Finite Group Databasebeta

← #17978949

Subgroups — #17978949

Order 4352.

2714 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545283C214yesmaximal, complemented
2#14545281C212yesmaximal, complemented
3#14545280C212yesmaximal, complemented
4#14545277C212yesmaximal, complemented
5#14545273C212yesmaximal, complemented
6#14545269C214yesmaximal, complemented
7#14545246C212yesmaximal, complemented
8#14545245C212yesmaximal, complemented
9#14545241C212yesmaximal, complemented
10#14545238C212yesmaximal, complemented
11#14545238C212yesmaximal, complemented
12#14545228C211yesmaximal, characteristic, complemented
13C4×D4×#595C212yesmaximal, complemented
14C2×C4×C22⋊#595C211yesmaximal, characteristic, complemented
15D17×#525C211yesmaximal, characteristic
16C2×D4×#595C2214yes—
17C2×#10587677C2211yescharacteristic
18C2×#10587677C2211yescharacteristic
19C2×#10587677C2212yescomplemented
20C22×C22⋊#595C2212yes—
21C22×C4×#595C2211yescharacteristic
22C22×C4×#595C2211yescharacteristic
23C22×C4×#595C2212yescomplemented
24(C2×#595)⋊Q8C2214yescomplemented
25#11763761C2214yes—
26#11763761C2214yes—
27#11763760C2214yescomplemented
28#11763759C2214yes—
29#11763759C2214yes—
30#11763759C2214yes—
31#11763759C2214yes—
32#11763759C2214yescomplemented
33#11763759C2214yescomplemented
34#11763758C2214yescomplemented
35#11763758C2214yescomplemented
36#11763758C2214yescomplemented
37#11763758C2214yescomplemented
38#11763757C2214yes—
39#11763757C2214yes—
40#11763757C2214yes—
41#11763757C2214yescomplemented
42#11763756C2214yes—
43#11763756C2214yescomplemented
44#11763752C2212yes—
45#11763751C2212yes—
46#11763751C2212yes—
47#11763750C2212yes—
48C4⋊C4×#595C2214yescomplemented
49C4×C4⋊#595C2212yescomplemented
50C4×C4⋊#595C2212yescomplemented
51C22⋊C4×#595C2214yes—
52C22⋊C4×#595C2214yescomplemented
53C4×C22⋊#595C2212yes—
54C4×C22⋊#595C2212yes—
55C4×C22⋊#595C2212yes—
56C4×C22⋊#595C2212yes—
57C4×C22⋊#595C2212yes—
58C4×C22⋊#595C2212yes—
59C4×C22⋊#595C2212yescomplemented
60C4×C22⋊#595C2212yescomplemented
61#11763745C2212yescomplemented
62C2×(C2×#595)⋊C4C2212yes—
63C42×#595C2212yescomplemented
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×#595C2312yes—
89C23×#595C2314yes—
90C23×#595C2312yes—
91C2×#41×C17C2×C411yescharacteristic, complemented
92C23×C4×C17C2×C411yescharacteristic, complemented
93C23×Dic17C2×C411yescharacteristic, complemented
94#41×D17—42no—
95#41×D17—42no—
96C2×#63256C2×C411yescharacteristic, complemented
97C2×Q8×D17C2311yescharacteristic
98C2×#63254C2×C412yescomplemented
99C2×#63254C2×C411yescharacteristic, complemented
100C2×D4×D17C2312yes—
101C2×D4×D17C2312yes—
102C2×D4×D17C2312yes—
103C2×D4×D17C2311yescharacteristic
104C2×#63252C2×C412yescomplemented
105C2×#63252C2×C411yescharacteristic, complemented
106C22×C4×D17—42no—
107C22×C4×D17—42no—
108C22×C4×D17C2×C411yescharacteristic, complemented
109C22×C4×D17C2×C411yescharacteristic, complemented
110C22×C4×D17C2×C411yescharacteristic, complemented
111C22×C4×D17C2×C411yescharacteristic, complemented
112C22×C4×D17C2×C411yescharacteristic, complemented
113C22×C4×D17C2×C411yescharacteristic, complemented
114C22×C4×D17C2311yescharacteristic
115C22×C4×D17C2311yescharacteristic
116C22×C4×D17C2311yescharacteristic
117C22×C4×D17C2312yes—
118C22×C4×D17C2311yescharacteristic
119C22×C4×D17C2311yescharacteristic
120C22×C4×D17C2311yescharacteristic
121C2×C22⋊#595—28no—
122C2×C22⋊#595C2314yes—
123C2×C22⋊#595C2314yes—
124C2×C22⋊#595C2314yes—
125C2×C22⋊#595C2314yes—
126C2×C22⋊#595C2314yes—
127C2×C22⋊#595C2314yes—
128C2×C22⋊#595C2312yes—
129C2×C22⋊#595C2312yes—
130C2×C22⋊#595C2314yes—
131D4×#595—216no—
132#10587677—42no—
133#10587677—42no—
134#10587677—44no—
135C2×C4⋊#595C2314yes—
136C2×C4⋊#595C2314yes—
137C2×C4⋊#595C2312yes—
138C2×C4⋊#595C2312yes—
139C2×C4⋊#595C2314yes—
140C2×C4×#595—42no—
141C2×C4×#595—42no—
142C2×C4×#595—44no—
143C2×C4×#595C2312yes—
144C2×C4×#595C2312yes—
145C2×C4×#595C2314yes—
146C2×C4×#595C2312yes—
147C2×C4×#595C2312yes—
148C2×C4×#595C2314yes—
149C2×C4×#595C2312yes—
150C2×C4×#595C2312yes—
151C2×C4×#595C2314yes—
152C17×#123C2×C412yescomplemented
153C17×C22⋊Q8C2×C411yescharacteristic, complemented
154C17×C22⋊Q8C2×C411yescharacteristic, complemented
155C17×#121C2×C411yescharacteristic
156C17×#121C2×C411yescharacteristic, complemented
157C17×#120C2×C412yescomplemented
158C4×D4×C17C2×C412yescomplemented
159C4×D4×C17C2×C412yescomplemented
160C17×#117C2×C411yescharacteristic, complemented
161#10587639C2×C412yescomplemented
162#10587632C2×C411yescharacteristic, complemented
163#10587632C2×C411yescharacteristic, complemented
164#10587625C2×C412yes—
165#10587625C2×C412yescomplemented
166#10587624C2×C411yescharacteristic
167#10587624C2×C411yescharacteristic, complemented
168#10587623C2×C412yescomplemented
169#10587623C2×C412yescomplemented
170#10587623C2×C412yescomplemented
171#10587621C2×C412yescomplemented
172D4×Dic17C2×C412yescomplemented
173D4×Dic17C2×C412yescomplemented
174#10587616C2×C411yescharacteristic
175#10587616C2×C411yescharacteristic, complemented
176#10587615C2×C412yescomplemented
177C4×C22⋊D17C2×C412yescomplemented
178C4×C22⋊D17C2×C412yescomplemented
179C4×C22⋊D17C2×C412yescomplemented
180C4×C22⋊D17C2×C412yescomplemented
181#10587612C2×C411yescharacteristic, complemented
182#10587610C2×C411yescharacteristic, complemented
183#10587610C2×C411yescharacteristic, complemented
184#10587583C2×C411yescharacteristic, complemented
185#10587583C2×C411yescharacteristic, complemented
186#10587582C2×C412yescomplemented
187#10587582C2×C412yescomplemented
188#10587581C2×C411yescharacteristic
189#10587581C2×C411yescharacteristic, complemented
190#10587580C2×C412yescomplemented
191#10587580C2×C412yescomplemented
192#10587579C2×C412yescomplemented
193#10587579C2×C412yescomplemented
194#10587578C2×C411yescharacteristic, complemented
195#10587578C2×C411yescharacteristic, complemented
196C4⋊C4×D17C2312yes—
197C4⋊C4×D17C2311yescharacteristic
198C4⋊C4×D17C2311yescharacteristic
199C4⋊C4×D17C2312yes—
200#10587572C2×C412yescomplemented
201#10587570C2×C412yes—
202#10587570C2×C412yescomplemented
203#10587569C2×C412yescomplemented
204#10587569C2×C412yescomplemented
205#10587568C2×C412yescomplemented
206#10587568C2×C412yescomplemented
207#10587568C2×C412yescomplemented
208#10587567C2×C412yescomplemented
209#10587567C2×C412yescomplemented
210#10587567C2×C412yescomplemented
211#10587567C2×C412yescomplemented
212C22⋊C4×D17C2312yes—
213C22⋊C4×D17C2312yes—
214C22⋊C4×D17C2312yes—
215C22⋊C4×D17C2312yes—
216C22⋊C4×D17C2312yes—
217#10587564C2×C412yescomplemented
218#10587564C2×C412yescomplemented
219#10587563C2×C412yescomplemented
220C4×D68C2×C412yescomplemented
221C4×D68C2×C412yescomplemented
222#10587558C2×C412yescomplemented
223C42×D17C2312yes—
224(C2×#595)⋊C4C2314yes—
225(C2×#595)⋊C4C2314yes—
226(C2×#595)⋊C4C2314yes—
227(C2×#595)⋊C4C2314yes—
228(C2×#595)⋊C4C2314yes—
229(C2×#595)⋊C4C2314yes—
230(C2×#595)⋊C4C2314yes—
231(C2×#595)⋊C4C2314yes—
232(C2×#595)⋊C4C2314yes—
233(C2×#595)⋊C4C2314yes—
234C24×C17C22×C411yescharacteristic
235C23×D17—24no—
236C23×D17—41no—
237C23×D17—41no—
238C23×D17—42no—
239C23×D17C22×C411yescharacteristic
240C23×D17C22×C411yescharacteristic
241C23×D17C22×C411yescharacteristic
242C23×D17C2411yescharacteristic
243C23×D17C2411yescharacteristic
244C23×D17C2412yes—
245C23×D17C2411yescharacteristic
246C22×#595—24no—
247C22×#595—28no—
248C22×#595—42no—
249C22×#595—44no—
250C22×#595—42no—
251C22×#595—42no—
252C22×#595—44no—
253C22×#595—42no—
254C22×#595#4118yescomplemented
255C22×#595C2414yes—
256C22×#595C2414yes—
257C22×#595C2414yes—
258C22×#595C2414yes—
259#41×C17—42no—
260C2×Q8×C17C22×C411yescharacteristic
261C2×D4×C17C22×C412yes—
262C2×D4×C17C22×C412yes—
263C2×D4×C17C22×C411yescharacteristic
264C2×D4×C17C22×C412yes—
265C22×C4×C17—42no—
266C22×C4×C17C22×C411yescharacteristic
267C22×C4×C17C22×C411yescharacteristic
268C22×C4×C17C22×C411yescharacteristic
269C22×C4×C17C22×C412yes—
270C22×C4×C17C22×C411yescharacteristic
271C22×C4×C17C22×C411yescharacteristic
272C22×C4×C17C22×C411yescharacteristic
273C2×C22⋊D17C22×C412yes—
274C2×C22⋊D17C22×C412yes—
275C2×C22⋊D17C22×C412yes—
276C2×C22⋊D17C22×C412yes—
277C2×C22⋊D17C22×C412yes—
278C2×C22⋊D17C22×C412yes—
279C2×C22⋊D17C22×C412yes—
280C22×Dic17—42no—
281C22×Dic17C22×C411yescharacteristic
282C22×Dic17C22×C411yescharacteristic
283C22×Dic17C22×C411yescharacteristic
284C22×Dic17C22×C412yes—
285C22×Dic17C22×C411yescharacteristic
286C22×Dic17C22×C411yescharacteristic
287C22×Dic17C22×C411yescharacteristic
288#63256—42no—
289Q8×D17—41no—
290Q8×D17—41no—
291#63254—42no—
292#63254—44no—
293D4×D17—28no—
294D4×D17—44no—
295D4×D17—42no—
296D4×D17—42no—
297D4×D17—41no—
298D4×D17—41no—
299#63252—44no—
300#63252—42no—
301C2×D68C22×C412yes—
302C2×D68C22×C412yes—
303C2×D68C22×C411yescharacteristic
304C2×D68C22×C412yes—
305C2×C4×D17—22no—
306C2×C4×D17—22no—
307C2×C4×D17—24no—
308C2×C4×D17—22no—
309C2×C4×D17—22no—
310C2×C4×D17—24no—
311C2×C4×D17—22no—
312C2×C4×D17—22no—
313C2×C4×D17—42no—
314C2×C4×D17—42no—
315C2×C4×D17—42no—
316C2×C4×D17—42no—
317C2×C4×D17—42no—
318C2×C4×D17—42no—
319C2×C4×D17—41no—
320C2×C4×D17—41no—
321C2×C4×D17—41no—
322C2×C4×D17—41no—
323C2×C4×D17—41no—
324C2×C4×D17—41no—
325C2×C4×D17C22×C411yescharacteristic
326C2×C4×D17C22×C411yescharacteristic
327C2×C4×D17C22×C411yescharacteristic
328C2×C4×D17C22×C411yescharacteristic
329C2×C4×D17C22×C411yescharacteristic
330C2×C4×D17C22×C411yescharacteristic
331C2×C4×D17C22×C412yes—
332C2×C4×D17C22×C412yes—
333C2×C4×D17C22×C411yescharacteristic
334C2×C4×D17C22×C411yescharacteristic
335C2×C4×D17C22×C411yescharacteristic
336C2×C4×D17C22×C411yescharacteristic
337C2×C4×D17C22×C411yescharacteristic
338C2×C4×D17C22×C411yescharacteristic
339C2×C4×D17C2411yescharacteristic
340C2×C4×D17C2412yes—
341C2×C4×D17C2412yes—
342C2×C4×D17C2412yes—
343C2×C4×D17C2411yescharacteristic
344C2×C4×D17C2411yescharacteristic
345C2×C4×D17C2411yescharacteristic
346C2×Dic34C22×C412yes—
347C2×Dic34C22×C411yescharacteristic
348C22⋊#595—28no—
349C22⋊#595—28no—
350C22⋊#595—28no—
351C22⋊#595—28no—
352C22⋊#595—42no—
353C22⋊#595—44no—
354C22⋊#595—42no—
355C22⋊#595—44no—
356C22⋊#595—44no—
357C4⋊#595—28no—
358C4⋊#595—44no—
359C4⋊#595—42no—
360C4⋊#595—42no—
361C4⋊#595—44no—
362C4×#595—28no—
363C4×#595—24no—
364C4×#595—24no—
365C4×#595—24no—
366C4×#595—24no—
367C4×#595—42no—
368C4×#595—42no—
369C4×#595—44no—
370C4×#595—44no—
371C4⋊C4×C17C22×C412yes—
372C4⋊C4×C17C22×C412yes—
373C4⋊C4×C17C22×C411yescharacteristic
374C4⋊C4×C17C22×C411yescharacteristic
375C22⋊C4×C17C22×C412yes—
376C22⋊C4×C17C22×C412yes—
377C22⋊C4×C17C22×C412yes—
378C22⋊C4×C17C22×C412yes—
379C22⋊C4×C17C22×C412yes—
380C42×C17C22×C412yes—
381C22⋊Dic17C22×C412yes—
382C22⋊Dic17C22×C412yes—
383C22⋊Dic17C22×C412yes—
384C22⋊Dic17C22×C412yes—
385C22⋊Dic17C22×C412yes—
386#63227C22×C412yes—
387#63227C22×C412yes—
388#63227C22×C412yes—
389#63227C22×C412yes—
390#63227C22×C412yes—
391#63227C22×C412yes—
392#63227C22×C412yes—
393#63227C22×C412yes—
394#63227C22×C412yes—
395#63227C22×C412yes—
396C4⋊Dic17C22×C412yes—
397C4⋊Dic17C22×C412yes—
398C4⋊Dic17C22×C411yescharacteristic
399C4⋊Dic17C22×C411yescharacteristic
400#63225C22×C412yes—
401#63225C22×C412yes—
402#63225C22×C412yes—
403#63225C22×C412yes—
404#63225C22×C412yes—
405#63225C22×C412yes—
406C4×Dic17C22×C412yes—
407C4×Dic17C22×C412yes—
408C4×Dic17C22×C412yes—
409#34082—171nomaximal, Sylow
410C23×C17—22no—
411C23×C17—41no—
412C23×C17—41no—
413C23×C17C23×C411yescharacteristic
414C23×C17C23×C411yescharacteristic
415C23×C17C23×C412yes—
416C23×C17C23×C411yescharacteristic
417C22×D17—21no—
418C22×D17—21no—
419C22×D17—22no—
420C22×D17—22no—
421C22×D17—22no—
422C22×D17—22no—
423C22×D17—22no—
424C22×D17—22no—
425C22×D17—24no—
426C22×D17—21no—
427C22×D17—21no—
428C22×D17—22no—
429C22×D17—21no—
430C22×D17—21no—
431C22×D17—22no—
432C22×D17—22no—
433C22×D17—24no—
434C22×D17—22no—
435C22×D17—41no—
436C22×D17—41no—
437C22×D17—41no—
438C22×D17—41no—
439C22×D17—41no—
440C22×D17—41no—
441C22×D17—48no—
442C22×D17—48no—
443C22×D17C23×C411yescharacteristic
444C22×D17C23×C411yescharacteristic
445C22×D17C23×C412yes—
446C22×D17C23×C411yescharacteristic
447C22×D17C2×#4114yes—
448C22×D17C2511yescharacteristic
449C2×#595—24no—
450C2×#595—24no—
451C2×#595—24no—
452C2×#595—24no—
453C2×#595—24no—
454C2×#595—24no—
455C2×#595—24no—
456C2×#595—24no—
457C2×#595—24no—
458C2×#595—24no—
459C2×#595—24no—
460C2×#595—48no—
461C2×#595—416no—
462C2×#595—48no—
463C2×#595C2×#4118yes—
464Q8×C17—41no—
465D4×C17—24no—
466D4×C17—41no—
467D4×C17—42no—
468D4×C17—42no—
469C2×C4×C17—22no—
470C2×C4×C17—22no—
471C2×C4×C17—22no—
472C2×C4×C17—24no—
473C2×C4×C17—41no—
474C2×C4×C17—41no—
475C2×C4×C17—41no—
476C2×C4×C17C23×C412yes—
477C2×C4×C17C23×C412yes—
478C2×C4×C17C23×C412yes—
479C2×C4×C17C23×C411yescharacteristic
480C2×C4×C17C23×C411yescharacteristic
481C2×C4×C17C23×C411yescharacteristic
482C2×C4×C17C23×C411yescharacteristic
483C22⋊D17—24no—
484C22⋊D17—24no—
485C22⋊D17—42no—
486C22⋊D17—42no—
487C22⋊D17—42no—
488C22⋊D17—42no—
489C22⋊D17—42no—
490C2×Dic17—22no—
491C2×Dic17—22no—
492C2×Dic17—22no—
493C2×Dic17—24no—
494C2×Dic17—41no—
495C2×Dic17—41no—
496C2×Dic17—41no—
497C2×Dic17C23×C412yes—
498C2×Dic17C23×C412yes—
499C2×Dic17C23×C412yes—
500C2×Dic17C23×C411yescharacteristic
501C2×Dic17C23×C411yescharacteristic
502C2×Dic17C23×C411yescharacteristic
503C2×Dic17C23×C411yescharacteristic
504D68—24no—
505D68—41no—
506D68—42no—
507D68—42no—
508C4×D17—24no—
509C4×D17—21no—
510C4×D17—21no—
511C4×D17—22no—
512C4×D17—21no—
513C4×D17—21no—
514C4×D17—22no—
515C4×D17—21no—
516C4×D17—21no—
517C4×D17—24no—
518C4×D17—22no—
519C4×D17—22no—
520C4×D17—22no—
521C4×D17—24no—
522C4×D17—22no—
523C4×D17—22no—
524C4×D17—22no—
525C4×D17—24no—
526C4×D17—41no—
527C4×D17—41no—
528C4×D17—41no—
529C4×D17—41no—
530C4×D17—41no—
531C4×D17—41no—
532C4×D17H(5,𝔽2)12yes—
533C4×D17H(5,𝔽2)12yes—
534Dic34—42no—
535Dic34—41no—
536C2×#525—171no—
537#2335—174no—
538#2333—172no—
539#2332—172no—
540#2329—172no—
541#2325—172no—
542#2321—174no—
543#2298—172no—
544#2297—172no—
545#2293—172no—
546#2290—172no—
547#2290—172no—
548#2280—171no—
549C42×D4—172no—
550C2×C4×C22⋊C4—171no—
551C22×C17—21no—
552C22×C17—21no—
553C22×C17—22no—
554C22×C17—21no—
555C22×C17—21no—
556C22×C17—21no—
557C22×C17—21no—
558C22×C17—22no—
559C22×C17—21no—
560C22×C17—22no—
561C22×C17—21no—
562C22×C17—44no—
563C22×C17C4×#4112yes—
564C22×C17C24×C411yescharacteristic
565C2×D17—21no—
566C2×D17—21no—
567C2×D17—24no—
568C2×D17—24no—
569C2×D17—22no—
570C2×D17—21no—
571C2×D17—21no—
572C2×D17—21no—
573C2×D17—21no—
574C2×D17—22no—
575C2×D17—21no—
576C2×D17—22no—
577C2×D17—21no—
578C2×D17—44no—
579C2×D17—44no—
580C2×D17—44no—
581C2×D17—44no—
582C2×D17—42no—
583C2×D17—42no—
584C2×D17—44no—
585C2×D17—42no—
586C2×D17—42no—
587C2×D17C4×#4112yes—
588C2×D17C22×#4112yes—
589C2×D17C2×H(5,𝔽2)11yescharacteristic
590C2×D17C2×H(5,𝔽2)11yescharacteristic
591C2×D17#58512yes—
592#595—28no—
593#595—44no—
594#595—44no—
595#595—44no—
596C4×C17—22no—
597C4×C17—21no—
598C4×C17—22no—
599C4×C17—21no—
600C4×C17—21no—
601C4×C17—22no—
602C4×C17#51812yes—
603Dic17—22no—
604Dic17—21no—
605Dic17—22no—
606Dic17—21no—
607Dic17—21no—
608Dic17—22no—
609Dic17#51812yes—
610C22×#41—171no—
611C24×C4—171no—
612#525—171no—
613#525—171no—
614#525—172no—
615#525—171no—
616#525—171no—
617#525—171no—
618#525—171no—
619#525—172no—
620#525—172no—
621#525—172no—
622#525—171no—
623#525#59511yescharacteristic, complemented
624C2×#123—172no—
625C2×C22⋊Q8—171no—
626C2×C22⋊Q8—171no—
627C2×#121—171no—
628C2×#121—171no—
629C2×#120—172no—
630C2×C4×D4—172no—
631C2×C4×D4—172no—
632C2×C4×D4—174no—
633C2×#117—171no—
634C2×#117—171no—
635C2×#117—171no—
636C2×#117—172no—
637C22×C22⋊C4—172no—
638C22×C42—171no—
639C22×C42—171no—
640C22×C42—172no—
641#391—174no—
642#390—174no—
643#390—174no—
644#389—174no—
645#388—174no—
646#388—174no—
647#388—174no—
648#388—174no—
649#388—174no—
650#388—174no—
651#387—174no—
652#387—174no—
653#387—174no—
654#387—174no—
655#386—174no—
656#386—174no—
657#386—174no—
658#386—174no—
659#385—174no—
660#385—174no—
661#381—172no—
662#380—172no—
663#380—172no—
664#379—172no—
665C4×C4⋊C4—174no—
666C4×C4⋊C4—172no—
667C4×C4⋊C4—172no—
668C4×C22⋊C4—174no—
669C4×C22⋊C4—172no—
670C4×C22⋊C4—174no—
671C4×C22⋊C4—172no—
672C4×C22⋊C4—172no—
673C4×C22⋊C4—172no—
674C4×C22⋊C4—172no—
675C4×C22⋊C4—172no—
676C4×C22⋊C4—172no—
677C4×C22⋊C4—172no—
678#376—172no—
679C2×#95—172no—
680C43—172no—
681C2×C17—22no—
682C2×C17—41no—
683C2×C17—41no—
684C2×C17—42no—
685C2×C17C2×C4×#4111yescharacteristic
686C2×C17C2×#51811yescharacteristic
687C2×C17#342811yescharacteristic
688D17—22no—
689D17—42no—
690D17—41no—
691D17—41no—
692D17#345912yes—
693D17#346012yes—
694C25—171no—
695C2×#41—171no—
696C2×#41—172no—
697C2×#41—171no—
698C2×#41—172no—
699C2×#41—171no—
700C2×#41—682no—
701C2×#41—682no—
702C2×#41C2×#59511yescharacteristic, complemented
703C22×Q8—171no—
704C22×D4—172no—
705C22×D4—172no—
706C22×D4—172no—
707C22×D4—171no—
708C23×C4—172no—
709C23×C4—171no—
710C23×C4—171no—
711C23×C4—172no—
712C23×C4—171no—
713C23×C4—171no—
714C23×C4—171no—
715C23×C4—171no—
716C23×C4—171no—
717C23×C4—171no—
718C23×C4—171no—
719C23×C4—171no—
720C23×C4—171no—
721C23×C4—171no—
722C23×C4—171no—
723C23×C4—172no—
724C23×C4—174no—
725C23×C4—682no—
726C23×C4—682no—
727C23×C4C2×#59511yescharacteristic, complemented
728#123—172no—
729#123—172no—
730#123—172no—
731#123—172no—
732#123—172no—
733#123—172no—
734#123—172no—
735#123C2×#59512yescomplemented
736C22⋊Q8—171no—
737C22⋊Q8—171no—
738C22⋊Q8—171no—
739C22⋊Q8—171no—
740C22⋊Q8—172no—
741C22⋊Q8—172no—
742C22⋊Q8—171no—
743C22⋊Q8—171no—
744C22⋊Q8—172no—
745C22⋊Q8—172no—
746C22⋊Q8C2×#59511yescharacteristic, complemented
747C22⋊Q8C2×#59511yescharacteristic, complemented
748#121—171no—
749#121—171no—
750#121—172no—
751#121—172no—
752#121—171no—
753#121—171no—
754#121—171no—
755#121—171no—
756#121—172no—
757#121—172no—
758#121C2×#59511yescharacteristic
759#121C2×#59511yescharacteristic, complemented
760#120—172no—
761#120—172no—
762#120—172no—
763#120—172no—
764#120—172no—
765#120—172no—
766#120—172no—
767#120C2×#59512yescomplemented
768C4×D4—172no—
769C4×D4—172no—
770C4×D4—172no—
771C4×D4—172no—
772C4×D4—172no—
773C4×D4—172no—
774C4×D4—172no—
775C4×D4—172no—
776C4×D4—172no—
777C4×D4—172no—
778C4×D4—172no—
779C4×D4—172no—
780C4×D4—172no—
781C4×D4—172no—
782C4×D4—3416no—
783C4×D4C2×#59512yescomplemented
784C4×D4C2×#59512yescomplemented
785#117—171no—
786#117—171no—
787#117—171no—
788#117—172no—
789#117—172no—
790#117—682no—
791#117—684no—
792#117—682no—
793#117C2×#59511yescharacteristic, complemented
794C2×C4⋊C4—171no—
795C2×C4⋊C4—171no—
796C2×C4⋊C4—172no—
797C2×C4⋊C4—172no—
798C2×C4⋊C4—174no—
799C2×C4⋊C4—172no—
800C2×C4⋊C4—172no—
801C2×C4⋊C4—174no—
802C2×C4⋊C4—174no—
803C2×C22⋊C4—172no—
804C2×C22⋊C4—172no—
805C2×C22⋊C4—172no—
806C2×C22⋊C4—172no—
807C2×C22⋊C4—172no—
808C2×C22⋊C4—174no—
809C2×C22⋊C4—174no—
810C2×C22⋊C4—174no—
811C2×C22⋊C4—174no—
812C2×C22⋊C4—172no—
813C2×C22⋊C4—172no—
814C2×C22⋊C4—174no—
815C2×C22⋊C4—174no—
816C2×C22⋊C4—174no—
817C2×C22⋊C4—348no—
818C2×C42—172no—
819C2×C42—172no—
820C2×C42—172no—
821C2×C42—172no—
822C2×C42—174no—
823C2×C42—172no—
824C2×C42—174no—
825C2×C42—172no—
826C2×C42—172no—
827C2×C42—174no—
828C2×C42—682no—
829C2×C42—684no—
830C2×C42—682no—
831#95—174no—
832#95—174no—
833#95—174no—
834#95—174no—
835#95—174no—
836#95—174no—
837#95—174no—
838#95—174no—
839#95—174no—
840#95—174no—
841C17#3408211yescharacteristic, complemented, Sylow
842C24—171no—
843C24—171no—
844C24—171no—
845C24—172no—
846C24—171no—
847C24—171no—
848C24—171no—
849C24—344no—
850C24—681no—
851C24—681no—
852C24—682no—
853C24C22×#59511yescharacteristic
854#41—42no—
855#41—682no—
856#41—684no—
857#41—682no—
858#41—684no—
859#41—682no—
860C2×Q8—171no—
861C2×Q8—172no—
862C2×Q8—681no—
863C2×Q8—681no—
864C2×Q8C22×#59511yescharacteristic
865C2×D4—172no—
866C2×D4—172no—
867C2×D4—172no—
868C2×D4—172no—
869C2×D4—172no—
870C2×D4—172no—
871C2×D4—172no—
872C2×D4—172no—
873C2×D4—172no—
874C2×D4—172no—
875C2×D4—171no—
876C2×D4—348no—
877C2×D4—684no—
878C2×D4—682no—
879C2×D4—682no—
880C2×D4—681no—
881C2×D4—681no—
882C2×D4C22×#59512yes—
883C2×D4C22×#59512yes—
884C2×D4C22×#59512yes—
885C2×D4C22×#59511yescharacteristic
886C22×C4—42no—
887C22×C4—171no—
888C22×C4—174no—
889C22×C4—171no—
890C22×C4—171no—
891C22×C4—171no—
892C22×C4—172no—
893C22×C4—178no—
894C22×C4—171no—
895C22×C4—171no—
896C22×C4—171no—
897C22×C4—171no—
898C22×C4—171no—
899C22×C4—171no—
900C22×C4—172no—
901C22×C4—171no—
902C22×C4—171no—
903C22×C4—172no—
904C22×C4—172no—
905C22×C4—172no—
906C22×C4—171no—
907C22×C4—171no—
908C22×C4—171no—
909C22×C4—171no—
910C22×C4—172no—
911C22×C4—171no—
912C22×C4—171no—
913C22×C4—171no—
914C22×C4—171no—
915C22×C4—171no—
916C22×C4—171no—
917C22×C4—174no—
918C22×C4—174no—
919C22×C4—174no—
920C22×C4—342no—
921C22×C4—342no—
922C22×C4—344no—
923C22×C4—342no—
924C22×C4—342no—
925C22×C4—344no—
926C22×C4—342no—
927C22×C4—342no—
928C22×C4—348no—
929C22×C4—344no—
930C22×C4—682no—
931C22×C4—682no—
932C22×C4—682no—
933C22×C4—682no—
934C22×C4—682no—
935C22×C4—682no—
936C22×C4—681no—
937C22×C4—681no—
938C22×C4—681no—
939C22×C4—681no—
940C22×C4—681no—
941C22×C4—681no—
942C22×C4—682no—
943C22×C4—682no—
944C22×C4—684no—
945C22×C4—682no—
946C22×C4—682no—
947C22×C4—684no—
948C22×C4—682no—
949C22×C4C22×#59511yescharacteristic
950C22×C4C22×#59511yescharacteristic
951C22×C4C22×#59511yescharacteristic
952C22×C4C22×#59512yes—
953C22×C4C22×#59511yescharacteristic
954C22×C4C22×#59511yescharacteristic
955C22×C4C22×#59511yescharacteristic
956C4⋊C4—172no—
957C4⋊C4—172no—
958C4⋊C4—171no—
959C4⋊C4—171no—
960C4⋊C4—172no—
961C4⋊C4—172no—
962C4⋊C4—172no—
963C4⋊C4—172no—
964C4⋊C4—172no—
965C4⋊C4—172no—
966C4⋊C4—348no—
967C4⋊C4—684no—
968C4⋊C4—682no—
969C4⋊C4—682no—
970C4⋊C4—684no—
971C4⋊C4C22×#59511yescharacteristic
972C4⋊C4C22×#59511yescharacteristic
973C4⋊C4C22×#59512yes—
974C4⋊C4C22×#59512yes—
975C22⋊C4—172no—
976C22⋊C4—172no—
977C22⋊C4—172no—
978C22⋊C4—172no—
979C22⋊C4—172no—
980C22⋊C4—172no—
981C22⋊C4—172no—
982C22⋊C4—172no—
983C22⋊C4—172no—
984C22⋊C4—172no—
985C22⋊C4—172no—
986C22⋊C4—172no—
987C22⋊C4—172no—
988C22⋊C4—172no—
989C22⋊C4—172no—
990C22⋊C4—348no—
991C22⋊C4—348no—
992C22⋊C4—348no—
993C22⋊C4—348no—
994C22⋊C4—684no—
995C22⋊C4—684no—
996C22⋊C4—682no—
997C22⋊C4—684no—
998C22⋊C4—682no—
999C22⋊C4C22×#59512yes—
1000C22⋊C4C22×#59512yes—
1001C22⋊C4C22×#59512yes—
1002C22⋊C4C22×#59512yes—
1003C22⋊C4C22×#59512yes—
1004C42—172no—
1005C42—172no—
1006C42—172no—
1007C42—344no—
1008C42—344no—
1009C42—344no—
1010C42—344no—
1011C42—348no—
1012C42—684no—
1013C42—682no—
1014C42—682no—
1015C42—684no—
1016C42C22×#59512yes—
1017C23—22no—
1018C23—41no—
1019C23—41no—
1020C23—171no—
1021C23—174no—
1022C23—171no—
1023C23—171no—
1024C23—171no—
1025C23—172no—
1026C23—341no—
1027C23—341no—
1028C23—342no—
1029C23—342no—
1030C23—342no—
1031C23—344no—
1032C23—341no—
1033C23—341no—
1034C23—342no—
1035C23—342no—
1036C23—344no—
1037C23—342no—
1038C23—341no—
1039C23—341no—
1040C23—342no—
1041C23—342no—
1042C23—342no—
1043C23—342no—
1044C23—681no—
1045C23—681no—
1046C23—681no—
1047C23—681no—
1048C23—681no—
1049C23—681no—
1050C23—688no—
1051C23—688no—
1052C23C23×#59511yescharacteristic
1053C23C23×#59511yescharacteristic
1054C23C23×#59512yes—
1055C23C23×#59511yescharacteristic
1056Q8—41no—
1057Q8—681no—
1058Q8—682no—
1059D4—24no—
1060D4—41no—
1061D4—42no—
1062D4—42no—
1063D4—344no—
1064D4—344no—
1065D4—344no—
1066D4—681no—
1067D4—682no—
1068D4—682no—
1069D4—682no—
1070D4—682no—
1071D4—682no—
1072D4—682no—
1073D4—682no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—171no—
1082C2×C4—172no—
1083C2×C4—172no—
1084C2×C4—178no—
1085C2×C4—172no—
1086C2×C4—172no—
1087C2×C4—171no—
1088C2×C4—171no—
1089C2×C4—172no—
1090C2×C4—171no—
1091C2×C4—342no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—344no—
1095C2×C4—344no—
1096C2×C4—341no—
1097C2×C4—341no—
1098C2×C4—342no—
1099C2×C4—344no—
1100C2×C4—341no—
1101C2×C4—341no—
1102C2×C4—342no—
1103C2×C4—341no—
1104C2×C4—341no—
1105C2×C4—342no—
1106C2×C4—342no—
1107C2×C4—342no—
1108C2×C4—344no—
1109C2×C4—344no—
1110C2×C4—344no—
1111C2×C4—342no—
1112C2×C4—342no—
1113C2×C4—342no—
1114C2×C4—344no—
1115C2×C4—344no—
1116C2×C4—344no—
1117C2×C4—344no—
1118C2×C4—344no—
1119C2×C4—344no—
1120C2×C4—344no—
1121C2×C4—344no—
1122C2×C4—344no—
1123C2×C4—344no—
1124C2×C4—681no—
1125C2×C4—681no—
1126C2×C4—681no—
1127C2×C4—681no—
1128C2×C4—681no—
1129C2×C4—681no—
1130C2×C4—681no—
1131C2×C4—681no—
1132C2×C4—681no—
1133C2×C4—688no—
1134C2×C4—6816no—
1135C2×C4—688no—
1136C2×C4C23×#59512yes—
1137C2×C4C23×#59512yes—
1138C2×C4C23×#59511yescharacteristic
1139C2×C4C23×#59511yescharacteristic
1140C2×C4C23×#59512yes—
1141C2×C4C23×#59511yescharacteristic
1142C2×C4C23×#59511yescharacteristic
1143C22—21no—
1144C22—21no—
1145C22—22no—
1146C22—21no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—22no—
1151C22—21no—
1152C22—22no—
1153C22—21no—
1154C22—44no—
1155C22—172no—
1156C22—171no—
1157C22—171no—
1158C22—172no—
1159C22—172no—
1160C22—344no—
1161C22—344no—
1162C22—341no—
1163C22—341no—
1164C22—342no—
1165C22—341no—
1166C22—341no—
1167C22—341no—
1168C22—341no—
1169C22—342no—
1170C22—341no—
1171C22—342no—
1172C22—341no—
1173C22—684no—
1174C22—684no—
1175C22—682no—
1176C22—682no—
1177C22—682no—
1178C22—682no—
1179C22—684no—
1180C22—684no—
1181C22—684no—
1182C22#41×#59512yes—
1183C22C24×#59511yescharacteristic
1184C4—22no—
1185C4—21no—
1186C4—21no—
1187C4—21no—
1188C4—22no—
1189C4—22no—
1190C4—172no—
1191C4—348no—
1192C4—342no—
1193C4—341no—
1194C4—341no—
1195C4—341no—
1196C4—342no—
1197C4—342no—
1198C4—684no—
1199C4—684no—
1200C4—684no—
1201C4#1176387612yes—
1202C2—22no—
1203C2—41no—
1204C2—41no—
1205C2—42no—
1206C2—172no—
1207C2—172no—
1208C2—342no—
1209C2—681no—
1210C2—681no—
1211C2—682no—
1212C2C2×#41×#59511yescharacteristic
1213C2C2×#1176387611yescharacteristic
1214C2#1454576411yescharacteristic
subgroupG/H
centerC2×C4C23×#595
commutator, socleC22×C17C24×C4
FrattiniC22C24×#595
FittingC17×#525C4
prime radicalD17×#525C2
cosocleC22×D17C25
hypercenter#525#595
hypocenterC17#34082
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14545283C2semidirect
2. #14545281C2semidirect
3. #14545280C2semidirect
4. #14545277C2semidirect
5. #14545273C2semidirect
6. #14545269C2semidirect
7. #14545246C2semidirect
8. #14545245C2semidirect
9. #14545241C2semidirect
10. #14545238C2semidirect
11. #14545238C2semidirect
12. #14545228C2semidirect
13. C4×D4×#595C2semidirect
14. C2×C4×C22⋊#595C2semidirect
19. C2×#10587677C22semidirect
23. C22×C4×#595C22semidirect
24. (C2×#595)⋊Q8C22semidirect
27. #11763760C22semidirect
32. #11763759C22semidirect
33. #11763759C22semidirect
34. #11763758C22semidirect
35. #11763758C22semidirect
36. #11763758C22semidirect
37. #11763758C22semidirect
41. #11763757C22semidirect
43. #11763756C22semidirect
48. C4⋊C4×#595C22semidirect
49. C4×C4⋊#595C22semidirect
50. C4×C4⋊#595C22semidirect
52. C22⋊C4×#595C22semidirect
59. C4×C22⋊#595C22semidirect
60. C4×C22⋊#595C22semidirect
61. #11763745C22semidirect
63. C42×#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
91. C2×#41×C17C2×C4semidirect
92. C23×C4×C17C2×C4semidirect
93. C23×Dic17C2×C4semidirect
96. C2×#63256C2×C4semidirect
98. C2×#63254C2×C4semidirect
99. C2×#63254C2×C4semidirect
104. C2×#63252C2×C4semidirect
105. C2×#63252C2×C4semidirect
108. C22×C4×D17C2×C4semidirect
109. C22×C4×D17C2×C4semidirect
110. C22×C4×D17C2×C4semidirect
111. C22×C4×D17C2×C4semidirect
112. C22×C4×D17C2×C4semidirect
113. C22×C4×D17C2×C4semidirect
152. C17×#123C2×C4semidirect
153. C17×C22⋊Q8C2×C4semidirect
154. C17×C22⋊Q8C2×C4semidirect
156. C17×#121C2×C4semidirect
157. C17×#120C2×C4semidirect
158. C4×D4×C17C2×C4semidirect
159. C4×D4×C17C2×C4semidirect
160. C17×#117C2×C4semidirect
161. #10587639C2×C4semidirect
162. #10587632C2×C4semidirect
163. #10587632C2×C4semidirect
165. #10587625C2×C4semidirect
167. #10587624C2×C4semidirect
168. #10587623C2×C4semidirect
169. #10587623C2×C4semidirect
170. #10587623C2×C4semidirect
171. #10587621C2×C4semidirect
172. D4×Dic17C2×C4semidirect
173. D4×Dic17C2×C4semidirect
175. #10587616C2×C4semidirect
176. #10587615C2×C4semidirect
177. C4×C22⋊D17C2×C4semidirect
178. C4×C22⋊D17C2×C4semidirect
179. C4×C22⋊D17C2×C4semidirect
180. C4×C22⋊D17C2×C4semidirect
181. #10587612C2×C4semidirect
182. #10587610C2×C4semidirect
183. #10587610C2×C4semidirect
184. #10587583C2×C4semidirect
185. #10587583C2×C4semidirect
186. #10587582C2×C4semidirect
187. #10587582C2×C4semidirect
189. #10587581C2×C4semidirect
190. #10587580C2×C4semidirect
191. #10587580C2×C4semidirect
192. #10587579C2×C4semidirect
193. #10587579C2×C4semidirect
194. #10587578C2×C4semidirect
195. #10587578C2×C4semidirect
200. #10587572C2×C4semidirect
202. #10587570C2×C4semidirect
203. #10587569C2×C4semidirect
204. #10587569C2×C4semidirect
205. #10587568C2×C4semidirect
206. #10587568C2×C4semidirect
207. #10587568C2×C4semidirect
208. #10587567C2×C4semidirect
209. #10587567C2×C4semidirect
210. #10587567C2×C4semidirect
211. #10587567C2×C4semidirect
217. #10587564C2×C4semidirect
218. #10587564C2×C4semidirect
219. #10587563C2×C4semidirect
220. C4×D68C2×C4semidirect
221. C4×D68C2×C4semidirect
222. #10587558C2×C4semidirect
254. C22×#595#41semidirect
623. #525#595semidirect
702. C2×#41C2×#595semidirect
727. C23×C4C2×#595semidirect
735. #123C2×#595semidirect
746. C22⋊Q8C2×#595semidirect
747. C22⋊Q8C2×#595semidirect
759. #121C2×#595semidirect
767. #120C2×#595semidirect
783. C4×D4C2×#595semidirect
784. C4×D4C2×#595semidirect
793. #117C2×#595semidirect
841. C17#34082semidirect

Maximal subgroups

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

subgroupindex
#145452832
#145452812
#145452802
#145452772
#145452732
#145452692
#145452462
#145452452
#145452412
#145452382
#145452282
C4×D4×#5952
C2×C4×C22⋊#5952
D17×#5252
#3408217