Finite Group Databasebeta

← #30620162

Subgroups — #30620162

Order 15616.

1498 conjugacy classes of subgroups.

The subgroup lattice has 1270 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×#14519840C211yesmaximal, characteristic, complemented
4#21462335C211yesmaximal, characteristic, complemented
5#21461987C211yesmaximal, characteristic, complemented
6#21461948C211yesmaximal, characteristic, complemented
7#21461833C211yesmaximal, characteristic, complemented
8#21461832C211yesmaximal, characteristic, complemented
9#21461806C211yesmaximal, characteristic, complemented
10#21461805C211yesmaximal, characteristic, complemented
11#21461690C211yesmaximal, characteristic, complemented
12#21461659C211yesmaximal, characteristic, complemented
13#21461658C211yesmaximal, characteristic, complemented
14C4×#14519840C211yesmaximal, characteristic, complemented
15#548×D61C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20#16840790—21no—
21#16840789—21no—
22#16840789—21no—
23D4×#92420—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic
25#16840752—24no—
26C2×#14519840—24no—
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30C2×#14519840C2211yescharacteristic
31C2×#14519840C2211yescharacteristic
32C2×#14519840C2211yescharacteristic
33C2×#14519840C2211yescharacteristic
34C2×#14519840C2211yescharacteristic
35C2×#14519839C2211yescharacteristic
36C2×#14519839C2211yescharacteristic
37C2×#14519839C2211yescharacteristic
38C2×#14519839C2211yescharacteristic
39D61⋊(C22⋊C8)C2211yescharacteristic
40D61⋊(C22⋊C8)C2211yescharacteristic
41C4×D61⋊C8C2211yescharacteristic
42#16840712—21no—
43#16840711—21no—
44#16840710—21no—
45#16840706C2211yescharacteristic
46#16840704C2211yescharacteristic
47#16840704C2211yescharacteristic
48C4×C4⋊#6923C2211yescharacteristic
49C22⋊C4×#6923—21no—
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840635C2211yescharacteristic
53#16840635C2211yescharacteristic
54C2×#41×D61C2211yescharacteristic
55C22×Q8×D61C2211yescharacteristic
56#16840424C411yescharacteristic, complemented
57#16840423C411yescharacteristic, complemented
58#16840422—21no—
59#16840422C411yescharacteristic, complemented
60#16840421—21no—
61#16840421C411yescharacteristic, complemented
62#16840420—21no—
63#16840420C411yescharacteristic, complemented
64#16840419C411yescharacteristic, complemented
65#16840418—21no—
66#16840418C411yescharacteristic, complemented
67#124×D61—21no—
68#124×D61C2211yescharacteristic
69C22⋊Q8×D61—21no—
70C22⋊Q8×D61C2211yescharacteristic
71#121×D61—21no—
72#121×D61C2211yescharacteristic
73C4×Q8×D61C2211yescharacteristic
74C4×D4×D61—21no—
75C4×D4×D61C2211yescharacteristic
76C61×#548C411yescharacteristic, 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—22no—
109#14519840—22no—
110#14519840—22no—
111#14519840—41no—
112#14519840—41no—
113#14519840D414yescomplemented
114#14519839—22no—
115#14519839—22no—
116#14519839—41no—
117#14519839—41no—
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—
129C2×#11758226C2×C411yescharacteristic, complemented
130C2×#11758222—21no—
131C2×#11758222C2×C411yescharacteristic, complemented
132C2×#11758224—21no—
133C2×#11758224C2×C411yescharacteristic, complemented
134#41×D61—22no—
135#41×D61—22no—
136#41×D61—41no—
137#41×D61—41no—
138C22×Dic122—21no—
139C22×Dic122C2×C411yescharacteristic
140C2×Q8×D61—21no—
141C2×Q8×D61—21no—
142C2×Q8×D61—22no—
143C2×Q8×D61—22no—
144C2×Q8×D61—41no—
145C2×Q8×D61—41no—
146C2×Q8×D61C2×C411yescharacteristic
147C2×Q8×D61C2×C411yescharacteristic
148C2×Q8×D61C2311yescharacteristic
149C2×Q8×D61C2311yescharacteristic
150C2×D4×D61—21no—
151C2×D4×D61—21no—
152C2×D4×D61D411yescharacteristic
153C2×D4×D61C2311yescharacteristic
154C22×C4×D61—21no—
155C22×C4×D61—21no—
156C22×C4×D61C2311yescharacteristic
157C22×C4×D61C2311yescharacteristic
158#14519766—21no—
159#14519766C2×C411yescharacteristic, complemented
160#14519765—21no—
161#14519765C2×C411yescharacteristic, complemented
162#14519764—21no—
163#14519764C2×C411yescharacteristic, complemented
164#14519763—21no—
165#14519763—21no—
166#14519763—21no—
167#14519763—21no—
168#14519763—21no—
169#14519763—21no—
170#14519757—21no—
171#14519757C2×C411yescharacteristic, complemented
172#14519756—21no—
173#14519756C2×C411yescharacteristic, complemented
174#14519755—21no—
175#14519755—21no—
176#14519755—21no—
177#14519754—21no—
178#14519754—21no—
179#14519754—21no—
180#14519753—21no—
181#14519753C2×C411yescharacteristic, complemented
182#14519752—21no—
183#14519752C2×C411yescharacteristic
184#14519751—21no—
185#14519751C2×C411yescharacteristic
186#14519750—21no—
187#14519750—21no—
188#14519750—21no—
189#14519749—21no—
190#14519749—21no—
191#14519749—21no—
192#14519748—21no—
193#14519748C2×C411yescharacteristic
194Q8×Dic61C2×C411yescharacteristic, complemented
195C4×Dic122—21no—
196C4×Dic122C2×C411yescharacteristic, complemented
197#14519742—21no—
198#14519742C2×C411yescharacteristic, complemented
199C4×D244—21no—
200C4×D244C2×C411yescharacteristic
201D4×Dic61—21no—
202D4×Dic61D411yescharacteristic
203#14519739—21no—
204#14519739D411yescharacteristic
205C4×C22⋊D61—21no—
206C4×C22⋊D61—21no—
207C4×C22⋊D61C2×C411yescharacteristic
208C4×C22⋊D61C2×C411yescharacteristic
209#14519737—21no—
210#14519737—21no—
211#14519737D411yescharacteristic
212#14519737D411yescharacteristic
213C4⋊C4×D61—21no—
214C4⋊C4×D61—21no—
215C4⋊C4×D61D411yescharacteristic
216C4⋊C4×D61C2311yescharacteristic
217C22⋊C4×D61—21no—
218C22⋊C4×D61—21no—
219C22⋊C4×D61—21no—
220C22⋊C4×D61—21no—
221C22⋊C4×D61D411yescharacteristic
222C22⋊C4×D61D411yescharacteristic
223C42×D61—21no—
224C42×D61C2311yescharacteristic
225C2×#41×C61C2×C411yescharacteristic, complemented
226C22×Q8×C61C2×C411yescharacteristic
227#124×C61—21no—
228#124×C61C2×C411yescharacteristic, complemented
229C22⋊Q8×C61—21no—
230C22⋊Q8×C61C2×C411yescharacteristic, complemented
231#121×C61—21no—
232#121×C61C2×C411yescharacteristic
233C4×Q8×C61C2×C411yescharacteristic, complemented
234C4×D4×C61—21no—
235C4×D4×C61C2×C411yescharacteristic
236C23×D61—21no—
237C23×D61C2×D411yescharacteristic
238C23×D61C2×D411yescharacteristic
239C22×#6923—21no—
240C22×#6923—21no—
241C22×#6923—21no—
242C22×#6923—21no—
243C22×#6923—42no—
244C22×#6923—42no—
245C22×#6923—81no—
246#41×C61—22no—
247#41×C61—41no—
248C2×Q8×C61—21no—
249C2×Q8×C61—22no—
250C2×Q8×C61—41no—
251C2×Q8×C61C22×C411yescharacteristic
252C2×Q8×C61C22×C411yescharacteristic
253C2×D4×C61—21no—
254C2×D4×C61—21no—
255C2×D4×C61C22⋊C411yescharacteristic
256C2×D4×C61C22×C411yescharacteristic
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61C22×C411yescharacteristic
260C22×C4×C61C22×C411yescharacteristic
261C2×C22⋊D61—21no—
262C2×C22⋊D61—21no—
263C2×C22⋊D61—21no—
264C2×C22⋊D61—21no—
265C2×C22⋊D61—21no—
266C2×C22⋊D61C22⋊C411yescharacteristic
267C2×C22⋊D61C22⋊C411yescharacteristic
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61C2×D411yescharacteristic
271C22×Dic61C2×D411yescharacteristic
272#11758226—22no—
273#11758226—41no—
274Q8×D61—21no—
275Q8×D61—21no—
276Q8×D61—22no—
277Q8×D61—21no—
278Q8×D61—21no—
279Q8×D61—21no—
280Q8×D61—21no—
281Q8×D61—22no—
282Q8×D61—41no—
283Q8×D61—41no—
284Q8×D61—42no—
285Q8×D61—42no—
286Q8×D61—42no—
287Q8×D61—42no—
288Q8×D61C2×D412yes—
289Q8×D61#4112yes—
290#11758224—22no—
291#11758224—41no—
292#11758224—42no—
293#11758224—42no—
294D4×D61—22no—
295D4×D61—22no—
296D4×D61—21no—
297D4×D61—21no—
298D4×D61—21no—
299D4×D61—21no—
300D4×D61—42no—
301D4×D61—42no—
302D4×D61—42no—
303D4×D61—42no—
304#11758222—22no—
305#11758222—42no—
306#11758222—42no—
307#11758222—41no—
308C2×D244—21no—
309C2×D244—21no—
310C2×D244C22⋊C411yescharacteristic
311C2×D244C22×C411yescharacteristic
312C2×C4×D61—21no—
313C2×C4×D61—21no—
314C2×C4×D61—21no—
315C2×C4×D61—21no—
316C2×C4×D61—21no—
317C2×C4×D61—21no—
318C2×C4×D61—21no—
319C2×C4×D61—21no—
320C2×C4×D61—21no—
321C2×C4×D61—21no—
322C2×C4×D61—21no—
323C2×C4×D61—21no—
324C2×C4×D61—21no—
325C2×C4×D61—21no—
326C2×C4×D61—21no—
327C2×C4×D61—42no—
328C2×C4×D61—42no—
329C2×C4×D61—42no—
330C2×C4×D61—42no—
331C2×C4×D61C22×C411yescharacteristic
332C2×C4×D61C22×C411yescharacteristic
333C2×C4×D61C2×D411yescharacteristic
334C2×C4×D61C2×D411yescharacteristic
335C2×C4×D61C2×D411yescharacteristic
336C2×C4×D61C2×D411yescharacteristic
337C2×C4×D61C2×D411yescharacteristic
338C2×C4×D61C2×D411yescharacteristic
339C2×C4×D61C2411yescharacteristic
340C2×Dic122—21no—
341C2×Dic122—22no—
342C2×Dic122—21no—
343C2×Dic122—21no—
344C2×Dic122—21no—
345C2×Dic122—21no—
346C2×Dic122—41no—
347C2×Dic122—42no—
348C2×Dic122—42no—
349C2×Dic122C22×C411yescharacteristic
350C2×Dic122C22×C411yescharacteristic
351C22⋊#6923—42no—
352C22⋊#6923—42no—
353C22⋊#6923—81no—
354C2×#92420—21no—
355C2×#92420—21no—
356C2×#92420—21no—
357C2×#92420—21no—
358C2×#92420—42no—
359C2×#92420—42no—
360C4⋊#6923—21no—
361C4⋊#6923—21no—
362C4⋊#6923—21no—
363C4⋊#6923—21no—
364C4⋊#6923—21no—
365C4⋊#6923—21no—
366C4⋊#6923—21no—
367C4⋊#6923—42no—
368C4⋊#6923C2×D412yes—
369C4×#6923—42no—
370C4×#6923—81no—
371D61⋊C8—21no—
372D61⋊C8—21no—
373D61⋊C8—21no—
374D61⋊C8—21no—
375D61⋊C8—21no—
376D61⋊C8—21no—
377D61⋊C8—21no—
378D61⋊C8—42no—
379D61⋊C8—42no—
380D61⋊C8C2×D412yes—
381C4⋊C4×C61—21no—
382C4⋊C4×C61—21no—
383C4⋊C4×C61C22⋊C411yescharacteristic
384C4⋊C4×C61C22×C411yescharacteristic
385C22⋊C4×C61—21no—
386C22⋊C4×C61—21no—
387C22⋊C4×C61—21no—
388C22⋊C4×C61—21no—
389C22⋊C4×C61C22⋊C411yescharacteristic
390C22⋊C4×C61C22⋊C411yescharacteristic
391C42×C61—21no—
392C42×C61C22×C411yescharacteristic
393C22⋊Dic61—21no—
394C22⋊Dic61—21no—
395C22⋊Dic61—21no—
396C22⋊Dic61—21no—
397C22⋊Dic61C22⋊C411yescharacteristic
398C22⋊Dic61C22⋊C411yescharacteristic
399#11758198—21no—
400#11758198—21no—
401#11758198—21no—
402#11758198—21no—
403#11758198—21no—
404#11758198—21no—
405#11758198—21no—
406#11758198—21no—
407#11758198C22⋊C411yescharacteristic
408#11758198C22⋊C411yescharacteristic
409#11758198C22⋊C411yescharacteristic
410#11758198C22⋊C411yescharacteristic
411C4⋊Dic61—21no—
412C4⋊Dic61—21no—
413C4⋊Dic61C22⋊C411yescharacteristic
414C4⋊Dic61C22×C411yescharacteristic
415#11758196—21no—
416#11758196—21no—
417#11758196—21no—
418#11758196—21no—
419#11758196—21no—
420#11758196C22⋊C411yescharacteristic
421#11758196C22⋊C411yescharacteristic
422C4×Dic61—21no—
423C4×Dic61—21no—
424C4×Dic61—21no—
425C4×Dic61C22×C411yescharacteristic
426C4×Dic61C2×D411yescharacteristic
427C4×Dic61C2×D411yescharacteristic
428C23×C61—21no—
429C23×C61C2×C22⋊C411yescharacteristic
430C23×C61C2×C22⋊C411yescharacteristic
431C22×D61—21no—
432C22×D61—21no—
433C22×D61—21no—
434C22×D61—21no—
435C22×D61—21no—
436C22×D61—21no—
437C22×D61—21no—
438C22×D61—21no—
439C22×D61—21no—
440C22×D61—21no—
441C22×D61—21no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61C2×C22⋊C411yescharacteristic
449C22×D61C2×C22⋊C411yescharacteristic
450C22×D61#13512yes—
451C22×D61#13512yes—
452C22×D61C22×D411yescharacteristic
453C2×#6923—22no—
454C2×#6923—41no—
455C2×#6923—41no—
456C2×#6923—41no—
457C2×#6923—41no—
458C2×#6923—41no—
459C2×#6923—41no—
460C2×#6923—41no—
461C2×#6923—41no—
462C2×#6923—41no—
463C2×#6923—41no—
464C2×#6923—41no—
465C2×#6923—84no—
466Q8×C61—21no—
467Q8×C61—21no—
468Q8×C61—21no—
469Q8×C61—42no—
470Q8×C61C4×D412yes—
471D4×C61—22no—
472D4×C61—21no—
473D4×C61—21no—
474D4×C61—42no—
475D4×C61—42no—
476C2×C4×C61—21no—
477C2×C4×C61—21no—
478C2×C4×C61—21no—
479C2×C4×C61—21no—
480C2×C4×C61—21no—
481C2×C4×C61—21no—
482C2×C4×C61—21no—
483C2×C4×C61—42no—
484C2×C4×C61—42no—
485C2×C4×C61C2×C22⋊C411yescharacteristic
486C2×C4×C61C2×C22⋊C411yescharacteristic
487C2×C4×C61C2×C22⋊C411yescharacteristic
488C2×C4×C61C2×C22⋊C411yescharacteristic
489C2×C4×C61C23×C411yescharacteristic
490C22⋊D61—22no—
491C22⋊D61—22no—
492C22⋊D61—42no—
493C22⋊D61—42no—
494C22⋊D61—42no—
495C22⋊D61—42no—
496C22⋊D61—41no—
497C22⋊D61—41no—
498C2×Dic61—21no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—21no—
502C2×Dic61—21no—
503C2×Dic61—21no—
504C2×Dic61—21no—
505C2×Dic61—42no—
506C2×Dic61—42no—
507C2×Dic61C2×C22⋊C411yescharacteristic
508C2×Dic61C2×C22⋊C411yescharacteristic
509C2×Dic61C2×C22⋊C411yescharacteristic
510C2×Dic61C2×C22⋊C411yescharacteristic
511C2×Dic61C22×D411yescharacteristic
512D244—22no—
513D244—21no—
514D244—21no—
515D244—42no—
516D244—42no—
517C4×D61—21no—
518C4×D61—21no—
519C4×D61—22no—
520C4×D61—21no—
521C4×D61—21no—
522C4×D61—22no—
523C4×D61—21no—
524C4×D61—21no—
525C4×D61—21no—
526C4×D61—21no—
527C4×D61—21no—
528C4×D61—21no—
529C4×D61—21no—
530C4×D61—21no—
531C4×D61—21no—
532C4×D61—21no—
533C4×D61—21no—
534C4×D61—21no—
535C4×D61—42no—
536C4×D61—42no—
537C4×D61—42no—
538C4×D61—42no—
539C4×D61—41no—
540C4×D61—41no—
541C4×D61—41no—
542C4×D61—41no—
543C4×D61C22×D411yescharacteristic
544C4×D61C2×#4111yescharacteristic
545C4×D61H(5,𝔽2)11yescharacteristic
546C4×D61H(5,𝔽2)11yescharacteristic
547Dic122—21no—
548Dic122—22no—
549Dic122—22no—
550Dic122—21no—
551Dic122—21no—
552Dic122—42no—
553Dic122—42no—
554Dic122—42no—
555Dic122—41no—
556Dic122—41no—
557Dic122C4×D412yes—
558#92420—22no—
559#92420—41no—
560#92420—41no—
561#92420—41no—
562#22416—611nomaximal, Sylow
563C22×C61—21no—
564C22×C61—21no—
565C22×C61—21no—
566C22×C61—21no—
567C22×C61—21no—
568C22×C61—41no—
569C22×C61—41no—
570C22×C61—41no—
571C22×C61#41612yescomplemented
572C22×C61C22×C22⋊C411yescharacteristic
573C2×D61—21no—
574C2×D61—21no—
575C2×D61—22no—
576C2×D61—22no—
577C2×D61—22no—
578C2×D61—22no—
579C2×D61—21no—
580C2×D61—21no—
581C2×D61—21no—
582C2×D61—41no—
583C2×D61—41no—
584C2×D61—41no—
585C2×D61—41no—
586C2×D61—41no—
587C2×D61—41no—
588C2×D61—41no—
589C2×D61—81no—
590C2×D61—81no—
591C2×D61—81no—
592C2×D61—81no—
593C2×D61#41612yescomplemented
594C2×D61D4211yescharacteristic
595C2×D61#54611yescharacteristic
596C2×D61C2×#13511yescharacteristic
597C2×D61C2×#13511yescharacteristic
598C2×D61#57711yescharacteristic
599C2×D61#57811yescharacteristic
600#6923—42no—
601#6923—81no—
602#6923—81no—
603#6923—81no—
604C4×C61—22no—
605C4×C61—21no—
606C4×C61—21no—
607C4×C61—21no—
608C4×C61—21no—
609C4×C61—41no—
610C4×C61—41no—
611C4×C61C2×C4×D411yescharacteristic
612C4×C61#51811yescharacteristic
613Dic61—22no—
614Dic61—21no—
615Dic61—21no—
616Dic61—21no—
617Dic61—21no—
618Dic61—41no—
619Dic61—41no—
620Dic61D4211yescharacteristic
621Dic61#54611yescharacteristic
622C2×#548—611no—
623C2×C8×D4—611no—
624C2×#416—611no—
625C22×#103—611no—
626#2352—611no—
627#1983—611no—
628#1958—611no—
629#1893—611no—
630#1892—611no—
631#1874—611no—
632#1873—611no—
633#1805—611no—
634#1788—611no—
635#1787—611no—
636C4×#103—611no—
637C2×C61—22no—
638C2×C61—41no—
639C2×C61—81no—
640C2×C61D4×C22⋊C411yescharacteristic
641C2×C61C2×#41611yescharacteristic
642C2×C61#289811yescharacteristic
643D61—22no—
644D61—41no—
645D61—81no—
646D61#328211yescharacteristic
647D61#328511yescharacteristic
648D61#330011yescharacteristic
649D61#330111yescharacteristic
650C22×#41—611no—
651C23×Q8—611no—
652C23×C8—611no—
653C23×C8—611no—
654#548—611no—
655#548—611no—
656#548—611no—
657#548—611no—
658#548—611no—
659#548—611no—
660#548—611no—
661#548—1221no—
662#548—1221no—
663#548—1221no—
664#548—1221no—
665#548#692311yescharacteristic, complemented
666C2×#124—611no—
667C2×#124—1221no—
668C2×C22⋊Q8—611no—
669C2×C22⋊Q8—1221no—
670C2×#121—611no—
671C2×#121—1221no—
672C2×C4×Q8—611no—
673C2×C4×D4—611no—
674C2×C4×D4—1221no—
675C2×#117—611no—
676C22×C4⋊C4—611no—
677C8×D4—1221no—
678C8×D4—1221no—
679C8×D4—1221no—
680C8×D4—1221no—
681C2×C4⋊C8—611no—
682#416—1224no—
683C2×#103—611no—
684C2×#103—611no—
685C2×#103—611no—
686C2×#103—611no—
687C2×#103—611no—
688C2×#103—611no—
689C2×#103—611no—
690C2×#103—611no—
691C2×#103—1224no—
692C2×#102—611no—
693C2×#102—611no—
694C2×#102—611no—
695C2×#102—611no—
696C2×C22⋊C8—611no—
697C2×C22⋊C8—611no—
698C2×C4×C8—611no—
699#388—1221no—
700#387—1221no—
701#386—1221no—
702#382—611no—
703#380—611no—
704#380—611no—
705C4×C4⋊C4—611no—
706C4×C22⋊C4—1221no—
707#340—611no—
708#340—611no—
709#340—611no—
710#340—611no—
711C61#2241611yescharacteristic, complemented, Sylow
712C2×#41—611no—
713C2×#41—611no—
714C2×#41—611no—
715C2×#41—1221no—
716C2×#41—1221no—
717C2×#41—1222no—
718C2×#41—1222no—
719C2×#41—2441no—
720C2×#41—2441no—
721C2×#41C2×#692311yescharacteristic, complemented
722C22×Q8—611no—
723C22×Q8—611no—
724C22×Q8—611no—
725C22×Q8—611no—
726C22×Q8—611no—
727C22×Q8—1221no—
728C22×Q8—1221no—
729C22×Q8—1221no—
730C22×Q8—1222no—
731C22×Q8—1222no—
732C22×Q8—2441no—
733C22×Q8—2441no—
734C22×Q8C2×#692311yescharacteristic
735C22×D4—611no—
736C22×D4—611no—
737C22×D4—1221no—
738C22×D4—1221no—
739C23×C4—611no—
740C23×C4—611no—
741C23×C4—1221no—
742C23×C4—1221no—
743C23×C4—1221no—
744C22×C8—611no—
745C22×C8—611no—
746C22×C8—611no—
747C22×C8—611no—
748C22×C8—1222no—
749C22×C8—1222no—
750C22×C8—1221no—
751C22×C8—1221no—
752C22×C8—1221no—
753C22×C8—1221no—
754C22×C8—2441no—
755C22×C8—2441no—
756#124—21no—
757#124—611no—
758#124—611no—
759#124—611no—
760#124—1221no—
761#124—1221no—
762#124—1221no—
763#124—1221no—
764#124—1221no—
765#124—1221no—
766#124—1221no—
767#124—1221no—
768#124—1221no—
769#124C2×#692311yescharacteristic, complemented
770C22⋊Q8—21no—
771C22⋊Q8—611no—
772C22⋊Q8—611no—
773C22⋊Q8—611no—
774C22⋊Q8—1221no—
775C22⋊Q8—1221no—
776C22⋊Q8—1221no—
777C22⋊Q8—1221no—
778C22⋊Q8—1221no—
779C22⋊Q8—1221no—
780C22⋊Q8—1221no—
781C22⋊Q8—1221no—
782C22⋊Q8—1221no—
783C22⋊Q8C2×#692311yescharacteristic, complemented
784#121—21no—
785#121—611no—
786#121—611no—
787#121—611no—
788#121—1221no—
789#121—1221no—
790#121—1221no—
791#121—1221no—
792#121—1221no—
793#121—1221no—
794#121—1221no—
795#121—1221no—
796#121—1221no—
797#121C2×#692311yescharacteristic
798C4×Q8—611no—
799C4×Q8—611no—
800C4×Q8—611no—
801C4×Q8—1221no—
802C4×Q8—1221no—
803C4×Q8C2×#692311yescharacteristic, complemented
804C4×D4—21no—
805C4×D4—611no—
806C4×D4—611no—
807C4×D4—611no—
808C4×D4—611no—
809C4×D4—611no—
810C4×D4—611no—
811C4×D4—611no—
812C4×D4—1221no—
813C4×D4—1221no—
814C4×D4—1221no—
815C4×D4—1221no—
816C4×D4—1221no—
817C4×D4—1221no—
818C4×D4—1221no—
819C4×D4C2×#692311yescharacteristic
820#117—1222no—
821#117—2441no—
822C2×C4⋊C4—611no—
823C2×C4⋊C4—611no—
824C2×C4⋊C4—611no—
825C2×C4⋊C4—611no—
826C2×C4⋊C4—611no—
827C2×C4⋊C4—611no—
828C2×C4⋊C4—1221no—
829C2×C4⋊C4—1221no—
830C2×C4⋊C4—1222no—
831C2×C4⋊C4—1221no—
832C2×C4⋊C4—2441no—
833C2×C22⋊C4—611no—
834C2×C22⋊C4—611no—
835C2×C22⋊C4—1221no—
836C2×C22⋊C4—1221no—
837C2×C22⋊C4—1221no—
838C2×C22⋊C4—1221no—
839C2×C22⋊C4—1221no—
840C2×C22⋊C4—1221no—
841C2×C22⋊C4—1221no—
842C2×C42—611no—
843C2×C42—1221no—
844C2×C42—1221no—
845C2×C42—1221no—
846C4⋊C8—1221no—
847C4⋊C8—1221no—
848#103—614no—
849#103—1222no—
850#103—1222no—
851#103—1222no—
852#103—1222no—
853#103—1222no—
854#103—2441no—
855#103—2441no—
856#102—1222no—
857#102—1222no—
858#102—2441no—
859#102—2441no—
860C22⋊C8—1221no—
861C22⋊C8—1221no—
862C22⋊C8—1221no—
863C22⋊C8—1221no—
864C4×C8—1221no—
865C4×C8—1221no—
866#95—1221no—
867#95—1221no—
868#95—1221no—
869#95—1221no—
870#95—1221no—
871C24—611no—
872C24—611no—
873C24—1221no—
874#41—22no—
875#41—41no—
876#41—1222no—
877#41—1222no—
878#41—1222no—
879#41—2441no—
880#41—2442no—
881#41—2442no—
882#41—2441no—
883#41—2442no—
884#41—2442no—
885#41—2441no—
886C2×Q8—21no—
887C2×Q8—22no—
888C2×Q8—41no—
889C2×Q8—612no—
890C2×Q8—612no—
891C2×Q8—611no—
892C2×Q8—611no—
893C2×Q8—1221no—
894C2×Q8—1221no—
895C2×Q8—1221no—
896C2×Q8—1221no—
897C2×Q8—1222no—
898C2×Q8—1221no—
899C2×Q8—1221no—
900C2×Q8—1221no—
901C2×Q8—1221no—
902C2×Q8—1221no—
903C2×Q8—1221no—
904C2×Q8—1221no—
905C2×Q8—1222no—
906C2×Q8—1222no—
907C2×Q8—2441no—
908C2×Q8—2442no—
909C2×Q8—2442no—
910C2×Q8—2442no—
911C2×Q8—2442no—
912C2×Q8—2441no—
913C2×Q8—2441no—
914C2×Q8—2442no—
915C2×Q8—2442no—
916C2×Q8C22×#692311yescharacteristic
917C2×Q8C22×#692311yescharacteristic
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—611no—
921C2×D4—611no—
922C2×D4—611no—
923C2×D4—611no—
924C2×D4—1221no—
925C2×D4—1221no—
926C2×D4—1221no—
927C2×D4—1221no—
928C2×D4—1221no—
929C2×D4—1221no—
930C2×D4—1221no—
931C2×D4—1222no—
932C2×D4—1222no—
933C2×D4—1221no—
934C2×D4—1221no—
935C2×D4—1221no—
936C2×D4—1221no—
937C2×D4—2442no—
938C2×D4—2442no—
939C2×D4—2442no—
940C2×D4—2442no—
941C2×D4C22⋊#692311yescharacteristic
942C2×D4C22×#692311yescharacteristic
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—611no—
946C22×C4—611no—
947C22×C4—611no—
948C22×C4—611no—
949C22×C4—611no—
950C22×C4—611no—
951C22×C4—611no—
952C22×C4—611no—
953C22×C4—611no—
954C22×C4—611no—
955C22×C4—611no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1221no—
977C22×C4—4881no—
978C22×C4—2442no—
979C22×C4—2442no—
980C22×C4—2442no—
981C22×C4—2442no—
982C22×C4—2442no—
983C22×C4—2442no—
984C22×C4C22×#692311yescharacteristic
985C22×C4C22×#692311yescharacteristic
986C2×C8—612no—
987C2×C8—1221no—
988C2×C8—1221no—
989C2×C8—1221no—
990C2×C8—1221no—
991C2×C8—1221no—
992C2×C8—1221no—
993C2×C8—1221no—
994C2×C8—1221no—
995C2×C8—1221no—
996C2×C8—1221no—
997C2×C8—1221no—
998C2×C8—2442no—
999C2×C8—2442no—
1000C2×C8—2442no—
1001C2×C8—2442no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—611no—
1005C4⋊C4—611no—
1006C4⋊C4—611no—
1007C4⋊C4—612no—
1008C4⋊C4—611no—
1009C4⋊C4—1221no—
1010C4⋊C4—1221no—
1011C4⋊C4—1221no—
1012C4⋊C4—1221no—
1013C4⋊C4—1221no—
1014C4⋊C4—1221no—
1015C4⋊C4—1221no—
1016C4⋊C4—1221no—
1017C4⋊C4—1221no—
1018C4⋊C4—1221no—
1019C4⋊C4—1221no—
1020C4⋊C4—1221no—
1021C4⋊C4—1221no—
1022C4⋊C4—1221no—
1023C4⋊C4—2442no—
1024C4⋊C4C22⋊#692311yescharacteristic
1025C4⋊C4C22×#692311yescharacteristic
1026C22⋊C4—21no—
1027C22⋊C4—21no—
1028C22⋊C4—21no—
1029C22⋊C4—21no—
1030C22⋊C4—611no—
1031C22⋊C4—611no—
1032C22⋊C4—611no—
1033C22⋊C4—611no—
1034C22⋊C4—611no—
1035C22⋊C4—611no—
1036C22⋊C4—1221no—
1037C22⋊C4—1221no—
1038C22⋊C4—1221no—
1039C22⋊C4—1221no—
1040C22⋊C4—1221no—
1041C22⋊C4—1221no—
1042C22⋊C4—1221no—
1043C22⋊C4—1221no—
1044C22⋊C4—1221no—
1045C22⋊C4—1221no—
1046C22⋊C4—1221no—
1047C22⋊C4—1221no—
1048C22⋊C4—4881no—
1049C22⋊C4—2442no—
1050C22⋊C4—2442no—
1051C22⋊C4C22⋊#692311yescharacteristic
1052C22⋊C4C22⋊#692311yescharacteristic
1053C42—21no—
1054C42—611no—
1055C42—611no—
1056C42—611no—
1057C42—1221no—
1058C42—1221no—
1059C42—1221no—
1060C42—4881no—
1061C42—2442no—
1062C42C22×#692311yescharacteristic
1063C23—21no—
1064C23—611no—
1065C23—612no—
1066C23—612no—
1067C23—611no—
1068C23—611no—
1069C23—1221no—
1070C23—1221no—
1071C23—1221no—
1072C23—1221no—
1073C23—1221no—
1074C23—1221no—
1075C23—1221no—
1076C23—1221no—
1077C23—1221no—
1078C23—1221no—
1079C23—1221no—
1080C23—2441no—
1081C23—2441no—
1082C23—2441no—
1083C23—2441no—
1084C23—2441no—
1085C23—2441no—
1086C23C2×C22⋊#692311yescharacteristic
1087C23C2×C22⋊#692311yescharacteristic
1088Q8—21no—
1089Q8—21no—
1090Q8—21no—
1091Q8—42no—
1092Q8—612no—
1093Q8—1222no—
1094Q8—1222no—
1095Q8—1221no—
1096Q8—1221no—
1097Q8—1221no—
1098Q8—2442no—
1099Q8—2442no—
1100Q8—2441no—
1101Q8—2441no—
1102Q8—2442no—
1103Q8D4×#692312yes—
1104D4—22no—
1105D4—21no—
1106D4—21no—
1107D4—42no—
1108D4—42no—
1109D4—1222no—
1110D4—1222no—
1111D4—1222no—
1112D4—1221no—
1113D4—1221no—
1114D4—2442no—
1115D4—2442no—
1116D4—2441no—
1117D4—2441no—
1118D4—2442no—
1119D4—2442no—
1120D4—2442no—
1121D4—2442no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—611no—
1132C2×C4—611no—
1133C2×C4—611no—
1134C2×C4—611no—
1135C2×C4—611no—
1136C2×C4—611no—
1137C2×C4—611no—
1138C2×C4—611no—
1139C2×C4—611no—
1140C2×C4—1221no—
1141C2×C4—1221no—
1142C2×C4—1221no—
1143C2×C4—1221no—
1144C2×C4—1221no—
1145C2×C4—1221no—
1146C2×C4—1221no—
1147C2×C4—1221no—
1148C2×C4—1221no—
1149C2×C4—1221no—
1150C2×C4—1221no—
1151C2×C4—1221no—
1152C2×C4—1222no—
1153C2×C4—1222no—
1154C2×C4—1221no—
1155C2×C4—1221no—
1156C2×C4—1221no—
1157C2×C4—1221no—
1158C2×C4—1221no—
1159C2×C4—1221no—
1160C2×C4—1221no—
1161C2×C4—1221no—
1162C2×C4—1221no—
1163C2×C4—1222no—
1164C2×C4—1221no—
1165C2×C4—1221no—
1166C2×C4—4884no—
1167C2×C4—2442no—
1168C2×C4—2442no—
1169C2×C4—2442no—
1170C2×C4—2442no—
1171C2×C4—2441no—
1172C2×C4—2441no—
1173C2×C4—2441no—
1174C2×C4—2441no—
1175C2×C4—2442no—
1176C2×C4—2442no—
1177C2×C4—2441no—
1178C2×C4—2441no—
1179C2×C4—2441no—
1180C2×C4—2441no—
1181C2×C4—2441no—
1182C2×C4—2441no—
1183C2×C4—2441no—
1184C2×C4—2441no—
1185C2×C4—2441no—
1186C2×C4—2441no—
1187C2×C4—2441no—
1188C2×C4C2×C22⋊#692311yescharacteristic
1189C2×C4C2×C22⋊#692311yescharacteristic
1190C2×C4C2×C22⋊#692311yescharacteristic
1191C2×C4C2×C22⋊#692311yescharacteristic
1192C2×C4C23×#692311yescharacteristic
1193C8—1222no—
1194C8—2441no—
1195C8—2441no—
1196C8—2441no—
1197C22—21no—
1198C22—21no—
1199C22—21no—
1200C22—21no—
1201C22—21no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—611no—
1206C22—611no—
1207C22—611no—
1208C22—611no—
1209C22—611no—
1210C22—611no—
1211C22—612no—
1212C22—1222no—
1213C22—1222no—
1214C22—1222no—
1215C22—1222no—
1216C22—1221no—
1217C22—1221no—
1218C22—1221no—
1219C22—1221no—
1220C22—1221no—
1221C22—4881no—
1222C22—4881no—
1223C22—4881no—
1224C22—4881no—
1225C22—2441no—
1226C22—2441no—
1227C22—2441no—
1228C22—2441no—
1229C22—2441no—
1230C22—2441no—
1231C22—2441no—
1232C22#1684075212yescomplemented
1233C22C22×C22⋊#692311yescharacteristic
1234C4—21no—
1235C4—21no—
1236C4—22no—
1237C4—21no—
1238C4—21no—
1239C4—41no—
1240C4—41no—
1241C4—611no—
1242C4—611no—
1243C4—1221no—
1244C4—1221no—
1245C4—1222no—
1246C4—1221no—
1247C4—1221no—
1248C4—4881no—
1249C4—4881no—
1250C4—4881no—
1251C4—2442no—
1252C4—2441no—
1253C4—2441no—
1254C4C2×D4×#692311yescharacteristic
1255C4#1684082911yescharacteristic
1256C2—22no—
1257C2—41no—
1258C2—81no—
1259C2—611no—
1260C2—611no—
1261C2—611no—
1262C2—611no—
1263C2—1222no—
1264C2—4881no—
1265C2—2441no—
1266C2D4×C22⋊#692311yescharacteristic
1267C2C2×#1684075211yescharacteristic
1268C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#548C4
socleC22×C61C22×C22⋊C4
prime radical#548×D61C2
cosocleC2×C4×D61C24
hypercenter#548#6923
hypocenterC61#22416
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. D4×D61⋊C8C2semidirect
2. C2×#16840752C2semidirect
3. C22×#14519840C2semidirect
4. #21462335C2semidirect
5. #21461987C2semidirect
6. #21461948C2semidirect
7. #21461833C2semidirect
8. #21461832C2semidirect
9. #21461806C2semidirect
10. #21461805C2semidirect
11. #21461690C2semidirect
12. #21461659C2semidirect
13. #21461658C2semidirect
14. C4×#14519840C2semidirect
56. #16840424C4semidirect
57. #16840423C4semidirect
59. #16840422C4semidirect
61. #16840421C4semidirect
63. #16840420C4semidirect
64. #16840419C4semidirect
66. #16840418C4semidirect
76. C61×#548C4semidirect
113. #14519840D4semidirect
129. C2×#11758226C2×C4semidirect
131. C2×#11758222C2×C4semidirect
133. C2×#11758224C2×C4semidirect
159. #14519766C2×C4semidirect
161. #14519765C2×C4semidirect
163. #14519764C2×C4semidirect
171. #14519757C2×C4semidirect
173. #14519756C2×C4semidirect
181. #14519753C2×C4semidirect
194. Q8×Dic61C2×C4semidirect
196. C4×Dic122C2×C4semidirect
198. #14519742C2×C4semidirect
225. C2×#41×C61C2×C4semidirect
228. #124×C61C2×C4semidirect
230. C22⋊Q8×C61C2×C4semidirect
233. C4×Q8×C61C2×C4semidirect
571. C22×C61#416semidirect
593. C2×D61#416semidirect
665. #548#6923semidirect
711. C61#22416semidirect
721. C2×#41C2×#6923semidirect
769. #124C2×#6923semidirect
783. C22⋊Q8C2×#6923semidirect
803. C4×Q8C2×#6923semidirect
1232. 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×#145198402
#214623352
#214619872
#214619482
#214618332
#214618322
#214618062
#214618052
#214616902
#214616592
#214616582
C4×#145198402
#548×D612
#2241661