Finite Group Databasebeta

← #30616742

Subgroups — #30616742

Order 15616.

1678 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462263C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
3#21462010C212yesmaximal, complemented
4#21461960C212yesmaximal, complemented
5#21461841C212yesmaximal, complemented
6#21461840C212yesmaximal, complemented
7#21461566C212yesmaximal, complemented
8#21461564C212yesmaximal, complemented
9C2×#16840270C211yesmaximal, characteristic
10C2×#14519856—21no—
11C22×C22⋊#6923C2212yes—
12C22×C4×#6923—21no—
13C2×#14519836C2214yes—
14C2×#14519835C2214yes—
15#16840705—21no—
16#16840704—21no—
17#16840704C2212yes—
18#16840703C2212yes—
19C4×C22⋊#6923—21no—
20C4×C22⋊#6923—21no—
21C4×C22⋊#6923—21no—
22C4×C22⋊#6923C2212yes—
23C4×C22⋊#6923C2212yes—
24C4×C22⋊#6923C2212yes—
25C2×(C2×#6923)⋊C4—21no—
26#16840640C2214yes—
27#16840640C2214yes—
28C22×#11758224C411yescharacteristic, complemented
29C23×C4×D61C2211yescharacteristic
30#16840270—21no—
31#16840270—21no—
32#16840270—21no—
33#16840270—21no—
34#16840270—21no—
35#16840270—21no—
36#16840270—21no—
37#16840270—21no—
38C2×#14519760C411yescharacteristic, complemented
39C2×#14519755C411yescharacteristic, complemented
40C2×#14519755C2211yescharacteristic
41C2×#14519750C411yescharacteristic, complemented
42C2×#14519750C2211yescharacteristic
43C2×#14519747C2211yescharacteristic
44C2×#14519745C2211yescharacteristic
45C2×#14519739C411yescharacteristic, complemented
46C2×#14519739C2211yescharacteristic
47C2×#14519737C411yescharacteristic, complemented
48C2×#14519737C2211yescharacteristic
49C2×#14519733C411yescharacteristic, complemented
50C2×#123×C61C411yescharacteristic, complemented
51C23×#6923—22no—
52#14519856—44no—
53C2×C4⋊#6923—22no—
54C2×C22⋊#6923—22no—
55C2×C22⋊#6923—28no—
56C2×C22⋊#6923—22no—
57C2×C22⋊#6923—22no—
58C2×C22⋊#6923C2314yes—
59C2×C22⋊#6923C2314yes—
60C2×C4×#6923—22no—
61C2×C4×#6923—22no—
62C2×C4×#6923—22no—
63C2×C4×#6923—44no—
64#14519836—28no—
65#14519835—28no—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4—22no—
68(C2×#6923)⋊C4—22no—
69(C2×#6923)⋊C4—22no—
70C24×D61C2311yescharacteristic
71C2×#11758224—21no—
72C2×#11758224—21no—
73C2×#11758224—21no—
74C2×#11758224—21no—
75C2×#11758224—44no—
76C22×Dic122C2×C411yescharacteristic, complemented
77C22×D244C2×C411yescharacteristic
78C22×D244C2311yescharacteristic
79C22×C22⋊D61C2×C411yescharacteristic
80C22×C22⋊D61C2×C411yescharacteristic
81C22×C22⋊D61C2×C411yescharacteristic, complemented
82C22×C22⋊D61C2311yescharacteristic
83C23×Dic61C2×C411yescharacteristic
84C23×Dic61C2×C411yescharacteristic, complemented
85C22×C4×D61—44no—
86C22×C4×D61C2×C411yescharacteristic
87C22×C4×D61C2×C411yescharacteristic
88C22×C4×D61C2×C411yescharacteristic, complemented
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61D411yescharacteristic
92C22×C4×D61D411yescharacteristic
93C22×C4×D61D411yescharacteristic
94C22×C4×D61D411yescharacteristic
95C22×C4×D61D411yescharacteristic
96C22×C4×D61D411yescharacteristic
97C22×C4×D61C2311yescharacteristic
98C22×C4×D61C2311yescharacteristic
99#14519760—21no—
100#14519760—21no—
101#14519760—21no—
102#14519760—21no—
103#14519755—21no—
104#14519755—21no—
105#14519755—21no—
106#14519755—21no—
107#14519755—21no—
108#14519755—21no—
109#14519755—21no—
110#14519755—21no—
111#14519750—21no—
112#14519750—21no—
113#14519750—21no—
114#14519750—21no—
115#14519750—21no—
116#14519750—21no—
117#14519750—21no—
118#14519750—21no—
119#14519747—21no—
120#14519747—21no—
121#14519747—21no—
122#14519747—21no—
123#14519745—21no—
124#14519745—21no—
125#14519745—21no—
126#14519745—21no—
127#14519739—21no—
128#14519739—21no—
129#14519739—21no—
130#14519739—21no—
131#14519739—21no—
132#14519739—21no—
133#14519739—21no—
134#14519739—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519737—21no—
140#14519737—21no—
141#14519737—21no—
142#14519737—21no—
143#14519733—21no—
144#14519733—21no—
145#14519733—21no—
146#14519733—21no—
147C2×#11758196C2×C411yescharacteristic, complemented
148C2×#11758196C2×C411yescharacteristic, complemented
149C2×#11758196C2×C411yescharacteristic, complemented
150C2×#11758196C2×C411yescharacteristic, complemented
151C2×C22⋊Dic61C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic, complemented
155C2×#11758198C2×C411yescharacteristic, complemented
156C2×#11758198C2311yescharacteristic
157C2×#11758198C2311yescharacteristic
158C2×C4×Dic61C2×C411yescharacteristic, complemented
159C2×C4×Dic61C2×C411yescharacteristic, complemented
160C22×D4×C61C2×C411yescharacteristic
161C23×C4×C61C2×C411yescharacteristic
162#123×C61—21no—
163#123×C61—21no—
164#123×C61—21no—
165#123×C61—21no—
166C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
167C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
168C2×C22⋊C4×C61C2×C411yescharacteristic
169C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
170C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
171C24×C61C22×C411yescharacteristic
172C24×C61C22×C411yescharacteristic
173C23×D61—24no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61C22×C411yescharacteristic
177C23×D61C22×C411yescharacteristic
178C23×D61C2×D411yescharacteristic
179C23×D61C2×D411yescharacteristic
180C23×D61C2×D411yescharacteristic
181C23×D61C2×D411yescharacteristic
182C23×D61C2411yescharacteristic
183C22×#6923—28no—
184C22×#6923—24no—
185C22×#6923—24no—
186C22×#6923—44no—
187C22×#6923—44no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—42no—
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
198C22×C4×C61C22×C411yescharacteristic
199C22×C4×C61C22×C411yescharacteristic
200C22×C4×C61C22×C411yescharacteristic
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—42no—
211C2×C22⋊D61—42no—
212C2×C22⋊D61—42no—
213C22×Dic61—24no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—42no—
217C22×Dic61C22⋊C411yescharacteristic
218C22×Dic61C22⋊C411yescharacteristic
219C22×Dic61C22⋊C411yescharacteristic
220C22×Dic61C22⋊C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226#11758224—44no—
227#11758224—44no—
228#11758224—44no—
229#11758224—44no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—24no—
235C2×D244—42no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—42no—
241C2×C4×D61—42no—
242C2×C4×D61—42no—
243C2×C4×D61—42no—
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×D61C22⋊C411yescharacteristic
252C2×C4×D61C22⋊C411yescharacteristic
253C2×C4×D61C22⋊C411yescharacteristic
254C2×C4×D61C22⋊C411yescharacteristic
255C2×C4×D61C22⋊C411yescharacteristic
256C2×C4×D61C22⋊C411yescharacteristic
257C2×C4×D61C22⋊C411yescharacteristic
258C2×C4×D61C22⋊C411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122—42no—
270C22⋊#6923—28no—
271C22⋊#6923—24no—
272C22⋊#6923—24no—
273C22⋊#6923—24no—
274C22⋊#6923—44no—
275C22⋊#6923—44no—
276C22⋊#6923#4118yescomplemented
277C4⋊#6923—44no—
278C4×#6923—44no—
279C4×#6923—44no—
280C4×#6923—44no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—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—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—21no—
320C23×C61—22no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61C2×C22⋊C411yescharacteristic
325C23×C61C2×C22⋊C411yescharacteristic
326C23×C61C23×C411yescharacteristic
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—21no—
338C22×D61—22no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—416no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61C2×C22⋊C411yescharacteristic
350C22×D61C2×C22⋊C411yescharacteristic
351C22×D61C22×D411yescharacteristic
352C22×D61C22×D411yescharacteristic
353C22×D61C2×#4114yes—
354C2×#6923—28no—
355C2×#6923—44no—
356C2×#6923—416no—
357C2×#6923—44no—
358C2×#6923—44no—
359C2×#6923—44no—
360C2×#6923—44no—
361D4×C61—42no—
362D4×C61—42no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—22no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C22⋊D61—42no—
380C22⋊D61—42no—
381C22⋊D61—42no—
382C22⋊D61—42no—
383C22⋊D61—42no—
384C22⋊D61—42no—
385C22⋊D61—42no—
386C22⋊D61—42no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—22no—
396C2×Dic61—42no—
397C2×Dic61—42no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61#9914yescomplemented
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405D244—42no—
406D244—42no—
407D244—42no—
408D244—42no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—42no—
426C4×D61—42no—
427Dic122—42no—
428Dic122—42no—
429#21420—611nomaximal, Sylow
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—44no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—82no—
442C22×C61C2×#9912yes—
443C22×C61C22×C22⋊C411yescharacteristic
444C22×C61C4×#4112yes—
445C2×D61—28no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—44no—
456C2×D61—44no—
457C2×D61—44no—
458C2×D61—44no—
459C2×D61—44no—
460C2×D61—41no—
461C2×D61—41no—
462C2×D61—41no—
463C2×D61—82no—
464C2×D61#41012yes—
465C2×D61#52512yes—
466C2×D61#53212yes—
467#6923—48no—
468#6923—84no—
469C4×C61—21no—
470C4×C61—21no—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—41no—
474C4×C61—41no—
475C4×C61—41no—
476Dic61—21no—
477Dic61—21no—
478Dic61—41no—
479Dic61—41no—
480Dic61—41no—
481Dic61C2×#9912yes—
482Dic61C2×#9912yes—
483C2×#525—611no—
484#2280—611no—
485C2×C4×C22⋊C4—611no—
486#1996—612no—
487#1964—612no—
488#1898—612no—
489#1898—612no—
490C4×#99—612no—
491C4×#99—612no—
492C2×C61—22no—
493C2×C61—22no—
494C2×C61—41no—
495C2×C61—81no—
496C2×C61#229711yescharacteristic
497C2×C61C22×#9911yescharacteristic
498C2×C61C2×#41011yescharacteristic
499D61—22no—
500D61—22no—
501D61—22no—
502D61—41no—
503D61—81no—
504C22×#41—611no—
505C24×C4—611no—
506#525—1221no—
507#525—1221no—
508#525—1221no—
509#525—1221no—
510#525—1221no—
511#525—1221no—
512#525—1221no—
513#525—1221no—
514C2×#123—611no—
515C2×#123#692311yescharacteristic, complemented
516C2×C22⋊Q8—611no—
517C2×C22⋊Q8—611no—
518C2×#121—611no—
519C2×#121—611no—
520C2×#120—611no—
521C2×#120—611no—
522C2×C4×D4—611no—
523C2×C4×D4—611no—
524C2×C4×D4—611no—
525C2×C4×D4—611no—
526C2×#117—611no—
527C2×#117—1221no—
528C22×C22⋊C4—612no—
529C22×C42—1221no—
530C2×#99—614no—
531C2×#99—614no—
532#381—1221no—
533#380—612no—
534#380—1221no—
535#379—612no—
536C4×C22⋊C4—612no—
537C4×C22⋊C4—612no—
538C4×C22⋊C4—612no—
539C4×C22⋊C4—1221no—
540C4×C22⋊C4—1221no—
541C4×C22⋊C4—1221no—
542C2×#95—1221no—
543#342—614no—
544#342—614no—
545C61#2142011yescharacteristic, complemented, Sylow
546C25—611no—
547C2×#41—1221no—
548C2×#41—1221no—
549C2×#41—1221no—
550C2×#41—1221no—
551C2×#41—2444no—
552C22×Q8—611no—
553C22×D4—611no—
554C22×D4—611no—
555C22×D4—611no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—611no—
559C22×D4C2×#692311yescharacteristic
560C23×C4—611no—
561C23×C4—611no—
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—1222no—
576C23×C4—2444no—
577C23×C4C2×#692311yescharacteristic
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586C22⋊Q8—1221no—
587C22⋊Q8—1221no—
588C22⋊Q8—1221no—
589C22⋊Q8—1221no—
590C22⋊Q8—1221no—
591C22⋊Q8—1221no—
592C22⋊Q8—1221no—
593C22⋊Q8—1221no—
594#121—1221no—
595#121—1221no—
596#121—1221no—
597#121—1221no—
598#121—1221no—
599#121—1221no—
600#121—1221no—
601#121—1221no—
602#120—1221no—
603#120—1221no—
604#120—1221no—
605#120—1221no—
606#120—1221no—
607#120—1221no—
608#120—1221no—
609#120—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—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626#117—1221no—
627#117—1221no—
628#117—1221no—
629#117—1221no—
630#117—2444no—
631C2×C4⋊C4—611no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—611no—
635C2×C4⋊C4—1222no—
636C2×C4⋊C4C2×#692311yescharacteristic, complemented
637C2×C4⋊C4C2×#692311yescharacteristic, complemented
638C2×C22⋊C4—614no—
639C2×C22⋊C4—611no—
640C2×C22⋊C4—611no—
641C2×C22⋊C4—611no—
642C2×C22⋊C4—611no—
643C2×C22⋊C4—611no—
644C2×C22⋊C4—611no—
645C2×C22⋊C4—611no—
646C2×C22⋊C4—614no—
647C2×C22⋊C4—1228no—
648C2×C22⋊C4—1222no—
649C2×C22⋊C4—1222no—
650C2×C22⋊C4—1222no—
651C2×C22⋊C4C2×#692311yescharacteristic
652C2×C22⋊C4C2×#692311yescharacteristic, complemented
653C2×C22⋊C4C2×#692311yescharacteristic, complemented
654C2×C42—611no—
655C2×C42—611no—
656C2×C42—1222no—
657C2×C42—1222no—
658C2×C42—1222no—
659C2×C42—2444no—
660#99—1228no—
661#99—1228no—
662#95—1222no—
663#95—1222no—
664#95—1222no—
665#95—1222no—
666C24—611no—
667C24—611no—
668C24—611no—
669C24—611no—
670C24—611no—
671C24—611no—
672C24—611no—
673C24—1224no—
674C24—2442no—
675C24—2442no—
676C24C22×#692311yescharacteristic
677C24C22×#692311yescharacteristic
678#41—2444no—
679#41—2444no—
680#41—2444no—
681#41—2444no—
682C2×Q8—1221no—
683C2×Q8—1221no—
684C2×Q8—2442no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—42no—
688C2×D4—1224no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—1221no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1224no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—2442no—
703C2×D4—2442no—
704C2×D4—2442no—
705C2×D4—2442no—
706C22×C4—42no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
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—1224no—
733C22×C4—1224no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1224no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1224no—
740C22×C4—1228no—
741C22×C4—1224no—
742C22×C4—2442no—
743C22×C4—2442no—
744C22×C4—2442no—
745C22×C4—2442no—
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—2444no—
755C22×C4—2444no—
756C22×C4C22⋊#692311yescharacteristic
757C22×C4C22⋊#692311yescharacteristic
758C22×C4C22⋊#692311yescharacteristic
759C22×C4C22⋊#692311yescharacteristic
760C22×C4C22×#692311yescharacteristic
761C22×C4C22×#692311yescharacteristic
762C22×C4C22×#692311yescharacteristic
763C22×C4C22×#692311yescharacteristic
764C22×C4C22×#692311yescharacteristic
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—2444no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—618no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1224no—
794C22⋊C4—1228no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4—1224no—
802C22⋊C4—1224no—
803C22⋊C4—2444no—
804C22⋊C4—2444no—
805C42—1221no—
806C42—1221no—
807C42—1221no—
808C42—1221no—
809C42—2444no—
810C42—2444no—
811C42—2444no—
812C23—22no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—611no—
820C23—611no—
821C23—611no—
822C23—614no—
823C23—611no—
824C23—1222no—
825C23—1222no—
826C23—1222no—
827C23—1222no—
828C23—1222no—
829C23—1222no—
830C23—1222no—
831C23—1222no—
832C23—1222no—
833C23—1222no—
834C23—1222no—
835C23—1221no—
836C23—2441no—
837C23—2441no—
838C23—2441no—
839C23—2441no—
840C23—2441no—
841C23—2441no—
842C23—2441no—
843C23—2441no—
844C23—2441no—
845C23—24416no—
846C23C2×C22⋊#692311yescharacteristic
847C23C2×C22⋊#692311yescharacteristic
848C23C23×#692311yescharacteristic
849Q8—2442no—
850Q8—2442no—
851D4—42no—
852D4—42no—
853D4—2442no—
854D4—2442no—
855D4—2442no—
856D4—2442no—
857D4—2442no—
858D4—2442no—
859D4—2442no—
860D4—2442no—
861D4—2442no—
862D4—2442no—
863D4—2442no—
864D4—2442no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—22no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—614no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
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—1222no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2442no—
909C2×C4—2442no—
910C2×C4—2442no—
911C2×C4—2442no—
912C2×C4—2444no—
913C2×C4—2444no—
914C2×C4—2444no—
915C2×C4—2444no—
916C2×C4—24416no—
917C2×C4—2444no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4C2×C22⋊#692311yescharacteristic
921C2×C4C2×C22⋊#692311yescharacteristic
922C2×C4C2×C22⋊#692311yescharacteristic
923C2×C4C2×C22⋊#692311yescharacteristic
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—44no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—82no—
936C22—612no—
937C22—612no—
938C22—612no—
939C22—1228no—
940C22—1221no—
941C22—1221no—
942C22—1221no—
943C22—1221no—
944C22—1221no—
945C22—1221no—
946C22—1221no—
947C22—1221no—
948C22—1221no—
949C22—4882no—
950C22—2444no—
951C22—2444no—
952C22—2444no—
953C22—2444no—
954C22—2444no—
955C22—2441no—
956C22—2441no—
957C22—2441no—
958C22D61⋊#9912yes—
959C22C22×C22⋊#692311yescharacteristic
960C22#41×#692312yes—
961C4—21no—
962C4—21no—
963C4—21no—
964C4—21no—
965C4—41no—
966C4—41no—
967C4—41no—
968C4—612no—
969C4—612no—
970C4—1221no—
971C4—1221no—
972C4—4884no—
973C4—2448no—
974C4—2441no—
975C4—2441no—
976C4—2441no—
977C2—22no—
978C2—22no—
979C2—41no—
980C2—81no—
981C2—1222no—
982C2—1222no—
983C2—1222no—
984C2—4881no—
985C2—2441no—
986C2#2146228011yescharacteristic
987C2C2×D61⋊#9911yescharacteristic
988C2D61⋊#41011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840270C2
cosocleC23×D61C24
hypercenterC2×#123#6923
hypocenterC61#21420
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462263C2semidirect
2. C2×C4×C22⋊#6923C2semidirect
3. #21462010C2semidirect
4. #21461960C2semidirect
5. #21461841C2semidirect
6. #21461840C2semidirect
7. #21461566C2semidirect
8. #21461564C2semidirect
28. C22×#11758224C4semidirect
38. C2×#14519760C4semidirect
39. C2×#14519755C4semidirect
41. C2×#14519750C4semidirect
45. C2×#14519739C4semidirect
47. C2×#14519737C4semidirect
49. C2×#14519733C4semidirect
50. C2×#123×C61C4semidirect
76. C22×Dic122C2×C4semidirect
81. C22×C22⋊D61C2×C4semidirect
84. C23×Dic61C2×C4semidirect
88. C22×C4×D61C2×C4semidirect
147. C2×#11758196C2×C4semidirect
148. C2×#11758196C2×C4semidirect
149. C2×#11758196C2×C4semidirect
150. C2×#11758196C2×C4semidirect
154. C2×#11758198C2×C4semidirect
155. C2×#11758198C2×C4semidirect
158. C2×C4×Dic61C2×C4semidirect
159. C2×C4×Dic61C2×C4semidirect
166. C2×C4⋊C4×C61C2×C4semidirect
167. C2×C4⋊C4×C61C2×C4semidirect
169. C2×C22⋊C4×C61C2×C4semidirect
170. C2×C22⋊C4×C61C2×C4semidirect
276. C22⋊#6923#41semidirect
400. C2×Dic61#99semidirect
515. C2×#123#6923semidirect
545. C61#21420semidirect
636. C2×C4⋊C4C2×#6923semidirect
637. C2×C4⋊C4C2×#6923semidirect
652. C2×C22⋊C4C2×#6923semidirect
653. C2×C22⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214622632
C2×C4×C22⋊#69232
#214620102
#214619602
#214618412
#214618402
#214615662
#214615642
C2×#168402702
#2142061