2×D4—12216no—
1094C2×D4—12216no—
1095C2×D4—1228no—
1096C2×D4—1221no—
1097C2×D4—1222no—
1098C2×D4—1222no—
1099C2×D4—1222no—
1100C2×D4—1222no—
1101C2×D4—1228no—
1102C2×D4—12216no—
1103C2×D4—12216no—
1104C2×D4—12216no—
1105C2×D4—12216no—
1106C2×D4—1222no—
1107C2×D4—1221no—
1108C2×D4—1224no—
1109C2×D4—1224no—
1110C2×D4—1222no—
1111C2×D4—1222no—
1112C2×D4—1221no—
1113C2×D4—2444no—
1114C2×D4D4×D6112yes—
1115C2×D4D4×D6111yescharacteristic
1116C2×D4D4×D6114yes—
1117C2×D4C23×D6111yescharacteristic
1118C2×D4C23×D6112yes—
1119C22×C4—22no—
1120C22×C4—21no—
1121C22×C4—21no—
1122C22×C4—611no—
1123C22×C4—611no—
1124C22×C4—611no—
1125C22×C4—614no—
1126C22×C4—614no—
1127C22×C4—611no—
1128C22×C4—611no—
1129C22×C4—612no—
1130C22×C4—612no—
1131C22×C4—612no—
1132C22×C4—612no—
1133C22×C4—1224no—
1134C22×C4—1224no—
1135C22×C4—1221no—
1136C22×C4—1228no—
1137C22×C4—1222no—
1138C22×C4—1222no—
1139C22×C4—1221no—
1140C22×C4—1222no—
1141C22×C4—12216no—
1142C22×C4—1222no—
1143C22×C4—1221no—
1144C22×C4—1222no—
1145C22×C4—1222no—
1146C22×C4—1222no—
1147C22×C4—1222no—
1148C22×C4—1228no—
1149C22×C4—12216no—
1150C22×C4—1222no—
1151C22×C4—1221no—
1152C22×C4—1222no—
1153C22×C4—1221no—
1154C22×C4—2444no—
1155C22×C4C23×D6112yes—
1156C22×C4C23×D6111yescharacteristic
1157Q16—24no—
1158Q16—1228no—
1159Q16—1224no—
1160SD16—28no—
1161SD16—24no—
1162SD16—1228no—
1163SD16—1224no—
1164SD16—1224no—
1165SD16—1224no—
1166D8—1224no—
1167D8—1228no—
1168D8—1224no—
1169M16—22no—
1170M16—1224no—
1171M16—1222no—
1172C2×C8—22no—
1173C2×C8—612no—
1174C2×C8—612no—
1175C2×C8—1224no—
1176C2×C8—1224no—
1177C2×C8—1224no—
1178C2×C8—1222no—
1179C2×C8C23×D6112yes—
1180C2×C8C23×D6112yes—
1181C4⋊C4—24no—
1182C4⋊C4—612no—
1183C4⋊C4—1222no—
1184C4⋊C4—1224no—
1185C4⋊C4C23×D6112yes—
1186C22⋊C4—21no—
1187C22⋊C4—24no—
1188C22⋊C4—1224no—
1189C22⋊C4—1222no—
1190C22⋊C4—1224no—
1191C22⋊C4—1221no—
1192C22⋊C4—1224no—
1193C42—21no—
1194C42—1222no—
1195C42—1221no—
1196C23—28no—
1197C23—22no—
1198C23—21no—
1199C23—24no—
1200C23—82no—
1201C23—84no—
1202C23—611no—
1203C23—611no—
1204C23—614no—
1205C23—612no—
1206C23—1224no—
1207C23—1224no—
1208C23—1228no—
1209C23—1221no—
1210C23—1222no—
1211C23—4882no—
1212C23—4882no—
1213C23—4884no—
1214C23—2444no—
1215C23—2442no—
1216C23—2442no—
1217C23C2×D4×D6112yes—
1218C23C2×D4×D6111yescharacteristic
1219Q8—22no—
1220Q8—21no—
1221Q8—22no—
1222Q8—22no—
1223Q8—42no—
1224Q8—612no—
1225Q8—614no—
1226Q8—1224no—
1227Q8—1224no—
1228Q8—1228no—
1229Q8—1228no—
1230Q8—1222no—
1231Q8—1224no—
1232Q8—1222no—
1233Q8—1221no—
1234Q8C2×D4×D6112yes—
1235D4—28no—
1236D4—28no—
1237D4—24no—
1238D4—24no—
1239D4—22no—
1240D4—24no—
1241D4—22no—
1242D4—21no—
1243D4—612no—
1244D4—1224no—
1245D4—1224no—
1246D4—1224no—
1247D4—1224no—
1248D4—1224no—
1249D4—1224no—
1250D4—1228no—
1251D4—1228no—
1252D4—1228no—
1253D4—1228no—
1254D4—1228no—
1255D4—1228no—
1256D4—1224no—
1257D4—1224no—
1258D4—1222no—
1259D4—1221no—
1260D4—1222no—
1261D4—1222no—
1262D4—4884no—
1263D4—4884no—
1264D4—2444no—
1265D4—2444no—
1266D4—2442no—
1267D4C2×D4×D6112yes—
1268D4C2×D4×D6114yes—
1269C2×C4—28no—
1270C2×C4—21no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—42no—
1277C2×C4—614no—
1278C2×C4—611no—
1279C2×C4—611no—
1280C2×C4—614no—
1281C2×C4—614no—
1282C2×C4—612no—
1283C2×C4—612no—
1284C2×C4—612no—
1285C2×C4—612no—
1286C2×C4—612no—
1287C2×C4—1224no—
1288C2×C4—1224no—
1289C2×C4—1224no—
1290C2×C4—1224no—
1291C2×C4—1228no—
1292C2×C4—1228no—
1293C2×C4—1224no—
1294C2×C4—1224no—
1295C2×C4—1228no—
1296C2×C4—1228no—
1297C2×C4—1228no—
1298C2×C4—1228no—
1299C2×C4—1228no—
1300C2×C4—1224no—
1301C2×C4—1221no—
1302C2×C4—1222no—
1303C2×C4—1224no—
1304C2×C4—1222no—
1305C2×C4—1222no—
1306C2×C4—1222no—
1307C2×C4—4882no—
1308C2×C4—2444no—
1309C2×C4—2444no—
1310C2×C4C2×D4×D6112yes—
1311C2×C4C2×D4×D6111yescharacteristic
1312C2×C4C2×D4×D6112yes—
1313C2×C4C2×D4×D6112yes—
1314C2×C4C24×D6111yescharacteristic
1315C8—22no—
1316C8—22no—
1317C8—1222no—
1318C8—1222no—
1319C22—22no—
1320C22—22no—
1321C22—24no—
1322C22—22no—
1323C22—24no—
1324C22—44no—
1325C22—42no—
1326C22—84no—
1327C22—88no—
1328C22—612no—
1329C22—612no—
1330C22—1222no—
1331C22—1222no—
1332C22—1222no—
1333C22—1222no—
1334C22—1224no—
1335C22—4884no—
1336C22—4884no—
1337C22—4884no—
1338C22—4888no—
1339C22—2444no—
1340C22—2442no—
1341C22—2444no—
1342C22—2442no—
1343C22#120×D6112yes—
1344C22C22×D4×D6111yescharacteristic
1345C4—22no—
1346C4—22no—
1347C4—42no—
1348C4—42no—
1349C4—612no—
1350C4—612no—
1351C4—1222no—
1352C4—1222no—
1353C4—1224no—
1354C4—2442no—
1355C4#120×D6112yes—
1356C4C22×D4×D6111yescharacteristic
1357C4C22×D4×D6111yescharacteristic
1358C2—22no—
1359C2—42no—
1360C2—44no—
1361C2—42no—
1362C2—1222no—
1363C2—1222no—
1364C2—4882no—
1365C2—2442no—
1366C2—2442no—
1367C2C2×#120×D6111yescharacteristic
1368C2#2146059112yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3009C2
socleC22×C61C23×D4
hypercenter#3009D61
hypocenterC61#60366
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3009

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16840597C2semidirect
2. C2×#16840561C2semidirect
3. C22×#14519798C2semidirect
4. #21459151C2semidirect
5. #21455138C2semidirect
6. #21455124C2semidirect
7. #21455113C2semidirect
8. #21455112C2semidirect
9. #21455108C2semidirect
10. #21455107C2semidirect
11. #21455092C2semidirect
12. #21455088C2semidirect
13. #21455087C2semidirect
14. #21455040C2semidirect
15. #21455038C2semidirect
16. #21454333C2semidirect
17. #416×D61C2semidirect
18. #408×D61C2semidirect
19. C61×#3009C2semidirect
25. C2×#14519824C22semidirect
29. C2×#14519822C22semidirect
30. C22×#11758226C22semidirect
34. C22×#11758224C22semidirect
38. C2×#41×D61C22semidirect
40. C2×#14519809C22semidirect
41. C2×#14519808C22semidirect
42. C2×#14519805C22semidirect
43. C2×#14519804C22semidirect
44. C2×#14519802C22semidirect
45. C2×#14519800C22semidirect
47. C2×#14519798C22semidirect
48. C2×#14519798C22semidirect
49. C2×#14519798C22semidirect
50. C22×#11758202C22semidirect
51. C22×#11758190C22semidirect
52. C22×#11758199C22semidirect
53. C2×M16×D61C22semidirect
54. C22×C8×D61C22semidirect
55. #16840342C22semidirect
57. #16840336C22semidirect
58. #16840331C22semidirect
60. #16840326C22semidirect
64. #16840275C22semidirect
66. #117×D61C22semidirect
67. #16839922C22semidirect
68. #16839921C22semidirect
69. #16839921C22semidirect
70. #16839917C22semidirect
71. #16839916C22semidirect
72. #16839911C22semidirect
73. #16839909C22semidirect
74. #16839908C22semidirect
75. #16839908C22semidirect
76. #16839907C22semidirect
77. #16839903C22semidirect
78. #16839902C22semidirect
79. #16839897C22semidirect
80. #16839896C22semidirect
81. #16839772C22semidirect
82. #16839770C22semidirect
83. #16839767C22semidirect
84. #16839760C22semidirect
85. #16839759C22semidirect
86. #16839758C22semidirect
87. #16839757C22semidirect
88. #16839756C22semidirect
89. #16839755C22semidirect
90. #16839755C22semidirect
91. #103×D61C22semidirect
92. #102×D61C22semidirect
93. #16839730C22semidirect
94. #16839729C22semidirect
95. #16839728C22semidirect
96. #16839727C22semidirect
97. C22⋊C8×D61C22semidirect
99. C2×#137×C61C22semidirect
100. C22×SD16×C61C22semidirect
101. C61×#536C22semidirect
102. C61×#452C22semidirect
103. C61×#450C22semidirect
104. C61×#418C22semidirect
105. C61×#416C22semidirect
106. C61×#408C22semidirect
156. C2×#11758224D4semidirect
168. #41×D61D4semidirect
685. #3009D61semidirect
727. C2×#137C2×D61semidirect
738. C22×SD16C2×D61semidirect
745. #536C2×D61semidirect
758. #452C2×D61semidirect
762. #450C2×D61semidirect
774. #418C2×D61semidirect
782. #416C2×D61semidirect
789. #408C2×D61semidirect
791. C61#60366semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168405972
C2×#168405612
C22×#145197982
#214591512
#214551382
#214551242
#214551132
#214551122
#214551082
#214551072
#214550922
#214550882
#214550872
#214550402
#214550382
#214543332
#416×D612
#408×D612
C61×#30092
#6036661