Finite Group Databasebeta

← D61⋊#1472 #30610065

Subgroups — D61⋊#1472 #30610065

Order 15616.

1426 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
3#21461099C212yesmaximal, complemented
4#21461098C214yesmaximal, complemented
5#21461097C212yesmaximal, complemented
6D61⋊#324C214yesmaximal, complemented
7C2×C22⋊Q8×D61C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9C22×D61⋊C8—21no—
10#16840734—21no—
11#16840733—21no—
12#16840733C2212yes—
13#16840732C2212yes—
14C2×#14519834—21no—
15D61⋊(C22⋊C8)—21no—
16D61⋊(C22⋊C8)—21no—
17D61⋊(C22⋊C8)—21no—
18D61⋊(C22⋊C8)C2212yes—
19D61⋊(C22⋊C8)C2212yes—
20D61⋊(C22⋊C8)C2212yes—
21C2×C22⋊#92420C2212yes—
22#16840608C2218yescomplemented
23#16840607C2218yescomplemented
24C22×Q8×D61C411yescharacteristic
25C23×C4×D61C2211yescharacteristic
26C2×#14519757C2211yescharacteristic
27C2×#14519756C411yescharacteristic
28C2×#14519755C412yes—
29C2×#14519754C2212yes—
30C2×#14519753C2211yescharacteristic
31C22⋊Q8×D61—21no—
32C22⋊Q8×D61—21no—
33C22⋊Q8×D61—21no—
34C22⋊Q8×D61—21no—
35C22⋊Q8×D61—21no—
36C22⋊Q8×D61—21no—
37C22⋊Q8×D61—21no—
38C22⋊Q8×D61—21no—
39C2×C4⋊C4×D61C411yescharacteristic
40C2×C4⋊C4×D61C2212yes—
41C2×C22⋊C4×D61C412yes—
42C2×C22⋊Q8×C61C411yescharacteristic
43C2×#11758213—22no—
44D61⋊M16—44no—
45C2×#11758217—22no—
46C2×D61⋊C8—22no—
47C2×D61⋊C8—22no—
48C2×D61⋊C8—22no—
49C2×D61⋊C8—44no—
50C22×#92420—22no—
51#14519834—22no—
52#14519834—22no—
53#14519834—22no—
54#14519834—22no—
55C22⋊#92420—22no—
56C22⋊#92420—22no—
57C22⋊#92420C2314yes—
58C22⋊#92420C2314yes—
59C24×D61C2×C411yescharacteristic
60C22×Dic122C2×C412yes—
61C22×Dic122C2×C411yescharacteristic
62C2×Q8×D61—21no—
63C2×Q8×D61—21no—
64C2×Q8×D61—21no—
65C2×Q8×D61—21no—
66C2×Q8×D61—44no—
67C23×Dic61C2311yescharacteristic
68C22×C4×D61—44no—
69C22×C4×D61C2×C412yes—
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2×C412yes—
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61C2311yescharacteristic
82C22×C4×D61C2311yescharacteristic
83#14519757—21no—
84#14519757—21no—
85#14519757—21no—
86#14519757—21no—
87#14519756—21no—
88#14519756—21no—
89#14519756—21no—
90#14519756—21no—
91#14519755—22no—
92#14519755—22no—
93#14519755—22no—
94#14519755—22no—
95#14519754—22no—
96#14519754—22no—
97#14519754—22no—
98#14519754—22no—
99#14519753—21no—
100#14519753—21no—
101#14519753—21no—
102#14519753—21no—
103C2×C4⋊Dic61C2×C411yescharacteristic
104C2×C4⋊Dic61C2312yes—
105C2×#11758196C2×C412yes—
106C2×#11758196C2×C412yes—
107C2×#11758196C2312yes—
108C4⋊C4×D61—21no—
109C4⋊C4×D61—21no—
110C4⋊C4×D61—21no—
111C4⋊C4×D61—21no—
112C4⋊C4×D61—22no—
113C4⋊C4×D61—22no—
114C4⋊C4×D61—22no—
115C4⋊C4×D61—22no—
116C2×C22⋊Dic61C2×C412yes—
117C2×#11758198C2×C412yes—
118C2×#11758198C2×C412yes—
119C22⋊C4×D61—22no—
120C22⋊C4×D61—22no—
121C22⋊C4×D61—22no—
122C22⋊C4×D61—22no—
123C22×Q8×C61C2×C411yescharacteristic
124C23×C4×C61C2×C411yescharacteristic
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61—21no—
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C4⋊C4×C61C2×C412yes—
131C2×C22⋊C4×C61C2×C412yes—
132C24×C61C22×C411yescharacteristic
133C23×D61—24no—
134C23×D61—24no—
135C23×D61—42no—
136C23×D61C22⋊C411yescharacteristic
137C23×D61C22⋊C411yescharacteristic
138C23×D61C22⋊C411yescharacteristic
139C23×D61C22⋊C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—42no—
145C22×C4×C61—42no—
146C22×C4×C61C22⋊C411yescharacteristic
147C22×C4×C61C22⋊C411yescharacteristic
148C22×C4×C61C22⋊C411yescharacteristic
149C22×C4×C61C22⋊C411yescharacteristic
150C22×C4×C61C22×C412yes—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C412yes—
153C22×C4×C61C22×C411yescharacteristic
154C22×Dic61—42no—
155C22×Dic61C22×C412yes—
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C412yes—
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2411yescharacteristic
163Q8×D61—44no—
164Q8×D61—44no—
165Q8×D61—44no—
166Q8×D61—44no—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—24no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—28no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×C4×D61—42no—
178C2×C4×D61—42no—
179C2×C4×D61—42no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—44no—
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C22⋊C411yescharacteristic
190C2×C4×D61C22⋊C411yescharacteristic
191C2×C4×D61C22⋊C411yescharacteristic
192C2×C4×D61C22⋊C411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61C2×D411yescharacteristic
197C2×C4×D61C2×D411yescharacteristic
198C2×C4×D61C2×D411yescharacteristic
199C2×C4×D61C2×D411yescharacteristic
200C2×C4×D61C2×D411yescharacteristic
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—22no—
204C2×Dic122—22no—
205C2×Dic122—44no—
206C2×Dic122—42no—
207#11758217—44no—
208C2×#92420—24no—
209C2×#92420—24no—
210C2×#92420—44no—
211#11758213—44no—
212D61⋊C8—44no—
213D61⋊C8—44no—
214D61⋊C8—44no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223#11758198—22no—
224#11758198—22no—
225#11758198—22no—
226#11758198—22no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—22no—
230C4⋊Dic61—22no—
231#11758196—22no—
232#11758196—22no—
233#11758196—22no—
234#11758196—22no—
235#11758196—22no—
236#11758196—22no—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—41no—
240C23×C61C2×C22⋊C411yescharacteristic
241C23×C61C2×C22⋊C411yescharacteristic
242C23×C61C23×C411yescharacteristic
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—416no—
260C22×D61#10114yes—
261C22×D61C2×C22⋊C411yescharacteristic
262C22×D61C2×C22⋊C411yescharacteristic
263C22×D61C2×C22⋊C411yescharacteristic
264C22×D61C2×C22⋊C411yescharacteristic
265C22×D61#13114yes—
266Q8×C61—42no—
267Q8×C61—42no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—24no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—42no—
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61C2×C22⋊C411yescharacteristic
280C2×C4×C61C2×C22⋊C411yescharacteristic
281C2×C4×C61C2×C22⋊C411yescharacteristic
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—24no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—42no—
292C2×Dic61C2×C22⋊C411yescharacteristic
293C2×Dic61C2×C22⋊C411yescharacteristic
294C2×Dic61C22×D411yescharacteristic
295C2×Dic61C22×D411yescharacteristic
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—22no—
299C4×D61—22no—
300C4×D61—22no—
301C4×D61—22no—
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—41no—
306C4×D61—41no—
307C4×D61—41no—
308C4×D61—41no—
309C4×D61—41no—
310C4×D61—41no—
311C4×D61—44no—
312C4×D61—44no—
313C4×D61—44no—
314C4×D61—44no—
315C4×D61#9914yes—
316Dic122—44no—
317Dic122—42no—
318Dic122—42no—
319Dic122—44no—
320#92420—44no—
321#92420—44no—
322C2×#1472—611nomaximal, Sylow
323C22×C61—21no—
324C22×C61—21no—
325C22×C61—21no—
326C22×C61—21no—
327C22×C61—21no—
328C22×C61—21no—
329C22×C61—21no—
330C22×C61—44no—
331C22×C61C2×#10112yes—
332C22×C61C22×C22⋊C411yescharacteristic
333C22×C61C2×#13112yes—
334C2×D61—21no—
335C2×D61—21no—
336C2×D61—21no—
337C2×D61—21no—
338C2×D61—28no—
339C2×D61—28no—
340C2×D61—21no—
341C2×D61—21no—
342C2×D61—21no—
343C2×D61—44no—
344C2×D61—44no—
345C2×D61—44no—
346C2×D61—44no—
347C2×D61#40812yes—
348C2×D61#40812yes—
349C2×D61C2×#9912yes—
350C2×D61C2×#10112yes—
351C2×D61C2×#10112yes—
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61C2×#9912yes—
358Dic61—21no—
359Dic61—21no—
360Dic61—21no—
361Dic61—42no—
362Dic61—42no—
363Dic61C2×#9912yes—
364C22×C22⋊Q8—611no—
365C2×#407—611no—
366C22×C22⋊C8—611no—
367#1472—612no—
368#1472—614no—
369#1472—612no—
370C2×#324—614no—
371C2×C61—22no—
372C2×C61—22no—
373C2×C61—41no—
374C2×C61C2×#40811yescharacteristic
375C2×C61C22×#9911yescharacteristic
376C2×C61C22×#10111yescharacteristic
377D61—22no—
378D61—22no—
379D61—41no—
380D61#147214yescomplemented
381C23×Q8—611no—
382C24×C4—611no—
383C22×M16—1221no—
384C23×C8—1221no—
385C2×C22⋊Q8—611no—
386C2×C22⋊Q8—611no—
387C2×C22⋊Q8—612no—
388C2×C22⋊Q8—611no—
389C2×C22⋊Q8—612no—
390C2×C22⋊Q8—1221no—
391C2×C22⋊Q8—1221no—
392C2×C22⋊Q8—1221no—
393C2×C22⋊Q8—1221no—
394C2×C22⋊Q8—1221no—
395C2×C22⋊Q8—1221no—
396C2×C22⋊Q8—1221no—
397C2×C22⋊Q8—1221no—
398C2×C22⋊Q8#692311yescharacteristic
399C22×C4⋊C4—611no—
400C22×C4⋊C4—612no—
401C22×C22⋊C4—612no—
402#407—612no—
403#407—612no—
404#407—1221no—
405#407—1221no—
406C2×C22⋊C8—612no—
407C2×C22⋊C8—612no—
408C2×C22⋊C8—612no—
409C2×C22⋊C8—612no—
410C2×C22⋊C8—1221no—
411C2×C22⋊C8—1221no—
412C2×C22⋊C8—1221no—
413C2×C22⋊C8—1221no—
414#324—618no—
415#324—618no—
416C61C2×#147211yescharacteristic, complemented, Sylow
417C25—611no—
418C22×Q8—612no—
419C22×Q8—611no—
420C22×Q8—1221no—
421C22×Q8—1221no—
422C22×Q8—1221no—
423C22×Q8—1221no—
424C22×Q8—2444no—
425C22×Q8C2×#692311yescharacteristic
426C23×C4—611no—
427C23×C4—611no—
428C23×C4—611no—
429C23×C4—611no—
430C23×C4—611no—
431C23×C4—611no—
432C23×C4—611no—
433C23×C4—611no—
434C23×C4—611no—
435C23×C4—611no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4—611no—
439C23×C4—612no—
440C23×C4—612no—
441C23×C4—2444no—
442C23×C4C2×#692311yescharacteristic
443C2×M16—1222no—
444C2×M16—1222no—
445C2×M16—2444no—
446C22×C8—1222no—
447C22×C8—1222no—
448C22×C8—1222no—
449C22×C8—1222no—
450C22×C8—2444no—
451C22⋊Q8—21no—
452C22⋊Q8—21no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8—1222no—
456C22⋊Q8—1222no—
457C22⋊Q8—1222no—
458C22⋊Q8—1222no—
459C22⋊Q8—1222no—
460C22⋊Q8—1222no—
461C22⋊Q8—1222no—
462C22⋊Q8—1222no—
463C22⋊Q8—1221no—
464C22⋊Q8—1221no—
465C22⋊Q8—1221no—
466C22⋊Q8—1221no—
467C22⋊Q8—1221no—
468C22⋊Q8—1221no—
469C22⋊Q8—1221no—
470C22⋊Q8—1221no—
471C22⋊Q8—1221no—
472C22⋊Q8—1221no—
473C22⋊Q8—1221no—
474C22⋊Q8—1221no—
475C2×C4⋊C4—612no—
476C2×C4⋊C4—612no—
477C2×C4⋊C4—612no—
478C2×C4⋊C4—612no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1222no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4C2×#692311yescharacteristic
489C2×C4⋊C4C2×#692312yes—
490C2×C22⋊C4—612no—
491C2×C22⋊C4—612no—
492C2×C22⋊C4—612no—
493C2×C22⋊C4—1222no—
494C2×C22⋊C4—1222no—
495C2×C22⋊C4—1222no—
496C2×C22⋊C4—1222no—
497C2×C22⋊C4C2×#692312yes—
498C22⋊C8—614no—
499C22⋊C8—614no—
500C22⋊C8—1222no—
501C22⋊C8—1222no—
502C22⋊C8—1222no—
503C22⋊C8—1222no—
504C22⋊C8—1222no—
505C22⋊C8—1222no—
506C24—611no—
507C24—611no—
508C24—611no—
509C24—611no—
510C24—611no—
511C24—611no—
512C24—1224no—
513C24—1224no—
514C24—2442no—
515C24C22×#692311yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—42no—
519C2×Q8—1222no—
520C2×Q8—1222no—
521C2×Q8—1221no—
522C2×Q8—1221no—
523C2×Q8—2442no—
524C2×Q8—2444no—
525C2×Q8—2444no—
526C2×Q8—2444no—
527C2×Q8—2444no—
528C2×Q8—2444no—
529C22×C4—42no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—1224no—
555C22×C4—1224no—
556C22×C4—1224no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1228no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4—2442no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2444no—
572C22×C4—2442no—
573C22×C4C22⋊#692311yescharacteristic
574C22×C4C22⋊#692311yescharacteristic
575C22×C4C22⋊#692311yescharacteristic
576C22×C4C22⋊#692311yescharacteristic
577C22×C4C22×#692312yes—
578C22×C4C22×#692311yescharacteristic
579C22×C4C22×#692312yes—
580C22×C4C22×#692311yescharacteristic
581M16—2444no—
582M16—2444no—
583C2×C8—1224no—
584C2×C8—1224no—
585C2×C8—2444no—
586C2×C8—2444no—
587C2×C8—2444no—
588C2×C8—2444no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—1222no—
594C4⋊C4—1222no—
595C4⋊C4—1222no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—1222no—
600C4⋊C4—1222no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—1222no—
611C23—22no—
612C23—22no—
613C23—41no—
614C23—611no—
615C23—614no—
616C23—611no—
617C23—611no—
618C23—614no—
619C23—611no—
620C23—1222no—
621C23—1222no—
622C23—1222no—
623C23—1222no—
624C23—1222no—
625C23—1222no—
626C23—1222no—
627C23—1222no—
628C23—1222no—
629C23—1222no—
630C23—1222no—
631C23—1222no—
632C23—1222no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—24416no—
637C23C2×C22⋊#692311yescharacteristic
638C23C2×C22⋊#692311yescharacteristic
639C23C23×#692311yescharacteristic
640Q8—42no—
641Q8—42no—
642Q8—2442no—
643Q8—2444no—
644Q8—2444no—
645Q8—2442no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—611no—
657C2×C4—614no—
658C2×C4—611no—
659C2×C4—611no—
660C2×C4—611no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1224no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2444no—
683C2×C4—2444no—
684C2×C4—2444no—
685C2×C4—2444no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2442no—
690C2×C4C2×C22⋊#692311yescharacteristic
691C2×C4C2×C22⋊#692311yescharacteristic
692C2×C4C2×C22⋊#692311yescharacteristic
693C2×C4C2×C22⋊#692311yescharacteristic
694C8—2444no—
695C8—2444no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—44no—
704C22—612no—
705C22—612no—
706C22—612no—
707C22—612no—
708C22—612no—
709C22—1228no—
710C22—1228no—
711C22—1221no—
712C22—1221no—
713C22—1221no—
714C22—1221no—
715C22—1221no—
716C22—1221no—
717C22—1221no—
718C22—2444no—
719C22—2444no—
720C22—2444no—
721C22—2444no—
722C22D61⋊#10112yes—
723C22C22×C22⋊#692311yescharacteristic
724C22D61⋊#13112yes—
725C4—21no—
726C4—21no—
727C4—21no—
728C4—42no—
729C4—42no—
730C4—612no—
731C4—1221no—
732C4—1221no—
733C4—1221no—
734C4—2442no—
735C4—2442no—
736C4D61⋊#9912yes—
737C2—22no—
738C2—22no—
739C2—41no—
740C2—614no—
741C2—1222no—
742C2—1222no—
743C2—2441no—
744C2D61⋊#40811yescharacteristic
745C2C2×D61⋊#9911yescharacteristic
746C2C2×D61⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61C2×#1472
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21461099C2semidirect
4. #21461098C2semidirect
5. #21461097C2semidirect
6. D61⋊#324C2semidirect
22. #16840608C22semidirect
23. #16840607C22semidirect
380. D61#1472semidirect
416. C61C2×#1472semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C2×D61⋊(C22⋊C8)2
#214610992
#214610982
#214610972
D61⋊#3242
C2×C22⋊Q8×D612
C2×#147261