Finite Group Databasebeta

← #30616874

Subgroups — #30616874

Order 15616.

1468 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×#6923C211yesmaximal, characteristic
2C2×#16840802C211yesmaximal, characteristic, complemented
3C2×#16840801C211yesmaximal, characteristic, complemented
4C22⋊Q8×#6923C211yesmaximal, characteristic, complemented
5#21461813C211yesmaximal, characteristic, complemented
6#21461812C211yesmaximal, characteristic, complemented
7#21461805C211yesmaximal, characteristic, complemented
8#21461784C211yesmaximal, characteristic, complemented
9#21461783C211yesmaximal, characteristic, complemented
10#21461770C211yesmaximal, characteristic, complemented
11#21461659C211yesmaximal, characteristic
12#21461592C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic, complemented
14#21461547C211yesmaximal, characteristic, complemented
15#452×D61C211yesmaximal, characteristic
16#41×#6923—24no—
17#41×#6923—24no—
18C2×Q8×#6923C2211yescharacteristic
19C2×Q8×#6923C2211yescharacteristic
20C2×Q8×#6923C2211yescharacteristic
21C2×D4×#6923—21no—
22C2×D4×#6923—21no—
23C2×D4×#6923C2211yescharacteristic
24C2×D4×#6923C2211yescharacteristic
25C2×#14519856—21no—
26C2×#14519856C2211yescharacteristic
27C22×C4×#6923—21no—
28C22×C4×#6923C2211yescharacteristic
29#16840802—24no—
30#16840801—24no—
31C2×#14519846C2211yescharacteristic
32C2×#14519845C2211yescharacteristic
33C2×#14519840C2211yescharacteristic
34C2×#14519840C2211yescharacteristic
35C2×#14519840C2211yescharacteristic
36C2×#14519840C2211yescharacteristic
37C2×#14519839C2211yescharacteristic
38C2×#14519839C2211yescharacteristic
39D61⋊(C22⋊C8)C2211yescharacteristic
40C2×#14519831C2211yescharacteristic
41C2×#14519831C2211yescharacteristic
42(C2×#6923)⋊Q8C2211yescharacteristic
43#16840713C2211yescharacteristic
44#16840711—21no—
45#16840709—21no—
46#16840704C2211yescharacteristic
47C4⋊C4×#6923—21no—
48C4⋊C4×#6923C2211yescharacteristic
49C22⋊C4×#6923—21no—
50#16840636C2211yescharacteristic
51#16840636C2211yescharacteristic
52#16840635C2211yescharacteristic
53#16840635C2211yescharacteristic
54(C2×#6923)⋊C8C2211yescharacteristic
55(C2×#6923)⋊C8C2211yescharacteristic
56C2×#41×D61C2211yescharacteristic
57C2×Q16×D61C2211yescharacteristic
58C2×SD16×D61C2211yescharacteristic
59C22⋊Q8×D61C2211yescharacteristic
60#16839927C411yescharacteristic, complemented
61#16839926C411yescharacteristic, complemented
62#16839925C411yescharacteristic, complemented
63#16839924C411yescharacteristic, complemented
64#16839923C411yescharacteristic, complemented
65#16839922C411yescharacteristic, complemented
66#16839921C411yescharacteristic, complemented
67#103×D61C2211yescharacteristic
68#102×D61C2211yescharacteristic
69C22⋊C8×D61C2211yescharacteristic
70C61×#452C411yescharacteristic, complemented
71C23×#6923—21no—
72C23×#6923—21no—
73C23×#6923D411yescharacteristic
74C23×#6923D411yescharacteristic
75C2×D61⋊C8C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77Q8×#6923—22no—
78Q8×#6923—22no—
79Q8×#6923—22no—
80Q8×#6923—22no—
81Q8×#6923—22no—
82Q8×#6923D414yes—
83D4×#6923—28no—
84D4×#6923—28no—
85D4×#6923—22no—
86D4×#6923—22no—
87D4×#6923—22no—
88D4×#6923D414yes—
89#14519856—28no—
90#14519856—22no—
91#14519856—22no—
92C2×C4⋊#6923—21no—
93C2×C4⋊#6923—21no—
94C2×C4⋊#6923—21no—
95C2×C4⋊#6923—21no—
96C2×C4⋊#6923C2311yescharacteristic
97C2×C4⋊#6923C2311yescharacteristic
98C2×C4⋊#6923C2311yescharacteristic
99C2×C4⋊#6923C2311yescharacteristic
100C2×C22⋊#6923—21no—
101C2×C22⋊#6923—21no—
102C2×C22⋊#6923—21no—
103C2×C22⋊#6923—21no—
104C2×C4×#6923—28no—
105C2×C4×#6923—21no—
106C2×C4×#6923—21no—
107C2×C4×#6923—21no—
108C2×C4×#6923—22no—
109C2×C4×#6923—22no—
110C2×C4×#6923—21no—
111C2×C4×#6923—21no—
112C2×C4×#6923D411yescharacteristic
113C2×C4×#6923D411yescharacteristic
114C2×C4×#6923C2311yescharacteristic
115C2×C4×#6923C2311yescharacteristic
116#14519846—22no—
117#14519845—22no—
118#14519840—22no—
119#14519840—22no—
120#14519840—22no—
121#14519840—22no—
122#14519839—22no—
123#14519839—22no—
124#14519834—21no—
125C22⋊#92420—21no—
126#14519831—22no—
127#14519831—22no—
128(C2×#6923)⋊C4—21no—
129(C2×#6923)⋊C4—21no—
130(C2×#6923)⋊C4—21no—
131(C2×#6923)⋊C4—21no—
132(C2×#6923)⋊C4—21no—
133C2×#11758226C2×C411yescharacteristic
134C2×#11758222—21no—
135C2×#11758222C2×C411yescharacteristic
136C2×#11758224—21no—
137C2×#11758224C2×C411yescharacteristic
138#41×D61—22no—
139#41×D61—22no—
140#41×D61—22no—
141#41×D61—22no—
142C2×Q8×D61C2311yescharacteristic
143C2×Q8×D61C2311yescharacteristic
144C2×D4×D61—21no—
145C2×D4×D61C2311yescharacteristic
146C22×C4×D61—21no—
147C22×C4×D61C2311yescharacteristic
148C2×Dic244C2×C411yescharacteristic, complemented
149C2×#11758202C2×C411yescharacteristic, complemented
150C2×#11758202C2×C411yescharacteristic, complemented
151Q16×D61—22no—
152Q16×D61—22no—
153C2×#11758190C2×C411yescharacteristic, complemented
154C2×#11758200C2×C411yescharacteristic, complemented
155C2×#11758201C2×C411yescharacteristic, complemented
156SD16×D61—22no—
157SD16×D61—22no—
158C2×C8×D61C2311yescharacteristic
159C2×C8×D61C2311yescharacteristic
160#14519757C2×C411yescharacteristic, complemented
161#14519756C2×C411yescharacteristic, complemented
162#14519755—21no—
163#14519754—21no—
164#14519753C2×C411yescharacteristic, complemented
165C4⋊C4×D61—21no—
166C4⋊C4×D61C2311yescharacteristic
167C22⋊C4×D61—21no—
168#14519702C2×C411yescharacteristic, complemented
169#14519701C2×C411yescharacteristic, complemented
170#14519700C2×C411yescharacteristic, complemented
171#14519699C2×C411yescharacteristic, complemented
172#14519698C2×C411yescharacteristic, complemented
173#14519697C2×C411yescharacteristic, complemented
174C22⋊#92418C2×C411yescharacteristic, complemented
175#14519689C2×C411yescharacteristic, complemented
176#14519689C2×C411yescharacteristic, complemented
177C2×#41×C61C2×C411yescharacteristic
178C2×Q16×C61C2×C411yescharacteristic, complemented
179C2×SD16×C61C2×C411yescharacteristic, complemented
180C22⋊Q8×C61C2×C411yescharacteristic, complemented
181#103×C61C2×C411yescharacteristic, complemented
182#102×C61C2×C411yescharacteristic, complemented
183C22⋊C8×C61C2×C411yescharacteristic, complemented
184C23×D61—21no—
185C23×D61C2×D411yescharacteristic
186C22×#6923—24no—
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923—22no—
190C22×#6923—22no—
191C22×#6923—24no—
192C22×#6923—22no—
193C22×#6923—21no—
194C22×#6923—21no—
195C22×#6923—41no—
196C22×#6923—41no—
197C22×#6923—41no—
198C22×#6923—42no—
199C22×#6923—42no—
200C22×#6923—42no—
201C22×#6923—42no—
202C22×#6923C2×D411yescharacteristic
203C22×#6923C2×D411yescharacteristic
204C22×#6923C2×D411yescharacteristic
205C22×#6923C2×D411yescharacteristic
206#41×C61—22no—
207#41×C61—22no—
208C2×Q8×C61C22×C411yescharacteristic
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61C22×C411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61C22×C411yescharacteristic
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C22×Dic61—21no—
218C22×Dic61#4111yescharacteristic
219#11758226—22no—
220#11758226—22no—
221Q8×D61—21no—
222Q8×D61—21no—
223Q8×D61—21no—
224Q8×D61—21no—
225Q8×D61—21no—
226Q8×D61—21no—
227Q8×D61C2×D412yes—
228Q8×D61#4112yes—
229#11758224—24no—
230#11758224—24no—
231#11758224—22no—
232#11758224—22no—
233D4×D61—24no—
234D4×D61—24no—
235D4×D61—21no—
236D4×D61—21no—
237D4×D61C2×D412yes—
238D4×D61#4112yes—
239#11758222—24no—
240#11758222—24no—
241#11758222—22no—
242#11758222—22no—
243C2×D244—21no—
244C2×D244C22×C411yescharacteristic
245C2×C4×D61—24no—
246C2×C4×D61—24no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61C22×C411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61#4111yescharacteristic
259C2×C4×D61C2411yescharacteristic
260C2×Dic122—21no—
261C2×Dic122—21no—
262C2×Dic122C22×C411yescharacteristic
263C2×Dic122C22×C411yescharacteristic
264C22⋊#6923—24no—
265C22⋊#6923—24no—
266C22⋊#6923—24no—
267C22⋊#6923—42no—
268C2×#92420—21no—
269C2×#92420—21no—
270C4⋊#6923—24no—
271C4⋊#6923—24no—
272C4⋊#6923—21no—
273C4⋊#6923—21no—
274C4⋊#6923—21no—
275C4⋊#6923—21no—
276C4⋊#6923—21no—
277C4⋊#6923—21no—
278C4⋊#6923—42no—
279C4⋊#6923—42no—
280C4⋊#6923C2×D412yes—
281C4⋊#6923C2×D412yes—
282C4×#6923—24no—
283C4×#6923—24no—
284C4×#6923—22no—
285C4×#6923—24no—
286C4×#6923—22no—
287C4×#6923—21no—
288C4×#6923—21no—
289C4×#6923—42no—
290C4×#6923—42no—
291C4×#6923C2×D412yes—
292C4×#6923C2×D412yes—
293D61⋊C8—21no—
294D61⋊C8—21no—
295D61⋊C8—21no—
296D61⋊C8—21no—
297Q16×C61—22no—
298SD16×C61—22no—
299C2×C8×C61C22×C411yescharacteristic
300C2×C8×C61C22×C411yescharacteristic
301C4⋊C4×C61—21no—
302C4⋊C4×C61C22×C411yescharacteristic
303C22⋊C4×C61—21no—
304C22⋊Dic61—21no—
305#11758202—22no—
306#11758202—22no—
307#11758201—22no—
308#11758200—22no—
309#11758198—21no—
310#11758198—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61C22×C411yescharacteristic
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316C2×#92418C22×C411yescharacteristic
317C2×#92418C22×C411yescharacteristic
318Dic244—22no—
319#11758190—22no—
320C8×D61—21no—
321C8×D61—21no—
322C8×D61—21no—
323C8×D61—21no—
324C23×C61—21no—
325C23×C61C4×D411yescharacteristic
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—22no—
329C22×D61—21no—
330C22×D61—22no—
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61C4×D411yescharacteristic
340C22×D61C22×D411yescharacteristic
341C2×#6923—21no—
342C2×#6923—21no—
343C2×#6923—21no—
344C2×#6923—21no—
345C2×#6923—21no—
346C2×#6923—21no—
347C2×#6923—21no—
348C2×#6923—22no—
349C2×#6923—22no—
350C2×#6923—21no—
351C2×#6923—21no—
352C2×#6923—44no—
353C2×#6923—44no—
354C2×#6923—48no—
355C2×#6923—48no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923—41no—
363C2×#6923—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366C2×#6923#12012yes—
367C2×#6923#12012yes—
368C2×#6923#13712yes—
369Q8×C61—21no—
370Q8×C61—21no—
371Q8×C61—21no—
372Q8×C61C4×D412yes—
373D4×C61—24no—
374D4×C61—21no—
375D4×C61C4×D412yes—
376C2×C4×C61—24no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61C4×D411yescharacteristic
383C2×C4×C61C23×C411yescharacteristic
384C22⋊D61—24no—
385C22⋊D61—24no—
386C22⋊D61—22no—
387C22⋊D61—22no—
388C2×Dic61—24no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61C4×D411yescharacteristic
395C2×Dic61C2×#4111yescharacteristic
396D244—24no—
397D244—21no—
398D244C4×D412yes—
399C4×D61—24no—
400C4×D61—24no—
401C4×D61—21no—
402C4×D61—22no—
403C4×D61—21no—
404C4×D61—22no—
405C4×D61—21no—
406C4×D61—21no—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61C22×D411yescharacteristic
414C4×D61C22×D411yescharacteristic
415C4×D61C2×#4111yescharacteristic
416C4×D61C2×#4111yescharacteristic
417Dic122—21no—
418Dic122—22no—
419Dic122—22no—
420Dic122—21no—
421Dic122—21no—
422Dic122—41no—
423Dic122—41no—
424Dic122C4×D412yes—
425#92420—41no—
426#92420—41no—
427C8×C61—21no—
428C8×C61—21no—
429#92418—21no—
430#92418—21no—
431#21457—611nomaximal, Sylow
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—22no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61C2×C4×D411yescharacteristic
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—22no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—42no—
447C2×D61—41no—
448C2×D61—42no—
449C2×D61—41no—
450C2×D61—42no—
451C2×D61—41no—
452C2×D61—42no—
453C2×D61C2×#12011yescharacteristic
454C2×D61#52511yescharacteristic
455C2×D61C2×#13711yescharacteristic
456C2×D61#57511yescharacteristic
457C2×D61#57511yescharacteristic
458C2×D61#57511yescharacteristic
459#6923—22no—
460#6923—22no—
461#6923—22no—
462#6923—41no—
463#6923—42no—
464#6923—42no—
465#6923—81no—
466#6923—81no—
467C4×C61—22no—
468C4×C61—21no—
469C4×C61—41no—
470C4×C61—41no—
471C4×C61C2×C4×D411yescharacteristic
472C4×C61C2×C4×D411yescharacteristic
473Dic61—22no—
474Dic61—21no—
475Dic61—41no—
476Dic61—41no—
477Dic61#52511yescharacteristic
478Dic61#52511yescharacteristic
479C2×C4×#41—611no—
480C2×#452—611no—
481C2×#441—611no—
482C2×#440—611no—
483C4×C22⋊Q8—611no—
484#1878—611no—
485#1877—611no—
486#1873—611no—
487#1864—611no—
488#1863—611no—
489#1854—611no—
490#1788—611no—
491#1763—611no—
492#1762—611no—
493#1749—611no—
494C2×C61—41no—
495C2×C61—42no—
496C2×C61C4×#12011yescharacteristic
497C2×C61#294311yescharacteristic
498C2×C61C4×#13711yescharacteristic
499D61—41no—
500D61—42no—
501D61#300511yescharacteristic
502D61#300711yescharacteristic
503D61#311111yescharacteristic
504D61#311611yescharacteristic
505C22×#41—611no—
506C22×Q16—611no—
507C22×SD16—611no—
508C2×C22⋊Q8—611no—
509C4×#41—1224no—
510C4×#41—1224no—
511C2×C4×Q8—611no—
512C2×C4×Q8—611no—
513C2×C4×Q8—611no—
514C2×C4×D4—611no—
515C2×C4×D4—611no—
516C2×C4×D4—1221no—
517C2×C4×D4—1221no—
518C2×#117—611no—
519C2×#117—1221no—
520C22×C42—611no—
521C22×C42—1221no—
522#452—611no—
523#452—611no—
524#452—611no—
525#452—611no—
526#452—611no—
527#452—611no—
528#452—611no—
529#452#692311yescharacteristic, complemented
530#441—1224no—
531#440—1224no—
532C2×#107—611no—
533C2×#106—611no—
534C2×#103—611no—
535C2×#103—611no—
536C2×#103—611no—
537C2×#103—611no—
538C2×#103—611no—
539C2×#102—611no—
540C2×#102—611no—
541C2×#102—611no—
542C2×C22⋊C8—611no—
543C2×C22⋊C8—611no—
544C2×#97—611no—
545C2×#97—611no—
546#391—611no—
547#389—611no—
548#387—1221no—
549#385—1221no—
550#380—611no—
551C4×C4⋊C4—611no—
552C4×C4⋊C4—1221no—
553C4×C22⋊C4—1221no—
554#340—611no—
555#340—611no—
556#340—611no—
557#340—611no—
558#336—611no—
559#336—611no—
560C61#2145711yescharacteristic, complemented, Sylow
561C2×#41—611no—
562C2×#41—611no—
563C2×#41—611no—
564C2×#41—1221no—
565C2×#41—1221no—
566C2×#41—1222no—
567C2×#41—1222no—
568C2×#41—1222no—
569C2×#41—1222no—
570C2×#41C2×#692311yescharacteristic
571C22×Q8—611no—
572C22×Q8—611no—
573C22×D4—611no—
574C22×D4—1221no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—1221no—
579C23×C4—1221no—
580C23×C4—1221no—
581C2×Q16—611no—
582C2×Q16—611no—
583C2×Q16—611no—
584C2×Q16—1222no—
585C2×Q16—1222no—
586C2×Q16C2×#692311yescharacteristic, complemented
587C2×SD16—611no—
588C2×SD16—611no—
589C2×SD16—611no—
590C2×SD16—1222no—
591C2×SD16—1222no—
592C2×SD16C2×#692311yescharacteristic, complemented
593C22×C8—611no—
594C22×C8—611no—
595C22×C8—611no—
596C22×C8—611no—
597C22⋊Q8—611no—
598C22⋊Q8—611no—
599C22⋊Q8—611no—
600C22⋊Q8—1221no—
601C22⋊Q8—1221no—
602C22⋊Q8C2×#692311yescharacteristic, complemented
603C4×Q8—614no—
604C4×Q8—1222no—
605C4×Q8—1222no—
606C4×Q8—1222no—
607C4×Q8—1222no—
608C4×Q8—1222no—
609C4×D4—614no—
610C4×D4—1222no—
611C4×D4—1222no—
612C4×D4—1222no—
613C4×D4—1228no—
614C4×D4—1228no—
615#117—1222no—
616#117—1222no—
617#117—1228no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—1221no—
624C2×C4⋊C4—1221no—
625C2×C4⋊C4—1221no—
626C2×C4⋊C4—1221no—
627C2×C4⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C42—611no—
634C2×C42—611no—
635C2×C42—611no—
636C2×C42—611no—
637C2×C42—1222no—
638C2×C42—1222no—
639C2×C42—1221no—
640C2×C42—1221no—
641C2×C42—1221no—
642C2×C42—1228no—
643C2×C42—1221no—
644C2×C42—1221no—
645#107—1222no—
646#106—1222no—
647#103—611no—
648#103—611no—
649#103—611no—
650#103—1222no—
651#103—1222no—
652#103—1222no—
653#103—1222no—
654#103C2×#692311yescharacteristic, complemented
655#102—611no—
656#102—611no—
657#102—611no—
658#102—1222no—
659#102—1222no—
660#102C2×#692311yescharacteristic, complemented
661C22⋊C8—611no—
662C22⋊C8—611no—
663C22⋊C8—611no—
664C22⋊C8—1221no—
665C22⋊C8—1221no—
666C22⋊C8C2×#692311yescharacteristic, complemented
667#97—1222no—
668#97—1222no—
669#95—1221no—
670#95—1221no—
671#95—1221no—
672#95—1221no—
673#95—1221no—
674C24—611no—
675C24—1221no—
676#41—22no—
677#41—22no—
678#41—1222no—
679#41—1222no—
680#41—1224no—
681#41—1224no—
682#41—1222no—
683#41—1224no—
684#41—1224no—
685#41—1222no—
686#41—1222no—
687#41—1222no—
688C2×Q8—612no—
689C2×Q8—612no—
690C2×Q8—611no—
691C2×Q8—611no—
692C2×Q8—1221no—
693C2×Q8—1221no—
694C2×Q8—1221no—
695C2×Q8—1221no—
696C2×Q8—1221no—
697C2×Q8—1221no—
698C2×Q8—1221no—
699C2×Q8—1221no—
700C2×Q8C22×#692311yescharacteristic
701C2×Q8C22×#692311yescharacteristic
702C2×D4—21no—
703C2×D4—612no—
704C2×D4—612no—
705C2×D4—611no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1224no—
711C2×D4—1224no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4C22×#692311yescharacteristic
715C22×C4—21no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1224no—
732C22×C4—1224no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1224no—
737C22×C4—1222no—
738C22×C4—1222no—
739C22×C4—1222no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1224no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—2442no—
747C22×C4—2441no—
748C22×C4—2441no—
749C22×C4—2441no—
750C22×C4—2442no—
751C22×C4—2442no—
752C22×C4—2442no—
753C22×C4C22×#692311yescharacteristic
754Q16—22no—
755Q16—1222no—
756Q16—1222no—
757Q16—1222no—
758SD16—22no—
759SD16—1222no—
760SD16—1222no—
761SD16—1222no—
762C2×C8—611no—
763C2×C8—611no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—1221no—
769C2×C8—1221no—
770C2×C8—1221no—
771C2×C8—1221no—
772C2×C8—1221no—
773C2×C8—1221no—
774C2×C8C22×#692311yescharacteristic
775C2×C8C22×#692311yescharacteristic
776C4⋊C4—21no—
777C4⋊C4—612no—
778C4⋊C4—612no—
779C4⋊C4—611no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1224no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—1224no—
791C4⋊C4—1221no—
792C4⋊C4—2442no—
793C4⋊C4—2442no—
794C4⋊C4C22×#692311yescharacteristic
795C22⋊C4—21no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1224no—
799C22⋊C4—1224no—
800C22⋊C4—1224no—
801C22⋊C4—1221no—
802C22⋊C4—2442no—
803C42—612no—
804C42—612no—
805C42—1222no—
806C42—1222no—
807C42—1221no—
808C42—1221no—
809C42—1224no—
810C42—1224no—
811C42—1224no—
812C42—2442no—
813C42—2442no—
814C23—21no—
815C23—611no—
816C23—611no—
817C23—1222no—
818C23—1221no—
819C23—1221no—
820C23—1222no—
821C23—1221no—
822C23—1221no—
823C23—1221no—
824C23—1221no—
825C23—1221no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23—2441no—
830C23D4×#692311yescharacteristic
831Q8—21no—
832Q8—21no—
833Q8—21no—
834Q8—612no—
835Q8—1222no—
836Q8—1222no—
837Q8—1221no—
838Q8—1221no—
839Q8—1221no—
840Q8—2441no—
841Q8—2441no—
842Q8D4×#692312yes—
843D4—24no—
844D4—21no—
845D4—612no—
846D4—1224no—
847D4—1222no—
848D4—1222no—
849D4—1224no—
850D4—1224no—
851D4—1221no—
852D4D4×#692312yes—
853C2×C4—24no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—612no—
865C2×C4—612no—
866C2×C4—612no—
867C2×C4—611no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1222no—
872C2×C4—1221no—
873C2×C4—1222no—
874C2×C4—1224no—
875C2×C4—1224no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1224no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—1221no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2444no—
900C2×C4—2444no—
901C2×C4—2448no—
902C2×C4—2448no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4D4×#692311yescharacteristic
914C2×C4C23×#692311yescharacteristic
915C8—21no—
916C8—21no—
917C8—1221no—
918C8—1221no—
919C8—2441no—
920C8—2441no—
921C22—21no—
922C22—22no—
923C22—21no—
924C22—21no—
925C22—41no—
926C22—41no—
927C22—611no—
928C22—611no—
929C22—611no—
930C22—611no—
931C22—611no—
932C22—611no—
933C22—1222no—
934C22—1221no—
935C22—1221no—
936C22—1221no—
937C22—2441no—
938C22—2441no—
939C22—2442no—
940C22—2442no—
941C22—2441no—
942C22—2441no—
943C22—2442no—
944C22—2442no—
945C22—2441no—
946C22—2441no—
947C22C2×D4×#692311yescharacteristic
948C4—21no—
949C4—22no—
950C4—41no—
951C4—41no—
952C4—611no—
953C4—611no—
954C4—1222no—
955C4—1222no—
956C4—1222no—
957C4—1221no—
958C4—1222no—
959C4—4881no—
960C4—4881no—
961C4—2441no—
962C4—2442no—
963C4—2442no—
964C4—2441no—
965C4—2441no—
966C4C2×D4×#692311yescharacteristic
967C4C2×D4×#692311yescharacteristic
968C2—41no—
969C2—42no—
970C2—611no—
971C2—611no—
972C2—611no—
973C2—611no—
974C2—2441no—
975C2—2442no—
976C2#120×#692311yescharacteristic
977C2#2146257311yescharacteristic
978C2#137×#692311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#452C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#452#6923
hypocenterC61#21457
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C2×#16840802C2semidirect
3. C2×#16840801C2semidirect
4. C22⋊Q8×#6923C2semidirect
5. #21461813C2semidirect
6. #21461812C2semidirect
7. #21461805C2semidirect
8. #21461784C2semidirect
9. #21461783C2semidirect
10. #21461770C2semidirect
12. #21461592C2semidirect
13. #21461590C2semidirect
14. #21461547C2semidirect
60. #16839927C4semidirect
61. #16839926C4semidirect
62. #16839925C4semidirect
63. #16839924C4semidirect
64. #16839923C4semidirect
65. #16839922C4semidirect
66. #16839921C4semidirect
70. C61×#452C4semidirect
148. C2×Dic244C2×C4semidirect
149. C2×#11758202C2×C4semidirect
150. C2×#11758202C2×C4semidirect
153. C2×#11758190C2×C4semidirect
154. C2×#11758200C2×C4semidirect
155. C2×#11758201C2×C4semidirect
160. #14519757C2×C4semidirect
161. #14519756C2×C4semidirect
164. #14519753C2×C4semidirect
168. #14519702C2×C4semidirect
169. #14519701C2×C4semidirect
170. #14519700C2×C4semidirect
171. #14519699C2×C4semidirect
172. #14519698C2×C4semidirect
173. #14519697C2×C4semidirect
174. C22⋊#92418C2×C4semidirect
175. #14519689C2×C4semidirect
176. #14519689C2×C4semidirect
178. C2×Q16×C61C2×C4semidirect
179. C2×SD16×C61C2×C4semidirect
180. C22⋊Q8×C61C2×C4semidirect
181. #103×C61C2×C4semidirect
182. #102×C61C2×C4semidirect
183. C22⋊C8×C61C2×C4semidirect
529. #452#6923semidirect
560. C61#21457semidirect
586. C2×Q16C2×#6923semidirect
592. C2×SD16C2×#6923semidirect
602. C22⋊Q8C2×#6923semidirect
654. #103C2×#6923semidirect
660. #102C2×#6923semidirect
666. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#41×#69232
C2×#168408022
C2×#168408012
C22⋊Q8×#69232
#214618132
#214618122
#214618052
#214617842
#214617832
#214617702
#214616592
#214615922
#214615902
#214615472
#452×D612
#2145761