Finite Group Databasebeta

← #17979229

Subgroups — #17979229

Order 4352.

2586 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545326C212yesmaximal, complemented
2#14545325C212yesmaximal, complemented
3#14545316C212yesmaximal, complemented
4#14545312C212yesmaximal, complemented
5#14545302C212yesmaximal, complemented
6#14545300C212yesmaximal, complemented
7#14545300C212yesmaximal, complemented
8D4×C4⋊#595C212yesmaximal, complemented
9#14545283C214yesmaximal, complemented
10#14545269C214yesmaximal, complemented
11#14545262C212yesmaximal, complemented
12#14545259C212yesmaximal, complemented
13#14545228C211yesmaximal, characteristic, complemented
14C2×#11763751C211yesmaximal, characteristic, complemented
15D17×#525C211yesmaximal, characteristic
16C2×D4×#595C2214yes—
17C2×#10587677C2212yes—
18C2×#10587677C2212yescomplemented
19C22×C4⋊#595C2212yes—
20C22×C4⋊#595C2212yescomplemented
21C22×C22⋊#595C2212yes—
22(C2×#595)⋊Q8C2214yescomplemented
23#11763761C2214yes—
24#11763761C2214yes—
25#11763760C2214yescomplemented
26#11763759C2214yes—
27#11763759C2214yes—
28#11763759C2214yes—
29#11763759C2214yes—
30#11763759C2214yescomplemented
31#11763759C2214yescomplemented
32#11763758C2214yescomplemented
33#11763758C2214yescomplemented
34#11763758C2214yescomplemented
35#11763758C2214yescomplemented
36#11763757C2214yes—
37#11763757C2214yes—
38#11763757C2214yes—
39#11763757C2214yescomplemented
40#11763756C2214yes—
41#11763756C2214yescomplemented
42#11763755C2212yescomplemented
43#11763753C2212yescomplemented
44#11763752C2212yes—
45#11763751C2212yes—
46#11763751C2212yes—
47#11763751C2211yescharacteristic
48#11763751C2211yescharacteristic
49#11763751C2212yes—
50#11763751C2212yes—
51#11763751C2211yescharacteristic
52#11763751C2211yescharacteristic
53#11763751C2212yescomplemented
54#11763751C2212yescomplemented
55#11763750C2212yes—
56C4⋊C4×#595C2214yescomplemented
57C4×C4⋊#595C2212yescomplemented
58C4×C4⋊#595C2212yescomplemented
59C22⋊C4×#595C2214yes—
60C22⋊C4×#595C2214yescomplemented
61C4×C22⋊#595C2212yes—
62C4×C22⋊#595C2212yes—
63C2×(C2×#595)⋊C4C2212yes—
64C2×#41×D17C2211yescharacteristic
65C23×C4×D17C2211yescharacteristic
66#11763322C411yescharacteristic, complemented
67#11763322C411yescharacteristic, complemented
68#11763321C411yescharacteristic, complemented
69#11763320C411yescharacteristic, complemented
70#11763319C411yescharacteristic, complemented
71#11763319C411yescharacteristic, complemented
72#11763318C412yescomplemented
73#11763318C412yescomplemented
74#11763317C412yescomplemented
75#11763316C411yescharacteristic, complemented
76#11763315C412yescomplemented
77#123×D17C2212yes—
78C22⋊Q8×D17C2211yescharacteristic
79C22⋊Q8×D17C2211yescharacteristic
80#121×D17C2211yescharacteristic
81#121×D17C2211yescharacteristic
82#120×D17C2212yes—
83C4×D4×D17C2212yes—
84C4×D4×D17C2212yes—
85#117×D17C2211yescharacteristic
86C17×#525C411yescharacteristic, complemented
87C24×D17C2311yescharacteristic
88C23×#595C2314yes—
89C23×#595C2314yes—
90C2×#41×C17C2×C411yescharacteristic, complemented
91C23×C4×C17C2×C411yescharacteristic, complemented
92C23×Dic17C2×C411yescharacteristic, complemented
93#41×D17—44no—
94C2×#63256C2×C411yescharacteristic, complemented
95C2×Q8×D17C2311yescharacteristic
96C2×#63254C2×C412yescomplemented
97C2×#63254C2×C411yescharacteristic, complemented
98C2×D4×D17C2312yes—
99C2×D4×D17C2312yes—
100C2×D4×D17C2312yes—
101C2×D4×D17C2311yescharacteristic
102C2×#63252C2×C412yescomplemented
103C2×#63252C2×C411yescharacteristic, complemented
104C22×C4×D17—44no—
105C22×C4×D17C2×C411yescharacteristic, complemented
106C22×C4×D17C2×C411yescharacteristic, complemented
107C22×C4×D17C2×C411yescharacteristic, complemented
108C22×C4×D17C2×C411yescharacteristic, complemented
109C22×C4×D17C2×C411yescharacteristic, complemented
110C22×C4×D17C2×C411yescharacteristic, complemented
111C22×C4×D17C2311yescharacteristic
112C22×C4×D17C2311yescharacteristic
113C22×C4×D17C2311yescharacteristic
114C22×C4×D17C2312yes—
115C22×C4×D17C2311yescharacteristic
116C22×C4×D17C2311yescharacteristic
117C22×C4×D17C2311yescharacteristic
118C2×C22⋊#595—44no—
119C2×C22⋊#595C2312yes—
120C2×C22⋊#595C2312yes—
121C2×C22⋊#595C2314yes—
122C2×C22⋊#595C2314yes—
123C2×C22⋊#595C2314yes—
124C2×C22⋊#595C2312yes—
125C2×C22⋊#595C2314yes—
126C2×C22⋊#595C2312yes—
127C2×C22⋊#595C2314yes—
128C2×C22⋊#595C2314yes—
129D4×#595—48no—
130#10587677—44no—
131#10587677—44no—
132C2×C4⋊#595—44no—
133C2×C4⋊#595—44no—
134C2×C4⋊#595C2312yes—
135C2×C4⋊#595C2312yes—
136C2×C4⋊#595C2312yes—
137C2×C4⋊#595C2312yes—
138C2×C4⋊#595C2314yes—
139C2×C4⋊#595C2314yes—
140C2×C4⋊#595C2314yes—
141C2×C4⋊#595C2314yes—
142C2×C4×#595C2314yes—
143C2×C4×#595C2314yes—
144C2×C4×#595C2314yes—
145C2×C4×#595C2314yes—
146C17×#123C2×C412yescomplemented
147C17×C22⋊Q8C2×C411yescharacteristic, complemented
148C17×C22⋊Q8C2×C411yescharacteristic, complemented
149C17×#121C2×C411yescharacteristic
150C17×#121C2×C411yescharacteristic, complemented
151C17×#120C2×C412yescomplemented
152C4×D4×C17C2×C412yescomplemented
153C4×D4×C17C2×C412yescomplemented
154C17×#117C2×C411yescharacteristic, complemented
155#10587639C2×C412yescomplemented
156#10587632C2×C411yescharacteristic, complemented
157#10587632C2×C411yescharacteristic, complemented
158#10587625C2×C412yes—
159#10587625C2×C412yescomplemented
160#10587624C2×C411yescharacteristic
161#10587624C2×C411yescharacteristic, complemented
162#10587623C2×C412yescomplemented
163#10587623C2×C412yescomplemented
164#10587623C2×C412yescomplemented
165#10587621C2×C412yescomplemented
166D4×Dic17C2×C412yescomplemented
167D4×Dic17C2×C412yescomplemented
168#10587616C2×C411yescharacteristic
169#10587616C2×C411yescharacteristic, complemented
170#10587615C2×C412yescomplemented
171C4×C22⋊D17C2×C412yescomplemented
172C4×C22⋊D17C2×C412yescomplemented
173C4×C22⋊D17C2×C412yescomplemented
174C4×C22⋊D17C2×C412yescomplemented
175#10587612C2×C411yescharacteristic, complemented
176#10587610C2×C411yescharacteristic, complemented
177#10587610C2×C411yescharacteristic, complemented
178#10587583C2×C411yescharacteristic, complemented
179#10587583C2×C411yescharacteristic, complemented
180#10587582C2×C412yescomplemented
181#10587582C2×C412yescomplemented
182#10587581C2×C411yescharacteristic
183#10587581C2×C411yescharacteristic, complemented
184#10587580C2×C412yescomplemented
185#10587580C2×C412yescomplemented
186#10587579C2×C412yescomplemented
187#10587579C2×C412yescomplemented
188#10587578C2×C411yescharacteristic, complemented
189#10587578C2×C411yescharacteristic, complemented
190C4⋊C4×D17C2312yes—
191C4⋊C4×D17C2311yescharacteristic
192C4⋊C4×D17C2311yescharacteristic
193C4⋊C4×D17C2312yes—
194#10587572C2×C412yescomplemented
195#10587570C2×C412yes—
196#10587570C2×C412yescomplemented
197#10587569C2×C412yescomplemented
198#10587569C2×C412yescomplemented
199#10587568C2×C412yescomplemented
200#10587568C2×C412yescomplemented
201#10587568C2×C412yescomplemented
202#10587567C2×C412yescomplemented
203#10587567C2×C412yescomplemented
204#10587567C2×C412yescomplemented
205#10587567C2×C412yescomplemented
206C22⋊C4×D17C2312yes—
207C22⋊C4×D17C2312yes—
208C22⋊C4×D17C2312yes—
209C22⋊C4×D17C2312yes—
210C22⋊C4×D17C2312yes—
211#10587564C2×C412yescomplemented
212#10587564C2×C412yescomplemented
213#10587563C2×C412yescomplemented
214C4×D68C2×C412yescomplemented
215C4×D68C2×C412yescomplemented
216#10587558C2×C412yescomplemented
217C42×D17C2312yes—
218(C2×#595)⋊C4C2312yes—
219(C2×#595)⋊C4C2312yes—
220(C2×#595)⋊C4C2314yes—
221(C2×#595)⋊C4C2312yes—
222(C2×#595)⋊C4C2314yes—
223(C2×#595)⋊C4C2312yes—
224(C2×#595)⋊C4C2314yes—
225(C2×#595)⋊C4C2314yes—
226(C2×#595)⋊C4C2314yes—
227(C2×#595)⋊C4C2314yes—
228(C2×#595)⋊C4C2314yes—
229(C2×#595)⋊C4C2314yes—
230C24×C17C22×C411yescharacteristic
231C23×D17—22no—
232C23×D17—22no—
233C23×D17—42no—
234C23×D17—42no—
235C23×D17C22×C411yescharacteristic
236C23×D17C22×C411yescharacteristic
237C23×D17C22×C411yescharacteristic
238C23×D17C2411yescharacteristic
239C23×D17C2411yescharacteristic
240C23×D17C2412yes—
241C23×D17C2411yescharacteristic
242C22×#595—28no—
243C22×#595—44no—
244C22×#595—44no—
245C22×#595—44no—
246C22×#595—44no—
247C22×#595—44no—
248C22×#595C2414yes—
249C22×#595C2414yes—
250C22×#595C2414yes—
251C22×#595C2414yes—
252#41×C17—42no—
253C2×Q8×C17C22×C411yescharacteristic
254C2×D4×C17C22×C412yes—
255C2×D4×C17C22×C412yes—
256C2×D4×C17C22×C411yescharacteristic
257C2×D4×C17C22×C412yes—
258C22×C4×C17—42no—
259C22×C4×C17C22×C411yescharacteristic
260C22×C4×C17C22×C411yescharacteristic
261C22×C4×C17C22×C411yescharacteristic
262C22×C4×C17C22×C412yes—
263C22×C4×C17C22×C411yescharacteristic
264C22×C4×C17C22×C411yescharacteristic
265C22×C4×C17C22×C411yescharacteristic
266C2×C22⋊D17C22×C412yes—
267C2×C22⋊D17C22×C412yes—
268C2×C22⋊D17C22×C412yes—
269C2×C22⋊D17C22×C412yes—
270C2×C22⋊D17C22×C412yes—
271C2×C22⋊D17C22×C412yes—
272C2×C22⋊D17C22×C412yes—
273C22×Dic17—42no—
274C22×Dic17C22×C411yescharacteristic
275C22×Dic17C22×C411yescharacteristic
276C22×Dic17C22×C411yescharacteristic
277C22×Dic17C22×C412yes—
278C22×Dic17C22×C411yescharacteristic
279C22×Dic17C22×C411yescharacteristic
280C22×Dic17C22×C411yescharacteristic
281#63256—42no—
282Q8×D17—42no—
283#63254—42no—
284#63254—44no—
285D4×D17—24no—
286D4×D17—24no—
287D4×D17—42no—
288D4×D17—42no—
289D4×D17—42no—
290D4×D17—42no—
291D4×D17—42no—
292#63252—44no—
293#63252—42no—
294C2×D68C22×C412yes—
295C2×D68C22×C412yes—
296C2×D68C22×C411yescharacteristic
297C2×D68C22×C412yes—
298C2×C4×D17—24no—
299C2×C4×D17—24no—
300C2×C4×D17—24no—
301C2×C4×D17—24no—
302C2×C4×D17—24no—
303C2×C4×D17—42no—
304C2×C4×D17—42no—
305C2×C4×D17—42no—
306C2×C4×D17—42no—
307C2×C4×D17—42no—
308C2×C4×D17—42no—
309C2×C4×D17—42no—
310C2×C4×D17—42no—
311C2×C4×D17—42no—
312C2×C4×D17C22×C411yescharacteristic
313C2×C4×D17C22×C411yescharacteristic
314C2×C4×D17C22×C411yescharacteristic
315C2×C4×D17C22×C411yescharacteristic
316C2×C4×D17C22×C411yescharacteristic
317C2×C4×D17C22×C411yescharacteristic
318C2×C4×D17C22×C412yes—
319C2×C4×D17C22×C412yes—
320C2×C4×D17C22×C411yescharacteristic
321C2×C4×D17C22×C411yescharacteristic
322C2×C4×D17C22×C411yescharacteristic
323C2×C4×D17C22×C411yescharacteristic
324C2×C4×D17C22×C411yescharacteristic
325C2×C4×D17C22×C411yescharacteristic
326C2×C4×D17C2411yescharacteristic
327C2×C4×D17C2412yes—
328C2×C4×D17C2412yes—
329C2×C4×D17C2412yes—
330C2×C4×D17C2411yescharacteristic
331C2×C4×D17C2411yescharacteristic
332C2×C4×D17C2411yescharacteristic
333C2×Dic34C22×C412yes—
334C2×Dic34C22×C411yescharacteristic
335C22⋊#595—24no—
336C22⋊#595—24no—
337C22⋊#595—44no—
338C22⋊#595—44no—
339C22⋊#595—44no—
340C22⋊#595—42no—
341C22⋊#595—44no—
342C22⋊#595—42no—
343C22⋊#595—44no—
344C22⋊#595—44no—
345C4⋊#595—24no—
346C4⋊#595—24no—
347C4⋊#595—24no—
348C4⋊#595—24no—
349C4⋊#595—44no—
350C4⋊#595—44no—
351C4⋊#595—44no—
352C4⋊#595—44no—
353C4×#595—44no—
354C4×#595—44no—
355C4×#595—44no—
356C4×#595—44no—
357C4⋊C4×C17C22×C412yes—
358C4⋊C4×C17C22×C412yes—
359C4⋊C4×C17C22×C411yescharacteristic
360C4⋊C4×C17C22×C411yescharacteristic
361C22⋊C4×C17C22×C412yes—
362C22⋊C4×C17C22×C412yes—
363C22⋊C4×C17C22×C412yes—
364C22⋊C4×C17C22×C412yes—
365C22⋊C4×C17C22×C412yes—
366C42×C17C22×C412yes—
367C22⋊Dic17C22×C412yes—
368C22⋊Dic17C22×C412yes—
369C22⋊Dic17C22×C412yes—
370C22⋊Dic17C22×C412yes—
371C22⋊Dic17C22×C412yes—
372#63227C22×C412yes—
373#63227C22×C412yes—
374#63227C22×C412yes—
375#63227C22×C412yes—
376#63227C22×C412yes—
377#63227C22×C412yes—
378#63227C22×C412yes—
379#63227C22×C412yes—
380#63227C22×C412yes—
381#63227C22×C412yes—
382C4⋊Dic17C22×C412yes—
383C4⋊Dic17C22×C412yes—
384C4⋊Dic17C22×C411yescharacteristic
385C4⋊Dic17C22×C411yescharacteristic
386#63225C22×C412yes—
387#63225C22×C412yes—
388#63225C22×C412yes—
389#63225C22×C412yes—
390#63225C22×C412yes—
391#63225C22×C412yes—
392C4×Dic17C22×C412yes—
393C4×Dic17C22×C412yes—
394C4×Dic17C22×C412yes—
395#34362—171nomaximal, Sylow
396C23×C17—22no—
397C23×C17—41no—
398C23×C17—41no—
399C23×C17C23×C411yescharacteristic
400C23×C17C23×C411yescharacteristic
401C23×C17C23×C412yes—
402C23×C17C23×C411yescharacteristic
403C22×D17—22no—
404C22×D17—22no—
405C22×D17—22no—
406C22×D17—22no—
407C22×D17—22no—
408C22×D17—21no—
409C22×D17—21no—
410C22×D17—22no—
411C22×D17—22no—
412C22×D17—22no—
413C22×D17—22no—
414C22×D17—22no—
415C22×D17—22no—
416C22×D17—21no—
417C22×D17—21no—
418C22×D17—22no—
419C22×D17—22no—
420C22×D17—22no—
421C22×D17—22no—
422C22×D17—41no—
423C22×D17—41no—
424C22×D17—41no—
425C22×D17—41no—
426C22×D17—41no—
427C22×D17—41no—
428C22×D17—48no—
429C22×D17—48no—
430C22×D17C23×C411yescharacteristic
431C22×D17C23×C411yescharacteristic
432C22×D17C23×C412yes—
433C22×D17C23×C411yescharacteristic
434C22×D17H(5,𝔽2)12yes—
435C22×D172−1+412yes—
436C22×D17C2511yescharacteristic
437C2×#595—24no—
438C2×#595—24no—
439C2×#595—24no—
440C2×#595—24no—
441C2×#595—24no—
442C2×#595—24no—
443C2×#595—24no—
444C2×#595—24no—
445C2×#595—24no—
446C2×#595—24no—
447C2×#595—24no—
448C2×#595—24no—
449C2×#595—88no—
450C2×#595—88no—
451Q8×C17—41no—
452D4×C17—24no—
453D4×C17—41no—
454D4×C17—42no—
455D4×C17—42no—
456C2×C4×C17—22no—
457C2×C4×C17—22no—
458C2×C4×C17—22no—
459C2×C4×C17—24no—
460C2×C4×C17—41no—
461C2×C4×C17—41no—
462C2×C4×C17—41no—
463C2×C4×C17C23×C412yes—
464C2×C4×C17C23×C412yes—
465C2×C4×C17C23×C412yes—
466C2×C4×C17C23×C411yescharacteristic
467C2×C4×C17C23×C411yescharacteristic
468C2×C4×C17C23×C411yescharacteristic
469C2×C4×C17C23×C411yescharacteristic
470C22⋊D17—24no—
471C22⋊D17—24no—
472C22⋊D17—42no—
473C22⋊D17—42no—
474C22⋊D17—42no—
475C22⋊D17—42no—
476C22⋊D17—42no—
477C2×Dic17—22no—
478C2×Dic17—22no—
479C2×Dic17—22no—
480C2×Dic17—24no—
481C2×Dic17—41no—
482C2×Dic17—41no—
483C2×Dic17—41no—
484C2×Dic17C23×C412yes—
485C2×Dic17C23×C412yes—
486C2×Dic17C23×C412yes—
487C2×Dic17C23×C411yescharacteristic
488C2×Dic17C23×C411yescharacteristic
489C2×Dic17C23×C411yescharacteristic
490C2×Dic17C23×C411yescharacteristic
491D68—24no—
492D68—41no—
493D68—42no—
494D68—42no—
495C4×D17—22no—
496C4×D17—22no—
497C4×D17—22no—
498C4×D17—22no—
499C4×D17—22no—
500C4×D17—22no—
501C4×D17—22no—
502C4×D17—22no—
503C4×D17—22no—
504C4×D17—22no—
505C4×D17—22no—
506C4×D17—22no—
507C4×D17—24no—
508C4×D17—22no—
509C4×D17—22no—
510C4×D17—22no—
511C4×D17—24no—
512C4×D17—41no—
513C4×D17—41no—
514C4×D17—41no—
515C4×D17—41no—
516C4×D17—41no—
517C4×D17—41no—
518C4×D17H(5,𝔽2)14yes—
519Dic34—42no—
520Dic34—41no—
521C2×#525—171no—
522#2378—172no—
523#2377—172no—
524#2368—172no—
525#2364—172no—
526#2354—172no—
527#2352—172no—
528#2352—172no—
529D4×C4⋊C4—172no—
530#2335—174no—
531#2321—174no—
532#2314—172no—
533#2311—172no—
534#2280—171no—
535C2×#380—171no—
536C22×C17—21no—
537C22×C17—21no—
538C22×C17—21no—
539C22×C17—21no—
540C22×C17—22no—
541C22×C17—22no—
542C22×C17—21no—
543C22×C17—21no—
544C22×C17—21no—
545C22×C17—22no—
546C22×C17—21no—
547C22×C17—44no—
548C22×C17#52012yes—
549C22×C17C24×C411yescharacteristic
550C2×D17—21no—
551C2×D17—21no—
552C2×D17—24no—
553C2×D17—24no—
554C2×D17—21no—
555C2×D17—21no—
556C2×D17—22no—
557C2×D17—22no—
558C2×D17—21no—
559C2×D17—21no—
560C2×D17—21no—
561C2×D17—22no—
562C2×D17—21no—
563C2×D17—44no—
564C2×D17—44no—
565C2×D17—44no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—42no—
569C2×D17—42no—
570C2×D17—42no—
571C2×D17—42no—
572C2×D17—42no—
573C2×D17—42no—
574C2×D17#52012yes—
575C2×D17C2×H(5,𝔽2)12yes—
576C2×D17C2×H(5,𝔽2)11yescharacteristic
577C2×D17C2×2−1+411yescharacteristic
578C2×D17#58512yes—
579#595—44no—
580#595—44no—
581#595—44no—
582#595—44no—
583C4×C17—21no—
584C4×C17—22no—
585C4×C17—21no—
586C4×C17—21no—
587C4×C17—22no—
588C4×C17—22no—
589C4×C17#51812yes—
590Dic17—21no—
591Dic17—22no—
592Dic17—21no—
593Dic17—21no—
594Dic17—22no—
595Dic17—22no—
596Dic17#51812yes—
597C22×#41—171no—
598C24×C4—171no—
599#525—171no—
600#525—171no—
601#525—172no—
602#525—171no—
603#525—171no—
604#525—171no—
605#525—171no—
606#525—172no—
607#525—172no—
608#525—172no—
609#525—171no—
610#525#59511yescharacteristic, complemented
611C2×#123—172no—
612C2×C22⋊Q8—171no—
613C2×C22⋊Q8—171no—
614C2×#121—171no—
615C2×#121—171no—
616C2×#120—172no—
617C2×C4×D4—172no—
618C2×C4×D4—172no—
619C2×C4×D4—174no—
620C2×#117—171no—
621C2×#117—172no—
622C2×#117—172no—
623C22×C4⋊C4—172no—
624C22×C4⋊C4—172no—
625C22×C22⋊C4—172no—
626#391—174no—
627#390—174no—
628#390—174no—
629#389—174no—
630#388—174no—
631#388—174no—
632#388—174no—
633#388—174no—
634#388—174no—
635#388—174no—
636#387—174no—
637#387—174no—
638#387—174no—
639#387—174no—
640#386—174no—
641#386—174no—
642#386—174no—
643#386—174no—
644#385—174no—
645#385—174no—
646#384—172no—
647#382—172no—
648#381—172no—
649#380—172no—
650#380—172no—
651#380—172no—
652#380—172no—
653#380—172no—
654#380—171no—
655#380—171no—
656#380—171no—
657#380—171no—
658#380—172no—
659#379—172no—
660C4×C4⋊C4—172no—
661C4×C4⋊C4—172no—
662C4×C4⋊C4—174no—
663C4×C22⋊C4—174no—
664C4×C22⋊C4—172no—
665C4×C22⋊C4—174no—
666C4×C22⋊C4—172no—
667C2×#95—172no—
668C2×C17—22no—
669C2×C17—41no—
670C2×C17—41no—
671C2×C17—42no—
672C2×C17C2×#51811yescharacteristic
673C2×C17C2×#52011yescharacteristic
674C2×C17#342811yescharacteristic
675D17—22no—
676D17—42no—
677D17—41no—
678D17—41no—
679D17#354112yes—
680D17#354212yes—
681C25—171no—
682C2×#41—171no—
683C2×#41—172no—
684C2×#41—171no—
685C2×#41—172no—
686C2×#41—171no—
687C2×#41—684no—
688C2×#41C2×#59511yescharacteristic, complemented
689C22×Q8—171no—
690C22×D4—172no—
691C22×D4—172no—
692C22×D4—172no—
693C22×D4—171no—
694C23×C4—171no—
695C23×C4—171no—
696C23×C4—172no—
697C23×C4—171no—
698C23×C4—171no—
699C23×C4—171no—
700C23×C4—171no—
701C23×C4—171no—
702C23×C4—171no—
703C23×C4—171no—
704C23×C4—171no—
705C23×C4—171no—
706C23×C4—171no—
707C23×C4—171no—
708C23×C4—174no—
709C23×C4—174no—
710C23×C4—684no—
711C23×C4C2×#59511yescharacteristic, complemented
712#123—172no—
713#123—172no—
714#123—172no—
715#123—172no—
716#123—172no—
717#123—172no—
718#123—172no—
719#123C2×#59512yescomplemented
720C22⋊Q8—171no—
721C22⋊Q8—171no—
722C22⋊Q8—171no—
723C22⋊Q8—171no—
724C22⋊Q8—172no—
725C22⋊Q8—172no—
726C22⋊Q8—171no—
727C22⋊Q8—171no—
728C22⋊Q8—172no—
729C22⋊Q8—172no—
730C22⋊Q8C2×#59511yescharacteristic, complemented
731C22⋊Q8C2×#59511yescharacteristic, complemented
732#121—171no—
733#121—171no—
734#121—172no—
735#121—172no—
736#121—171no—
737#121—171no—
738#121—171no—
739#121—171no—
740#121—172no—
741#121—172no—
742#121C2×#59511yescharacteristic
743#121C2×#59511yescharacteristic, complemented
744#120—172no—
745#120—172no—
746#120—172no—
747#120—172no—
748#120—172no—
749#120—172no—
750#120—172no—
751#120C2×#59512yescomplemented
752C4×D4—172no—
753C4×D4—172no—
754C4×D4—172no—
755C4×D4—172no—
756C4×D4—172no—
757C4×D4—172no—
758C4×D4—172no—
759C4×D4—172no—
760C4×D4—172no—
761C4×D4—172no—
762C4×D4—172no—
763C4×D4—172no—
764C4×D4—172no—
765C4×D4—172no—
766C4×D4—688no—
767C4×D4C2×#59512yescomplemented
768C4×D4C2×#59512yescomplemented
769#117—171no—
770#117—171no—
771#117—171no—
772#117—172no—
773#117—172no—
774#117—684no—
775#117—684no—
776#117C2×#59511yescharacteristic, complemented
777C2×C4⋊C4—171no—
778C2×C4⋊C4—171no—
779C2×C4⋊C4—172no—
780C2×C4⋊C4—172no—
781C2×C4⋊C4—172no—
782C2×C4⋊C4—172no—
783C2×C4⋊C4—172no—
784C2×C4⋊C4—172no—
785C2×C4⋊C4—174no—
786C2×C4⋊C4—174no—
787C2×C4⋊C4—174no—
788C2×C4⋊C4—174no—
789C2×C4⋊C4—684no—
790C2×C4⋊C4—684no—
791C2×C22⋊C4—172no—
792C2×C22⋊C4—172no—
793C2×C22⋊C4—172no—
794C2×C22⋊C4—172no—
795C2×C22⋊C4—172no—
796C2×C22⋊C4—172no—
797C2×C22⋊C4—172no—
798C2×C22⋊C4—172no—
799C2×C22⋊C4—174no—
800C2×C22⋊C4—172no—
801C2×C22⋊C4—174no—
802C2×C22⋊C4—174no—
803C2×C22⋊C4—174no—
804C2×C22⋊C4—174no—
805C2×C22⋊C4—174no—
806C2×C22⋊C4—684no—
807C2×C42—172no—
808C2×C42—174no—
809C2×C42—174no—
810C2×C42—174no—
811C2×C42—174no—
812#95—172no—
813#95—172no—
814#95—174no—
815#95—172no—
816#95—174no—
817#95—172no—
818#95—174no—
819#95—174no—
820#95—174no—
821#95—174no—
822#95—174no—
823#95—174no—
824C17#3436211yescharacteristic, complemented, Sylow
825C24—171no—
826C24—171no—
827C24—171no—
828C24—172no—
829C24—171no—
830C24—171no—
831C24—171no—
832C24—342no—
833C24—342no—
834C24—682no—
835C24—682no—
836C24C22×#59511yescharacteristic
837#41—42no—
838#41—682no—
839#41—684no—
840#41—682no—
841#41—684no—
842#41—682no—
843C2×Q8—171no—
844C2×Q8—172no—
845C2×Q8—682no—
846C2×Q8C22×#59511yescharacteristic
847C2×D4—172no—
848C2×D4—172no—
849C2×D4—172no—
850C2×D4—172no—
851C2×D4—172no—
852C2×D4—172no—
853C2×D4—172no—
854C2×D4—172no—
855C2×D4—172no—
856C2×D4—172no—
857C2×D4—171no—
858C2×D4—344no—
859C2×D4—344no—
860C2×D4—682no—
861C2×D4—682no—
862C2×D4—682no—
863C2×D4—682no—
864C2×D4—682no—
865C2×D4C22×#59512yes—
866C2×D4C22×#59512yes—
867C2×D4C22×#59512yes—
868C2×D4C22×#59511yescharacteristic
869C22×C4—42no—
870C22×C4—171no—
871C22×C4—171no—
872C22×C4—171no—
873C22×C4—171no—
874C22×C4—172no—
875C22×C4—171no—
876C22×C4—171no—
877C22×C4—171no—
878C22×C4—171no—
879C22×C4—171no—
880C22×C4—171no—
881C22×C4—171no—
882C22×C4—171no—
883C22×C4—171no—
884C22×C4—172no—
885C22×C4—172no—
886C22×C4—171no—
887C22×C4—171no—
888C22×C4—172no—
889C22×C4—172no—
890C22×C4—172no—
891C22×C4—171no—
892C22×C4—171no—
893C22×C4—171no—
894C22×C4—171no—
895C22×C4—171no—
896C22×C4—171no—
897C22×C4—171no—
898C22×C4—174no—
899C22×C4—174no—
900C22×C4—174no—
901C22×C4—174no—
902C22×C4—344no—
903C22×C4—344no—
904C22×C4—344no—
905C22×C4—344no—
906C22×C4—344no—
907C22×C4—348no—
908C22×C4—682no—
909C22×C4—682no—
910C22×C4—682no—
911C22×C4—682no—
912C22×C4—682no—
913C22×C4—682no—
914C22×C4—682no—
915C22×C4—682no—
916C22×C4—682no—
917C22×C4—682no—
918C22×C4—684no—
919C22×C4—684no—
920C22×C4—684no—
921C22×C4—684no—
922C22×C4—684no—
923C22×C4C22×#59511yescharacteristic
924C22×C4C22×#59511yescharacteristic
925C22×C4C22×#59511yescharacteristic
926C22×C4C22×#59512yes—
927C22×C4C22×#59511yescharacteristic
928C22×C4C22×#59511yescharacteristic
929C22×C4C22×#59511yescharacteristic
930C4⋊C4—172no—
931C4⋊C4—172no—
932C4⋊C4—171no—
933C4⋊C4—171no—
934C4⋊C4—172no—
935C4⋊C4—172no—
936C4⋊C4—172no—
937C4⋊C4—172no—
938C4⋊C4—172no—
939C4⋊C4—172no—
940C4⋊C4—344no—
941C4⋊C4—344no—
942C4⋊C4—344no—
943C4⋊C4—344no—
944C4⋊C4—684no—
945C4⋊C4—684no—
946C4⋊C4—684no—
947C4⋊C4—684no—
948C4⋊C4C22×#59511yescharacteristic
949C4⋊C4C22×#59511yescharacteristic
950C4⋊C4C22×#59512yes—
951C4⋊C4C22×#59512yes—
952C22⋊C4—172no—
953C22⋊C4—172no—
954C22⋊C4—172no—
955C22⋊C4—172no—
956C22⋊C4—172no—
957C22⋊C4—172no—
958C22⋊C4—172no—
959C22⋊C4—172no—
960C22⋊C4—172no—
961C22⋊C4—172no—
962C22⋊C4—172no—
963C22⋊C4—172no—
964C22⋊C4—172no—
965C22⋊C4—172no—
966C22⋊C4—172no—
967C22⋊C4—344no—
968C22⋊C4—344no—
969C22⋊C4—684no—
970C22⋊C4—684no—
971C22⋊C4—682no—
972C22⋊C4—684no—
973C22⋊C4—682no—
974C22⋊C4—684no—
975C22⋊C4—684no—
976C22⋊C4—684no—
977C22⋊C4C22×#59512yes—
978C22⋊C4C22×#59512yes—
979C22⋊C4C22×#59512yes—
980C22⋊C4C22×#59512yes—
981C22⋊C4C22×#59512yes—
982C42—172no—
983C42—172no—
984C42—172no—
985C42—684no—
986C42—684no—
987C42—684no—
988C42—684no—
989C42C22×#59512yes—
990C23—22no—
991C23—41no—
992C23—41no—
993C23—171no—
994C23—172no—
995C23—172no—
996C23—171no—
997C23—171no—
998C23—171no—
999C23—172no—
1000C23—342no—
1001C23—342no—
1002C23—341no—
1003C23—341no—
1004C23—342no—
1005C23—342no—
1006C23—342no—
1007C23—342no—
1008C23—342no—
1009C23—342no—
1010C23—342no—
1011C23—342no—
1012C23—342no—
1013C23—342no—
1014C23—341no—
1015C23—341no—
1016C23—342no—
1017C23—342no—
1018C23—342no—
1019C23—681no—
1020C23—681no—
1021C23—681no—
1022C23—681no—
1023C23—681no—
1024C23—681no—
1025C23—688no—
1026C23—688no—
1027C23C23×#59511yescharacteristic
1028C23C23×#59511yescharacteristic
1029C23C23×#59512yes—
1030C23C23×#59511yescharacteristic
1031Q8—41no—
1032Q8—681no—
1033Q8—682no—
1034D4—24no—
1035D4—41no—
1036D4—42no—
1037D4—42no—
1038D4—344no—
1039D4—344no—
1040D4—344no—
1041D4—681no—
1042D4—682no—
1043D4—682no—
1044D4—682no—
1045D4—682no—
1046D4—682no—
1047D4—682no—
1048D4—682no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—171no—
1057C2×C4—174no—
1058C2×C4—172no—
1059C2×C4—172no—
1060C2×C4—171no—
1061C2×C4—171no—
1062C2×C4—172no—
1063C2×C4—171no—
1064C2×C4—342no—
1065C2×C4—342no—
1066C2×C4—342no—
1067C2×C4—344no—
1068C2×C4—342no—
1069C2×C4—342no—
1070C2×C4—342no—
1071C2×C4—342no—
1072C2×C4—342no—
1073C2×C4—342no—
1074C2×C4—342no—
1075C2×C4—342no—
1076C2×C4—342no—
1077C2×C4—342no—
1078C2×C4—342no—
1079C2×C4—342no—
1080C2×C4—344no—
1081C2×C4—342no—
1082C2×C4—342no—
1083C2×C4—342no—
1084C2×C4—344no—
1085C2×C4—344no—
1086C2×C4—344no—
1087C2×C4—344no—
1088C2×C4—344no—
1089C2×C4—344no—
1090C2×C4—344no—
1091C2×C4—344no—
1092C2×C4—344no—
1093C2×C4—344no—
1094C2×C4—344no—
1095C2×C4—344no—
1096C2×C4—344no—
1097C2×C4—681no—
1098C2×C4—681no—
1099C2×C4—681no—
1100C2×C4—681no—
1101C2×C4—681no—
1102C2×C4—681no—
1103C2×C4—681no—
1104C2×C4—681no—
1105C2×C4—681no—
1106C2×C4—1368no—
1107C2×C4—1368no—
1108C2×C4C23×#59512yes—
1109C2×C4C23×#59512yes—
1110C2×C4C23×#59511yescharacteristic
1111C2×C4C23×#59511yescharacteristic
1112C2×C4C23×#59512yes—
1113C2×C4C23×#59511yescharacteristic
1114C2×C4C23×#59511yescharacteristic
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—22no—
1120C22—22no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—22no—
1125C22—21no—
1126C22—44no—
1127C22—172no—
1128C22—171no—
1129C22—171no—
1130C22—172no—
1131C22—172no—
1132C22—344no—
1133C22—344no—
1134C22—341no—
1135C22—341no—
1136C22—341no—
1137C22—341no—
1138C22—342no—
1139C22—342no—
1140C22—341no—
1141C22—341no—
1142C22—341no—
1143C22—342no—
1144C22—341no—
1145C22—684no—
1146C22—682no—
1147C22—682no—
1148C22—682no—
1149C22—682no—
1150C22—682no—
1151C22—682no—
1152C22—682no—
1153C22—682no—
1154C22—684no—
1155C22—684no—
1156C22#1176387812yes—
1157C22C24×#59511yescharacteristic
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—172no—
1165C4—341no—
1166C4—341no—
1167C4—341no—
1168C4—342no—
1169C4—342no—
1170C4—342no—
1171C4—684no—
1172C4—684no—
1173C4—684no—
1174C4—684no—
1175C4#1176387612yes—
1176C2—22no—
1177C2—41no—
1178C2—41no—
1179C2—42no—
1180C2—172no—
1181C2—172no—
1182C2—342no—
1183C2—681no—
1184C2—681no—
1185C2—682no—
1186C2C2×#1176387611yescharacteristic
1187C2C2×#1176387811yescharacteristic
1188C2#1454576411yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#525C4
prime radicalD17×#525C2
cosocleC22×D17C25
hypercenter#525#595
hypocenterC17#34362
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14545326C2semidirect
2. #14545325C2semidirect
3. #14545316C2semidirect
4. #14545312C2semidirect
5. #14545302C2semidirect
6. #14545300C2semidirect
7. #14545300C2semidirect
8. D4×C4⋊#595C2semidirect
9. #14545283C2semidirect
10. #14545269C2semidirect
11. #14545262C2semidirect
12. #14545259C2semidirect
13. #14545228C2semidirect
14. C2×#11763751C2semidirect
18. C2×#10587677C22semidirect
20. C22×C4⋊#595C22semidirect
22. (C2×#595)⋊Q8C22semidirect
25. #11763760C22semidirect
30. #11763759C22semidirect
31. #11763759C22semidirect
32. #11763758C22semidirect
33. #11763758C22semidirect
34. #11763758C22semidirect
35. #11763758C22semidirect
39. #11763757C22semidirect
41. #11763756C22semidirect
42. #11763755C22semidirect
43. #11763753C22semidirect
53. #11763751C22semidirect
54. #11763751C22semidirect
56. C4⋊C4×#595C22semidirect
57. C4×C4⋊#595C22semidirect
58. C4×C4⋊#595C22semidirect
60. C22⋊C4×#595C22semidirect
66. #11763322C4semidirect
67. #11763322C4semidirect
68. #11763321C4semidirect
69. #11763320C4semidirect
70. #11763319C4semidirect
71. #11763319C4semidirect
72. #11763318C4semidirect
73. #11763318C4semidirect
74. #11763317C4semidirect
75. #11763316C4semidirect
76. #11763315C4semidirect
86. C17×#525C4semidirect
90. C2×#41×C17C2×C4semidirect
91. C23×C4×C17C2×C4semidirect
92. C23×Dic17C2×C4semidirect
94. C2×#63256C2×C4semidirect
96. C2×#63254C2×C4semidirect
97. C2×#63254C2×C4semidirect
102. C2×#63252C2×C4semidirect
103. C2×#63252C2×C4semidirect
105. C22×C4×D17C2×C4semidirect
106. C22×C4×D17C2×C4semidirect
107. C22×C4×D17C2×C4semidirect
108. C22×C4×D17C2×C4semidirect
109. C22×C4×D17C2×C4semidirect
110. C22×C4×D17C2×C4semidirect
146. C17×#123C2×C4semidirect
147. C17×C22⋊Q8C2×C4semidirect
148. C17×C22⋊Q8C2×C4semidirect
150. C17×#121C2×C4semidirect
151. C17×#120C2×C4semidirect
152. C4×D4×C17C2×C4semidirect
153. C4×D4×C17C2×C4semidirect
154. C17×#117C2×C4semidirect
155. #10587639C2×C4semidirect
156. #10587632C2×C4semidirect
157. #10587632C2×C4semidirect
159. #10587625C2×C4semidirect
161. #10587624C2×C4semidirect
162. #10587623C2×C4semidirect
163. #10587623C2×C4semidirect
164. #10587623C2×C4semidirect
165. #10587621C2×C4semidirect
166. D4×Dic17C2×C4semidirect
167. D4×Dic17C2×C4semidirect
169. #10587616C2×C4semidirect
170. #10587615C2×C4semidirect
171. C4×C22⋊D17C2×C4semidirect
172. C4×C22⋊D17C2×C4semidirect
173. C4×C22⋊D17C2×C4semidirect
174. C4×C22⋊D17C2×C4semidirect
175. #10587612C2×C4semidirect
176. #10587610C2×C4semidirect
177. #10587610C2×C4semidirect
178. #10587583C2×C4semidirect
179. #10587583C2×C4semidirect
180. #10587582C2×C4semidirect
181. #10587582C2×C4semidirect
183. #10587581C2×C4semidirect
184. #10587580C2×C4semidirect
185. #10587580C2×C4semidirect
186. #10587579C2×C4semidirect
187. #10587579C2×C4semidirect
188. #10587578C2×C4semidirect
189. #10587578C2×C4semidirect
194. #10587572C2×C4semidirect
196. #10587570C2×C4semidirect
197. #10587569C2×C4semidirect
198. #10587569C2×C4semidirect
199. #10587568C2×C4semidirect
200. #10587568C2×C4semidirect
201. #10587568C2×C4semidirect
202. #10587567C2×C4semidirect
203. #10587567C2×C4semidirect
204. #10587567C2×C4semidirect
205. #10587567C2×C4semidirect
211. #10587564C2×C4semidirect
212. #10587564C2×C4semidirect
213. #10587563C2×C4semidirect
214. C4×D68C2×C4semidirect
215. C4×D68C2×C4semidirect
216. #10587558C2×C4semidirect
610. #525#595semidirect
688. C2×#41C2×#595semidirect
711. C23×C4C2×#595semidirect
719. #123C2×#595semidirect
730. C22⋊Q8C2×#595semidirect
731. C22⋊Q8C2×#595semidirect
743. #121C2×#595semidirect
751. #120C2×#595semidirect
767. C4×D4C2×#595semidirect
768. C4×D4C2×#595semidirect
776. #117C2×#595semidirect
824. C17#34362semidirect

Maximal subgroups

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

subgroupindex
#145453262
#145453252
#145453162
#145453122
#145453022
#145453002
D4×C4⋊#5952
#145452832
#145452692
#145452622
#145452592
#145452282
C2×#117637512
D17×#5252
#3436217