Finite Group Databasebeta

← #17979271

Subgroups — #17979271

Order 4352.

2586 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#14545324C214yesmaximal, complemented
2#14545309C212yesmaximal, complemented
3#14545308C212yesmaximal, complemented
4#14545301C212yesmaximal, complemented
5#14545297C212yesmaximal, complemented
6#14545295C211yesmaximal, characteristic, complemented
7#14545294C211yesmaximal, characteristic, complemented
8#14545289C211yesmaximal, characteristic, complemented
9#14545287C211yesmaximal, characteristic, complemented
10#14545272C212yesmaximal, complemented
11#14545271C212yesmaximal, complemented
12#14545269C214yesmaximal, complemented
13#14545267C212yesmaximal, complemented
14#14545266C212yesmaximal, complemented
15#14545228C211yesmaximal, characteristic, complemented
16C2×#11763751C211yesmaximal, characteristic, complemented
17D17×#525C211yesmaximal, characteristic
18C2×Q8×#595C2212yescomplemented
19C2×D4×#595C2214yes—
20C2×D4×#595C2212yescomplemented
21C2×#10587677C2212yes—
22C22×C4⋊#595C2212yes—
23C22×C22⋊#595C2212yes—
24(C2×#595)⋊Q8C2212yescomplemented
25#11763761C2214yes—
26#11763761C2214yes—
27#11763761C2212yescomplemented
28#11763760C2214yescomplemented
29#11763760C2212yescomplemented
30#11763760C2214yescomplemented
31#11763760C2212yescomplemented
32#11763759C2214yes—
33#11763759C2214yes—
34#11763759C2214yes—
35#11763759C2214yes—
36#11763759C2214yescomplemented
37#11763759C2214yescomplemented
38#11763758C2214yescomplemented
39#11763758C2214yescomplemented
40#11763757C2214yes—
41#11763757C2214yes—
42#11763757C2214yes—
43#11763756C2214yes—
44#11763756C2214yescomplemented
45#11763756C2214yescomplemented
46#11763754C2212yescomplemented
47#11763753C2212yescomplemented
48#11763752C2211yescharacteristic
49#11763752C2211yescharacteristic
50#11763752C2212yescomplemented
51#11763751C2212yes—
52#11763751C2212yes—
53#11763751C2211yescharacteristic
54#11763751C2211yescharacteristic
55#11763751C2212yes—
56#11763751C2211yescharacteristic
57#11763751C2211yescharacteristic
58#11763751C2212yes—
59#11763751C2212yescomplemented
60#11763750C2212yes—
61C4⋊C4×#595C2212yescomplemented
62C4⋊C4×#595C2212yescomplemented
63C4×C4⋊#595C2212yescomplemented
64C22⋊C4×#595C2214yes—
65C4×C22⋊#595C2211yescharacteristic
66C4×C22⋊#595C2211yescharacteristic
67C4×C22⋊#595C2212yes—
68C4×C22⋊#595C2212yescomplemented
69#11763745C2212yescomplemented
70C2×(C2×#595)⋊C4C2212yes—
71C2×(C2×#595)⋊C4C2212yescomplemented
72C2×#41×D17C2211yescharacteristic
73C23×C4×D17C2211yescharacteristic
74#11763322C411yescharacteristic, complemented
75#11763322C411yescharacteristic, complemented
76#11763321C411yescharacteristic, complemented
77#11763320C411yescharacteristic, complemented
78#11763319C411yescharacteristic, complemented
79#11763319C411yescharacteristic, complemented
80#11763318C412yescomplemented
81#11763318C412yescomplemented
82#11763317C412yescomplemented
83#11763316C411yescharacteristic, complemented
84#11763315C412yescomplemented
85#123×D17C2212yes—
86C22⋊Q8×D17C2211yescharacteristic
87C22⋊Q8×D17C2211yescharacteristic
88#121×D17C2211yescharacteristic
89#121×D17C2211yescharacteristic
90#120×D17C2212yes—
91C4×D4×D17C2212yes—
92C4×D4×D17C2212yes—
93#117×D17C2211yescharacteristic
94C17×#525C411yescharacteristic, complemented
95C24×D17C2311yescharacteristic
96C23×#595C2314yes—
97C23×#595C2314yes—
98C2×#41×C17C2×C411yescharacteristic, complemented
99C23×C4×C17C2×C411yescharacteristic, complemented
100C23×Dic17C2×C411yescharacteristic, complemented
101#41×D17—44no—
102C2×#63256C2×C411yescharacteristic, complemented
103C2×Q8×D17C2311yescharacteristic
104C2×#63254C2×C412yescomplemented
105C2×#63254C2×C411yescharacteristic, complemented
106C2×D4×D17C2312yes—
107C2×D4×D17C2311yescharacteristic
108C2×D4×D17C2312yes—
109C2×D4×D17C2312yes—
110C2×#63252C2×C412yescomplemented
111C2×#63252C2×C411yescharacteristic, complemented
112C22×C4×D17—44no—
113C22×C4×D17C2×C411yescharacteristic, complemented
114C22×C4×D17C2×C411yescharacteristic, complemented
115C22×C4×D17C2×C411yescharacteristic, complemented
116C22×C4×D17C2×C411yescharacteristic, complemented
117C22×C4×D17C2×C411yescharacteristic, complemented
118C22×C4×D17C2×C411yescharacteristic, complemented
119C22×C4×D17C2311yescharacteristic
120C22×C4×D17C2311yescharacteristic
121C22×C4×D17C2311yescharacteristic
122C22×C4×D17C2311yescharacteristic
123C22×C4×D17C2312yes—
124C22×C4×D17C2311yescharacteristic
125C22×C4×D17C2311yescharacteristic
126C2×C22⋊#595—44no—
127C2×C22⋊#595C2312yes—
128C2×C22⋊#595C2312yes—
129C2×C22⋊#595C2312yes—
130C2×C22⋊#595C2312yes—
131C2×C22⋊#595C2314yes—
132C2×C22⋊#595C2312yes—
133C2×C22⋊#595C2312yes—
134C2×C22⋊#595C2312yes—
135C2×C22⋊#595C2314yes—
136C2×C22⋊#595C2312yes—
137C2×C22⋊#595C2314yes—
138C2×C22⋊#595C2314yes—
139Q8×#595—44no—
140D4×#595—44no—
141D4×#595—48no—
142#10587677—44no—
143C2×C4⋊#595—44no—
144C2×C4⋊#595C2312yes—
145C2×C4⋊#595C2312yes—
146C2×C4⋊#595C2314yes—
147C2×C4⋊#595C2312yes—
148C2×C4⋊#595C2314yes—
149C2×C4⋊#595C2312yes—
150C2×C4⋊#595C2314yes—
151C2×C4⋊#595C2314yes—
152C2×C4×#595C2312yes—
153C2×C4×#595C2312yes—
154C2×C4×#595C2314yes—
155C2×C4×#595C2314yes—
156C2×C4×#595C2314yes—
157C17×#123C2×C412yescomplemented
158C17×C22⋊Q8C2×C411yescharacteristic, complemented
159C17×C22⋊Q8C2×C411yescharacteristic, complemented
160C17×#121C2×C411yescharacteristic
161C17×#121C2×C411yescharacteristic, complemented
162C17×#120C2×C412yescomplemented
163C4×D4×C17C2×C412yescomplemented
164C4×D4×C17C2×C412yescomplemented
165C17×#117C2×C411yescharacteristic, complemented
166#10587639C2×C412yescomplemented
167#10587632C2×C411yescharacteristic, complemented
168#10587632C2×C411yescharacteristic, complemented
169#10587625C2×C412yes—
170#10587625C2×C412yescomplemented
171#10587624C2×C411yescharacteristic
172#10587624C2×C411yescharacteristic, complemented
173#10587623C2×C412yescomplemented
174#10587623C2×C412yescomplemented
175#10587623C2×C412yescomplemented
176#10587621C2×C412yescomplemented
177D4×Dic17C2×C412yescomplemented
178D4×Dic17C2×C412yescomplemented
179#10587616C2×C411yescharacteristic
180#10587616C2×C411yescharacteristic, complemented
181#10587615C2×C412yescomplemented
182C4×C22⋊D17C2×C412yescomplemented
183C4×C22⋊D17C2×C412yescomplemented
184C4×C22⋊D17C2×C412yescomplemented
185C4×C22⋊D17C2×C412yescomplemented
186#10587612C2×C411yescharacteristic, complemented
187#10587610C2×C411yescharacteristic, complemented
188#10587610C2×C411yescharacteristic, complemented
189#10587583C2×C411yescharacteristic, complemented
190#10587583C2×C411yescharacteristic, complemented
191#10587582C2×C412yescomplemented
192#10587582C2×C412yescomplemented
193#10587581C2×C411yescharacteristic
194#10587581C2×C411yescharacteristic, complemented
195#10587580C2×C412yescomplemented
196#10587580C2×C412yescomplemented
197#10587579C2×C412yescomplemented
198#10587579C2×C412yescomplemented
199#10587578C2×C411yescharacteristic, complemented
200#10587578C2×C411yescharacteristic, complemented
201C4⋊C4×D17C2311yescharacteristic
202C4⋊C4×D17C2311yescharacteristic
203C4⋊C4×D17C2312yes—
204C4⋊C4×D17C2312yes—
205#10587572C2×C412yescomplemented
206#10587570C2×C412yes—
207#10587570C2×C412yescomplemented
208#10587569C2×C412yescomplemented
209#10587569C2×C412yescomplemented
210#10587568C2×C412yescomplemented
211#10587568C2×C412yescomplemented
212#10587568C2×C412yescomplemented
213#10587567C2×C412yescomplemented
214#10587567C2×C412yescomplemented
215#10587567C2×C412yescomplemented
216#10587567C2×C412yescomplemented
217C22⋊C4×D17C2312yes—
218C22⋊C4×D17C2312yes—
219C22⋊C4×D17C2312yes—
220C22⋊C4×D17C2312yes—
221C22⋊C4×D17C2312yes—
222#10587564C2×C412yescomplemented
223#10587564C2×C412yescomplemented
224#10587563C2×C412yescomplemented
225C4×D68C2×C412yescomplemented
226C4×D68C2×C412yescomplemented
227#10587558C2×C412yescomplemented
228C42×D17C2312yes—
229(C2×#595)⋊C4C2312yes—
230(C2×#595)⋊C4C2312yes—
231(C2×#595)⋊C4C2314yes—
232(C2×#595)⋊C4C2311yescharacteristic
233(C2×#595)⋊C4C2314yes—
234(C2×#595)⋊C4C2311yescharacteristic
235(C2×#595)⋊C4C2314yes—
236(C2×#595)⋊C4C2311yescharacteristic
237(C2×#595)⋊C4C2311yescharacteristic
238(C2×#595)⋊C4C2312yes—
239(C2×#595)⋊C4C2312yes—
240(C2×#595)⋊C4C2314yes—
241(C2×#595)⋊C4C2314yes—
242(C2×#595)⋊C4C2314yes—
243(C2×#595)⋊C4C2314yes—
244C24×C17C22×C411yescharacteristic
245C23×D17—22no—
246C23×D17—22no—
247C23×D17—42no—
248C23×D17—42no—
249C23×D17C22×C411yescharacteristic
250C23×D17C22×C411yescharacteristic
251C23×D17C22×C411yescharacteristic
252C23×D17C2411yescharacteristic
253C23×D17C2411yescharacteristic
254C23×D17C2412yes—
255C23×D17C2411yescharacteristic
256C22×#595—28no—
257C22×#595—44no—
258C22×#595—44no—
259C22×#595—44no—
260C22×#595—44no—
261C22×#595—44no—
262C22×#595C2412yes—
263C22×#595C2412yes—
264C22×#595C2412yes—
265C22×#595C2414yes—
266C22×#595C2412yes—
267C22×#595C2414yes—
268#41×C17—42no—
269C2×Q8×C17C22×C411yescharacteristic
270C2×D4×C17C22×C411yescharacteristic
271C2×D4×C17C22×C412yes—
272C2×D4×C17C22×C412yes—
273C2×D4×C17C22×C412yes—
274C22×C4×C17—42no—
275C22×C4×C17C22×C411yescharacteristic
276C22×C4×C17C22×C411yescharacteristic
277C22×C4×C17C22×C411yescharacteristic
278C22×C4×C17C22×C411yescharacteristic
279C22×C4×C17C22×C411yescharacteristic
280C22×C4×C17C22×C411yescharacteristic
281C22×C4×C17C22×C412yes—
282C2×C22⋊D17C22×C412yes—
283C2×C22⋊D17C22×C412yes—
284C2×C22⋊D17C22×C412yes—
285C2×C22⋊D17C22×C412yes—
286C2×C22⋊D17C22×C412yes—
287C2×C22⋊D17C22×C412yes—
288C2×C22⋊D17C22×C412yes—
289C22×Dic17—42no—
290C22×Dic17C22×C411yescharacteristic
291C22×Dic17C22×C411yescharacteristic
292C22×Dic17C22×C411yescharacteristic
293C22×Dic17C22×C411yescharacteristic
294C22×Dic17C22×C411yescharacteristic
295C22×Dic17C22×C411yescharacteristic
296C22×Dic17C22×C412yes—
297#63256—42no—
298Q8×D17—24no—
299#63254—42no—
300#63254—44no—
301D4×D17—24no—
302D4×D17—24no—
303D4×D17—24no—
304D4×D17—44no—
305D4×D17—44no—
306#63252—44no—
307#63252—42no—
308C2×D68C22×C411yescharacteristic
309C2×D68C22×C412yes—
310C2×D68C22×C412yes—
311C2×D68C22×C412yes—
312C2×C4×D17—24no—
313C2×C4×D17—24no—
314C2×C4×D17—24no—
315C2×C4×D17—42no—
316C2×C4×D17—42no—
317C2×C4×D17—42no—
318C2×C4×D17—42no—
319C2×C4×D17—42no—
320C2×C4×D17—42no—
321C2×C4×D17—42no—
322C2×C4×D17—42no—
323C2×C4×D17—42no—
324C2×C4×D17—44no—
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×C411yescharacteristic
332C2×C4×D17C22×C411yescharacteristic
333C2×C4×D17C22×C411yescharacteristic
334C2×C4×D17C22×C411yescharacteristic
335C2×C4×D17C22×C411yescharacteristic
336C2×C4×D17C22×C411yescharacteristic
337C2×C4×D17C22×C412yes—
338C2×C4×D17C22×C412yes—
339C2×C4×D17C2412yes—
340C2×C4×D17C2412yes—
341C2×C4×D17C2412yes—
342C2×C4×D17C2411yescharacteristic
343C2×C4×D17C2411yescharacteristic
344C2×C4×D17C2411yescharacteristic
345C2×C4×D17C2411yescharacteristic
346C2×Dic34C22×C412yes—
347C2×Dic34C22×C411yescharacteristic
348C22⋊#595—24no—
349C22⋊#595—24no—
350C22⋊#595—42no—
351C22⋊#595—42no—
352C22⋊#595—44no—
353C22⋊#595—44no—
354C22⋊#595—42no—
355C22⋊#595—44no—
356C22⋊#595—42no—
357C22⋊#595—42no—
358C22⋊#595—44no—
359C22⋊#595—42no—
360C4⋊#595—24no—
361C4⋊#595—24no—
362C4⋊#595—44no—
363C4⋊#595—44no—
364C4⋊#595—42no—
365C4⋊#595—42no—
366C4⋊#595—44no—
367C4⋊#595—44no—
368C4×#595—24no—
369C4×#595—24no—
370C4×#595—44no—
371C4×#595—44no—
372C4×#595—44no—
373C4⋊C4×C17C22×C412yes—
374C4⋊C4×C17C22×C412yes—
375C4⋊C4×C17C22×C411yescharacteristic
376C4⋊C4×C17C22×C411yescharacteristic
377C22⋊C4×C17C22×C412yes—
378C22⋊C4×C17C22×C412yes—
379C22⋊C4×C17C22×C412yes—
380C22⋊C4×C17C22×C412yes—
381C22⋊C4×C17C22×C412yes—
382C42×C17C22×C412yes—
383C22⋊Dic17C22×C412yes—
384C22⋊Dic17C22×C412yes—
385C22⋊Dic17C22×C412yes—
386C22⋊Dic17C22×C412yes—
387C22⋊Dic17C22×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—
396#63227C22×C412yes—
397#63227C22×C412yes—
398C4⋊Dic17C22×C412yes—
399C4⋊Dic17C22×C412yes—
400C4⋊Dic17C22×C411yescharacteristic
401C4⋊Dic17C22×C411yescharacteristic
402#63225C22×C412yes—
403#63225C22×C412yes—
404#63225C22×C412yes—
405#63225C22×C412yes—
406#63225C22×C412yes—
407#63225C22×C412yes—
408C4×Dic17C22×C412yes—
409C4×Dic17C22×C412yes—
410C4×Dic17C22×C412yes—
411#34404—171nomaximal, Sylow
412C23×C17—22no—
413C23×C17—41no—
414C23×C17—41no—
415C23×C17C23×C411yescharacteristic
416C23×C17C23×C411yescharacteristic
417C23×C17C23×C412yes—
418C23×C17C23×C411yescharacteristic
419C22×D17—22no—
420C22×D17—22no—
421C22×D17—22no—
422C22×D17—22no—
423C22×D17—22no—
424C22×D17—21no—
425C22×D17—21no—
426C22×D17—22no—
427C22×D17—22no—
428C22×D17—24no—
429C22×D17—22no—
430C22×D17—22no—
431C22×D17—21no—
432C22×D17—21no—
433C22×D17—22no—
434C22×D17—24no—
435C22×D17—22no—
436C22×D17—41no—
437C22×D17—41no—
438C22×D17—41no—
439C22×D17—41no—
440C22×D17—41no—
441C22×D17—41no—
442C22×D17—48no—
443C22×D17—48no—
444C22×D17C23×C411yescharacteristic
445C22×D17C23×C411yescharacteristic
446C22×D17C23×C412yes—
447C22×D17C23×C411yescharacteristic
448C22×D17H(5,𝔽2)12yes—
449C22×D172−1+412yes—
450C22×D17C2511yescharacteristic
451C2×#595—22no—
452C2×#595—22no—
453C2×#595—22no—
454C2×#595—22no—
455C2×#595—22no—
456C2×#595—24no—
457C2×#595—24no—
458C2×#595—24no—
459C2×#595—22no—
460C2×#595—24no—
461C2×#595—22no—
462C2×#595—22no—
463C2×#595—22no—
464C2×#595—24no—
465C2×#595—22no—
466C2×#595—24no—
467C2×#595—22no—
468C2×#595—22no—
469C2×#595—88no—
470C2×#595—88no—
471Q8×C17—22no—
472D4×C17—24no—
473D4×C17—22no—
474D4×C17—42no—
475D4×C17—42no—
476C2×C4×C17—22no—
477C2×C4×C17—22no—
478C2×C4×C17—22no—
479C2×C4×C17—41no—
480C2×C4×C17—41no—
481C2×C4×C17—41no—
482C2×C4×C17—42no—
483C2×C4×C17C23×C411yescharacteristic
484C2×C4×C17C23×C412yes—
485C2×C4×C17C23×C412yes—
486C2×C4×C17C23×C412yes—
487C2×C4×C17C23×C411yescharacteristic
488C2×C4×C17C23×C411yescharacteristic
489C2×C4×C17C23×C411yescharacteristic
490C22⋊D17—24no—
491C22⋊D17—24no—
492C22⋊D17—24no—
493C22⋊D17—42no—
494C22⋊D17—42no—
495C22⋊D17—42no—
496C22⋊D17—42no—
497C2×Dic17—22no—
498C2×Dic17—22no—
499C2×Dic17—22no—
500C2×Dic17—41no—
501C2×Dic17—41no—
502C2×Dic17—41no—
503C2×Dic17—42no—
504C2×Dic17C23×C412yes—
505C2×Dic17C23×C412yes—
506C2×Dic17C23×C412yes—
507C2×Dic17C23×C411yescharacteristic
508C2×Dic17C23×C411yescharacteristic
509C2×Dic17C23×C411yescharacteristic
510C2×Dic17C23×C411yescharacteristic
511D68—24no—
512D68—22no—
513D68—42no—
514D68—42no—
515C4×D17—22no—
516C4×D17—24no—
517C4×D17—22no—
518C4×D17—22no—
519C4×D17—22no—
520C4×D17—22no—
521C4×D17—24no—
522C4×D17—22no—
523C4×D17—22no—
524C4×D17—22no—
525C4×D17—22no—
526C4×D17—22no—
527C4×D17—22no—
528C4×D17—41no—
529C4×D17—41no—
530C4×D17—41no—
531C4×D17—41no—
532C4×D17—41no—
533C4×D17—41no—
534C4×D17—42no—
535C4×D17—42no—
536C4×D17H(5,𝔽2)14yes—
537Dic34—22no—
538Dic34—24no—
539C2×#525—171no—
540#2376—174no—
541#2361—172no—
542#2360—172no—
543#2353—172no—
544#2349—172no—
545#2347—171no—
546#2346—171no—
547#2341—171no—
548#2339—171no—
549#2324—172no—
550#2323—172no—
551#2321—174no—
552#2319—172no—
553#2318—172no—
554#2280—171no—
555C2×#380—171no—
556C22×C17—21no—
557C22×C17—21no—
558C22×C17—21no—
559C22×C17—21no—
560C22×C17—22no—
561C22×C17—22no—
562C22×C17—21no—
563C22×C17—21no—
564C22×C17—21no—
565C22×C17—22no—
566C22×C17—21no—
567C22×C17—44no—
568C22×C17#52012yes—
569C22×C17C24×C411yescharacteristic
570C2×D17—21no—
571C2×D17—21no—
572C2×D17—24no—
573C2×D17—24no—
574C2×D17—21no—
575C2×D17—21no—
576C2×D17—22no—
577C2×D17—22no—
578C2×D17—21no—
579C2×D17—21no—
580C2×D17—21no—
581C2×D17—22no—
582C2×D17—21no—
583C2×D17—44no—
584C2×D17—44no—
585C2×D17—44no—
586C2×D17—44no—
587C2×D17—42no—
588C2×D17—42no—
589C2×D17—44no—
590C2×D17—42no—
591C2×D17—42no—
592C2×D17#52012yes—
593C2×D17C2×H(5,𝔽2)12yes—
594C2×D17C2×H(5,𝔽2)11yescharacteristic
595C2×D17C2×2−1+411yescharacteristic
596C2×D17#58512yes—
597#595—42no—
598#595—42no—
599#595—42no—
600#595—44no—
601#595—42no—
602#595—44no—
603C4×C17—22no—
604C4×C17—21no—
605C4×C17—21no—
606C4×C17—21no—
607C4×C17—22no—
608C4×C17—22no—
609C4×C17#51812yes—
610Dic17—22no—
611Dic17—21no—
612Dic17—21no—
613Dic17—21no—
614Dic17—22no—
615Dic17—22no—
616Dic17#51812yes—
617C22×#41—171no—
618C24×C4—171no—
619#525—171no—
620#525—171no—
621#525—172no—
622#525—171no—
623#525—171no—
624#525—171no—
625#525—171no—
626#525—172no—
627#525—172no—
628#525—172no—
629#525—171no—
630#525#59511yescharacteristic, complemented
631C2×#123—172no—
632C2×C22⋊Q8—171no—
633C2×C22⋊Q8—171no—
634C2×#121—171no—
635C2×#121—171no—
636C2×#120—172no—
637C2×C4×Q8—172no—
638C2×C4×D4—172no—
639C2×C4×D4—172no—
640C2×C4×D4—174no—
641C2×C4×D4—172no—
642C2×#117—171no—
643C2×#117—172no—
644C22×C4⋊C4—172no—
645C22×C22⋊C4—172no—
646#391—172no—
647#390—174no—
648#390—174no—
649#390—172no—
650#389—174no—
651#389—172no—
652#389—174no—
653#389—172no—
654#388—174no—
655#388—174no—
656#388—174no—
657#388—174no—
658#388—174no—
659#388—174no—
660#387—174no—
661#387—174no—
662#386—174no—
663#386—174no—
664#386—174no—
665#385—174no—
666#385—174no—
667#385—174no—
668#383—172no—
669#382—172no—
670#381—171no—
671#381—171no—
672#381—172no—
673#380—172no—
674#380—172no—
675#380—172no—
676#380—171no—
677#380—171no—
678#380—171no—
679#380—171no—
680#380—172no—
681#380—172no—
682#379—172no—
683C4×C4⋊C4—172no—
684C4×C4⋊C4—172no—
685C4×C4⋊C4—172no—
686C4×C22⋊C4—172no—
687C4×C22⋊C4—174no—
688C4×C22⋊C4—171no—
689C4×C22⋊C4—171no—
690C4×C22⋊C4—172no—
691#376—172no—
692C2×#95—172no—
693C2×#95—172no—
694C2×C17—22no—
695C2×C17—41no—
696C2×C17—41no—
697C2×C17—42no—
698C2×C17C2×#51811yescharacteristic
699C2×C17C2×#52011yescharacteristic
700C2×C17#342811yescharacteristic
701D17—22no—
702D17—42no—
703D17—41no—
704D17—41no—
705D17#354112yes—
706D17#354212yes—
707C25—171no—
708C2×#41—171no—
709C2×#41—172no—
710C2×#41—171no—
711C2×#41—172no—
712C2×#41—171no—
713C2×#41—684no—
714C2×#41C2×#59511yescharacteristic, complemented
715C22×Q8—171no—
716C22×D4—172no—
717C22×D4—171no—
718C22×D4—172no—
719C22×D4—172no—
720C23×C4—171no—
721C23×C4—171no—
722C23×C4—171no—
723C23×C4—171no—
724C23×C4—171no—
725C23×C4—171no—
726C23×C4—172no—
727C23×C4—171no—
728C23×C4—171no—
729C23×C4—171no—
730C23×C4—171no—
731C23×C4—171no—
732C23×C4—171no—
733C23×C4—171no—
734C23×C4—174no—
735C23×C4—174no—
736C23×C4—684no—
737C23×C4C2×#59511yescharacteristic, complemented
738#123—172no—
739#123—172no—
740#123—172no—
741#123—172no—
742#123—172no—
743#123—172no—
744#123—172no—
745#123C2×#59512yescomplemented
746C22⋊Q8—171no—
747C22⋊Q8—171no—
748C22⋊Q8—171no—
749C22⋊Q8—171no—
750C22⋊Q8—172no—
751C22⋊Q8—172no—
752C22⋊Q8—171no—
753C22⋊Q8—171no—
754C22⋊Q8—172no—
755C22⋊Q8—172no—
756C22⋊Q8C2×#59511yescharacteristic, complemented
757C22⋊Q8C2×#59511yescharacteristic, complemented
758#121—171no—
759#121—171no—
760#121—172no—
761#121—172no—
762#121—171no—
763#121—171no—
764#121—171no—
765#121—171no—
766#121—172no—
767#121—172no—
768#121C2×#59511yescharacteristic
769#121C2×#59511yescharacteristic, complemented
770#120—172no—
771#120—172no—
772#120—172no—
773#120—172no—
774#120—172no—
775#120—172no—
776#120—172no—
777#120C2×#59512yescomplemented
778C4×Q8—684no—
779C4×D4—172no—
780C4×D4—172no—
781C4×D4—172no—
782C4×D4—172no—
783C4×D4—172no—
784C4×D4—172no—
785C4×D4—172no—
786C4×D4—172no—
787C4×D4—172no—
788C4×D4—172no—
789C4×D4—172no—
790C4×D4—172no—
791C4×D4—172no—
792C4×D4—172no—
793C4×D4—684no—
794C4×D4—688no—
795C4×D4C2×#59512yescomplemented
796C4×D4C2×#59512yescomplemented
797#117—171no—
798#117—171no—
799#117—171no—
800#117—172no—
801#117—172no—
802#117—684no—
803#117C2×#59511yescharacteristic, complemented
804C2×C4⋊C4—171no—
805C2×C4⋊C4—171no—
806C2×C4⋊C4—172no—
807C2×C4⋊C4—172no—
808C2×C4⋊C4—172no—
809C2×C4⋊C4—172no—
810C2×C4⋊C4—174no—
811C2×C4⋊C4—172no—
812C2×C4⋊C4—172no—
813C2×C4⋊C4—174no—
814C2×C4⋊C4—174no—
815C2×C4⋊C4—174no—
816C2×C4⋊C4—684no—
817C2×C22⋊C4—172no—
818C2×C22⋊C4—172no—
819C2×C22⋊C4—172no—
820C2×C22⋊C4—172no—
821C2×C22⋊C4—172no—
822C2×C22⋊C4—172no—
823C2×C22⋊C4—172no—
824C2×C22⋊C4—172no—
825C2×C22⋊C4—174no—
826C2×C22⋊C4—172no—
827C2×C22⋊C4—172no—
828C2×C22⋊C4—172no—
829C2×C22⋊C4—174no—
830C2×C22⋊C4—174no—
831C2×C22⋊C4—172no—
832C2×C22⋊C4—172no—
833C2×C22⋊C4—174no—
834C2×C22⋊C4—684no—
835C2×C42—172no—
836C2×C42—172no—
837C2×C42—172no—
838C2×C42—174no—
839C2×C42—174no—
840C2×C42—174no—
841#95—171no—
842#95—172no—
843#95—172no—
844#95—174no—
845#95—174no—
846#95—171no—
847#95—174no—
848#95—171no—
849#95—171no—
850#95—172no—
851#95—172no—
852#95—174no—
853#95—174no—
854#95—174no—
855#95—174no—
856C17#3440411yescharacteristic, complemented, Sylow
857C24—171no—
858C24—171no—
859C24—171no—
860C24—172no—
861C24—171no—
862C24—171no—
863C24—171no—
864C24—342no—
865C24—342no—
866C24—682no—
867C24—682no—
868C24C22×#59511yescharacteristic
869#41—42no—
870#41—682no—
871#41—684no—
872#41—682no—
873#41—684no—
874#41—682no—
875C2×Q8—172no—
876C2×Q8—171no—
877C2×Q8—344no—
878C2×Q8C22×#59511yescharacteristic
879C2×D4—172no—
880C2×D4—172no—
881C2×D4—172no—
882C2×D4—172no—
883C2×D4—172no—
884C2×D4—172no—
885C2×D4—172no—
886C2×D4—172no—
887C2×D4—171no—
888C2×D4—172no—
889C2×D4—172no—
890C2×D4—344no—
891C2×D4—344no—
892C2×D4—344no—
893C2×D4—684no—
894C2×D4—684no—
895C2×D4C22×#59512yes—
896C2×D4C22×#59511yescharacteristic
897C2×D4C22×#59512yes—
898C2×D4C22×#59512yes—
899C22×C4—42no—
900C22×C4—171no—
901C22×C4—171no—
902C22×C4—171no—
903C22×C4—171no—
904C22×C4—171no—
905C22×C4—171no—
906C22×C4—172no—
907C22×C4—171no—
908C22×C4—171no—
909C22×C4—171no—
910C22×C4—171no—
911C22×C4—171no—
912C22×C4—171no—
913C22×C4—171no—
914C22×C4—171no—
915C22×C4—172no—
916C22×C4—172no—
917C22×C4—172no—
918C22×C4—171no—
919C22×C4—171no—
920C22×C4—171no—
921C22×C4—171no—
922C22×C4—171no—
923C22×C4—171no—
924C22×C4—172no—
925C22×C4—172no—
926C22×C4—171no—
927C22×C4—171no—
928C22×C4—172no—
929C22×C4—172no—
930C22×C4—172no—
931C22×C4—174no—
932C22×C4—174no—
933C22×C4—172no—
934C22×C4—344no—
935C22×C4—344no—
936C22×C4—344no—
937C22×C4—348no—
938C22×C4—682no—
939C22×C4—682no—
940C22×C4—682no—
941C22×C4—682no—
942C22×C4—682no—
943C22×C4—682no—
944C22×C4—682no—
945C22×C4—682no—
946C22×C4—682no—
947C22×C4—684no—
948C22×C4—682no—
949C22×C4—684no—
950C22×C4—684no—
951C22×C4—684no—
952C22×C4—684no—
953C22×C4—684no—
954C22×C4C22×#59511yescharacteristic
955C22×C4C22×#59511yescharacteristic
956C22×C4C22×#59511yescharacteristic
957C22×C4C22×#59511yescharacteristic
958C22×C4C22×#59511yescharacteristic
959C22×C4C22×#59512yes—
960C22×C4C22×#59511yescharacteristic
961C4⋊C4—172no—
962C4⋊C4—172no—
963C4⋊C4—171no—
964C4⋊C4—171no—
965C4⋊C4—172no—
966C4⋊C4—172no—
967C4⋊C4—172no—
968C4⋊C4—172no—
969C4⋊C4—172no—
970C4⋊C4—172no—
971C4⋊C4—344no—
972C4⋊C4—344no—
973C4⋊C4—684no—
974C4⋊C4—684no—
975C4⋊C4—682no—
976C4⋊C4—682no—
977C4⋊C4—684no—
978C4⋊C4—684no—
979C4⋊C4C22×#59511yescharacteristic
980C4⋊C4C22×#59511yescharacteristic
981C4⋊C4C22×#59512yes—
982C4⋊C4C22×#59512yes—
983C22⋊C4—172no—
984C22⋊C4—172no—
985C22⋊C4—172no—
986C22⋊C4—172no—
987C22⋊C4—172no—
988C22⋊C4—172no—
989C22⋊C4—172no—
990C22⋊C4—172no—
991C22⋊C4—172no—
992C22⋊C4—172no—
993C22⋊C4—172no—
994C22⋊C4—172no—
995C22⋊C4—172no—
996C22⋊C4—172no—
997C22⋊C4—172no—
998C22⋊C4—344no—
999C22⋊C4—344no—
1000C22⋊C4—682no—
1001C22⋊C4—684no—
1002C22⋊C4—682no—
1003C22⋊C4—682no—
1004C22⋊C4—684no—
1005C22⋊C4—682no—
1006C22⋊C4—682no—
1007C22⋊C4—682no—
1008C22⋊C4—684no—
1009C22⋊C4—684no—
1010C22⋊C4C22×#59512yes—
1011C22⋊C4C22×#59512yes—
1012C22⋊C4C22×#59512yes—
1013C22⋊C4C22×#59512yes—
1014C22⋊C4C22×#59512yes—
1015C42—172no—
1016C42—172no—
1017C42—172no—
1018C42—344no—
1019C42—344no—
1020C42—684no—
1021C42—684no—
1022C42—684no—
1023C42C22×#59512yes—
1024C23—22no—
1025C23—41no—
1026C23—41no—
1027C23—171no—
1028C23—172no—
1029C23—172no—
1030C23—171no—
1031C23—171no—
1032C23—171no—
1033C23—172no—
1034C23—342no—
1035C23—342no—
1036C23—341no—
1037C23—341no—
1038C23—342no—
1039C23—342no—
1040C23—342no—
1041C23—344no—
1042C23—344no—
1043C23—342no—
1044C23—342no—
1045C23—342no—
1046C23—341no—
1047C23—341no—
1048C23—342no—
1049C23—342no—
1050C23—342no—
1051C23—681no—
1052C23—681no—
1053C23—681no—
1054C23—681no—
1055C23—681no—
1056C23—681no—
1057C23—688no—
1058C23—688no—
1059C23C23×#59511yescharacteristic
1060C23C23×#59511yescharacteristic
1061C23C23×#59512yes—
1062C23C23×#59511yescharacteristic
1063Q8—22no—
1064Q8—344no—
1065Q8—342no—
1066D4—24no—
1067D4—22no—
1068D4—42no—
1069D4—42no—
1070D4—344no—
1071D4—344no—
1072D4—344no—
1073D4—344no—
1074D4—342no—
1075D4—682no—
1076D4—682no—
1077D4—682no—
1078D4—682no—
1079D4—682no—
1080D4—682no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—42no—
1088C2×C4—171no—
1089C2×C4—174no—
1090C2×C4—171no—
1091C2×C4—172no—
1092C2×C4—172no—
1093C2×C4—171no—
1094C2×C4—171no—
1095C2×C4—172no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—342no—
1099C2×C4—342no—
1100C2×C4—344no—
1101C2×C4—344no—
1102C2×C4—342no—
1103C2×C4—342no—
1104C2×C4—342no—
1105C2×C4—342no—
1106C2×C4—342no—
1107C2×C4—342no—
1108C2×C4—342no—
1109C2×C4—342no—
1110C2×C4—342no—
1111C2×C4—342no—
1112C2×C4—342no—
1113C2×C4—342no—
1114C2×C4—342no—
1115C2×C4—342no—
1116C2×C4—342no—
1117C2×C4—342no—
1118C2×C4—344no—
1119C2×C4—344no—
1120C2×C4—344no—
1121C2×C4—342no—
1122C2×C4—342no—
1123C2×C4—342no—
1124C2×C4—344no—
1125C2×C4—342no—
1126C2×C4—344no—
1127C2×C4—342no—
1128C2×C4—342no—
1129C2×C4—344no—
1130C2×C4—681no—
1131C2×C4—681no—
1132C2×C4—681no—
1133C2×C4—681no—
1134C2×C4—681no—
1135C2×C4—681no—
1136C2×C4—682no—
1137C2×C4—682no—
1138C2×C4—681no—
1139C2×C4—681no—
1140C2×C4—681no—
1141C2×C4—682no—
1142C2×C4—1368no—
1143C2×C4—1368no—
1144C2×C4C23×#59511yescharacteristic
1145C2×C4C23×#59512yes—
1146C2×C4C23×#59512yes—
1147C2×C4C23×#59511yescharacteristic
1148C2×C4C23×#59511yescharacteristic
1149C2×C4C23×#59512yes—
1150C2×C4C23×#59511yescharacteristic
1151C22—21no—
1152C22—21no—
1153C22—21no—
1154C22—21no—
1155C22—22no—
1156C22—22no—
1157C22—21no—
1158C22—21no—
1159C22—21no—
1160C22—22no—
1161C22—21no—
1162C22—44no—
1163C22—172no—
1164C22—171no—
1165C22—171no—
1166C22—172no—
1167C22—172no—
1168C22—344no—
1169C22—344no—
1170C22—341no—
1171C22—341no—
1172C22—341no—
1173C22—341no—
1174C22—342no—
1175C22—342no—
1176C22—341no—
1177C22—341no—
1178C22—341no—
1179C22—342no—
1180C22—341no—
1181C22—684no—
1182C22—684no—
1183C22—682no—
1184C22—682no—
1185C22—682no—
1186C22—682no—
1187C22—684no—
1188C22—684no—
1189C22—684no—
1190C22#1176387812yes—
1191C22C24×#59511yescharacteristic
1192C4—21no—
1193C4—21no—
1194C4—21no—
1195C4—22no—
1196C4—22no—
1197C4—22no—
1198C4—172no—
1199C4—341no—
1200C4—341no—
1201C4—341no—
1202C4—342no—
1203C4—342no—
1204C4—342no—
1205C4—682no—
1206C4—684no—
1207C4—684no—
1208C4—682no—
1209C4—682no—
1210C4—682no—
1211C4#1176387612yes—
1212C2—22no—
1213C2—41no—
1214C2—41no—
1215C2—42no—
1216C2—172no—
1217C2—172no—
1218C2—342no—
1219C2—681no—
1220C2—681no—
1221C2—682no—
1222C2C2×#1176387611yescharacteristic
1223C2C2×#1176387811yescharacteristic
1224C2#1454576411yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#525C4
prime radicalD17×#525C2
cosocleC22×D17C25
hypercenter#525#595
hypocenterC17#34404
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14545324C2semidirect
2. #14545309C2semidirect
3. #14545308C2semidirect
4. #14545301C2semidirect
5. #14545297C2semidirect
6. #14545295C2semidirect
7. #14545294C2semidirect
8. #14545289C2semidirect
9. #14545287C2semidirect
10. #14545272C2semidirect
11. #14545271C2semidirect
12. #14545269C2semidirect
13. #14545267C2semidirect
14. #14545266C2semidirect
15. #14545228C2semidirect
16. C2×#11763751C2semidirect
18. C2×Q8×#595C22semidirect
20. C2×D4×#595C22semidirect
24. (C2×#595)⋊Q8C22semidirect
27. #11763761C22semidirect
28. #11763760C22semidirect
29. #11763760C22semidirect
30. #11763760C22semidirect
31. #11763760C22semidirect
36. #11763759C22semidirect
37. #11763759C22semidirect
38. #11763758C22semidirect
39. #11763758C22semidirect
44. #11763756C22semidirect
45. #11763756C22semidirect
46. #11763754C22semidirect
47. #11763753C22semidirect
50. #11763752C22semidirect
59. #11763751C22semidirect
61. C4⋊C4×#595C22semidirect
62. C4⋊C4×#595C22semidirect
63. C4×C4⋊#595C22semidirect
68. C4×C22⋊#595C22semidirect
69. #11763745C22semidirect
71. C2×(C2×#595)⋊C4C22semidirect
74. #11763322C4semidirect
75. #11763322C4semidirect
76. #11763321C4semidirect
77. #11763320C4semidirect
78. #11763319C4semidirect
79. #11763319C4semidirect
80. #11763318C4semidirect
81. #11763318C4semidirect
82. #11763317C4semidirect
83. #11763316C4semidirect
84. #11763315C4semidirect
94. C17×#525C4semidirect
98. C2×#41×C17C2×C4semidirect
99. C23×C4×C17C2×C4semidirect
100. C23×Dic17C2×C4semidirect
102. C2×#63256C2×C4semidirect
104. C2×#63254C2×C4semidirect
105. C2×#63254C2×C4semidirect
110. C2×#63252C2×C4semidirect
111. C2×#63252C2×C4semidirect
113. C22×C4×D17C2×C4semidirect
114. C22×C4×D17C2×C4semidirect
115. C22×C4×D17C2×C4semidirect
116. C22×C4×D17C2×C4semidirect
117. C22×C4×D17C2×C4semidirect
118. C22×C4×D17C2×C4semidirect
157. C17×#123C2×C4semidirect
158. C17×C22⋊Q8C2×C4semidirect
159. C17×C22⋊Q8C2×C4semidirect
161. C17×#121C2×C4semidirect
162. C17×#120C2×C4semidirect
163. C4×D4×C17C2×C4semidirect
164. C4×D4×C17C2×C4semidirect
165. C17×#117C2×C4semidirect
166. #10587639C2×C4semidirect
167. #10587632C2×C4semidirect
168. #10587632C2×C4semidirect
170. #10587625C2×C4semidirect
172. #10587624C2×C4semidirect
173. #10587623C2×C4semidirect
174. #10587623C2×C4semidirect
175. #10587623C2×C4semidirect
176. #10587621C2×C4semidirect
177. D4×Dic17C2×C4semidirect
178. D4×Dic17C2×C4semidirect
180. #10587616C2×C4semidirect
181. #10587615C2×C4semidirect
182. C4×C22⋊D17C2×C4semidirect
183. C4×C22⋊D17C2×C4semidirect
184. C4×C22⋊D17C2×C4semidirect
185. C4×C22⋊D17C2×C4semidirect
186. #10587612C2×C4semidirect
187. #10587610C2×C4semidirect
188. #10587610C2×C4semidirect
189. #10587583C2×C4semidirect
190. #10587583C2×C4semidirect
191. #10587582C2×C4semidirect
192. #10587582C2×C4semidirect
194. #10587581C2×C4semidirect
195. #10587580C2×C4semidirect
196. #10587580C2×C4semidirect
197. #10587579C2×C4semidirect
198. #10587579C2×C4semidirect
199. #10587578C2×C4semidirect
200. #10587578C2×C4semidirect
205. #10587572C2×C4semidirect
207. #10587570C2×C4semidirect
208. #10587569C2×C4semidirect
209. #10587569C2×C4semidirect
210. #10587568C2×C4semidirect
211. #10587568C2×C4semidirect
212. #10587568C2×C4semidirect
213. #10587567C2×C4semidirect
214. #10587567C2×C4semidirect
215. #10587567C2×C4semidirect
216. #10587567C2×C4semidirect
222. #10587564C2×C4semidirect
223. #10587564C2×C4semidirect
224. #10587563C2×C4semidirect
225. C4×D68C2×C4semidirect
226. C4×D68C2×C4semidirect
227. #10587558C2×C4semidirect
630. #525#595semidirect
714. C2×#41C2×#595semidirect
737. C23×C4C2×#595semidirect
745. #123C2×#595semidirect
756. C22⋊Q8C2×#595semidirect
757. C22⋊Q8C2×#595semidirect
769. #121C2×#595semidirect
777. #120C2×#595semidirect
795. C4×D4C2×#595semidirect
796. C4×D4C2×#595semidirect
803. #117C2×#595semidirect
856. C17#34404semidirect

Maximal subgroups

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

subgroupindex
#145453242
#145453092
#145453082
#145453012
#145452972
#145452952
#145452942
#145452892
#145452872
#145452722
#145452712
#145452692
#145452672
#145452662
#145452282
C2×#117637512
D17×#5252
#3440417