Finite Group Databasebeta

← #30610964

Subgroups — #30610964

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840734C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
3#21461217C212yesmaximal, complemented
4#21461214C212yesmaximal, complemented
5#21461207C212yesmaximal, complemented
6#21461205C212yesmaximal, complemented
7#21461197C212yesmaximal, complemented
8#21461195C212yesmaximal, complemented
9#525×D61C211yesmaximal, characteristic
10C22×#11758217—21no—
11C22×C22⋊#6923—21no—
12C22×C4×#6923—21no—
13#16840734—21no—
14#16840734—21no—
15#16840734C2212yes—
16#16840734C2212yescomplemented
17C2×#14519834—21no—
18C2×#14519834C2212yescomplemented
19C4×C22⋊#6923—21no—
20C4×C22⋊#6923—21no—
21C4×C22⋊#6923C2212yes—
22C4×C22⋊#6923C2212yescomplemented
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—22no—
52C2×#11758217—22no—
53C2×#11758217—22no—
54C2×#11758217—44no—
55C22×#92420—22no—
56C2×C22⋊#6923—28no—
57C2×C22⋊#6923—22no—
58C2×C22⋊#6923—22no—
59C2×C4×#6923—22no—
60C2×C4×#6923—22no—
61C2×C4×#6923—44no—
62#14519834—22no—
63#14519834—22no—
64#14519834—22no—
65#14519834C2314yes—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4C2314yes—
68C24×D61D411yescharacteristic
69C2×#11758226C2×C411yescharacteristic, complemented
70C2×#11758222—21no—
71C2×#11758222C2×C411yescharacteristic
72C2×#11758224—21no—
73C2×#11758224C2×C411yescharacteristic, complemented
74#41×D61—44no—
75C2×Q8×D61C2×C411yescharacteristic, complemented
76C2×D4×D61—21no—
77C2×D4×D61—21no—
78C2×D4×D61—21no—
79C2×D4×D61C2×C411yescharacteristic, complemented
80C23×Dic61D411yescharacteristic
81C22×C4×D61—21no—
82C22×C4×D61—44no—
83C22×C4×D61C2×C411yescharacteristic
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61D411yescharacteristic
92C22×C4×D61C2311yescharacteristic
93C22×C4×D61C2311yescharacteristic
94C22×C4×D61C2311yescharacteristic
95#14519762—21no—
96#14519762—21no—
97#14519761—21no—
98#14519760—21no—
99#14519759—21no—
100#14519759—21no—
101#14519758—21no—
102#14519757C2×C411yescharacteristic
103#14519757C2311yescharacteristic
104#14519756C2×C411yescharacteristic, complemented
105#14519756C2×C411yescharacteristic, complemented
106#14519755—21no—
107#14519755—21no—
108#14519754—21no—
109#14519754—21no—
110#14519753C2×C411yescharacteristic
111#14519753C2311yescharacteristic
112#14519752C2×C411yescharacteristic
113#14519752C2311yescharacteristic
114#14519751C2×C411yescharacteristic, complemented
115#14519751C2×C411yescharacteristic, complemented
116#14519750—21no—
117#14519750—21no—
118#14519749—21no—
119#14519749—21no—
120#14519748C2×C411yescharacteristic
121#14519748C2311yescharacteristic
122#14519747—21no—
123#14519747—21no—
124#14519747—21no—
125#14519746—21no—
126#14519745—21no—
127#14519745—21no—
128#14519745—21no—
129C4×D244—21no—
130C4×D244—21no—
131D4×Dic61—21no—
132D4×Dic61—21no—
133#14519739—21no—
134#14519739—21no—
135C4×C22⋊D61—21no—
136C4×C22⋊D61—21no—
137C4×C22⋊D61—21no—
138C4×C22⋊D61—21no—
139#14519737—21no—
140#14519737—21no—
141#14519737—21no—
142#14519737—21no—
143#14519736C2×C411yescharacteristic
144#14519735C2×C411yescharacteristic, complemented
145#14519735C2×C411yescharacteristic, complemented
146#14519734—21no—
147#14519733—21no—
148C4⋊C4×D61—21no—
149C4⋊C4×D61—21no—
150C4⋊C4×D61C2×C411yescharacteristic, complemented
151C4⋊C4×D61C2×C411yescharacteristic, complemented
152C22⋊C4×D61—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C42×D61—21no—
158C2×#41×C61C2×C411yescharacteristic
159C23×C4×C61C2×C411yescharacteristic
160#123×C61—21no—
161C22⋊Q8×C61C2×C411yescharacteristic, complemented
162C22⋊Q8×C61C2×C411yescharacteristic, complemented
163#121×C61C2×C411yescharacteristic, complemented
164#121×C61C2×C411yescharacteristic, complemented
165#120×C61—21no—
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168#117×C61C2×C411yescharacteristic
169C24×C61C22⋊C411yescharacteristic
170C23×D61—24no—
171C23×D61—21no—
172C23×D61—42no—
173C23×D61—42no—
174C23×D61C22⋊C411yescharacteristic
175C23×D61C22⋊C411yescharacteristic
176C23×D61C22⋊C411yescharacteristic
177C23×D61C2×D411yescharacteristic
178C23×D61C2×D411yescharacteristic
179C23×D61C2×D411yescharacteristic
180C22×#6923—28no—
181C22×#6923—24no—
182C22×#6923—44no—
183C22×#6923—44no—
184#41×C61—42no—
185C2×Q8×C61C22×C411yescharacteristic
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61C22×C411yescharacteristic
190C22×C4×C61—21no—
191C22×C4×C61—42no—
192C22×C4×C61C22⋊C411yescharacteristic
193C22×C4×C61C22⋊C411yescharacteristic
194C22×C4×C61C22⋊C411yescharacteristic
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C22×C411yescharacteristic
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C22×Dic61—24no—
206C22×Dic61—21no—
207C22×Dic61C22⋊C411yescharacteristic
208C22×Dic61C22⋊C411yescharacteristic
209C22×Dic61C22⋊C411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213#11758226—42no—
214Q8×D61—42no—
215#11758224—42no—
216#11758224—44no—
217D4×D61—42no—
218D4×D61—44no—
219D4×D61—44no—
220D4×D61—44no—
221#11758222—44no—
222#11758222—42no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244C22×C411yescharacteristic
227C2×C4×D61—24no—
228C2×C4×D61—24no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61—42no—
238C2×C4×D61—42no—
239C2×C4×D61—42no—
240C2×C4×D61—42no—
241C2×C4×D61—42no—
242C2×C4×D61—44no—
243C2×C4×D61—42no—
244C2×C4×D61—42no—
245C2×C4×D61C22⋊C411yescharacteristic
246C2×C4×D61C22⋊C411yescharacteristic
247C2×C4×D61C22⋊C411yescharacteristic
248C2×C4×D61C22⋊C411yescharacteristic
249C2×C4×D61C22⋊C411yescharacteristic
250C2×C4×D61C22⋊C411yescharacteristic
251C2×C4×D61C22×C411yescharacteristic
252C2×C4×D61C22×C411yescharacteristic
253C2×C4×D61C22×C411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2411yescharacteristic
261C2×Dic122—21no—
262C2×Dic122C22×C411yescharacteristic
263C22⋊#6923—28no—
264C22⋊#6923—28no—
265#11758217—44no—
266#11758217—44no—
267C2×#92420—24no—
268C2×#92420—44no—
269C4×#6923—44no—
270C4×#6923—44no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61C22×C411yescharacteristic
274C4⋊C4×C61C22×C411yescharacteristic
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C42×C61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61C22×C411yescharacteristic
299C4⋊Dic61C22×C411yescharacteristic
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—21no—
312C23×C61—41no—
313C23×C61C2×C22⋊C411yescharacteristic
314C23×C61C2×C22⋊C411yescharacteristic
315C23×C61C2×C22⋊C411yescharacteristic
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—21no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—416no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61#10414yes—
339C22×D61C2×C22⋊C411yescharacteristic
340C22×D61C2×C22⋊C411yescharacteristic
341C22×D61C2×C22⋊C411yescharacteristic
342C22×D61C22×D411yescharacteristic
343C2×#6923—28no—
344C2×#6923—44no—
345C2×#6923—416no—
346C2×#6923—44no—
347Q8×C61—41no—
348D4×C61—41no—
349D4×C61—42no—
350D4×C61—42no—
351D4×C61—42no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—42no—
362C2×C4×C61C2×C22⋊C411yescharacteristic
363C2×C4×C61C2×C22⋊C411yescharacteristic
364C2×C4×C61C2×C22⋊C411yescharacteristic
365C2×C4×C61C23×C411yescharacteristic
366C22⋊D61—42no—
367C22⋊D61—42no—
368C22⋊D61—42no—
369C22⋊D61—42no—
370C22⋊D61—42no—
371C22⋊D61—42no—
372C22⋊D61—42no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—42no—
382C2×Dic61#9914yes—
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61C22×D411yescharacteristic
387D244—41no—
388D244—42no—
389D244—42no—
390D244—42no—
391C4×D61—22no—
392C4×D61—22no—
393C4×D61—22no—
394C4×D61—22no—
395C4×D61—22no—
396C4×D61—22no—
397C4×D61—22no—
398C4×D61—22no—
399C4×D61—41no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—42no—
408C4×D61—42no—
409C4×D61—42no—
410C4×D61—42no—
411C4×D61—42no—
412Dic122—42no—
413Dic122—41no—
414#92420—44no—
415#17542—611nomaximal, Sylow
416C22×C61—21no—
417C22×C61—21no—
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—44no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61C2×#9912yes—
428C22×C61C2×#10412yes—
429C22×C61C22×C22⋊C411yescharacteristic
430C2×D61—28no—
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—21no—
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—44no—
441C2×D61—44no—
442C2×D61—44no—
443C2×D61—44no—
444C2×D61—44no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—84no—
449C2×D61C2×#10412yes—
450C2×D61C2×#10412yes—
451C2×D61#57512yes—
452#6923—48no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—41no—
458C4×C61—41no—
459C4×C61—41no—
460Dic61—21no—
461Dic61—21no—
462Dic61—41no—
463Dic61—41no—
464Dic61—41no—
465Dic61C2×#9912yes—
466Dic61C2×#9912yes—
467C2×#525—611no—
468C2×#407—611no—
469C2×C4×C22⋊C4—611no—
470#1508—612no—
471#1507—612no—
472#1504—612no—
473#1504—612no—
474#1501—612no—
475#1501—612no—
476C2×C61—22no—
477C2×C61—22no—
478C2×C61—41no—
479C2×C61—81no—
480C2×C61C22×#9911yescharacteristic
481C2×C61#289611yescharacteristic
482C2×C61C22×#10411yescharacteristic
483D61—22no—
484D61—22no—
485D61—22no—
486D61—41no—
487D61—81no—
488C22×#41—611no—
489C24×C4—611no—
490C22×M16—1221no—
491#525—611no—
492#525—611no—
493#525—611no—
494#525—611no—
495#525—611no—
496#525—611no—
497#525—611no—
498#525—1221no—
499#525—1221no—
500#525—1221no—
501#525—1221no—
502#525#692311yescharacteristic, complemented
503C2×#123—1221no—
504C2×C22⋊Q8—611no—
505C2×C22⋊Q8—611no—
506C2×#121—611no—
507C2×#121—611no—
508C2×#120—1221no—
509C2×C4×D4—1221no—
510C2×C4×D4—1221no—
511C2×#117—611no—
512C22×C22⋊C4—1221no—
513C22×C42—1221no—
514#407—612no—
515#407—612no—
516#407—1221no—
517#407—1221no—
518C2×C22⋊C8—612no—
519C2×C22⋊C8—1221no—
520C4×C22⋊C4—612no—
521C4×C22⋊C4—612no—
522C4×C22⋊C4—1221no—
523C4×C22⋊C4—1221no—
524C2×#95—612no—
525#328—614no—
526#328—614no—
527#327—614no—
528#327—614no—
529C61#1754211yescharacteristic, complemented, Sylow
530C25—611no—
531C2×#41—611no—
532C2×#41—611no—
533C2×#41—611no—
534C2×#41—1221no—
535C2×#41—1221no—
536C2×#41—2444no—
537C2×#41C2×#692311yescharacteristic
538C22×Q8—611no—
539C22×D4—611no—
540C22×D4—1221no—
541C22×D4—1221no—
542C22×D4—1221no—
543C23×C4—611no—
544C23×C4—611no—
545C23×C4—611no—
546C23×C4—611no—
547C23×C4—611no—
548C23×C4—611no—
549C23×C4—611no—
550C23×C4—611no—
551C23×C4—611no—
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—611no—
555C23×C4—611no—
556C23×C4—1221no—
557C23×C4—1222no—
558C23×C4—2444no—
559C23×C4C2×#692311yescharacteristic
560C2×M16—1222no—
561C2×M16—1222no—
562C2×M16—2444no—
563C22×C8—1222no—
564#123—21no—
565#123—1221no—
566#123—1221no—
567#123—1221no—
568#123—1221no—
569#123—1221no—
570#123—1221no—
571#123—1221no—
572C22⋊Q8—611no—
573C22⋊Q8—611no—
574C22⋊Q8—611no—
575C22⋊Q8—611no—
576C22⋊Q8—611no—
577C22⋊Q8—611no—
578C22⋊Q8—1221no—
579C22⋊Q8—1221no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8C2×#692311yescharacteristic, complemented
583C22⋊Q8C2×#692311yescharacteristic, complemented
584#121—611no—
585#121—611no—
586#121—611no—
587#121—611no—
588#121—611no—
589#121—611no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121—1221no—
594#121C2×#692311yescharacteristic, complemented
595#121C2×#692311yescharacteristic, complemented
596#120—21no—
597#120—1221no—
598#120—1221no—
599#120—1221no—
600#120—1221no—
601#120—1221no—
602#120—1221no—
603#120—1221no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620#117—611no—
621#117—611no—
622#117—611no—
623#117—1221no—
624#117—1221no—
625#117C2×#692311yescharacteristic
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1222no—
636C2×C22⋊C4—1222no—
637C2×C22⋊C4—1228no—
638C2×C42—1221no—
639C2×C42—1222no—
640C2×C42—1222no—
641C2×C42—2444no—
642C22⋊C8—614no—
643C22⋊C8—1222no—
644C22⋊C8—1222no—
645C22⋊C8—1222no—
646#95—614no—
647#95—1222no—
648C24—611no—
649C24—611no—
650C24—611no—
651C24—611no—
652C24—611no—
653C24—611no—
654C24—1224no—
655C24—1221no—
656C24—2442no—
657C24—2442no—
658C24C22⋊#692311yescharacteristic
659#41—42no—
660#41—2442no—
661#41—2444no—
662#41—2444no—
663#41—2442no—
664#41—2442no—
665C2×Q8—611no—
666C2×Q8—1221no—
667C2×Q8—2442no—
668C2×Q8C22×#692311yescharacteristic
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—611no—
673C2×D4—1221no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—2442no—
684C2×D4—2444no—
685C2×D4—2444no—
686C2×D4—2444no—
687C2×D4C22×#692311yescharacteristic
688C22×C4—21no—
689C22×C4—42no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—1224no—
713C22×C4—1224no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1224no—
719C22×C4—1221no—
720C22×C4—1224no—
721C22×C4—1228no—
722C22×C4—1221no—
723C22×C4—2442no—
724C22×C4—2442no—
725C22×C4—2442no—
726C22×C4—2442no—
727C22×C4—2442no—
728C22×C4—2442no—
729C22×C4—2442no—
730C22×C4—2442no—
731C22×C4—2442no—
732C22×C4—2442no—
733C22×C4—2444no—
734C22×C4—2444no—
735C22×C4—2444no—
736C22×C4C22⋊#692311yescharacteristic
737C22×C4C22⋊#692311yescharacteristic
738C22×C4C22⋊#692311yescharacteristic
739C22×C4C22×#692311yescharacteristic
740C22×C4C22×#692311yescharacteristic
741C22×C4C22×#692311yescharacteristic
742M16—2444no—
743M16—2444no—
744C2×C8—1224no—
745C2×C8—2444no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4C22×#692311yescharacteristic
759C4⋊C4C22×#692311yescharacteristic
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4—1221no—
774C22⋊C4—1221no—
775C22⋊C4—1228no—
776C22⋊C4—1228no—
777C22⋊C4—1221no—
778C22⋊C4—1221no—
779C22⋊C4—1221no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C42—21no—
783C42—1221no—
784C42—1221no—
785C42—1221no—
786C42—2444no—
787C42—2444no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—41no—
792C23—611no—
793C23—611no—
794C23—611no—
795C23—614no—
796C23—611no—
797C23—1222no—
798C23—1222no—
799C23—1222no—
800C23—1222no—
801C23—1222no—
802C23—1222no—
803C23—1222no—
804C23—1222no—
805C23—1222no—
806C23—1222no—
807C23—1221no—
808C23—2441no—
809C23—2441no—
810C23—2441no—
811C23—2441no—
812C23—2441no—
813C23—2441no—
814C23—2441no—
815C23—2442no—
816C23—2442no—
817C23—2442no—
818C23—24416no—
819C23C2×C22⋊#692311yescharacteristic
820C23C2×C22⋊#692311yescharacteristic
821C23C2×C22⋊#692311yescharacteristic
822Q8—41no—
823Q8—2441no—
824Q8—2442no—
825D4—41no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—2441no—
830D4—2442no—
831D4—2442no—
832D4—2442no—
833D4—2442no—
834D4—2442no—
835D4—2442no—
836D4—2442no—
837D4—2442no—
838D4—2442no—
839D4—2442no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—42no—
850C2×C4—614no—
851C2×C4—611no—
852C2×C4—611no—
853C2×C4—611no—
854C2×C4—611no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1228no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2442no—
881C2×C4—2442no—
882C2×C4—2442no—
883C2×C4—2442no—
884C2×C4—2442no—
885C2×C4—2442no—
886C2×C4—2444no—
887C2×C4—2444no—
888C2×C4—24416no—
889C2×C4C2×C22⋊#692311yescharacteristic
890C2×C4C2×C22⋊#692311yescharacteristic
891C2×C4C2×C22⋊#692311yescharacteristic
892C2×C4C23×#692311yescharacteristic
893C8—2444no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—44no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—612no—
906C22—612no—
907C22—612no—
908C22—1228no—
909C22—1221no—
910C22—1221no—
911C22—1221no—
912C22—1221no—
913C22—1221no—
914C22—1221no—
915C22—1221no—
916C22—1221no—
917C22—1221no—
918C22—4884no—
919C22—2444no—
920C22—2444no—
921C22—2444no—
922C22—2444no—
923C22—2444no—
924C22—2441no—
925C22—2441no—
926C22—2441no—
927C22D61⋊#9912yes—
928C22D61⋊#10412yes—
929C22C22×C22⋊#692311yescharacteristic
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—612no—
938C4—612no—
939C4—1221no—
940C4—1221no—
941C4—2448no—
942C4—2441no—
943C4—2441no—
944C4—2441no—
945C2—22no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—1222no—
950C2—1222no—
951C2—1222no—
952C2—4881no—
953C2—2441no—
954C2C2×D61⋊#9911yescharacteristic
955C2#2146243911yescharacteristic
956C2C2×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
hypocenterC61#17542
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. C2×#16840734C2semidirect
2. C2×C4×C22⋊#6923C2semidirect
3. #21461217C2semidirect
4. #21461214C2semidirect
5. #21461207C2semidirect
6. #21461205C2semidirect
7. #21461197C2semidirect
8. #21461195C2semidirect
16. #16840734C22semidirect
18. C2×#14519834C22semidirect
22. C4×C22⋊#6923C22semidirect
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
69. C2×#11758226C2×C4semidirect
73. C2×#11758224C2×C4semidirect
75. C2×Q8×D61C2×C4semidirect
79. C2×D4×D61C2×C4semidirect
104. #14519756C2×C4semidirect
105. #14519756C2×C4semidirect
114. #14519751C2×C4semidirect
115. #14519751C2×C4semidirect
144. #14519735C2×C4semidirect
145. #14519735C2×C4semidirect
150. C4⋊C4×D61C2×C4semidirect
151. C4⋊C4×D61C2×C4semidirect
161. C22⋊Q8×C61C2×C4semidirect
162. C22⋊Q8×C61C2×C4semidirect
163. #121×C61C2×C4semidirect
164. #121×C61C2×C4semidirect
502. #525#6923semidirect
529. C61#17542semidirect
582. C22⋊Q8C2×#6923semidirect
583. C22⋊Q8C2×#6923semidirect
594. #121C2×#6923semidirect
595. #121C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407342
C2×C4×C22⋊#69232
#214612172
#214612142
#214612072
#214612052
#214611972
#214611952
#525×D612
#1754261