Finite Group Databasebeta

← D61⋊#1504 #30610943

Subgroups — D61⋊#1504 #30610943

Order 15616.

1834 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic, complemented
2C22×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
3#21461207C212yesmaximal, complemented
4#21461206C212yesmaximal, complemented
5#21461205C212yesmaximal, complemented
6#21461204C212yesmaximal, complemented
7D61⋊#328C212yesmaximal, complemented
8D61⋊#327C212yesmaximal, complemented
9#525×D61C211yesmaximal, characteristic
10C24×#6923—21no—
11C2×D61⋊M16—21no—
12#16840734C2212yescomplemented
13#16840733—21no—
14#16840733C2212yescomplemented
15#16840732—21no—
16D61⋊(C22⋊C8)—21no—
17D61⋊(C22⋊C8)C2212yes—
18C2×(C2×#6923)⋊C4—21no—
19C2×(C2×#6923)⋊C4—21no—
20C2×(C2×#6923)⋊C4—21no—
21C2×(C2×#6923)⋊C4C2212yes—
22C2×(C2×#6923)⋊C4C2212yescomplemented
23C2×(C2×#6923)⋊C4C2212yescomplemented
24#16840616C2214yescomplemented
25#16840615C2214yescomplemented
26#16840614C2214yescomplemented
27#16840613C2214yescomplemented
28C2×#41×D61C411yescharacteristic, complemented
29C23×C4×D61C2211yescharacteristic
30#16840275C411yescharacteristic, complemented
31#16840275C2211yescharacteristic
32#16840274C2211yescharacteristic
33#16840273C411yescharacteristic, complemented
34#16840272C411yescharacteristic, complemented
35#16840272C2211yescharacteristic
36#16840271—21no—
37#16840271—21no—
38#16840270—21no—
39#16840269C2211yescharacteristic
40#16840268—21no—
41#123×D61—21no—
42C22⋊Q8×D61C411yescharacteristic, complemented
43C22⋊Q8×D61C2211yescharacteristic
44#121×D61C411yescharacteristic, complemented
45#121×D61C2211yescharacteristic
46#120×D61—21no—
47C4×D4×D61—21no—
48C4×D4×D61—21no—
49#117×D61C411yescharacteristic, complemented
50C61×#525C411yescharacteristic, complemented
51C23×#6923—28no—
52C23×#6923—22no—
53C23×#6923—22no—
54C23×#6923—22no—
55C23×#6923—44no—
56C23×#6923—44no—
57C2×#11758213—22no—
58D61⋊M16—44no—
59C2×#11758217—22no—
60C2×D61⋊C8—22no—
61#14519834—22no—
62#14519834C2314yes—
63C22⋊#92420—22no—
64C22⋊#92420—22no—
65(C2×#6923)⋊C4—22no—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4—22no—
68(C2×#6923)⋊C4C2314yes—
69C24×D61D411yescharacteristic
70C2×#11758226C2×C411yescharacteristic, complemented
71C2×#11758222—21no—
72C2×#11758222C2×C411yescharacteristic, complemented
73C2×#11758224—21no—
74C2×#11758224C2×C411yescharacteristic, complemented
75#41×D61—44no—
76C2×Q8×D61C2×C411yescharacteristic, complemented
77C2×D4×D61—21no—
78C2×D4×D61—21no—
79C2×D4×D61—21no—
80C2×D4×D61C2×C411yescharacteristic, complemented
81C23×Dic61D411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—44no—
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2×C411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61D411yescharacteristic
92C22×C4×D61D411yescharacteristic
93C22×C4×D61C2311yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96#14519762—21no—
97#14519762—21no—
98#14519761—21no—
99#14519760—21no—
100#14519759—21no—
101#14519759—21no—
102#14519758—21no—
103#14519757C2×C411yescharacteristic, complemented
104#14519757C2311yescharacteristic
105#14519756C2×C411yescharacteristic, complemented
106#14519756C2×C411yescharacteristic, complemented
107#14519755—21no—
108#14519755—21no—
109#14519754—21no—
110#14519754—21no—
111#14519753C2×C411yescharacteristic, complemented
112#14519753C2311yescharacteristic
113#14519752C2×C411yescharacteristic, complemented
114#14519752C2311yescharacteristic
115#14519751C2×C411yescharacteristic, complemented
116#14519751C2×C411yescharacteristic, complemented
117#14519750—21no—
118#14519750—21no—
119#14519749—21no—
120#14519749—21no—
121#14519748C2×C411yescharacteristic, complemented
122#14519748C2311yescharacteristic
123#14519747—21no—
124#14519747—21no—
125#14519747—21no—
126#14519746—21no—
127#14519745—21no—
128#14519745—21no—
129#14519745—21no—
130C4×D244—21no—
131C4×D244—21no—
132D4×Dic61—21no—
133D4×Dic61—21no—
134#14519739—21no—
135#14519739—21no—
136C4×C22⋊D61—21no—
137C4×C22⋊D61—21no—
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140#14519737—21no—
141#14519737—21no—
142#14519737—21no—
143#14519737—21no—
144#14519736C2×C411yescharacteristic, complemented
145#14519735C2×C411yescharacteristic, complemented
146#14519735C2×C411yescharacteristic, complemented
147#14519734—21no—
148#14519733—21no—
149C4⋊C4×D61—21no—
150C4⋊C4×D61—21no—
151C4⋊C4×D61C2×C411yescharacteristic, complemented
152C4⋊C4×D61C2×C411yescharacteristic, complemented
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C22⋊C4×D61—21no—
158C42×D61—21no—
159C2×#41×C61C2×C411yescharacteristic, complemented
160C23×C4×C61C2×C411yescharacteristic
161#123×C61—21no—
162C22⋊Q8×C61C2×C411yescharacteristic, complemented
163C22⋊Q8×C61C2×C411yescharacteristic, complemented
164#121×C61C2×C411yescharacteristic, complemented
165#121×C61C2×C411yescharacteristic, complemented
166#120×C61—21no—
167C4×D4×C61—21no—
168C4×D4×C61—21no—
169#117×C61C2×C411yescharacteristic, complemented
170C24×C61C22⋊C411yescharacteristic
171C23×D61—24no—
172C23×D61—24no—
173C23×D61—22no—
174C23×D61—22no—
175C23×D61—21no—
176C23×D61C22⋊C411yescharacteristic
177C23×D61C22⋊C411yescharacteristic
178C23×D61C22⋊C411yescharacteristic
179C23×D61C2×D411yescharacteristic
180C23×D61C2×D411yescharacteristic
181C23×D61C2×D411yescharacteristic
182C22×#6923—28no—
183C22×#6923—28no—
184C22×#6923—28no—
185C22×#6923—24no—
186C22×#6923—432no—
187C22×#6923—44no—
188C22×#6923—44no—
189C22×#6923—44no—
190C22×#6923—44no—
191C22×#6923—44no—
192C22×#6923—44no—
193#41×C61—42no—
194C2×Q8×C61C22×C411yescharacteristic, complemented
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61C22×C411yescharacteristic, complemented
199C22×C4×C61—21no—
200C22×C4×C61—42no—
201C22×C4×C61C22⋊C411yescharacteristic
202C22×C4×C61C22⋊C411yescharacteristic
203C22×C4×C61C22⋊C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C22×C411yescharacteristic
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C22×Dic61—21no—
215C22×Dic61—42no—
216C22×Dic61C22⋊C411yescharacteristic
217C22×Dic61C22⋊C411yescharacteristic
218C22×Dic61C22⋊C411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222#11758226—42no—
223Q8×D61—42no—
224#11758224—42no—
225#11758224—44no—
226D4×D61—42no—
227D4×D61—44no—
228D4×D61—44no—
229D4×D61—42no—
230D4×D61—42no—
231#11758222—44no—
232#11758222—42no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244C22×C411yescharacteristic, complemented
237C2×C4×D61—24no—
238C2×C4×D61—24no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—42no—
245C2×C4×D61—42no—
246C2×C4×D61—42no—
247C2×C4×D61—42no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—44no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61C22⋊C411yescharacteristic
256C2×C4×D61C22⋊C411yescharacteristic
257C2×C4×D61C22⋊C411yescharacteristic
258C2×C4×D61C22⋊C411yescharacteristic
259C2×C4×D61C22⋊C411yescharacteristic
260C2×C4×D61C22⋊C411yescharacteristic
261C2×C4×D61C22×C411yescharacteristic
262C2×C4×D61C22×C411yescharacteristic
263C2×C4×D61C22×C411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2411yescharacteristic
271C2×Dic122—21no—
272C2×Dic122C22×C411yescharacteristic, complemented
273#11758217—44no—
274C2×#92420—24no—
275#11758213—44no—
276D61⋊C8—44no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C22×C411yescharacteristic, complemented
280C4⋊C4×C61C22×C411yescharacteristic, complemented
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C42×C61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61C22×C411yescharacteristic, complemented
305C4⋊Dic61C22×C411yescharacteristic, complemented
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—21no—
319C23×C61C2×C22⋊C411yescharacteristic
320C23×C61C2×C22⋊C411yescharacteristic
321C23×C61C2×C22⋊C411yescharacteristic
322C22×D61—216no—
323C22×D61—216no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—21no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61#9914yes—
346C22×D61#10414yes—
347C22×D61C2×C22⋊C411yescharacteristic
348C22×D61C2×C22⋊C411yescharacteristic
349C22×D61C2×C22⋊C411yescharacteristic
350C22×D61AGL(1,ℤ/8)12yes—
351C22×D61#13712yes—
352C22×D61C22×D411yescharacteristic
353C2×#6923—28no—
354C2×#6923—416no—
355C2×#6923—416no—
356C2×#6923—44no—
357C2×#6923—416no—
358C2×#6923—44no—
359Q8×C61—41no—
360D4×C61—41no—
361D4×C61—42no—
362D4×C61—42no—
363D4×C61—42no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—42no—
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C23×C411yescharacteristic
378C22⋊D61—42no—
379C22⋊D61—42no—
380C22⋊D61—42no—
381C22⋊D61—42no—
382C22⋊D61—41no—
383C22⋊D61—41no—
384C22⋊D61—42no—
385C22⋊D61—42no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—42no—
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C22×D411yescharacteristic
400D244—41no—
401D244—41no—
402D244—41no—
403D244—42no—
404D244—42no—
405C4×D61—22no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—42no—
422C4×D61—42no—
423C4×D61—42no—
424C4×D61—42no—
425C4×D61—42no—
426Dic122—42no—
427Dic122—41no—
428#92420—44no—
429C2×#1504—611nomaximal, Sylow
430C22×C61—28no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61C2×#9912yes—
441C22×C61#41712yes—
442C22×C61C2×#10412yes—
443C22×C61C22×C22⋊C411yescharacteristic
444C2×D61—24no—
445C2×D61—24no—
446C2×D61—24no—
447C2×D61—24no—
448C2×D61—28no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—24no—
456C2×D61—28no—
457C2×D61—28no—
458C2×D61—24no—
459C2×D61—41no—
460C2×D61—41no—
461C2×D61—41no—
462C2×D61—84no—
463C2×D61C2×#9912yes—
464C2×D61C2×#9912yes—
465C2×D61#41712yes—
466C2×D61C2×#10412yes—
467C2×D61C2×#10412yes—
468C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
469C2×D61C2×#13711yescharacteristic
470#6923—48no—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—21no—
474C4×C61—21no—
475C4×C61—41no—
476C4×C61—41no—
477C4×C61—41no—
478Dic61—21no—
479Dic61—21no—
480Dic61—21no—
481Dic61—21no—
482Dic61—41no—
483Dic61—41no—
484Dic61—41no—
485C2×#525—611no—
486C2×#407—611no—
487C22×#95—611no—
488#1504—612no—
489#1504—612no—
490#1504—612no—
491#1504—612no—
492C2×#328—612no—
493C2×#327—612no—
494C2×C61—22no—
495C2×C61—22no—
496C2×C61—22no—
497C2×C61—81no—
498C2×C61C22×#9911yescharacteristic
499C2×C61C2×#41711yescharacteristic
500C2×C61C22×#10411yescharacteristic
501D61—21no—
502D61—21no—
503D61—22no—
504D61—22no—
505D61—81no—
506D61#150414yescomplemented
507C22×#41—611no—
508C24×C4—611no—
509C24×C4—1221no—
510C22×M16—1221no—
511#525—611no—
512#525—611no—
513#525—611no—
514#525—611no—
515#525—611no—
516#525—611no—
517#525—611no—
518#525—1221no—
519#525—1221no—
520#525—1221no—
521#525—1221no—
522#525#692311yescharacteristic, complemented
523C2×#123—1221no—
524C2×C22⋊Q8—611no—
525C2×C22⋊Q8—611no—
526C2×#121—611no—
527C2×#121—611no—
528C2×#120—1221no—
529C2×C4×D4—1221no—
530C2×C4×D4—1221no—
531C2×#117—611no—
532#407—612no—
533#407—612no—
534#407—1221no—
535#407—1221no—
536C2×C22⋊C8—612no—
537C2×C22⋊C8—1221no—
538C2×#95—612no—
539C2×#95—612no—
540C2×#95—612no—
541C2×#95—1221no—
542C2×#95—1221no—
543C2×#95—1221no—
544#328—614no—
545#328—614no—
546#327—614no—
547#327—614no—
548C61C2×#150411yescharacteristic, complemented, Sylow
549C25—611no—
550C2×#41—611no—
551C2×#41—611no—
552C2×#41—611no—
553C2×#41—1221no—
554C2×#41—1221no—
555C2×#41—2444no—
556C2×#41C2×#692311yescharacteristic, complemented
557C22×Q8—611no—
558C22×D4—611no—
559C22×D4—1221no—
560C22×D4—1221no—
561C22×D4—1221no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—611no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—1221no—
576C23×C4—1222no—
577C23×C4—1222no—
578C23×C4—1222no—
579C23×C4—1228no—
580C23×C4—2444no—
581C23×C4—2444no—
582C23×C4—2444no—
583C23×C4C2×#692311yescharacteristic
584C2×M16—1222no—
585C2×M16—1222no—
586C2×M16—2444no—
587C22×C8—1222no—
588#123—21no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596C22⋊Q8—611no—
597C22⋊Q8—611no—
598C22⋊Q8—611no—
599C22⋊Q8—611no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—1221no—
603C22⋊Q8—1221no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8C2×#692311yescharacteristic, complemented
607C22⋊Q8C2×#692311yescharacteristic, complemented
608#121—611no—
609#121—611no—
610#121—611no—
611#121—611no—
612#121—611no—
613#121—611no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121C2×#692311yescharacteristic, complemented
619#121C2×#692311yescharacteristic, complemented
620#120—21no—
621#120—1221no—
622#120—1221no—
623#120—1221no—
624#120—1221no—
625#120—1221no—
626#120—1221no—
627#120—1221no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—1221no—
631C4×D4—1221no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4—1221no—
638C4×D4—1221no—
639C4×D4—1221no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644#117—611no—
645#117—611no—
646#117—611no—
647#117—1221no—
648#117—1221no—
649#117C2×#692311yescharacteristic, complemented
650C2×C4⋊C4—611no—
651C2×C4⋊C4—611no—
652C2×C4⋊C4—1221no—
653C2×C4⋊C4—1221no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C42—1221no—
660C22⋊C8—614no—
661C22⋊C8—1222no—
662C22⋊C8—1222no—
663C22⋊C8—1222no—
664#95—614no—
665#95—1222no—
666#95—1222no—
667#95—1222no—
668C24—611no—
669C24—611no—
670C24—611no—
671C24—611no—
672C24—611no—
673C24—611no—
674C24—1224no—
675C24—1224no—
676C24—1222no—
677C24—1222no—
678C24—1221no—
679C24C22⋊#692311yescharacteristic
680#41—42no—
681#41—2442no—
682#41—2444no—
683#41—2444no—
684#41—2442no—
685#41—2442no—
686C2×Q8—611no—
687C2×Q8—1221no—
688C2×Q8—2442no—
689C2×Q8C22×#692311yescharacteristic, complemented
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—611no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—2442no—
705C2×D4—2444no—
706C2×D4—2442no—
707C2×D4—2442no—
708C2×D4—2444no—
709C2×D4C22×#692311yescharacteristic, complemented
710C22×C4—21no—
711C22×C4—42no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—1221no—
735C22×C4—1224no—
736C22×C4—1224no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1224no—
742C22×C4—1228no—
743C22×C4—1228no—
744C22×C4—1228no—
745C22×C4—1221no—
746C22×C4—2442no—
747C22×C4—2442no—
748C22×C4—2442no—
749C22×C4—2442no—
750C22×C4—2442no—
751C22×C4—2442no—
752C22×C4—2442no—
753C22×C4—2442no—
754C22×C4—2442no—
755C22×C4—2442no—
756C22×C4—2444no—
757C22×C4—2442no—
758C22×C4—2444no—
759C22×C4—2444no—
760C22×C4—2444no—
761C22×C4—2444no—
762C22×C4—2444no—
763C22×C4—24432no—
764C22×C4—2444no—
765C22×C4C22⋊#692311yescharacteristic
766C22×C4C22⋊#692311yescharacteristic
767C22×C4C22⋊#692311yescharacteristic
768C22×C4C22×#692311yescharacteristic
769C22×C4C22×#692311yescharacteristic
770C22×C4C22×#692311yescharacteristic
771M16—2444no—
772M16—2444no—
773C2×C8—1224no—
774C2×C8—2444no—
775C4⋊C4—21no—
776C4⋊C4—21no—
777C4⋊C4—611no—
778C4⋊C4—611no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4C22×#692311yescharacteristic, complemented
788C4⋊C4C22×#692311yescharacteristic, complemented
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C42—21no—
810C42—1221no—
811C42—1221no—
812C42—1221no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—21no—
817C23—611no—
818C23—614no—
819C23—612no—
820C23—612no—
821C23—614no—
822C23—611no—
823C23—611no—
824C23—611no—
825C23—1222no—
826C23—1222no—
827C23—1222no—
828C23—1222no—
829C23—1221no—
830C23—1221no—
831C23—1222no—
832C23—1222no—
833C23—1222no—
834C23—1222no—
835C23—1221no—
836C23—1221no—
837C23—1222no—
838C23—1222no—
839C23—12216no—
840C23—12216no—
841C23—1222no—
842C23—1222no—
843C23—1222no—
844C23—1221no—
845C23—2442no—
846C23—2442no—
847C23—2442no—
848C23C2×C22⋊#692311yescharacteristic
849C23C2×C22⋊#692311yescharacteristic
850C23C2×C22⋊#692311yescharacteristic
851Q8—41no—
852Q8—2441no—
853Q8—2442no—
854D4—41no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—2441no—
859D4—2441no—
860D4—2441no—
861D4—2442no—
862D4—2442no—
863D4—2442no—
864D4—2441no—
865D4—2441no—
866D4—2442no—
867D4—2442no—
868D4—2442no—
869D4—2442no—
870D4—2442no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1228no—
896C2×C4—1221no—
897C2×C4—1221no—
898C2×C4—1221no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2442no—
908C2×C4—2442no—
909C2×C4—2442no—
910C2×C4—2442no—
911C2×C4—2442no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2442no—
917C2×C4—2444no—
918C2×C4—24416no—
919C2×C4—24416no—
920C2×C4—24416no—
921C2×C4—2444no—
922C2×C4C2×C22⋊#692311yescharacteristic
923C2×C4C2×C22⋊#692311yescharacteristic
924C2×C4C2×C22⋊#692311yescharacteristic
925C2×C4C23×#692311yescharacteristic
926C8—2444no—
927C22—28no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—612no—
938C22—612no—
939C22—612no—
940C22—612no—
941C22—611no—
942C22—611no—
943C22—612no—
944C22—1224no—
945C22—1228no—
946C22—1224no—
947C22—1228no—
948C22—1224no—
949C22—1224no—
950C22—1224no—
951C22—1228no—
952C22—1224no—
953C22—1221no—
954C22—1221no—
955C22—1221no—
956C22—1221no—
957C22—1221no—
958C22—1221no—
959C22—4884no—
960C22—2441no—
961C22—2441no—
962C22—2441no—
963C22D61⋊#9912yes—
964C22#1684075312yes—
965C22D61⋊#10412yes—
966C22C22×C22⋊#692311yescharacteristic
967C4—21no—
968C4—21no—
969C4—21no—
970C4—21no—
971C4—41no—
972C4—41no—
973C4—41no—
974C4—1221no—
975C4—1221no—
976C4—1221no—
977C4—1221no—
978C4—2448no—
979C4—2441no—
980C4—2441no—
981C4—2441no—
982C2—22no—
983C2—22no—
984C2—22no—
985C2—81no—
986C2—614no—
987C2—1221no—
988C2—1222no—
989C2—1221no—
990C2—1222no—
991C2—4881no—
992C2C2×D61⋊#9911yescharacteristic
993C2C2×#1684075311yescharacteristic
994C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#525C4
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC2×C4×D61C24
hypercenter#525#6923
hypocenterC61C2×#1504
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. D61⋊#407C2semidirect
2. C22×(C2×#6923)⋊C4C2semidirect
3. #21461207C2semidirect
4. #21461206C2semidirect
5. #21461205C2semidirect
6. #21461204C2semidirect
7. D61⋊#328C2semidirect
8. D61⋊#327C2semidirect
12. #16840734C22semidirect
14. #16840733C22semidirect
22. C2×(C2×#6923)⋊C4C22semidirect
23. C2×(C2×#6923)⋊C4C22semidirect
24. #16840616C22semidirect
25. #16840615C22semidirect
26. #16840614C22semidirect
27. #16840613C22semidirect
28. C2×#41×D61C4semidirect
30. #16840275C4semidirect
33. #16840273C4semidirect
34. #16840272C4semidirect
42. C22⋊Q8×D61C4semidirect
44. #121×D61C4semidirect
49. #117×D61C4semidirect
50. C61×#525C4semidirect
70. C2×#11758226C2×C4semidirect
72. C2×#11758222C2×C4semidirect
74. C2×#11758224C2×C4semidirect
76. C2×Q8×D61C2×C4semidirect
80. C2×D4×D61C2×C4semidirect
103. #14519757C2×C4semidirect
105. #14519756C2×C4semidirect
106. #14519756C2×C4semidirect
111. #14519753C2×C4semidirect
113. #14519752C2×C4semidirect
115. #14519751C2×C4semidirect
116. #14519751C2×C4semidirect
121. #14519748C2×C4semidirect
144. #14519736C2×C4semidirect
145. #14519735C2×C4semidirect
146. #14519735C2×C4semidirect
151. C4⋊C4×D61C2×C4semidirect
152. C4⋊C4×D61C2×C4semidirect
159. C2×#41×C61C2×C4semidirect
162. C22⋊Q8×C61C2×C4semidirect
163. C22⋊Q8×C61C2×C4semidirect
164. #121×C61C2×C4semidirect
165. #121×C61C2×C4semidirect
169. #117×C61C2×C4semidirect
194. C2×Q8×C61C22×C4semidirect
198. C2×D4×C61C22×C4semidirect
236. C2×D244C22×C4semidirect
272. C2×Dic122C22×C4semidirect
279. C4⋊C4×C61C22×C4semidirect
280. C4⋊C4×C61C22×C4semidirect
304. C4⋊Dic61C22×C4semidirect
305. C4⋊Dic61C22×C4semidirect
506. D61#1504semidirect
522. #525#6923semidirect
548. C61C2×#1504semidirect
556. C2×#41C2×#6923semidirect
606. C22⋊Q8C2×#6923semidirect
607. C22⋊Q8C2×#6923semidirect
618. #121C2×#6923semidirect
619. #121C2×#6923semidirect
649. #117C2×#6923semidirect
689. C2×Q8C22×#6923semidirect
709. C2×D4C22×#6923semidirect
787. C4⋊C4C22×#6923semidirect
788. C4⋊C4C22×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C22×(C2×#6923)⋊C42
#214612072
#214612062
#214612052
#214612042
D61⋊#3282
D61⋊#3272
#525×D612
C2×#150461