Finite Group Databasebeta

← #29689397

Subgroups — #29689397

Order 15616.

1250 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840337C211yesmaximal, characteristic
2C2×#16839822C211yesmaximal, characteristic, complemented
3#21448424C211yesmaximal, characteristic, complemented
4#21446751C211yesmaximal, characteristic, complemented
5#21446749C211yesmaximal, characteristic, complemented
6#21446743C211yesmaximal, characteristic, complemented
7#21446637C211yesmaximal, characteristic, complemented
8#21446632C211yesmaximal, characteristic, complemented
9#21446627C211yesmaximal, characteristic, complemented
10#21446619C211yesmaximal, characteristic, complemented
11#21445758C211yesmaximal, characteristic
12#21445758C211yesmaximal, characteristic
13#21445752C211yesmaximal, characteristic, complemented
14#21445752C211yesmaximal, characteristic, complemented
15C61×#1981C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18#16840337—24no—
19#16840337C418yescomplemented
20C2×#14519775C2211yescharacteristic
21C2×#14519766C2211yescharacteristic
22C2×#14519765C2211yescharacteristic
23C2×#14519762—21no—
24C2×#14519762—21no—
25C2×#14519755—21no—
26C2×#14519755—21no—
27C2×#14519734C2211yescharacteristic
28#16839822—24no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46#16839653—21no—
47#16839651—21no—
48#16839646—21no—
49#16839644—21no—
50#16839631C2211yescharacteristic
51#16839627C2211yescharacteristic
52#16839619C2211yescharacteristic
53#16839619C2211yescharacteristic
54C4×C4⋊Dic61C2211yescharacteristic
55C2×C4⋊Q8×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C4×C4⋊C4×C61C2211yescharacteristic
62C2×#11758226—22no—
63C2×#11758226—41no—
64C2×#11758226—41no—
65C2×#11758226—41no—
66C2×#11758226—41no—
67C2×#11758226C2×C414yes—
68C22×Dic122—21no—
69C22×Dic122C2311yescharacteristic
70C2×Q8×D61—22no—
71C2×Q8×D61—41no—
72C2×Q8×D61—41no—
73C2×Q8×D61—41no—
74C2×Q8×D61—41no—
75C2×Q8×D61C2×C414yes—
76C22×D244—21no—
77C22×D244C2311yescharacteristic
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C22×C4×D61C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519775—22no—
84#14519775C2×C414yes—
85#14519766—22no—
86#14519766C2×C414yes—
87#14519765—22no—
88#14519765C2×C414yes—
89#14519762—28no—
90#14519762—28no—
91#14519755—28no—
92#14519755—28no—
93#14519734C2×C414yes—
94#14519734D414yes—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196D411yescharacteristic
102C2×#11758196D411yescharacteristic
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198D411yescharacteristic
110C2×#11758198D411yescharacteristic
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113C4⋊#92418—22no—
114#14519702—41no—
115#14519702—41no—
116#14519701—41no—
117#14519701—41no—
118#14519701—41no—
119#14519701—41no—
120#14519700—41no—
121#14519700—41no—
122#14519699—41no—
123#14519699—41no—
124#14519697—41no—
125#14519697—41no—
126#14519689—22no—
127#14519689—22no—
128#14519687—22no—
129C8×Dic61—22no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×Q8×C61C2311yescharacteristic
136C22×Q8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C4⋊Q8×C61—22no—
140C4⋊Q8×C61C2×C414yes—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C42×C61—21no—
146C2×C42×C61C2311yescharacteristic
147C4⋊C8×C61—22no—
148#103×C61—41no—
149#103×C61—41no—
150#103×C61—41no—
151#103×C61—41no—
152#95×C61—21no—
153C23×D61—21no—
154C23×D61C2×D411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61C22×C412yes—
166C2×Q8×C61C22×C412yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180#11758226—44no—
181#11758226—44no—
182#11758226—44no—
183#11758226—44no—
184Q8×D61—44no—
185Q8×D61—44no—
186Q8×D61—44no—
187Q8×D61—44no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—24no—
193C2×D244—21no—
194C2×D244—42no—
195C2×D244—42no—
196C2×D244C22×C412yes—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—24no—
202C2×C4×D61—24no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61C22×C412yes—
208C2×C4×D61C2×D412yes—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—24no—
215C2×Dic122—42no—
216C2×Dic122—42no—
217C2×Dic122C22×C412yes—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C4⋊C4×C61—24no—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C42×C61—81no—
231C42×C61C22×C412yes—
232C42×C61C2×D412yes—
233#11758198—24no—
234#11758198—24no—
235#11758198—24no—
236#11758198—24no—
237#11758198—81no—
238#11758198—81no—
239#11758198C22⋊C414yes—
240#11758198C22⋊C414yes—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245#11758196—24no—
246#11758196—24no—
247#11758196—81no—
248#11758196—81no—
249#11758196C22⋊C414yes—
250#11758196C22⋊C414yes—
251C4×Dic61—81no—
252C4×Dic61C22×C412yes—
253C4×Dic61C2×D412yes—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C23×C61C22×D411yescharacteristic
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—22no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61C2×C22⋊C412yes—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—22no—
278Q8×C61—22no—
279Q8×C61—41no—
280Q8×C61—41no—
281Q8×C61—41no—
282Q8×C61—41no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61C2×C22⋊C412yes—
300C2×C4×C61C2×C22⋊C412yes—
301C2×C4×C61C23×C411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61C2×C22⋊C412yes—
323C2×Dic61C2×C22⋊C412yes—
324C2×Dic61C2×C22⋊C412yes—
325D244—22no—
326D244—22no—
327D244—48no—
328D244—41no—
329D244—41no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—48no—
335C4×D61—48no—
336Dic122—22no—
337Dic122—22no—
338Dic122—48no—
339Dic122—41no—
340Dic122—41no—
341C8×C61—41no—
342C8×C61—41no—
343#92418—41no—
344#92418—41no—
345#21814—611nomaximal, Sylow
346C22×C61C22×C22⋊C411yescharacteristic
347C22×C61#53511yescharacteristic
348C22×C61#53511yescharacteristic
349C22×C61#57711yescharacteristic
350C22×C61#57711yescharacteristic
351C22×C61#57811yescharacteristic
352C22×C61#57811yescharacteristic
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61—81no—
367C4×C61—22no—
368C4×C61—22no—
369C4×C61—42no—
370C4×C61—42no—
371C4×C61—81no—
372C4×C61—81no—
373C4×C61#51811yescharacteristic
374C4×C61#51811yescharacteristic
375C4×C61#53511yescharacteristic
376C4×C61#53511yescharacteristic
377Dic61—22no—
378Dic61—22no—
379Dic61—22no—
380Dic61—42no—
381Dic61—81no—
382Dic61—81no—
383C2×#536—611no—
384C2×#433—611no—
385#2314—611no—
386#1983—611no—
387#1983—611no—
388#1981—611no—
389#1981D6111yescharacteristic, complemented
390#1960—611no—
391#1959—611no—
392#1958—611no—
393#1956—611no—
394#1788—611no—
395#1788—611no—
396#1787—611no—
397#1787—611no—
398C2×C61#230911yescharacteristic
399C2×C61#289811yescharacteristic
400C2×C61#289811yescharacteristic
401C2×C61#322111yescharacteristic
402C2×C61#322311yescharacteristic
403C2×C61#322511yescharacteristic
404C2×C61#322511yescharacteristic
405D61—42no—
406D61—82no—
407C22×#41—611no—
408C23×Q8—611no—
409#536—618no—
410#536—1224no—
411C2×C4⋊Q8—611no—
412C2×C4⋊Q8C2×D6111yescharacteristic
413C2×#124—611no—
414C2×#124—611no—
415C2×#123—1221no—
416C2×#123—1221no—
417C2×C22⋊Q8—1221no—
418C2×C22⋊Q8—1221no—
419C2×#117—611no—
420#433—1224no—
421C2×C4⋊C8—611no—
422C2×C4⋊C8C2×D6111yescharacteristic
423C2×#103—611no—
424C2×#103—611no—
425C2×#103—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#103C2×D6111yescharacteristic
432C2×#103C2×D6111yescharacteristic
433C2×#103C2×D6111yescharacteristic
434C2×#103C2×D6111yescharacteristic
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×#97—611no—
442C2×C4×C8—611no—
443#388—1221no—
444#388—1221no—
445#387—1221no—
446#387—1221no—
447#384—611no—
448#382—611no—
449#380—611no—
450#380—611no—
451C4×C4⋊C4—611no—
452C4×C4⋊C4C2×D6111yescharacteristic
453C61#2181411yescharacteristic, complemented, Sylow
454C2×#41—614no—
455C2×#41—1222no—
456C2×#41—2441no—
457C2×#41—2441no—
458C2×#41—2441no—
459C2×#41—2441no—
460C22×Q8—614no—
461C22×Q8—611no—
462C22×Q8—1221no—
463C22×Q8—1222no—
464C22×Q8—2441no—
465C22×Q8—2441no—
466C22×Q8—2441no—
467C22×Q8—2441no—
468C22×Q8C22×D6111yescharacteristic
469C22×Q8C22×D6111yescharacteristic
470C22×D4—611no—
471C22×D4—1221no—
472C23×C4—611no—
473C23×C4—1221no—
474C23×C4—1221no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479C4⋊Q8—22no—
480C4⋊Q8—614no—
481C4⋊Q8—1222no—
482C4⋊Q8C4×D6114yes—
483#124—614no—
484#124—614no—
485#124—1222no—
486#124—1222no—
487#123—1228no—
488#123—1228no—
489C22⋊Q8—1228no—
490C22⋊Q8—1228no—
491#117—614no—
492#117—614no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C42—21no—
514C2×C42—611no—
515C2×C42—1221no—
516C2×C42C22×D6111yescharacteristic
517C4⋊C8—22no—
518C4⋊C8—1222no—
519#103—41no—
520#103—41no—
521#103—41no—
522#103—41no—
523#103—2441no—
524#103—2441no—
525#103—2441no—
526#103—2441no—
527#103—2441no—
528#103—2441no—
529#103—2441no—
530#103—2441no—
531#102—2441no—
532#102—2441no—
533#102—2441no—
534#102—2441no—
535C22⋊C8—1222no—
536C22⋊C8—1222no—
537#97—1222no—
538C4×C8—1222no—
539#95—21no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543#95—1221no—
544#95—1221no—
545C24—611no—
546C24—1221no—
547#41—2444no—
548#41—2444no—
549#41—2444no—
550#41—2444no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—612no—
562C2×Q8—1224no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8—1221no—
567C2×Q8—1221no—
568C2×Q8—2442no—
569C2×Q8—2442no—
570C2×Q8—2444no—
571C2×Q8—2444no—
572C2×Q8—2444no—
573C2×Q8—2444no—
574C2×Q8C2×C4×D6112yes—
575C2×Q8C2×C4×D6112yes—
576C2×D4—612no—
577C2×D4—1224no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—2442no—
584C2×D4—2442no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—1224no—
595C22×C4—1224no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4D4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4C23×D6111yescharacteristic
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—614no—
629C4⋊C4—614no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—4881no—
637C4⋊C4—4881no—
638C22⋊C4—614no—
639C22⋊C4—614no—
640C22⋊C4—1224no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—4881no—
645C22⋊C4—4881no—
646C42—81no—
647C42—612no—
648C42—612no—
649C42—4881no—
650C42C2×C4×D6112yes—
651C42D4×D6112yes—
652C23—612no—
653C23—1221no—
654C23—1221no—
655C23—1221no—
656C23—1221no—
657C23—1221no—
658C23—1221no—
659C23—1222no—
660C23—2441no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23C2×D4×D6111yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—1222no—
676Q8—1222no—
677Q8—2448no—
678Q8—2441no—
679Q8—2441no—
680D4—1222no—
681D4—1222no—
682D4—2448no—
683D4—2441no—
684D4—2441no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—612no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—2448no—
716C2×C4—2448no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4C22⋊C4×D6112yes—
726C2×C4C22⋊C4×D6112yes—
727C2×C4C22×C4×D6111yescharacteristic
728C2×C4C2×D4×D6111yescharacteristic
729C2×C4#1451982211yescharacteristic
730C2×C4#1451982211yescharacteristic
731C2×C4#1451982311yescharacteristic
732C2×C4#1451982311yescharacteristic
733C8—41no—
734C8—41no—
735C8—2441no—
736C8—2441no—
737C22—1222no—
738C22—1222no—
739C22—1222no—
740C22—4881no—
741C22—4881no—
742C22—4881no—
743C22—4881no—
744C22—2442no—
745C22—2442no—
746C22—2442no—
747C22—2441no—
748C22—2441no—
749C22—2441no—
750C22—2441no—
751C22C2×C22⋊C4×D6111yescharacteristic
752C22#1684032811yescharacteristic
753C22#1684032811yescharacteristic
754C22#1684056811yescharacteristic
755C22#1684057111yescharacteristic
756C22#1684057511yescharacteristic
757C22#1684057811yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—42no—
762C4—81no—
763C4—81no—
764C4—1222no—
765C4—1222no—
766C4—1222no—
767C4—4881no—
768C4—4881no—
769C4—2442no—
770C4#1684023411yescharacteristic
771C4#1684023411yescharacteristic
772C4#1684032511yescharacteristic
773C4#1684033011yescharacteristic
774C2—4882no—
775C2—2442no—
776C2#2144839811yescharacteristic
777C2#2145434711yescharacteristic
778C2#2145435111yescharacteristic
779C2#2145687911yescharacteristic
780C2#2145690111yescharacteristic
781C2#2145692711yescharacteristic
782C2#2145693511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1981C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenter#1981D61
hypocenterC61#21814
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
2. C2×#16839822C2semidirect
3. #21448424C2semidirect
4. #21446751C2semidirect
5. #21446749C2semidirect
6. #21446743C2semidirect
7. #21446637C2semidirect
8. #21446632C2semidirect
9. #21446627C2semidirect
10. #21446619C2semidirect
13. #21445752C2semidirect
14. #21445752C2semidirect
15. C61×#1981C2semidirect
19. #16840337C4semidirect
389. #1981D61semidirect
453. C61#21814semidirect

Maximal subgroups

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

subgroupindex
C2×#168403372
C2×#168398222
#214484242
#214467512
#214467492
#214467432
#214466372
#214466322
#214466272
#214466192
#214457582
#214457522
C61×#19812
#2181461