Finite Group Databasebeta

← #17899559

Subgroups — #17899559

Order 4352.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542342C211yesmaximal, characteristic
2#14537955C212yesmaximal, complemented
3#14537950C212yesmaximal, complemented
4#14537937C212yesmaximal, complemented
5#14537926C212yesmaximal, complemented
6#14537924C212yesmaximal, complemented
7#14537919C212yesmaximal, complemented
8#14537904C212yesmaximal, complemented
9#14537896C212yesmaximal, complemented
10#14537727C211yesmaximal, characteristic, complemented
11#14537724C211yesmaximal, characteristic, complemented
12D4×#63223C211yesmaximal, characteristic, complemented
13#14537505C211yesmaximal, characteristic, complemented
14#14537505C211yesmaximal, characteristic, complemented
15#14537487C211yesmaximal, characteristic, complemented
16#14537478C211yesmaximal, characteristic, complemented
17#14537438C211yesmaximal, characteristic, complemented
18#14537438C211yesmaximal, characteristic, complemented
19#14537433C211yesmaximal, characteristic, complemented
20#14537349C211yesmaximal, characteristic, complemented
21#14537347C211yesmaximal, characteristic, complemented
22C2×#11762835C211yesmaximal, characteristic, complemented
23C2×C17×#435C211yesmaximal, characteristic, complemented
24C2×#10587587C2211yescharacteristic
25C2×#10587587C2211yescharacteristic
26C22×#63223C2211yescharacteristic
27C22×#63223C2211yescharacteristic
28#11763529C411yescharacteristic
29#11763524C411yescharacteristic
30#11763516C411yescharacteristic
31#11763505C411yescharacteristic
32#11763505C411yescharacteristic
33#11763499C411yescharacteristic
34#11763499C411yescharacteristic
35#11763494C412yes—
36#11763485C412yes—
37#11763485C412yes—
38#11763463C411yescharacteristic
39#11763453C412yes—
40#11763366C2211yescharacteristic
41#11763341C2212yes—
42#11763339C2212yes—
43#11763339C2212yes—
44#11763320C2211yescharacteristic
45#11763320C2211yescharacteristic
46C4×#63252C2211yescharacteristic
47C4×#63254C2212yes—
48C2×#10587612C2211yescharacteristic
49C2×#10587612C2211yescharacteristic
50#11762938C2212yescomplemented
51#11762938C2212yescomplemented
52#11762937C2212yescomplemented
53#11762937C2212yescomplemented
54#11762937C2212yescomplemented
55#11762937C2212yescomplemented
56#11762936C2212yescomplemented
57#11762933C2212yescomplemented
58#11762887C2212yes—
59#11762885C2212yescomplemented
60#11762885C2212yescomplemented
61#11762884C2212yescomplemented
62#11762884C2212yescomplemented
63#11762883C2212yescomplemented
64#11762883C2212yescomplemented
65#11762881C2212yes—
66#11762881C2212yes—
67#11762880C2212yescomplemented
68#11762880C2212yescomplemented
69#11762878C2212yescomplemented
70#11762878C2212yescomplemented
71#11762877C2212yescomplemented
72#11762877C2212yescomplemented
73D4×#3622C2212yes—
74C8×C22⋊D17C2212yescomplemented
75C8×C22⋊D17C2212yescomplemented
76#11762872C2212yescomplemented
77#11762872C2212yescomplemented
78#11762871C2212yescomplemented
79#11762871C2212yescomplemented
80#11762867C2212yescomplemented
81#11762867C2212yescomplemented
82#11762867C2212yescomplemented
83#11762867C2212yescomplemented
84#11762864C2212yescomplemented
85#11762864C2212yescomplemented
86#11762863C2212yescomplemented
87#11762863C2212yescomplemented
88#11762859C2212yescomplemented
89#11762859C2212yescomplemented
90#11762837C2212yescomplemented
91#11762837C2212yescomplemented
92#11762835C2211yescharacteristic
93#11762835C2211yescharacteristic
94#11762835C2211yescharacteristic
95#11762835C2211yescharacteristic
96#11762835C2211yescharacteristic
97#11762835C2211yescharacteristic
98#11762835C2211yescharacteristic
99#11762835C2211yescharacteristic
100#11762835C2212yescomplemented
101#11762835C2212yescomplemented
102#11762834C2212yescomplemented
103#11762834C2212yescomplemented
104#11762833C2211yescharacteristic
105#11762832C2212yescomplemented
106#11762832C2212yescomplemented
107#11762831C2212yescomplemented
108C2×#10587485C2212yescomplemented
109C2×#10587485C2212yescomplemented
110C4⋊C8×D17C2212yescomplemented
111#11762775C2211yescharacteristic
112#11762775C2211yescharacteristic
113#11762773C2211yescharacteristic
114#11762773C2211yescharacteristic
115#11762764C2211yescharacteristic
116#11762764C2211yescharacteristic
117#11762764C2211yescharacteristic
118#11762764C2211yescharacteristic
119C4×#63223C2211yescharacteristic
120C22×M16×C17C2211yescharacteristic
121C23×C8×C17C2211yescharacteristic
122C2×C4×D4×C17C2211yescharacteristic
123C17×#435C2211yescharacteristic
124C17×#435C2211yescharacteristic
125C17×#435C2211yescharacteristic
126C17×#435C2211yescharacteristic
127C17×#435C2211yescharacteristic
128C17×#435C2211yescharacteristic
129C17×#435C2211yescharacteristic
130C17×#435C2211yescharacteristic
131C2×C17×C4⋊C8C2211yescharacteristic
132C2×C17×C22⋊C8C2211yescharacteristic
133C2×C17×C22⋊C8C2211yescharacteristic
134C2×C17×#97C2211yescharacteristic
135C22×D4×C17C2×C411yescharacteristic
136C23×C4×C17C2311yescharacteristic
137C23×C4×C17C2311yescharacteristic
138C2×#63254C2×C412yes—
139C2×#63252C2311yescharacteristic
140C2×M16×C17—42no—
141C2×M16×C17C2311yescharacteristic
142C2×M16×C17C2311yescharacteristic
143C2×M16×C17C2311yescharacteristic
144C2×M16×C17C2311yescharacteristic
145C22×C8×C17—42no—
146C22×C8×C17C2311yescharacteristic
147C22×C8×C17C2311yescharacteristic
148C22×C8×C17C2311yescharacteristic
149C22×C8×C17C2311yescharacteristic
150C22×C8×C17C2311yescharacteristic
151C22×C8×C17C2311yescharacteristic
152C22×C8×C17C2311yescharacteristic
153C22×C8×C17C2311yescharacteristic
154C4×D4×C17C2×C411yescharacteristic
155C4×D4×C17C2×C411yescharacteristic
156C4×D4×C17C2×C411yescharacteristic
157C4×D4×C17C2×C411yescharacteristic
158C4×D4×C17C2311yescharacteristic
159C4×D4×C17C2311yescharacteristic
160C4×D4×C17C2311yescharacteristic
161C4×D4×C17C2311yescharacteristic
162C2×C4⋊C4×C17C2×C411yescharacteristic
163C2×C22⋊C4×C17C2×C411yescharacteristic
164C2×C22⋊C4×C17C2×C411yescharacteristic
165C2×C42×C17C2311yescharacteristic
166#10587639C2×C412yes—
167#10587639C2×C412yes—
168C2×C22⋊Dic17C2×C412yes—
169C2×C22⋊Dic17C2×C412yes—
170#10587625C2×C412yes—
171#10587625C2×C412yes—
172#10587624C2×C412yes—
173#10587622C2×C412yes—
174#10587621C2×C412yes—
175#10587621C2×C412yes—
176D4×Dic17C2×C412yes—
177#10587616C2×C411yescharacteristic
178#10587616C2×C411yescharacteristic
179#10587616C2×C411yescharacteristic
180#10587616C2×C411yescharacteristic
181#10587615C2×C412yes—
182#10587615C2×C412yes—
183C4×C22⋊D17C2×C412yes—
184C4×C22⋊D17C2×C412yes—
185C4×C22⋊D17C2312yes—
186C4×C22⋊D17C2312yes—
187C4×C22⋊D17C2312yes—
188C4×C22⋊D17C2312yes—
189#10587612C2×C412yes—
190#10587612C2×C412yes—
191#10587612C2×C411yescharacteristic
192#10587612C2×C411yescharacteristic
193#10587612C2×C411yescharacteristic
194#10587612C2×C411yescharacteristic
195#10587612C2311yescharacteristic
196#10587612C2311yescharacteristic
197#10587612C2311yescharacteristic
198#10587612C2312yes—
199#10587612C2312yes—
200C2×C4⋊Dic17C2×C411yescharacteristic
201C2×C4⋊Dic17C2×C411yescharacteristic
202C2×C4⋊Dic17C2×C411yescharacteristic
203C2×C4⋊Dic17C2×C411yescharacteristic
204#10587610C2×C412yes—
205#10587610C2×C412yes—
206#10587610C2×C411yescharacteristic
207#10587610C2×C411yescharacteristic
208#10587610C2×C411yescharacteristic
209#10587610C2×C411yescharacteristic
210C2×C4×Dic17C2312yes—
211C2×C4×Dic17C2312yes—
212C2×#63223—42no—
213C2×#63223—42no—
214C2×#63223C2311yescharacteristic
215C2×#63223C2311yescharacteristic
216C2×#63223C2311yescharacteristic
217C2×#63223C2311yescharacteristic
218C2×#63223C2312yes—
219C2×#63223C2312yes—
220C22×#3622C2312yes—
221C22×#3622C2312yes—
222#10587587—42no—
223#10587587—42no—
224C2×#63218C2312yes—
225C2×#63218C2312yes—
226C2×C8×D17C2312yes—
227C2×C8×D17C2312yes—
228#10587584C2×C412yes—
229#10587584C2×C412yes—
230#10587583C2×C412yes—
231#10587578C2×C412yes—
232#10587576C2×C412yes—
233#10587575C2×C412yes—
234#10587575C2×C412yes—
235#10587573C2×C412yes—
236#10587572C2×C412yes—
237#10587572C2×C412yes—
238#10587571C2×C412yes—
239#10587571C2×C412yes—
240#10587569C2×C412yes—
241#10587569C2×C412yes—
242#10587567C2×C412yes—
243#10587567C2×C412yes—
244#10587565C2×C412yes—
245#10587565C2×C412yes—
246#10587565C2×C412yes—
247#10587565C2×C412yes—
248#10587564C2×C412yes—
249#10587564C2×C412yes—
250#10587563C2×C412yes—
251#10587563C2×C412yes—
252C4×D68C2×C411yescharacteristic
253C4×D68C2×C411yescharacteristic
254#10587558C2312yes—
255C42×D17C2312yes—
256#10587556C2×C411yescharacteristic
257#10587556C2×C411yescharacteristic
258#10587555C2×C411yescharacteristic
259#10587555C2×C411yescharacteristic
260C4×Dic34C2×C411yescharacteristic
261C4×Dic34C2×C411yescharacteristic
262C4×Dic34C2312yes—
263C4×Dic34C2312yes—
264C17×C4⋊C8C2311yescharacteristic
265C17×C4⋊C8C2311yescharacteristic
266C17×C4⋊C8C2311yescharacteristic
267C17×C4⋊C8C2311yescharacteristic
268C17×C22⋊C8C2311yescharacteristic
269C17×C22⋊C8C2311yescharacteristic
270C17×C22⋊C8C2311yescharacteristic
271C17×C22⋊C8C2311yescharacteristic
272C17×C22⋊C8C2311yescharacteristic
273C17×C22⋊C8C2311yescharacteristic
274C17×C22⋊C8C2311yescharacteristic
275C17×C22⋊C8C2311yescharacteristic
276C17×#97C2311yescharacteristic
277C17×#97C2311yescharacteristic
278C17×#97C2311yescharacteristic
279C17×#97C2311yescharacteristic
280C22⋊#3622C2312yes—
281C22⋊#3622C2312yes—
282C22⋊#3622C2312yes—
283C22⋊#3622C2312yes—
284#10587491C2312yes—
285#10587491C2312yes—
286#10587491C2312yes—
287#10587491C2312yes—
288#10587486C2312yes—
289#10587486C2312yes—
290#10587486C2312yes—
291#10587486C2312yes—
292#10587485C2312yes—
293#10587485C2312yes—
294#10587485C2312yes—
295#10587485C2312yes—
296#10587485C2312yes—
297#10587485C2312yes—
298#10587485C2312yes—
299#10587485C2312yes—
300#10587485C2312yes—
301#10587485C2312yes—
302#10587485C2312yes—
303#10587485C2312yes—
304#10587485C2312yes—
305#10587485C2312yes—
306#10587485C2312yes—
307#10587485C2312yes—
308C8×Dic17C2312yes—
309C8×Dic17C2312yes—
310C8×Dic17C2312yes—
311C8×Dic17C2312yes—
312C4⋊#3622C2312yes—
313C4⋊#3622C2312yes—
314#10587474C2312yes—
315C4×#3622C2312yes—
316C24×C17C22×C411yescharacteristic
317C24×C17C22×C411yescharacteristic
318C2×D4×C17—42no—
319C2×D4×C17C22×C411yescharacteristic
320C2×D4×C17C22×C411yescharacteristic
321C2×D4×C17C22×C411yescharacteristic
322C2×D4×C17C22×C411yescharacteristic
323C22×C4×C17—22no—
324C22×C4×C17—22no—
325C22×C4×C17—22no—
326C22×C4×C17—22no—
327C22×C4×C17C22×C411yescharacteristic
328C22×C4×C17C22×C411yescharacteristic
329C22×C4×C17C22×C411yescharacteristic
330C22×C4×C17C22×C411yescharacteristic
331C22×C4×C17C22×C411yescharacteristic
332C22×C4×C17C22×C411yescharacteristic
333C22×C4×C17C22×C411yescharacteristic
334C22×C4×C17C22×C411yescharacteristic
335C22×C4×C17C2411yescharacteristic
336C22×C4×C17C2411yescharacteristic
337C22×C4×C17C2411yescharacteristic
338C22×C4×C17C2411yescharacteristic
339C22×C4×C17C2411yescharacteristic
340C2×C22⋊D17C22×C412yes—
341C2×C22⋊D17C22×C412yes—
342C2×C22⋊D17C22×C412yes—
343C2×C22⋊D17C22×C412yes—
344C2×C22⋊D17C22×C412yes—
345C22×Dic17C22×C412yes—
346C22×Dic17C22×C412yes—
347C22×Dic17C22×C412yes—
348C22×Dic17C22×C412yes—
349#63254—44no—
350#63252—22no—
351#63252—22no—
352C2×D68C22×C411yescharacteristic
353C2×C4×D17C22×C412yes—
354C2×C4×D17C22×C412yes—
355C2×C4×D17C2412yes—
356C2×Dic34C22×C411yescharacteristic
357C2×Dic34C22×C412yes—
358C2×Dic34C22×C412yes—
359M16×C17—41no—
360M16×C17—41no—
361M16×C17—41no—
362M16×C17—41no—
363C2×C8×C17—22no—
364C2×C8×C17—22no—
365C2×C8×C17—22no—
366C2×C8×C17—22no—
367C2×C8×C17—41no—
368C2×C8×C17—41no—
369C2×C8×C17—41no—
370C2×C8×C17—41no—
371C2×C8×C17C2411yescharacteristic
372C2×C8×C17C2411yescharacteristic
373C2×C8×C17C2411yescharacteristic
374C2×C8×C17C2411yescharacteristic
375C2×C8×C17C2411yescharacteristic
376C2×C8×C17C2411yescharacteristic
377C2×C8×C17C2411yescharacteristic
378C2×C8×C17C2411yescharacteristic
379C4⋊C4×C17C22×C411yescharacteristic
380C4⋊C4×C17C22×C411yescharacteristic
381C4⋊C4×C17C22×C411yescharacteristic
382C4⋊C4×C17C22×C411yescharacteristic
383C22⋊C4×C17C22×C411yescharacteristic
384C22⋊C4×C17C22×C411yescharacteristic
385C22⋊C4×C17C22×C411yescharacteristic
386C22⋊C4×C17C22×C411yescharacteristic
387C22⋊C4×C17C22×C411yescharacteristic
388C22⋊C4×C17C22×C411yescharacteristic
389C22⋊C4×C17C22×C411yescharacteristic
390C22⋊C4×C17C22×C411yescharacteristic
391C42×C17C22×C411yescharacteristic
392C42×C17C22×C411yescharacteristic
393C42×C17C2411yescharacteristic
394C42×C17C2411yescharacteristic
395C22⋊Dic17C22×C412yes—
396C22⋊Dic17C22×C412yes—
397C22⋊Dic17C22×C412yes—
398C22⋊Dic17C22×C412yes—
399C22⋊Dic17C22×C412yes—
400C22⋊Dic17C22×C412yes—
401C22⋊Dic17C22×C412yes—
402C22⋊Dic17C22×C412yes—
403C22⋊Dic17C22×C412yes—
404C22⋊Dic17C22×C412yes—
405C22⋊Dic17C22×C412yes—
406#63227C22×C412yes—
407#63227C22×C412yes—
408#63227C22×C412yes—
409#63227C22×C412yes—
410#63227C22×C412yes—
411#63227C22×C412yes—
412C4⋊Dic17C22×C411yescharacteristic
413C4⋊Dic17C22×C411yescharacteristic
414C4⋊Dic17C22×C412yes—
415C4⋊Dic17C22×C412yes—
416C4⋊Dic17C22×C411yescharacteristic
417C4⋊Dic17C22×C411yescharacteristic
418C4⋊Dic17C22×C411yescharacteristic
419C4⋊Dic17C22×C411yescharacteristic
420C4⋊Dic17C22×C412yes—
421C4⋊Dic17C22×C412yes—
422C4⋊Dic17C22×C412yes—
423C4⋊Dic17C22×C412yes—
424#63225C22×C412yes—
425#63225C22×C412yes—
426#63225C22×C412yes—
427#63225C22×C412yes—
428#63225C22×C412yes—
429#63225C22×C412yes—
430#63225C22×C412yes—
431#63225C22×C412yes—
432#63225C22×C412yes—
433#63225C22×C412yes—
434C4×Dic17C22×C412yes—
435C4×Dic17C22×C412yes—
436C4×Dic17C22×C412yes—
437C4×Dic17C22×C412yes—
438C4×Dic17C22×C412yes—
439C4×Dic17C22×C412yes—
440C4×Dic17C2412yes—
441C4×Dic17C2412yes—
442C4×Dic17C2412yes—
443#63223—22no—
444#63223—22no—
445#63223—22no—
446#63223—22no—
447#63223—42no—
448#63223—42no—
449C2×#3622—42no—
450C2×#3622—42no—
451C2×#3622C2412yes—
452C2×#3622C2412yes—
453C2×#3622C2412yes—
454C2×#3622C2412yes—
455#63218—42no—
456#63218—42no—
457C8×D17—42no—
458C8×D17—42no—
459#60272—171nomaximal, Sylow
460C23×C17—22no—
461C23×C17—22no—
462C23×C17—22no—
463C23×C17—41no—
464C23×C17—41no—
465C23×C17—41no—
466C23×C17C23×C411yescharacteristic
467C23×C17C23×C411yescharacteristic
468C23×C17C23×C411yescharacteristic
469C23×C17C23×C411yescharacteristic
470C23×C17C23×C411yescharacteristic
471C22×D17C23×C412yes—
472D4×C17—22no—
473D4×C17—22no—
474D4×C17—41no—
475D4×C17—41no—
476C2×C4×C17—22no—
477C2×C4×C17—22no—
478C2×C4×C17—22no—
479C2×C4×C17—22no—
480C2×C4×C17—22no—
481C2×C4×C17—22no—
482C2×C4×C17—21no—
483C2×C4×C17—21no—
484C2×C4×C17—21no—
485C2×C4×C17—21no—
486C2×C4×C17—21no—
487C2×C4×C17—21no—
488C2×C4×C17—21no—
489C2×C4×C17—21no—
490C2×C4×C17—41no—
491C2×C4×C17—41no—
492C2×C4×C17C23×C411yescharacteristic
493C2×C4×C17C23×C411yescharacteristic
494C2×C4×C17C23×C411yescharacteristic
495C2×C4×C17C23×C411yescharacteristic
496C2×C4×C17C23×C411yescharacteristic
497C2×C4×C17C23×C411yescharacteristic
498C2×C4×C17C23×C411yescharacteristic
499C2×C4×C17C23×C411yescharacteristic
500C2×C4×C17C23×C411yescharacteristic
501C2×C4×C17H(5,𝔽2)12yes—
502C2×C4×C172−1+412yes—
503C2×C4×C17C2511yescharacteristic
504C22⋊D17—24no—
505C22⋊D17—24no—
506C22⋊D17—42no—
507C22⋊D17—42no—
508C22⋊D17—42no—
509C2×Dic17—24no—
510C2×Dic17—42no—
511C2×Dic17—42no—
512C2×Dic17—42no—
513C2×Dic17C23×C412yes—
514C2×Dic17C23×C412yes—
515C2×Dic17C23×C412yes—
516C2×Dic17C23×C412yes—
517C2×Dic17C23×C412yes—
518C2×Dic17C23×C412yes—
519C2×Dic17C23×C412yes—
520D68—22no—
521C4×D17—22no—
522C4×D17—22no—
523C4×D17—42no—
524C4×D17—42no—
525Dic34—22no—
526Dic34—42no—
527Dic34—42no—
528C8×C17—21no—
529C8×C17—21no—
530C8×C17—21no—
531C8×C17—21no—
532C8×C17—21no—
533C8×C17—21no—
534C8×C17—21no—
535C8×C17—21no—
536#3622—22no—
537#3622—22no—
538#3622—22no—
539#3622—22no—
540#3475—171no—
541#2995—172no—
542#2995—172no—
543#2994—172no—
544#2993—172no—
545#2992—172no—
546#2992—172no—
547#2990—172no—
548#2989—172no—
549#2962—171no—
550#2961—171no—
551D4×M16—171no—
552#2933—171no—
553#2933—171no—
554#2930—171no—
555#2929—171no—
556C2×#435D1711yescharacteristic, complemented
557#2924—171no—
558#2924—171no—
559#2923—171no—
560#2906—171no—
561#2905—171no—
562C2×#424—171no—
563C22×C17—21no—
564C22×C17—21no—
565C22×C17—21no—
566C22×C17—21no—
567C22×C17—21no—
568C22×C17—21no—
569C22×C17—21no—
570C22×C17—21no—
571C22×C17—21no—
572C22×C17—21no—
573C22×C17—21no—
574C22×C17—21no—
575C22×C17—21no—
576C22×C17—44no—
577C22×C17—82no—
578C22×C17#52012yes—
579C22×C17#56812yes—
580C22×C17C24×C411yescharacteristic
581C2×D17—22no—
582C2×D17—22no—
583C2×D17—22no—
584C4×C17—21no—
585C4×C17—21no—
586C4×C17—21no—
587C4×C17—21no—
588C4×C17—21no—
589C4×C17—21no—
590C4×C17—21no—
591C4×C17—21no—
592C4×C17#52012yes—
593C4×C17C2×H(5,𝔽2)11yescharacteristic
594C4×C17C2×2−1+411yescharacteristic
595Dic17—22no—
596Dic17—22no—
597Dic17—22no—
598Dic17—22no—
599Dic17—22no—
600Dic17—22no—
601Dic17—22no—
602C2×#131—171no—
603C2×#131—171no—
604C22×M16—171no—
605C22×M16—171no—
606C22×M16C2×D1711yescharacteristic
607C23×C8C2×D1711yescharacteristic
608#556—171no—
609#555—171no—
610#554—171no—
611#553—171no—
612#553—171no—
613#552—171no—
614#552—171no—
615#552—172no—
616#551—172no—
617#551—172no—
618#547—171no—
619#546—172no—
620#533—171no—
621#529—172no—
622#529—172no—
623#529—172no—
624#525—171no—
625#525—171no—
626C4×#41—172no—
627C4×#41—171no—
628C2×C4×D4C2×D1711yescharacteristic
629C2×#117—171no—
630C2×#117—171no—
631#446—172no—
632#446—172no—
633#446—172no—
634#446—172no—
635#446—172no—
636#446—172no—
637#446—172no—
638C8×Q8—172no—
639#436—172no—
640#436—172no—
641#436—172no—
642#436—172no—
643#436—172no—
644#435—172no—
645#435—172no—
646#435—172no—
647#435—172no—
648#435—172no—
649#435—172no—
650#435—172no—
651#435—172no—
652#435—172no—
653#435—172no—
654#435C2×D1711yescharacteristic
655#435C2×D1711yescharacteristic
656#435C2×D1711yescharacteristic
657#435C2×D1711yescharacteristic
658#435C2×D1711yescharacteristic
659#435C2×D1711yescharacteristic
660#435C2×D1711yescharacteristic
661#435C2×D1711yescharacteristic
662C8×D4—172no—
663C8×D4—172no—
664C8×D4—172no—
665C8×D4—172no—
666C8×D4—172no—
667#433—172no—
668#433—172no—
669#433—172no—
670#433—172no—
671#433—172no—
672#433—172no—
673#432—172no—
674#432—172no—
675#432—172no—
676#432—172no—
677#431—172no—
678#431—172no—
679#424—172no—
680#424—172no—
681#424—171no—
682#424—171no—
683#424—171no—
684#424—171no—
685#424—172no—
686#424—172no—
687#424—171no—
688#424—171no—
689#424—171no—
690#424—171no—
691#424—172no—
692#424—172no—
693#423—172no—
694#423—172no—
695#423—171no—
696#423—172no—
697C2×C4⋊C8—172no—
698C2×C4⋊C8—172no—
699C2×C4⋊C8—172no—
700C2×C4⋊C8C2×D1711yescharacteristic
701#408—171no—
702#408—171no—
703#407—171no—
704#407—171no—
705C2×C22⋊C8C2×D1711yescharacteristic
706C2×C22⋊C8C2×D1711yescharacteristic
707#405—171no—
708#405—171no—
709#405—171no—
710#405—171no—
711C4×M16—171no—
712C2×#97C2×D1711yescharacteristic
713C2×C17—22no—
714C2×C17—22no—
715C2×C17—41no—
716C2×C17—41no—
717C2×C17—41no—
718C2×C17C2×#52011yescharacteristic
719C2×C17C2×#56811yescharacteristic
720C2×C17#357311yescharacteristic
721D17—42no—
722C2×#41—172no—
723C2×#41—171no—
724C22×D4C4×D1711yescharacteristic
725C23×C4C22×D1711yescharacteristic
726C23×C4C22×D1711yescharacteristic
727#131—682no—
728#131—682no—
729C2×M16—42no—
730C2×M16—171no—
731C2×M16—171no—
732C2×M16—171no—
733C2×M16—171no—
734C2×M16—172no—
735C2×M16—172no—
736C2×M16—172no—
737C2×M16—172no—
738C2×M16—682no—
739C2×M16—682no—
740C2×M16C22×D1711yescharacteristic
741C2×M16C22×D1711yescharacteristic
742C2×M16C22×D1711yescharacteristic
743C2×M16C22×D1711yescharacteristic
744C22×C8—42no—
745C22×C8—172no—
746C22×C8—172no—
747C22×C8—172no—
748C22×C8—172no—
749C22×C8C22×D1711yescharacteristic
750C22×C8C22×D1711yescharacteristic
751C22×C8C22×D1711yescharacteristic
752C22×C8C22×D1711yescharacteristic
753C22×C8C22×D1711yescharacteristic
754C22×C8C22×D1711yescharacteristic
755C22×C8C22×D1711yescharacteristic
756C22×C8C22×D1711yescharacteristic
757C4⋊Q8—171no—
758C4⋊Q8—171no—
759#126—172no—
760#126—172no—
761#126—172no—
762#126—172no—
763#126—172no—
764#126—172no—
765#125—172no—
766#125—172no—
767#125—172no—
768#125—171no—
769#125—171no—
770#124—172no—
771#124—172no—
772#124—172no—
773#123—172no—
774#123—172no—
775#123—172no—
776#123—172no—
777#123—172no—
778#123—172no—
779#123—172no—
780#123—172no—
781C22⋊Q8—171no—
782C22⋊Q8—171no—
783C22⋊Q8—171no—
784C22⋊Q8—171no—
785C22⋊Q8—172no—
786C22⋊Q8—172no—
787C22⋊Q8—172no—
788C22⋊Q8—172no—
789C22⋊Q8—172no—
790#121—172no—
791#121—172no—
792#121—172no—
793#121—171no—
794#121—171no—
795#121—171no—
796#121—171no—
797#120—172no—
798#120—172no—
799C4×Q8—172no—
800C4×Q8—171no—
801C4×Q8—171no—
802C4×Q8—172no—
803C4×Q8—172no—
804C4×D4—172no—
805C4×D4—172no—
806C4×D4—172no—
807C4×D4—172no—
808C4×D4—172no—
809C4×D4—172no—
810C4×D4—172no—
811C4×D4—172no—
812C4×D4—172no—
813C4×D4—171no—
814C4×D4—171no—
815C4×D4C4×D1711yescharacteristic
816C4×D4C4×D1711yescharacteristic
817C4×D4C4×D1711yescharacteristic
818C4×D4C4×D1711yescharacteristic
819C4×D4C22×D1711yescharacteristic
820C4×D4C22×D1711yescharacteristic
821C4×D4C22×D1711yescharacteristic
822C4×D4C22×D1711yescharacteristic
823#117—172no—
824#117—172no—
825#117—171no—
826#117—171no—
827#117—171no—
828#117—171no—
829#117—171no—
830#117—171no—
831#117—171no—
832#117—172no—
833#117—172no—
834#117—172no—
835#117—172no—
836#117—172no—
837#117—172no—
838C2×C4⋊C4—171no—
839C2×C4⋊C4—171no—
840C2×C4⋊C4—171no—
841C2×C4⋊C4—171no—
842C2×C4⋊C4C4×D1711yescharacteristic
843C2×C22⋊C4—172no—
844C2×C22⋊C4—172no—
845C2×C22⋊C4C4×D1711yescharacteristic
846C2×C22⋊C4C4×D1711yescharacteristic
847C2×C42—172no—
848C2×C42—172no—
849C2×C42—172no—
850C2×C42C22×D1711yescharacteristic
851C4⋊C8—172no—
852C4⋊C8—172no—
853C4⋊C8—172no—
854C4⋊C8—172no—
855C4⋊C8—172no—
856C4⋊C8—172no—
857C4⋊C8—172no—
858C4⋊C8—172no—
859C4⋊C8—172no—
860C4⋊C8—172no—
861C4⋊C8—172no—
862C4⋊C8—172no—
863C4⋊C8—172no—
864C4⋊C8—172no—
865C4⋊C8—172no—
866C4⋊C8—172no—
867C4⋊C8—172no—
868C4⋊C8—172no—
869C4⋊C8C22×D1711yescharacteristic
870C4⋊C8C22×D1711yescharacteristic
871C4⋊C8C22×D1711yescharacteristic
872C4⋊C8C22×D1711yescharacteristic
873C22⋊C8—172no—
874C22⋊C8—172no—
875C22⋊C8—172no—
876C22⋊C8—172no—
877C22⋊C8—172no—
878C22⋊C8—172no—
879C22⋊C8—172no—
880C22⋊C8—172no—
881C22⋊C8C22×D1711yescharacteristic
882C22⋊C8C22×D1711yescharacteristic
883C22⋊C8C22×D1711yescharacteristic
884C22⋊C8C22×D1711yescharacteristic
885C22⋊C8C22×D1711yescharacteristic
886C22⋊C8C22×D1711yescharacteristic
887C22⋊C8C22×D1711yescharacteristic
888C22⋊C8C22×D1711yescharacteristic
889#97—172no—
890#97—172no—
891#97—172no—
892#97—172no—
893#97—172no—
894#97C22×D1711yescharacteristic
895#97C22×D1711yescharacteristic
896#97C22×D1711yescharacteristic
897#97C22×D1711yescharacteristic
898C4×C8—172no—
899C4×C8—172no—
900C4×C8—172no—
901C4×C8—172no—
902C4×C8—172no—
903C17#6027211yescharacteristic, complemented, Sylow
904C24C2×C4×D1711yescharacteristic
905C24C2×C4×D1711yescharacteristic
906#41—342no—
907#41—342no—
908#41—684no—
909C2×Q8—171no—
910C2×Q8—172no—
911C2×Q8—172no—
912C2×D4—42no—
913C2×D4—172no—
914C2×D4—172no—
915C2×D4—172no—
916C2×D4—172no—
917C2×D4—172no—
918C2×D4—171no—
919C2×D4C2×C4×D1711yescharacteristic
920C2×D4C2×C4×D1711yescharacteristic
921C2×D4C2×C4×D1711yescharacteristic
922C2×D4C2×C4×D1711yescharacteristic
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—172no—
928C22×C4—172no—
929C22×C4—172no—
930C22×C4—172no—
931C22×C4—172no—
932C22×C4—172no—
933C22×C4—172no—
934C22×C4C2×C4×D1711yescharacteristic
935C22×C4C2×C4×D1711yescharacteristic
936C22×C4C2×C4×D1711yescharacteristic
937C22×C4C2×C4×D1711yescharacteristic
938C22×C4C2×C4×D1711yescharacteristic
939C22×C4C2×C4×D1711yescharacteristic
940C22×C4C2×C4×D1711yescharacteristic
941C22×C4C2×C4×D1711yescharacteristic
942C22×C4C23×D1711yescharacteristic
943C22×C4C23×D1711yescharacteristic
944C22×C4C23×D1711yescharacteristic
945C22×C4C23×D1711yescharacteristic
946C22×C4C23×D1711yescharacteristic
947M16—41no—
948M16—41no—
949M16—41no—
950M16—41no—
951M16—342no—
952M16—342no—
953M16—342no—
954M16—342no—
955M16—682no—
956M16—682no—
957M16—682no—
958M16—682no—
959C2×C8—22no—
960C2×C8—22no—
961C2×C8—22no—
962C2×C8—22no—
963C2×C8—41no—
964C2×C8—41no—
965C2×C8—41no—
966C2×C8—41no—
967C2×C8—172no—
968C2×C8—172no—
969C2×C8—172no—
970C2×C8—172no—
971C2×C8—682no—
972C2×C8—682no—
973C2×C8—682no—
974C2×C8—682no—
975C2×C8C23×D1711yescharacteristic
976C2×C8C23×D1711yescharacteristic
977C2×C8C23×D1711yescharacteristic
978C2×C8C23×D1711yescharacteristic
979C2×C8C23×D1711yescharacteristic
980C2×C8C23×D1711yescharacteristic
981C2×C8C23×D1711yescharacteristic
982C2×C8C23×D1711yescharacteristic
983C4⋊C4—171no—
984C4⋊C4—171no—
985C4⋊C4—171no—
986C4⋊C4—171no—
987C4⋊C4—171no—
988C4⋊C4—171no—
989C4⋊C4—172no—
990C4⋊C4—172no—
991C4⋊C4—172no—
992C4⋊C4—172no—
993C4⋊C4—172no—
994C4⋊C4—172no—
995C4⋊C4—172no—
996C4⋊C4—172no—
997C4⋊C4—172no—
998C4⋊C4—172no—
999C4⋊C4—172no—
1000C4⋊C4—172no—
1001C4⋊C4—172no—
1002C4⋊C4—172no—
1003C4⋊C4—172no—
1004C4⋊C4—172no—
1005C4⋊C4C2×C4×D1711yescharacteristic
1006C4⋊C4C2×C4×D1711yescharacteristic
1007C4⋊C4C2×C4×D1711yescharacteristic
1008C4⋊C4C2×C4×D1711yescharacteristic
1009C22⋊C4—172no—
1010C22⋊C4—172no—
1011C22⋊C4—172no—
1012C22⋊C4—172no—
1013C22⋊C4—172no—
1014C22⋊C4—172no—
1015C22⋊C4—172no—
1016C22⋊C4—172no—
1017C22⋊C4—172no—
1018C22⋊C4—172no—
1019C22⋊C4—172no—
1020C22⋊C4—172no—
1021C22⋊C4—172no—
1022C22⋊C4—172no—
1023C22⋊C4—172no—
1024C22⋊C4—172no—
1025C22⋊C4—172no—
1026C22⋊C4C2×C4×D1711yescharacteristic
1027C22⋊C4C2×C4×D1711yescharacteristic
1028C22⋊C4C2×C4×D1711yescharacteristic
1029C22⋊C4C2×C4×D1711yescharacteristic
1030C22⋊C4C2×C4×D1711yescharacteristic
1031C22⋊C4C2×C4×D1711yescharacteristic
1032C22⋊C4C2×C4×D1711yescharacteristic
1033C22⋊C4C2×C4×D1711yescharacteristic
1034C42—172no—
1035C42—172no—
1036C42—172no—
1037C42—172no—
1038C42—172no—
1039C42—172no—
1040C42—172no—
1041C42—172no—
1042C42—172no—
1043C42C2×C4×D1711yescharacteristic
1044C42C2×C4×D1711yescharacteristic
1045C42C23×D1711yescharacteristic
1046C42C23×D1711yescharacteristic
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—172no—
1054C23C22×C4×D1711yescharacteristic
1055C23C22×C4×D1711yescharacteristic
1056C23C22×C4×D1711yescharacteristic
1057C23C22×C4×D1711yescharacteristic
1058C23C22×C4×D1711yescharacteristic
1059Q8—342no—
1060Q8—682no—
1061Q8—682no—
1062D4—22no—
1063D4—22no—
1064D4—41no—
1065D4—41no—
1066D4—344no—
1067D4—344no—
1068D4—342no—
1069D4—682no—
1070D4—682no—
1071D4—682no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—172no—
1089C2×C4—172no—
1090C2×C4—172no—
1091C2×C4—172no—
1092C2×C4—172no—
1093C2×C4—172no—
1094C2×C4—172no—
1095C2×C4—344no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—682no—
1099C2×C4—682no—
1100C2×C4—682no—
1101C2×C4—682no—
1102C2×C4—682no—
1103C2×C4C22×C4×D1711yescharacteristic
1104C2×C4C22×C4×D1711yescharacteristic
1105C2×C4C22×C4×D1711yescharacteristic
1106C2×C4C22×C4×D1711yescharacteristic
1107C2×C4C22×C4×D1711yescharacteristic
1108C2×C4C22×C4×D1711yescharacteristic
1109C2×C4C22×C4×D1711yescharacteristic
1110C2×C4C22×C4×D1711yescharacteristic
1111C2×C4C22×C4×D1711yescharacteristic
1112C2×C4#1058769112yes—
1113C2×C4#1058769712yes—
1114C2×C4C24×D1711yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—21no—
1120C8—21no—
1121C8—21no—
1122C8—21no—
1123C8—342no—
1124C8—342no—
1125C8—342no—
1126C8—342no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—21no—
1137C22—21no—
1138C22—21no—
1139C22—21no—
1140C22—44no—
1141C22—82no—
1142C22—342no—
1143C22—342no—
1144C22—342no—
1145C22#1176328812yes—
1146C22#1176357512yes—
1147C22C23×C4×D1711yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—21no—
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—21no—
1156C4—342no—
1157C4—342no—
1158C4—342no—
1159C4—342no—
1160C4—342no—
1161C4—342no—
1162C4—342no—
1163C4#1176328812yes—
1164C4C2×#1058769111yescharacteristic
1165C4C2×#1058769711yescharacteristic
1166C2—22no—
1167C2—22no—
1168C2—41no—
1169C2—41no—
1170C2—41no—
1171C2—682no—
1172C2C2×#1176328811yescharacteristic
1173C2C2×#1176357511yescharacteristic
1174C2#1454349511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
FittingC2×C17×#435C2
prime radical#14542342C2
cosocleC2×C4×C17C25
hypercenterC2×#435D17
hypocenterC17#60272
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #14537955C2semidirect
3. #14537950C2semidirect
4. #14537937C2semidirect
5. #14537926C2semidirect
6. #14537924C2semidirect
7. #14537919C2semidirect
8. #14537904C2semidirect
9. #14537896C2semidirect
10. #14537727C2semidirect
11. #14537724C2semidirect
12. D4×#63223C2semidirect
13. #14537505C2semidirect
14. #14537505C2semidirect
15. #14537487C2semidirect
16. #14537478C2semidirect
17. #14537438C2semidirect
18. #14537438C2semidirect
19. #14537433C2semidirect
20. #14537349C2semidirect
21. #14537347C2semidirect
22. C2×#11762835C2semidirect
23. C2×C17×#435C2semidirect
50. #11762938C22semidirect
51. #11762938C22semidirect
52. #11762937C22semidirect
53. #11762937C22semidirect
54. #11762937C22semidirect
55. #11762937C22semidirect
56. #11762936C22semidirect
57. #11762933C22semidirect
59. #11762885C22semidirect
60. #11762885C22semidirect
61. #11762884C22semidirect
62. #11762884C22semidirect
63. #11762883C22semidirect
64. #11762883C22semidirect
67. #11762880C22semidirect
68. #11762880C22semidirect
69. #11762878C22semidirect
70. #11762878C22semidirect
71. #11762877C22semidirect
72. #11762877C22semidirect
74. C8×C22⋊D17C22semidirect
75. C8×C22⋊D17C22semidirect
76. #11762872C22semidirect
77. #11762872C22semidirect
78. #11762871C22semidirect
79. #11762871C22semidirect
80. #11762867C22semidirect
81. #11762867C22semidirect
82. #11762867C22semidirect
83. #11762867C22semidirect
84. #11762864C22semidirect
85. #11762864C22semidirect
86. #11762863C22semidirect
87. #11762863C22semidirect
88. #11762859C22semidirect
89. #11762859C22semidirect
90. #11762837C22semidirect
91. #11762837C22semidirect
100. #11762835C22semidirect
101. #11762835C22semidirect
102. #11762834C22semidirect
103. #11762834C22semidirect
105. #11762832C22semidirect
106. #11762832C22semidirect
107. #11762831C22semidirect
108. C2×#10587485C22semidirect
109. C2×#10587485C22semidirect
110. C4⋊C8×D17C22semidirect
556. C2×#435D17semidirect
903. C17#60272semidirect

Maximal subgroups

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

subgroupindex
#145423422
#145379552
#145379502
#145379372
#145379262
#145379242
#145379192
#145379042
#145378962
#145377272
#145377242
D4×#632232
#145375052
#145374872
#145374782
#145374382
#145374332
#145373492
#145373472
C2×#117628352
C2×C17×#4352
#6027217