Finite Group Databasebeta

← #29689124

Subgroups — #29689124

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840340C211yesmaximal, characteristic
2C2×#16839729C211yesmaximal, characteristic, complemented
3#21446255C211yesmaximal, characteristic, complemented
4#21446250C211yesmaximal, characteristic, complemented
5#21446245C211yesmaximal, characteristic, complemented
6#21446240C211yesmaximal, characteristic, complemented
7#21446141C211yesmaximal, characteristic, complemented
8#21446136C211yesmaximal, characteristic, complemented
9#21446131C211yesmaximal, characteristic, complemented
10#21446126C211yesmaximal, characteristic, complemented
11#21445907C211yesmaximal, characteristic, complemented
12#21445903C211yesmaximal, characteristic, complemented
13#21445757C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic, complemented
15C61×#2311C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19#16840340—24no—
20#16840340C418yescomplemented
21C2×#14519756C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519753—21no—
24C2×#14519751C2211yescharacteristic
25C2×#14519751C2211yescharacteristic
26C2×#14519749—21no—
27C2×#14519749—21no—
28C2×#14519748—21no—
29C22×C4⋊Dic61C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38#16839729—24no—
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51C22×#41×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C61×#391—21no—
55C61×#390—21no—
56C61×#386—21no—
57C61×#386—21no—
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yescomplemented
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C2×#11758194—22no—
76C2×#11758194—41no—
77C2×#11758194—41no—
78C22×#92418—22no—
79C22×#92418—41no—
80C22×#92418—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519756—22no—
86#14519756—22no—
87#14519756C2×C414yes—
88#14519756C2×C414yescomplemented
89#14519753—28no—
90#14519751—22no—
91#14519751—22no—
92#14519751C2×C414yes—
93#14519751C2×C414yescomplemented
94#14519749—28no—
95#14519749—28no—
96#14519748—28no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61—22no—
99C2×C4⋊Dic61C2×C414yescomplemented
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108#14519700—41no—
109#14519700—41no—
110#14519700—41no—
111#14519700—41no—
112#14519697—41no—
113#14519697—41no—
114#14519697—41no—
115#14519697—41no—
116C22⋊#92418—22no—
117C22⋊#92418—22no—
118C22⋊#92418—22no—
119C22⋊#92418—22no—
120C2×#41×C61—41no—
121C2×#41×C61—41no—
122C2×#41×C61—41no—
123C2×#41×C61—41no—
124C2×#41×C61C2×C414yes—
125C2×#41×C61D414yes—
126C22×Q8×C61D411yescharacteristic
127C22×D4×C61D411yescharacteristic
128C22×D4×C61D411yescharacteristic
129C22×D4×C61D411yescharacteristic
130C23×C4×C61—21no—
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134#117×C61—41no—
135#117×C61—41no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61—41no—
138C2×C4⋊C4×C61—41no—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C42×C61—21no—
149#95×C61—21no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153C24×C61C2×D411yescharacteristic
154C24×C61C2×D411yescharacteristic
155C24×C61C2×D411yescharacteristic
156C23×D61—21no—
157#41×C61—44no—
158#41×C61—44no—
159#41×C61—44no—
160#41×C61—44no—
161C2×Q8×C61—41no—
162C2×Q8×C61—41no—
163C2×Q8×C61C22⋊C414yes—
164C2×D4×C61—41no—
165C2×D4×C61—41no—
166C2×D4×C61—41no—
167C2×D4×C61—41no—
168C2×D4×C61—41no—
169C2×D4×C61—41no—
170C2×D4×C61C22⋊C414yes—
171C2×D4×C61C22⋊C414yes—
172C2×D4×C61C22⋊C414yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—42no—
190C22×C4×C61—81no—
191C22×C4×C61—81no—
192C22×C4×C61C22×C412yes—
193C22×C4×C61C22×C412yes—
194C22×C4×C61C22×C412yes—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2×D412yes—
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—81no—
208C2×C22⋊D61—81no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61—81no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—81no—
216C22×Dic61—81no—
217#11758222—44no—
218#11758222—44no—
219#11758222—44no—
220#11758222—44no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244C22×C412yes—
227C2×C4×D61—24no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122C22×C412yes—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—42no—
245C22⋊C4×C61—42no—
246C22⋊C4×C61—81no—
247C22⋊C4×C61—81no—
248C22⋊C4×C61—81no—
249C22⋊C4×C61—81no—
250C42×C61—42no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253#11758198—24no—
254#11758198—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61C22×C412yes—
259C4⋊Dic61C22×C412yes—
260#11758196—24no—
261#11758196—24no—
262#11758194—44no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—44no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61C2×C22⋊C412yes—
295C23×C61C2×C22⋊C412yes—
296C23×C61C2×C22⋊C412yes—
297C23×C61C22×D411yescharacteristic
298C22×D61—22no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305Q8×C61—44no—
306D4×C61—44no—
307D4×C61—44no—
308D4×C61—44no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—84no—
340C2×C4×C61C2×C22⋊C412yes—
341C2×C4×C61C2×C22⋊C412yes—
342C2×C4×C61C2×C22⋊C412yes—
343C2×C4×C61C23×C411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C2×C4×C61H(5,𝔽2)11yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C22⋊D61—48no—
350C22⋊D61—84no—
351C22⋊D61—84no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—84no—
362D244—22no—
363D244—22no—
364D244—41no—
365D244—41no—
366C4×D61—48no—
367Dic122—22no—
368Dic122—22no—
369Dic122—41no—
370Dic122—41no—
371#92418—41no—
372#92418—41no—
373#92418—41no—
374#92418—41no—
375#21772—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61C22×C22⋊C411yescharacteristic
398C22×C61#53411yescharacteristic
399C22×C61#53411yescharacteristic
400C22×C61#57611yescharacteristic
401C22×C61#57711yescharacteristic
402C22×C61#57711yescharacteristic
403C22×C61#57811yescharacteristic
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—81no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—81no—
415C4×C61—81no—
416C4×C61—81no—
417C4×C61—81no—
418C4×C61#51811yescharacteristic
419C4×C61#51811yescharacteristic
420C4×C61#53411yescharacteristic
421C4×C61#53411yescharacteristic
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425C2×#537—611no—
426C2×#408—611no—
427#2311D6111yescharacteristic, complemented
428#1895—611no—
429#1894—611no—
430#1893—611no—
431#1892—611no—
432#1875—611no—
433#1874—611no—
434#1873—611no—
435#1872—611no—
436#1824—611no—
437#1823—611no—
438#1788—611no—
439#1788—611no—
440C2×C61—42no—
441C2×C61—42no—
442C2×C61—42no—
443C2×C61#230811yescharacteristic
444C2×C61#289711yescharacteristic
445C2×C61#289811yescharacteristic
446C2×C61#319811yescharacteristic
447C2×C61#320111yescharacteristic
448C2×C61#320311yescharacteristic
449C2×C61#320411yescharacteristic
450D61—82no—
451C22×#41—611no—
452C22×#41C2×D6111yescharacteristic
453C22×M16—611no—
454C23×C8—611no—
455#537—618no—
456#537—1224no—
457C2×C22⋊Q8—611no—
458C2×C22⋊Q8—611no—
459C2×C22⋊Q8—1221no—
460C2×#121—611no—
461C2×#121—611no—
462C2×#121—1221no—
463C2×#121—1221no—
464C2×#121—1221no—
465C2×#117C2×D6111yescharacteristic
466C22×C4⋊C4—611no—
467C22×C4⋊C4C2×D6111yescharacteristic
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476#408—1224no—
477C2×C22⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481#391—21no—
482#390—21no—
483#386—21no—
484#386—21no—
485#380C2×D6111yescharacteristic
486#380C2×D6111yescharacteristic
487#380C2×D6111yescharacteristic
488#380C2×D6111yescharacteristic
489#340—611no—
490#340—611no—
491#340—611no—
492#340—611no—
493#340—611no—
494#340—611no—
495#340—611no—
496#340—611no—
497C61#2177211yescharacteristic, complemented, Sylow
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—614no—
503C2×#41—1222no—
504C2×#41—2441no—
505C2×#41—2441no—
506C2×#41—2441no—
507C2×#41—2441no—
508C2×#41C4×D6114yes—
509C2×#41D24414yes—
510C22×Q8—611no—
511C22×Q8C22⋊D6111yescharacteristic
512C22×D4—611no—
513C22×D4—1221no—
514C22×D4—1221no—
515C22×D4—1221no—
516C22×D4C22⋊D6111yescharacteristic
517C22×D4C22⋊D6111yescharacteristic
518C22×D4C22⋊D6111yescharacteristic
519C23×C4—21no—
520C23×C4—1221no—
521C23×C4—1221no—
522C23×C4C22×D6111yescharacteristic
523C23×C4C22×D6111yescharacteristic
524C23×C4C22×D6111yescharacteristic
525C2×M16—1222no—
526C2×M16—2441no—
527C2×M16—2441no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—611no—
531C22×C8—611no—
532C22×C8—1222no—
533C22×C8—2441no—
534C22×C8—2441no—
535C22⋊Q8—614no—
536C22⋊Q8—614no—
537C22⋊Q8—1228no—
538C22⋊Q8—1222no—
539C22⋊Q8—1222no—
540#121—614no—
541#121—614no—
542#121—1228no—
543#121—1228no—
544#121—1228no—
545#121—1222no—
546#121—1222no—
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—614no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C4⋊C4C22×D6111yescharacteristic
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C42—21no—
573#103—2441no—
574#103—2441no—
575#103—2441no—
576#103—2441no—
577#102—2441no—
578#102—2441no—
579#102—2441no—
580#102—2441no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583C22⋊C8—1222no—
584C22⋊C8—1222no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—1221no—
590C24C2×C22⋊D6111yescharacteristic
591C24C2×C22⋊D6111yescharacteristic
592C24C2×C22⋊D6111yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—2444no—
598#41—2444no—
599#41—2444no—
600#41—2444no—
601C2×Q8—41no—
602C2×Q8—41no—
603C2×Q8—612no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8#1175819814yes—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—612no—
617C2×D4—1224no—
618C2×D4—1224no—
619C2×D4—1224no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—4881no—
626C2×D4—4881no—
627C2×D4—4881no—
628C2×D4—4881no—
629C2×D4—2442no—
630C2×D4—2442no—
631C2×D4#1175819814yes—
632C2×D4#1175819814yes—
633C2×D4#1175819814yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—42no—
651C22×C4—81no—
652C22×C4—81no—
653C22×C4—1224no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1224no—
658C22×C4—4881no—
659C22×C4—4881no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4C2×C4×D6112yes—
663C22×C4C2×C4×D6112yes—
664C22×C4C2×C4×D6112yes—
665C22×C4C2×D24412yes—
666C22×C4C2×D24412yes—
667C22×C4C2×D24412yes—
668C22×C4C2×C22⋊D6111yescharacteristic
669C22×C4C2×C22⋊D6111yescharacteristic
670C22×C4C2×C22⋊D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672M16—2444no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—2444no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—42no—
695C4⋊C4—612no—
696C4⋊C4—612no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1224no—
700C4⋊C4—1224no—
701C4⋊C4—1224no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—1222no—
731C23—2441no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23C2×#1175819812yes—
738C23C2×#1175819812yes—
739C23C2×#1175819812yes—
740C23C22×C22⋊D6111yescharacteristic
741Q8—44no—
742Q8—1222no—
743Q8—1222no—
744Q8—2441no—
745Q8—2441no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—1222no—
750D4—1222no—
751D4—4884no—
752D4—4884no—
753D4—2448no—
754D4—2441no—
755D4—2441no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—84no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—4884no—
791C2×C4—2448no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4C2×#1175819812yes—
799C2×C4C2×#1175819812yes—
800C2×C4C2×#1175819812yes—
801C2×C4C22×C4×D6111yescharacteristic
802C2×C4C22×D24411yescharacteristic
803C2×C4#1451982211yescharacteristic
804C2×C4#1451982211yescharacteristic
805C2×C4#1451982211yescharacteristic
806C2×C4#1451982211yescharacteristic
807C8—2441no—
808C8—2441no—
809C8—2441no—
810C8—2441no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—4881no—
833C22—4881no—
834C22—4881no—
835C22—4881no—
836C22—2442no—
837C22—2442no—
838C22—2442no—
839C22C22×#1175819811yescharacteristic
840C22#1684032111yescharacteristic
841C22#1684032111yescharacteristic
842C22#1684056511yescharacteristic
843C22#1684057011yescharacteristic
844C22#1684057311yescharacteristic
845C22#1684057711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—2442no—
854C4—2442no—
855C4—2442no—
856C4#1684023511yescharacteristic
857C4#1684023511yescharacteristic
858C4#1684032411yescharacteristic
859C4#1684032411yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—4882no—
864C2#2144839411yescharacteristic
865C2#2145434211yescharacteristic
866C2#2145434911yescharacteristic
867C2#2145667111yescharacteristic
868C2#2145670111yescharacteristic
869C2#2145671611yescharacteristic
870C2#2145672511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2311C2
socleC23×C61C22×D4
prime radicalC2×#16840340C2
cosocleC22×C4×C61C24
hypercenter#2311D61
hypocenterC61#21772
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#16839729C2semidirect
3. #21446255C2semidirect
4. #21446250C2semidirect
5. #21446245C2semidirect
6. #21446240C2semidirect
7. #21446141C2semidirect
8. #21446136C2semidirect
9. #21446131C2semidirect
10. #21446126C2semidirect
11. #21445907C2semidirect
12. #21445903C2semidirect
13. #21445757C2semidirect
14. #21445757C2semidirect
15. C61×#2311C2semidirect
20. #16840340C4semidirect
67. C2×#11758222C2×C4semidirect
88. #14519756C2×C4semidirect
93. #14519751C2×C4semidirect
99. C2×C4⋊Dic61C2×C4semidirect
427. #2311D61semidirect
497. C61#21772semidirect

Maximal subgroups

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

subgroupindex
C2×#168403402
C2×#168397292
#214462552
#214462502
#214462452
#214462402
#214461412
#214461362
#214461312
#214461262
#214459072
#214459032
#214457572
C61×#23112
#2177261