Finite Group Databasebeta

← C2×#21455135 #30546470

Subgroups — C2×#21455135 #30546470

Order 15616.

4782 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519825C211yesmaximal, characteristic, complemented
2C22×#14519809C211yesmaximal, characteristic, complemented
3C22×#14519800C211yesmaximal, characteristic, complemented
4C2×#16840342C211yesmaximal, characteristic, complemented
5#21455135C2116yesmaximal, direct product factor
6C2×#16839923C211yesmaximal, characteristic, complemented
7C2×#16839922C211yesmaximal, characteristic, complemented
8C2×#16839910C211yesmaximal, characteristic, complemented
9C2×#16839909C211yesmaximal, characteristic, complemented
10C2×#16839916C211yesmaximal, characteristic, complemented
11C2×#16839902C211yesmaximal, characteristic, complemented
12C2×#16839901C211yesmaximal, characteristic, complemented
13C2×#16839762C211yesmaximal, characteristic, complemented
14C2×#103×D61C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#451C211yesmaximal, characteristic, complemented
17C2×#14519825—28no—
18C2×#14519825—24no—
19C2×#14519825—28no—
20C2×#14519825C2218yescomplemented
21C22×#11758226—21no—
22C22×#11758226C2211yescharacteristic
23C22×#11758226C2211yescharacteristic
24C22×#11758226C2211yescharacteristic
25C22×#11758222—21no—
26C22×#11758222—21no—
27C22×#11758222C2211yescharacteristic
28C22×#11758222C2211yescharacteristic
29C22×Q8×D61—21no—
30C22×Q8×D61C2211yescharacteristic
31C22×Q8×D61C2211yescharacteristic
32C2×#14519809—28no—
33C2×#14519809C2218yescomplemented
34C2×#14519800—28no—
35C2×#14519800C2218yescomplemented
36C22×#11758202C2211yescharacteristic
37C22×#11758190C2211yescharacteristic
38C22×#11758201C2211yescharacteristic
39C22×#11758201C2211yescharacteristic
40C22×#11758201C2211yescharacteristic
41C22×D488C2211yescharacteristic
42C22×#11758189C2211yescharacteristic
43C22×C8×D61C2211yescharacteristic
44#16840342—24no—
45#16840342C2218yescomplemented
46C2×#14519755—21no—
47C2×#14519753C2211yescharacteristic
48C2×#14519752—21no—
49C2×#14519752C2211yescharacteristic
50C2×#14519751C2211yescharacteristic
51C2×#14519750—21no—
52C2×#14519750—21no—
53C2×C4⋊C4×D61C2211yescharacteristic
54#16839923C2218yescomplemented
55#16839922C2218yescomplemented
56#16839916C2218yescomplemented
57#16839910C2218yescomplemented
58#16839909C2218yescomplemented
59#16839902C2218yescomplemented
60#16839901C2218yescomplemented
61#16839762C2218yescomplemented
62C2×#14519702C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66#103×D61C2218yescomplemented
67C2×#14519699C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69#16839727C2218yescomplemented
70C2×C22⋊#92418C2211yescharacteristic
71C2×#14519689C2211yescharacteristic
72C2×#14519689C2211yescharacteristic
73C23×Q8×C61C2211yescharacteristic
74C22×Q16×C61C2211yescharacteristic
75C22×Q16×C61C2211yescharacteristic
76C2×C22⋊Q8×C61C2211yescharacteristic
77C61×#451C2218yescomplemented
78C2×#103×C61C2211yescharacteristic
79C2×#103×C61C2211yescharacteristic
80C2×C22⋊C8×C61C2211yescharacteristic
81#14519825—264no—
82#14519825—232no—
83#14519825—232no—
84C2×#11758226—216no—
85C2×#11758226—24no—
86C2×#11758226—28no—
87C2×#11758226—24no—
88C2×#11758226—24no—
89C2×#11758226—22no—
90C2×#11758226—22no—
91C2×#11758226—22no—
92C2×#11758226—24no—
93C2×#11758226—24no—
94C2×#11758226D418yescomplemented
95C2×#11758226C2314yes—
96C2×#11758226C2314yes—
97C2×#11758226C2314yes—
98C2×#11758222—216no—
99C2×#11758222—216no—
100C2×#11758222—22no—
101C2×#11758222—28no—
102C2×#11758222—28no—
103C2×#11758222—24no—
104C2×#11758222—24no—
105C2×#11758222—24no—
106C2×#11758222—24no—
107C2×#11758222D414yes—
108C2×#11758222C2314yes—
109C2×#11758222C2314yes—
110C22×Dic122—21no—
111C22×Dic122—21no—
112C22×Dic122D411yescharacteristic
113C22×Dic122C2311yescharacteristic
114C2×Q8×D61—216no—
115C2×Q8×D61—24no—
116C2×Q8×D61—24no—
117C2×Q8×D61—22no—
118C2×Q8×D61—22no—
119C2×Q8×D61—28no—
120C2×Q8×D61—24no—
121C2×Q8×D61D418yescomplemented
122C2×Q8×D61C2314yes—
123C2×Q8×D61C2314yes—
124C22×D244—21no—
125C22×D244—21no—
126C22×D244—21no—
127C22×D244—21no—
128C22×D244D411yescharacteristic
129C22×D244C2311yescharacteristic
130C22×D244C2311yescharacteristic
131C22×C22⋊D61—21no—
132C22×C22⋊D61—21no—
133C22×C22⋊D61D411yescharacteristic
134C22×C22⋊D61D411yescharacteristic
135C22×C4×D61—21no—
136C22×C4×D61—21no—
137C22×C4×D61—21no—
138C22×C4×D61—21no—
139C22×C4×D61—21no—
140C22×C4×D61—21no—
141C22×C4×D61—21no—
142C22×C4×D61C2311yescharacteristic
143C22×C4×D61C2311yescharacteristic
144#14519809—232no—
145#14519800—232no—
146C2×#11758202—24no—
147C2×#11758202C2314yes—
148C2×#11758190—24no—
149C2×#11758190C2314yes—
150C2×#11758201—24no—
151C2×#11758201—24no—
152C2×#11758201—24no—
153C2×#11758201C2314yes—
154C2×#11758201C2314yes—
155C2×#11758201C2314yes—
156C2×D488—24no—
157C2×D488C2314yes—
158C2×#11758189—24no—
159C2×#11758189C2314yes—
160C22×#92418C2311yescharacteristic
161C22×#92418C2311yescharacteristic
162C2×C8×D61—24no—
163C2×C8×D61C2314yes—
164#14519755—28no—
165#14519753—22no—
166#14519753C2314yes—
167#14519752—28no—
168#14519752—22no—
169#14519752C2314yes—
170#14519751—22no—
171#14519751C2314yes—
172#14519750—28no—
173#14519750—28no—
174C2×C4⋊Dic61C2311yescharacteristic
175C2×#11758196—21no—
176C2×#11758196—21no—
177C4⋊C4×D61—22no—
178C4⋊C4×D61C2314yes—
179C2×#11758198—21no—
180C2×#11758198—21no—
181C2×#11758198—21no—
182#14519702C2314yes—
183#14519701C2314yes—
184#14519701C2314yes—
185#14519700C2314yes—
186#14519699C2314yes—
187#14519697C2314yes—
188C22⋊#92418C2314yes—
189#14519689C2314yes—
190#14519689C2314yes—
191C22×Q8×C61—24no—
192C22×Q8×C61—24no—
193C22×Q8×C61—21no—
194C22×Q8×C61—22no—
195C22×Q8×C61C2311yescharacteristic
196C22×Q8×C61C2314yes—
197C22×Q8×C61C2311yescharacteristic
198C22×Q8×C61C2311yescharacteristic
199C23×C4×C61—21no—
200C23×C4×C61C2311yescharacteristic
201C2×Q16×C61—24no—
202C2×Q16×C61—24no—
203C2×Q16×C61C2314yes—
204C2×Q16×C61C2314yes—
205C22×C8×C61C2311yescharacteristic
206C22×C8×C61C2311yescharacteristic
207C22⋊Q8×C61—22no—
208C22⋊Q8×C61C2314yes—
209C2×C4⋊C4×C61—21no—
210C2×C4⋊C4×C61C2311yescharacteristic
211C2×C22⋊C4×C61—21no—
212#103×C61C2314yes—
213#103×C61C2314yes—
214C22⋊C8×C61C2314yes—
215C24×C61C2×D411yescharacteristic
216C23×D61—21no—
217C23×D61—21no—
218C23×D61C2×D411yescharacteristic
219C23×D61C2×D411yescharacteristic
220C2×Q8×C61—28no—
221C2×Q8×C61—216no—
222C2×Q8×C61—28no—
223C2×Q8×C61—28no—
224C2×Q8×C61—22no—
225C2×Q8×C61—22no—
226C2×Q8×C61—24no—
227C2×Q8×C61—21no—
228C2×Q8×C61—21no—
229C2×Q8×C61—21no—
230C2×Q8×C61—22no—
231C2×Q8×C61—22no—
232C2×Q8×C61C2×D414yes—
233C2×Q8×C61C2×D414yes—
234C2×Q8×C61C2412yes—
235C2×Q8×C61C2412yes—
236C2×Q8×C61C2412yes—
237C22×C4×C61—28no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—24no—
241C22×C4×C61—22no—
242C22×C4×C61—22no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2412yes—
248C22×C4×C61C2411yescharacteristic
249C2×C22⋊D61—28no—
250C2×C22⋊D61—24no—
251C2×C22⋊D61—24no—
252C2×C22⋊D61—24no—
253C2×C22⋊D61—24no—
254C2×C22⋊D61—82no—
255C2×C22⋊D61C2×D414yes—
256C2×C22⋊D61C2×D414yes—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61C2×D411yescharacteristic
260C22×Dic61C2×D411yescharacteristic
261#11758226—264no—
262#11758226—216no—
263#11758226—28no—
264#11758226—28no—
265#11758226—216no—
266#11758226—28no—
267#11758226—28no—
268#11758226—28no—
269#11758226—48no—
270#11758226C2×D4116yescomplemented
271Q8×D61—216no—
272Q8×D61—264no—
273Q8×D61—28no—
274Q8×D61—216no—
275Q8×D61—28no—
276Q8×D61—28no—
277Q8×D61C2×D4116yescomplemented
278#11758222—264no—
279#11758222—216no—
280#11758222—264no—
281#11758222—28no—
282#11758222—216no—
283#11758222—28no—
284#11758222—28no—
285#11758222—28no—
286C2×D244—28no—
287C2×D244—28no—
288C2×D244—24no—
289C2×D244—24no—
290C2×D244—24no—
291C2×D244—21no—
292C2×D244—22no—
293C2×D244—22no—
294C2×D244—22no—
295C2×D244—24no—
296C2×D244—21no—
297C2×D244—24no—
298C2×D244—44no—
299C2×D244—82no—
300C2×D244C2×D414yes—
301C2×D244C2×D414yes—
302C2×D244C2412yes—
303C2×D244C2412yes—
304C2×C4×D61—28no—
305C2×C4×D61—28no—
306C2×C4×D61—28no—
307C2×C4×D61—28no—
308C2×C4×D61—24no—
309C2×C4×D61—24no—
310C2×C4×D61—24no—
311C2×C4×D61—22no—
312C2×C4×D61—22no—
313C2×C4×D61—28no—
314C2×C4×D61—24no—
315C2×C4×D61—24no—
316C2×C4×D61—24no—
317C2×C4×D61—24no—
318C2×C4×D61—44no—
319C2×C4×D61—82no—
320C2×C4×D61C2×D412yes—
321C2×C4×D61C2×D412yes—
322C2×C4×D61C2×D414yes—
323C2×C4×D61C2×D414yes—
324C2×C4×D61C2412yes—
325C2×C4×D61C2412yes—
326C2×Dic122—28no—
327C2×Dic122—21no—
328C2×Dic122—22no—
329C2×Dic122—24no—
330C2×Dic122—28no—
331C2×Dic122—24no—
332C2×Dic122—24no—
333C2×Dic122C2×D414yes—
334C2×Dic122C2×D414yes—
335C2×Dic122C2412yes—
336Q16×C61—28no—
337Q16×C61—28no—
338C2×C8×C61—22no—
339C2×C8×C61—22no—
340C2×C8×C61C2412yes—
341C2×C8×C61C2412yes—
342C4⋊C4×C61—24no—
343C4⋊C4×C61—21no—
344C4⋊C4×C61C2412yes—
345C22⋊C4×C61—24no—
346#11758202—28no—
347#11758201—28no—
348#11758201—28no—
349#11758201—28no—
350#11758198—24no—
351#11758198—24no—
352#11758198—24no—
353C4⋊Dic61—21no—
354C4⋊Dic61C2412yes—
355#11758196—24no—
356#11758196—24no—
357C2×#92418—22no—
358C2×#92418—22no—
359C2×#92418C2412yes—
360C2×#92418C2412yes—
361D488—28no—
362#11758190—28no—
363#11758189—28no—
364C8×D61—28no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61C22×D412yes—
369C23×C61C22×D411yescharacteristic
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—24no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—42no—
379C22×D61—42no—
380C22×D61—42no—
381C22×D61—42no—
382C22×D61—42no—
383C22×D61#12014yes—
384C22×D61C22×D412yes—
385C22×D61C22×D412yes—
386Q8×C61—216no—
387Q8×C61—24no—
388Q8×C61—24no—
389Q8×C61—22no—
390Q8×C61—22no—
391Q8×C61—22no—
392Q8×C61—22no—
393Q8×C61—42no—
394Q8×C61C22×D414yes—
395Q8×C61C22×D414yes—
396C2×C4×C61—216no—
397C2×C4×C61—24no—
398C2×C4×C61—24no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—24no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—42no—
408C2×C4×C61—42no—
409C2×C4×C61C22×D412yes—
410C2×C4×C61C22×D411yescharacteristic
411C2×C4×C61C22×D412yes—
412C2×C4×C61C22×D412yes—
413C2×C4×C61C2511yescharacteristic
414C22⋊D61—216no—
415C22⋊D61—28no—
416C22⋊D61—28no—
417C22⋊D61—84no—
418C2×Dic61—22no—
419C2×Dic61—24no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—42no—
423C2×Dic61#12014yes—
424C2×Dic61C22×D412yes—
425C2×Dic61C22×D412yes—
426D244—216no—
427D244—216no—
428D244—28no—
429D244—24no—
430D244—22no—
431D244—22no—
432D244—22no—
433D244—48no—
434D244—42no—
435D244—84no—
436D244C22×D414yes—
437C4×D61—216no—
438C4×D61—216no—
439C4×D61—216no—
440C4×D61—216no—
441C4×D61—24no—
442C4×D61—22no—
443C4×D61—22no—
444C4×D61—216no—
445C4×D61—48no—
446C4×D61—84no—
447C4×D61#12018yes—
448C4×D61C22×D414yes—
449C4×D61C22×D414yes—
450Dic122—216no—
451Dic122—24no—
452Dic122—22no—
453Dic122—216no—
454Dic122—28no—
455Dic122C22×D414yes—
456C8×C61—22no—
457C8×C61—22no—
458#92418—22no—
459#92418—22no—
460C2×#3013—611nomaximal, Sylow
461C22×C61—22no—
462C22×C61—22no—
463C22×C61—22no—
464C22×C61—44no—
465C22×C61C2×#12012yes—
466C22×C61#57712yes—
467C22×C61#57812yes—
468C22×C61C23×D411yescharacteristic
469C2×D61—28no—
470C2×D61—22no—
471C2×D61—22no—
472C2×D61—22no—
473C2×D61—24no—
474C2×D61—22no—
475C2×D61—22no—
476C2×D61—44no—
477C2×D61—48no—
478C2×D61—42no—
479C2×D61—42no—
480C2×D61—42no—
481C2×D61—42no—
482C2×D61—42no—
483C2×D61—84no—
484C2×D61C2×#12014yes—
485C4×C61—24no—
486C4×C61—24no—
487C4×C61—22no—
488C4×C61—42no—
489C4×C61—42no—
490C4×C61C2×#12012yes—
491C4×C61C23×D411yescharacteristic
492C4×C61C23×D411yescharacteristic
493Dic61—22no—
494Dic61—24no—
495Dic61—42no—
496Dic61C2×#12014yes—
497C22×2−1+4—611no—
498C22×#137—611no—
499C22×#135—611no—
500C2×#537—611no—
501#3013—6116no—
502C2×#452—611no—
503C2×#452—611no—
504C2×#449—611no—
505C2×#449—611no—
506C2×#451—611no—
507C2×#451D6111yescharacteristic, complemented
508C2×#448—611no—
509C2×#448—611no—
510C2×#417—611no—
511C22×#103—611no—
512C2×#408—611no—
513C2×C61—42no—
514C2×C61#301314yescomplemented
515C2×C61C22×#12011yescharacteristic
516C2×C61C2×#57711yescharacteristic
517C2×C61C2×#57811yescharacteristic
518D61—24no—
519D61—42no—
520D61—44no—
521D61—82no—
522C2×2−1+4—618no—
523C2×2−1+4—1228no—
524C2×2−1+4—1228no—
525C2×2−1+4—1224no—
526C22×#41—611no—
527C22×#41—611no—
528C22×#41—611no—
529C22×#41—611no—
530C22×#41—611no—
531C22×#41—1221no—
532C22×#41—1221no—
533C22×#41—1221no—
534C23×Q8—611no—
535C23×Q8—611no—
536C23×Q8—1221no—
537C23×Q8C2×D6111yescharacteristic
538C2×#137—618no—
539C2×#137—1228no—
540C2×#135—618no—
541C2×#135—1228no—
542C22×Q16—611no—
543C22×Q16C2×D6111yescharacteristic
544C22×Q16C2×D6111yescharacteristic
545C22×SD16—611no—
546C22×SD16—611no—
547C22×SD16—611no—
548C22×SD16—611no—
549C22×D8—611no—
550C22×M16—611no—
551C23×C8—611no—
552#537—618no—
553#537—1224no—
554C2×C22⋊Q8—611no—
555C2×C22⋊Q8—1221no—
556C2×C22⋊Q8C2×D6111yescharacteristic
557C2×#121—611no—
558C2×#121—611no—
559C2×#121—1221no—
560C2×#121—1221no—
561C2×#121—1221no—
562C22×C4⋊C4—611no—
563#452—618no—
564#452—618no—
565#451—618no—
566#451C2×D6118yescomplemented
567#449—618no—
568#449—618no—
569#448—618no—
570#448—618no—
571#417—618no—
572C2×#103—611no—
573C2×#103—611no—
574C2×#103—611no—
575C2×#103—611no—
576C2×#103—618no—
577C2×#103C2×D6111yescharacteristic
578C2×#103C2×D6111yescharacteristic
579C2×#102—611no—
580C2×#102—611no—
581#408—618no—
582C2×C22⋊C8—611no—
583C2×C22⋊C8—611no—
584C2×C22⋊C8—611no—
585C2×C22⋊C8C2×D6111yescharacteristic
586C61C2×#301311yescharacteristic, complemented, Sylow
5872−1+4—12232no—
5882−1+4—12232no—
5892−1+4—12264no—
590C2×#41—614no—
591C2×#41—614no—
592C2×#41—618no—
593C2×#41—614no—
594C2×#41—614no—
595C2×#41—614no—
596C2×#41—614no—
597C2×#41—1224no—
598C2×#41—1224no—
599C2×#41—1224no—
600C2×#41—1228no—
601C2×#41—1228no—
602C2×#41—1224no—
603C2×#41—12216no—
604C2×#41—12216no—
605C2×#41—1222no—
606C2×#41—1224no—
607C2×#41—1222no—
608C2×#41—1222no—
609C2×#41—1224no—
610C2×#41—1224no—
611C2×#41—1224no—
612C2×#41—1228no—
613C2×#41—12216no—
614C2×#41—1224no—
615C2×#41—1222no—
616C22×Q8—24no—
617C22×Q8—24no—
618C22×Q8—21no—
619C22×Q8—22no—
620C22×Q8—611no—
621C22×Q8—618no—
622C22×Q8—614no—
623C22×Q8—614no—
624C22×Q8—611no—
625C22×Q8—1221no—
626C22×Q8—1221no—
627C22×Q8—1222no—
628C22×Q8—1224no—
629C22×Q8—1222no—
630C22×Q8—1224no—
631C22×Q8—1228no—
632C22×Q8—12216no—
633C22×Q8—1224no—
634C22×Q8C22×D6111yescharacteristic
635C22×Q8C22×D6114yes—
636C22×Q8C22×D6111yescharacteristic
637C22×Q8C22×D6111yescharacteristic
638C22×D4—611no—
639C22×D4—611no—
640C22×D4—611no—
641C22×D4—611no—
642C22×D4—611no—
643C22×D4—1221no—
644C22×D4—1221no—
645C22×D4—1221no—
646C22×D4—1221no—
647C22×D4—1221no—
648C22×D4—1221no—
649C23×C4—21no—
650C23×C4—611no—
651C23×C4—611no—
652C23×C4—1221no—
653C23×C4—1221no—
654C23×C4—1221no—
655C23×C4—1221no—
656C23×C4—1221no—
657C23×C4—1221no—
658C23×C4—1221no—
659C23×C4C22×D6111yescharacteristic
660#137—12232no—
661#135—12232no—
662C2×Q16—24no—
663C2×Q16—24no—
664C2×Q16—614no—
665C2×Q16—1224no—
666C2×Q16C22×D6114yes—
667C2×Q16C22×D6114yes—
668C2×SD16—614no—
669C2×SD16—614no—
670C2×SD16—614no—
671C2×SD16—614no—
672C2×SD16—1224no—
673C2×SD16—1224no—
674C2×SD16—1224no—
675C2×SD16—1224no—
676C2×D8—614no—
677C2×D8—1224no—
678C2×M16—614no—
679C2×M16—1224no—
680C22×C8—611no—
681C22×C8—611no—
682C22×C8—614no—
683C22×C8—1224no—
684C22×C8C22×D6111yescharacteristic
685C22×C8C22×D6111yescharacteristic
686C22⋊Q8—22no—
687C22⋊Q8—614no—
688C22⋊Q8—1228no—
689C22⋊Q8—1222no—
690C22⋊Q8C22×D6114yes—
691#121—614no—
692#121—614no—
693#121—1228no—
694#121—1228no—
695#121—1222no—
696#121—1228no—
697#121—1222no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—611no—
700C2×C4⋊C4—614no—
701C2×C4⋊C4—1222no—
702C2×C4⋊C4—1221no—
703C2×C4⋊C4—1221no—
704C2×C4⋊C4C22×D6111yescharacteristic
705C2×C22⋊C4—21no—
706C2×C22⋊C4—1221no—
707C2×C22⋊C4—1221no—
708C2×C22⋊C4—1221no—
709#103—614no—
710#103—614no—
711#103—614no—
712#103—614no—
713#103C22×D6114yes—
714#103C22×D6114yes—
715#102—614no—
716#102—614no—
717C22⋊C8—614no—
718C22⋊C8—614no—
719C22⋊C8—614no—
720C22⋊C8C22×D6114yes—
721C24—611no—
722C24—611no—
723C24—1221no—
724C24—1221no—
725C24D4×D6111yescharacteristic
726#41—6116no—
727#41—12216no—
728#41—1228no—
729#41—1228no—
730#41—1228no—
731#41—1228no—
732#41—12264no—
733#41—12264no—
734#41—12216no—
735#41—12216no—
736#41—1228no—
737#41—1228no—
738#41—1228no—
739#41—1228no—
740#41—12264no—
741#41—12216no—
742#41—1228no—
743#41—2448no—
744C2×Q8—28no—
745C2×Q8—216no—
746C2×Q8—28no—
747C2×Q8—28no—
748C2×Q8—22no—
749C2×Q8—22no—
750C2×Q8—24no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—22no—
755C2×Q8—22no—
756C2×Q8—614no—
757C2×Q8—6116no—
758C2×Q8—614no—
759C2×Q8—612no—
760C2×Q8—1228no—
761C2×Q8—1224no—
762C2×Q8—1224no—
763C2×Q8—1224no—
764C2×Q8—1228no—
765C2×Q8—12216no—
766C2×Q8—1228no—
767C2×Q8—1228no—
768C2×Q8—12264no—
769C2×Q8—12216no—
770C2×Q8—1228no—
771C2×Q8—1222no—
772C2×Q8—1221no—
773C2×Q8D4×D6114yes—
774C2×Q8D4×D6114yes—
775C2×Q8C23×D6112yes—
776C2×Q8C23×D6112yes—
777C2×Q8C23×D6112yes—
778C2×D4—614no—
779C2×D4—614no—
780C2×D4—614no—
781C2×D4—614no—
782C2×D4—612no—
783C2×D4—612no—
784C2×D4—1224no—
785C2×D4—1228no—
786C2×D4—1224no—
787C2×D4—1224no—
788C2×D4—1228no—
789C2×D4—1224no—
790C2×D4—1224no—
791C2×D4—1224no—
792C2×D4—1224no—
793C2×D4—1228no—
794C2×D4—1224no—
795C2×D4—1224no—
796C2×D4—1221no—
797C2×D4—1222no—
798C2×D4—1222no—
799C2×D4—1222no—
800C2×D4—1221no—
801C2×D4—4882no—
802C2×D4—4882no—
803C2×D4—2444no—
804C22×C4—28no—
805C22×C4—24no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—611no—
813C22×C4—612no—
814C22×C4—614no—
815C22×C4—614no—
816C22×C4—612no—
817C22×C4—611no—
818C22×C4—612no—
819C22×C4—612no—
820C22×C4—1228no—
821C22×C4—1224no—
822C22×C4—1224no—
823C22×C4—1224no—
824C22×C4—1228no—
825C22×C4—1224no—
826C22×C4—1224no—
827C22×C4—1228no—
828C22×C4—1228no—
829C22×C4—1228no—
830C22×C4—1224no—
831C22×C4—1221no—
832C22×C4—1222no—
833C22×C4—1222no—
834C22×C4—1224no—
835C22×C4—1221no—
836C22×C4—4882no—
837C22×C4—2444no—
838C22×C4D4×D6112yes—
839C22×C4D4×D6111yescharacteristic
840C22×C4C23×D6112yes—
841C22×C4C23×D6111yescharacteristic
842Q16—28no—
843Q16—28no—
844Q16—1228no—
845SD16—1228no—
846SD16—1228no—
847SD16—1228no—
848SD16—1228no—
849D8—1228no—
850M16—1228no—
851C2×C8—22no—
852C2×C8—22no—
853C2×C8—612no—
854C2×C8—612no—
855C2×C8—1228no—
856C2×C8—1222no—
857C2×C8—1222no—
858C2×C8C23×D6112yes—
859C2×C8C23×D6112yes—
860C4⋊C4—24no—
861C4⋊C4—21no—
862C4⋊C4—612no—
863C4⋊C4—1224no—
864C4⋊C4—1224no—
865C4⋊C4—1221no—
866C4⋊C4C23×D6112yes—
867C22⋊C4—24no—
868C22⋊C4—1224no—
869C22⋊C4—1224no—
870C22⋊C4—1224no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—614no—
875C23—612no—
876C23—612no—
877C23—1222no—
878C23—1222no—
879C23—1224no—
880C23—1222no—
881C23—1222no—
882C23—1222no—
883C23—1222no—
884C23—1222no—
885C23—2442no—
886C23—2442no—
887C23—2442no—
888C23—2442no—
889C23—2442no—
890C23C2×D4×D6112yes—
891C23C2×D4×D6111yescharacteristic
892Q8—216no—
893Q8—24no—
894Q8—24no—
895Q8—22no—
896Q8—22no—
897Q8—22no—
898Q8—22no—
899Q8—42no—
900Q8—614no—
901Q8—12216no—
902Q8—1228no—
903Q8—12216no—
904Q8—1224no—
905Q8—1222no—
906Q8C2×D4×D6114yes—
907Q8C2×D4×D6114yes—
908D4—614no—
909D4—1228no—
910D4—12216no—
911D4—12216no—
912D4—1228no—
913D4—1228no—
914D4—12216no—
915D4—1224no—
916D4—1222no—
917D4—1222no—
918D4—1222no—
919D4—4884no—
920D4—4884no—
921D4—2448no—
922D4—2442no—
923C2×C4—216no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—614no—
937C2×C4—612no—
938C2×C4—618no—
939C2×C4—614no—
940C2×C4—614no—
941C2×C4—612no—
942C2×C4—12216no—
943C2×C4—12216no—
944C2×C4—12216no—
945C2×C4—12216no—
946C2×C4—12216no—
947C2×C4—1222no—
948C2×C4—1224no—
949C2×C4—1222no—
950C2×C4—1224no—
951C2×C4—1222no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—4884no—
955C2×C4—2448no—
956C2×C4—2442no—
957C2×C4C2×D4×D6112yes—
958C2×C4C2×D4×D6111yescharacteristic
959C2×C4C2×D4×D6112yes—
960C2×C4C2×D4×D6112yes—
961C2×C4C24×D6111yescharacteristic
962C8—22no—
963C8—22no—
964C8—1222no—
965C8—1222no—
966C22—22no—
967C22—22no—
968C22—22no—
969C22—44no—
970C22—614no—
971C22—1228no—
972C22—1222no—
973C22—1222no—
974C22—1224no—
975C22—1222no—
976C22—1222no—
977C22—1222no—
978C22—4884no—
979C22—2442no—
980C22—2442no—
981C22—2442no—
982C22—2444no—
983C22—2448no—
984C22—2442no—
985C22—2442no—
986C22#120×D6112yes—
987C22#1684057112yes—
988C22#1684057512yes—
989C22C22×D4×D6111yescharacteristic
990C4—24no—
991C4—24no—
992C4—22no—
993C4—42no—
994C4—42no—
995C4—614no—
996C4—1222no—
997C4—1224no—
998C4—2442no—
999C4#120×D6112yes—
1000C4C22×D4×D6111yescharacteristic
1001C4C22×D4×D6111yescharacteristic
1002C2—42no—
1003C2—1224no—
1004C2—4882no—
1005C2—2442no—
1006C2—2444no—
1007C2#2145513514yesdirect product factor
1008C2C2×#120×D6111yescharacteristic
1009C2C2×#1684057111yescharacteristic
1010C2C2×#1684057511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#451C2
socleC23×C61C22×D4
hypercenterC2×#451D61
hypocenterC61C2×#3013
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C22×#14519825C2semidirect
2. C22×#14519809C2semidirect
3. C22×#14519800C2semidirect
4. C2×#16840342C2semidirect
5. #21455135C2direct (N × H)
6. C2×#16839923C2semidirect
7. C2×#16839922C2semidirect
8. C2×#16839910C2semidirect
9. C2×#16839909C2semidirect
10. C2×#16839916C2semidirect
11. C2×#16839902C2semidirect
12. C2×#16839901C2semidirect
13. C2×#16839762C2semidirect
14. C2×#103×D61C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#451C2semidirect
20. C2×#14519825C22semidirect
33. C2×#14519809C22semidirect
35. C2×#14519800C22semidirect
45. #16840342C22semidirect
54. #16839923C22semidirect
55. #16839922C22semidirect
56. #16839916C22semidirect
57. #16839910C22semidirect
58. #16839909C22semidirect
59. #16839902C22semidirect
60. #16839901C22semidirect
61. #16839762C22semidirect
66. #103×D61C22semidirect
69. #16839727C22semidirect
77. C61×#451C22semidirect
94. C2×#11758226D4semidirect
121. C2×Q8×D61D4semidirect
270. #11758226C2×D4semidirect
277. Q8×D61C2×D4semidirect
507. C2×#451D61semidirect
514. C2×C61#3013semidirect
566. #451C2×D61semidirect
586. C61C2×#3013semidirect
1007. C2#21455135direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198252
C22×#145198092
C22×#145198002
C2×#168403422
#214551352
C2×#168399232
C2×#168399222
C2×#168399102
C2×#168399092
C2×#168399162
C2×#168399022
C2×#168399012
C2×#168397622
C2×#103×D612
C2×#168397272
C2×C61×#4512
C2×#301361