Finite Group Databasebeta

← #29695674

Subgroups — #29695674

Order 15616.

1582 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840430C211yesmaximal, characteristic
2C2×#16839837C211yesmaximal, characteristic, complemented
3C2×#16839761C211yesmaximal, characteristic, complemented
4C2×#16839760C211yesmaximal, characteristic, complemented
5C4⋊C4×C22⋊D61C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446623C211yesmaximal, characteristic, complemented
8#21446258C211yesmaximal, characteristic, complemented
9#21446256C211yesmaximal, characteristic, complemented
10#21446135C211yesmaximal, characteristic, complemented
11#21445823C211yesmaximal, characteristic, complemented
12#21445760C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445638C211yesmaximal, characteristic, complemented
15C61×#1874C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20#16840430—24no—
21#16840430C418yescomplemented
22C2×#14519773—21no—
23C2×#14519773C2211yescharacteristic
24C2×#14519752C2211yescharacteristic
25C2×#14519750—21no—
26C2×#14519749—21no—
27C2×#14519742C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519737—21no—
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839837—24no—
33C2×#14519706C2211yescharacteristic
34#16839761—24no—
35#16839760—24no—
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48#16839657—21no—
49#16839635—21no—
50#16839633—21no—
51#16839631C2211yescharacteristic
52#16839622C2211yescharacteristic
53#16839619C2211yescharacteristic
54C4⋊C4×Dic61C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C22×C4⋊C4×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C2×#11758222C2×C414yescomplemented
70C2×#11758224—22no—
71C2×#11758224—22no—
72C2×#11758224—22no—
73C2×#11758224—41no—
74C2×#11758224—41no—
75C2×#11758224C2×C414yescomplemented
76C22×Dic122C2311yescharacteristic
77C22×D244—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61D411yescharacteristic
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61C2311yescharacteristic
88C2×#11758194—22no—
89C2×#11758194—22no—
90C2×#11758194—41no—
91C2×#11758189—22no—
92C2×#11758189—22no—
93C2×#11758189—41no—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96#14519773—28no—
97#14519773—22no—
98#14519773C2×C414yescomplemented
99#14519752—22no—
100#14519752C2×C414yescomplemented
101#14519750—28no—
102#14519749—28no—
103#14519742—22no—
104#14519742C2×C414yescomplemented
105C4×C22⋊D61—44no—
106C4×C22⋊D61C2×C414yes—
107C4×C22⋊D61D414yes—
108#14519737—28no—
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×#11758196D411yescharacteristic
116C4⋊C4×D61—22no—
117C4⋊C4×D61—41no—
118C2×C22⋊Dic61—21no—
119C2×C22⋊Dic61D411yescharacteristic
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C2×C4×Dic61—21no—
124C2×C4×Dic61—21no—
125C2×C4×Dic61C2311yescharacteristic
126#14519706—22no—
127#14519702—22no—
128#14519702—22no—
129#14519700—22no—
130#14519700D414yescomplemented
131#14519699—41no—
132#14519699—41no—
133#14519698—22no—
134#14519698—41no—
135#14519697—22no—
136#14519697—22no—
137#14519689—22no—
138C8×Dic61—22no—
139#14519684—21no—
140#14519684—21no—
141#14519684—21no—
142C22×D4×C61—21no—
143C22×D4×C61C2311yescharacteristic
144C23×C4×C61—21no—
145C23×C4×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148#121×C61—22no—
149#121×C61C2×C414yescomplemented
150C2×C4⋊C4×C61—22no—
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61—41no—
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C22⋊C4×C61—21no—
157#102×C61—22no—
158#102×C61—41no—
159C22⋊C8×C61—22no—
160C24×C61—21no—
161C24×C61C2×D411yescharacteristic
162C23×D61—21no—
163C23×D61C2×D411yescharacteristic
164C2×D4×C61—24no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—81no—
171C2×D4×C61—81no—
172C2×D4×C61C22×C412yes—
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—42no—
181C22×C4×C61—42no—
182C22×C4×C61—81no—
183C22×C4×C61C22×C412yes—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D412yes—
186C22×C4×C61C2411yescharacteristic
187C2×C22⋊D61—24no—
188C2×C22⋊D61—24no—
189C2×C22⋊D61—24no—
190C2×C22⋊D61—24no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61—81no—
200C2×C22⋊D61—81no—
201C2×C22⋊D61C22⋊C414yes—
202C22×Dic61—21no—
203C22×Dic61—24no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—42no—
207C22×Dic61—42no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211#11758224—28no—
212#11758224—44no—
213#11758224—44no—
214#11758224—44no—
215#11758222—28no—
216#11758222—44no—
217#11758222—44no—
218#11758222—44no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—24no—
225C2×D244—81no—
226C2×D244—81no—
227C2×D244C22×C412yes—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—24no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61—81no—
238C2×C4×D61C22×C412yes—
239C2×C4×D61C2×D412yes—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122C22×C412yes—
244C2×Dic122C2×D412yes—
245C2×Dic122#4112yes—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—42no—
257C4⋊C4×C61C22×C412yes—
258C4⋊C4×C61C2×D412yes—
259C22⋊C4×C61—24no—
260C22⋊Dic61—42no—
261C22⋊Dic61C22⋊C414yes—
262#11758198—24no—
263#11758198—42no—
264#11758198C22⋊C414yes—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269#11758196—24no—
270#11758196—42no—
271#11758196—42no—
272#11758196—81no—
273#11758196C22⋊C414yes—
274C4×Dic61—24no—
275C4×Dic61—42no—
276C4×Dic61C22×C412yes—
277C4×Dic61C2×D412yes—
278#11758194—44no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418C2×D412yes—
285#11758189—44no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—22no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61C2×C22⋊C412yes—
300C23×C61C22×D411yescharacteristic
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—22no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61C2×C22⋊C412yes—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—41no—
318D4×C61—41no—
319D4×C61—84no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
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—84no—
336C2×C4×C61C2×C22⋊C412yes—
337C2×C4×C61C23×C411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C22⋊D61—28no—
344C22⋊D61—48no—
345C22⋊D61—48no—
346C22⋊D61—48no—
347C22⋊D61—84no—
348C2×Dic61—22no—
349C2×Dic61—21no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—48no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61C2×C22⋊C412yes—
363C2×Dic61C2×C22⋊C412yes—
364C2×Dic61C2×C22⋊C412yes—
365C2×Dic61AGL(1,ℤ/8)12yes—
366C2×Dic61#13712yes—
367D244—22no—
368D244—22no—
369D244—41no—
370D244—41no—
371D244—84no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—48no—
377C4×D61—84no—
378Dic122—22no—
379Dic122—22no—
380Dic122—22no—
381Dic122C4×D414yescomplemented
382C8×C61—41no—
383C8×C61—41no—
384#92418—22no—
385#92418—41no—
386#22432—611nomaximal, Sylow
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61C22×C22⋊C411yescharacteristic
402C22×C61D4211yescharacteristic
403C22×C61#54611yescharacteristic
404C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C61C2×#13711yescharacteristic
406C22×C61#57611yescharacteristic
407C22×C61#57711yescharacteristic
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61—81no—
421C2×D61—81no—
422C4×C61—22no—
423C4×C61—42no—
424C4×C61—42no—
425C4×C61—81no—
426C4×C61C2×C4×D411yescharacteristic
427C4×C61#51811yescharacteristic
428C4×C61D4211yescharacteristic
429C4×C61#54611yescharacteristic
430Dic61—24no—
431Dic61—22no—
432Dic61—22no—
433Dic61—81no—
434Dic61—81no—
435Dic61#41714yescomplemented
436C2×#550—611no—
437C2×#436—611no—
438C2×#417—611no—
439C2×#417—611no—
440D4×C4⋊C4—611no—
441#1982—611no—
442#1957—611no—
443#1895—611no—
444#1895—611no—
445#1874—611no—
446#1874D6111yescharacteristic, complemented
447#1803—611no—
448#1788—611no—
449#1788—611no—
450C4×#103—611no—
451C2×C61—42no—
452C2×C61—82no—
453C2×C61D4×C22⋊C411yescharacteristic
454C2×C61C2×#41711yescharacteristic
455C2×C61#289711yescharacteristic
456C2×C61#327411yescharacteristic
457C2×C61#327811yescharacteristic
458C2×C61#333211yescharacteristic
459C2×C61#333311yescharacteristic
460D61—42no—
461D61—82no—
462C22×#41—611no—
463C22×#41—611no—
464C22×M16—611no—
465C22×M16—611no—
466#550—618no—
467#550—1224no—
468C2×#127—611no—
469C2×#127—1221no—
470C2×#121—611no—
471C2×#121—1221no—
472C2×#121—1221no—
473C2×#121C2×D6111yescharacteristic
474C2×C4×Q8—611no—
475C2×C4×D4—611no—
476C2×C4×D4—1221no—
477C2×C4×D4—1221no—
478C22×C4⋊C4—611no—
479C22×C4⋊C4C2×D6111yescharacteristic
480#436—1224no—
481C2×C4⋊C8—611no—
482#417—1224no—
483#417—1224no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#103—611no—
487C2×#103—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102C2×D6111yescharacteristic
495C2×#102C2×D6111yescharacteristic
496C2×C22⋊C8—611no—
497C2×C22⋊C8C2×D6111yescharacteristic
498C2×C4×C8—611no—
499#389—1221no—
500#385—1221no—
501#385—1221no—
502#384—611no—
503#380—611no—
504#380—611no—
505C4×C4⋊C4—611no—
506#340—611no—
507#340—611no—
508#340C2×D6111yescharacteristic
509#340C2×D6111yescharacteristic
510C61#2243211yescharacteristic, complemented, Sylow
511C2×#41—614no—
512C2×#41—614no—
513C2×#41—1222no—
514C2×#41—1222no—
515C2×#41—1222no—
516C2×#41—1222no—
517C2×#41—1222no—
518C2×#41—1222no—
519C2×#41—2441no—
520C2×#41—2441no—
521C2×#41—2441no—
522C2×#41—2441no—
523C22×Q8—611no—
524C22×D4—21no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—1221no—
528C22×D4—1221no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4—1221no—
532C22×D4C22×D6111yescharacteristic
533C23×C4—21no—
534C23×C4—611no—
535C23×C4—1221no—
536C23×C4—1221no—
537C23×C4—1221no—
538C23×C4C22×D6111yescharacteristic
539C2×M16—1222no—
540C2×M16—1222no—
541C2×M16—1222no—
542C2×M16—1222no—
543C2×M16—2441no—
544C2×M16—2441no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8C22×D6111yescharacteristic
548C22×C8C22×D6111yescharacteristic
549#127—614no—
550#127—1222no—
551#127—1228no—
552#121—22no—
553#121—614no—
554#121—1228no—
555#121—1228no—
556#121—1222no—
557#121C4×D6114yescomplemented
558C4×Q8—614no—
559C4×Q8—1222no—
560C4×D4—614no—
561C4×D4—614no—
562C4×D4—1228no—
563C4×D4—2444no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1222no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—2441no—
576C2×C4⋊C4C22×D6111yescharacteristic
577C2×C4⋊C4C22×D6111yescharacteristic
578C2×C4⋊C4C22×D6111yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—611no—
581C2×C22⋊C4—611no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C42—611no—
586C2×C42—1221no—
587C2×C42—1221no—
588C4⋊C8—1222no—
589#103—614no—
590#103—1222no—
591#103—1222no—
592#103—1222no—
593#102—22no—
594#102—41no—
595#102—1222no—
596#102—1222no—
597#102—1222no—
598#102—2441no—
599#102—2441no—
600#102—2441no—
601C22⋊C8—22no—
602C22⋊C8—1222no—
603C4×C8—1222no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607C24—21no—
608C24—611no—
609C24—1221no—
610C24D4×D6111yescharacteristic
611#41—1228no—
612#41—1228no—
613#41—2444no—
614#41—2444no—
615#41—2444no—
616#41—2444no—
617#41—2444no—
618#41—2444no—
619C2×Q8—612no—
620C2×Q8—612no—
621C2×Q8—612no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—614no—
634C2×D4—612no—
635C2×D4—1224no—
636C2×D4—1222no—
637C2×D4—1222no—
638C2×D4—1224no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1224no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—4881no—
648C2×D4—4881no—
649C2×D4—4881no—
650C2×D4—4881no—
651C2×D4—2442no—
652C2×D4—2442no—
653C2×D4—2442no—
654C2×D4—2442no—
655C2×D4—2442no—
656C2×D4—2442no—
657C2×D4C2×C4×D6112yes—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—1224no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1224no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—4881no—
683C22×C4—2442no—
684C22×C4—2442no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4—2442no—
688C22×C4—2442no—
689C22×C4C2×C4×D6112yes—
690C22×C4D4×D6112yes—
691C22×C4D4×D6111yescharacteristic
692C22×C4C23×D6111yescharacteristic
693M16—2444no—
694M16—2444no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—612no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—42no—
712C4⋊C4—614no—
713C4⋊C4—1224no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—4881no—
719C4⋊C4—2442no—
720C4⋊C4—2442no—
721C4⋊C4C2×C4×D6112yes—
722C4⋊C4D4×D6112yes—
723C22⋊C4—24no—
724C22⋊C4—614no—
725C22⋊C4—614no—
726C22⋊C4—1224no—
727C22⋊C4—2442no—
728C22⋊C4—2442no—
729C42—612no—
730C42—612no—
731C42—1224no—
732C42—2442no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—612no—
747C23—1221no—
748C23—1221no—
749C23—1221no—
750C23—1221no—
751C23—1221no—
752C23—1221no—
753C23—1222no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23C22⋊C4×D6112yes—
761C23C2×D4×D6111yescharacteristic
762Q8—614no—
763Q8—1222no—
764Q8—1222no—
765Q8—1222no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—84no—
771D4—1228no—
772D4—1222no—
773D4—1222no—
774D4—4884no—
775D4—4884no—
776D4—2448no—
777D4—2448no—
778D4—2448no—
779D4—2441no—
780D4—2441no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4—612no—
798C2×C4—612no—
799C2×C4—612no—
800C2×C4—612no—
801C2×C4—612no—
802C2×C4—1222no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1222no—
807C2×C4—1221no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—4884no—
814C2×C4—2448no—
815C2×C4—2448no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4C22⋊C4×D6112yes—
823C2×C4C22×C4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4#41×D6111yescharacteristic
827C2×C4#1451982211yescharacteristic
828C2×C4#1451982311yescharacteristic
829C8—41no—
830C8—41no—
831C8—1222no—
832C8—2441no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—1222no—
848C22—1222no—
849C22—1222no—
850C22—4881no—
851C22—4881no—
852C22—4881no—
853C22—4881no—
854C22—2442no—
855C22—2442no—
856C22—2442no—
857C22—2441no—
858C22—2441no—
859C22—2441no—
860C22—2441no—
861C22C2×C22⋊C4×D6111yescharacteristic
862C22#1684039411yescharacteristic
863C22#1684040411yescharacteristic
864C22AGL(1,ℤ/8)×D6111yescharacteristic
865C22#137×D6111yescharacteristic
866C22#1684056311yescharacteristic
867C22#1684056811yescharacteristic
868C4—22no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—614no—
873C4—1222no—
874C4—1222no—
875C4—1224no—
876C4—4881no—
877C4—4881no—
878C4C4×D4×D6111yescharacteristic
879C4#1684023411yescharacteristic
880C4#1684039611yescharacteristic
881C4#1684040111yescharacteristic
882C2—42no—
883C2—82no—
884C2—4882no—
885C2—2442no—
886C2#2144863711yescharacteristic
887C2#417×D6111yescharacteristic
888C2#2145434011yescharacteristic
889C2#2145743711yescharacteristic
890C2#2145748311yescharacteristic
891C2#2145814411yescharacteristic
892C2#2145815511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1874C2
socleC23×C61C22×D4
prime radicalC2×#16840430C2
cosocleC22×C4×C61C24
hypercenter#1874D61
hypocenterC61#22432
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#16839837C2semidirect
3. C2×#16839761C2semidirect
4. C2×#16839760C2semidirect
5. C4⋊C4×C22⋊D61C2semidirect
6. #21446744C2semidirect
7. #21446623C2semidirect
8. #21446258C2semidirect
9. #21446256C2semidirect
10. #21446135C2semidirect
11. #21445823C2semidirect
12. #21445760C2semidirect
13. #21445756C2semidirect
14. #21445638C2semidirect
15. C61×#1874C2semidirect
21. #16840430C4semidirect
69. C2×#11758222C2×C4semidirect
75. C2×#11758224C2×C4semidirect
98. #14519773C2×C4semidirect
100. #14519752C2×C4semidirect
104. #14519742C2×C4semidirect
130. #14519700D4semidirect
149. #121×C61C2×C4semidirect
381. Dic122C4×D4semidirect
435. Dic61#417semidirect
446. #1874D61semidirect
510. C61#22432semidirect
557. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404302
C2×#168398372
C2×#168397612
C2×#168397602
C4⋊C4×C22⋊D612
#214467442
#214466232
#214462582
#214462562
#214461352
#214458232
#214457602
#214457562
#214456382
C61×#18742
#2243261