Finite Group Databasebeta

← #17979394

Subgroups — #17979394

Order 4352.

2216 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545330C211yesmaximal, characteristic, complemented
2#14545327C211yesmaximal, characteristic, complemented
3#14545327C211yesmaximal, characteristic, complemented
4#14545322C212yesmaximal, complemented
5#14545312C212yesmaximal, complemented
6#14545310C212yesmaximal, complemented
7#14545309C212yesmaximal, complemented
8#14545308C212yesmaximal, complemented
9#14545307C212yesmaximal, complemented
10#14545283C212yesmaximal, complemented
11#14545281C212yesmaximal, complemented
12#14545280C212yesmaximal, complemented
13#14545277C212yesmaximal, complemented
14#14545272C212yesmaximal, complemented
15#14545270C212yesmaximal, complemented
16#125×#595C211yesmaximal, characteristic, complemented
17#124×#595C211yesmaximal, characteristic, complemented
18#124×#595C211yesmaximal, characteristic, complemented
19D17×#562C211yesmaximal, characteristic
20C2×Q8×#595C2211yescharacteristic
21C2×Q8×#595C2211yescharacteristic
22C2×D4×#595C2211yescharacteristic
23C2×D4×#595C2211yescharacteristic
24C2×D4×#595C2212yes—
25C2×D4×#595C2212yes—
26C2×#10587677C2212yes—
27C22×C4⋊#595C2212yes—
28(C2×#595)⋊Q8C2211yescharacteristic
29(C2×#595)⋊Q8C2211yescharacteristic
30(C2×#595)⋊Q8C2212yes—
31(C2×#595)⋊Q8C2212yes—
32#11763761C2211yescharacteristic
33#11763761C2211yescharacteristic
34#11763761C2212yes—
35#11763761C2212yes—
36#11763760C2211yescharacteristic
37#11763760C2211yescharacteristic
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#11763759C2212yes—
51#11763759C2212yes—
52#11763759C2212yes—
53#11763759C2212yes—
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#11763757C2212yes—
68#11763757C2212yes—
69#11763757C2212yes—
70#11763756C2212yes—
71#11763756C2212yes—
72#11763756C2212yes—
73#11763756C2212yes—
74#11763756C2212yes—
75#11763756C2212yes—
76#11763753C2211yescharacteristic
77#11763753C2211yescharacteristic
78#11763753C2211yescharacteristic
79#11763752C2212yes—
80#11763751C2212yes—
81C4⋊C4×#595C2212yes—
82C4⋊C4×#595C2211yescharacteristic
83C4⋊C4×#595C2212yes—
84C4⋊C4×#595C2211yescharacteristic
85C4⋊C4×#595C2212yes—
86C4⋊C4×#595C2212yes—
87C22⋊C4×#595C2212yes—
88C22⋊C4×#595C2212yes—
89C22⋊C4×#595C2212yes—
90C22⋊C4×#595C2212yes—
91C22⋊C4×#595C2212yes—
92C22⋊C4×#595C2212yes—
93C4×C22⋊#595C2212yes—
94C4×C22⋊#595C2212yes—
95C4×C22⋊#595C2212yes—
96C2×(C2×#595)⋊C4C2212yes—
97C42×#595C2211yescharacteristic
98#11763557C411yescharacteristic, complemented
99#11763556C412yescomplemented
100#11763556C412yescomplemented
101#11763555C412yescomplemented
102#11763555C412yescomplemented
103#11763554C412yescomplemented
104#11763554C412yescomplemented
105#11763553C411yescharacteristic, complemented
106#11763553C411yescharacteristic, complemented
107#125×D17C2211yescharacteristic
108#124×D17C2211yescharacteristic
109#124×D17C2211yescharacteristic
110#123×D17C2212yes—
111#123×D17C2212yes—
112C22⋊Q8×D17C2212yes—
113C22⋊Q8×D17C2212yes—
114#121×D17C2212yes—
115#121×D17C2212yes—
116C17×#562C411yescharacteristic, complemented
117C23×#595C2312yes—
118C23×#595C2312yes—
119C23×#595C2312yes—
120C23×#595C2312yes—
121C2×Q8×D17C2311yescharacteristic
122C2×Q8×D17C2311yescharacteristic
123C2×D4×D17C2312yes—
124C2×D4×D17C2312yes—
125C2×D4×D17C2311yescharacteristic
126C2×D4×D17C2311yescharacteristic
127C22×C4×D17C2312yes—
128C22×C4×D17C2312yes—
129C2×C22⋊#595C2312yes—
130C2×C22⋊#595C2312yes—
131C2×C22⋊#595C2312yes—
132C2×C22⋊#595C2312yes—
133C2×C22⋊#595C2312yes—
134C2×C22⋊#595C2312yes—
135C2×C22⋊#595C2312yes—
136C2×C22⋊#595C2312yes—
137C2×C22⋊#595C2312yes—
138C2×C22⋊#595C2312yes—
139C2×C22⋊#595C2312yes—
140C2×C22⋊#595C2312yes—
141Q8×#595—42no—
142Q8×#595—42no—
143D4×#595—44no—
144D4×#595—42no—
145D4×#595—42no—
146D4×#595—44no—
147#10587677—44no—
148C2×C4⋊#595—44no—
149C2×C4⋊#595C2312yes—
150C2×C4⋊#595C2312yes—
151C2×C4⋊#595C2312yes—
152C2×C4⋊#595C2312yes—
153C2×C4⋊#595C2311yescharacteristic
154C2×C4⋊#595C2311yescharacteristic
155C2×C4⋊#595C2312yes—
156C2×C4⋊#595C2311yescharacteristic
157C2×C4⋊#595C2311yescharacteristic
158C2×C4⋊#595C2311yescharacteristic
159C2×C4⋊#595C2311yescharacteristic
160C2×C4⋊#595C2312yes—
161C2×C4⋊#595C2312yes—
162C2×C4⋊#595C2312yes—
163C2×C4×#595C2311yescharacteristic
164C2×C4×#595C2311yescharacteristic
165C2×C4×#595C2311yescharacteristic
166C2×C4×#595C2312yes—
167C2×C4×#595C2311yescharacteristic
168C2×C4×#595C2311yescharacteristic
169C2×C4×#595C2311yescharacteristic
170C2×C4×#595C2312yes—
171C2×C4×#595C2312yes—
172C2×C4×#595C2312yes—
173C2×C4×#595C2312yes—
174C2×C4×#595C2312yes—
175C2×C4×#595C2312yes—
176C2×C4×#595C2312yes—
177C17×#125C2×C411yescharacteristic, complemented
178C17×#124C2×C411yescharacteristic, complemented
179C17×#124C2×C411yescharacteristic, complemented
180C17×#123C2×C412yescomplemented
181C17×#123C2×C412yescomplemented
182C17×C22⋊Q8C2×C412yescomplemented
183C17×C22⋊Q8C2×C412yescomplemented
184C17×#121C2×C412yescomplemented
185C17×#121C2×C412yescomplemented
186#10587633C2×C411yescharacteristic, complemented
187#10587633C2×C411yescharacteristic, complemented
188#10587632C2×C412yescomplemented
189#10587632C2×C412yescomplemented
190#10587625C2×C412yescomplemented
191#10587625C2×C412yescomplemented
192#10587625C2×C412yescomplemented
193#10587625C2×C412yescomplemented
194#10587624C2×C412yescomplemented
195#10587624C2×C412yescomplemented
196#10587622C2×C411yescharacteristic, complemented
197#10587622C2×C411yescharacteristic, complemented
198#10587621C2×C412yescomplemented
199#10587621C2×C412yescomplemented
200#10587616C2×C412yescomplemented
201#10587616C2×C412yescomplemented
202#10587615C2×C412yescomplemented
203#10587615C2×C412yescomplemented
204#10587610C2×C412yescomplemented
205#10587610C2×C412yescomplemented
206#10587583C2×C412yescomplemented
207#10587583C2×C412yescomplemented
208#10587582C2×C412yescomplemented
209#10587582C2×C412yescomplemented
210#10587582C2×C412yescomplemented
211#10587582C2×C412yescomplemented
212#10587581C2×C412yescomplemented
213#10587581C2×C412yescomplemented
214#10587580C2×C412yescomplemented
215#10587580C2×C412yescomplemented
216#10587580C2×C412yescomplemented
217#10587580C2×C412yescomplemented
218C4⋊C4×D17C2312yes—
219C4⋊C4×D17C2312yes—
220C4⋊C4×D17C2312yes—
221C4⋊C4×D17C2312yes—
222C4⋊C4×D17C2311yescharacteristic
223C4⋊C4×D17C2311yescharacteristic
224#10587576C2×C411yescharacteristic, complemented
225#10587576C2×C411yescharacteristic, complemented
226#10587575C2×C412yescomplemented
227#10587575C2×C412yescomplemented
228#10587572C2×C412yescomplemented
229#10587572C2×C412yescomplemented
230#10587571C2×C412yescomplemented
231#10587571C2×C412yescomplemented
232#10587571C2×C412yescomplemented
233#10587571C2×C412yescomplemented
234#10587570C2×C412yescomplemented
235#10587570C2×C412yescomplemented
236#10587570C2×C412yescomplemented
237#10587570C2×C412yescomplemented
238#10587569C2×C412yescomplemented
239#10587569C2×C412yescomplemented
240#10587569C2×C412yescomplemented
241#10587569C2×C412yescomplemented
242C22⋊C4×D17C2312yes—
243C22⋊C4×D17C2312yes—
244C22⋊C4×D17C2312yes—
245C22⋊C4×D17C2312yes—
246C22⋊C4×D17C2312yes—
247C22⋊C4×D17C2312yes—
248#10587564C2×C412yescomplemented
249#10587564C2×C412yescomplemented
250#10587564C2×C412yescomplemented
251#10587564C2×C412yescomplemented
252#10587561C2×C411yescharacteristic, complemented
253#10587561C2×C411yescharacteristic, complemented
254C42×D17C2311yescharacteristic
255#10587556C2×C411yescharacteristic, complemented
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×D17C2412yes—
280C22×#595—24no—
281C22×#595—24no—
282C22×#595—42no—
283C22×#595—42no—
284C22×#595—42no—
285C22×#595—42no—
286C22×#595—42no—
287C22×#595—42no—
288C22×#595—42no—
289C22×#595—42no—
290C22×#595—42no—
291C22×#595—42no—
292C22×#595C2412yes—
293C22×#595C2412yes—
294C22×#595C2411yescharacteristic
295C22×#595C2412yes—
296C22×#595C2412yes—
297C22×#595C2412yes—
298C22×#595C2412yes—
299C22×#595C2411yescharacteristic
300C22×#595C2411yescharacteristic
301C22×#595C2411yescharacteristic
302C2×Q8×C17C22×C411yescharacteristic
303C2×Q8×C17C22×C411yescharacteristic
304C2×D4×C17C22×C412yes—
305C2×D4×C17C22×C412yes—
306C2×D4×C17C22×C411yescharacteristic
307C2×D4×C17C22×C411yescharacteristic
308C22×C4×C17C22×C412yes—
309C22×C4×C17C22×C412yes—
310C2×C22⋊D17C22×C412yes—
311C2×C22⋊D17C22×C412yes—
312C2×C22⋊D17C22×C412yes—
313C2×C22⋊D17C22×C412yes—
314C2×C22⋊D17C22×C412yes—
315C2×C22⋊D17C22×C412yes—
316C22×Dic17C22×C412yes—
317C22×Dic17C22×C412yes—
318Q8×D17—41no—
319Q8×D17—41no—
320Q8×D17—41no—
321Q8×D17—41no—
322D4×D17—42no—
323D4×D17—41no—
324D4×D17—41no—
325D4×D17—42no—
326D4×D17—42no—
327D4×D17—41no—
328D4×D17—41no—
329D4×D17—42no—
330C2×D68C22×C411yescharacteristic
331C2×D68C22×C411yescharacteristic
332C2×D68C22×C412yes—
333C2×D68C22×C412yes—
334C2×C4×D17—42no—
335C2×C4×D17—42no—
336C2×C4×D17—42no—
337C2×C4×D17—42no—
338C2×C4×D17C22×C412yes—
339C2×C4×D17C22×C412yes—
340C2×C4×D17C22×C412yes—
341C2×C4×D17C22×C412yes—
342C2×C4×D17C2412yes—
343C2×C4×D17C2412yes—
344C2×C4×D17C2412yes—
345C2×C4×D17C2412yes—
346C2×C4×D17C2411yescharacteristic
347C2×C4×D17C2411yescharacteristic
348C2×C4×D17C2411yescharacteristic
349C2×Dic34C22×C411yescharacteristic
350C2×Dic34C22×C411yescharacteristic
351C2×Dic34C22×C412yes—
352C2×Dic34C22×C412yes—
353C22⋊#595—24no—
354C22⋊#595—24no—
355C22⋊#595—24no—
356C22⋊#595—24no—
357C22⋊#595—42no—
358C22⋊#595—42no—
359C22⋊#595—42no—
360C22⋊#595—42no—
361C22⋊#595—42no—
362C22⋊#595—42no—
363C22⋊#595—42no—
364C22⋊#595—42no—
365C4⋊#595—24no—
366C4⋊#595—24no—
367C4⋊#595—24no—
368C4⋊#595—42no—
369C4⋊#595—42no—
370C4⋊#595—41no—
371C4⋊#595—41no—
372C4⋊#595—42no—
373C4⋊#595—42no—
374C4⋊#595—42no—
375C4⋊#595—41no—
376C4⋊#595—41no—
377C4⋊#595—41no—
378C4⋊#595—41no—
379C4×#595—24no—
380C4×#595—22no—
381C4×#595—22no—
382C4×#595—22no—
383C4×#595—41no—
384C4×#595—42no—
385C4×#595—42no—
386C4×#595—42no—
387C4×#595—41no—
388C4×#595—41no—
389C4×#595—42no—
390C4×#595—42no—
391C4×#595—42no—
392C4×#595—42no—
393C4⋊C4×C17C22×C412yes—
394C4⋊C4×C17C22×C412yes—
395C4⋊C4×C17C22×C412yes—
396C4⋊C4×C17C22×C412yes—
397C4⋊C4×C17C22×C411yescharacteristic
398C4⋊C4×C17C22×C411yescharacteristic
399C22⋊C4×C17C22×C412yes—
400C22⋊C4×C17C22×C412yes—
401C22⋊C4×C17C22×C412yes—
402C22⋊C4×C17C22×C412yes—
403C22⋊C4×C17C22×C412yes—
404C22⋊C4×C17C22×C412yes—
405C42×C17C22×C411yescharacteristic
406C22⋊Dic17C22×C412yes—
407C22⋊Dic17C22×C412yes—
408C22⋊Dic17C22×C412yes—
409C22⋊Dic17C22×C412yes—
410C22⋊Dic17C22×C412yes—
411C22⋊Dic17C22×C412yes—
412#63227C22×C412yes—
413#63227C22×C412yes—
414#63227C22×C412yes—
415#63227C22×C412yes—
416#63227C22×C412yes—
417#63227C22×C412yes—
418#63227C22×C412yes—
419#63227C22×C412yes—
420#63227C22×C412yes—
421#63227C22×C412yes—
422#63227C22×C412yes—
423#63227C22×C412yes—
424C4⋊Dic17C22×C411yescharacteristic
425C4⋊Dic17C22×C411yescharacteristic
426C4⋊Dic17C22×C412yes—
427C4⋊Dic17C22×C412yes—
428C4⋊Dic17C22×C412yes—
429C4⋊Dic17C22×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×C411yescharacteristic
441C4×Dic17C22×C411yescharacteristic
442C4×Dic17C22×C411yescharacteristic
443#34527—171nomaximal, Sylow
444C23×C17C23×C412yes—
445C23×C17C23×C412yes—
446C22×D17—22no—
447C22×D17—22no—
448C22×D17—22no—
449C22×D17—22no—
450C22×D17—22no—
451C22×D17—22no—
452C22×D17—22no—
453C22×D17—22no—
454C22×D17—22no—
455C22×D17—22no—
456C22×D17—22no—
457C22×D17—22no—
458C22×D17C23×C412yes—
459C22×D17C23×C412yes—
460C22×D17C2511yescharacteristic
461C2×#595—21no—
462C2×#595—21no—
463C2×#595—21no—
464C2×#595—21no—
465C2×#595—21no—
466C2×#595—21no—
467C2×#595—22no—
468C2×#595—22no—
469C2×#595—22no—
470C2×#595—22no—
471C2×#595—22no—
472C2×#595—22no—
473C2×#595—22no—
474C2×#595—22no—
475C2×#595—22no—
476C2×#595—22no—
477C2×#595—22no—
478C2×#595—21no—
479C2×#595—22no—
480C2×#595—22no—
481C2×#595—21no—
482C2×#595—21no—
483C2×#595—22no—
484C2×#595—22no—
485C2×#595—22no—
486C2×#595—22no—
487C2×#595—22no—
488C2×#595—84no—
489C2×#595—84no—
490C2×#595—84no—
491C2×#595—84no—
492C2×#595H(5,𝔽2)12yes—
493C2×#595H(5,𝔽2)12yes—
494C2×#5952−1+412yes—
495Q8×C17—41no—
496Q8×C17—41no—
497D4×C17—41no—
498D4×C17—41no—
499D4×C17—42no—
500D4×C17—42no—
501C2×C4×C17—42no—
502C2×C4×C17—42no—
503C2×C4×C17C23×C411yescharacteristic
504C2×C4×C17C23×C411yescharacteristic
505C2×C4×C17C23×C411yescharacteristic
506C2×C4×C17C23×C412yes—
507C2×C4×C17C23×C412yes—
508C2×C4×C17C23×C412yes—
509C2×C4×C17C23×C412yes—
510C22⋊D17—42no—
511C22⋊D17—42no—
512C22⋊D17—42no—
513C22⋊D17—42no—
514C22⋊D17—42no—
515C22⋊D17—42no—
516C2×Dic17—42no—
517C2×Dic17—42no—
518C2×Dic17C23×C411yescharacteristic
519C2×Dic17C23×C412yes—
520C2×Dic17C23×C412yes—
521C2×Dic17C23×C411yescharacteristic
522C2×Dic17C23×C411yescharacteristic
523C2×Dic17C23×C412yes—
524C2×Dic17C23×C412yes—
525D68—41no—
526D68—41no—
527D68—42no—
528D68—42no—
529C4×D17—22no—
530C4×D17—21no—
531C4×D17—21no—
532C4×D17—22no—
533C4×D17—22no—
534C4×D17—22no—
535C4×D17—21no—
536C4×D17—21no—
537C4×D17—22no—
538C4×D17—22no—
539C4×D17—22no—
540C4×D17—21no—
541C4×D17—21no—
542C4×D17—22no—
543C4×D17—42no—
544C4×D17—42no—
545C4×D17—42no—
546C4×D17—42no—
547Dic34—41no—
548Dic34—41no—
549Dic34—42no—
550Dic34—42no—
551C2×#562—171no—
552#2382—171no—
553#2379—171no—
554#2379—171no—
555#2374—172no—
556#2364—172no—
557#2362—172no—
558#2361—172no—
559#2360—172no—
560#2359—172no—
561#2335—172no—
562#2333—172no—
563#2332—172no—
564#2329—172no—
565#2324—172no—
566#2322—172no—
567C4×#125—171no—
568C4×#124—171no—
569C4×#124—171no—
570C22×C17—22no—
571C22×C17—22no—
572C22×C17—22no—
573C22×C17—22no—
574C22×C17—22no—
575C22×C17—22no—
576C22×C17C24×C411yescharacteristic
577C2×D17—22no—
578C2×D17—22no—
579C2×D17—22no—
580C2×D17—22no—
581C2×D17—22no—
582C2×D17—22no—
583C2×D17—42no—
584C2×D17—42no—
585C2×D17—42no—
586C2×D17—42no—
587C2×D17—42no—
588C2×D17—42no—
589C2×D17—42no—
590C2×D17—42no—
591C2×D17C2×H(5,𝔽2)11yescharacteristic
592C2×D17C2×H(5,𝔽2)11yescharacteristic
593C2×D17C2×2−1+411yescharacteristic
594C2×D17#58511yescharacteristic
595C2×D17#58511yescharacteristic
596C2×D17#58511yescharacteristic
597#595—22no—
598#595—22no—
599#595—22no—
600#595—42no—
601#595—42no—
602#595—42no—
603#595—42no—
604#595—42no—
605#595—42no—
606#595—41no—
607C4×C17—22no—
608C4×C17—22no—
609C4×C17—21no—
610C4×C17—21no—
611C4×C17—22no—
612C4×C17—22no—
613C4×C17—21no—
614Dic17—22no—
615Dic17—22no—
616Dic17—21no—
617Dic17—21no—
618Dic17—22no—
619Dic17—22no—
620Dic17—21no—
621#562—171no—
622#562—171no—
623#562—171no—
624#562—172no—
625#562—172no—
626#562—172no—
627#562—172no—
628#562—172no—
629#562—172no—
630#562#59511yescharacteristic, complemented
631C2×#125—171no—
632C2×#124—171no—
633C2×#124—171no—
634C2×#123—172no—
635C2×#123—172no—
636C2×C22⋊Q8—172no—
637C2×C22⋊Q8—172no—
638C2×#121—172no—
639C2×#121—172no—
640C2×C4×Q8—171no—
641C2×C4×Q8—171no—
642C2×C4×D4—172no—
643C2×C4×D4—172no—
644C2×C4×D4—171no—
645C2×C4×D4—171no—
646C2×#117—172no—
647C22×C4⋊C4—172no—
648#391—171no—
649#391—172no—
650#391—171no—
651#391—172no—
652#390—171no—
653#390—172no—
654#390—172no—
655#390—171no—
656#389—171no—
657#389—171no—
658#389—172no—
659#389—172no—
660#389—172no—
661#389—172no—
662#388—172no—
663#388—172no—
664#388—172no—
665#388—172no—
666#388—172no—
667#388—172no—
668#388—172no—
669#388—172no—
670#388—172no—
671#388—172no—
672#388—172no—
673#388—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#387—172no—
683#387—172no—
684#386—172no—
685#386—172no—
686#386—172no—
687#386—172no—
688#386—172no—
689#386—172no—
690#385—172no—
691#385—172no—
692#385—172no—
693#385—172no—
694#385—172no—
695#385—172no—
696#382—171no—
697#382—171no—
698#382—171no—
699#381—172no—
700#380—172no—
701C4×C4⋊C4—172no—
702C4×C4⋊C4—171no—
703C4×C4⋊C4—172no—
704C4×C4⋊C4—171no—
705C4×C4⋊C4—172no—
706C4×C4⋊C4—172no—
707C4×C22⋊C4—172no—
708C4×C22⋊C4—172no—
709C4×C22⋊C4—172no—
710C4×C22⋊C4—172no—
711C4×C22⋊C4—172no—
712C4×C22⋊C4—172no—
713C4×C22⋊C4—172no—
714C4×C22⋊C4—172no—
715C4×C22⋊C4—172no—
716C2×#95—172no—
717C43—171no—
718C2×C17—42no—
719C2×C17—42no—
720C2×C17C4×H(5,𝔽2)11yescharacteristic
721C2×C17C4×H(5,𝔽2)11yescharacteristic
722C2×C17C4×2−1+411yescharacteristic
723D17—42no—
724D17—42no—
725D17#355811yescharacteristic
726D17#355911yescharacteristic
727D17#356111yescharacteristic
728D17#356711yescharacteristic
729C22×Q8—171no—
730C22×Q8—171no—
731C22×D4—172no—
732C22×D4—172no—
733C22×D4—171no—
734C22×D4—171no—
735C23×C4—172no—
736C23×C4—172no—
737C23×C4—172no—
738C23×C4—172no—
739C23×C4—172no—
740C23×C4—172no—
741#125—172no—
742#125—172no—
743#125—171no—
744#125—171no—
745#125—171no—
746#125C2×#59511yescharacteristic, complemented
747#124—171no—
748#124—171no—
749#124—171no—
750#124—171no—
751#124—172no—
752#124—172no—
753#124—172no—
754#124—172no—
755#124—171no—
756#124—171no—
757#124C2×#59511yescharacteristic, complemented
758#124C2×#59511yescharacteristic, complemented
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#123—172no—
771#123—172no—
772#123—172no—
773#123C2×#59512yescomplemented
774#123C2×#59512yescomplemented
775C22⋊Q8—172no—
776C22⋊Q8—172no—
777C22⋊Q8—172no—
778C22⋊Q8—172no—
779C22⋊Q8—172no—
780C22⋊Q8—172no—
781C22⋊Q8—172no—
782C22⋊Q8—172no—
783C22⋊Q8—172no—
784C22⋊Q8—172no—
785C22⋊Q8—172no—
786C22⋊Q8—172no—
787C22⋊Q8—172no—
788C22⋊Q8—172no—
789C22⋊Q8C2×#59512yescomplemented
790C22⋊Q8C2×#59512yescomplemented
791#121—172no—
792#121—172no—
793#121—172no—
794#121—172no—
795#121—172no—
796#121—172no—
797#121—172no—
798#121—172no—
799#121—172no—
800#121—172no—
801#121—172no—
802#121—172no—
803#121—172no—
804#121—172no—
805#121C2×#59512yescomplemented
806#121C2×#59512yescomplemented
807C4×Q8—682no—
808C4×Q8—682no—
809C4×D4—684no—
810C4×D4—682no—
811C4×D4—682no—
812C4×D4—684no—
813#117—684no—
814C2×C4⋊C4—172no—
815C2×C4⋊C4—172no—
816C2×C4⋊C4—172no—
817C2×C4⋊C4—172no—
818C2×C4⋊C4—171no—
819C2×C4⋊C4—171no—
820C2×C4⋊C4—172no—
821C2×C4⋊C4—172no—
822C2×C4⋊C4—172no—
823C2×C4⋊C4—172no—
824C2×C4⋊C4—172no—
825C2×C4⋊C4—172no—
826C2×C4⋊C4—172no—
827C2×C4⋊C4—171no—
828C2×C4⋊C4—171no—
829C2×C4⋊C4—171no—
830C2×C4⋊C4—171no—
831C2×C4⋊C4—172no—
832C2×C4⋊C4—171no—
833C2×C4⋊C4—171no—
834C2×C4⋊C4—684no—
835C2×C22⋊C4—172no—
836C2×C22⋊C4—172no—
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×C22⋊C4—172no—
851C2×C22⋊C4—172no—
852C2×C22⋊C4—172no—
853C2×C42—171no—
854C2×C42—172no—
855C2×C42—171no—
856C2×C42—171no—
857C2×C42—171no—
858C2×C42—172no—
859C2×C42—172no—
860C2×C42—172no—
861C2×C42—172no—
862C2×C42—171no—
863C2×C42—171no—
864C2×C42—171no—
865C2×C42—172no—
866C2×C42—172no—
867C2×C42—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—
888#95—172no—
889#95—172no—
890C17#3452711yescharacteristic, complemented, Sylow
891C24—172no—
892C24—172no—
893C2×Q8—172no—
894C2×Q8—172no—
895C2×Q8—171no—
896C2×Q8—171no—
897C2×Q8—681no—
898C2×Q8—681no—
899C2×Q8—681no—
900C2×Q8—681no—
901C2×Q8C22×#59511yescharacteristic
902C2×Q8C22×#59511yescharacteristic
903C2×D4—172no—
904C2×D4—172no—
905C2×D4—172no—
906C2×D4—172no—
907C2×D4—172no—
908C2×D4—172no—
909C2×D4—172no—
910C2×D4—172no—
911C2×D4—171no—
912C2×D4—171no—
913C2×D4—682no—
914C2×D4—681no—
915C2×D4—681no—
916C2×D4—682no—
917C2×D4—682no—
918C2×D4—681no—
919C2×D4—681no—
920C2×D4—682no—
921C2×D4C22×#59512yes—
922C2×D4C22×#59512yes—
923C2×D4C22×#59511yescharacteristic
924C2×D4C22×#59511yescharacteristic
925C22×C4—171no—
926C22×C4—171no—
927C22×C4—171no—
928C22×C4—172no—
929C22×C4—172no—
930C22×C4—171no—
931C22×C4—171no—
932C22×C4—171no—
933C22×C4—172no—
934C22×C4—172no—
935C22×C4—172no—
936C22×C4—172no—
937C22×C4—172no—
938C22×C4—172no—
939C22×C4—172no—
940C22×C4—172no—
941C22×C4—172no—
942C22×C4—172no—
943C22×C4—172no—
944C22×C4—171no—
945C22×C4—172no—
946C22×C4—172no—
947C22×C4—172no—
948C22×C4—344no—
949C22×C4—344no—
950C22×C4—682no—
951C22×C4—682no—
952C22×C4—682no—
953C22×C4—682no—
954C22×C4—682no—
955C22×C4—682no—
956C22×C4—682no—
957C22×C4—682no—
958C22×C4—682no—
959C22×C4—682no—
960C22×C4—682no—
961C22×C4—682no—
962C22×C4—682no—
963C22×C4—682no—
964C22×C4C22×#59512yes—
965C22×C4C22×#59512yes—
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—172no—
975C4⋊C4—172no—
976C4⋊C4—172no—
977C4⋊C4—172no—
978C4⋊C4—172no—
979C4⋊C4—172no—
980C4⋊C4—171no—
981C4⋊C4—171no—
982C4⋊C4—344no—
983C4⋊C4—344no—
984C4⋊C4—344no—
985C4⋊C4—681no—
986C4⋊C4—681no—
987C4⋊C4—682no—
988C4⋊C4—682no—
989C4⋊C4—682no—
990C4⋊C4—682no—
991C4⋊C4—682no—
992C4⋊C4—681no—
993C4⋊C4—681no—
994C4⋊C4—681no—
995C4⋊C4—681no—
996C4⋊C4C22×#59512yes—
997C4⋊C4C22×#59512yes—
998C4⋊C4C22×#59512yes—
999C4⋊C4C22×#59512yes—
1000C4⋊C4C22×#59511yescharacteristic
1001C4⋊C4C22×#59511yescharacteristic
1002C22⋊C4—172no—
1003C22⋊C4—172no—
1004C22⋊C4—172no—
1005C22⋊C4—172no—
1006C22⋊C4—172no—
1007C22⋊C4—172no—
1008C22⋊C4—172no—
1009C22⋊C4—172no—
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—344no—
1021C22⋊C4—344no—
1022C22⋊C4—344no—
1023C22⋊C4—344no—
1024C22⋊C4—682no—
1025C22⋊C4—682no—
1026C22⋊C4—682no—
1027C22⋊C4—682no—
1028C22⋊C4—682no—
1029C22⋊C4—682no—
1030C22⋊C4—682no—
1031C22⋊C4—682no—
1032C22⋊C4C22×#59512yes—
1033C22⋊C4C22×#59512yes—
1034C22⋊C4C22×#59512yes—
1035C22⋊C4C22×#59512yes—
1036C22⋊C4C22×#59512yes—
1037C22⋊C4C22×#59512yes—
1038C42—171no—
1039C42—171no—
1040C42—171no—
1041C42—342no—
1042C42—344no—
1043C42—342no—
1044C42—342no—
1045C42—681no—
1046C42—682no—
1047C42—682no—
1048C42—682no—
1049C42—681no—
1050C42—681no—
1051C42—682no—
1052C42—682no—
1053C42—682no—
1054C42—682no—
1055C42C22×#59511yescharacteristic
1056C23—171no—
1057C23—172no—
1058C23—172no—
1059C23—342no—
1060C23—342no—
1061C23—342no—
1062C23—342no—
1063C23—342no—
1064C23—342no—
1065C23—342no—
1066C23—342no—
1067C23—342no—
1068C23—342no—
1069C23—342no—
1070C23—342no—
1071C23C23×#59512yes—
1072C23C23×#59512yes—
1073Q8—41no—
1074Q8—41no—
1075Q8—682no—
1076Q8—682no—
1077Q8—681no—
1078Q8—681no—
1079D4—42no—
1080D4—42no—
1081D4—41no—
1082D4—41no—
1083D4—682no—
1084D4—682no—
1085D4—681no—
1086D4—681no—
1087D4—682no—
1088D4—682no—
1089D4—682no—
1090D4—682no—
1091D4—682no—
1092D4—682no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—172no—
1096C2×C4—172no—
1097C2×C4—172no—
1098C2×C4—171no—
1099C2×C4—171no—
1100C2×C4—171no—
1101C2×C4—172no—
1102C2×C4—172no—
1103C2×C4—172no—
1104C2×C4—172no—
1105C2×C4—342no—
1106C2×C4—341no—
1107C2×C4—341no—
1108C2×C4—341no—
1109C2×C4—342no—
1110C2×C4—342no—
1111C2×C4—342no—
1112C2×C4—341no—
1113C2×C4—342no—
1114C2×C4—342no—
1115C2×C4—342no—
1116C2×C4—341no—
1117C2×C4—341no—
1118C2×C4—342no—
1119C2×C4—341no—
1120C2×C4—341no—
1121C2×C4—341no—
1122C2×C4—341no—
1123C2×C4—341no—
1124C2×C4—341no—
1125C2×C4—342no—
1126C2×C4—342no—
1127C2×C4—342no—
1128C2×C4—342no—
1129C2×C4—342no—
1130C2×C4—342no—
1131C2×C4—341no—
1132C2×C4—341no—
1133C2×C4—342no—
1134C2×C4—342no—
1135C2×C4—342no—
1136C2×C4—342no—
1137C2×C4—341no—
1138C2×C4—342no—
1139C2×C4—342no—
1140C2×C4—342no—
1141C2×C4—342no—
1142C2×C4—342no—
1143C2×C4—342no—
1144C2×C4—342no—
1145C2×C4—342no—
1146C2×C4—682no—
1147C2×C4—682no—
1148C2×C4—682no—
1149C2×C4—682no—
1150C2×C4—682no—
1151C2×C4—682no—
1152C2×C4—1364no—
1153C2×C4—1364no—
1154C2×C4—1364no—
1155C2×C4—1364no—
1156C2×C4C23×#59511yescharacteristic
1157C2×C4C23×#59511yescharacteristic
1158C2×C4C23×#59511yescharacteristic
1159C2×C4C23×#59512yes—
1160C2×C4C23×#59512yes—
1161C2×C4C23×#59512yes—
1162C2×C4C23×#59512yes—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—22no—
1169C22—171no—
1170C22—171no—
1171C22—171no—
1172C22—171no—
1173C22—171no—
1174C22—171no—
1175C22—342no—
1176C22—342no—
1177C22—342no—
1178C22—342no—
1179C22—342no—
1180C22—342no—
1181C22—682no—
1182C22—682no—
1183C22—682no—
1184C22—682no—
1185C22—682no—
1186C22—682no—
1187C22—682no—
1188C22—682no—
1189C22C24×#59511yescharacteristic
1190C4—22no—
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—21no—
1195C4—21no—
1196C4—21no—
1197C4—342no—
1198C4—342no—
1199C4—342no—
1200C4—342no—
1201C4—342no—
1202C4—342no—
1203C4—342no—
1204C4—341no—
1205C4—341no—
1206C4—341no—
1207C4—682no—
1208C4—682no—
1209C4—682no—
1210C4—682no—
1211C4—682no—
1212C4—682no—
1213C4—681no—
1214C2—42no—
1215C2—42no—
1216C2—171no—
1217C2—171no—
1218C2—171no—
1219C2—171no—
1220C2—682no—
1221C2—682no—
1222C2H(5,𝔽2)×#59511yescharacteristic
1223C2H(5,𝔽2)×#59511yescharacteristic
1224C22−1+4×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#562C4
prime radicalD17×#562C2
cosocleC22×D17C25
hypercenter#562#595
hypocenterC17#34527
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #14545330C2semidirect
2. #14545327C2semidirect
3. #14545327C2semidirect
4. #14545322C2semidirect
5. #14545312C2semidirect
6. #14545310C2semidirect
7. #14545309C2semidirect
8. #14545308C2semidirect
9. #14545307C2semidirect
10. #14545283C2semidirect
11. #14545281C2semidirect
12. #14545280C2semidirect
13. #14545277C2semidirect
14. #14545272C2semidirect
15. #14545270C2semidirect
16. #125×#595C2semidirect
17. #124×#595C2semidirect
18. #124×#595C2semidirect
98. #11763557C4semidirect
99. #11763556C4semidirect
100. #11763556C4semidirect
101. #11763555C4semidirect
102. #11763555C4semidirect
103. #11763554C4semidirect
104. #11763554C4semidirect
105. #11763553C4semidirect
106. #11763553C4semidirect
116. C17×#562C4semidirect
177. C17×#125C2×C4semidirect
178. C17×#124C2×C4semidirect
179. C17×#124C2×C4semidirect
180. C17×#123C2×C4semidirect
181. C17×#123C2×C4semidirect
182. C17×C22⋊Q8C2×C4semidirect
183. C17×C22⋊Q8C2×C4semidirect
184. C17×#121C2×C4semidirect
185. C17×#121C2×C4semidirect
186. #10587633C2×C4semidirect
187. #10587633C2×C4semidirect
188. #10587632C2×C4semidirect
189. #10587632C2×C4semidirect
190. #10587625C2×C4semidirect
191. #10587625C2×C4semidirect
192. #10587625C2×C4semidirect
193. #10587625C2×C4semidirect
194. #10587624C2×C4semidirect
195. #10587624C2×C4semidirect
196. #10587622C2×C4semidirect
197. #10587622C2×C4semidirect
198. #10587621C2×C4semidirect
199. #10587621C2×C4semidirect
200. #10587616C2×C4semidirect
201. #10587616C2×C4semidirect
202. #10587615C2×C4semidirect
203. #10587615C2×C4semidirect
204. #10587610C2×C4semidirect
205. #10587610C2×C4semidirect
206. #10587583C2×C4semidirect
207. #10587583C2×C4semidirect
208. #10587582C2×C4semidirect
209. #10587582C2×C4semidirect
210. #10587582C2×C4semidirect
211. #10587582C2×C4semidirect
212. #10587581C2×C4semidirect
213. #10587581C2×C4semidirect
214. #10587580C2×C4semidirect
215. #10587580C2×C4semidirect
216. #10587580C2×C4semidirect
217. #10587580C2×C4semidirect
224. #10587576C2×C4semidirect
225. #10587576C2×C4semidirect
226. #10587575C2×C4semidirect
227. #10587575C2×C4semidirect
228. #10587572C2×C4semidirect
229. #10587572C2×C4semidirect
230. #10587571C2×C4semidirect
231. #10587571C2×C4semidirect
232. #10587571C2×C4semidirect
233. #10587571C2×C4semidirect
234. #10587570C2×C4semidirect
235. #10587570C2×C4semidirect
236. #10587570C2×C4semidirect
237. #10587570C2×C4semidirect
238. #10587569C2×C4semidirect
239. #10587569C2×C4semidirect
240. #10587569C2×C4semidirect
241. #10587569C2×C4semidirect
248. #10587564C2×C4semidirect
249. #10587564C2×C4semidirect
250. #10587564C2×C4semidirect
251. #10587564C2×C4semidirect
252. #10587561C2×C4semidirect
253. #10587561C2×C4semidirect
255. #10587556C2×C4semidirect
630. #562#595semidirect
746. #125C2×#595semidirect
757. #124C2×#595semidirect
758. #124C2×#595semidirect
773. #123C2×#595semidirect
774. #123C2×#595semidirect
789. C22⋊Q8C2×#595semidirect
790. C22⋊Q8C2×#595semidirect
805. #121C2×#595semidirect
806. #121C2×#595semidirect
890. C17#34527semidirect

Maximal subgroups

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

subgroupindex
#145453302
#145453272
#145453222
#145453122
#145453102
#145453092
#145453082
#145453072
#145452832
#145452812
#145452802
#145452772
#145452722
#145452702
#125×#5952
#124×#5952
D17×#5622
#3452717