Finite Group Databasebeta

← #30620147

Subgroups — #30620147

Order 15616.

1378 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462557C212yesmaximal
2C2×D61⋊#101C211yesmaximal, characteristic, complemented
3C22×#14519838C211yesmaximal, characteristic, complemented
4#21461962C212yesmaximal, complemented
5#21461847C212yesmaximal, complemented
6#21461846C212yesmaximal, complemented
7#21461686C211yesmaximal, characteristic, complemented
8#21461654C211yesmaximal, characteristic, complemented
9#21461653C211yesmaximal, characteristic, complemented
10#21461572C211yesmaximal, characteristic, complemented
11C2×#16840425C211yesmaximal, characteristic
12C2×D61⋊M16C2212yes—
13C22×#11758217C2212yes—
14#16840795—22no—
15#16840794—22no—
16#16840791—22no—
17#16840789—22no—
18#16840765C2212yes—
19D61⋊#101—24no—
20C2×#14519838—24no—
21C2×#14519838C2211yescharacteristic
22C2×#14519838C2212yes—
23C2×#14519838C2212yes—
24C2×#14519838C2211yescharacteristic
25C2×#14519838C2211yescharacteristic
26C2×#14519838C2212yes—
27C2×#14519838C2212yes—
28C2×#14519838C2211yescharacteristic
29#16840734C2212yes—
30#16840732C2212yes—
31C4×#11758217C2212yes—
32#16840642C2212yes—
33#16840642C2212yes—
34C23×Dic122C2211yescharacteristic
35C22×Q8×D61C2211yescharacteristic
36#16840425—22no—
37#16840425—22no—
38#16840425—22no—
39#16840425—22no—
40C2×#14519776C411yescharacteristic
41C2×#14519776C2211yescharacteristic
42C2×#14519775C411yescharacteristic
43C2×#14519757C411yescharacteristic
44C2×#14519755C411yescharacteristic
45C2×#14519755C2211yescharacteristic
46C2×#14519754C411yescharacteristic
47C2×#14519754C2211yescharacteristic
48C2×#14519742C2211yescharacteristic
49C2×C4×C22⋊D61C411yescharacteristic
50C2×#14519737C411yescharacteristic
51C2×#14519737C2211yescharacteristic
52C2×C22⋊Q8×C61C411yescharacteristic
53C2×#11758213—22no—
54D61⋊M16—24no—
55D61⋊M16—42no—
56C2×#11758217—22no—
57C2×#11758217—24no—
58C2×#11758217—42no—
59C2×#11758217C2312yes—
60C2×#11758217C2312yes—
61C2×#11758217C2312yes—
62C2×#11758217C2312yes—
63C2×D61⋊C8—22no—
64C22×#92420—22no—
65#14519844—22no—
66C4⋊#92420—22no—
67#14519838—22no—
68#14519838—22no—
69#14519838—22no—
70#14519838—24no—
71#14519838—24no—
72#14519838—42no—
73#14519838—42no—
74#14519838D414yescomplemented
75#14519834—22no—
76#14519834—22no—
77C22⋊#92420—22no—
78C22⋊#92420—22no—
79#14519832—22no—
80C4×#92420—22no—
81C22×Dic122—22no—
82C22×Dic122—22no—
83C22×Dic122—22no—
84C22×Dic122—22no—
85C22×Dic122—42no—
86C22×Dic122C2×C411yescharacteristic
87C22×Dic122C2×C411yescharacteristic
88C22×Dic122C2×C411yescharacteristic
89C22×Dic122C2311yescharacteristic
90C22×Dic122C2311yescharacteristic
91C22×Dic122C2311yescharacteristic
92C2×Q8×D61—22no—
93C2×Q8×D61—22no—
94C2×Q8×D61—22no—
95C2×Q8×D61—22no—
96C2×Q8×D61—42no—
97C22×C22⋊D61C2×C411yescharacteristic
98C23×Dic61C2×C411yescharacteristic
99C23×Dic61C2311yescharacteristic
100C22×C4×D61C2×C411yescharacteristic
101C22×C4×D61C2×C411yescharacteristic
102C22×C4×D61C2311yescharacteristic
103#14519776—22no—
104#14519776—22no—
105#14519776—22no—
106#14519776—22no—
107#14519775—22no—
108#14519775—22no—
109#14519757—22no—
110#14519757—22no—
111#14519755—22no—
112#14519755—22no—
113#14519755—22no—
114#14519755—22no—
115#14519754—22no—
116#14519754—22no—
117#14519754—22no—
118#14519754—22no—
119#14519742—22no—
120#14519742—22no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125#14519737—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737D412yes—
130#14519737D412yes—
131#14519737D412yes—
132#14519737D412yes—
133C2×C4⋊Dic61C2×C411yescharacteristic
134C2×C4⋊Dic61C2×C411yescharacteristic
135C2×#11758196C2×C411yescharacteristic
136C2×#11758196C2×C411yescharacteristic
137C2×#11758196C2×C411yescharacteristic
138C2×#11758196C2×C411yescharacteristic
139C2×#11758196C2×C411yescharacteristic
140C2×#11758196C2×C411yescharacteristic
141C2×#11758196C2311yescharacteristic
142C2×C22⋊Dic61C2×C411yescharacteristic
143C2×#11758198C2×C411yescharacteristic
144C2×#11758198C2×C411yescharacteristic
145C2×#11758198C2×C411yescharacteristic
146C2×C4×Dic61C2×C411yescharacteristic
147C2×C4×Dic61C2×C411yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149C22×Q8×C61C2×C411yescharacteristic
150C23×C4×C61C2×C411yescharacteristic
151C22⋊Q8×C61—22no—
152C22⋊Q8×C61—22no—
153C2×C4⋊C4×C61C2×C411yescharacteristic
154C2×C4⋊C4×C61C2×C411yescharacteristic
155C2×C4⋊C4×C61C2×C411yescharacteristic
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C22⋊C4×C61C2×C411yescharacteristic
158C24×C61C22×C411yescharacteristic
159C23×D61C22×C411yescharacteristic
160C2×Q8×C61—22no—
161C2×Q8×C61—22no—
162C2×Q8×C61—41no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—22no—
166C22×C4×C61—41no—
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C2×C22⋊D61—24no—
174C2×C22⋊D61C22⋊C411yescharacteristic
175C2×C22⋊D61C22⋊C411yescharacteristic
176C2×C22⋊D61C22⋊C411yescharacteristic
177C2×C22⋊D61C22⋊C411yescharacteristic
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—22no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—41no—
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C2×D412yes—
192C22×Dic61C2×D412yes—
193C22×Dic61C2411yescharacteristic
194Q8×D61—44no—
195Q8×D61—44no—
196Q8×D61—44no—
197Q8×D61—44no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—22no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—41no—
208C2×C4×D61—41no—
209C2×C4×D61C2×D412yes—
210C2×C4×D61C2×D412yes—
211C2×Dic122—22no—
212C2×Dic122—22no—
213C2×Dic122—22no—
214C2×Dic122—22no—
215C2×Dic122—22no—
216C2×Dic122—22no—
217C2×Dic122—22no—
218C2×Dic122—22no—
219C2×Dic122—21no—
220C2×Dic122—22no—
221C2×Dic122—21no—
222C2×Dic122—22no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—22no—
226C2×Dic122—22no—
227C2×Dic122—44no—
228C2×Dic122—44no—
229C2×Dic122—44no—
230C2×Dic122—44no—
231C2×Dic122—41no—
232C2×Dic122—41no—
233C2×Dic122—41no—
234C2×Dic122C2×D412yes—
235C2×Dic122#4112yes—
236#11758217—22no—
237#11758217—22no—
238#11758217—22no—
239#11758217—22no—
240#11758217—22no—
241#11758217—22no—
242#11758217—22no—
243#11758217—44no—
244#11758217C2×D414yes—
245C2×#92420—22no—
246C2×#92420—22no—
247C2×#92420—22no—
248C2×#92420—22no—
249C2×#92420—44no—
250#11758213—44no—
251D61⋊C8—44no—
252C4⋊C4×C61—22no—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—22no—
255C22⋊C4×C61—21no—
256C22⋊C4×C61—21no—
257C22⋊C4×C61C22⋊C412yes—
258C22⋊C4×C61C22⋊C412yes—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265#11758198C22⋊C412yes—
266#11758198C22⋊C412yes—
267C4⋊Dic61—22no—
268C4⋊Dic61—22no—
269#11758196—22no—
270#11758196—22no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—22no—
276#11758196—22no—
277#11758196C22⋊C412yes—
278#11758196C22⋊C412yes—
279C4×Dic61—21no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C4×Dic61C2×D412yes—
284C4×Dic61C2×D412yes—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—22no—
288C23×C61—41no—
289C23×C61C2×C22⋊C411yescharacteristic
290C23×C61C2×C22⋊C411yescharacteristic
291C23×C61C23×C411yescharacteristic
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—22no—
295C22×D61—41no—
296C22×D61C2×C22⋊C411yescharacteristic
297C22×D61C2×C22⋊C411yescharacteristic
298Q8×C61—44no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—41no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—41no—
314C2×C4×C61C2×C22⋊C412yes—
315C2×C4×C61C2×C22⋊C412yes—
316C2×C4×C61C4×D412yes—
317C22⋊D61—22no—
318C22⋊D61—22no—
319C22⋊D61—22no—
320C22⋊D61#10114yescomplemented
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—41no—
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C412yes—
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C4×D412yes—
344C2×Dic61C22×D411yescharacteristic
345C2×Dic61C22×D412yes—
346C2×Dic61C2×#4111yescharacteristic
347C2×Dic61H(5,𝔽2)12yes—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—42no—
353C4×D61—42no—
354C4×D61—42no—
355C4×D61—42no—
356Dic122—24no—
357Dic122—24no—
358Dic122—44no—
359Dic122—44no—
360Dic122—44no—
361Dic122—42no—
362Dic122—42no—
363Dic122—42no—
364Dic122—42no—
365#92420—24no—
366#92420—42no—
367#92420—42no—
368#92420—42no—
369D4×#101—611nomaximal, Sylow
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61C2×#10112yescomplemented
380C22×C61C22×C22⋊C411yescharacteristic
381C22×C61C2×C4×D411yescharacteristic
382C22×C61#51811yescharacteristic
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61C2×#10112yescomplemented
391C4×C61—22no—
392C4×C61—22no—
393C4×C61—22no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61—41no—
397Dic61—22no—
398Dic61—22no—
399Dic61—21no—
400Dic61—41no—
401Dic61—41no—
402Dic61—41no—
403Dic61C2×#10112yescomplemented
404Dic61D4212yes—
405Dic61#54612yes—
406C2×D4×Q8—611no—
407D4×M16—612no—
408C22×#101—611no—
409C22×#101—611no—
410#1966—612no—
411#1901—612no—
412#1901—612no—
413#1801—611no—
414#1784—611no—
415#1784—611no—
416C4×#101—611no—
417C2×C61—21no—
418C2×C61—21no—
419C2×C61—22no—
420C2×C61—41no—
421C2×C61D4×C22⋊C411yescharacteristic
422C2×C61C22×#10111yescharacteristic
423C2×C61#288911yescharacteristic
424D61—22no—
425D61—41no—
426C23×Q8—611no—
427C23×Q8—611no—
428C22×M16—612no—
429C22×M16—612no—
430D4×Q8—1222no—
431D4×Q8—1222no—
432D4×Q8—1222no—
433D4×Q8—1222no—
434C2×C4⋊Q8—611no—
435C2×C4⋊Q8—611no—
436C2×C4⋊Q8—611no—
437C2×C22⋊Q8—611no—
438C2×C22⋊Q8—611no—
439C2×C22⋊Q8—611no—
440C2×C22⋊Q8—611no—
441C2×C22⋊Q8—611no—
442C2×C22⋊Q8#692311yescharacteristic
443C2×C4×Q8—611no—
444C2×C4×D4—611no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447#436—1222no—
448#435—1222no—
449#435—1222no—
450C8×D4—1222no—
451#423—612no—
452C2×#101—611no—
453C2×#101—611no—
454C2×#101—611no—
455C2×#101—612no—
456C2×#101—612no—
457C2×#101—611no—
458C2×#101—612no—
459C2×#101—612no—
460C2×#101—1224no—
461C2×#101—1224no—
462#407—612no—
463#407—612no—
464C4×M16—612no—
465#343—612no—
466#343—612no—
467C61D4×#10111yescharacteristic, complemented, Sylow
468C22×Q8—611no—
469C22×Q8—611no—
470C22×Q8—611no—
471C22×Q8—611no—
472C22×Q8—611no—
473C22×Q8—611no—
474C22×Q8—1222no—
475C22×Q8—1222no—
476C22×Q8—1222no—
477C22×Q8—1222no—
478C22×Q8—1222no—
479C22×Q8—1222no—
480C22×Q8—1222no—
481C22×Q8—1222no—
482C22×Q8—2442no—
483C22×Q8—2442no—
484C22×Q8C2×#692311yescharacteristic
485C22×D4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4C2×#692311yescharacteristic
492C2×M16—612no—
493C2×M16—612no—
494C2×M16—612no—
495C2×M16—612no—
496C2×M16—1222no—
497C2×M16—1222no—
498C2×M16—1224no—
499C2×M16—1224no—
500C2×M16—2442no—
501C2×M16—2442no—
502C22×C8—1222no—
503C22×C8—1222no—
504C4⋊Q8—1222no—
505C4⋊Q8—1222no—
506C4⋊Q8—1222no—
507C4⋊Q8—1222no—
508C4⋊Q8—1222no—
509C4⋊Q8—1222no—
510C22⋊Q8—22no—
511C22⋊Q8—22no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514C22⋊Q8—1222no—
515C22⋊Q8—1222no—
516C22⋊Q8—1222no—
517C22⋊Q8—1222no—
518C22⋊Q8—1222no—
519C22⋊Q8—1222no—
520C22⋊Q8—1222no—
521C22⋊Q8—1222no—
522C4×Q8—1222no—
523C4×Q8—1222no—
524C4×D4—612no—
525C4×D4—612no—
526C4×D4—612no—
527C4×D4—612no—
528C4×D4—1221no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4C2×#692311yescharacteristic
546C2×C4⋊C4C2×#692311yescharacteristic
547C2×C4⋊C4C2×#692311yescharacteristic
548C2×C22⋊C4—611no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4C2×#692311yescharacteristic
553C2×C22⋊C4C2×#692311yescharacteristic
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—611no—
557C4⋊C8—1222no—
558C4⋊C8—1222no—
559#101—614no—
560#101—1224no—
561#101—1224no—
562#101—1222no—
563#101—1222no—
564#101—1222no—
565#101—2442no—
566#101—2442no—
567C22⋊C8—1222no—
568C22⋊C8—1222no—
569C22⋊C8—1222no—
570C22⋊C8—1222no—
571#97—1222no—
572C4×C8—1222no—
573C24—611no—
574C24C22×#692311yescharacteristic
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8—612no—
579C2×Q8—612no—
580C2×Q8—1222no—
581C2×Q8—1222no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1222no—
585C2×Q8—1222no—
586C2×Q8—1222no—
587C2×Q8—1222no—
588C2×Q8—1222no—
589C2×Q8—1222no—
590C2×Q8—1222no—
591C2×Q8—1221no—
592C2×Q8—1222no—
593C2×Q8—1221no—
594C2×Q8—1222no—
595C2×Q8—1222no—
596C2×Q8—2441no—
597C2×Q8—2441no—
598C2×Q8—2441no—
599C2×Q8—2444no—
600C2×Q8—2444no—
601C2×Q8—2444no—
602C2×Q8—2444no—
603C2×Q8—2444no—
604C2×Q8—2444no—
605C2×Q8—2444no—
606C2×Q8—2444no—
607C2×D4—611no—
608C2×D4—611no—
609C2×D4—611no—
610C2×D4—611no—
611C2×D4—1224no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—41no—
616C22×C4—611no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—1221no—
628C22×C4—1222no—
629C22×C4—1221no—
630C22×C4—1222no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1222no—
637C22×C4—1221no—
638C22×C4—1222no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1222no—
642C22×C4—2441no—
643C22×C4—2441no—
644C22×C4—2441no—
645C22×C4C22×#692311yescharacteristic
646C22×C4C22×#692311yescharacteristic
647C22×C4C22×#692311yescharacteristic
648C22×C4C22×#692311yescharacteristic
649C22×C4C22×#692311yescharacteristic
650C22×C4C22×#692311yescharacteristic
651M16—614no—
652M16—1222no—
653M16—1222no—
654M16—1222no—
655M16—1222no—
656M16—1222no—
657M16—1222no—
658M16—1222no—
659M16—2444no—
660M16—2444no—
661C2×C8—1222no—
662C2×C8—1222no—
663C2×C8—1222no—
664C2×C8—1222no—
665C2×C8—2444no—
666C2×C8—2444no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—612no—
671C4⋊C4—612no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1222no—
677C4⋊C4—1222no—
678C4⋊C4—1222no—
679C4⋊C4—1222no—
680C4⋊C4—1222no—
681C4⋊C4—1222no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—612no—
685C22⋊C4—612no—
686C22⋊C4—1221no—
687C22⋊C4—1221no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4C22⋊#692312yes—
693C22⋊C4C22⋊#692312yes—
694C42—612no—
695C42—612no—
696C42—1221no—
697C42—1221no—
698C42—1221no—
699C42—1221no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—41no—
704C23—611no—
705C23—611no—
706C23—1222no—
707C23—1221no—
708C23—1221no—
709C23—2441no—
710C23C2×C22⋊#692311yescharacteristic
711C23C2×C22⋊#692311yescharacteristic
712C23C23×#692311yescharacteristic
713Q8—44no—
714Q8—1224no—
715Q8—1224no—
716Q8—2444no—
717Q8—2444no—
718Q8—2442no—
719Q8—2442no—
720Q8—2442no—
721Q8—2442no—
722Q8—2444no—
723D4—614no—
724D4—1222no—
725D4—1222no—
726D4—1222no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—611no—
743C2×C4—612no—
744C2×C4—611no—
745C2×C4—611no—
746C2×C4—612no—
747C2×C4—611no—
748C2×C4—612no—
749C2×C4—612no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4—2442no—
775C2×C4—2442no—
776C2×C4—2441no—
777C2×C4C2×C22⋊#692312yes—
778C2×C4C2×C22⋊#692312yes—
779C2×C4D4×#692312yes—
780C8—1224no—
781C8—2442no—
782C8—2442no—
783C8—2442no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—42no—
792C22—42no—
793C22—612no—
794C22—1221no—
795C22—1221no—
796C22—1221no—
797C22—1221no—
798C22—1221no—
799C22—2442no—
800C22—2442no—
801C22D61⋊#10112yescomplemented
802C22C22×C22⋊#692311yescharacteristic
803C22C2×D4×#692311yescharacteristic
804C22#1684082911yescharacteristic
805C4—22no—
806C4—22no—
807C4—22no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—612no—
812C4—612no—
813C4—612no—
814C4—1222no—
815C4—1222no—
816C4—1221no—
817C4—2441no—
818C4—2441no—
819C4—2441no—
820C2—21no—
821C2—21no—
822C2—22no—
823C2—41no—
824C2—1222no—
825C2—2441no—
826C2D4×C22⋊#692311yescharacteristic
827C2C2×D61⋊#10111yescharacteristic
828C2#2146243111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61D4×#101
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×D61⋊#101C2semidirect
3. C22×#14519838C2semidirect
4. #21461962C2semidirect
5. #21461847C2semidirect
6. #21461846C2semidirect
7. #21461686C2semidirect
8. #21461654C2semidirect
9. #21461653C2semidirect
10. #21461572C2semidirect
74. #14519838D4semidirect
320. C22⋊D61#101semidirect
379. C22×C61C2×#101semidirect
390. C2×D61C2×#101semidirect
403. Dic61C2×#101semidirect
467. C61D4×#101semidirect
801. C22D61⋊#101semidirect

Maximal subgroups

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

subgroupindex
#214625572
C2×D61⋊#1012
C22×#145198382
#214619622
#214618472
#214618462
#214616862
#214616542
#214616532
#214615722
C2×#168404252
D4×#10161