Finite Group Databasebeta

← #17979294

Subgroups — #17979294

Order 4352.

2202 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545330C212yesmaximal, complemented
2#14545324C212yesmaximal, complemented
3#14545318C212yesmaximal, complemented
4#14545307C212yesmaximal, complemented
5#14545307C212yesmaximal, complemented
6#14545307C212yesmaximal, complemented
7#14545300C212yesmaximal, complemented
8#14545297C212yesmaximal, complemented
9#14545282C212yesmaximal, complemented
10#14545282C212yesmaximal, complemented
11#14545277C211yesmaximal, characteristic, complemented
12#14545277C212yesmaximal, complemented
13#14545273C211yesmaximal, characteristic
14#14545271C212yesmaximal, complemented
15#14545264C211yesmaximal, characteristic, complemented
16C22⋊Q8×#595C211yesmaximal, characteristic, complemented
17#121×#595C211yesmaximal, characteristic
18C2×#11763758C211yesmaximal, characteristic, complemented
19D17×#539C211yesmaximal, characteristic
20C2×Q8×#595C2211yescharacteristic
21C2×D4×#595C2212yes—
22C2×D4×#595C2211yescharacteristic
23C2×D4×#595C2212yes—
24C2×#10587677C2212yes—
25C2×#10587677C2212yes—
26C22×C4⋊#595C2211yescharacteristic
27C22×C4×#595C2211yescharacteristic
28(C2×#595)⋊Q8C2211yescharacteristic
29(C2×#595)⋊Q8C2212yes—
30#11763761C2211yescharacteristic
31#11763760C2211yescharacteristic
32#11763760C2211yescharacteristic
33#11763760C2212yes—
34#11763760C2212yes—
35#11763760C2212yes—
36#11763760C2212yes—
37#11763760C2212yes—
38#11763760C2212yes—
39#11763760C2212yes—
40#11763760C2212yes—
41#11763760C2212yes—
42#11763759C2212yes—
43#11763759C2212yes—
44#11763759C2212yes—
45#11763759C2212yes—
46#11763759C2212yes—
47#11763759C2212yes—
48#11763759C2212yes—
49#11763759C2212yes—
50#11763758C2212yes—
51#11763758C2212yes—
52#11763758C2212yes—
53#11763758C2212yes—
54#11763758C2212yes—
55#11763758C2212yes—
56#11763758C2212yes—
57#11763758C2212yes—
58#11763758C2212yes—
59#11763758C2212yes—
60#11763758C2212yes—
61#11763758C2212yes—
62#11763758C2212yes—
63#11763758C2212yes—
64#11763757C2212yes—
65#11763757C2212yes—
66#11763757C2212yes—
67#11763756C2212yes—
68#11763756C2212yes—
69#11763756C2212yes—
70#11763756C2212yes—
71#11763756C2212yes—
72#11763756C2212yes—
73#11763756C2212yes—
74#11763753C2212yes—
75#11763753C2212yes—
76#11763751C2211yescharacteristic
77#11763751C2211yescharacteristic
78#11763751C2212yes—
79#11763751C2212yes—
80#11763751C2212yes—
81C4⋊C4×#595C2211yescharacteristic
82C4⋊C4×#595C2211yescharacteristic
83C4⋊C4×#595C2212yes—
84C4⋊C4×#595C2212yes—
85C4⋊C4×#595C2212yes—
86C4×C4⋊#595C2212yes—
87C4×C4⋊#595C2212yes—
88C22⋊C4×#595C2212yes—
89C22⋊C4×#595C2212yes—
90C22⋊C4×#595C2212yes—
91C22⋊C4×#595C2212yes—
92C22⋊C4×#595C2212yes—
93C2×(C2×#595)⋊C4C2211yescharacteristic
94C2×(C2×#595)⋊C4C2211yescharacteristic
95C2×(C2×#595)⋊C4C2211yescharacteristic
96C2×(C2×#595)⋊C4C2211yescharacteristic
97C2×(C2×#595)⋊C4C2212yes—
98#11763408C411yescharacteristic, complemented
99#11763407C412yescomplemented
100#11763406C411yescharacteristic, complemented
101#11763405C412yescomplemented
102#11763404C411yescharacteristic, complemented
103#11763403C412yescomplemented
104#11763402C412yescomplemented
105#11763401C412yescomplemented
106#11763400C412yescomplemented
107#126×D17C2212yes—
108#125×D17C2212yes—
109#123×D17C2212yes—
110#123×D17C2212yes—
111C22⋊Q8×D17C2211yescharacteristic
112C22⋊Q8×D17C2212yes—
113#121×D17C2211yescharacteristic
114C4×D4×D17C2212yes—
115C2×C4⋊C4×D17C2211yescharacteristic
116C17×#539C411yescharacteristic, complemented
117C23×#595C2311yescharacteristic
118C23×#595C2311yescharacteristic
119C23×#595C2311yescharacteristic
120C23×#595C2311yescharacteristic
121C23×#595C2312yes—
122C23×#595C2312yes—
123C2×Q8×D17C2311yescharacteristic
124C2×D4×D17C2312yes—
125C2×D4×D17C2311yescharacteristic
126C22×C4×D17C2311yescharacteristic
127C22×C4×D17C2311yescharacteristic
128C22×C4×D17C2311yescharacteristic
129C22×C4×D17C2312yes—
130C2×C22⋊#595C2312yes—
131C2×C22⋊#595C2312yes—
132C2×C22⋊#595C2312yes—
133C2×C22⋊#595C2312yes—
134C2×C22⋊#595C2312yes—
135C2×C22⋊#595C2312yes—
136C2×C22⋊#595C2312yes—
137C2×C22⋊#595C2312yes—
138Q8×#595—42no—
139D4×#595—42no—
140D4×#595—44no—
141D4×#595—44no—
142#10587677—44no—
143#10587677—44no—
144C2×C4⋊#595—42no—
145C2×C4⋊#595C2312yes—
146C2×C4⋊#595C2312yes—
147C2×C4⋊#595C2312yes—
148C2×C4⋊#595C2312yes—
149C2×C4⋊#595C2312yes—
150C2×C4⋊#595C2311yescharacteristic
151C2×C4⋊#595C2311yescharacteristic
152C2×C4⋊#595C2312yes—
153C2×C4⋊#595C2312yes—
154C2×C4⋊#595C2312yes—
155C2×C4⋊#595C2311yescharacteristic
156C2×C4⋊#595C2311yescharacteristic
157C2×C4⋊#595C2312yes—
158C2×C4⋊#595C2312yes—
159C2×C4⋊#595C2312yes—
160C2×C4⋊#595C2312yes—
161C2×C4×#595—42no—
162C2×C4×#595C2312yes—
163C2×C4×#595C2311yescharacteristic
164C2×C4×#595C2311yescharacteristic
165C2×C4×#595C2312yes—
166C2×C4×#595C2312yes—
167C2×C4×#595C2311yescharacteristic
168C2×C4×#595C2312yes—
169C2×C4×#595C2312yes—
170C2×C4×#595C2312yes—
171C2×C4×#595C2312yes—
172C2×C4×#595C2312yes—
173C2×C4×#595C2311yescharacteristic
174C17×#126C2×C412yescomplemented
175C17×#125C2×C412yescomplemented
176C17×#123C2×C412yescomplemented
177C17×#123C2×C412yescomplemented
178C17×C22⋊Q8C2×C412yescomplemented
179C17×C22⋊Q8C2×C411yescharacteristic, complemented
180C17×#121C2×C411yescharacteristic
181C4×D4×C17C2×C412yescomplemented
182C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
183#10587632C2×C411yescharacteristic, complemented
184#10587632C2×C412yescomplemented
185#10587625C2×C412yes—
186#10587624C2×C411yescharacteristic
187#10587621C2×C412yescomplemented
188#10587621C2×C412yescomplemented
189D4×Dic17C2×C412yescomplemented
190#10587616C2×C411yescharacteristic
191#10587615C2×C412yescomplemented
192#10587615C2×C412yescomplemented
193C4×C22⋊D17C2×C412yescomplemented
194C4×C22⋊D17C2×C412yescomplemented
195C2×C4⋊Dic17C2×C411yescharacteristic, complemented
196#10587610C2×C412yescomplemented
197#10587610C2×C411yescharacteristic, complemented
198C2×#63225C2×C411yescharacteristic, complemented
199C2×#63225C2×C411yescharacteristic, complemented
200#10587584C2×C412yescomplemented
201#10587584C2×C412yescomplemented
202#10587584C2×C412yescomplemented
203#10587583C2×C411yescharacteristic, complemented
204#10587583C2×C412yescomplemented
205#10587582C2×C412yescomplemented
206#10587582C2×C412yescomplemented
207#10587582C2×C412yescomplemented
208#10587581C2×C411yescharacteristic
209#10587580C2×C412yescomplemented
210#10587580C2×C412yescomplemented
211#10587580C2×C412yescomplemented
212#10587580C2×C412yescomplemented
213#10587579C2×C412yescomplemented
214C4⋊C4×D17C2×C412yescomplemented
215C4⋊C4×D17C2×C412yescomplemented
216C4⋊C4×D17C2311yescharacteristic
217C4⋊C4×D17C2312yes—
218C4⋊C4×D17C2312yes—
219C4⋊C4×D17C2311yescharacteristic
220C4⋊C4×D17C2312yes—
221C4⋊C4×D17C2312yes—
222C4⋊C4×D17C2312yes—
223C4⋊C4×D17C2312yes—
224#10587576C2×C412yescomplemented
225#10587576C2×C412yescomplemented
226#10587575C2×C412yescomplemented
227#10587575C2×C412yescomplemented
228#10587575C2×C412yescomplemented
229#10587575C2×C412yescomplemented
230#10587572C2×C412yescomplemented
231#10587572C2×C412yescomplemented
232#10587570C2×C412yes—
233#10587569C2×C412yescomplemented
234#10587569C2×C412yescomplemented
235#10587569C2×C412yescomplemented
236#10587569C2×C412yescomplemented
237#10587567C2×C412yescomplemented
238#10587567C2×C412yescomplemented
239C22⋊C4×D17C2312yes—
240C22⋊C4×D17C2312yes—
241C22⋊C4×D17C2312yes—
242C22⋊C4×D17C2312yes—
243C22⋊C4×D17C2312yes—
244#10587565C2×C412yescomplemented
245#10587565C2×C412yescomplemented
246#10587565C2×C412yescomplemented
247#10587564C2×C412yescomplemented
248#10587564C2×C412yescomplemented
249#10587564C2×C412yescomplemented
250#10587562C2×C412yescomplemented
251C4×D68C2×C412yescomplemented
252C42×D17C2312yes—
253#10587556C2×C412yescomplemented
254(C2×#595)⋊C4C2312yes—
255(C2×#595)⋊C4C2312yes—
256(C2×#595)⋊C4C2312yes—
257(C2×#595)⋊C4C2312yes—
258(C2×#595)⋊C4C2312yes—
259(C2×#595)⋊C4C2312yes—
260(C2×#595)⋊C4C2312yes—
261(C2×#595)⋊C4C2312yes—
262(C2×#595)⋊C4C2312yes—
263(C2×#595)⋊C4C2312yes—
264(C2×#595)⋊C4C2312yes—
265(C2×#595)⋊C4C2312yes—
266(C2×#595)⋊C4C2312yes—
267(C2×#595)⋊C4C2312yes—
268(C2×#595)⋊C4C2312yes—
269(C2×#595)⋊C4C2312yes—
270(C2×#595)⋊C4C2312yes—
271(C2×#595)⋊C4C2312yes—
272(C2×#595)⋊C4C2312yes—
273(C2×#595)⋊C4C2312yes—
274(C2×#595)⋊C4C2312yes—
275(C2×#595)⋊C4C2312yes—
276(C2×#595)⋊C4C2312yes—
277(C2×#595)⋊C4C2312yes—
278C23×D17C2412yes—
279C23×D17C2411yescharacteristic
280C22×#595—22no—
281C22×#595—22no—
282C22×#595—22no—
283C22×#595—22no—
284C22×#595—22no—
285C22×#595—22no—
286C22×#595—24no—
287C22×#595—41no—
288C22×#595—41no—
289C22×#595—41no—
290C22×#595—42no—
291C22×#595—42no—
292C22×#595—42no—
293C22×#595—41no—
294C22×#595—42no—
295C22×#595—42no—
296C22×#595—41no—
297C22×#595—41no—
298C22×#595C2412yes—
299C22×#595C2412yes—
300C22×#595C2411yescharacteristic
301C22×#595C2412yes—
302C22×#595C2412yes—
303C22×#595C2411yescharacteristic
304C22×#595C2412yes—
305C22×#595C2412yes—
306C22×#595C2411yescharacteristic
307C22×#595C2411yescharacteristic
308C2×Q8×C17C22×C411yescharacteristic
309C2×D4×C17C22×C412yes—
310C2×D4×C17C22×C411yescharacteristic
311C22×C4×C17C22×C411yescharacteristic
312C22×C4×C17C22×C412yes—
313C22×C4×C17C22×C411yescharacteristic
314C22×C4×C17C22×C411yescharacteristic
315C2×C22⋊D17C22×C412yes—
316C2×C22⋊D17C22×C412yes—
317C2×C22⋊D17C22×C412yes—
318C22×Dic17C22×C411yescharacteristic
319C22×Dic17C22×C412yes—
320C22×Dic17C22×C411yescharacteristic
321C22×Dic17C22×C411yescharacteristic
322Q8×D17—41no—
323Q8×D17—41no—
324D4×D17—24no—
325D4×D17—24no—
326D4×D17—41no—
327D4×D17—41no—
328C2×D68C22×C412yes—
329C2×D68C22×C411yescharacteristic
330C2×C4×D17—22no—
331C2×C4×D17—22no—
332C2×C4×D17—41no—
333C2×C4×D17—41no—
334C2×C4×D17—42no—
335C2×C4×D17—41no—
336C2×C4×D17—42no—
337C2×C4×D17—41no—
338C2×C4×D17C22×C412yes—
339C2×C4×D17C22×C412yes—
340C2×C4×D17C22×C412yes—
341C2×C4×D17C22×C412yes—
342C2×C4×D17C22×C411yescharacteristic
343C2×C4×D17C22×C411yescharacteristic
344C2×C4×D17C2411yescharacteristic
345C2×C4×D17C2412yes—
346C2×C4×D17C2411yescharacteristic
347C2×C4×D17C2412yes—
348C2×C4×D17C2412yes—
349C2×C4×D17C2412yes—
350C2×C4×D17C2412yes—
351C2×Dic34C22×C411yescharacteristic
352C2×Dic34C22×C412yes—
353C22⋊#595—24no—
354C22⋊#595—24no—
355C22⋊#595—24no—
356C22⋊#595—42no—
357C22⋊#595—42no—
358C22⋊#595—42no—
359C22⋊#595—42no—
360C22⋊#595—42no—
361C4⋊#595—24no—
362C4⋊#595—24no—
363C4⋊#595—42no—
364C4⋊#595—42no—
365C4⋊#595—42no—
366C4⋊#595—41no—
367C4⋊#595—42no—
368C4⋊#595—41no—
369C4⋊#595—42no—
370C4⋊#595—42no—
371C4⋊#595—42no—
372C4⋊#595—41no—
373C4⋊#595—42no—
374C4⋊#595—42no—
375C4⋊#595—42no—
376C4⋊#595—41no—
377C4×#595—22no—
378C4×#595—22no—
379C4×#595—24no—
380C4×#595—41no—
381C4×#595—41no—
382C4×#595—42no—
383C4×#595—42no—
384C4×#595—42no—
385C4×#595—42no—
386C4×#595—42no—
387C4×#595—42no—
388C4×#595—42no—
389C4⋊C4×C17C22×C412yes—
390C4⋊C4×C17C22×C412yes—
391C4⋊C4×C17C22×C412yes—
392C4⋊C4×C17C22×C411yescharacteristic
393C4⋊C4×C17C22×C412yes—
394C4⋊C4×C17C22×C412yes—
395C4⋊C4×C17C22×C412yes—
396C4⋊C4×C17C22×C411yescharacteristic
397C22⋊C4×C17C22×C412yes—
398C22⋊C4×C17C22×C412yes—
399C22⋊C4×C17C22×C412yes—
400C22⋊C4×C17C22×C412yes—
401C22⋊C4×C17C22×C412yes—
402C42×C17C22×C412yes—
403C22⋊Dic17C22×C412yes—
404C22⋊Dic17C22×C412yes—
405C22⋊Dic17C22×C412yes—
406C22⋊Dic17C22×C412yes—
407C22⋊Dic17C22×C412yes—
408#63227C22×C412yes—
409#63227C22×C412yes—
410#63227C22×C412yes—
411#63227C22×C412yes—
412#63227C22×C412yes—
413#63227C22×C412yes—
414#63227C22×C412yes—
415#63227C22×C412yes—
416#63227C22×C412yes—
417#63227C22×C412yes—
418C4⋊Dic17C22×C412yes—
419C4⋊Dic17C22×C412yes—
420C4⋊Dic17C22×C412yes—
421C4⋊Dic17C22×C412yes—
422C4⋊Dic17C22×C411yescharacteristic
423C4⋊Dic17C22×C412yes—
424C4⋊Dic17C22×C412yes—
425C4⋊Dic17C22×C411yescharacteristic
426#63225C22×C412yes—
427#63225C22×C412yes—
428#63225C22×C412yes—
429#63225C22×C412yes—
430#63225C22×C412yes—
431#63225C22×C412yes—
432#63225C22×C412yes—
433#63225C22×C412yes—
434#63225C22×C412yes—
435#63225C22×C412yes—
436#63225C22×C412yes—
437#63225C22×C412yes—
438#63225C22×C412yes—
439#63225C22×C412yes—
440C4×Dic17C22×C412yes—
441C4×Dic17C22×C412yes—
442C4×Dic17C22×C412yes—
443#34427—171nomaximal, Sylow
444C23×C17C23×C412yes—
445C23×C17C23×C411yescharacteristic
446C22×D17—21no—
447C22×D17—21no—
448C22×D17—21no—
449C22×D17—21no—
450C22×D17—22no—
451C22×D17—22no—
452C22×D17—22no—
453C22×D17—22no—
454C22×D17—22no—
455C22×D17—22no—
456C22×D17C23×C412yes—
457C22×D17C23×C411yescharacteristic
458C22×D17H(5,𝔽2)12yes—
459C22×D172−1+412yes—
460C22×D17C2511yescharacteristic
461C2×#595—21no—
462C2×#595—21no—
463C2×#595—21no—
464C2×#595—21no—
465C2×#595—21no—
466C2×#595—22no—
467C2×#595—21no—
468C2×#595—22no—
469C2×#595—22no—
470C2×#595—22no—
471C2×#595—22no—
472C2×#595—22no—
473C2×#595—22no—
474C2×#595—22no—
475C2×#595—21no—
476C2×#595—22no—
477C2×#595—21no—
478C2×#595—22no—
479C2×#595—21no—
480C2×#595—22no—
481C2×#595—22no—
482C2×#595—22no—
483C2×#595—22no—
484C2×#595—22no—
485C2×#595—22no—
486C2×#595—22no—
487C2×#595—22no—
488C2×#595—21no—
489C2×#595—44no—
490C2×#595—44no—
491C2×#595—84no—
492C2×#595—82no—
493C2×#595—82no—
494C2×#595—84no—
495C2×#595H(5,𝔽2)12yes—
496C2×#5952−1+412yes—
497Q8×C17—41no—
498D4×C17—24no—
499D4×C17—41no—
500C2×C4×C17—22no—
501C2×C4×C17—42no—
502C2×C4×C17—41no—
503C2×C4×C17—41no—
504C2×C4×C17C23×C412yes—
505C2×C4×C17C23×C412yes—
506C2×C4×C17C23×C412yes—
507C2×C4×C17C23×C412yes—
508C2×C4×C17C23×C412yes—
509C2×C4×C17C23×C411yescharacteristic
510C2×C4×C17C23×C411yescharacteristic
511C22⋊D17—24no—
512C22⋊D17—24no—
513C22⋊D17—42no—
514C2×Dic17—22no—
515C2×Dic17—42no—
516C2×Dic17—41no—
517C2×Dic17—41no—
518C2×Dic17C23×C412yes—
519C2×Dic17C23×C411yescharacteristic
520C2×Dic17C23×C412yes—
521C2×Dic17C23×C412yes—
522C2×Dic17C23×C412yes—
523C2×Dic17C23×C412yes—
524C2×Dic17C23×C411yescharacteristic
525D68—24no—
526D68—41no—
527C4×D17—24no—
528C4×D17—21no—
529C4×D17—21no—
530C4×D17—22no—
531C4×D17—22no—
532C4×D17—22no—
533C4×D17—22no—
534C4×D17—22no—
535C4×D17—22no—
536C4×D17—22no—
537C4×D17—22no—
538C4×D17—22no—
539C4×D17—21no—
540C4×D17—22no—
541C4×D17—21no—
542C4×D17—42no—
543C4×D17—41no—
544C4×D17—42no—
545C4×D17—42no—
546C4×D17—41no—
547Dic34—41no—
548Dic34—42no—
549C2×#539—171no—
550#2382—172no—
551#2376—172no—
552#2370—172no—
553#2359—172no—
554#2359—172no—
555#2359—172no—
556#2352—172no—
557#2349—172no—
558#2334—172no—
559#2334—172no—
560#2329—172no—
561#2329—171no—
562#2325—171no—
563#2323—172no—
564#2316—171no—
565C4×C22⋊Q8—171no—
566C4×#121—171no—
567C2×#387—171no—
568C22×C17—21no—
569C22×C17—21no—
570C22×C17—22no—
571C22×C17—22no—
572C22×C17—22no—
573C22×C17#52012yes—
574C22×C17C24×C411yescharacteristic
575C2×D17—21no—
576C2×D17—21no—
577C2×D17—22no—
578C2×D17—22no—
579C2×D17—22no—
580C2×D17—22no—
581C2×D17—22no—
582C2×D17—22no—
583C2×D17—22no—
584C2×D17—42no—
585C2×D17—42no—
586C2×D17—42no—
587C2×D17—42no—
588C2×D17#52012yes—
589C2×D17C2×H(5,𝔽2)11yescharacteristic
590C2×D17C2×H(5,𝔽2)11yescharacteristic
591C2×D17C2×2−1+411yescharacteristic
592C2×D17C2×2−1+411yescharacteristic
593C2×D17#58511yescharacteristic
594C2×D17#58511yescharacteristic
595#595—22no—
596#595—22no—
597#595—41no—
598#595—42no—
599#595—42no—
600#595—41no—
601#595—42no—
602#595—42no—
603#595—42no—
604#595—42no—
605C4×C17—22no—
606C4×C17—22no—
607C4×C17—21no—
608C4×C17—22no—
609C4×C17—22no—
610C4×C17—21no—
611C4×C17—22no—
612Dic17—22no—
613Dic17—22no—
614Dic17—21no—
615Dic17—22no—
616Dic17—22no—
617Dic17—21no—
618Dic17—22no—
619#539—172no—
620#539—172no—
621#539—172no—
622#539—172no—
623#539—172no—
624#539—171no—
625#539—171no—
626#539—172no—
627#539—171no—
628#539#59511yescharacteristic, complemented
629C2×#126—172no—
630C2×#125—172no—
631C2×#123—172no—
632C2×#123—172no—
633C2×C22⋊Q8—172no—
634C2×C22⋊Q8—171no—
635C2×#121—171no—
636C2×C4×Q8—171no—
637C2×C4×D4—172no—
638C2×C4×D4—172no—
639C2×C4×D4—172no—
640C2×C4×D4—171no—
641C2×#117—172no—
642C2×#117—172no—
643C22×C4⋊C4—171no—
644C22×C4⋊C4—171no—
645C22×C42—171no—
646#391—172no—
647#391—171no—
648#390—171no—
649#389—172no—
650#389—172no—
651#389—172no—
652#389—172no—
653#389—172no—
654#389—172no—
655#389—172no—
656#389—172no—
657#389—171no—
658#389—172no—
659#389—171no—
660#388—172no—
661#388—172no—
662#388—172no—
663#388—172no—
664#388—172no—
665#388—172no—
666#388—172no—
667#388—172no—
668#387—172no—
669#387—172no—
670#387—172no—
671#387—172no—
672#387—172no—
673#387—172no—
674#387—172no—
675#387—172no—
676#387—172no—
677#387—172no—
678#387—172no—
679#387—172no—
680#387—172no—
681#387—172no—
682#386—172no—
683#386—172no—
684#386—172no—
685#385—172no—
686#385—172no—
687#385—172no—
688#385—172no—
689#385—172no—
690#385—172no—
691#385—172no—
692#382—172no—
693#382—172no—
694#380—171no—
695#380—171no—
696#380—172no—
697#380—172no—
698#380—172no—
699C4×C4⋊C4—172no—
700C4×C4⋊C4—171no—
701C4×C4⋊C4—172no—
702C4×C4⋊C4—172no—
703C4×C4⋊C4—172no—
704C4×C4⋊C4—172no—
705C4×C4⋊C4—171no—
706C4×C22⋊C4—172no—
707C4×C22⋊C4—172no—
708C4×C22⋊C4—172no—
709C4×C22⋊C4—172no—
710C4×C22⋊C4—172no—
711C2×#95—171no—
712C2×#95—172no—
713C2×#95—171no—
714C2×#95—171no—
715C2×#95—171no—
716C2×C17—22no—
717C2×C17—42no—
718C2×C17C2×#52011yescharacteristic
719C2×C17C4×H(5,𝔽2)11yescharacteristic
720C2×C17C4×2−1+411yescharacteristic
721D17—22no—
722D17—42no—
723D17#353511yescharacteristic
724D17#353611yescharacteristic
725D17#356011yescharacteristic
726D17#356311yescharacteristic
727C22×Q8—171no—
728C22×D4—172no—
729C22×D4—171no—
730C23×C4—171no—
731C23×C4—171no—
732C23×C4—171no—
733C23×C4—172no—
734C23×C4—171no—
735C23×C4—171no—
736C23×C4—171no—
737C23×C4—171no—
738C23×C4—172no—
739C23×C4—172no—
740#126—172no—
741#126—172no—
742#126—172no—
743#126—172no—
744#126—172no—
745#126—172no—
746#126—172no—
747#126C2×#59512yescomplemented
748#125—172no—
749#125—172no—
750#125—172no—
751#125—172no—
752#125—172no—
753#125—172no—
754#125—172no—
755#125C2×#59512yescomplemented
756#123—172no—
757#123—172no—
758#123—172no—
759#123—172no—
760#123—172no—
761#123—172no—
762#123—172no—
763#123—172no—
764#123—172no—
765#123—172no—
766#123—172no—
767#123—172no—
768#123—172no—
769#123—172no—
770#123C2×#59512yescomplemented
771#123C2×#59512yescomplemented
772C22⋊Q8—171no—
773C22⋊Q8—172no—
774C22⋊Q8—171no—
775C22⋊Q8—172no—
776C22⋊Q8—172no—
777C22⋊Q8—172no—
778C22⋊Q8—172no—
779C22⋊Q8—171no—
780C22⋊Q8—172no—
781C22⋊Q8—172no—
782C22⋊Q8—172no—
783C22⋊Q8—172no—
784C22⋊Q8C2×#59511yescharacteristic, complemented
785C22⋊Q8C2×#59512yescomplemented
786#121—171no—
787#121—172no—
788#121—171no—
789#121—171no—
790#121—172no—
791#121C2×#59511yescharacteristic
792C4×Q8—682no—
793C4×D4—172no—
794C4×D4—172no—
795C4×D4—172no—
796C4×D4—172no—
797C4×D4—172no—
798C4×D4—172no—
799C4×D4—172no—
800C4×D4—682no—
801C4×D4—684no—
802C4×D4—684no—
803C4×D4C2×#59512yescomplemented
804#117—684no—
805#117—684no—
806C2×C4⋊C4—171no—
807C2×C4⋊C4—171no—
808C2×C4⋊C4—171no—
809C2×C4⋊C4—172no—
810C2×C4⋊C4—172no—
811C2×C4⋊C4—172no—
812C2×C4⋊C4—172no—
813C2×C4⋊C4—172no—
814C2×C4⋊C4—171no—
815C2×C4⋊C4—172no—
816C2×C4⋊C4—172no—
817C2×C4⋊C4—171no—
818C2×C4⋊C4—172no—
819C2×C4⋊C4—172no—
820C2×C4⋊C4—172no—
821C2×C4⋊C4—172no—
822C2×C4⋊C4—172no—
823C2×C4⋊C4—172no—
824C2×C4⋊C4—172no—
825C2×C4⋊C4—171no—
826C2×C4⋊C4—172no—
827C2×C4⋊C4—172no—
828C2×C4⋊C4—172no—
829C2×C4⋊C4—171no—
830C2×C4⋊C4—172no—
831C2×C4⋊C4—172no—
832C2×C4⋊C4—171no—
833C2×C4⋊C4—171no—
834C2×C4⋊C4—172no—
835C2×C4⋊C4—682no—
836C2×C4⋊C4C2×#59511yescharacteristic, complemented
837C2×C22⋊C4—172no—
838C2×C22⋊C4—172no—
839C2×C22⋊C4—172no—
840C2×C22⋊C4—172no—
841C2×C22⋊C4—172no—
842C2×C22⋊C4—172no—
843C2×C22⋊C4—172no—
844C2×C22⋊C4—172no—
845C2×C22⋊C4—172no—
846C2×C22⋊C4—172no—
847C2×C22⋊C4—172no—
848C2×C22⋊C4—172no—
849C2×C22⋊C4—172no—
850C2×C42—172no—
851C2×C42—172no—
852C2×C42—171no—
853C2×C42—171no—
854C2×C42—172no—
855C2×C42—172no—
856C2×C42—172no—
857C2×C42—172no—
858C2×C42—172no—
859C2×C42—172no—
860C2×C42—171no—
861C2×C42—172no—
862C2×C42—171no—
863C2×C42—682no—
864#95—172no—
865#95—172no—
866#95—172no—
867#95—172no—
868#95—172no—
869#95—172no—
870#95—172no—
871#95—172no—
872#95—172no—
873#95—172no—
874#95—172no—
875#95—172no—
876#95—172no—
877#95—172no—
878#95—172no—
879#95—172no—
880#95—172no—
881#95—172no—
882#95—172no—
883#95—172no—
884#95—172no—
885#95—172no—
886#95—172no—
887#95—172no—
888C17#3442711yescharacteristic, complemented, Sylow
889C24—171no—
890C24—172no—
891C2×Q8—171no—
892C2×Q8—172no—
893C2×Q8—681no—
894C2×Q8—681no—
895C2×Q8C22×#59511yescharacteristic
896C2×D4—172no—
897C2×D4—172no—
898C2×D4—172no—
899C2×D4—172no—
900C2×D4—171no—
901C2×D4—344no—
902C2×D4—344no—
903C2×D4—681no—
904C2×D4—681no—
905C2×D4C22×#59512yes—
906C2×D4C22×#59511yescharacteristic
907C22×C4—171no—
908C22×C4—171no—
909C22×C4—171no—
910C22×C4—171no—
911C22×C4—171no—
912C22×C4—172no—
913C22×C4—172no—
914C22×C4—172no—
915C22×C4—172no—
916C22×C4—172no—
917C22×C4—172no—
918C22×C4—171no—
919C22×C4—171no—
920C22×C4—172no—
921C22×C4—172no—
922C22×C4—171no—
923C22×C4—171no—
924C22×C4—172no—
925C22×C4—172no—
926C22×C4—171no—
927C22×C4—172no—
928C22×C4—172no—
929C22×C4—171no—
930C22×C4—172no—
931C22×C4—172no—
932C22×C4—172no—
933C22×C4—172no—
934C22×C4—342no—
935C22×C4—342no—
936C22×C4—342no—
937C22×C4—342no—
938C22×C4—344no—
939C22×C4—342no—
940C22×C4—342no—
941C22×C4—342no—
942C22×C4—342no—
943C22×C4—681no—
944C22×C4—681no—
945C22×C4—682no—
946C22×C4—681no—
947C22×C4—682no—
948C22×C4—681no—
949C22×C4—681no—
950C22×C4—681no—
951C22×C4—681no—
952C22×C4—682no—
953C22×C4—682no—
954C22×C4—682no—
955C22×C4—681no—
956C22×C4—682no—
957C22×C4—682no—
958C22×C4—681no—
959C22×C4—681no—
960C22×C4C22×#59511yescharacteristic
961C22×C4C22×#59511yescharacteristic
962C22×C4C22×#59511yescharacteristic
963C22×C4C22×#59512yes—
964C4⋊C4—172no—
965C4⋊C4—172no—
966C4⋊C4—172no—
967C4⋊C4—172no—
968C4⋊C4—172no—
969C4⋊C4—172no—
970C4⋊C4—172no—
971C4⋊C4—172no—
972C4⋊C4—172no—
973C4⋊C4—172no—
974C4⋊C4—171no—
975C4⋊C4—172no—
976C4⋊C4—172no—
977C4⋊C4—172no—
978C4⋊C4—172no—
979C4⋊C4—172no—
980C4⋊C4—172no—
981C4⋊C4—172no—
982C4⋊C4—171no—
983C4⋊C4—172no—
984C4⋊C4—172no—
985C4⋊C4—172no—
986C4⋊C4—344no—
987C4⋊C4—344no—
988C4⋊C4—682no—
989C4⋊C4—682no—
990C4⋊C4—681no—
991C4⋊C4—682no—
992C4⋊C4—681no—
993C4⋊C4—682no—
994C4⋊C4—682no—
995C4⋊C4—682no—
996C4⋊C4—682no—
997C4⋊C4—681no—
998C4⋊C4—682no—
999C4⋊C4—682no—
1000C4⋊C4—682no—
1001C4⋊C4—681no—
1002C4⋊C4C22×#59512yes—
1003C4⋊C4C22×#59512yes—
1004C4⋊C4C22×#59512yes—
1005C4⋊C4C22×#59511yescharacteristic
1006C4⋊C4C22×#59512yes—
1007C4⋊C4C22×#59512yes—
1008C4⋊C4C22×#59511yescharacteristic
1009C4⋊C4C22×#59512yes—
1010C22⋊C4—172no—
1011C22⋊C4—172no—
1012C22⋊C4—172no—
1013C22⋊C4—172no—
1014C22⋊C4—172no—
1015C22⋊C4—172no—
1016C22⋊C4—172no—
1017C22⋊C4—172no—
1018C22⋊C4—172no—
1019C22⋊C4—172no—
1020C22⋊C4—172no—
1021C22⋊C4—172no—
1022C22⋊C4—172no—
1023C22⋊C4—172no—
1024C22⋊C4—172no—
1025C22⋊C4—344no—
1026C22⋊C4—344no—
1027C22⋊C4—344no—
1028C22⋊C4—682no—
1029C22⋊C4—682no—
1030C22⋊C4—682no—
1031C22⋊C4—682no—
1032C22⋊C4—682no—
1033C22⋊C4C22×#59512yes—
1034C22⋊C4C22×#59512yes—
1035C22⋊C4C22×#59512yes—
1036C22⋊C4C22×#59512yes—
1037C22⋊C4C22×#59512yes—
1038C42—172no—
1039C42—172no—
1040C42—172no—
1041C42—342no—
1042C42—342no—
1043C42—344no—
1044C42—682no—
1045C42—682no—
1046C42—681no—
1047C42—681no—
1048C42—682no—
1049C42—682no—
1050C42—682no—
1051C42—682no—
1052C42—682no—
1053C42C22×#59512yes—
1054C23—171no—
1055C23—172no—
1056C23—172no—
1057C23—171no—
1058C23—172no—
1059C23—341no—
1060C23—341no—
1061C23—341no—
1062C23—341no—
1063C23—342no—
1064C23—342no—
1065C23—342no—
1066C23—342no—
1067C23—342no—
1068C23—342no—
1069C23C23×#59512yes—
1070C23C23×#59511yescharacteristic
1071Q8—41no—
1072Q8—682no—
1073Q8—681no—
1074D4—24no—
1075D4—41no—
1076D4—344no—
1077D4—344no—
1078D4—344no—
1079D4—681no—
1080D4—682no—
1081C2×C4—22no—
1082C2×C4—41no—
1083C2×C4—42no—
1084C2×C4—41no—
1085C2×C4—172no—
1086C2×C4—172no—
1087C2×C4—172no—
1088C2×C4—172no—
1089C2×C4—172no—
1090C2×C4—172no—
1091C2×C4—172no—
1092C2×C4—171no—
1093C2×C4—171no—
1094C2×C4—341no—
1095C2×C4—341no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—342no—
1099C2×C4—342no—
1100C2×C4—342no—
1101C2×C4—342no—
1102C2×C4—342no—
1103C2×C4—341no—
1104C2×C4—342no—
1105C2×C4—341no—
1106C2×C4—342no—
1107C2×C4—344no—
1108C2×C4—342no—
1109C2×C4—341no—
1110C2×C4—341no—
1111C2×C4—341no—
1112C2×C4—341no—
1113C2×C4—342no—
1114C2×C4—341no—
1115C2×C4—342no—
1116C2×C4—342no—
1117C2×C4—342no—
1118C2×C4—341no—
1119C2×C4—342no—
1120C2×C4—342no—
1121C2×C4—342no—
1122C2×C4—342no—
1123C2×C4—342no—
1124C2×C4—342no—
1125C2×C4—342no—
1126C2×C4—342no—
1127C2×C4—341no—
1128C2×C4—341no—
1129C2×C4—342no—
1130C2×C4—342no—
1131C2×C4—342no—
1132C2×C4—342no—
1133C2×C4—342no—
1134C2×C4—341no—
1135C2×C4—341no—
1136C2×C4—342no—
1137C2×C4—342no—
1138C2×C4—682no—
1139C2×C4—682no—
1140C2×C4—681no—
1141C2×C4—682no—
1142C2×C4—681no—
1143C2×C4—681no—
1144C2×C4—682no—
1145C2×C4—681no—
1146C2×C4—684no—
1147C2×C4—684no—
1148C2×C4—1364no—
1149C2×C4—1362no—
1150C2×C4—1362no—
1151C2×C4—1364no—
1152C2×C4C23×#59512yes—
1153C2×C4C23×#59512yes—
1154C2×C4C23×#59512yes—
1155C2×C4C23×#59512yes—
1156C2×C4C23×#59512yes—
1157C2×C4C23×#59511yescharacteristic
1158C2×C4C23×#59511yescharacteristic
1159C22—21no—
1160C22—21no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—171no—
1165C22—171no—
1166C22—171no—
1167C22—171no—
1168C22—171no—
1169C22—171no—
1170C22—172no—
1171C22—342no—
1172C22—342no—
1173C22—342no—
1174C22—342no—
1175C22—341no—
1176C22—341no—
1177C22—342no—
1178C22—342no—
1179C22—342no—
1180C22—682no—
1181C22—682no—
1182C22—682no—
1183C22—682no—
1184C22#1176387812yes—
1185C22C24×#59511yescharacteristic
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—21no—
1190C4—22no—
1191C4—21no—
1192C4—22no—
1193C4—342no—
1194C4—342no—
1195C4—342no—
1196C4—342no—
1197C4—342no—
1198C4—341no—
1199C4—342no—
1200C4—341no—
1201C4—342no—
1202C4—681no—
1203C4—681no—
1204C4—682no—
1205C4—682no—
1206C4—682no—
1207C4—682no—
1208C4—682no—
1209C4—682no—
1210C2—22no—
1211C2—42no—
1212C2—171no—
1213C2—171no—
1214C2—171no—
1215C2—171no—
1216C2—342no—
1217C2—682no—
1218C2C2×#1176387811yescharacteristic
1219C2H(5,𝔽2)×#59511yescharacteristic
1220C22−1+4×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#539C4
prime radical#121×D17C22
cosocleC22×D17C25
hypercenter#539#595
hypocenterC17#34427
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #14545330C2semidirect
2. #14545324C2semidirect
3. #14545318C2semidirect
4. #14545307C2semidirect
5. #14545307C2semidirect
6. #14545307C2semidirect
7. #14545300C2semidirect
8. #14545297C2semidirect
9. #14545282C2semidirect
10. #14545282C2semidirect
11. #14545277C2semidirect
12. #14545277C2semidirect
14. #14545271C2semidirect
15. #14545264C2semidirect
16. C22⋊Q8×#595C2semidirect
18. C2×#11763758C2semidirect
98. #11763408C4semidirect
99. #11763407C4semidirect
100. #11763406C4semidirect
101. #11763405C4semidirect
102. #11763404C4semidirect
103. #11763403C4semidirect
104. #11763402C4semidirect
105. #11763401C4semidirect
106. #11763400C4semidirect
116. C17×#539C4semidirect
174. C17×#126C2×C4semidirect
175. C17×#125C2×C4semidirect
176. C17×#123C2×C4semidirect
177. C17×#123C2×C4semidirect
178. C17×C22⋊Q8C2×C4semidirect
179. C17×C22⋊Q8C2×C4semidirect
181. C4×D4×C17C2×C4semidirect
182. C2×C4⋊C4×C17C2×C4semidirect
183. #10587632C2×C4semidirect
184. #10587632C2×C4semidirect
187. #10587621C2×C4semidirect
188. #10587621C2×C4semidirect
189. D4×Dic17C2×C4semidirect
191. #10587615C2×C4semidirect
192. #10587615C2×C4semidirect
193. C4×C22⋊D17C2×C4semidirect
194. C4×C22⋊D17C2×C4semidirect
195. C2×C4⋊Dic17C2×C4semidirect
196. #10587610C2×C4semidirect
197. #10587610C2×C4semidirect
198. C2×#63225C2×C4semidirect
199. C2×#63225C2×C4semidirect
200. #10587584C2×C4semidirect
201. #10587584C2×C4semidirect
202. #10587584C2×C4semidirect
203. #10587583C2×C4semidirect
204. #10587583C2×C4semidirect
205. #10587582C2×C4semidirect
206. #10587582C2×C4semidirect
207. #10587582C2×C4semidirect
209. #10587580C2×C4semidirect
210. #10587580C2×C4semidirect
211. #10587580C2×C4semidirect
212. #10587580C2×C4semidirect
213. #10587579C2×C4semidirect
214. C4⋊C4×D17C2×C4semidirect
215. C4⋊C4×D17C2×C4semidirect
224. #10587576C2×C4semidirect
225. #10587576C2×C4semidirect
226. #10587575C2×C4semidirect
227. #10587575C2×C4semidirect
228. #10587575C2×C4semidirect
229. #10587575C2×C4semidirect
230. #10587572C2×C4semidirect
231. #10587572C2×C4semidirect
233. #10587569C2×C4semidirect
234. #10587569C2×C4semidirect
235. #10587569C2×C4semidirect
236. #10587569C2×C4semidirect
237. #10587567C2×C4semidirect
238. #10587567C2×C4semidirect
244. #10587565C2×C4semidirect
245. #10587565C2×C4semidirect
246. #10587565C2×C4semidirect
247. #10587564C2×C4semidirect
248. #10587564C2×C4semidirect
249. #10587564C2×C4semidirect
250. #10587562C2×C4semidirect
251. C4×D68C2×C4semidirect
253. #10587556C2×C4semidirect
628. #539#595semidirect
747. #126C2×#595semidirect
755. #125C2×#595semidirect
770. #123C2×#595semidirect
771. #123C2×#595semidirect
784. C22⋊Q8C2×#595semidirect
785. C22⋊Q8C2×#595semidirect
803. C4×D4C2×#595semidirect
836. C2×C4⋊C4C2×#595semidirect
888. C17#34427semidirect

Maximal subgroups

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

subgroupindex
#145453302
#145453242
#145453182
#145453072
#145453002
#145452972
#145452822
#145452772
#145452732
#145452712
#145452642
C22⋊Q8×#5952
#121×#5952
C2×#117637582
D17×#5392
#3442717