Finite Group Databasebeta

← #17898975

Subgroups — #17898975

Order 4352.

1920 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#14537794C212yesmaximal, complemented
3#14537781C212yesmaximal, complemented
4#14537779C212yesmaximal, complemented
5#14537775C212yesmaximal, complemented
6#14537766C212yesmaximal, complemented
7#14537763C212yesmaximal, complemented
8#14537754C212yesmaximal, complemented
9#14537744C212yesmaximal, 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#14537449C211yesmaximal, characteristic, complemented
18#14537438C211yesmaximal, characteristic, complemented
19#14537438C211yesmaximal, characteristic, complemented
20#14537209C211yesmaximal, characteristic, complemented
21#14537202C211yesmaximal, characteristic, complemented
22C2×#11762764C211yesmaximal, 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#11762869C2212yescomplemented
79#11762869C2212yescomplemented
80#11762867C2212yescomplemented
81#11762867C2212yescomplemented
82#11762867C2212yescomplemented
83#11762867C2212yescomplemented
84#11762865C2212yescomplemented
85#11762863C2212yescomplemented
86#11762863C2212yescomplemented
87#11762861C2212yescomplemented
88#11762859C2212yescomplemented
89#11762859C2212yescomplemented
90#11762835C2211yescharacteristic
91#11762835C2211yescharacteristic
92#11762835C2211yescharacteristic
93#11762835C2211yescharacteristic
94#11762833C2211yescharacteristic
95#11762775C2211yescharacteristic
96#11762775C2211yescharacteristic
97#11762773C2211yescharacteristic
98#11762773C2211yescharacteristic
99#11762767C2212yescomplemented
100#11762767C2212yescomplemented
101#11762766C2212yescomplemented
102#11762766C2212yescomplemented
103#11762764C2211yescharacteristic
104#11762764C2211yescharacteristic
105#11762764C2211yescharacteristic
106#11762764C2211yescharacteristic
107#11762764C2211yescharacteristic
108#11762764C2211yescharacteristic
109#11762764C2211yescharacteristic
110#11762764C2211yescharacteristic
111#11762764C2212yescomplemented
112#11762764C2212yescomplemented
113C4×#63223C2211yescharacteristic
114#11762761C2212yescomplemented
115M16×Dic17C2212yescomplemented
116M16×Dic17C2212yescomplemented
117C2×#10587486C2212yescomplemented
118#97×D17C2212yescomplemented
119C2×C8×Dic17C2212yescomplemented
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—24no—
141C2×M16×C17C2311yescharacteristic
142C2×M16×C17C2311yescharacteristic
143C2×M16×C17C2311yescharacteristic
144C2×M16×C17C2311yescharacteristic
145C22×C8×C17—24no—
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—24no—
213C2×#63223—24no—
214C2×#63223C2312yes—
215C2×#63223C2311yescharacteristic
216C2×#63223C2311yescharacteristic
217C2×#63223C2311yescharacteristic
218C2×#63223C2312yes—
219C2×#63223C2311yescharacteristic
220C22×#3622C2312yes—
221C22×#3622C2312yes—
222#10587587—24no—
223#10587587—24no—
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#10587486C2312yes—
293#10587486C2312yes—
294#10587486C2312yes—
295#10587486C2312yes—
296#10587485C2312yes—
297#10587485C2312yes—
298#10587485C2312yes—
299#10587485C2312yes—
300#10587485C2312yes—
301#10587485C2312yes—
302#10587485C2312yes—
303#10587485C2312yes—
304C8×Dic17C2312yes—
305C8×Dic17C2312yes—
306C8×Dic17C2312yes—
307C8×Dic17C2312yes—
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—22no—
360M16×C17—22no—
361M16×C17—22no—
362M16×C17—22no—
363C2×C8×C17—22no—
364C2×C8×C17—22no—
365C2×C8×C17—22no—
366C2×C8×C17—22no—
367C2×C8×C17—22no—
368C2×C8×C17—22no—
369C2×C8×C17—22no—
370C2×C8×C17#4114yescomplemented
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—24no—
447#63223—24no—
448#63223#4114yescomplemented
449C2×#3622—24no—
450C2×#3622—24no—
451C2×#3622C2412yes—
452C2×#3622C2412yes—
453C2×#3622C2412yes—
454C2×#3622C2412yes—
455#63218—24no—
456#63218—24no—
457C8×D17—24no—
458C8×D17—24no—
459#60216—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×C17C2×#4112yes—
502C2×C4×C17C2×#4112yes—
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×C17C2×#4112yes—
535C8×C17C2×#4112yes—
536#3622—22no—
537#3622—22no—
538#3622—22no—
539#3622C2×#4114yes—
540#3475—171no—
541#2970—172no—
542#2969—172no—
543#2968—172no—
544#2968—172no—
545#2967—172no—
546#2967—172no—
547#2966—172no—
548#2965—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#2925—171no—
558#2924—171no—
559#2924—171no—
560#2875—171no—
561#2873—171no—
562C2×#405—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×C17C4×#4112yes—
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×C17C4×#4112yes—
593C4×C17C22×#4111yescharacteristic
594C4×C17C22×#4111yescharacteristic
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#431—172no—
677#431—172no—
678#431—172no—
679#424—171no—
680#424—171no—
681#424—171no—
682#424—171no—
683#423—171no—
684C2×C4⋊C8C2×D1711yescharacteristic
685#408—171no—
686#408—171no—
687#407—171no—
688#407—171no—
689C2×C22⋊C8C2×D1711yescharacteristic
690C2×C22⋊C8C2×D1711yescharacteristic
691#405—172no—
692#405—172no—
693#405—171no—
694#405—171no—
695#405—171no—
696#405—171no—
697#405—172no—
698#405—172no—
699#405—171no—
700#405—171no—
701#405—171no—
702#405—171no—
703#405—172no—
704#405—172no—
705C4×M16—172no—
706C4×M16—172no—
707C4×M16—171no—
708C4×M16—172no—
709C2×#97—172no—
710C2×#97—172no—
711C2×#97C2×D1711yescharacteristic
712C2×C4×C8—172no—
713C2×C17—22no—
714C2×C17—22no—
715C2×C17—41no—
716C2×C17—41no—
717C2×C17—41no—
718C2×C17C2×C4×#4111yescharacteristic
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—344no—
728#131—344no—
729C2×M16—24no—
730C2×M16—171no—
731C2×M16—172no—
732C2×M16—171no—
733C2×M16—171no—
734C2×M16—172no—
735C2×M16—171no—
736C2×M16—172no—
737C2×M16—172no—
738C2×M16—344no—
739C2×M16—344no—
740C2×M16C22×D1711yescharacteristic
741C2×M16C22×D1711yescharacteristic
742C2×M16C22×D1711yescharacteristic
743C2×M16C22×D1711yescharacteristic
744C22×C8—24no—
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⋊C8C22×D1711yescharacteristic
862C4⋊C8C22×D1711yescharacteristic
863C4⋊C8C22×D1711yescharacteristic
864C4⋊C8C22×D1711yescharacteristic
865C22⋊C8—172no—
866C22⋊C8—172no—
867C22⋊C8—172no—
868C22⋊C8—172no—
869C22⋊C8—172no—
870C22⋊C8—172no—
871C22⋊C8—172no—
872C22⋊C8—172no—
873C22⋊C8C22×D1711yescharacteristic
874C22⋊C8C22×D1711yescharacteristic
875C22⋊C8C22×D1711yescharacteristic
876C22⋊C8C22×D1711yescharacteristic
877C22⋊C8C22×D1711yescharacteristic
878C22⋊C8C22×D1711yescharacteristic
879C22⋊C8C22×D1711yescharacteristic
880C22⋊C8C22×D1711yescharacteristic
881#97—172no—
882#97—172no—
883#97—172no—
884#97—172no—
885#97—172no—
886#97—172no—
887#97—172no—
888#97—172no—
889#97—172no—
890#97C22×D1711yescharacteristic
891#97C22×D1711yescharacteristic
892#97C22×D1711yescharacteristic
893#97C22×D1711yescharacteristic
894C4×C8—172no—
895C4×C8—172no—
896C4×C8—172no—
897C4×C8—172no—
898C4×C8—172no—
899C4×C8—172no—
900C4×C8—172no—
901C4×C8—172no—
902C4×C8—172no—
903C17#6021611yescharacteristic, 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—22no—
948M16—22no—
949M16—22no—
950M16—22no—
951M16—174no—
952M16—344no—
953M16—344no—
954M16—344no—
955M16—342no—
956M16—342no—
957M16—342no—
958M16—344no—
959C2×C8—22no—
960C2×C8—22no—
961C2×C8—22no—
962C2×C8—22no—
963C2×C8—22no—
964C2×C8—22no—
965C2×C8—22no—
966C2×C8—172no—
967C2×C8—172no—
968C2×C8—172no—
969C2×C8—172no—
970C2×C8—344no—
971C2×C8—344no—
972C2×C8—344no—
973C2×C8—344no—
974C2×C8#6325414yescomplemented
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×C4C2×#6325412yes—
1113C2×C4#41×D1712yes—
1114C2×C4C24×D1711yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—21no—
1120C8—21no—
1121C8—174no—
1122C8—342no—
1123C8—342no—
1124C8—342no—
1125C8C2×#6325412yes—
1126C8C2×#6325412yes—
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—
1145C22C4×#6325412yes—
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—
1163C4C4×#6325412yes—
1164C4C2×#41×D1711yescharacteristic
1165C4C22×#6325411yescharacteristic
1166C2—22no—
1167C2—22no—
1168C2—41no—
1169C2—41no—
1170C2—41no—
1171C2—682no—
1172C2C2×C4×#6325411yescharacteristic
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#60216
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #14537794C2semidirect
3. #14537781C2semidirect
4. #14537779C2semidirect
5. #14537775C2semidirect
6. #14537766C2semidirect
7. #14537763C2semidirect
8. #14537754C2semidirect
9. #14537744C2semidirect
10. #14537727C2semidirect
11. #14537724C2semidirect
12. D4×#63223C2semidirect
13. #14537505C2semidirect
14. #14537505C2semidirect
15. #14537487C2semidirect
16. #14537478C2semidirect
17. #14537449C2semidirect
18. #14537438C2semidirect
19. #14537438C2semidirect
20. #14537209C2semidirect
21. #14537202C2semidirect
22. C2×#11762764C2semidirect
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. #11762869C22semidirect
79. #11762869C22semidirect
80. #11762867C22semidirect
81. #11762867C22semidirect
82. #11762867C22semidirect
83. #11762867C22semidirect
84. #11762865C22semidirect
85. #11762863C22semidirect
86. #11762863C22semidirect
87. #11762861C22semidirect
88. #11762859C22semidirect
89. #11762859C22semidirect
99. #11762767C22semidirect
100. #11762767C22semidirect
101. #11762766C22semidirect
102. #11762766C22semidirect
111. #11762764C22semidirect
112. #11762764C22semidirect
114. #11762761C22semidirect
115. M16×Dic17C22semidirect
116. M16×Dic17C22semidirect
117. C2×#10587486C22semidirect
118. #97×D17C22semidirect
119. C2×C8×Dic17C22semidirect
370. C2×C8×C17#41semidirect
448. #63223#41semidirect
556. C2×#435D17semidirect
903. C17#60216semidirect
974. C2×C8#63254semidirect

Maximal subgroups

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

subgroupindex
#145423422
#145377942
#145377812
#145377792
#145377752
#145377662
#145377632
#145377542
#145377442
#145377272
#145377242
D4×#632232
#145375052
#145374872
#145374782
#145374492
#145374382
#145372092
#145372022
C2×#117627642
C2×C17×#4352
#6021617