Finite Group Databasebeta

← #29645969

Subgroups — #29645969

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840289C211yesmaximal, characteristic
2#21454448C211yesmaximal, characteristic, complemented
3C2×#16839812C211yesmaximal, characteristic, complemented
4#21444173C212yesmaximal, complemented
5#21444169C212yesmaximal, complemented
6#21444168C211yesmaximal, characteristic, complemented
7#21444167C211yesmaximal, characteristic, complemented
8#21444165C211yesmaximal, characteristic, complemented
9#21444132C212yesmaximal, complemented
10#21444130C212yesmaximal, complemented
11C61×#1468C211yesmaximal, characteristic, complemented
12#16840289—21no—
13#16840289—21no—
14#16840289—21no—
15#16840289—21no—
16#16840289—21no—
17#16840289—21no—
18#16840289—21no—
19#16840289—21no—
20C2×#14519772C411yescharacteristic
21C2×#14519770C411yescharacteristic
22C2×#14519767C2211yescharacteristic
23C2×#14519763C2211yescharacteristic
24C2×#14519760C2211yescharacteristic
25C2×#14519754C411yescharacteristic
26C2×#14519749C411yescharacteristic
27C2×#14519742C411yescharacteristic
28C2×D4×Dic61C411yescharacteristic
29C2×#14519737C411yescharacteristic
30C2×#14519737C411yescharacteristic
31C2×#14519735C2211yescharacteristic
32C2×#14519733C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839816—21no—
35#16839816C2212yes—
36#16839812—21no—
37#16839812—21no—
38#16839812—21no—
39#16839812C2212yes—
40#16839812C2212yes—
41#16839812C2212yes—
42#16839785—21no—
43C2×#14519706—21no—
44#16839726C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46M16×Dic61—21no—
47C2×C8×Dic61—21no—
48#16839488C2212yes—
49#16839487C2212yes—
50#16839487C2212yes—
51#16839486C2212yes—
52#16839485C2212yes—
53#16839485C2212yes—
54C2×#123×C61C2211yescharacteristic
55C61×#407C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#324C2212yes—
58C61×#323C2212yes—
59C22×Dic122C2×C411yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C23×Dic61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C2×#11758194—21no—
67C22×#92418—21no—
68#14519772—21no—
69#14519772—21no—
70#14519772—21no—
71#14519772—21no—
72#14519770—21no—
73#14519770—21no—
74#14519770—21no—
75#14519770—21no—
76#14519767—21no—
77#14519767—21no—
78#14519767—21no—
79#14519767—21no—
80#14519763—21no—
81#14519763—21no—
82#14519763—21no—
83#14519763—21no—
84#14519760—21no—
85#14519760—21no—
86#14519760—21no—
87#14519760—21no—
88#14519754—21no—
89#14519754—21no—
90#14519754—21no—
91#14519754—21no—
92#14519749—21no—
93#14519749—21no—
94#14519749—21no—
95#14519749—21no—
96#14519742—21no—
97#14519742—21no—
98#14519742—21no—
99#14519742—21no—
100D4×Dic61—21no—
101D4×Dic61—21no—
102D4×Dic61—21no—
103D4×Dic61—21no—
104#14519737—21no—
105#14519737—21no—
106#14519737—21no—
107#14519737—21no—
108#14519737—21no—
109#14519737—21no—
110#14519737—21no—
111#14519737—21no—
112#14519735—21no—
113#14519735—21no—
114#14519735—21no—
115#14519735—21no—
116#14519733—21no—
117#14519733—21no—
118#14519733—21no—
119#14519733—21no—
120C2×C4⋊Dic61C2×C411yescharacteristic
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2311yescharacteristic
128C2×C22⋊Dic61C2×C411yescharacteristic
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2311yescharacteristic
135C2×C4×Dic61C2×C411yescharacteristic
136C2×C4×Dic61C2×C411yescharacteristic
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61C2×C411yescharacteristic
139C2×C4×Dic61D411yescharacteristic
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C2×C4×Dic61D411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149#14519706—22no—
150#14519706—22no—
151#14519706—22no—
152#14519706—22no—
153C22⋊#92418—21no—
154C22⋊#92418—21no—
155C22⋊#92418C2312yes—
156C22⋊#92418C2312yes—
157#14519687—22no—
158C8×Dic61—22no—
159C8×Dic61—22no—
160C8×Dic61—22no—
161C22×D4×C61C2×C411yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C2×M16×C61—21no—
164C22×C8×C61—21no—
165#123×C61—21no—
166#123×C61—21no—
167#123×C61—21no—
168#123×C61—21no—
169C2×C4⋊C4×C61C2×C411yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C22⋊C4×C61C2×C411yescharacteristic
172C2×C22⋊C4×C61C2×C411yescharacteristic
173C2×C22⋊C4×C61C2311yescharacteristic
174C22⋊C8×C61—21no—
175C22⋊C8×C61—21no—
176C22⋊C8×C61C2312yes—
177C22⋊C8×C61C2312yes—
178C24×C61C22×C411yescharacteristic
179C24×C61C22×C411yescharacteristic
180C23×D61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—42no—
184C22×C4×C61—42no—
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C22×C411yescharacteristic
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C22×C411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61—42no—
200C22×Dic61—24no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—24no—
204C22×Dic61—42no—
205C22×Dic61C22⋊C411yescharacteristic
206C22×Dic61C22⋊C411yescharacteristic
207C22×Dic61C22⋊C411yescharacteristic
208C22×Dic61C22⋊C411yescharacteristic
209C22×Dic61C22⋊C411yescharacteristic
210C22×Dic61C22⋊C411yescharacteristic
211C22×Dic61C22⋊C411yescharacteristic
212C22×Dic61C22⋊C411yescharacteristic
213C22×Dic61C22×C411yescharacteristic
214C22×Dic61C22×C411yescharacteristic
215C22×Dic61C22×C411yescharacteristic
216C22×Dic61C22×C411yescharacteristic
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—24no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—42no—
226M16×C61—42no—
227C2×C8×C61—22no—
228C2×C8×C61—22no—
229C2×C8×C61—42no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊Dic61—21no—
241C22⋊Dic61—21no—
242C22⋊Dic61—21no—
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246#11758198—21no—
247#11758198—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258#11758196—21no—
259#11758196—21no—
260#11758196—21no—
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61C22⋊C411yescharacteristic
275C4×Dic61C22⋊C411yescharacteristic
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C2×D411yescharacteristic
283C4×Dic61C2×D411yescharacteristic
284C4×Dic61C2×D411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290#11758194—42no—
291C2×#92418—22no—
292C2×#92418—22no—
293C2×#92418—42no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—21no—
297C23×C61—22no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61C2×C22⋊C411yescharacteristic
302C23×C61C2×C22⋊C411yescharacteristic
303C23×C61C23×C411yescharacteristic
304C22×D61—21no—
305C22×D61—22no—
306C22×D61—41no—
307C22×D61—41no—
308D4×C61—42no—
309D4×C61—42no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—22no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C22⋊D61—42no—
327C22⋊D61—42no—
328C22⋊D61—42no—
329C22⋊D61—42no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—22no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356C2×Dic61C2×C22⋊C411yescharacteristic
357C2×Dic61#13114yes—
358C4×D61—42no—
359C4×D61—42no—
360Dic122—42no—
361Dic122—42no—
362C8×C61—42no—
363C8×C61—42no—
364#92418—42no—
365#92418—42no—
366#17376—611nomaximal, Sylow
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—44no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—82no—
379C22×C61#41012yes—
380C22×C61C22×C22⋊C411yescharacteristic
381C22×C61C2×#13112yes—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—82no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393Dic61—21no—
394Dic61—21no—
395Dic61—21no—
396Dic61—21no—
397Dic61—21no—
398Dic61—41no—
399Dic61—41no—
400Dic61—41no—
401Dic61#40812yes—
402Dic61#40812yes—
403Dic61#41312yes—
404C2×#529—611no—
405#2920—611no—
406C2×#431—611no—
407#1470—612no—
408#1469—612no—
409#1468—611no—
410#1468—611no—
411#1468—611no—
412#1468D6111yescharacteristic, complemented
413#1458—612no—
414#1458—612no—
415C2×C61—22no—
416C2×C61—22no—
417C2×C61—41no—
418C2×C61—81no—
419C2×C61C2×#40811yescharacteristic
420C2×C61C2×#41011yescharacteristic
421C2×C61C2×#41311yescharacteristic
422D61—81no—
423#529—1221no—
424#529—1221no—
425#529—1221no—
426#529—1221no—
427#529—1221no—
428#529—1221no—
429#529—1221no—
430#529—1221no—
431C2×#126—611no—
432C2×#126—611no—
433C2×#125—611no—
434C2×#124—611no—
435C2×#123—611no—
436C2×#123C2×D6111yescharacteristic
437C2×C22⋊Q8—611no—
438C2×#121—611no—
439C2×C4×Q8—611no—
440C2×C4×D4—611no—
441C2×C4×D4—611no—
442C2×C4×D4—611no—
443C2×#117—611no—
444C2×#117—611no—
445C22×C42—611no—
446#432—612no—
447#432—1221no—
448#431—612no—
449#431—612no—
450#431—612no—
451#431—1221no—
452#431—1221no—
453#431—1221no—
454#423—1221no—
455C2×C4⋊C8—1221no—
456#407—611no—
457#407C2×D6111yescharacteristic
458C2×C22⋊C8—611no—
459C2×C22⋊C8C2×D6111yescharacteristic
460C4×M16—1221no—
461C2×C4×C8—1221no—
462#324—612no—
463#324—612no—
464#324—612no—
465#324C2×D6112yes—
466#323—612no—
467#323—612no—
468#323—612no—
469#323C2×D6112yes—
470C61#1737611yescharacteristic, complemented, Sylow
471C22×Q8—611no—
472C22×D4—611no—
473C22×D4—611no—
474C22×D4C4×D6111yescharacteristic
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4C22×D6111yescharacteristic
480C2×M16—21no—
481C2×M16—1221no—
482C22×C8—21no—
483C22×C8—1221no—
484#126—1221no—
485#126—1221no—
486#126—1221no—
487#126—1221no—
488#126—1221no—
489#126—1221no—
490#126—1221no—
491#126—1221no—
492#125—1221no—
493#125—1221no—
494#125—1221no—
495#125—1221no—
496#124—1221no—
497#124—1221no—
498#124—1221no—
499#124—1221no—
500#123—21no—
501#123—21no—
502#123—21no—
503#123—21no—
504#123—1221no—
505#123—1221no—
506#123—1221no—
507#123—1221no—
508C22⋊Q8—1221no—
509C22⋊Q8—1221no—
510C22⋊Q8—1221no—
511C22⋊Q8—1221no—
512#121—1221no—
513#121—1221no—
514#121—1221no—
515#121—1221no—
516C4×Q8—1221no—
517C4×Q8—1221no—
518C4×Q8—1221no—
519C4×Q8—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1221no—
527C4×D4—1221no—
528C4×D4—1221no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532#117—1221no—
533#117—1221no—
534#117—1221no—
535#117—1221no—
536#117—1221no—
537#117—1221no—
538#117—1221no—
539#117—1221no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4C4×D6111yescharacteristic
549C2×C4⋊C4C22×D6111yescharacteristic
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—611no—
553C2×C22⋊C4—611no—
554C2×C22⋊C4—611no—
555C2×C22⋊C4—611no—
556C2×C22⋊C4—611no—
557C2×C22⋊C4C4×D6111yescharacteristic
558C2×C22⋊C4C4×D6111yescharacteristic
559C2×C22⋊C4C22×D6111yescharacteristic
560C2×C42—611no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—611no—
574C4⋊C8—1222no—
575C4⋊C8—1222no—
576C4⋊C8—1222no—
577C4⋊C8—1222no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—612no—
581C22⋊C8—612no—
582C22⋊C8—1221no—
583C22⋊C8—1221no—
584C22⋊C8C22×D6112yes—
585C22⋊C8C22×D6112yes—
586#97—1222no—
587C4×C8—1222no—
588C4×C8—1222no—
589C4×C8—1222no—
590C24—611no—
591C24C2×C4×D6111yescharacteristic
592C24C2×C4×D6111yescharacteristic
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—2442no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—42no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—2442no—
604C2×D4—2442no—
605C22×C4—42no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1224no—
628C22×C4—2442no—
629C22×C4C2×C4×D6111yescharacteristic
630C22×C4C2×C4×D6111yescharacteristic
631C22×C4C2×C4×D6111yescharacteristic
632C22×C4C2×C4×D6111yescharacteristic
633C22×C4D4×D6111yescharacteristic
634C22×C4D4×D6111yescharacteristic
635C22×C4D4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638M16—42no—
639M16—2442no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—42no—
643C2×C8—1222no—
644C2×C8—1222no—
645C2×C8—2442no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C42—611no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—611no—
702C42—1221no—
703C42—1221no—
704C42—1221no—
705C42—1221no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—1222no—
714C23—1221no—
715C23—2441no—
716C23—2441no—
717C23C22⋊C4×D6111yescharacteristic
718C23C22⋊C4×D6111yescharacteristic
719C23C22×C4×D6111yescharacteristic
720Q8—2442no—
721Q8—2442no—
722D4—42no—
723D4—42no—
724D4—2442no—
725D4—2442no—
726D4—2442no—
727D4—2442no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—611no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—614no—
744C2×C4—611no—
745C2×C4—611no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—611no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1222no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4C22⋊C4×D6111yescharacteristic
771C2×C4C22⋊C4×D6111yescharacteristic
772C2×C4C2×D4×D6111yescharacteristic
773C2×C4C2×D4×D6111yescharacteristic
774C8—42no—
775C8—42no—
776C8—2442no—
777C8—2442no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—44no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—82no—
790C22—4882no—
791C22—2441no—
792C22—2441no—
793C22—2441no—
794C22#1683973412yes—
795C22C2×C22⋊C4×D6111yescharacteristic
796C22#131×D6112yes—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—612no—
805C4—612no—
806C4—612no—
807C4—1221no—
808C4—1221no—
809C4—1221no—
810C4—1221no—
811C4—1221no—
812C4—2441no—
813C4—2441no—
814C4—2441no—
815C2—22no—
816C2—22no—
817C2—41no—
818C2—81no—
819C2—4881no—
820C2#408×D6111yescharacteristic
821C2C2×#1683973411yescharacteristic
822C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1468C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519749C4
cosocleC22×C4×C61C24
hypercenter#1468D61
hypocenterC61#17376
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #21454448C2semidirect
3. C2×#16839812C2semidirect
4. #21444173C2semidirect
5. #21444169C2semidirect
6. #21444168C2semidirect
7. #21444167C2semidirect
8. #21444165C2semidirect
9. #21444132C2semidirect
10. #21444130C2semidirect
11. C61×#1468C2semidirect
412. #1468D61semidirect
470. C61#17376semidirect

Maximal subgroups

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

subgroupindex
C2×#168402892
#214544482
C2×#168398122
#214441732
#214441692
#214441682
#214441672
#214441652
#214441322
#214441302
C61×#14682
#1737661