Finite Group Databasebeta

← #30545142

Subgroups — #30545142

Order 15616.

1872 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2#21454990C212yesmaximal, complemented
3#21454983C212yesmaximal, complemented
4#21454982C211yesmaximal, characteristic, complemented
5#21454980C211yesmaximal, characteristic, complemented
6#21454978C211yesmaximal, characteristic, complemented
7#21454974C211yesmaximal, characteristic, complemented
8#21454970C211yesmaximal, characteristic, complemented
9#21454968C211yesmaximal, characteristic, complemented
10#21454964C211yesmaximal, characteristic, complemented
11#21454956C212yesmaximal, complemented
12#21454953C212yesmaximal, complemented
13#21454771C211yesmaximal, characteristic, complemented
14Q8×#11758189C211yesmaximal, characteristic, complemented
15#21454555C211yesmaximal, characteristic, complemented
16#21454555C212yesmaximal, complemented
17#21454552C212yesmaximal, complemented
18D4×#11758189C211yesmaximal, characteristic, complemented
19#21454453C212yesmaximal, complemented
20#21454447C211yesmaximal, characteristic, complemented
21#21454380C212yesmaximal, complemented
22#423×D61C211yesmaximal, characteristic, complemented
23C61×#2993C211yesmaximal, characteristic, complemented
24C22×#11758189C2212yes—
25C2×M16×D61C2212yes—
26C2×M16×D61C2212yes—
27#16840299C2211yescharacteristic
28#16840298C411yescharacteristic
29#16840297C411yescharacteristic
30#16840296C2211yescharacteristic
31#16840295C412yes—
32#16840294C2211yescharacteristic
33#16840293C411yescharacteristic
34#16840292C2212yes—
35#16840291C411yescharacteristic
36#16840290C2212yes—
37#16840289C412yes—
38#126×D61C412yes—
39#125×D61C411yescharacteristic
40#124×D61C411yescharacteristic
41#123×D61C412yes—
42C22⋊Q8×D61C411yescharacteristic
43#121×D61C411yescharacteristic
44C4×Q8×D61C2211yescharacteristic
45C4×D4×D61C2211yescharacteristic
46C4×D4×D61C2212yes—
47#117×D61C2212yes—
48C2×C42×D61C2211yescharacteristic
49#16839893C2211yescharacteristic, complemented
50#16839892C2212yescomplemented
51#16839892C2211yescharacteristic, complemented
52#16839891C2212yescomplemented
53#16839890C2212yescomplemented
54#16839889C2212yescomplemented
55#16839889C2211yescharacteristic, complemented
56Q8×#92418C2211yescharacteristic, complemented
57C8×Dic122C2211yescharacteristic, complemented
58#16839886C2211yescharacteristic, complemented
59#16839841C2211yescharacteristic, complemented
60#16839840C2211yescharacteristic, complemented
61#16839840C2212yescomplemented
62#16839839C2211yescharacteristic, complemented
63#16839838C2212yescomplemented
64#16839837C2212yescomplemented
65#16839836C2212yescomplemented
66#16839836C2212yescomplemented
67#16839836C2212yescomplemented
68#16839835C2212yescomplemented
69#16839834C2212yescomplemented
70#16839833C2212yescomplemented
71#16839832C2212yescomplemented
72#16839831C2212yescomplemented
73#16839831C2212yescomplemented
74#16839831C2212yescomplemented
75#16839830C2212yescomplemented
76C8×D244C2212yescomplemented
77C8×D244C2211yescharacteristic, complemented
78D4×#92418C2211yescharacteristic, complemented
79#16839827C2212yescomplemented
80#16839827C2211yescharacteristic, complemented
81C8×C22⋊D61C2212yescomplemented
82#16839825C2212yescomplemented
83#16839824C2212yescomplemented
84#16839823C2212yescomplemented
85#16839822C2212yescomplemented
86#16839822C2212yescomplemented
87#16839821C2212yescomplemented
88#16839820C2212yescomplemented
89#16839820C2212yescomplemented
90#16839818C2211yescharacteristic, complemented
91#16839818C2211yescharacteristic, complemented
92#16839816C2211yescharacteristic, complemented
93#16839816C2211yescharacteristic, complemented
94#16839815C2211yescharacteristic, complemented
95#16839813C2211yescharacteristic, complemented
96#16839813C2211yescharacteristic, complemented
97#16839790C2212yescomplemented
98#16839789C2212yescomplemented
99#16839788C2212yescomplemented
100#16839787C2212yescomplemented
101#16839787C2212yescomplemented
102#16839787C2212yescomplemented
103#16839787C2212yescomplemented
104#16839786C2211yescharacteristic, complemented
105#16839785C2212yescomplemented
106#16839784C2212yes—
107#16839784C2211yescharacteristic
108#16839784C2211yescharacteristic
109#16839784C2211yescharacteristic
110#16839784C2212yes—
111#16839784C2212yes—
112#16839784C2211yescharacteristic
113C4⋊C8×D61C2212yescomplemented
114C4⋊C8×D61C2211yescharacteristic, complemented
115C4⋊C8×D61C2211yescharacteristic, complemented
116#16839724C2211yescharacteristic
117#16839724C2211yescharacteristic
118#16839724C2212yes—
119#16839724C2212yes—
120#16839714C2212yes—
121C4×#11758189C2211yescharacteristic
122C4×#11758189C2211yescharacteristic
123C4×#11758189C2212yes—
124C61×#529C2211yescharacteristic
125C61×#446C2211yescharacteristic, complemented
126C8×Q8×C61C2211yescharacteristic, complemented
127C61×#436C2211yescharacteristic, complemented
128C61×#436C2212yescomplemented
129C61×#435C2212yescomplemented
130C8×D4×C61C2211yescharacteristic, complemented
131C61×#433C2212yescomplemented
132C61×#431C2211yescharacteristic, complemented
133C61×#424C2212yescomplemented
134C61×#423C2211yescharacteristic, complemented
135C2×Q8×D61C2×C411yescharacteristic
136C2×D4×D61C2×C412yes—
137C2×D4×D61C2×C411yescharacteristic
138C22×C4×D61C2×C411yescharacteristic
139C22×C4×D61C2×C411yescharacteristic
140C22×C4×D61C2311yescharacteristic
141C22×C4×D61C2312yes—
142C2×#11758194C2312yes—
143C2×#11758194C2312yes—
144C2×#11758189—44no—
145C2×#11758189C2311yescharacteristic
146C2×#11758189C2311yescharacteristic
147C2×#11758189C2311yescharacteristic
148C2×#11758189C2312yes—
149C2×#11758189C2311yescharacteristic
150C2×#11758189C2312yes—
151C2×#11758189C2312yes—
152C2×#11758189C2312yes—
153M16×D61—44no—
154M16×D61—44no—
155C22×#92418C2312yes—
156C2×C8×D61C2312yes—
157C2×C8×D61C2312yes—
158C2×C8×D61C2312yes—
159C2×C8×D61C2312yes—
160#14519772C2×C412yes—
161#14519772C2×C412yes—
162#14519772C2×C412yes—
163#14519771C2×C412yes—
164#14519770C2×C412yes—
165#14519770C2×C412yes—
166#14519770C2×C412yes—
167#14519769C2×C411yescharacteristic
168#14519768C2×C411yescharacteristic
169#14519768C2×C411yescharacteristic
170#14519767C2×C412yes—
171#14519767C2×C412yes—
172#14519766C2×C411yescharacteristic
173#14519765C2×C411yescharacteristic
174#14519764C2×C411yescharacteristic
175#14519763C2×C412yes—
176#14519763C2×C412yes—
177#14519762C2×C412yes—
178#14519762C2×C412yes—
179#14519761C2×C412yes—
180#14519760C2×C412yes—
181#14519759C2×C412yes—
182#14519759C2×C412yes—
183#14519758C2×C412yes—
184#14519757C2×C411yescharacteristic
185#14519756C2×C411yescharacteristic
186#14519755C2×C412yes—
187#14519754C2×C412yes—
188#14519753C2×C411yescharacteristic
189#14519752C2×C411yescharacteristic
190#14519751C2×C411yescharacteristic
191#14519750C2×C412yes—
192#14519749C2×C412yes—
193#14519748C2×C411yescharacteristic
194Q8×Dic61C2×C411yescharacteristic
195C4×Dic122C2312yes—
196C4×Dic122C2311yescharacteristic
197#14519742C2×C412yes—
198#14519742C2×C411yescharacteristic
199C4×D244C2312yes—
200C4×D244C2311yescharacteristic
201D4×Dic61C2×C412yes—
202D4×Dic61C2×C411yescharacteristic
203#14519739C2×C412yes—
204#14519739C2×C411yescharacteristic
205C4×C22⋊D61C2312yes—
206C4×C22⋊D61C2312yes—
207C4×C22⋊D61C2312yes—
208#14519737C2×C412yes—
209#14519737C2×C412yes—
210#14519737C2×C412yes—
211#14519736C2312yes—
212#14519735C2×C412yes—
213#14519735C2×C412yes—
214#14519734C2312yes—
215#14519734C2312yes—
216#14519733C2×C412yes—
217#14519733C2×C412yes—
218C4⋊C4×D61C2×C412yes—
219C4⋊C4×D61C2×C412yes—
220C4⋊C4×D61C2×C411yescharacteristic
221C4⋊C4×D61C2×C412yes—
222C4⋊C4×D61C2×C411yescharacteristic
223C4⋊C4×D61C2×C412yes—
224C22⋊C4×D61C2×C412yes—
225C22⋊C4×D61C2×C412yes—
226C22⋊C4×D61C2×C412yes—
227C22⋊C4×D61C2×C412yes—
228C22⋊C4×D61C2×C412yes—
229C2×C4×Dic61C2×C411yescharacteristic
230C2×C4×Dic61C2×C411yescharacteristic
231C2×C4×Dic61C2311yescharacteristic
232C42×D61C2×C411yescharacteristic
233C42×D61C2×C411yescharacteristic
234C42×D61C2×C411yescharacteristic
235C42×D61C2×C411yescharacteristic
236C42×D61C2311yescharacteristic
237C42×D61C2311yescharacteristic
238C42×D61C2311yescharacteristic
239C42×D61C2311yescharacteristic
240C42×D61C2312yes—
241C4⋊#92418C2312yes—
242C4⋊#92418C2311yescharacteristic
243C4⋊#92418C2311yescharacteristic
244C4⋊#92418C2311yescharacteristic
245C4⋊#92418C2312yes—
246C4⋊#92418C2312yes—
247C4⋊#92418C2311yescharacteristic
248#14519706C2312yes—
249#14519706C2312yes—
250#14519706C2312yes—
251#14519706C2312yes—
252#14519706C2311yescharacteristic
253#14519706C2311yescharacteristic
254#14519706C2312yes—
255#14519706C2312yes—
256#14519706C2312yes—
257#14519706C2312yes—
258#14519706C2311yescharacteristic
259#14519706C2311yescharacteristic
260C22⋊#92418C2311yescharacteristic
261C22⋊#92418C2311yescharacteristic
262C22⋊#92418C2312yes—
263C22⋊#92418C2312yes—
264#14519689C2311yescharacteristic
265#14519689C2311yescharacteristic
266#14519689C2311yescharacteristic
267#14519689C2311yescharacteristic
268#14519689C2312yes—
269#14519689C2312yes—
270#14519689C2312yes—
271#14519689C2312yes—
272#14519688C2312yes—
273#14519687C2311yescharacteristic
274#14519687C2311yescharacteristic
275#14519687C2311yescharacteristic
276#14519687C2311yescharacteristic
277#14519687C2312yes—
278#14519687C2312yes—
279C4×#92418C2311yescharacteristic
280C4×#92418C2311yescharacteristic
281C4×#92418C2312yes—
282C8×Dic61C2312yes—
283C8×Dic61C2312yes—
284C2×M16×C61C2312yes—
285C2×M16×C61C2312yes—
286C22×C8×C61C2312yes—
287#126×C61C2×C412yes—
288#125×C61C2×C411yescharacteristic
289#124×C61C2×C411yescharacteristic
290#123×C61C2×C412yes—
291C22⋊Q8×C61C2×C411yescharacteristic
292#121×C61C2×C411yescharacteristic
293C4×Q8×C61C2311yescharacteristic
294C4×D4×C61C2312yes—
295C4×D4×C61C2311yescharacteristic
296#117×C61C2312yes—
297C2×C42×C61C2311yescharacteristic
298C4⋊C8×C61C2312yes—
299C4⋊C8×C61C2311yescharacteristic
300C4⋊C8×C61C2311yescharacteristic
301C4⋊C8×C61C2311yescharacteristic
302C4⋊C8×C61C2312yes—
303C4⋊C8×C61C2312yes—
304C4⋊C8×C61C2311yescharacteristic
305C22⋊C8×C61C2311yescharacteristic
306C22⋊C8×C61C2311yescharacteristic
307C22⋊C8×C61C2312yes—
308C22⋊C8×C61C2312yes—
309#97×C61C2312yes—
310C4×C8×C61C2311yescharacteristic
311C4×C8×C61C2311yescharacteristic
312C4×C8×C61C2312yes—
313C23×D61C22×C411yescharacteristic
314C23×D61C22×C412yes—
315C2×Q8×C61C22×C411yescharacteristic
316C2×D4×C61C22×C411yescharacteristic
317C2×D4×C61C22×C412yes—
318C22×C4×C61C22×C411yescharacteristic
319C22×C4×C61C22×C411yescharacteristic
320C22×C4×C61C2411yescharacteristic
321C22×C4×C61C2412yes—
322C2×C22⋊D61C22×C412yes—
323C2×C22⋊D61C22×C412yes—
324C2×C22⋊D61C22×C412yes—
325C22×Dic61C22×C411yescharacteristic
326C22×Dic61C22×C412yes—
327C22×Dic61C22×C411yescharacteristic
328C22×Dic61C22×C411yescharacteristic
329Q8×D61—42no—
330D4×D61—42no—
331D4×D61—44no—
332C2×D244C22×C412yes—
333C2×D244C22×C411yescharacteristic
334C2×C4×D61—22no—
335C2×C4×D61—24no—
336C2×C4×D61—22no—
337C2×C4×D61—24no—
338C2×C4×D61—42no—
339C2×C4×D61—42no—
340C2×C4×D61C22×C411yescharacteristic
341C2×C4×D61C22×C411yescharacteristic
342C2×C4×D61C22×C411yescharacteristic
343C2×C4×D61C22×C411yescharacteristic
344C2×C4×D61C22×C411yescharacteristic
345C2×C4×D61C22×C411yescharacteristic
346C2×C4×D61C22×C412yes—
347C2×C4×D61C22×C412yes—
348C2×C4×D61C22×C411yescharacteristic
349C2×C4×D61C22×C411yescharacteristic
350C2×C4×D61C22×C411yescharacteristic
351C2×C4×D61C22×C411yescharacteristic
352C2×C4×D61C22×C412yes—
353C2×C4×D61C22×C412yes—
354C2×C4×D61C2411yescharacteristic
355C2×C4×D61C2412yes—
356C2×C4×D61C2411yescharacteristic
357C2×Dic122C22×C411yescharacteristic
358C2×Dic122C22×C412yes—
359M16×C61—42no—
360M16×C61—42no—
361C2×C8×C61—42no—
362C2×C8×C61C2411yescharacteristic
363C2×C8×C61C2411yescharacteristic
364C2×C8×C61C2411yescharacteristic
365C2×C8×C61C2411yescharacteristic
366C2×C8×C61C2412yes—
367C2×C8×C61C2412yes—
368C4⋊C4×C61C22×C412yes—
369C4⋊C4×C61C22×C412yes—
370C4⋊C4×C61C22×C411yescharacteristic
371C4⋊C4×C61C22×C412yes—
372C4⋊C4×C61C22×C411yescharacteristic
373C4⋊C4×C61C22×C412yes—
374C22⋊C4×C61C22×C412yes—
375C22⋊C4×C61C22×C412yes—
376C22⋊C4×C61C22×C412yes—
377C22⋊C4×C61C22×C412yes—
378C22⋊C4×C61C22×C412yes—
379C42×C61C22×C411yescharacteristic
380C42×C61C22×C411yescharacteristic
381C42×C61C2411yescharacteristic
382C42×C61C2412yes—
383C42×C61C2411yescharacteristic
384C22⋊Dic61C22×C412yes—
385C22⋊Dic61C22×C412yes—
386C22⋊Dic61C22×C412yes—
387C22⋊Dic61C22×C412yes—
388C22⋊Dic61C22×C412yes—
389#11758198C22×C412yes—
390#11758198C22×C412yes—
391#11758198C22×C412yes—
392#11758198C22×C412yes—
393#11758198C22×C412yes—
394#11758198C22×C412yes—
395#11758198C22×C412yes—
396#11758198C22×C412yes—
397#11758198C22×C412yes—
398#11758198C22×C412yes—
399C4⋊Dic61C22×C412yes—
400C4⋊Dic61C22×C412yes—
401C4⋊Dic61C22×C411yescharacteristic
402C4⋊Dic61C22×C412yes—
403C4⋊Dic61C22×C411yescharacteristic
404C4⋊Dic61C22×C412yes—
405#11758196C22×C412yes—
406#11758196C22×C412yes—
407#11758196C22×C412yes—
408#11758196C22×C412yes—
409#11758196C22×C412yes—
410#11758196C22×C412yes—
411#11758196C22×C412yes—
412#11758196C22×C412yes—
413#11758196C22×C412yes—
414#11758196C22×C412yes—
415C4×Dic61C22×C411yescharacteristic
416C4×Dic61C22×C411yescharacteristic
417C4×Dic61C22×C411yescharacteristic
418C4×Dic61C22×C411yescharacteristic
419C4×Dic61C22×C411yescharacteristic
420C4×Dic61C22×C411yescharacteristic
421C4×Dic61C22×C411yescharacteristic
422C4×Dic61C22×C411yescharacteristic
423C4×Dic61C22×C411yescharacteristic
424C4×Dic61C22×C411yescharacteristic
425C4×Dic61C22×C412yes—
426C4×Dic61C22×C412yes—
427C4×Dic61C2412yes—
428C4×Dic61C2411yescharacteristic
429C4×Dic61C2411yescharacteristic
430#11758194—42no—
431#11758194—42no—
432C2×#92418—42no—
433C2×#92418C2411yescharacteristic
434C2×#92418C2412yes—
435C2×#92418C2411yescharacteristic
436C2×#92418C2411yescharacteristic
437C2×#92418C2412yes—
438C2×#92418C2411yescharacteristic
439#11758189—22no—
440#11758189—24no—
441#11758189—24no—
442#11758189—22no—
443#11758189—22no—
444#11758189—22no—
445#11758189—42no—
446#11758189—42no—
447C8×D61—42no—
448C8×D61—42no—
449C8×D61—42no—
450C8×D61—42no—
451C23×C61C23×C412yes—
452C23×C61C23×C411yescharacteristic
453C22×D61—22no—
454C22×D61—22no—
455C22×D61—24no—
456C22×D61—41no—
457C22×D61—42no—
458C22×D61—42no—
459C22×D61C23×C412yes—
460C22×D61C23×C411yescharacteristic
461C22×D61C23×C411yescharacteristic
462Q8×C61—22no—
463D4×C61—22no—
464D4×C61—42no—
465C2×C4×C61—22no—
466C2×C4×C61—22no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61—22no—
470C2×C4×C61—41no—
471C2×C4×C61C23×C411yescharacteristic
472C2×C4×C61C23×C411yescharacteristic
473C2×C4×C61C23×C411yescharacteristic
474C2×C4×C61C23×C411yescharacteristic
475C2×C4×C61C23×C412yes—
476C2×C4×C61C23×C412yes—
477C2×C4×C61C23×C412yes—
478C2×C4×C61C23×C411yescharacteristic
479C2×C4×C61C2511yescharacteristic
480C22⋊D61—24no—
481C22⋊D61—42no—
482C22⋊D61—42no—
483C2×Dic61—22no—
484C2×Dic61—24no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61C23×C411yescharacteristic
488C2×Dic61C23×C411yescharacteristic
489C2×Dic61C23×C411yescharacteristic
490C2×Dic61C23×C411yescharacteristic
491C2×Dic61C23×C411yescharacteristic
492C2×Dic61C23×C412yes—
493C2×Dic61C23×C412yes—
494C2×Dic61C23×C412yes—
495C2×Dic61C23×C411yescharacteristic
496D244—24no—
497D244—22no—
498C4×D61—22no—
499C4×D61—24no—
500C4×D61—22no—
501C4×D61—22no—
502C4×D61—22no—
503C4×D61—22no—
504C4×D61—21no—
505C4×D61—22no—
506C4×D61—21no—
507C4×D61—22no—
508C4×D61—22no—
509C4×D61—24no—
510C4×D61—41no—
511C4×D61—41no—
512C4×D61—41no—
513C4×D61—41no—
514C4×D61—42no—
515C4×D61—42no—
516C4×D61H(5,𝔽2)12yes—
517C4×D612−1+412yes—
518Dic122—22no—
519Dic122—42no—
520C8×C61—21no—
521C8×C61—22no—
522C8×C61—22no—
523C8×C61—21no—
524C8×C61—21no—
525C8×C61—21no—
526#92418—21no—
527#92418—22no—
528#92418—22no—
529#92418—21no—
530#92418—21no—
531#92418—21no—
532#60264—611nomaximal, Sylow
533C22×C61—21no—
534C22×C61—22no—
535C22×C61—21no—
536C22×C61—21no—
537C22×C61—22no—
538C22×C61—22no—
539C22×C61C24×C411yescharacteristic
540C2×D61—21no—
541C2×D61—21no—
542C2×D61—21no—
543C2×D61—21no—
544C2×D61—22no—
545C2×D61—22no—
546C2×D61—22no—
547C2×D61—44no—
548C2×D61—84no—
549C2×D61#52012yes—
550C2×D61#56812yes—
551C4×C61—22no—
552C4×C61—21no—
553C4×C61—22no—
554C4×C61—21no—
555C4×C61—21no—
556C4×C61—21no—
557C4×C61—22no—
558C4×C61#56812yes—
559C4×C61C2×H(5,𝔽2)11yescharacteristic
560C4×C61C2×2−1+411yescharacteristic
561Dic61—21no—
562Dic61—22no—
563Dic61—22no—
564Dic61—21no—
565Dic61—21no—
566Dic61—21no—
567Dic61—21no—
568Dic61—22no—
569Dic61#52012yes—
570C2×#529—611no—
571#2995—612no—
572#2995—612no—
573#2994—611no—
574#2994—611no—
575#2994—611no—
576#2994—611no—
577#2993—611no—
578#2993—611no—
579#2993—611no—
580#2993D6111yescharacteristic, complemented
581#2992—612no—
582#2992—612no—
583Q8×M16—611no—
584Q8×M16—611no—
585D4×M16—612no—
586D4×M16—611no—
587D4×M16—612no—
588D4×M16—611no—
589#2921—612no—
590#2920—611no—
591#2905—612no—
592C2×#423—611no—
593C2×C61—41no—
594C2×C61—42no—
595C2×C61C2×#52011yescharacteristic
596C2×C61C2×#56811yescharacteristic
597C2×C61C2×#56811yescharacteristic
598D61—22no—
599D61—22no—
600D61—42no—
601C22×M16—612no—
602C22×M16—612no—
603C22×M16—612no—
604#529—612no—
605#529—611no—
606#529—611no—
607#529—612no—
608#529—611no—
609#529—611no—
610#529—611no—
611#529—612no—
612#529—611no—
613#529—612no—
614#529—611no—
615#529C2×D6111yescharacteristic
616C2×#126—612no—
617C2×#125—611no—
618C2×#124—611no—
619C2×#123—612no—
620C2×C22⋊Q8—611no—
621C2×#121—611no—
622C2×C4×Q8—611no—
623C2×C4×D4—612no—
624C2×C4×D4—611no—
625C2×#117—612no—
626C22×C42—611no—
627#446—611no—
628#446—612no—
629#446—612no—
630#446—611no—
631#446—612no—
632#446—612no—
633#446—611no—
634#446C2×D6111yescharacteristic, complemented
635C8×Q8—611no—
636C8×Q8—611no—
637C8×Q8—611no—
638C8×Q8C2×D6111yescharacteristic, complemented
639#436—612no—
640#436—611no—
641#436—612no—
642#436—611no—
643#436—612no—
644#436—611no—
645#436C2×D6111yescharacteristic, complemented
646#436C2×D6112yescomplemented
647#435—612no—
648#435—612no—
649#435—612no—
650#435—612no—
651#435—612no—
652#435—612no—
653#435—612no—
654#435—612no—
655#435—612no—
656#435—612no—
657#435—612no—
658#435C2×D6112yescomplemented
659C8×D4—612no—
660C8×D4—611no—
661C8×D4—612no—
662C8×D4—611no—
663C8×D4—612no—
664C8×D4—612no—
665C8×D4—611no—
666C8×D4C2×D6111yescharacteristic, complemented
667#433—612no—
668#433—612no—
669#433—612no—
670#433—612no—
671#433—612no—
672#433—612no—
673#433—612no—
674#433C2×D6112yescomplemented
675#432—611no—
676#432—611no—
677#432—611no—
678#432—611no—
679#431—611no—
680#431—611no—
681#431—611no—
682#431C2×D6111yescharacteristic, complemented
683#424—612no—
684#424—612no—
685#424—612no—
686#424—612no—
687#424—612no—
688#424—612no—
689#424—612no—
690#424C2×D6112yescomplemented
691#423—612no—
692#423—611no—
693#423—612no—
694#423—611no—
695#423—611no—
696#423—611no—
697#423—612no—
698#423—612no—
699#423—611no—
700#423C2×D6111yescharacteristic, complemented
701C2×C4⋊C8—612no—
702C2×C4⋊C8—611no—
703C2×C4⋊C8—611no—
704#407—611no—
705#407—611no—
706#407—612no—
707#407—612no—
708C4×M16—612no—
709C4×M16—611no—
710C4×M16—611no—
711C4×M16—612no—
712C61#6026411yescharacteristic, complemented, Sylow
713C22×Q8—611no—
714C22×D4—612no—
715C22×D4—611no—
716C23×C4—612no—
717C23×C4—611no—
718C23×C4—611no—
719C23×C4—611no—
720C2×M16—612no—
721C2×M16—612no—
722C2×M16—612no—
723C2×M16—612no—
724C2×M16—611no—
725C2×M16—611no—
726C2×M16—611no—
727C2×M16—611no—
728C2×M16—612no—
729C2×M16—612no—
730C2×M16—2444no—
731C2×M16—2444no—
732C2×M16—2444no—
733C2×M16C22×D6112yes—
734C2×M16C22×D6112yes—
735C22×C8—612no—
736C22×C8—612no—
737C22×C8—612no—
738C22×C8—612no—
739C22×C8—612no—
740C22×C8C22×D6112yes—
741#126—612no—
742#126—612no—
743#126—612no—
744#126—612no—
745#126—612no—
746#126—612no—
747#126—612no—
748#126C4×D6112yes—
749#125—612no—
750#125—612no—
751#125—611no—
752#125—611no—
753#125—611no—
754#125C4×D6111yescharacteristic
755#124—611no—
756#124—611no—
757#124—612no—
758#124—612no—
759#124—611no—
760#124C4×D6111yescharacteristic
761#123—612no—
762#123—612no—
763#123—612no—
764#123—612no—
765#123—612no—
766#123—612no—
767#123—612no—
768#123C4×D6112yes—
769C22⋊Q8—611no—
770C22⋊Q8—611no—
771C22⋊Q8—612no—
772C22⋊Q8—611no—
773C22⋊Q8—612no—
774C22⋊Q8C4×D6111yescharacteristic
775#121—611no—
776#121—612no—
777#121—611no—
778#121—611no—
779#121—612no—
780#121C4×D6111yescharacteristic
781C4×Q8—611no—
782C4×Q8—612no—
783C4×Q8—611no—
784C4×Q8—611no—
785C4×Q8—612no—
786C4×Q8C22×D6111yescharacteristic
787C4×D4—611no—
788C4×D4—612no—
789C4×D4—612no—
790C4×D4—612no—
791C4×D4—612no—
792C4×D4—611no—
793C4×D4—612no—
794C4×D4—612no—
795C4×D4—612no—
796C4×D4—612no—
797C4×D4—612no—
798C4×D4—611no—
799C4×D4C22×D6111yescharacteristic
800C4×D4C22×D6112yes—
801#117—612no—
802#117—612no—
803#117—612no—
804#117—612no—
805#117—612no—
806#117—612no—
807#117—612no—
808#117C22×D6112yes—
809C2×C4⋊C4—612no—
810C2×C4⋊C4—612no—
811C2×C4⋊C4—611no—
812C2×C4⋊C4—612no—
813C2×C4⋊C4—611no—
814C2×C4⋊C4—612no—
815C2×C22⋊C4—612no—
816C2×C22⋊C4—612no—
817C2×C22⋊C4—612no—
818C2×C22⋊C4—612no—
819C2×C22⋊C4—612no—
820C2×C42—611no—
821C2×C42—611no—
822C2×C42—611no—
823C2×C42—611no—
824C2×C42—611no—
825C2×C42—611no—
826C2×C42—611no—
827C2×C42—611no—
828C2×C42—612no—
829C2×C42—611no—
830C2×C42—611no—
831C2×C42—611no—
832C2×C42C22×D6111yescharacteristic
833C4⋊C8—612no—
834C4⋊C8—612no—
835C4⋊C8—612no—
836C4⋊C8—612no—
837C4⋊C8—611no—
838C4⋊C8—611no—
839C4⋊C8—612no—
840C4⋊C8—612no—
841C4⋊C8—612no—
842C4⋊C8—612no—
843C4⋊C8—611no—
844C4⋊C8—611no—
845C4⋊C8—612no—
846C4⋊C8—611no—
847C4⋊C8—611no—
848C4⋊C8—611no—
849C4⋊C8—612no—
850C4⋊C8—612no—
851C4⋊C8—611no—
852C4⋊C8C22×D6112yes—
853C4⋊C8C22×D6111yescharacteristic
854C4⋊C8C22×D6111yescharacteristic
855C4⋊C8C22×D6111yescharacteristic
856C4⋊C8C22×D6112yes—
857C4⋊C8C22×D6112yes—
858C4⋊C8C22×D6111yescharacteristic
859C22⋊C8—611no—
860C22⋊C8—611no—
861C22⋊C8—612no—
862C22⋊C8—612no—
863C22⋊C8—611no—
864C22⋊C8—611no—
865C22⋊C8—611no—
866C22⋊C8—611no—
867C22⋊C8—612no—
868C22⋊C8—612no—
869C22⋊C8—612no—
870C22⋊C8—612no—
871C22⋊C8C22×D6111yescharacteristic
872C22⋊C8C22×D6111yescharacteristic
873C22⋊C8C22×D6112yes—
874C22⋊C8C22×D6112yes—
875#97—611no—
876#97—611no—
877#97—611no—
878#97—611no—
879#97—612no—
880#97—612no—
881#97—612no—
882#97C22×D6112yes—
883C4×C8—612no—
884C4×C8—612no—
885C4×C8—611no—
886C4×C8—611no—
887C4×C8—612no—
888C4×C8C22×D6111yescharacteristic
889C4×C8C22×D6111yescharacteristic
890C4×C8C22×D6112yes—
891C24—611no—
892C24—612no—
893C2×Q8—611no—
894C2×Q8—612no—
895C2×Q8—2442no—
896C2×Q8C2×C4×D6111yescharacteristic
897C2×D4—612no—
898C2×D4—612no—
899C2×D4—612no—
900C2×D4—612no—
901C2×D4—611no—
902C2×D4—2442no—
903C2×D4—2444no—
904C2×D4C2×C4×D6111yescharacteristic
905C2×D4C2×C4×D6112yes—
906C22×C4—611no—
907C22×C4—611no—
908C22×C4—612no—
909C22×C4—611no—
910C22×C4—611no—
911C22×C4—611no—
912C22×C4—611no—
913C22×C4—611no—
914C22×C4—611no—
915C22×C4—611no—
916C22×C4—611no—
917C22×C4—612no—
918C22×C4—612no—
919C22×C4—611no—
920C22×C4—612no—
921C22×C4—611no—
922C22×C4—611no—
923C22×C4—611no—
924C22×C4—611no—
925C22×C4—612no—
926C22×C4—612no—
927C22×C4—1224no—
928C22×C4—1222no—
929C22×C4—1224no—
930C22×C4—1222no—
931C22×C4—2442no—
932C22×C4—2442no—
933C22×C4C2×C4×D6111yescharacteristic
934C22×C4C2×C4×D6111yescharacteristic
935C22×C4C23×D6111yescharacteristic
936C22×C4C23×D6112yes—
937M16—42no—
938M16—42no—
939M16—1222no—
940M16—1222no—
941M16—1222no—
942M16—1224no—
943M16—1224no—
944M16—1222no—
945M16—2442no—
946M16—2442no—
947M16—2442no—
948M16—2442no—
949C2×C8—42no—
950C2×C8—611no—
951C2×C8—611no—
952C2×C8—612no—
953C2×C8—611no—
954C2×C8—611no—
955C2×C8—612no—
956C2×C8—2442no—
957C2×C8—2442no—
958C2×C8—2442no—
959C2×C8—2442no—
960C2×C8—2442no—
961C2×C8C23×D6111yescharacteristic
962C2×C8C23×D6112yes—
963C2×C8C23×D6111yescharacteristic
964C2×C8C23×D6111yescharacteristic
965C2×C8C23×D6112yes—
966C2×C8C23×D6111yescharacteristic
967C4⋊C4—612no—
968C4⋊C4—612no—
969C4⋊C4—612no—
970C4⋊C4—612no—
971C4⋊C4—612no—
972C4⋊C4—612no—
973C4⋊C4—612no—
974C4⋊C4—612no—
975C4⋊C4—612no—
976C4⋊C4—612no—
977C4⋊C4—612no—
978C4⋊C4—612no—
979C4⋊C4—611no—
980C4⋊C4—612no—
981C4⋊C4—611no—
982C4⋊C4—612no—
983C4⋊C4C2×C4×D6112yes—
984C4⋊C4C2×C4×D6112yes—
985C4⋊C4C2×C4×D6111yescharacteristic
986C4⋊C4C2×C4×D6112yes—
987C4⋊C4C2×C4×D6111yescharacteristic
988C4⋊C4C2×C4×D6112yes—
989C22⋊C4—612no—
990C22⋊C4—612no—
991C22⋊C4—612no—
992C22⋊C4—612no—
993C22⋊C4—612no—
994C22⋊C4—612no—
995C22⋊C4—612no—
996C22⋊C4—612no—
997C22⋊C4—612no—
998C22⋊C4—612no—
999C22⋊C4—612no—
1000C22⋊C4—612no—
1001C22⋊C4—612no—
1002C22⋊C4—612no—
1003C22⋊C4—612no—
1004C22⋊C4C2×C4×D6112yes—
1005C22⋊C4C2×C4×D6112yes—
1006C22⋊C4C2×C4×D6112yes—
1007C22⋊C4C2×C4×D6112yes—
1008C22⋊C4C2×C4×D6112yes—
1009C42—611no—
1010C42—611no—
1011C42—611no—
1012C42—611no—
1013C42—611no—
1014C42—611no—
1015C42—611no—
1016C42—611no—
1017C42—611no—
1018C42—611no—
1019C42—612no—
1020C42—612no—
1021C42—612no—
1022C42—611no—
1023C42—611no—
1024C42C2×C4×D6111yescharacteristic
1025C42C2×C4×D6111yescharacteristic
1026C42C23×D6111yescharacteristic
1027C42C23×D6112yes—
1028C42C23×D6111yescharacteristic
1029C23—611no—
1030C23—611no—
1031C23—612no—
1032C23—1224no—
1033C23—1222no—
1034C23—1222no—
1035C23—2442no—
1036C23—2442no—
1037C23—2441no—
1038C23C22×C4×D6112yes—
1039C23C22×C4×D6111yescharacteristic
1040Q8—22no—
1041Q8—1222no—
1042Q8—2442no—
1043D4—22no—
1044D4—42no—
1045D4—1224no—
1046D4—1224no—
1047D4—1222no—
1048D4—2442no—
1049D4—2442no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—41no—
1056C2×C4—611no—
1057C2×C4—612no—
1058C2×C4—612no—
1059C2×C4—611no—
1060C2×C4—611no—
1061C2×C4—611no—
1062C2×C4—611no—
1063C2×C4—611no—
1064C2×C4—612no—
1065C2×C4—612no—
1066C2×C4—612no—
1067C2×C4—1222no—
1068C2×C4—1224no—
1069C2×C4—1222no—
1070C2×C4—1224no—
1071C2×C4—1222no—
1072C2×C4—1222no—
1073C2×C4—1222no—
1074C2×C4—1224no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1221no—
1078C2×C4—1222no—
1079C2×C4—1221no—
1080C2×C4—1222no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2442no—
1086C2×C4—2442no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4C22×C4×D6111yescharacteristic
1090C2×C4C22×C4×D6111yescharacteristic
1091C2×C4C22×C4×D6111yescharacteristic
1092C2×C4C22×C4×D6111yescharacteristic
1093C2×C4C22×C4×D6112yes—
1094C2×C4C22×C4×D6112yes—
1095C2×C4C22×C4×D6112yes—
1096C2×C4C22×C4×D6111yescharacteristic
1097C2×C4C24×D6111yescharacteristic
1098C8—21no—
1099C8—22no—
1100C8—22no—
1101C8—21no—
1102C8—21no—
1103C8—21no—
1104C8—1221no—
1105C8—1222no—
1106C8—1222no—
1107C8—1221no—
1108C8—1221no—
1109C8—1221no—
1110C22—21no—
1111C22—22no—
1112C22—21no—
1113C22—22no—
1114C22—22no—
1115C22—21no—
1116C22—612no—
1117C22—612no—
1118C22—1221no—
1119C22—1221no—
1120C22—1221no—
1121C22—1221no—
1122C22—1222no—
1123C22—1222no—
1124C22—1222no—
1125C22—4884no—
1126C22—2444no—
1127C22C23×C4×D6111yescharacteristic
1128C4—21no—
1129C4—21no—
1130C4—22no—
1131C4—21no—
1132C4—22no—
1133C4—22no—
1134C4—21no—
1135C4—612no—
1136C4—1221no—
1137C4—1221no—
1138C4—1222no—
1139C4—1221no—
1140C4—1221no—
1141C4—1222no—
1142C4—1221no—
1143C4—1222no—
1144C4#1684052712yes—
1145C4H(5,𝔽2)×D6111yescharacteristic
1146C42−1+4×D6111yescharacteristic
1147C2—42no—
1148C2—41no—
1149C2—1222no—
1150C2—1222no—
1151C2—2442no—
1152C2#520×D6111yescharacteristic
1153C2#568×D6111yescharacteristic
1154C2C2×#1684052711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D61
commutator, socleC22×C61C24×C4
FittingC61×#2993C2
prime radical#121×D61C4
cosocleC2×C4×C61C25
hypercenter#2993D61
hypocenterC61#60264
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #21454990C2semidirect
3. #21454983C2semidirect
4. #21454982C2semidirect
5. #21454980C2semidirect
6. #21454978C2semidirect
7. #21454974C2semidirect
8. #21454970C2semidirect
9. #21454968C2semidirect
10. #21454964C2semidirect
11. #21454956C2semidirect
12. #21454953C2semidirect
13. #21454771C2semidirect
14. Q8×#11758189C2semidirect
15. #21454555C2semidirect
16. #21454555C2semidirect
17. #21454552C2semidirect
18. D4×#11758189C2semidirect
19. #21454453C2semidirect
20. #21454447C2semidirect
21. #21454380C2semidirect
22. #423×D61C2semidirect
23. C61×#2993C2semidirect
49. #16839893C22semidirect
50. #16839892C22semidirect
51. #16839892C22semidirect
52. #16839891C22semidirect
53. #16839890C22semidirect
54. #16839889C22semidirect
55. #16839889C22semidirect
56. Q8×#92418C22semidirect
57. C8×Dic122C22semidirect
58. #16839886C22semidirect
59. #16839841C22semidirect
60. #16839840C22semidirect
61. #16839840C22semidirect
62. #16839839C22semidirect
63. #16839838C22semidirect
64. #16839837C22semidirect
65. #16839836C22semidirect
66. #16839836C22semidirect
67. #16839836C22semidirect
68. #16839835C22semidirect
69. #16839834C22semidirect
70. #16839833C22semidirect
71. #16839832C22semidirect
72. #16839831C22semidirect
73. #16839831C22semidirect
74. #16839831C22semidirect
75. #16839830C22semidirect
76. C8×D244C22semidirect
77. C8×D244C22semidirect
78. D4×#92418C22semidirect
79. #16839827C22semidirect
80. #16839827C22semidirect
81. C8×C22⋊D61C22semidirect
82. #16839825C22semidirect
83. #16839824C22semidirect
84. #16839823C22semidirect
85. #16839822C22semidirect
86. #16839822C22semidirect
87. #16839821C22semidirect
88. #16839820C22semidirect
89. #16839820C22semidirect
90. #16839818C22semidirect
91. #16839818C22semidirect
92. #16839816C22semidirect
93. #16839816C22semidirect
94. #16839815C22semidirect
95. #16839813C22semidirect
96. #16839813C22semidirect
97. #16839790C22semidirect
98. #16839789C22semidirect
99. #16839788C22semidirect
100. #16839787C22semidirect
101. #16839787C22semidirect
102. #16839787C22semidirect
103. #16839787C22semidirect
104. #16839786C22semidirect
105. #16839785C22semidirect
113. C4⋊C8×D61C22semidirect
114. C4⋊C8×D61C22semidirect
115. C4⋊C8×D61C22semidirect
125. C61×#446C22semidirect
126. C8×Q8×C61C22semidirect
127. C61×#436C22semidirect
128. C61×#436C22semidirect
129. C61×#435C22semidirect
130. C8×D4×C61C22semidirect
131. C61×#433C22semidirect
132. C61×#431C22semidirect
133. C61×#424C22semidirect
134. C61×#423C22semidirect
580. #2993D61semidirect
634. #446C2×D61semidirect
638. C8×Q8C2×D61semidirect
645. #436C2×D61semidirect
646. #436C2×D61semidirect
658. #435C2×D61semidirect
666. C8×D4C2×D61semidirect
674. #433C2×D61semidirect
682. #431C2×D61semidirect
690. #424C2×D61semidirect
700. #423C2×D61semidirect
712. C61#60264semidirect

Maximal subgroups

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

subgroupindex
#529×D612
#214549902
#214549832
#214549822
#214549802
#214549782
#214549742
#214549702
#214549682
#214549642
#214549562
#214549532
#214547712
Q8×#117581892
#214545552
#214545522
D4×#117581892
#214544532
#214544472
#214543802
#423×D612
C61×#29932
#6026461