Finite Group Databasebeta

← #29711070

Subgroups — #29711070

Order 15616.

1800 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519797C211yesmaximal, characteristic, complemented
2C2×#16839924C211yesmaximal, characteristic, complemented
3C2×#16839922C211yesmaximal, characteristic, complemented
4C2×#16839907C211yesmaximal, characteristic, complemented
5#21449164C211yesmaximal, characteristic, complemented
6#21446919C211yesmaximal, characteristic, complemented
7#21446902C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446243C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446153C211yesmaximal, characteristic, complemented
13#21446112C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#547C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519797—24no—
18C2×#14519797—24no—
19C2×#14519797—24no—
20C22×#11758202C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×#11758201C2211yescharacteristic
25C22×#11758199C2211yescharacteristic
26C23×#92418C2211yescharacteristic
27C2×#14519756C2211yescharacteristic
28C2×#14519751C2211yescharacteristic
29#16839924—24no—
30#16839922—24no—
31#16839907—24no—
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43#16839677—21no—
44#16839670—21no—
45#16839668C2211yescharacteristic
46#16839664C2211yescharacteristic
47#16839638—21no—
48#16839633—21no—
49#16839622C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839517C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C22×#41×C61C2211yescharacteristic
56C61×#547—24no—
57C61×#547—24no—
58C2×C4⋊Q8×C61C2211yescharacteristic
59C2×#123×C61—21no—
60C2×#123×C61—21no—
61C2×C22⋊Q8×C61C2211yescharacteristic
62C2×C22⋊Q8×C61C2211yescharacteristic
63C2×#121×C61—21no—
64C2×C4×D4×C61C2211yescharacteristic
65C2×C4×D4×C61C2211yescharacteristic
66C22×C4⋊C4×C61—21no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—22no—
71C2×#11758222—41no—
72C2×#11758222—41no—
73C22×Dic122C2311yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C22×C4×D61—21no—
78#14519797—232no—
79C2×#11758202—22no—
80C2×#11758202—22no—
81C2×#11758202—22no—
82C2×#11758202—22no—
83C2×#11758202—22no—
84C2×#11758202—41no—
85C2×#11758200—22no—
86C2×#11758200—22no—
87C2×#11758200D414yescomplemented
88C2×#11758201—22no—
89C2×#11758201—22no—
90C2×#11758201—22no—
91C2×#11758201—22no—
92C2×#11758201—22no—
93C2×#11758201—41no—
94C2×#11758199—22no—
95C2×#11758199—22no—
96C2×#11758199D414yescomplemented
97C22×#92418—22no—
98C22×#92418—22no—
99C22×#92418—22no—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104#14519756—22no—
105#14519756—41no—
106#14519751—22no—
107#14519751—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116#14519701—22no—
117#14519701—22no—
118#14519701—41no—
119#14519701—41no—
120#14519700—22no—
121#14519698—22no—
122#14519698—22no—
123#14519697—22no—
124C22⋊#92418—22no—
125C22⋊#92418—22no—
126C22⋊#92418—22no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130C2×#41×C61—22no—
131C2×#41×C61—22no—
132C2×#41×C61—22no—
133C2×#41×C61—22no—
134C2×#41×C61—22no—
135C2×#41×C61—22no—
136C2×#41×C61—22no—
137C2×#41×C61—41no—
138C2×#41×C61—41no—
139C2×#41×C61—41no—
140C2×#41×C61—41no—
141C2×#41×C61D414yescomplemented
142C22×Q8×C61C2311yescharacteristic
143C22×Q8×C61C2311yescharacteristic
144C22×D4×C61—21no—
145C22×D4×C61—21no—
146C22×D4×C61D411yescharacteristic
147C22×D4×C61C2311yescharacteristic
148C23×C4×C61—21no—
149C23×C4×C61—21no—
150C23×C4×C61—21no—
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C4⋊Q8×C61—22no—
154C4⋊Q8×C61—22no—
155#123×C61—28no—
156#123×C61—28no—
157C22⋊Q8×C61—22no—
158C22⋊Q8×C61—22no—
159C22⋊Q8×C61—22no—
160C22⋊Q8×C61D414yescomplemented
161#121×C61—28no—
162C4×D4×C61—22no—
163C4×D4×C61—22no—
164C4×D4×C61—22no—
165C4×D4×C61—22no—
166C2×C4⋊C4×C61—28no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61D411yescharacteristic
177C2×C22⋊C4×C61D411yescharacteristic
178C2×C42×C61C2311yescharacteristic
179C24×C61—21no—
180C24×C61C2×D411yescharacteristic
181C24×C61C2×D411yescharacteristic
182C23×D61—21no—
183#41×C61—28no—
184#41×C61—44no—
185#41×C61—44no—
186#41×C61—44no—
187#41×C61—44no—
188#41×C61—44no—
189#41×C61—44no—
190#41×C61—44no—
191C2×Q8×C61—21no—
192C2×Q8×C61—21no—
193C2×Q8×C61—21no—
194C2×Q8×C61—21no—
195C2×Q8×C61—21no—
196C2×Q8×C61—21no—
197C2×Q8×C61—21no—
198C2×Q8×C61—21no—
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61C2×D412yes—
202C2×Q8×C61C2×D412yes—
203C2×D4×C61—24no—
204C2×D4×C61—22no—
205C2×D4×C61—24no—
206C2×D4×C61—22no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—41no—
211C2×D4×C61—42no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—42no—
215C2×D4×C61C2×D412yes—
216C2×D4×C61C2×D412yes—
217C2×D4×C61C2×D412yes—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—24no—
223C22×C4×C61—24no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—24no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—42no—
235C22×C4×C61—42no—
236C22×C4×C61—42no—
237C22×C4×C61—42no—
238C22×C4×C61—42no—
239C22×C4×C61—42no—
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2411yescharacteristic
247C2×C22⋊D61—42no—
248C2×C22⋊D61—42no—
249C2×C22⋊D61—42no—
250C2×C22⋊D61—42no—
251C2×C22⋊D61—42no—
252C2×C22⋊D61—81no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256#11758222—28no—
257#11758222—44no—
258#11758222—44no—
259#11758222—44no—
260C2×D244—21no—
261C2×D244—21no—
262C2×D244—21no—
263C2×D244—21no—
264C2×D244—21no—
265C2×D244C2×D412yes—
266C2×C4×D61—42no—
267C2×C4×D61—42no—
268C2×C4×D61—42no—
269C2×Dic122—21no—
270C2×Dic122—21no—
271C2×Dic122—21no—
272C2×Dic122—21no—
273C2×Dic122—21no—
274C2×Dic122C2×D412yes—
275C4⋊C4×C61—24no—
276C4⋊C4×C61—24no—
277C4⋊C4×C61—24no—
278C4⋊C4×C61—22no—
279C4⋊C4×C61—24no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61C2×D412yes—
282C22⋊C4×C61—24no—
283C22⋊C4×C61—24no—
284C22⋊C4×C61—24no—
285C22⋊C4×C61—22no—
286C22⋊C4×C61—22no—
287C42×C61—21no—
288C42×C61—21no—
289C22⋊Dic61—42no—
290C22⋊Dic61—81no—
291#11758202—28no—
292#11758202—44no—
293#11758201—28no—
294#11758201—44no—
295#11758200—28no—
296#11758199—28no—
297#11758198—42no—
298#11758198—42no—
299#11758198—81no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304#11758196—42no—
305C2×#92418—28no—
306C2×#92418—21no—
307C2×#92418—21no—
308C2×#92418—21no—
309C2×#92418—21no—
310C2×#92418—21no—
311C2×#92418—21no—
312C2×#92418—21no—
313C2×#92418—21no—
314C2×#92418—21no—
315C2×#92418—21no—
316C2×#92418C2×D412yes—
317C2×#92418C2×D412yes—
318C23×C61—22no—
319C23×C61—21no—
320C23×C61—21no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—21no—
331C23×C61—21no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61#12012yes—
339C23×C61C22×D411yescharacteristic
340C22×D61—22no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347Q8×C61—22no—
348Q8×C61—22no—
349Q8×C61—22no—
350Q8×C61—22no—
351Q8×C61—41no—
352Q8×C61—41no—
353Q8×C61—41no—
354Q8×C61—41no—
355D4×C61—22no—
356D4×C61—22no—
357D4×C61—22no—
358D4×C61—44no—
359D4×C61—48no—
360D4×C61—48no—
361D4×C61#12014yes—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—21no—
371C2×C4×C61—22no—
372C2×C4×C61—21no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—48no—
380C2×C4×C61—48no—
381C2×C4×C61—48no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61#12012yes—
393C2×C4×C61#13512yescomplemented
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D411yescharacteristic
396C2×C4×C61C22×D411yescharacteristic
397C2×C4×C61C22×D411yescharacteristic
398C2×C4×C61H(5,𝔽2)11yescharacteristic
399C2×C4×C61H(5,𝔽2)11yescharacteristic
400C22⋊D61—48no—
401C22⋊D61—84no—
402C2×Dic61—22no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411D244—22no—
412D244—22no—
413D244—41no—
414D244—41no—
415C4×D61—48no—
416Dic122—22no—
417Dic122—22no—
418Dic122—41no—
419Dic122—41no—
420#92418—22no—
421#92418—22no—
422#92418—41no—
423#92418—41no—
424#23853—611nomaximal, Sylow
425C22×C61—22no—
426C22×C61—24no—
427C22×C61—22no—
428C22×C61—22no—
429C22×C61—42no—
430C22×C61—41no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—41no—
434C22×C61—42no—
435C22×C61—41no—
436C22×C61—42no—
437C22×C61—41no—
438C22×C61—42no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61C2×#12011yescharacteristic
447C22×C61D4211yescharacteristic
448C22×C61D4211yescharacteristic
449C22×C61C2×#13511yescharacteristic
450C22×C61#57511yescharacteristic
451C22×C61#57711yescharacteristic
452C22×C61#57811yescharacteristic
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61—81no—
459C2×D61—81no—
460C4×C61—22no—
461C4×C61—22no—
462C4×C61—41no—
463C4×C61—42no—
464C4×C61—42no—
465C4×C61—42no—
466C4×C61—41no—
467C4×C61C2×#12011yescharacteristic
468C4×C61#53411yescharacteristic
469C4×C61D4211yescharacteristic
470C4×C61D4211yescharacteristic
471Dic61—42no—
472Dic61—81no—
473Dic61—81no—
474C22×#135—611no—
475C2×#547D6111yescharacteristic, complemented
476C2×#452—611no—
477C2×#452—611no—
478C2×#449—611no—
479#2407—611no—
480#2016—611no—
481#2013—611no—
482#2001—611no—
483#2000—611no—
484#1892—611no—
485#1879—611no—
486#1877—611no—
487#1869—611no—
488#1788—611no—
489C2×C61—42no—
490C2×C61—44no—
491C2×C61—81no—
492C2×C61#240311yescharacteristic
493C2×C61#300211yescharacteristic
494C2×C61#301311yescharacteristic
495C2×C61#326711yescharacteristic
496C2×C61#326911yescharacteristic
497C2×C61#328311yescharacteristic
498C2×C61#328411yescharacteristic
499D61—82no—
500C22×#41—611no—
501C22×#41C2×D6111yescharacteristic
502C22×#41C2×D6111yescharacteristic
503C2×#135—1224no—
504C2×#135—1224no—
505C2×#135—1224no—
506C22×Q16—611no—
507C22×Q16—611no—
508C22×SD16—611no—
509C22×SD16—611no—
510C22×SD16—611no—
511C22×D8—611no—
512C23×C8—611no—
513#547—24no—
514#547—24no—
515C2×C4⋊Q8C2×D6111yescharacteristic
516C2×#123—21no—
517C2×#123—21no—
518C2×C22⋊Q8—611no—
519C2×C22⋊Q8C2×D6111yescharacteristic
520C2×C22⋊Q8C2×D6111yescharacteristic
521C2×#121—21no—
522C2×#121—611no—
523C2×C4×D4C2×D6111yescharacteristic
524C2×C4×D4C2×D6111yescharacteristic
525C22×C4⋊C4—21no—
526#452—1224no—
527#452—1224no—
528#449—1224no—
529C2×#103—611no—
530C2×#103—611no—
531C2×#103—611no—
532C2×#103—611no—
533C2×#103—611no—
534C2×#102—611no—
535C2×#102—611no—
536C2×#102—611no—
537C2×C22⋊C8—611no—
538C2×C22⋊C8—611no—
539C2×C22⋊C8—611no—
540#394—1221no—
541#392—1221no—
542#391—611no—
543#390—611no—
544#386—1221no—
545#385—1221no—
546#380—611no—
547#340—611no—
548#340—611no—
549#336—611no—
550#336—611no—
551C61#2385311yescharacteristic, complemented, Sylow
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—41no—
560C2×#41—41no—
561C2×#41—41no—
562C2×#41—41no—
563C2×#41—1222no—
564C2×#41—1222no—
565C2×#41—1222no—
566C2×#41—1222no—
567C2×#41—2441no—
568C2×#41—2441no—
569C2×#41C22⋊D6114yescomplemented
570C22×Q8—611no—
571C22×Q8C22×D6111yescharacteristic
572C22×Q8C22×D6111yescharacteristic
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—611no—
576C22×D4—1221no—
577C22×D4—1221no—
578C22×D4C22⋊D6111yescharacteristic
579C22×D4C22×D6111yescharacteristic
580C23×C4—21no—
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—1221no—
584C23×C4C22×D6111yescharacteristic
585C23×C4C22×D6111yescharacteristic
586#135—12232no—
587C2×Q16—1222no—
588C2×Q16—1222no—
589C2×Q16—1222no—
590C2×Q16—1222no—
591C2×Q16—1222no—
592C2×Q16—2441no—
593C2×SD16—614no—
594C2×SD16—1222no—
595C2×SD16—1222no—
596C2×SD16—1222no—
597C2×SD16—1222no—
598C2×SD16—1222no—
599C2×SD16—1222no—
600C2×SD16—1222no—
601C2×SD16—2441no—
602C2×D8—614no—
603C2×D8—1222no—
604C2×D8—1222no—
605C22×C8—611no—
606C22×C8—611no—
607C22×C8—611no—
608C22×C8—611no—
609C22×C8—1222no—
610C22×C8—1222no—
611C22×C8—1222no—
612C4⋊Q8—22no—
613C4⋊Q8—22no—
614#123—28no—
615#123—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—1222no—
620C22⋊Q8—2441no—
621C22⋊Q8C22⋊D6114yescomplemented
622#121—28no—
623#121—1222no—
624#121—2441no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—611no—
635C2×C4⋊C4—611no—
636C2×C4⋊C4—1221no—
637C2×C4⋊C4C22⋊D6111yescharacteristic
638C2×C4⋊C4C22×D6111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4—1221no—
646C2×C22⋊C4—1221no—
647C2×C22⋊C4C22⋊D6111yescharacteristic
648C2×C22⋊C4C22⋊D6111yescharacteristic
649C2×C42C22×D6111yescharacteristic
650#103—1222no—
651#103—1222no—
652#103—1222no—
653#103—2441no—
654#103—2441no—
655#102—1222no—
656#102—1222no—
657#102—1222no—
658C22⋊C8—1222no—
659C22⋊C8—1222no—
660C22⋊C8—1222no—
661#95—1221no—
662#95—1221no—
663#95—1221no—
664C24—21no—
665C24—1221no—
666C24C2×C22⋊D6111yescharacteristic
667C24C2×C22⋊D6111yescharacteristic
668#41—28no—
669#41—44no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676#41—1228no—
677#41—2444no—
678#41—2444no—
679#41—2444no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—612no—
691C2×Q8—1221no—
692C2×Q8—1221no—
693C2×Q8—1221no—
694C2×Q8—1221no—
695C2×Q8—1221no—
696C2×Q8C2×C22⋊D6112yes—
697C2×Q8C2×C22⋊D6112yes—
698C2×D4—24no—
699C2×D4—22no—
700C2×D4—24no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—22no—
705C2×D4—41no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—612no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—4881no—
717C2×D4—2442no—
718C2×D4—2442no—
719C2×D4—2442no—
720C2×D4—2442no—
721C2×D4—2442no—
722C2×D4D4×D6112yes—
723C2×D4D4×D6112yes—
724C2×D4C2×C22⋊D6112yes—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—2442no—
751C22×C4—2442no—
752C22×C4—2442no—
753C22×C4C2×C22⋊D6111yescharacteristic
754C22×C4C2×C22⋊D6111yescharacteristic
755C22×C4C2×C22⋊D6112yes—
756C22×C4C2×C22⋊D6112yes—
757C22×C4C2×C22⋊D6111yescharacteristic
758C22×C4C2×C22⋊D6111yescharacteristic
759C22×C4C23×D6111yescharacteristic
760Q16—1228no—
761Q16—2444no—
762SD16—1228no—
763SD16—1228no—
764SD16—2444no—
765D8—1228no—
766C2×C8—612no—
767C2×C8—612no—
768C2×C8—1228no—
769C2×C8—1221no—
770C2×C8—1221no—
771C2×C8—1221no—
772C2×C8—1221no—
773C2×C8—1221no—
774C2×C8—1221no—
775C2×C8—1221no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—1221no—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—21no—
783C4⋊C4—22no—
784C4⋊C4—24no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—2442no—
790C4⋊C4C2×C22⋊D6112yes—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—4881no—
797C22⋊C4—4881no—
798C22⋊C4—2442no—
799C22⋊C4—2442no—
800C22⋊C4—2442no—
801C42—21no—
802C42—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—22no—
811C23—22no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—1222no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23—2441no—
830C23#1451974612yes—
831C23C22×C22⋊D6111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—1222no—
841Q8—1222no—
842Q8—2441no—
843Q8—2441no—
844D4—22no—
845D4—22no—
846D4—22no—
847D4—44no—
848D4—48no—
849D4—48no—
850D4—1222no—
851D4—1222no—
852D4—4884no—
853D4—2448no—
854D4—2441no—
855D4—2441no—
856D4#1451974514yes—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—48no—
875C2×C4—48no—
876C2×C4—48no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—1222no—
888C2×C4—2448no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4#1451974612yes—
898C2×C4#1451979712yescomplemented
899C2×C4C2×D4×D6111yescharacteristic
900C2×C4C2×D4×D6111yescharacteristic
901C2×C4C22×C22⋊D6111yescharacteristic
902C2×C4C22×C22⋊D6111yescharacteristic
903C2×C4#1451982211yescharacteristic
904C2×C4#1451982211yescharacteristic
905C8—1222no—
906C8—1222no—
907C8—2441no—
908C8—2441no—
909C22—22no—
910C22—22no—
911C22—24no—
912C22—22no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—41no—
922C22—42no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—4881no—
931C22—4881no—
932C22—4881no—
933C22—4881no—
934C22—2442no—
935C22—2442no—
936C22—2442no—
937C22C2×#1451974611yescharacteristic
938C22D4×C22⋊D6111yescharacteristic
939C22D4×C22⋊D6111yescharacteristic
940C22C2×#1451979711yescharacteristic
941C22#1684056011yescharacteristic
942C22#1684057011yescharacteristic
943C22#1684057711yescharacteristic
944C4—22no—
945C4—22no—
946C4—41no—
947C4—41no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—4881no—
952C4—4881no—
953C4—2442no—
954C4C2×#1451974511yescharacteristic
955C4#1684032111yescharacteristic
956C4D4×C22⋊D6111yescharacteristic
957C4D4×C22⋊D6111yescharacteristic
958C2—42no—
959C2—44no—
960C2—81no—
961C2—4882no—
962C2#2144912911yescharacteristic
963C2#2145503711yescharacteristic
964C2#2145513411yescharacteristic
965C2#2145734511yescharacteristic
966C2#2145737011yescharacteristic
967C2#2145753711yescharacteristic
968C2#2145754511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#547C2
socleC23×C61C22×D4
hypercenterC2×#547D61
hypocenterC61#23853
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#14519797C2semidirect
2. C2×#16839924C2semidirect
3. C2×#16839922C2semidirect
4. C2×#16839907C2semidirect
5. #21449164C2semidirect
6. #21446919C2semidirect
7. #21446902C2semidirect
8. #21446827C2semidirect
9. #21446820C2semidirect
10. #21446243C2semidirect
11. #21446167C2semidirect
12. #21446153C2semidirect
13. #21446112C2semidirect
14. #21445759C2semidirect
15. C2×C61×#547C2semidirect
87. C2×#11758200D4semidirect
96. C2×#11758199D4semidirect
141. C2×#41×C61D4semidirect
160. C22⋊Q8×C61D4semidirect
393. C2×C4×C61#135semidirect
475. C2×#547D61semidirect
551. C61#23853semidirect
569. C2×#41C22⋊D61semidirect
621. C22⋊Q8C22⋊D61semidirect
898. C2×C4#14519797semidirect

Maximal subgroups

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

subgroupindex
C22×#145197972
C2×#168399242
C2×#168399222
C2×#168399072
#214491642
#214469192
#214469022
#214468272
#214468202
#214462432
#214461672
#214461532
#214461122
#214457592
C2×C61×#5472
#2385361