Finite Group Databasebeta

← #30620208

Subgroups — #30620208

Order 15616.

1406 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840802C211yesmaximal, characteristic, complemented
2C2×Q16×#6923C211yesmaximal, characteristic, complemented
3#21462324C211yesmaximal, characteristic
4Q8×C22⋊#6923C211yesmaximal, characteristic, complemented
5#21461969C211yesmaximal, characteristic, complemented
6#21461964C211yesmaximal, characteristic, complemented
7#21461815C211yesmaximal, characteristic, complemented
8#21461815C211yesmaximal, characteristic, complemented
9#21461813C211yesmaximal, characteristic, complemented
10#21461813C211yesmaximal, characteristic, complemented
11#21461697C211yesmaximal, characteristic, complemented
12#21461659C211yesmaximal, characteristic
13#21461658C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15C2×#137×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×Q8×#6923C2211yescharacteristic
20#16840802—24no—
21Q16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32D61⋊(C22⋊C8)C2211yescharacteristic
33C2×#14519831C2211yescharacteristic
34C2×C8×#6923C2211yescharacteristic
35(C2×#6923)⋊Q8—21no—
36(C2×#6923)⋊Q8—21no—
37(C2×#6923)⋊Q8C2211yescharacteristic
38(C2×#6923)⋊Q8C2211yescharacteristic
39#16840714—21no—
40#16840714—21no—
41#16840714C2211yescharacteristic
42#16840714C2211yescharacteristic
43#16840704—21no—
44#16840704—21no—
45#16840704C2211yescharacteristic
46#16840704C2211yescharacteristic
47C4×C22⋊#6923—21no—
48C4×C22⋊#6923—21no—
49C4×C22⋊#6923C2211yescharacteristic
50#16840636C2211yescharacteristic
51#16840636C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×#41×D61C2211yescharacteristic
55C22×Q8×D61C2211yescharacteristic
56C2×#14519810C411yescharacteristic, complemented
57C2×#14519809C411yescharacteristic, complemented
58C2×#14519809C411yescharacteristic, complemented
59C2×#14519808C411yescharacteristic, complemented
60C2×#14519807C411yescharacteristic, complemented
61C2×#14519806C411yescharacteristic, complemented
62C2×#14519806C411yescharacteristic, complemented
63#137×D61—24no—
64#137×D61—24no—
65C2×Q16×D61C2211yescharacteristic
66C2×Q16×D61C2211yescharacteristic
67C2×SD16×D61C2211yescharacteristic
68C2×SD16×D61C2211yescharacteristic
69C2×M16×D61C2211yescharacteristic
70C2×#137×C61C411yescharacteristic, complemented
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73Q8×#6923—22no—
74Q8×#6923—22no—
75Q8×#6923—22no—
76Q8×#6923—22no—
77Q8×#6923—41no—
78Q8×#6923—41no—
79Q8×#6923—41no—
80Q8×#6923—41no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923D411yescharacteristic
96C2×C22⋊#6923D411yescharacteristic
97C2×C4×#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923—21no—
101C2×C4×#6923C2311yescharacteristic
102C2×C4×#6923C2311yescharacteristic
103#14519846—22no—
104#14519845—22no—
105#14519840—22no—
106#14519840—22no—
107#14519840—22no—
108#14519840—22no—
109#14519840—41no—
110#14519840—41no—
111#14519839—41no—
112#14519839—41no—
113#14519834—21no—
114C22⋊#92420—21no—
115#14519831—22no—
116C8×#6923—22no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4—21no—
122(C2×#6923)⋊C4—21no—
123(C2×#6923)⋊C4D411yescharacteristic
124(C2×#6923)⋊C4D411yescharacteristic
125C2×#11758226C2×C411yescharacteristic
126C2×#11758222—21no—
127C2×#11758222C2×C411yescharacteristic
128C2×#11758224—21no—
129C2×#11758224C2×C411yescharacteristic
130#41×D61—22no—
131#41×D61—22no—
132#41×D61—41no—
133#41×D61—41no—
134C22×Dic122—21no—
135C22×Dic122C2×C411yescharacteristic
136C2×Q8×D61—21no—
137C2×Q8×D61—21no—
138C2×Q8×D61—22no—
139C2×Q8×D61—22no—
140C2×Q8×D61—41no—
141C2×Q8×D61—41no—
142C2×Q8×D61C2×C411yescharacteristic
143C2×Q8×D61C2×C411yescharacteristic
144C2×Q8×D61C2311yescharacteristic
145C2×Q8×D61C2311yescharacteristic
146C2×Q8×D61C2311yescharacteristic
147C2×D4×D61—21no—
148C2×D4×D61C2311yescharacteristic
149C22×C4×D61—21no—
150C22×C4×D61—21no—
151C22×C4×D61C2311yescharacteristic
152#14519810—24no—
153#14519809—24no—
154#14519809—24no—
155#14519808—24no—
156#14519807—24no—
157#14519806—24no—
158#14519806—24no—
159C2×Dic244C2×C411yescharacteristic
160C2×Dic244C2×C411yescharacteristic
161C2×#11758202C2×C411yescharacteristic
162C2×#11758202C2×C411yescharacteristic
163C2×#11758202C2×C411yescharacteristic
164C2×#11758202C2×C411yescharacteristic
165Q16×D61—22no—
166Q16×D61—22no—
167Q16×D61D414yes—
168Q16×D61D414yes—
169C2×#11758190C2×C411yescharacteristic
170C2×#11758190C2×C411yescharacteristic
171C2×#11758200C2×C411yescharacteristic
172C2×#11758200C2×C411yescharacteristic
173C2×#11758201C2×C411yescharacteristic
174C2×#11758201C2×C411yescharacteristic
175SD16×D61—22no—
176SD16×D61—22no—
177SD16×D61—22no—
178SD16×D61—22no—
179C2×#11758194C2×C411yescharacteristic
180C2×#11758189C2×C411yescharacteristic
181C2×#11758189C2×C411yescharacteristic
182M16×D61—22no—
183M16×D61—22no—
184C2×C8×D61C2311yescharacteristic
185C2×C8×D61C2311yescharacteristic
186C2×#41×C61C2×C411yescharacteristic
187C22×Q8×C61C2×C411yescharacteristic
188#137×C61—24no—
189C2×Q16×C61C2×C411yescharacteristic
190C2×Q16×C61C2×C411yescharacteristic
191C2×SD16×C61C2×C411yescharacteristic
192C2×SD16×C61C2×C411yescharacteristic
193C2×M16×C61C2×C411yescharacteristic
194C23×D61—21no—
195C23×D61C2×D411yescharacteristic
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—21no—
200C22×#6923C2×D411yescharacteristic
201C22×#6923C2×D411yescharacteristic
202C22×#6923C2×D411yescharacteristic
203C22×#6923C2×D411yescharacteristic
204#41×C61—22no—
205#41×C61—41no—
206C2×Q8×C61—21no—
207C2×Q8×C61—22no—
208C2×Q8×C61—41no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×Q8×C61C22×C411yescharacteristic
211C2×Q8×C61C22×C411yescharacteristic
212C2×D4×C61—21no—
213C2×D4×C61C22×C411yescharacteristic
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61C22×C411yescharacteristic
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61#4111yescharacteristic
223#11758226—22no—
224#11758226—41no—
225Q8×D61—21no—
226Q8×D61—21no—
227Q8×D61—21no—
228Q8×D61—21no—
229Q8×D61—22no—
230Q8×D61—21no—
231Q8×D61—21no—
232Q8×D61—21no—
233Q8×D61—21no—
234Q8×D61—22no—
235Q8×D61—41no—
236Q8×D61—41no—
237Q8×D61—42no—
238Q8×D61—42no—
239Q8×D61—42no—
240Q8×D61—42no—
241Q8×D61C2×D412yes—
242Q8×D61C2×D412yes—
243Q8×D61C2×D412yes—
244Q8×D61C2×D412yes—
245#11758224—22no—
246#11758224—41no—
247#11758224—42no—
248#11758224—42no—
249D4×D61—21no—
250D4×D61—21no—
251D4×D61—21no—
252D4×D61—21no—
253D4×D61—42no—
254D4×D61—42no—
255#11758222—22no—
256#11758222—42no—
257#11758222—42no—
258#11758222—41no—
259C2×D244—21no—
260C2×D244C22×C411yescharacteristic
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—42no—
273C2×C4×D61—42no—
274C2×C4×D61—42no—
275C2×C4×D61—42no—
276C2×C4×D61C22×C411yescharacteristic
277C2×C4×D61C2×D411yescharacteristic
278C2×C4×D61#4111yescharacteristic
279C2×C4×D61C2411yescharacteristic
280C2×Dic122—21no—
281C2×Dic122—21no—
282C2×Dic122—22no—
283C2×Dic122—21no—
284C2×Dic122—21no—
285C2×Dic122—21no—
286C2×Dic122—21no—
287C2×Dic122—41no—
288C2×Dic122—42no—
289C2×Dic122—42no—
290C2×Dic122C22×C411yescharacteristic
291C2×Dic122C22×C411yescharacteristic
292C2×Dic122C22×C411yescharacteristic
293C22⋊#6923—22no—
294C22⋊#6923—41no—
295C22⋊#6923—42no—
296C22⋊#6923—42no—
297C22⋊#6923—42no—
298C22⋊#6923—81no—
299C22⋊#6923—81no—
300C22⋊#6923—81no—
301C2×#92420—21no—
302C2×#92420—21no—
303C4⋊#6923—21no—
304C4⋊#6923—21no—
305C4⋊#6923—21no—
306C4⋊#6923—21no—
307C4⋊#6923—21no—
308C4⋊#6923—21no—
309C4⋊#6923—21no—
310C4⋊#6923—21no—
311C4⋊#6923—42no—
312C4⋊#6923—42no—
313C4⋊#6923—42no—
314C4⋊#6923—42no—
315C4×#6923—21no—
316C4×#6923—21no—
317C4×#6923—21no—
318C4×#6923—21no—
319C4×#6923—42no—
320C4×#6923—42no—
321C4×#6923—42no—
322C4×#6923—42no—
323D61⋊C8—21no—
324D61⋊C8—21no—
325D61⋊C8—21no—
326D61⋊C8—21no—
327Q16×C61—22no—
328Q16×C61C22⋊C414yescomplemented
329SD16×C61—22no—
330SD16×C61—22no—
331M16×C61—22no—
332C2×C8×C61C22×C411yescharacteristic
333C2×C8×C61C22×C411yescharacteristic
334#11758202—22no—
335#11758202—22no—
336#11758202C22⋊C414yescomplemented
337#11758202C22⋊C414yescomplemented
338#11758201—22no—
339#11758201—22no—
340#11758200—22no—
341#11758200—22no—
342#11758194—22no—
343C2×#92418C22×C411yescharacteristic
344C2×#92418C22×C411yescharacteristic
345Dic244—22no—
346Dic244C22⋊C414yescomplemented
347#11758190—22no—
348#11758190—22no—
349#11758189—22no—
350#11758189—22no—
351C8×D61—21no—
352C8×D61—21no—
353C8×D61C2×D412yes—
354C8×D61C2×D412yes—
355C23×C61—21no—
356C23×C61C4×D411yescharacteristic
357C22×D61—21no—
358C22×D61—21no—
359C22×D61—21no—
360C22×D61—21no—
361C22×D61—21no—
362C22×D61—21no—
363C22×D61—21no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61C4×D411yescharacteristic
371C22×D61C22×D411yescharacteristic
372C2×#6923—21no—
373C2×#6923—21no—
374C2×#6923—21no—
375C2×#6923—21no—
376C2×#6923—21no—
377C2×#6923—21no—
378C2×#6923—21no—
379C2×#6923—21no—
380C2×#6923—21no—
381C2×#6923—21no—
382C2×#6923—21no—
383C2×#6923—41no—
384C2×#6923—41no—
385C2×#6923—41no—
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923#13712yescomplemented
396Q8×C61—21no—
397Q8×C61—21no—
398Q8×C61—21no—
399Q8×C61—21no—
400Q8×C61—42no—
401Q8×C61C2×C22⋊C412yes—
402Q8×C61C2×C22⋊C412yes—
403D4×C61—21no—
404D4×C61—21no—
405D4×C61—42no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—42no—
412C2×C4×C61—42no—
413C2×C4×C61C4×D411yescharacteristic
414C2×C4×C61C23×C411yescharacteristic
415C22⋊D61—42no—
416C22⋊D61—42no—
417C22⋊D61—41no—
418C22⋊D61—41no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—42no—
425C2×Dic61—42no—
426C2×Dic61C4×D411yescharacteristic
427C2×Dic61C2×#4111yescharacteristic
428D244—21no—
429D244—21no—
430D244—42no—
431C4×D61—22no—
432C4×D61—22no—
433C4×D61—22no—
434C4×D61—22no—
435C4×D61—21no—
436C4×D61—21no—
437C4×D61—21no—
438C4×D61—21no—
439C4×D61—21no—
440C4×D61—21no—
441C4×D61—42no—
442C4×D61—42no—
443C4×D61—42no—
444C4×D61—42no—
445C4×D61—41no—
446C4×D61—41no—
447C4×D61C22×D411yescharacteristic
448C4×D61C22×D411yescharacteristic
449C4×D61H(5,𝔽2)11yescharacteristic
450C4×D61H(5,𝔽2)11yescharacteristic
451Dic122—21no—
452Dic122—21no—
453Dic122—22no—
454Dic122—22no—
455Dic122—22no—
456Dic122—22no—
457Dic122—21no—
458Dic122—21no—
459Dic122—42no—
460Dic122—42no—
461Dic122—42no—
462Dic122—41no—
463Dic122—41no—
464Dic122C2×C22⋊C412yes—
465Dic122C2×C22⋊C412yes—
466#92420—41no—
467#92420—41no—
468C8×C61—21no—
469C8×C61C2×C22⋊C412yes—
470#92418—21no—
471#92418C2×C22⋊C412yes—
472#22445—611nomaximal, Sylow
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—41no—
477C22×C61—41no—
478C22×C61—41no—
479C22×C61C2×C4×D411yescharacteristic
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—41no—
484C2×D61—41no—
485C2×D61—41no—
486C2×D61—41no—
487C2×D61—41no—
488C2×D61—41no—
489C2×D61—41no—
490C2×D61—81no—
491C2×D61—81no—
492C2×D61—81no—
493C2×D61—81no—
494C2×D61D4211yescharacteristic
495C2×D61D4211yescharacteristic
496C2×D61C2×#13711yescharacteristic
497C2×D61#57511yescharacteristic
498C2×D61#57711yescharacteristic
499C2×D61#57811yescharacteristic
500#6923—22no—
501#6923—41no—
502#6923—41no—
503#6923—41no—
504#6923—81no—
505#6923—81no—
506#6923—81no—
507#6923—81no—
508C4×C61—22no—
509C4×C61—22no—
510C4×C61—21no—
511C4×C61—41no—
512C4×C61C22×C22⋊C411yescharacteristic
513C4×C61#51811yescharacteristic
514Dic61—22no—
515Dic61—22no—
516Dic61—21no—
517Dic61—41no—
518Dic61#54611yescharacteristic
519Dic61#54611yescharacteristic
520C22×#137—611no—
521C2×#441—611no—
522C2×C4×Q16—611no—
523#2341—611no—
524Q8×C22⋊C4—611no—
525#1973—611no—
526#1968—611no—
527#1880—611no—
528#1880—611no—
529#1878—611no—
530#1878—611no—
531#1809—611no—
532#1788—611no—
533#1787—611no—
534#1753—611no—
535C2×C61—41no—
536C2×C61—81no—
537C2×C61D4×C22⋊C411yescharacteristic
538C2×C61C4×#13711yescharacteristic
539C2×C61#294711yescharacteristic
540D61—41no—
541D61—81no—
542D61#327011yescharacteristic
543D61#327111yescharacteristic
544D61#327711yescharacteristic
545D61#327811yescharacteristic
546C22×#41—611no—
547C23×Q8—611no—
548C2×#137—611no—
549C2×#137—611no—
550C2×#137—611no—
551C2×#137—611no—
552C2×#137—611no—
553C2×#137—611no—
554C2×#137—611no—
555C2×#137—1224no—
556C2×#137—1224no—
557C2×#137#692311yescharacteristic, complemented
558C22×Q16—611no—
559C22×Q16—611no—
560C22×SD16—611no—
561C22×SD16—611no—
562C22×M16—611no—
563C2×C4×Q8—611no—
564C2×C4×Q8—611no—
565C2×C4×Q8—611no—
566C2×C4×Q8—611no—
567#441—1224no—
568C4×Q16—1224no—
569C2×#107—611no—
570C2×#106—611no—
571C2×#103—611no—
572C2×#103—611no—
573C2×#103—611no—
574C2×#103—611no—
575C2×#103—611no—
576C2×#103—611no—
577C2×#102—611no—
578C2×#102—611no—
579C2×C22⋊C8—611no—
580C2×#97—611no—
581C2×C4×C8—611no—
582#391—611no—
583#391—611no—
584#391—1221no—
585#391—1221no—
586#390—611no—
587#390—611no—
588#390—1221no—
589#390—1221no—
590#380—611no—
591#380—611no—
592#380—1221no—
593#380—1221no—
594C4×C22⋊C4—611no—
595C4×C22⋊C4—1221no—
596C4×C22⋊C4—1221no—
597#340—611no—
598#340—611no—
599#336—611no—
600#336—611no—
601C61#2244511yescharacteristic, complemented, Sylow
602C2×#41—611no—
603C2×#41—611no—
604C2×#41—611no—
605C2×#41—1221no—
606C2×#41—1221no—
607C2×#41—1222no—
608C2×#41—1222no—
609C2×#41—2441no—
610C2×#41—2441no—
611C2×#41C2×#692311yescharacteristic
612C22×Q8—611no—
613C22×Q8—611no—
614C22×Q8—611no—
615C22×Q8—611no—
616C22×Q8—611no—
617C22×Q8—611no—
618C22×Q8—1221no—
619C22×Q8—1221no—
620C22×Q8—1221no—
621C22×Q8—1222no—
622C22×Q8—1222no—
623C22×Q8—2441no—
624C22×Q8—2441no—
625C22×Q8C2×#692311yescharacteristic
626C22×D4—611no—
627C22×D4—1221no—
628C23×C4—611no—
629C23×C4—1221no—
630C23×C4—1221no—
631#137—24no—
632#137—1224no—
633#137—1224no—
634#137—1224no—
635#137—1224no—
636#137—1224no—
637#137—1224no—
638#137—1224no—
639C2×Q16—611no—
640C2×Q16—611no—
641C2×Q16—614no—
642C2×Q16—614no—
643C2×Q16—611no—
644C2×Q16—611no—
645C2×Q16—611no—
646C2×Q16—611no—
647C2×Q16—1222no—
648C2×Q16—1222no—
649C2×Q16C2×#692311yescharacteristic
650C2×Q16C2×#692311yescharacteristic
651C2×SD16—611no—
652C2×SD16—611no—
653C2×SD16—611no—
654C2×SD16—611no—
655C2×SD16—611no—
656C2×SD16—611no—
657C2×SD16—1222no—
658C2×SD16—1222no—
659C2×SD16—1222no—
660C2×SD16—1222no—
661C2×SD16C2×#692311yescharacteristic
662C2×SD16C2×#692311yescharacteristic
663C2×M16—611no—
664C2×M16—611no—
665C2×M16—611no—
666C2×M16—1222no—
667C2×M16—1222no—
668C2×M16C2×#692311yescharacteristic
669C22×C8—611no—
670C22×C8—611no—
671C22×C8—611no—
672C22×C8—611no—
673C4×Q8—1222no—
674C4×Q8—1222no—
675C4×Q8—1222no—
676C4×Q8—1222no—
677C4×Q8—2441no—
678C4×Q8—2441no—
679C4×Q8—2441no—
680C4×Q8—2441no—
681C2×C4⋊C4—611no—
682C2×C4⋊C4—611no—
683C2×C4⋊C4—611no—
684C2×C4⋊C4—611no—
685C2×C4⋊C4—1221no—
686C2×C4⋊C4—1221no—
687C2×C4⋊C4—1221no—
688C2×C4⋊C4—1221no—
689C2×C22⋊C4—611no—
690C2×C22⋊C4—611no—
691C2×C22⋊C4—1221no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4—1221no—
695C2×C22⋊C4—1221no—
696C2×C22⋊C4—1221no—
697C2×C42—611no—
698C2×C42—611no—
699C2×C42—1221no—
700C2×C42—1221no—
701C2×C42—1221no—
702C2×C42—1221no—
703#107—1222no—
704#106—1222no—
705#103—1222no—
706#103—1222no—
707#103—1222no—
708#103—1222no—
709#103—2441no—
710#103—2441no—
711#102—2441no—
712#102—2441no—
713C22⋊C8—1221no—
714C22⋊C8—1221no—
715#97—1222no—
716C4×C8—1222no—
717#95—611no—
718#95—611no—
719#95—1221no—
720#95—1221no—
721#95—1221no—
722#95—1221no—
723#95—1221no—
724#95—1221no—
725C24—611no—
726C24—1221no—
727#41—22no—
728#41—41no—
729#41—1222no—
730#41—1222no—
731#41—1222no—
732#41—2441no—
733#41—2442no—
734#41—2442no—
735#41—2441no—
736#41—2442no—
737#41—2442no—
738#41—2441no—
739C2×Q8—21no—
740C2×Q8—22no—
741C2×Q8—41no—
742C2×Q8—612no—
743C2×Q8—612no—
744C2×Q8—612no—
745C2×Q8—612no—
746C2×Q8—611no—
747C2×Q8—611no—
748C2×Q8—611no—
749C2×Q8—1221no—
750C2×Q8—1221no—
751C2×Q8—1221no—
752C2×Q8—1221no—
753C2×Q8—1221no—
754C2×Q8—1222no—
755C2×Q8—1221no—
756C2×Q8—1221no—
757C2×Q8—1221no—
758C2×Q8—1221no—
759C2×Q8—1221no—
760C2×Q8—1221no—
761C2×Q8—1221no—
762C2×Q8—1221no—
763C2×Q8—1221no—
764C2×Q8—1222no—
765C2×Q8—1222no—
766C2×Q8—2441no—
767C2×Q8—2442no—
768C2×Q8—2442no—
769C2×Q8—2442no—
770C2×Q8—2442no—
771C2×Q8—2441no—
772C2×Q8—2441no—
773C2×Q8—2442no—
774C2×Q8—2442no—
775C2×Q8C22×#692311yescharacteristic
776C2×Q8C22×#692311yescharacteristic
777C2×Q8C22×#692311yescharacteristic
778C2×D4—21no—
779C2×D4—611no—
780C2×D4—1221no—
781C2×D4—1221no—
782C2×D4—1221no—
783C2×D4—1221no—
784C2×D4—1221no—
785C2×D4—1221no—
786C2×D4—1221no—
787C2×D4—1221no—
788C2×D4—2442no—
789C2×D4—2442no—
790C2×D4C22×#692311yescharacteristic
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—2442no—
820C22×C4—2442no—
821C22×C4—2442no—
822C22×C4—2442no—
823C22×C4C22×#692311yescharacteristic
824Q16—22no—
825Q16—614no—
826Q16—614no—
827Q16—614no—
828Q16—1222no—
829Q16—1222no—
830Q16—1222no—
831Q16C22⋊#692314yescomplemented
832SD16—22no—
833SD16—22no—
834SD16—1222no—
835SD16—1222no—
836SD16—1222no—
837SD16—1222no—
838SD16—1222no—
839SD16—1222no—
840M16—22no—
841M16—1222no—
842M16—1222no—
843M16—1222no—
844C2×C8—611no—
845C2×C8—612no—
846C2×C8—612no—
847C2×C8—611no—
848C2×C8—1221no—
849C2×C8—1221no—
850C2×C8—1221no—
851C2×C8—1221no—
852C2×C8—1221no—
853C2×C8—1221no—
854C2×C8—1221no—
855C2×C8—1221no—
856C2×C8C22×#692311yescharacteristic
857C2×C8C22×#692311yescharacteristic
858C4⋊C4—1221no—
859C4⋊C4—1221no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—1221no—
864C4⋊C4—1221no—
865C4⋊C4—1221no—
866C4⋊C4—2442no—
867C4⋊C4—2442no—
868C4⋊C4—2442no—
869C4⋊C4—2442no—
870C22⋊C4—1222no—
871C22⋊C4—4881no—
872C22⋊C4—4881no—
873C22⋊C4—4881no—
874C22⋊C4—2442no—
875C22⋊C4—2441no—
876C22⋊C4—2442no—
877C22⋊C4—2442no—
878C42—1221no—
879C42—1221no—
880C42—1221no—
881C42—1221no—
882C42—2442no—
883C42—2442no—
884C42—2442no—
885C42—2442no—
886C23—21no—
887C23—611no—
888C23—611no—
889C23—1221no—
890C23—1221no—
891C23—1221no—
892C23—1221no—
893C23—1221no—
894C23—1221no—
895C23—1221no—
896C23—2441no—
897C23—2441no—
898C23—2441no—
899C23—2441no—
900C23—2441no—
901C23—2441no—
902C23D4×#692311yescharacteristic
903Q8—21no—
904Q8—21no—
905Q8—21no—
906Q8—21no—
907Q8—42no—
908Q8—612no—
909Q8—612no—
910Q8—1222no—
911Q8—1222no—
912Q8—1222no—
913Q8—1222no—
914Q8—1221no—
915Q8—1221no—
916Q8—1221no—
917Q8—1221no—
918Q8—2442no—
919Q8—2442no—
920Q8—2441no—
921Q8—2441no—
922Q8—2442no—
923Q8C2×C22⋊#692312yes—
924Q8C2×C22⋊#692312yes—
925D4—21no—
926D4—21no—
927D4—42no—
928D4—1221no—
929D4—1221no—
930D4—2442no—
931D4—2441no—
932D4—2441no—
933D4—2442no—
934D4—2442no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—611no—
943C2×C4—611no—
944C2×C4—611no—
945C2×C4—611no—
946C2×C4—611no—
947C2×C4—612no—
948C2×C4—611no—
949C2×C4—1221no—
950C2×C4—1221no—
951C2×C4—1222no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1221no—
956C2×C4—1221no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—1221no—
961C2×C4—1221no—
962C2×C4—1221no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—1221no—
967C2×C4—1221no—
968C2×C4—1221no—
969C2×C4—1221no—
970C2×C4—1221no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—2442no—
976C2×C4—2442no—
977C2×C4—2442no—
978C2×C4—2442no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2442no—
982C2×C4—2442no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4D4×#692311yescharacteristic
996C2×C4C23×#692311yescharacteristic
997C8—21no—
998C8—612no—
999C8—1221no—
1000C8—2441no—
1001C8—2441no—
1002C8C2×C22⋊#692312yes—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—611no—
1010C22—611no—
1011C22—611no—
1012C22—611no—
1013C22—611no—
1014C22—611no—
1015C22—1221no—
1016C22—1221no—
1017C22—1221no—
1018C22—4881no—
1019C22—4881no—
1020C22—4881no—
1021C22—4881no—
1022C22—2441no—
1023C22—2441no—
1024C22—2441no—
1025C22—2441no—
1026C22—2441no—
1027C22—2441no—
1028C22—2441no—
1029C22C2×D4×#692311yescharacteristic
1030C4—21no—
1031C4—22no—
1032C4—22no—
1033C4—41no—
1034C4—611no—
1035C4—611no—
1036C4—1222no—
1037C4—1221no—
1038C4—1222no—
1039C4—1222no—
1040C4—4881no—
1041C4—4881no—
1042C4—4881no—
1043C4—4881no—
1044C4—2441no—
1045C4—2441no—
1046C4—2441no—
1047C4—2441no—
1048C4C22×C22⋊#692311yescharacteristic
1049C4#1684082911yescharacteristic
1050C2—41no—
1051C2—81no—
1052C2—611no—
1053C2—611no—
1054C2—611no—
1055C2—611no—
1056C2—4881no—
1057C2—2441no—
1058C2D4×C22⋊#692311yescharacteristic
1059C2#137×#692311yescharacteristic
1060C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#137×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC2×#137#6923
hypocenterC61#22445
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#16840802C2semidirect
2. C2×Q16×#6923C2semidirect
4. Q8×C22⋊#6923C2semidirect
5. #21461969C2semidirect
6. #21461964C2semidirect
7. #21461815C2semidirect
8. #21461815C2semidirect
9. #21461813C2semidirect
10. #21461813C2semidirect
11. #21461697C2semidirect
13. #21461658C2semidirect
14. #21461559C2semidirect
56. C2×#14519810C4semidirect
57. C2×#14519809C4semidirect
58. C2×#14519809C4semidirect
59. C2×#14519808C4semidirect
60. C2×#14519807C4semidirect
61. C2×#14519806C4semidirect
62. C2×#14519806C4semidirect
70. C2×#137×C61C4semidirect
328. Q16×C61C22⋊C4semidirect
336. #11758202C22⋊C4semidirect
337. #11758202C22⋊C4semidirect
346. Dic244C22⋊C4semidirect
395. C2×#6923#137semidirect
557. C2×#137#6923semidirect
601. C61#22445semidirect
831. Q16C22⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408022
C2×Q16×#69232
#214623242
Q8×C22⋊#69232
#214619692
#214619642
#214618152
#214618132
#214616972
#214616592
#214616582
#214615592
C2×#137×D612
#2244561