Finite Group Databasebeta

← #29696560

Subgroups — #29696560

Order 15616.

1354 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840425C211yesmaximal, characteristic
2C22⋊C4×Dic122C211yesmaximal, characteristic, complemented
3#21448651C211yesmaximal, characteristic, complemented
4#21446805C211yesmaximal, characteristic, complemented
5#21446802C212yesmaximal, complemented
6#21446802C212yesmaximal, complemented
7#21445806C212yesmaximal
8#21445804C211yesmaximal, characteristic
9C4×#14519691C211yesmaximal, characteristic
10#21445606C212yesmaximal
11C61×#1996C211yesmaximal, characteristic, complemented
12C23×Dic122C2211yescharacteristic
13C22×Q8×D61C411yescharacteristic, complemented
14#16840425—21no—
15#16840425—21no—
16#16840425—22no—
17#16840425—22no—
18#16840425—21no—
19#16840425—21no—
20C2×#14519776C412yescomplemented
21C2×#14519775C411yescharacteristic, complemented
22C2×#14519757C411yescharacteristic, complemented
23C2×#14519755C412yescomplemented
24C2×#14519754C2212yes—
25C2×C4×Dic122—21no—
26C2×#14519742—21no—
27C2×#14519742C411yescharacteristic, complemented
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519737C2212yes—
30C2×#14519691C2212yes—
31C2×#14519691C2211yescharacteristic
32C2×#14519691C2211yescharacteristic
33#16839668—21no—
34#16839667—21no—
35#16839666—22no—
36#16839666—22no—
37#16839622C2211yescharacteristic
38#16839620C2212yes—
39#16839620C2212yes—
40C22⋊C4×Dic61C2212yes—
41C22⋊C4×Dic61C2212yes—
42C4×C22⋊Dic61C2211yescharacteristic
43#16839529C2212yes—
44#16839529C2212yes—
45#16839528C2212yes—
46#16839528C2211yescharacteristic
47#16839528C2211yescharacteristic
48C2×C22⋊Q8×C61C2211yescharacteristic
49C61×#380C2211yescharacteristic
50C4×C22⋊C4×C61C2211yescharacteristic
51C61×#342C2212yes—
52C61×#342C2212yes—
53C22×Dic122—44no—
54C22×Dic122C2×C411yescharacteristic
55C22×Dic122C2×C412yes—
56C22×Dic122C2×C412yes—
57C22×Dic122C2×C411yescharacteristic
58C22×Dic122D411yescharacteristic
59C22×Dic122D411yescharacteristic
60C22×Dic122D412yes—
61C22×Dic122D412yes—
62C22×Dic122D411yescharacteristic
63C22×Dic122D411yescharacteristic
64C2×Q8×D61—21no—
65C2×Q8×D61—22no—
66C2×Q8×D61—21no—
67C2×Q8×D61—44no—
68C22×C22⋊D61C2311yescharacteristic
69C23×Dic61C2312yes—
70C22×C4×D61C2×C412yes—
71C22×C4×D61C2×C411yescharacteristic
72#14519776—22no—
73#14519776—22no—
74#14519776—22no—
75#14519776—22no—
76#14519775—21no—
77#14519775—21no—
78#14519775—22no—
79#14519757—21no—
80#14519757—21no—
81#14519757—22no—
82#14519755—22no—
83#14519755—22no—
84#14519755—22no—
85#14519755—22no—
86#14519754—22no—
87#14519754—22no—
88#14519754—22no—
89#14519754—22no—
90C4×Dic122—44no—
91#14519742—22no—
92#14519742—21no—
93#14519742—21no—
94#14519742—44no—
95C4×C22⋊D61—21no—
96C4×C22⋊D61—21no—
97C4×C22⋊D61—21no—
98C4×C22⋊D61—21no—
99#14519737—22no—
100#14519737—22no—
101#14519737—22no—
102#14519737—22no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2×C412yes—
105C2×#11758196—22no—
106C2×#11758196—22no—
107C2×#11758196C2×C412yes—
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196C2×C412yes—
110C2×#11758196C2×C412yes—
111C2×C22⋊Dic61C2311yescharacteristic
112C2×C22⋊Dic61C2312yes—
113C2×C22⋊Dic61C2311yescharacteristic
114C2×C22⋊Dic61C2311yescharacteristic
115C2×#11758198C2×C412yes—
116C2×#11758198C2×C411yescharacteristic
117C2×C4×Dic61—21no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—22no—
120C2×C4×Dic61C2×C412yes—
121C2×C4×Dic61C2×C411yescharacteristic
122#14519691—24no—
123#14519691—22no—
124#14519691Q814yescomplemented
125#14519684—21no—
126#14519684—21no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131C22×Q8×C61C2×C411yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61—21no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C412yes—
140C2×C22⋊C4×C61C2311yescharacteristic
141C2×C22⋊C4×C61C2312yes—
142C2×C22⋊C4×C61C2312yes—
143C2×C22⋊C4×C61C2311yescharacteristic
144C2×C42×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147C24×C61C2411yescharacteristic
148C23×D61C22×C411yescharacteristic
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—42no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—22no—
155C22×C4×C61—42no—
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C412yes—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C2×C22⋊D61—21no—
165C2×C22⋊D61—21no—
166C2×C22⋊D61—21no—
167C2×C22⋊D61—21no—
168C2×C22⋊D61C2×Q812yes—
169C2×C22⋊D61#4112yes—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C22×Dic61—44no—
174C22×Dic61C22×C412yes—
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C412yes—
179C22×Dic61C2×D412yes—
180C22×Dic61C2×D412yes—
181C22×Dic61C2×D412yes—
182C22×Dic61C2×D412yes—
183Q8×D61—44no—
184Q8×D61—48no—
185Q8×D61—44no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—44no—
191C2×C4×D61—42no—
192C2×Dic122—24no—
193C2×Dic122—24no—
194C2×Dic122—24no—
195C2×Dic122—22no—
196C2×Dic122—22no—
197C2×Dic122—44no—
198C2×Dic122—44no—
199C2×Dic122—44no—
200C2×Dic122—42no—
201C2×Dic122—42no—
202C2×Dic122—42no—
203C2×Dic122—44no—
204C2×Dic122C22⋊C411yescharacteristic
205C2×Dic122C22⋊C412yes—
206C2×Dic122C22⋊C412yes—
207C2×Dic122C22⋊C412yes—
208C2×Dic122C22⋊C411yescharacteristic
209C2×Dic122C22⋊C411yescharacteristic
210C2×Dic122C22⋊C412yes—
211C2×Dic122C22⋊C412yes—
212C2×Dic122C22⋊C412yes—
213C2×Dic122C22⋊C411yescharacteristic
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—42no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—21no—
222C22⋊C4×C61—21no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—21no—
226C22⋊C4×C61C2×Q812yescomplemented
227C42×C61—42no—
228C22⋊Dic61—21no—
229C22⋊Dic61—21no—
230C22⋊Dic61—21no—
231C22⋊Dic61—21no—
232C22⋊Dic61—22no—
233C22⋊Dic61—21no—
234C22⋊Dic61—22no—
235C22⋊Dic61C2×Q812yescomplemented
236#11758198—21no—
237#11758198—21no—
238#11758198—22no—
239#11758198—22no—
240C4⋊Dic61—22no—
241C4⋊Dic61—22no—
242C4⋊Dic61—42no—
243#11758196—21no—
244#11758196—21no—
245#11758196—22no—
246#11758196—22no—
247#11758196—22no—
248#11758196—22no—
249#11758196—22no—
250#11758196—22no—
251#11758196—44no—
252#11758196—44no—
253C4×Dic61—21no—
254C4×Dic61—21no—
255C4×Dic61—22no—
256C4×Dic61—22no—
257C4×Dic61—44no—
258C4×Dic61—44no—
259C4×Dic61—42no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61C23×C411yescharacteristic
263C23×C61C22×D411yescharacteristic
264C23×C61C22×D411yescharacteristic
265C23×C61C22×Q811yescharacteristic
266C23×C61C2×#4111yescharacteristic
267C23×C612−1+411yescharacteristic
268C23×C612−1+411yescharacteristic
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61C4×Q812yescomplemented
274Q8×C61—42no—
275Q8×C61—42no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—41no—
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C22⋊D61—22no—
300C22⋊D61—22no—
301C22⋊D61—22no—
302C22⋊D61—22no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—24no—
306C2×Dic61—24no—
307C2×Dic61—24no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—42no—
320C2×Dic61—41no—
321C2×Dic61—42no—
322C2×Dic61—41no—
323C2×Dic61—42no—
324C2×Dic61C2×C22⋊C412yes—
325C2×Dic61C2×C22⋊C412yes—
326C2×Dic61C2×C22⋊C412yes—
327C2×Dic61C2×C22⋊C412yes—
328C2×Dic61C4×Q812yescomplemented
329C4×D61—44no—
330C4×D61—42no—
331C4×D61—42no—
332C4×D61—44no—
333Dic122—22no—
334Dic122—22no—
335Dic122—22no—
336Dic122—24no—
337Dic122—24no—
338Dic122—24no—
339Dic122—42no—
340Dic122—42no—
341Dic122—42no—
342Dic122—44no—
343Dic122—44no—
344Dic122#9914yescomplemented
345Q8×#99—611nomaximal, Sylow
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61C22×C22⋊C411yescharacteristic
357C22×C61C2×C4×Q811yescharacteristic
358C22×C61#51911yescharacteristic
359C22×C61#54811yescharacteristic
360C22×C61#54811yescharacteristic
361C22×C61D4×Q811yescharacteristic
362C22×C61D4×Q811yescharacteristic
363C2×D61—22no—
364C2×D61—42no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—42no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—42no—
372C4×C61—42no—
373C4×C61—42no—
374C4×C61—81no—
375C4×C61—82no—
376C4×C61C2×#9912yes—
377Dic61—22no—
378Dic61—22no—
379Dic61—22no—
380Dic61—22no—
381Dic61—42no—
382Dic61—41no—
383Dic61—41no—
384Dic61—82no—
385Dic61—81no—
386Dic61C2×#9914yes—
387C2×D4×Q8—611no—
388Q8×C22⋊C4—611no—
389Q8×C22⋊C4—611no—
390#1996—612no—
391#1996—612no—
392#1996—611no—
393#1996D6111yescharacteristic, complemented
394#1799—611no—
395#1799—612no—
396C4×#99—611no—
397C4×#99—612no—
398C2×C61—21no—
399C2×C61—21no—
400C2×C61—21no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—21no—
404C2×C61Q8×C22⋊C411yescharacteristic
405C2×C61C22×#9911yescharacteristic
406C2×C61#288411yescharacteristic
407D61—42no—
408C23×Q8—611no—
409C23×Q8—611no—
410D4×Q8—1221no—
411D4×Q8—1221no—
412D4×Q8—1222no—
413D4×Q8—1222no—
414D4×Q8—1221no—
415D4×Q8—1221no—
416C2×C4⋊Q8—611no—
417C2×C4⋊Q8—612no—
418C2×C22⋊Q8—612no—
419C2×C22⋊Q8—611no—
420C2×C22⋊Q8—612no—
421C2×C22⋊Q8C2×D6111yescharacteristic
422C2×C4×Q8—611no—
423C2×C4×Q8—1221no—
424C2×C4×Q8—1221no—
425C2×C4×D4—611no—
426C2×C4×D4—612no—
427C2×#99—611no—
428C2×#99—612no—
429C2×#99—611no—
430#391—1222no—
431#391—1222no—
432#391—1221no—
433#391—1221no—
434#380—611no—
435#380—612no—
436#380—612no—
437#380C2×D6111yescharacteristic
438C4×C22⋊C4—611no—
439C4×C22⋊C4—612no—
440C4×C22⋊C4—612no—
441C4×C22⋊C4C2×D6111yescharacteristic
442#342—612no—
443#342—612no—
444#342—611no—
445#342—611no—
446#342—612no—
447#342C2×D6112yes—
448#342C2×D6112yes—
449C61Q8×#9911yescharacteristic, complemented, Sylow
450C22×Q8—611no—
451C22×Q8—612no—
452C22×Q8—611no—
453C22×Q8—612no—
454C22×Q8—611no—
455C22×Q8—611no—
456C22×Q8—612no—
457C22×Q8—612no—
458C22×Q8—611no—
459C22×Q8—611no—
460C22×Q8—1221no—
461C22×Q8—1222no—
462C22×Q8—1221no—
463C22×Q8—2444no—
464C22×Q8—2444no—
465C22×Q8C4×D6111yescharacteristic
466C22×D4—611no—
467C23×C4—612no—
468C23×C4—612no—
469C23×C4—611no—
470C23×C4C22×D6111yescharacteristic
471C4⋊Q8—1222no—
472C4⋊Q8—1222no—
473C4⋊Q8—1222no—
474C4⋊Q8—1222no—
475C4⋊Q8—1221no—
476C4⋊Q8—1221no—
477C4⋊Q8—1222no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—1222no—
483C22⋊Q8—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8—1222no—
490C22⋊Q8—1221no—
491C22⋊Q8—1221no—
492C22⋊Q8—1222no—
493C4×Q8—1221no—
494C4×Q8—1222no—
495C4×Q8—1221no—
496C4×Q8—2444no—
497C4×Q8—2444no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502C4×D4—1221no—
503C4×D4—1221no—
504C4×D4—1221no—
505C4×D4—1221no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—612no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—612no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—612no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1222no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4C4×D6111yescharacteristic
516C2×C4⋊C4C4×D6112yes—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—612no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—612no—
523C2×C22⋊C4C22×D6112yes—
524C2×C22⋊C4C22×D6111yescharacteristic
525C2×C22⋊C4C22×D6112yes—
526C2×C22⋊C4C22×D6111yescharacteristic
527C2×C42—21no—
528C2×C42—612no—
529C2×C42—611no—
530C2×C42—1222no—
531C2×C42—1222no—
532C2×C42—1221no—
533#99—614no—
534#99—1224no—
535#99—1222no—
536#95—21no—
537#95—21no—
538#95—1222no—
539#95—1222no—
540#95—1222no—
541#95—1222no—
542#95—1221no—
543#95—1221no—
544C24—611no—
545C24C23×D6111yescharacteristic
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—42no—
549C2×Q8—611no—
550C2×Q8—612no—
551C2×Q8—611no—
552C2×Q8—612no—
553C2×Q8—612no—
554C2×Q8—611no—
555C2×Q8—611no—
556C2×Q8—612no—
557C2×Q8—612no—
558C2×Q8—612no—
559C2×Q8—1222no—
560C2×Q8—1222no—
561C2×Q8—1224no—
562C2×Q8—1224no—
563C2×Q8—1224no—
564C2×Q8—2442no—
565C2×Q8—2442no—
566C2×Q8—2442no—
567C2×Q8—2444no—
568C2×Q8—2444no—
569C2×Q8—2444no—
570C2×Q8—2444no—
571C2×Q8—2444no—
572C2×Q8—2448no—
573C2×Q8—2444no—
574C2×D4—612no—
575C2×D4—612no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—42no—
584C22×C4—611no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—612no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1222no—
600C22×C4—2442no—
601C22×C4—2444no—
602C22×C4—2444no—
603C22×C4C2×C4×D6111yescharacteristic
604C22×C4C2×C4×D6112yes—
605C22×C4C2×C4×D6112yes—
606C22×C4C2×C4×D6111yescharacteristic
607C22×C4D4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4D4×D6111yescharacteristic
610C22×C4D4×D6111yescharacteristic
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—42no—
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C4⋊C4—1222no—
621C4⋊C4—1222no—
622C4⋊C4—1222no—
623C4⋊C4—1222no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—2442no—
627C4⋊C4—2444no—
628C4⋊C4—2444no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—21no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—22no—
635C22⋊C4—21no—
636C22⋊C4—612no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1221no—
640C22⋊C4—1221no—
641C22⋊C4—1221no—
642C22⋊C4—1221no—
643C22⋊C4—1221no—
644C22⋊C4—1221no—
645C22⋊C4—1222no—
646C22⋊C4—1221no—
647C22⋊C4—1222no—
648C22⋊C4Q8×D6112yescomplemented
649C42—42no—
650C42—1222no—
651C42—1222no—
652C42—1221no—
653C42—1221no—
654C42—2442no—
655C42—2444no—
656C42—2444no—
657C23—41no—
658C23—41no—
659C23—612no—
660C23—1221no—
661C23—1221no—
662C23—2441no—
663C23—2441no—
664C23C22×C4×D6111yescharacteristic
665C23C2×D4×D6111yescharacteristic
666C23C2×D4×D6111yescharacteristic
667C23C2×Q8×D6111yescharacteristic
668C23#41×D6111yescharacteristic
669C23#1451982411yescharacteristic
670C23#1451982511yescharacteristic
671Q8—42no—
672Q8—42no—
673Q8—614no—
674Q8—1224no—
675Q8—1224no—
676Q8—1224no—
677Q8—1222no—
678Q8—1222no—
679Q8—1222no—
680Q8—2442no—
681Q8—2442no—
682Q8—2442no—
683Q8—2444no—
684Q8—2444no—
685D4—1222no—
686D4—1222no—
687D4—1222no—
688D4—1222no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—612no—
711C2×C4—612no—
712C2×C4—612no—
713C2×C4—1224no—
714C2×C4—1224no—
715C2×C4—1224no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1222no—
721C2×C4—2442no—
722C2×C4—2444no—
723C2×C4—2444no—
724C2×C4—2442no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2441no—
728C2×C4—2442no—
729C2×C4—2441no—
730C2×C4—2442no—
731C2×C4—2441no—
732C2×C4—2442no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2442no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4C22⋊C4×D6111yescharacteristic
739C2×C4C22⋊C4×D6111yescharacteristic
740C2×C4C22⋊C4×D6111yescharacteristic
741C2×C4C22⋊C4×D6111yescharacteristic
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—1222no—
753C22—2442no—
754C22—2442no—
755C22—2441no—
756C22—2441no—
757C22C2×C22⋊C4×D6111yescharacteristic
758C22C4×Q8×D6111yescharacteristic
759C22#1684023811yescharacteristic
760C22#1684042011yescharacteristic
761C22#1684042211yescharacteristic
762C22#1684042511yescharacteristic
763C22#1684042711yescharacteristic
764C4—21no—
765C4—21no—
766C4—21no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—82no—
771C4—81no—
772C4—614no—
773C4—1222no—
774C4—1222no—
775C4—1222no—
776C4—1222no—
777C4—4881no—
778C4—4882no—
779C4—2442no—
780C4—2441no—
781C4—2441no—
782C4#99×D6112yes—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—21no—
788C2—21no—
789C2—2442no—
790C2#2144865311yescharacteristic
791C2C2×#99×D6111yescharacteristic
792C2#2145428111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C23
cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61Q8×#99
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×Dic122C2semidirect
3. #21448651C2semidirect
4. #21446805C2semidirect
5. #21446802C2semidirect
6. #21446802C2semidirect
11. C61×#1996C2semidirect
13. C22×Q8×D61C4semidirect
20. C2×#14519776C4semidirect
21. C2×#14519775C4semidirect
22. C2×#14519757C4semidirect
23. C2×#14519755C4semidirect
27. C2×#14519742C4semidirect
124. #14519691Q8semidirect
226. C22⋊C4×C61C2×Q8semidirect
235. C22⋊Dic61C2×Q8semidirect
273. C22×D61C4×Q8semidirect
328. C2×Dic61C4×Q8semidirect
344. Dic122#99semidirect
393. #1996D61semidirect
449. C61Q8×#99semidirect
648. C22⋊C4Q8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404252
C22⋊C4×Dic1222
#214486512
#214468052
#214468022
#214458062
#214458042
C4×#145196912
#214456062
C61×#19962
Q8×#9961