Finite Group Databasebeta

← #30620160

Subgroups — #30620160

Order 15616.

1638 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D61⋊C8C211yesmaximal, characteristic, complemented
2C2×#16840752C211yesmaximal, characteristic, complemented
3C22×#14519839C211yesmaximal, characteristic, complemented
4#21462335C211yesmaximal, characteristic, complemented
5#21461987C211yesmaximal, characteristic, complemented
6#21461948C211yesmaximal, characteristic, complemented
7#21461833C211yesmaximal, characteristic, complemented
8#21461832C211yesmaximal, characteristic, complemented
9#21461807C211yesmaximal, characteristic, complemented
10#21461804C211yesmaximal, characteristic, complemented
11#21461689C211yesmaximal, characteristic, complemented
12#21461659C211yesmaximal, characteristic, complemented
13#21461657C211yesmaximal, characteristic, complemented
14C4×#14519839C211yesmaximal, characteristic, complemented
15#546×D61C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic, complemented
18C2×#14519856C2211yescharacteristic, complemented
19C22×C4⋊#6923C2211yescharacteristic
20#16840790—21no—
21#16840789—21no—
22#16840789—21no—
23D4×#92420—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic, complemented
25#16840752—24no—
26C2×#14519840C2211yescharacteristic, complemented
27C2×#14519840C2211yescharacteristic, complemented
28C2×#14519840C2211yescharacteristic, complemented
29C2×#14519840C2211yescharacteristic, complemented
30C2×#14519839—24no—
31C2×#14519839C2211yescharacteristic
32C2×#14519839C2211yescharacteristic
33C2×#14519839C2211yescharacteristic
34C2×#14519839C2211yescharacteristic
35C2×#14519839C2211yescharacteristic
36C2×#14519839C2211yescharacteristic
37C2×#14519839C2211yescharacteristic
38C2×#14519839C2211yescharacteristic
39D61⋊(C22⋊C8)C2211yescharacteristic
40D61⋊(C22⋊C8)C2211yescharacteristic, complemented
41C4×D61⋊C8C2211yescharacteristic, complemented
42#16840712—21no—
43#16840711—21no—
44#16840710—21no—
45#16840706C2211yescharacteristic, complemented
46#16840704C2211yescharacteristic
47#16840704C2211yescharacteristic, complemented
48C4×C4⋊#6923C2211yescharacteristic, complemented
49C22⋊C4×#6923—21no—
50#16840635C2211yescharacteristic, complemented
51#16840635C2211yescharacteristic, complemented
52#16840635C2211yescharacteristic, complemented
53#16840635C2211yescharacteristic, complemented
54C2×#41×D61C2211yescharacteristic
55C22×D4×D61C2211yescharacteristic
56#16840409C411yescharacteristic, complemented
57#16840408C411yescharacteristic, complemented
58#16840407C411yescharacteristic, complemented
59#16840406C411yescharacteristic, complemented
60#16840405C411yescharacteristic, complemented
61#16840404—21no—
62#16840403C411yescharacteristic, complemented
63#16840402—21no—
64#16840401—21no—
65#16840400C411yescharacteristic, complemented
66#16840399—21no—
67#124×D61C2211yescharacteristic
68#123×D61—21no—
69C22⋊Q8×D61C2211yescharacteristic
70#121×D61—21no—
71#121×D61C2211yescharacteristic
72#120×D61—21no—
73C4×D4×D61C2211yescharacteristic
74C4×D4×D61C2211yescharacteristic
75C2×C22⋊C4×D61—21no—
76C61×#546C411yescharacteristic, complemented
77C23×#6923—21no—
78C2×D61⋊C8—22no—
79C2×D61⋊C8—22no—
80C2×D61⋊C8—21no—
81C2×D61⋊C8—21no—
82C2×D61⋊C8—41no—
83C2×D61⋊C8—41no—
84C2×D61⋊C8C2311yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C2×D61⋊C8C2311yescharacteristic
88C22×#92420—21no—
89C22×#92420—21no—
90#14519856—22no—
91#14519856—41no—
92C2×C4⋊#6923—22no—
93C2×C4⋊#6923—21no—
94C2×C4⋊#6923—41no—
95C2×C4⋊#6923C2311yescharacteristic
96C2×C4⋊#6923C2311yescharacteristic
97C2×C4⋊#6923C2311yescharacteristic
98C2×C4⋊#6923C2311yescharacteristic
99C2×C22⋊#6923—21no—
100C2×C22⋊#6923—21no—
101C2×C22⋊#6923—21no—
102C2×C4×#6923—21no—
103C2×C4×#6923—21no—
104#14519844—21no—
105C4⋊#92420—21no—
106#14519840—22no—
107#14519840—22no—
108#14519840—41no—
109#14519840—41no—
110#14519839—22no—
111#14519839—22no—
112#14519839—22no—
113#14519839—22no—
114#14519839—22no—
115#14519839—41no—
116#14519839—41no—
117#14519839D414yescomplemented
118#14519834—21no—
119#14519834—21no—
120C22⋊#92420—21no—
121C22⋊#92420—21no—
122C4×#92420—21no—
123C4×#92420—21no—
124(C2×#6923)⋊C4—21no—
125(C2×#6923)⋊C4—21no—
126(C2×#6923)⋊C4—21no—
127(C2×#6923)⋊C4—21no—
128(C2×#6923)⋊C4—21no—
129C24×D61—21no—
130C2×#11758226C2×C411yescharacteristic, complemented
131C2×#11758222—21no—
132C2×#11758222C2×C411yescharacteristic, complemented
133C2×#11758224—21no—
134C2×#11758224C2×C411yescharacteristic, complemented
135#41×D61—22no—
136#41×D61—22no—
137#41×D61—41no—
138#41×D61—41no—
139C2×Q8×D61C2311yescharacteristic
140C22×D244C2×C411yescharacteristic
141C22×C22⋊D61—21no—
142C2×D4×D61—22no—
143C2×D4×D61—22no—
144C2×D4×D61—21no—
145C2×D4×D61—21no—
146C2×D4×D61—21no—
147C2×D4×D61—21no—
148C2×D4×D61—41no—
149C2×D4×D61—41no—
150C2×D4×D61C2×C411yescharacteristic
151C2×D4×D61C2×C411yescharacteristic
152C2×D4×D61D411yescharacteristic
153C2×D4×D61C2311yescharacteristic
154C2×D4×D61C2311yescharacteristic
155C22×C4×D61—21no—
156C22×C4×D61—21no—
157C22×C4×D61C2311yescharacteristic
158C22×C4×D61C2311yescharacteristic
159#14519766C2×C411yescharacteristic, complemented
160#14519765C2×C411yescharacteristic, complemented
161#14519764C2×C411yescharacteristic, complemented
162#14519763—21no—
163#14519763—21no—
164#14519762—21no—
165#14519762—21no—
166#14519761—21no—
167#14519760—21no—
168#14519759—21no—
169#14519759—21no—
170#14519758—21no—
171#14519757C2×C411yescharacteristic
172#14519756C2×C411yescharacteristic
173#14519755—21no—
174#14519754—21no—
175#14519753C2×C411yescharacteristic
176#14519752—21no—
177#14519752C2×C411yescharacteristic, complemented
178#14519751—21no—
179#14519751C2×C411yescharacteristic, complemented
180#14519750—21no—
181#14519750—21no—
182#14519750—21no—
183#14519749—21no—
184#14519749—21no—
185#14519749—21no—
186#14519748—21no—
187#14519748C2×C411yescharacteristic, complemented
188#14519747—21no—
189#14519747—21no—
190#14519747—21no—
191#14519746—21no—
192#14519745—21no—
193#14519745—21no—
194#14519745—21no—
195C4×D244C2×C411yescharacteristic
196C4×D244C2×C411yescharacteristic, complemented
197D4×Dic61C2×C411yescharacteristic, complemented
198D4×Dic61D411yescharacteristic
199#14519739C2×C411yescharacteristic, complemented
200#14519739D411yescharacteristic
201C4×C22⋊D61—21no—
202C4×C22⋊D61C2×C411yescharacteristic
203C4×C22⋊D61C2×C411yescharacteristic
204#14519737—21no—
205#14519737D411yescharacteristic
206#14519737D411yescharacteristic
207C4⋊C4×D61—21no—
208C4⋊C4×D61D411yescharacteristic
209C4⋊C4×D61C2311yescharacteristic
210C2×C22⋊Dic61—21no—
211C2×#11758198—21no—
212C2×#11758198—21no—
213C22⋊C4×D61—21no—
214C22⋊C4×D61—21no—
215C22⋊C4×D61—21no—
216C22⋊C4×D61—21no—
217C22⋊C4×D61—21no—
218C22⋊C4×D61—21no—
219C22⋊C4×D61—21no—
220C22⋊C4×D61—21no—
221C22⋊C4×D61—21no—
222C22⋊C4×D61D411yescharacteristic
223C22⋊C4×D61D411yescharacteristic
224C42×D61C2311yescharacteristic
225C2×#41×C61C2×C411yescharacteristic, complemented
226C22×D4×C61C2×C411yescharacteristic
227#124×C61C2×C411yescharacteristic, complemented
228#123×C61—21no—
229C22⋊Q8×C61C2×C411yescharacteristic
230#121×C61—21no—
231#121×C61C2×C411yescharacteristic, complemented
232#120×C61—21no—
233C4×D4×C61C2×C411yescharacteristic
234C4×D4×C61C2×C411yescharacteristic, complemented
235C2×C22⋊C4×C61—21no—
236C24×C61—21no—
237C23×D61—21no—
238C23×D61—21no—
239C23×D61—21no—
240C23×D61—21no—
241C23×D61—21no—
242C23×D61—42no—
243C23×D61—42no—
244C23×D61—42no—
245C23×D61—42no—
246C23×D61—81no—
247C23×D61—81no—
248C23×D61C2×D411yescharacteristic
249C23×D61C2×D411yescharacteristic
250C22×#6923—21no—
251C22×#6923—21no—
252C22×#6923—21no—
253C22×#6923—21no—
254C22×#6923—42no—
255C22×#6923—42no—
256C22×#6923—81no—
257#41×C61—22no—
258#41×C61—41no—
259C2×Q8×C61C22×C411yescharacteristic
260C2×D4×C61—22no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61—41no—
265C2×D4×C61C22⋊C411yescharacteristic
266C2×D4×C61C22×C411yescharacteristic
267C2×D4×C61C22×C411yescharacteristic
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61C22×C411yescharacteristic
271C22×C4×C61C22×C411yescharacteristic
272C2×C22⋊D61—21no—
273C2×C22⋊D61—21no—
274C2×C22⋊D61—21no—
275C2×C22⋊D61—21no—
276C2×C22⋊D61—21no—
277C2×C22⋊D61—21no—
278C2×C22⋊D61—21no—
279C2×C22⋊D61—21no—
280C2×C22⋊D61—42no—
281C2×C22⋊D61—42no—
282C2×C22⋊D61C22⋊C411yescharacteristic
283C2×C22⋊D61C22⋊C411yescharacteristic
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61C2×D411yescharacteristic
287C22×Dic61C2×D411yescharacteristic
288#11758226—22no—
289#11758226—41no—
290Q8×D61—21no—
291Q8×D61—21no—
292Q8×D61—21no—
293Q8×D61—21no—
294#11758224—22no—
295#11758224—41no—
296#11758224—42no—
297#11758224—42no—
298D4×D61—22no—
299D4×D61—22no—
300D4×D61—22no—
301D4×D61—22no—
302D4×D61—21no—
303D4×D61—21no—
304D4×D61—21no—
305D4×D61—21no—
306D4×D61—21no—
307D4×D61—21no—
308D4×D61—41no—
309D4×D61—41no—
310D4×D61—42no—
311D4×D61—42no—
312D4×D61—42no—
313D4×D61—42no—
314D4×D61—42no—
315D4×D61—42no—
316D4×D61—81no—
317D4×D61—81no—
318D4×D61C2×D412yes—
319D4×D61#4112yes—
320#11758222—22no—
321#11758222—41no—
322#11758222—42no—
323#11758222—42no—
324C2×D244—22no—
325C2×D244—21no—
326C2×D244—21no—
327C2×D244—21no—
328C2×D244—41no—
329C2×D244C22⋊C411yescharacteristic
330C2×D244C22×C411yescharacteristic
331C2×D244C22×C411yescharacteristic
332C2×C4×D61—21no—
333C2×C4×D61—21no—
334C2×C4×D61—21no—
335C2×C4×D61—21no—
336C2×C4×D61—21no—
337C2×C4×D61—21no—
338C2×C4×D61—21no—
339C2×C4×D61—21no—
340C2×C4×D61—21no—
341C2×C4×D61—21no—
342C2×C4×D61—21no—
343C2×C4×D61—21no—
344C2×C4×D61—21no—
345C2×C4×D61—21no—
346C2×C4×D61—42no—
347C2×C4×D61—42no—
348C2×C4×D61—81no—
349C2×C4×D61—81no—
350C2×C4×D61C22×C411yescharacteristic
351C2×C4×D61C22×C411yescharacteristic
352C2×C4×D61C2×D411yescharacteristic
353C2×C4×D61C2×D411yescharacteristic
354C2×C4×D61C2×D411yescharacteristic
355C2×C4×D61C2×D411yescharacteristic
356C2×C4×D61C2×D411yescharacteristic
357C2×C4×D61C2×D411yescharacteristic
358C2×C4×D61C2411yescharacteristic
359C2×Dic122—21no—
360C2×Dic122C22×C411yescharacteristic
361C22⋊#6923—42no—
362C22⋊#6923—42no—
363C22⋊#6923—81no—
364C2×#92420—21no—
365C2×#92420—21no—
366C2×#92420—21no—
367C2×#92420—21no—
368C2×#92420—42no—
369C2×#92420—42no—
370C4⋊#6923—21no—
371C4⋊#6923—21no—
372C4⋊#6923—21no—
373C4⋊#6923—21no—
374C4⋊#6923—21no—
375C4⋊#6923—21no—
376C4⋊#6923—21no—
377C4⋊#6923—42no—
378C4⋊#6923C2×D412yes—
379C4×#6923—42no—
380C4×#6923—81no—
381D61⋊C8—21no—
382D61⋊C8—21no—
383D61⋊C8—21no—
384D61⋊C8—21no—
385D61⋊C8—21no—
386D61⋊C8—21no—
387D61⋊C8—21no—
388D61⋊C8—42no—
389D61⋊C8—42no—
390D61⋊C8C2×D412yes—
391C4⋊C4×C61—21no—
392C4⋊C4×C61C22⋊C411yescharacteristic
393C4⋊C4×C61C22×C411yescharacteristic
394C22⋊C4×C61—21no—
395C22⋊C4×C61—21no—
396C22⋊C4×C61—21no—
397C22⋊C4×C61—21no—
398C22⋊C4×C61—21no—
399C22⋊C4×C61C22⋊C411yescharacteristic
400C22⋊C4×C61C22⋊C411yescharacteristic
401C42×C61C22×C411yescharacteristic
402C22⋊Dic61—21no—
403C22⋊Dic61—21no—
404C22⋊Dic61—21no—
405C22⋊Dic61—21no—
406C22⋊Dic61—21no—
407C22⋊Dic61C22⋊C411yescharacteristic
408C22⋊Dic61C22⋊C411yescharacteristic
409#11758198—21no—
410#11758198—21no—
411#11758198—21no—
412#11758198—21no—
413#11758198—21no—
414#11758198—21no—
415#11758198—21no—
416#11758198—21no—
417#11758198—21no—
418#11758198—21no—
419#11758198C22⋊C411yescharacteristic
420#11758198C22⋊C411yescharacteristic
421#11758198C22⋊C411yescharacteristic
422#11758198C22⋊C411yescharacteristic
423C4⋊Dic61—21no—
424C4⋊Dic61C22⋊C411yescharacteristic
425C4⋊Dic61C22×C411yescharacteristic
426#11758196—21no—
427#11758196—21no—
428#11758196—21no—
429#11758196C22⋊C411yescharacteristic
430#11758196C22⋊C411yescharacteristic
431C4×Dic61C22×C411yescharacteristic
432C4×Dic61C2×D411yescharacteristic
433C4×Dic61C2×D411yescharacteristic
434C23×C61—21no—
435C23×C61—21no—
436C23×C61—42no—
437C23×C61—42no—
438C23×C61—81no—
439C23×C61C2×C22⋊C411yescharacteristic
440C23×C61C2×C22⋊C411yescharacteristic
441C22×D61—21no—
442C22×D61—21no—
443C22×D61—21no—
444C22×D61—21no—
445C22×D61—21no—
446C22×D61—21no—
447C22×D61—22no—
448C22×D61—21no—
449C22×D61—22no—
450C22×D61—21no—
451C22×D61—21no—
452C22×D61—21no—
453C22×D61—21no—
454C22×D61—21no—
455C22×D61—42no—
456C22×D61—42no—
457C22×D61—42no—
458C22×D61—41no—
459C22×D61—41no—
460C22×D61—41no—
461C22×D61—41no—
462C22×D61—42no—
463C22×D61—41no—
464C22×D61—41no—
465C22×D61—41no—
466C22×D61—41no—
467C22×D61—41no—
468C22×D61—41no—
469C22×D61—42no—
470C22×D61—42no—
471C22×D61—81no—
472C22×D61—81no—
473C22×D61—84no—
474C22×D61—84no—
475C22×D61—84no—
476C22×D61—84no—
477C22×D61—81no—
478C22×D61C2×C22⋊C411yescharacteristic
479C22×D61C2×C22⋊C411yescharacteristic
480C22×D61#13512yes—
481C22×D61#13512yes—
482C22×D61C22×D411yescharacteristic
483C2×#6923—22no—
484C2×#6923—41no—
485C2×#6923—41no—
486C2×#6923—41no—
487C2×#6923—41no—
488C2×#6923—41no—
489C2×#6923—41no—
490C2×#6923—41no—
491C2×#6923—41no—
492C2×#6923—41no—
493C2×#6923—41no—
494C2×#6923—41no—
495C2×#6923—84no—
496Q8×C61—21no—
497Q8×C61—21no—
498D4×C61—22no—
499D4×C61—21no—
500D4×C61—21no—
501D4×C61—21no—
502D4×C61—42no—
503D4×C61—42no—
504D4×C61—81no—
505D4×C61C4×D412yes—
506C2×C4×C61—21no—
507C2×C4×C61—21no—
508C2×C4×C61—21no—
509C2×C4×C61—21no—
510C2×C4×C61—21no—
511C2×C4×C61—21no—
512C2×C4×C61—42no—
513C2×C4×C61—81no—
514C2×C4×C61C2×C22⋊C411yescharacteristic
515C2×C4×C61C2×C22⋊C411yescharacteristic
516C2×C4×C61C2×C22⋊C411yescharacteristic
517C2×C4×C61C2×C22⋊C411yescharacteristic
518C2×C4×C61C23×C411yescharacteristic
519C22⋊D61—22no—
520C22⋊D61—22no—
521C22⋊D61—22no—
522C22⋊D61—22no—
523C22⋊D61—42no—
524C22⋊D61—42no—
525C22⋊D61—42no—
526C22⋊D61—42no—
527C22⋊D61—41no—
528C22⋊D61—41no—
529C22⋊D61—81no—
530C22⋊D61—81no—
531C2×Dic61—21no—
532C2×Dic61—21no—
533C2×Dic61—21no—
534C2×Dic61—21no—
535C2×Dic61—21no—
536C2×Dic61—21no—
537C2×Dic61—42no—
538C2×Dic61—81no—
539C2×Dic61C2×C22⋊C411yescharacteristic
540C2×Dic61C2×C22⋊C411yescharacteristic
541C2×Dic61C2×C22⋊C411yescharacteristic
542C2×Dic61C2×C22⋊C411yescharacteristic
543C2×Dic61C22×D411yescharacteristic
544D244—22no—
545D244—21no—
546D244—21no—
547D244—21no—
548D244—42no—
549D244—42no—
550D244—81no—
551D244C4×D412yes—
552C4×D61—21no—
553C4×D61—21no—
554C4×D61—21no—
555C4×D61—21no—
556C4×D61—21no—
557C4×D61—21no—
558C4×D61—21no—
559C4×D61—21no—
560C4×D61—21no—
561C4×D61—21no—
562C4×D61—21no—
563C4×D61—21no—
564C4×D61—21no—
565C4×D61—21no—
566C4×D61—21no—
567C4×D61—21no—
568C4×D61—42no—
569C4×D61—42no—
570C4×D61—41no—
571C4×D61—41no—
572C4×D61—41no—
573C4×D61—41no—
574C4×D61—81no—
575C4×D61—81no—
576C4×D61C22×D411yescharacteristic
577C4×D61C2×#4111yescharacteristic
578C4×D61H(5,𝔽2)11yescharacteristic
579C4×D61H(5,𝔽2)11yescharacteristic
580Dic122—21no—
581Dic122—21no—
582Dic122—41no—
583Dic122—41no—
584#92420—22no—
585#92420—41no—
586#92420—41no—
587#92420—41no—
588#22414—611nomaximal, Sylow
589C22×C61—21no—
590C22×C61—21no—
591C22×C61—21no—
592C22×C61—22no—
593C22×C61—21no—
594C22×C61—21no—
595C22×C61—41no—
596C22×C61—41no—
597C22×C61—41no—
598C22×C61—41no—
599C22×C61—41no—
600C22×C61—84no—
601C22×C61#41612yescomplemented
602C22×C61C22×C22⋊C411yescharacteristic
603C2×D61—21no—
604C2×D61—21no—
605C2×D61—22no—
606C2×D61—22no—
607C2×D61—22no—
608C2×D61—22no—
609C2×D61—21no—
610C2×D61—22no—
611C2×D61—21no—
612C2×D61—21no—
613C2×D61—41no—
614C2×D61—41no—
615C2×D61—41no—
616C2×D61—42no—
617C2×D61—41no—
618C2×D61—42no—
619C2×D61—41no—
620C2×D61—42no—
621C2×D61—41no—
622C2×D61—42no—
623C2×D61—41no—
624C2×D61—41no—
625C2×D61—41no—
626C2×D61—84no—
627C2×D61—84no—
628C2×D61—84no—
629C2×D61—81no—
630C2×D61—81no—
631C2×D61—81no—
632C2×D61—81no—
633C2×D61#41612yescomplemented
634C2×D61D4211yescharacteristic
635C2×D61#54611yescharacteristic
636C2×D61C2×#13511yescharacteristic
637C2×D61C2×#13511yescharacteristic
638C2×D61#57611yescharacteristic
639C2×D61#57711yescharacteristic
640#6923—42no—
641#6923—81no—
642#6923—81no—
643#6923—81no—
644C4×C61—21no—
645C4×C61—21no—
646C4×C61—21no—
647C4×C61—21no—
648C4×C61—41no—
649C4×C61—41no—
650C4×C61C2×C4×D411yescharacteristic
651C4×C61#51811yescharacteristic
652Dic61—21no—
653Dic61—21no—
654Dic61—21no—
655Dic61—21no—
656Dic61—41no—
657Dic61—41no—
658Dic61D4211yescharacteristic
659Dic61#54611yescharacteristic
660C2×#546—611no—
661C2×C8×D4—611no—
662C2×#416—611no—
663C22×#102—611no—
664#2352—611no—
665#1983—611no—
666#1958—611no—
667#1893—611no—
668#1892—611no—
669#1875—611no—
670#1872—611no—
671#1804—611no—
672#1788—611no—
673#1786—611no—
674C4×#102—611no—
675C2×C61—22no—
676C2×C61—42no—
677C2×C61—41no—
678C2×C61—81no—
679C2×C61D4×C22⋊C411yescharacteristic
680C2×C61C2×#41611yescharacteristic
681C2×C61#289711yescharacteristic
682D61—22no—
683D61—41no—
684D61—42no—
685D61—81no—
686D61#328011yescharacteristic
687D61#328211yescharacteristic
688D61#329611yescharacteristic
689D61#329711yescharacteristic
690C22×#41—611no—
691C23×D4—611no—
692C23×C8—611no—
693C23×C8—611no—
694#546—611no—
695#546—611no—
696#546—611no—
697#546—611no—
698#546—611no—
699#546—611no—
700#546—611no—
701#546—1221no—
702#546—1221no—
703#546—1221no—
704#546—1221no—
705#546#692311yescharacteristic, complemented
706C2×#124—611no—
707C2×#123—1221no—
708C2×C22⋊Q8—611no—
709C2×#121—611no—
710C2×#121—1221no—
711C2×#120—1221no—
712C2×C4×D4—611no—
713C2×C4×D4—611no—
714C2×#117—611no—
715C22×C4⋊C4—611no—
716C22×C22⋊C4—1221no—
717C8×D4—1221no—
718C8×D4—1221no—
719C8×D4—1221no—
720C8×D4—1221no—
721C2×C4⋊C8—611no—
722#416—1224no—
723C2×#103—611no—
724C2×#103—611no—
725C2×#103—611no—
726C2×#103—611no—
727C2×#102—611no—
728C2×#102—611no—
729C2×#102—611no—
730C2×#102—611no—
731C2×#102—611no—
732C2×#102—611no—
733C2×#102—611no—
734C2×#102—611no—
735C2×#102—1224no—
736C2×C22⋊C8—611no—
737C2×C22⋊C8—611no—
738C2×C4×C8—611no—
739#388—1221no—
740#387—1221no—
741#386—1221no—
742#382—611no—
743#380—611no—
744#380—611no—
745C4×C4⋊C4—611no—
746C4×C22⋊C4—1221no—
747#340—611no—
748#340—611no—
749#340—611no—
750#340—611no—
751C61#2241411yescharacteristic, complemented, Sylow
752C25—1221no—
753C2×#41—611no—
754C2×#41—611no—
755C2×#41—611no—
756C2×#41—1221no—
757C2×#41—1221no—
758C2×#41—1222no—
759C2×#41—1222no—
760C2×#41—2441no—
761C2×#41—2441no—
762C2×#41C2×#692311yescharacteristic, complemented
763C22×Q8—611no—
764C22×D4—611no—
765C22×D4—611no—
766C22×D4—611no—
767C22×D4—611no—
768C22×D4—611no—
769C22×D4—611no—
770C22×D4—1221no—
771C22×D4—1221no—
772C22×D4—1221no—
773C22×D4—1222no—
774C22×D4—1222no—
775C22×D4—1221no—
776C22×D4—1221no—
777C22×D4—2441no—
778C22×D4—2441no—
779C22×D4C2×#692311yescharacteristic
780C23×C4—611no—
781C23×C4—611no—
782C23×C4—1221no—
783C23×C4—1221no—
784C23×C4—1221no—
785C22×C8—611no—
786C22×C8—611no—
787C22×C8—611no—
788C22×C8—611no—
789C22×C8—1222no—
790C22×C8—1222no—
791C22×C8—1221no—
792C22×C8—1221no—
793C22×C8—1221no—
794C22×C8—1221no—
795C22×C8—2441no—
796C22×C8—2441no—
797#124—611no—
798#124—611no—
799#124—611no—
800#124—1221no—
801#124—1221no—
802#124C2×#692311yescharacteristic, complemented
803#123—21no—
804#123—1221no—
805#123—1221no—
806#123—1221no—
807#123—1221no—
808#123—1221no—
809#123—1221no—
810#123—1221no—
811C22⋊Q8—611no—
812C22⋊Q8—611no—
813C22⋊Q8—611no—
814C22⋊Q8—1221no—
815C22⋊Q8—1221no—
816C22⋊Q8C2×#692311yescharacteristic
817#121—21no—
818#121—611no—
819#121—611no—
820#121—611no—
821#121—1221no—
822#121—1221no—
823#121—1221no—
824#121—1221no—
825#121—1221no—
826#121—1221no—
827#121—1221no—
828#121—1221no—
829#121—1221no—
830#121C2×#692311yescharacteristic, complemented
831#120—21no—
832#120—1221no—
833#120—1221no—
834#120—1221no—
835#120—1221no—
836#120—1221no—
837#120—1221no—
838#120—1221no—
839C4×D4—611no—
840C4×D4—611no—
841C4×D4—611no—
842C4×D4—611no—
843C4×D4—611no—
844C4×D4—611no—
845C4×D4—611no—
846C4×D4—611no—
847C4×D4—611no—
848C4×D4—611no—
849C4×D4—1221no—
850C4×D4—1221no—
851C4×D4C2×#692311yescharacteristic
852C4×D4C2×#692311yescharacteristic, complemented
853#117—1222no—
854#117—2441no—
855C2×C4⋊C4—611no—
856C2×C4⋊C4—611no—
857C2×C4⋊C4—611no—
858C2×C4⋊C4—611no—
859C2×C4⋊C4—611no—
860C2×C4⋊C4—611no—
861C2×C4⋊C4—1221no—
862C2×C4⋊C4—1222no—
863C2×C4⋊C4—1221no—
864C2×C4⋊C4—2441no—
865C2×C22⋊C4—21no—
866C2×C22⋊C4—611no—
867C2×C22⋊C4—611no—
868C2×C22⋊C4—1221no—
869C2×C22⋊C4—1221no—
870C2×C22⋊C4—1221no—
871C2×C22⋊C4—1221no—
872C2×C22⋊C4—1221no—
873C2×C22⋊C4—1221no—
874C2×C22⋊C4—1221no—
875C2×C22⋊C4—1221no—
876C2×C22⋊C4—1221no—
877C2×C22⋊C4—1221no—
878C2×C22⋊C4—1221no—
879C2×C22⋊C4—1221no—
880C2×C22⋊C4—1221no—
881C2×C22⋊C4—1221no—
882C2×C22⋊C4—1221no—
883C2×C42—611no—
884C2×C42—1221no—
885C2×C42—1221no—
886C4⋊C8—1221no—
887C4⋊C8—1221no—
888#103—1222no—
889#103—1222no—
890#103—2441no—
891#103—2441no—
892#102—614no—
893#102—1222no—
894#102—1222no—
895#102—1222no—
896#102—1222no—
897#102—1222no—
898#102—2441no—
899#102—2441no—
900C22⋊C8—1221no—
901C22⋊C8—1221no—
902C22⋊C8—1221no—
903C22⋊C8—1221no—
904C4×C8—1221no—
905C4×C8—1221no—
906#95—1221no—
907#95—1221no—
908#95—1221no—
909#95—1221no—
910#95—1221no—
911C24—21no—
912C24—611no—
913C24—611no—
914C24—1221no—
915C24—1221no—
916C24—1221no—
917C24—1221no—
918C24—1221no—
919C24—4881no—
920C24—4881no—
921C24—2442no—
922C24—2442no—
923C24—2442no—
924C24—2442no—
925#41—22no—
926#41—41no—
927#41—1222no—
928#41—1222no—
929#41—1222no—
930#41—2441no—
931#41—2442no—
932#41—2442no—
933#41—2441no—
934#41—2442no—
935#41—2442no—
936#41—2441no—
937C2×Q8—611no—
938C2×Q8—1221no—
939C2×Q8—1221no—
940C2×Q8—1221no—
941C2×Q8—1221no—
942C2×Q8—1221no—
943C2×Q8C22×#692311yescharacteristic
944C2×D4—22no—
945C2×D4—21no—
946C2×D4—21no—
947C2×D4—21no—
948C2×D4—41no—
949C2×D4—612no—
950C2×D4—612no—
951C2×D4—611no—
952C2×D4—611no—
953C2×D4—611no—
954C2×D4—611no—
955C2×D4—611no—
956C2×D4—1222no—
957C2×D4—1221no—
958C2×D4—1221no—
959C2×D4—1221no—
960C2×D4—1221no—
961C2×D4—1221no—
962C2×D4—1221no—
963C2×D4—1221no—
964C2×D4—1221no—
965C2×D4—1221no—
966C2×D4—1221no—
967C2×D4—1221no—
968C2×D4—1221no—
969C2×D4—1222no—
970C2×D4—1222no—
971C2×D4—1222no—
972C2×D4—1222no—
973C2×D4—1221no—
974C2×D4—1221no—
975C2×D4—1221no—
976C2×D4—1221no—
977C2×D4—1221no—
978C2×D4—4881no—
979C2×D4—4881no—
980C2×D4—2441no—
981C2×D4—2441no—
982C2×D4—2441no—
983C2×D4—2442no—
984C2×D4—2442no—
985C2×D4—2442no—
986C2×D4—2442no—
987C2×D4—2442no—
988C2×D4—2442no—
989C2×D4—2442no—
990C2×D4—2442no—
991C2×D4C22⋊#692311yescharacteristic
992C2×D4C22×#692311yescharacteristic
993C2×D4C22×#692311yescharacteristic
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—611no—
997C22×C4—611no—
998C22×C4—611no—
999C22×C4—611no—
1000C22×C4—611no—
1001C22×C4—611no—
1002C22×C4—611no—
1003C22×C4—611no—
1004C22×C4—611no—
1005C22×C4—611no—
1006C22×C4—611no—
1007C22×C4—1221no—
1008C22×C4—1221no—
1009C22×C4—1221no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1221no—
1014C22×C4—1221no—
1015C22×C4—1221no—
1016C22×C4—1221no—
1017C22×C4—1221no—
1018C22×C4—1221no—
1019C22×C4—1221no—
1020C22×C4—1221no—
1021C22×C4—1221no—
1022C22×C4—1221no—
1023C22×C4—1221no—
1024C22×C4—1221no—
1025C22×C4—1221no—
1026C22×C4—1221no—
1027C22×C4—4881no—
1028C22×C4—4881no—
1029C22×C4—4881no—
1030C22×C4—2442no—
1031C22×C4—2442no—
1032C22×C4—2442no—
1033C22×C4—2442no—
1034C22×C4C22×#692311yescharacteristic
1035C22×C4C22×#692311yescharacteristic
1036C2×C8—612no—
1037C2×C8—1221no—
1038C2×C8—1221no—
1039C2×C8—1221no—
1040C2×C8—1221no—
1041C2×C8—1221no—
1042C2×C8—1221no—
1043C2×C8—1221no—
1044C2×C8—1221no—
1045C2×C8—1221no—
1046C2×C8—1221no—
1047C2×C8—1221no—
1048C2×C8—2442no—
1049C2×C8—2442no—
1050C2×C8—2442no—
1051C2×C8—2442no—
1052C4⋊C4—21no—
1053C4⋊C4—611no—
1054C4⋊C4—611no—
1055C4⋊C4—611no—
1056C4⋊C4—612no—
1057C4⋊C4—611no—
1058C4⋊C4—1221no—
1059C4⋊C4—1221no—
1060C4⋊C4—1221no—
1061C4⋊C4—1221no—
1062C4⋊C4—1221no—
1063C4⋊C4—1221no—
1064C4⋊C4—1221no—
1065C4⋊C4—1221no—
1066C4⋊C4—1221no—
1067C4⋊C4—1221no—
1068C4⋊C4—1221no—
1069C4⋊C4—2442no—
1070C4⋊C4C22⋊#692311yescharacteristic
1071C4⋊C4C22×#692311yescharacteristic
1072C22⋊C4—21no—
1073C22⋊C4—21no—
1074C22⋊C4—21no—
1075C22⋊C4—21no—
1076C22⋊C4—21no—
1077C22⋊C4—611no—
1078C22⋊C4—611no—
1079C22⋊C4—611no—
1080C22⋊C4—611no—
1081C22⋊C4—611no—
1082C22⋊C4—611no—
1083C22⋊C4—1221no—
1084C22⋊C4—1221no—
1085C22⋊C4—1221no—
1086C22⋊C4—1221no—
1087C22⋊C4—1221no—
1088C22⋊C4—1221no—
1089C22⋊C4—1221no—
1090C22⋊C4—1221no—
1091C22⋊C4—1221no—
1092C22⋊C4—1221no—
1093C22⋊C4—1221no—
1094C22⋊C4—1221no—
1095C22⋊C4—1221no—
1096C22⋊C4—1221no—
1097C22⋊C4—1221no—
1098C22⋊C4—4881no—
1099C22⋊C4—2442no—
1100C22⋊C4—2442no—
1101C22⋊C4C22⋊#692311yescharacteristic
1102C22⋊C4C22⋊#692311yescharacteristic
1103C42—611no—
1104C42—611no—
1105C42—611no—
1106C42—4881no—
1107C42—2442no—
1108C42C22×#692311yescharacteristic
1109C23—21no—
1110C23—21no—
1111C23—42no—
1112C23—42no—
1113C23—81no—
1114C23—611no—
1115C23—612no—
1116C23—612no—
1117C23—611no—
1118C23—611no—
1119C23—1221no—
1120C23—1221no—
1121C23—1221no—
1122C23—1221no—
1123C23—1221no—
1124C23—1221no—
1125C23—1221no—
1126C23—1222no—
1127C23—1222no—
1128C23—1221no—
1129C23—1221no—
1130C23—1221no—
1131C23—1221no—
1132C23—1221no—
1133C23—4881no—
1134C23—4881no—
1135C23—4881no—
1136C23—4884no—
1137C23—4884no—
1138C23—4884no—
1139C23—4884no—
1140C23—2442no—
1141C23—2442no—
1142C23—2441no—
1143C23—2441no—
1144C23—2441no—
1145C23—2441no—
1146C23—2442no—
1147C23—2441no—
1148C23—2441no—
1149C23—2442no—
1150C23—2441no—
1151C23—2441no—
1152C23—2441no—
1153C23—2441no—
1154C23—2442no—
1155C23—2442no—
1156C23C2×C22⋊#692311yescharacteristic
1157C23C2×C22⋊#692311yescharacteristic
1158Q8—21no—
1159Q8—21no—
1160Q8—1221no—
1161Q8—1221no—
1162Q8—2441no—
1163Q8—2441no—
1164D4—22no—
1165D4—21no—
1166D4—21no—
1167D4—21no—
1168D4—42no—
1169D4—42no—
1170D4—81no—
1171D4—612no—
1172D4—1222no—
1173D4—1222no—
1174D4—1222no—
1175D4—1222no—
1176D4—1222no—
1177D4—1221no—
1178D4—1221no—
1179D4—1221no—
1180D4—4881no—
1181D4—4881no—
1182D4—4881no—
1183D4—2442no—
1184D4—2442no—
1185D4—2441no—
1186D4—2441no—
1187D4—2442no—
1188D4—2442no—
1189D4—2442no—
1190D4—2442no—
1191D4D4×#692312yes—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—42no—
1199C2×C4—81no—
1200C2×C4—611no—
1201C2×C4—611no—
1202C2×C4—611no—
1203C2×C4—611no—
1204C2×C4—611no—
1205C2×C4—611no—
1206C2×C4—611no—
1207C2×C4—611no—
1208C2×C4—611no—
1209C2×C4—1221no—
1210C2×C4—1221no—
1211C2×C4—1221no—
1212C2×C4—1221no—
1213C2×C4—1221no—
1214C2×C4—1221no—
1215C2×C4—1221no—
1216C2×C4—1221no—
1217C2×C4—1221no—
1218C2×C4—1221no—
1219C2×C4—1221no—
1220C2×C4—1221no—
1221C2×C4—1221no—
1222C2×C4—1221no—
1223C2×C4—1221no—
1224C2×C4—1221no—
1225C2×C4—1221no—
1226C2×C4—1221no—
1227C2×C4—1221no—
1228C2×C4—1221no—
1229C2×C4—1222no—
1230C2×C4—1221no—
1231C2×C4—1221no—
1232C2×C4—4881no—
1233C2×C4—4881no—
1234C2×C4—4881no—
1235C2×C4—4884no—
1236C2×C4—2442no—
1237C2×C4—2442no—
1238C2×C4—2441no—
1239C2×C4—2441no—
1240C2×C4—2441no—
1241C2×C4—2441no—
1242C2×C4—2442no—
1243C2×C4—2441no—
1244C2×C4—2441no—
1245C2×C4—2441no—
1246C2×C4—2441no—
1247C2×C4—2441no—
1248C2×C4—2441no—
1249C2×C4—2441no—
1250C2×C4—2441no—
1251C2×C4—2441no—
1252C2×C4—2441no—
1253C2×C4—2441no—
1254C2×C4C2×C22⋊#692311yescharacteristic
1255C2×C4C2×C22⋊#692311yescharacteristic
1256C2×C4C2×C22⋊#692311yescharacteristic
1257C2×C4C2×C22⋊#692311yescharacteristic
1258C2×C4C23×#692311yescharacteristic
1259C8—1222no—
1260C8—2441no—
1261C8—2441no—
1262C8—2441no—
1263C22—21no—
1264C22—21no—
1265C22—21no—
1266C22—22no—
1267C22—21no—
1268C22—21no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—84no—
1275C22—611no—
1276C22—611no—
1277C22—611no—
1278C22—611no—
1279C22—611no—
1280C22—611no—
1281C22—612no—
1282C22—1222no—
1283C22—1222no—
1284C22—1222no—
1285C22—1222no—
1286C22—1221no—
1287C22—1221no—
1288C22—1221no—
1289C22—1222no—
1290C22—1221no—
1291C22—1221no—
1292C22—4884no—
1293C22—4884no—
1294C22—4881no—
1295C22—4881no—
1296C22—4881no—
1297C22—4881no—
1298C22—4884no—
1299C22—2441no—
1300C22—2441no—
1301C22—2441no—
1302C22—2441no—
1303C22—2442no—
1304C22—2442no—
1305C22—2442no—
1306C22—2442no—
1307C22—2441no—
1308C22—2441no—
1309C22—2441no—
1310C22—2441no—
1311C22—2441no—
1312C22#1684075212yescomplemented
1313C22C22×C22⋊#692311yescharacteristic
1314C4—21no—
1315C4—21no—
1316C4—21no—
1317C4—21no—
1318C4—41no—
1319C4—41no—
1320C4—611no—
1321C4—611no—
1322C4—1221no—
1323C4—1221no—
1324C4—1221no—
1325C4—1221no—
1326C4—4881no—
1327C4—4881no—
1328C4—4881no—
1329C4—2442no—
1330C4—2441no—
1331C4—2441no—
1332C4C2×D4×#692311yescharacteristic
1333C4#1684082911yescharacteristic
1334C2—22no—
1335C2—41no—
1336C2—42no—
1337C2—81no—
1338C2—611no—
1339C2—611no—
1340C2—611no—
1341C2—611no—
1342C2—1222no—
1343C2—4881no—
1344C2—2441no—
1345C2—2442no—
1346C2D4×C22⋊#692311yescharacteristic
1347C2C2×#1684075211yescharacteristic
1348C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#546×D61C2
cosocleC2×C4×D61C24
hypercenter#546#6923
hypocenterC61#22414
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. D4×D61⋊C8C2semidirect
2. C2×#16840752C2semidirect
3. C22×#14519839C2semidirect
4. #21462335C2semidirect
5. #21461987C2semidirect
6. #21461948C2semidirect
7. #21461833C2semidirect
8. #21461832C2semidirect
9. #21461807C2semidirect
10. #21461804C2semidirect
11. #21461689C2semidirect
12. #21461659C2semidirect
13. #21461657C2semidirect
14. C4×#14519839C2semidirect
17. C22×D61⋊C8C22semidirect
18. C2×#14519856C22semidirect
24. D61⋊(C4⋊C8)C22semidirect
26. C2×#14519840C22semidirect
27. C2×#14519840C22semidirect
28. C2×#14519840C22semidirect
29. C2×#14519840C22semidirect
40. D61⋊(C22⋊C8)C22semidirect
41. C4×D61⋊C8C22semidirect
45. #16840706C22semidirect
47. #16840704C22semidirect
48. C4×C4⋊#6923C22semidirect
50. #16840635C22semidirect
51. #16840635C22semidirect
52. #16840635C22semidirect
53. #16840635C22semidirect
56. #16840409C4semidirect
57. #16840408C4semidirect
58. #16840407C4semidirect
59. #16840406C4semidirect
60. #16840405C4semidirect
62. #16840403C4semidirect
65. #16840400C4semidirect
76. C61×#546C4semidirect
117. #14519839D4semidirect
130. C2×#11758226C2×C4semidirect
132. C2×#11758222C2×C4semidirect
134. C2×#11758224C2×C4semidirect
159. #14519766C2×C4semidirect
160. #14519765C2×C4semidirect
161. #14519764C2×C4semidirect
177. #14519752C2×C4semidirect
179. #14519751C2×C4semidirect
187. #14519748C2×C4semidirect
196. C4×D244C2×C4semidirect
197. D4×Dic61C2×C4semidirect
199. #14519739C2×C4semidirect
225. C2×#41×C61C2×C4semidirect
227. #124×C61C2×C4semidirect
231. #121×C61C2×C4semidirect
234. C4×D4×C61C2×C4semidirect
601. C22×C61#416semidirect
633. C2×D61#416semidirect
705. #546#6923semidirect
751. C61#22414semidirect
762. C2×#41C2×#6923semidirect
802. #124C2×#6923semidirect
830. #121C2×#6923semidirect
852. C4×D4C2×#6923semidirect
1312. C22#16840752semidirect

Maximal subgroups

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

subgroupindex
D4×D61⋊C82
C2×#168407522
C22×#145198392
#214623352
#214619872
#214619482
#214618332
#214618322
#214618072
#214618042
#214616892
#214616592
#214616572
C4×#145198392
#546×D612
#2241461