Finite Group Databasebeta

← #30545140

Subgroups — #30545140

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#21454987C212yesmaximal, complemented
3#21454984C212yesmaximal, complemented
4#21454981C211yesmaximal, characteristic, complemented
5#21454979C211yesmaximal, characteristic, complemented
6#21454975C211yesmaximal, characteristic, complemented
7#21454971C211yesmaximal, characteristic, complemented
8#21454969C211yesmaximal, characteristic, complemented
9#21454967C211yesmaximal, characteristic, complemented
10#21454963C211yesmaximal, characteristic, complemented
11#21454959C212yesmaximal, complemented
12#21454952C212yesmaximal, complemented
13#21454771C211yesmaximal, characteristic, complemented
14Q8×#11758189C211yesmaximal, characteristic, complemented
15#21454555C211yesmaximal, characteristic, complemented
16#21454552C212yesmaximal, complemented
17D4×#11758189C212yesmaximal, complemented
18D4×#11758189C211yesmaximal, characteristic, complemented
19#21454453C212yesmaximal, complemented
20#21454447C211yesmaximal, characteristic, complemented
21#21454380C212yesmaximal, complemented
22C2×#16839784C211yesmaximal, characteristic, complemented
23C61×#2994C211yesmaximal, characteristic, complemented
24C22×#11758189C2212yes—
25C22×#11758189C2212yes—
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×D61C2212yes—
46C4×D4×D61C2211yescharacteristic
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#16839841C2212yescomplemented
60#16839841C2211yescharacteristic, complemented
61#16839840C2211yescharacteristic, complemented
62#16839839C2211yescharacteristic, complemented
63#16839839C2212yescomplemented
64#16839838C2212yescomplemented
65#16839837C2212yescomplemented
66#16839836C2212yescomplemented
67#16839835C2212yescomplemented
68#16839834C2212yescomplemented
69#16839833C2212yescomplemented
70#16839833C2212yescomplemented
71#16839833C2212yescomplemented
72#16839832C2212yescomplemented
73#16839831C2212yescomplemented
74#16839830C2212yescomplemented
75#16839830C2212yescomplemented
76#16839830C2212yescomplemented
77C8×D244C2211yescharacteristic, complemented
78D4×#92418C2212yescomplemented
79D4×#92418C2211yescharacteristic, complemented
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#16839784C2212yes—
105#16839784C2211yescharacteristic
106#16839784C2211yescharacteristic
107#16839784C2211yescharacteristic
108#16839784C2212yes—
109#16839784C2212yes—
110#16839784C2211yescharacteristic
111#16839784C2211yescharacteristic, complemented
112#16839784C2211yescharacteristic, complemented
113#16839784C2212yescomplemented
114C2×C4⋊#92418C2211yescharacteristic, complemented
115C2×#14519706C2212yescomplemented
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×#435C2212yescomplemented
129C8×D4×C61C2212yescomplemented
130C8×D4×C61C2211yescharacteristic, complemented
131C61×#433C2212yescomplemented
132C61×#431C2211yescharacteristic, complemented
133C61×#424C2212yescomplemented
134C2×C4⋊C8×C61C2211yescharacteristic, 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×#11758189—44no—
144C2×#11758189—44no—
145C2×#11758189C2311yescharacteristic
146C2×#11758189C2311yescharacteristic
147C2×#11758189C2311yescharacteristic
148C2×#11758189C2311yescharacteristic
149C2×#11758189C2312yes—
150C2×#11758189C2312yes—
151C2×#11758189C2312yes—
152C2×#11758189C2312yes—
153C2×#11758189C2312yes—
154C2×#11758189C2312yes—
155M16×D61—44no—
156C22×#92418C2312yes—
157C22×#92418C2312yes—
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—
285C22×C8×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×C412yes—
317C2×D4×C61C22×C411yescharacteristic
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×C411yescharacteristic
327C22×Dic61C22×C412yes—
328C22×Dic61C22×C411yescharacteristic
329Q8×D61—42no—
330D4×D61—42no—
331D4×D61—44no—
332C2×D244C22×C411yescharacteristic
333C2×D244C22×C412yes—
334C2×C4×D61—24no—
335C2×C4×D61—22no—
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×C412yes—
345C2×C4×D61C22×C412yes—
346C2×C4×D61C22×C411yescharacteristic
347C2×C4×D61C22×C411yescharacteristic
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—
360C2×C8×C61—42no—
361C2×C8×C61—42no—
362C2×C8×C61C2411yescharacteristic
363C2×C8×C61C2411yescharacteristic
364C2×C8×C61C2411yescharacteristic
365C2×C8×C61C2412yes—
366C2×C8×C61C2411yescharacteristic
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—
431C2×#92418—42no—
432C2×#92418—42no—
433C2×#92418C2411yescharacteristic
434C2×#92418C2412yes—
435C2×#92418C2411yescharacteristic
436C2×#92418C2411yescharacteristic
437C2×#92418C2411yescharacteristic
438C2×#92418C2412yes—
439#11758189—22no—
440#11758189—24no—
441#11758189—24no—
442#11758189—22no—
443#11758189—22no—
444#11758189—22no—
445#11758189—42no—
446#11758189—42no—
447#11758189—42no—
448#11758189—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—24no—
464D4×C61—22no—
465C2×C4×C61—22no—
466C2×C4×C61—22no—
467C2×C4×C61—21no—
468C2×C4×C61—22no—
469C2×C4×C61—21no—
470C2×C4×C61—22no—
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—22no—
485C2×Dic61—24no—
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—22no—
497D244—42no—
498C4×D61—24no—
499C4×D61—22no—
500C4×D61—22no—
501C4×D61—22no—
502C4×D61—22no—
503C4×D61—21no—
504C4×D61—21no—
505C4×D61—22no—
506C4×D61—24no—
507C4×D61—22no—
508C4×D61—41no—
509C4×D61—41no—
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—21no—
535C22×C61—22no—
536C22×C61—22no—
537C22×C61—22no—
538C22×C61#56812yes—
539C22×C61C24×C411yescharacteristic
540C2×D61—21no—
541C2×D61—21no—
542C2×D61—21no—
543C2×D61—22no—
544C2×D61—21no—
545C2×D61—21no—
546C2×D61—22no—
547C2×D61—22no—
548C2×D61—44no—
549C2×D61—84no—
550C2×D61#52012yes—
551C4×C61—21no—
552C4×C61—22no—
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—22no—
562Dic61—21no—
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#2994D6111yescharacteristic, complemented
577#2993—611no—
578#2993—611no—
579#2993—611no—
580#2993—611no—
581#2992—612no—
582#2992—612no—
583Q8×M16—611no—
584Q8×M16—611no—
585D4×M16—611no—
586D4×M16—612no—
587D4×M16—612no—
588D4×M16—611no—
589#2921—612no—
590#2920—611no—
591#2905—612no—
592C2×#423—611no—
593C2×C61—22no—
594C2×C61—42no—
595C2×C61C2×#52011yescharacteristic
596C2×C61C2×#56811yescharacteristic
597C2×C61C2×#56811yescharacteristic
598D61—22no—
599D61—41no—
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—611no—
642#436—612no—
643#436—612no—
644#436—611no—
645#436—612no—
646#436C2×D6111yescharacteristic, complemented
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—612no—
661C8×D4—611no—
662C8×D4—611no—
663C8×D4—612no—
664C8×D4—611no—
665C8×D4C2×D6112yescomplemented
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—611no—
694#423—611no—
695#423—611no—
696#423—612no—
697#423—611no—
698#423—612no—
699#423—612no—
700#423—611no—
701C2×C4⋊C8—612no—
702C2×C4⋊C8—611no—
703C2×C4⋊C8C2×D6111yescharacteristic, complemented
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—611no—
723C2×M16—612no—
724C2×M16—611no—
725C2×M16—611no—
726C2×M16—611no—
727C2×M16—612no—
728C2×M16—612no—
729C2×M16—612no—
730C2×M16—612no—
731C2×M16—2444no—
732C2×M16—2444no—
733C2×M16—2444no—
734C2×M16C22×D6112yes—
735C22×C8—612no—
736C22×C8—612no—
737C22×C8—612no—
738C22×C8—612no—
739C22×C8C22×D6112yes—
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—611no—
798C4×D4—612no—
799C4×D4C22×D6112yes—
800C4×D4C22×D6111yescharacteristic
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—611no—
901C2×D4—612no—
902C2×D4—2442no—
903C2×D4—2444no—
904C2×D4C2×C4×D6112yes—
905C2×D4C2×C4×D6111yescharacteristic
906C22×C4—611no—
907C22×C4—611no—
908C22×C4—611no—
909C22×C4—612no—
910C22×C4—611no—
911C22×C4—611no—
912C22×C4—611no—
913C22×C4—611no—
914C22×C4—611no—
915C22×C4—612no—
916C22×C4—612no—
917C22×C4—611no—
918C22×C4—612no—
919C22×C4—611no—
920C22×C4—611no—
921C22×C4—611no—
922C22×C4—611no—
923C22×C4—611no—
924C22×C4—611no—
925C22×C4—612no—
926C22×C4—612no—
927C22×C4—1222no—
928C22×C4—1224no—
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—1222no—
939M16—1222no—
940M16—1224no—
941M16—1222no—
942M16—1224no—
943M16—1222no—
944M16—2442no—
945M16—2442no—
946M16—2442no—
947M16—2442no—
948M16—2442no—
949C2×C8—42no—
950C2×C8—42no—
951C2×C8—611no—
952C2×C8—611no—
953C2×C8—612no—
954C2×C8—611no—
955C2×C8—611no—
956C2×C8—612no—
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×D6111yescharacteristic
966C2×C8C23×D6112yes—
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—612no—
1031C23—611no—
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—24no—
1044D4—22no—
1045D4—1224no—
1046D4—1222no—
1047D4—2442no—
1048D4—2442no—
1049D4—2442no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—22no—
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—1224no—
1073C2×C4—1222no—
1074C2×C4—1222no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1221no—
1078C2×C4—1221no—
1079C2×C4—1222no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2442no—
1087C2×C4—2442no—
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—1221no—
1107C8—1222no—
1108C8—1221no—
1109C8—1221no—
1110C22—21no—
1111C22—21no—
1112C22—22no—
1113C22—22no—
1114C22—22no—
1115C22—612no—
1116C22—1221no—
1117C22—1221no—
1118C22—1221no—
1119C22—1221no—
1120C22—1222no—
1121C22—1222no—
1122C22—1222no—
1123C22—1221no—
1124C22—4884no—
1125C22—2444no—
1126C22#1684052712yes—
1127C22C23×C4×D6111yescharacteristic
1128C4—21no—
1129C4—21no—
1130C4—21no—
1131C4—22no—
1132C4—22no—
1133C4—21no—
1134C4—22no—
1135C4—612no—
1136C4—1221no—
1137C4—1221no—
1138C4—1221no—
1139C4—1221no—
1140C4—1222no—
1141C4—1222no—
1142C4—1221no—
1143C4—1222no—
1144C4#1684052712yes—
1145C4H(5,𝔽2)×D6111yescharacteristic
1146C42−1+4×D6111yescharacteristic
1147C2—22no—
1148C2—42no—
1149C2—1222no—
1150C2—2442no—
1151C2—2441no—
1152C2#520×D6111yescharacteristic
1153C2C2×#1684052711yescharacteristic
1154C2C2×#1684052711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D61
commutator, socleC22×C61C24×C4
FittingC61×#2994C2
prime radical#121×D61C4
cosocleC2×C4×C61C25
hypercenter#2994D61
hypocenterC61#60264
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #21454987C2semidirect
3. #21454984C2semidirect
4. #21454981C2semidirect
5. #21454979C2semidirect
6. #21454975C2semidirect
7. #21454971C2semidirect
8. #21454969C2semidirect
9. #21454967C2semidirect
10. #21454963C2semidirect
11. #21454959C2semidirect
12. #21454952C2semidirect
13. #21454771C2semidirect
14. Q8×#11758189C2semidirect
15. #21454555C2semidirect
16. #21454552C2semidirect
17. D4×#11758189C2semidirect
18. D4×#11758189C2semidirect
19. #21454453C2semidirect
20. #21454447C2semidirect
21. #21454380C2semidirect
22. C2×#16839784C2semidirect
23. C61×#2994C2semidirect
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. #16839841C22semidirect
61. #16839840C22semidirect
62. #16839839C22semidirect
63. #16839839C22semidirect
64. #16839838C22semidirect
65. #16839837C22semidirect
66. #16839836C22semidirect
67. #16839835C22semidirect
68. #16839834C22semidirect
69. #16839833C22semidirect
70. #16839833C22semidirect
71. #16839833C22semidirect
72. #16839832C22semidirect
73. #16839831C22semidirect
74. #16839830C22semidirect
75. #16839830C22semidirect
76. #16839830C22semidirect
77. C8×D244C22semidirect
78. D4×#92418C22semidirect
79. D4×#92418C22semidirect
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
111. #16839784C22semidirect
112. #16839784C22semidirect
113. #16839784C22semidirect
114. C2×C4⋊#92418C22semidirect
115. C2×#14519706C22semidirect
125. C61×#446C22semidirect
126. C8×Q8×C61C22semidirect
127. C61×#436C22semidirect
128. C61×#435C22semidirect
129. C8×D4×C61C22semidirect
130. C8×D4×C61C22semidirect
131. C61×#433C22semidirect
132. C61×#431C22semidirect
133. C61×#424C22semidirect
134. C2×C4⋊C8×C61C22semidirect
576. #2994D61semidirect
634. #446C2×D61semidirect
638. C8×Q8C2×D61semidirect
646. #436C2×D61semidirect
658. #435C2×D61semidirect
665. C8×D4C2×D61semidirect
666. C8×D4C2×D61semidirect
674. #433C2×D61semidirect
682. #431C2×D61semidirect
690. #424C2×D61semidirect
703. C2×C4⋊C8C2×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
#214549872
#214549842
#214549812
#214549792
#214549752
#214549712
#214549692
#214549672
#214549632
#214549592
#214549522
#214547712
Q8×#117581892
#214545552
#214545522
D4×#117581892
#214544532
#214544472
#214543802
C2×#168397842
C61×#29942
#6026461