Finite Group Databasebeta

← #17899548

Subgroups — #17899548

Order 4352.

1882 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#14542344C211yesmaximal, characteristic
2#14537941C212yesmaximal, complemented
3#14537939C212yesmaximal, complemented
4#14537937C212yesmaximal, complemented
5#14537926C212yesmaximal, complemented
6#14537919C212yesmaximal, complemented
7#14537917C212yesmaximal, complemented
8#14537904C212yesmaximal, complemented
9#14537891C212yesmaximal, complemented
10#14537728C211yesmaximal, characteristic, complemented
11#14537717C211yesmaximal, characteristic, complemented
12#14537516C211yesmaximal, characteristic, complemented
13#14537511C211yesmaximal, characteristic, complemented
14#14537506C211yesmaximal, characteristic, complemented
15#14537481C211yesmaximal, characteristic, complemented
16C2×C8×C22⋊D17C211yesmaximal, characteristic, complemented
17#14537444C211yesmaximal, characteristic, complemented
18#14537439C211yesmaximal, characteristic, complemented
19#14537424C211yesmaximal, characteristic, complemented
20#14537350C211yesmaximal, characteristic, complemented
21C2×#11762835C211yesmaximal, characteristic, complemented
22D17×#424C211yesmaximal, characteristic, complemented
23C17×#2929C211yesmaximal, characteristic, complemented
24C2×#10587634C2211yescharacteristic
25C22×#63223C2211yescharacteristic
26C2×M16×D17C2211yescharacteristic
27C22×C8×D17C2211yescharacteristic
28#11763530C411yescharacteristic
29#11763523C411yescharacteristic
30#11763517C411yescharacteristic
31#11763511C411yescharacteristic
32#11763506C411yescharacteristic
33#11763501C411yescharacteristic
34#11763496C412yes—
35#11763493C411yescharacteristic
36#11763490C412yes—
37#11763482C412yes—
38#11763459C411yescharacteristic
39#11763446C412yes—
40#11763362C2211yescharacteristic
41#11763341C2212yes—
42#11763339C2212yes—
43#11763339C2212yes—
44#11763316C2211yescharacteristic
45#41×Dic17C2211yescharacteristic
46C4×#63254C2212yes—
47C2×C4×C22⋊D17C2211yescharacteristic
48C2×#10587612C2211yescharacteristic
49#117×D17C2211yescharacteristic
50#11762939C2212yescomplemented
51#11762938C2212yescomplemented
52#11762938C2212yescomplemented
53#11762937C2212yescomplemented
54#11762937C2212yescomplemented
55C8×Dic34C2212yescomplemented
56#11762933C2212yescomplemented
57#11762933C2212yescomplemented
58#11762887C2212yescomplemented
59#11762885C2212yescomplemented
60#11762884C2212yes—
61#11762883C2212yes—
62#11762883C2212yescomplemented
63#11762883C2212yescomplemented
64#11762881C2212yescomplemented
65#11762881C2212yescomplemented
66#11762880C2212yescomplemented
67#11762878C2212yescomplemented
68#11762877C2212yes—
69D4×#3622C2212yescomplemented
70C8×C22⋊D17C2211yescharacteristic
71C8×C22⋊D17C2211yescharacteristic
72C8×C22⋊D17C2211yescharacteristic
73C8×C22⋊D17C2211yescharacteristic
74C8×C22⋊D17C2211yescharacteristic
75C8×C22⋊D17C2211yescharacteristic
76C8×C22⋊D17C2211yescharacteristic
77C8×C22⋊D17C2211yescharacteristic
78C8×C22⋊D17C2212yescomplemented
79#11762872C2212yes—
80#11762872C2212yescomplemented
81#11762872C2212yescomplemented
82#11762871C2212yescomplemented
83#11762868C2212yescomplemented
84#11762867C2212yescomplemented
85#11762867C2212yescomplemented
86#11762867C2212yescomplemented
87#11762867C2212yescomplemented
88#11762864C2212yescomplemented
89#11762863C2212yescomplemented
90#11762860C2212yescomplemented
91#11762859C2212yescomplemented
92#11762859C2212yescomplemented
93#11762859C2212yescomplemented
94#11762837C2211yescharacteristic
95#11762837C2211yescharacteristic
96#11762837C2212yescomplemented
97#11762836C2211yescharacteristic
98#11762835C2211yescharacteristic
99#11762835C2211yescharacteristic
100#11762835C2211yescharacteristic
101#11762835C2211yescharacteristic
102#11762835C2212yescomplemented
103#11762835C2212yescomplemented
104#11762835C2212yescomplemented
105#11762834C2212yescomplemented
106#11762834C2212yescomplemented
107#11762832C2211yescharacteristic
108#11762832C2212yescomplemented
109C2×#10587485C2211yescharacteristic
110C2×#10587485C2212yescomplemented
111C2×#10587485C2212yescomplemented
112C2×#10587485C2212yescomplemented
113C4⋊C8×D17C2212yescomplemented
114C4⋊C8×D17C2212yescomplemented
115#11762776C2211yescharacteristic
116#11762772C2211yescharacteristic
117C2×C22⋊#3622C2211yescharacteristic
118C2×#10587491C2211yescharacteristic
119#11762767C2211yescharacteristic
120#11762767C2211yescharacteristic
121#11762765C2211yescharacteristic
122M16×Dic17C2211yescharacteristic
123C2×C8×Dic17C2211yescharacteristic
124C2×C17×#131C2211yescharacteristic
125C23×C8×C17C2211yescharacteristic
126C17×#525C2211yescharacteristic
127C17×#435C2212yescomplemented
128C17×#435C2212yescomplemented
129C8×D4×C17C2212yescomplemented
130C8×D4×C17C2212yescomplemented
131C17×#424C2211yescharacteristic
132C17×#408C2211yescharacteristic
133C17×#407C2211yescharacteristic
134C17×#405C2211yescharacteristic
135C2×#41×C17C2311yescharacteristic
136C23×C4×C17C2311yescharacteristic
137C22×C22⋊D17C2×C411yescharacteristic
138C2×#63254C2×C412yes—
139C22×C4×D17C2311yescharacteristic
140C17×#131—42no—
141C2×M16×C17C2311yescharacteristic
142C2×M16×C17C2311yescharacteristic
143C2×M16×C17C2312yes—
144C22×C8×C17—42no—
145C22×C8×C17C2311yescharacteristic
146C22×C8×C17C2311yescharacteristic
147C22×C8×C17C2311yescharacteristic
148C22×C8×C17C2311yescharacteristic
149C22×C8×C17C2311yescharacteristic
150C22×C8×C17C2311yescharacteristic
151C22×C8×C17C2312yes—
152C17×#123C2×C412yes—
153C17×C22⋊Q8C2×C411yescharacteristic
154C17×C22⋊Q8C2×C411yescharacteristic
155C17×#121C2×C411yescharacteristic
156C17×#121C2×C411yescharacteristic
157C17×#120C2×C412yes—
158C4×D4×C17C2312yes—
159C4×D4×C17C2312yes—
160C17×#117C2311yescharacteristic
161C2×C22⋊Dic17C2×C411yescharacteristic
162C2×C22⋊Dic17C2×C412yes—
163#10587634—42no—
164#10587632C2×C411yescharacteristic
165#10587632C2×C411yescharacteristic
166Q8×Dic17C2×C411yescharacteristic
167Q8×Dic17C2×C411yescharacteristic
168#10587625C2×C412yes—
169#10587625C2×C412yes—
170#10587624C2×C411yescharacteristic
171#10587624C2×C412yes—
172#10587624C2×C411yescharacteristic
173#10587623C2×C412yes—
174#10587622C2×C412yes—
175#10587621C2×C412yes—
176#10587621C2×C412yes—
177#10587621C2×C412yes—
178D4×Dic17C2×C411yescharacteristic
179D4×Dic17C2×C412yes—
180D4×Dic17C2×C412yes—
181D4×Dic17C2×C412yes—
182D4×Dic17C2×C411yescharacteristic
183C4×C22⋊D17C2×C411yescharacteristic
184C4×C22⋊D17C2×C411yescharacteristic
185C4×C22⋊D17C2×C411yescharacteristic
186C4×C22⋊D17C2×C411yescharacteristic
187C4×C22⋊D17C2311yescharacteristic
188C4×C22⋊D17C2311yescharacteristic
189C4×C22⋊D17C2311yescharacteristic
190C4×C22⋊D17C2311yescharacteristic
191C4×C22⋊D17C2312yes—
192C4×C22⋊D17C2312yes—
193C2×#63227C2×C411yescharacteristic
194#10587612C2×C412yes—
195#10587612C2×C411yescharacteristic
196#10587612C2×C411yescharacteristic
197#10587612C2311yescharacteristic
198#10587612C2311yescharacteristic
199#10587612C2312yes—
200#10587612C2312yes—
201C2×C4⋊Dic17C2×C411yescharacteristic
202C2×C4⋊Dic17C2×C411yescharacteristic
203C2×#63225C2×C411yescharacteristic
204C2×C4×Dic17C2312yes—
205C2×C4×Dic17C2311yescharacteristic
206C2×C4×Dic17C2312yes—
207C2×#63223—42no—
208C2×#63223C2311yescharacteristic
209C2×#63223C2311yescharacteristic
210C2×#63223C2312yes—
211C2×#63223C2312yes—
212C22×#3622C2311yescharacteristic
213C22×#3622C2311yescharacteristic
214C22×#3622C2312yes—
215C22×#3622C2312yes—
216M16×D17—42no—
217C2×#63218C2312yes—
218C2×C8×D17—42no—
219C2×C8×D17C2311yescharacteristic
220C2×C8×D17C2311yescharacteristic
221C2×C8×D17C2311yescharacteristic
222C2×C8×D17C2311yescharacteristic
223C2×C8×D17C2312yes—
224#10587584C2×C412yes—
225#10587584C2×C412yes—
226#10587583C2×C412yes—
227#10587578C2×C412yes—
228#10587578C2×C411yescharacteristic
229#10587578C2×C411yescharacteristic
230C4⋊C4×D17C2×C411yescharacteristic
231C4⋊C4×D17C2×C411yescharacteristic
232#10587576C2×C411yescharacteristic
233#10587576C2×C412yes—
234#10587576C2×C411yescharacteristic
235#10587575C2×C412yes—
236#10587575C2×C412yes—
237#10587574C2×C411yescharacteristic
238#10587574C2×C411yescharacteristic
239#10587573C2×C412yes—
240#10587572C2×C412yes—
241#10587572C2×C412yes—
242#10587571C2×C412yes—
243#10587571C2×C412yes—
244#10587569C2×C412yes—
245#10587569C2×C412yes—
246#10587567C2×C412yes—
247#10587567C2×C412yes—
248C22⋊C4×D17C2×C412yes—
249#10587565C2×C412yes—
250#10587565C2×C412yes—
251#10587565C2×C412yes—
252#10587565C2×C412yes—
253#10587564C2×C412yes—
254#10587564C2×C412yes—
255#10587564C2×C412yes—
256#10587564C2×C412yes—
257#10587563C2×C412yes—
258#10587563C2×C412yes—
259#10587563C2×C412yes—
260#10587558C2312yes—
261C42×D17C2312yes—
262C4×Dic34C2312yes—
263C4×Dic34C2312yes—
264C17×C4⋊C8C2312yes—
265C17×C4⋊C8C2312yes—
266C17×C22⋊C8C2312yes—
267C17×C22⋊C8C2312yes—
268C17×C22⋊C8C2312yes—
269C17×C22⋊C8C2312yes—
270C17×#97C2312yes—
271C4×C8×C17C2312yes—
272C22⋊#3622C2311yescharacteristic
273C22⋊#3622C2311yescharacteristic
274C22⋊#3622C2311yescharacteristic
275C22⋊#3622C2311yescharacteristic
276C22⋊#3622C2312yes—
277C22⋊#3622C2312yes—
278#10587491C2311yescharacteristic
279#10587491C2311yescharacteristic
280#10587491C2311yescharacteristic
281#10587491C2311yescharacteristic
282#10587491C2312yes—
283#10587491C2312yes—
284#10587486C2312yes—
285#10587486C2312yes—
286#10587486C2312yes—
287#10587485C2312yes—
288#10587485C2312yes—
289#10587485C2312yes—
290#10587485C2312yes—
291#10587485C2311yescharacteristic
292#10587485C2311yescharacteristic
293#10587485C2311yescharacteristic
294#10587485C2311yescharacteristic
295#10587485C2312yes—
296#10587485C2312yes—
297#10587485C2312yes—
298#10587485C2312yes—
299#10587485C2312yes—
300#10587485C2312yes—
301#10587485C2312yes—
302#10587485C2312yes—
303#10587485C2312yes—
304#10587485C2312yes—
305C8×Dic17C2311yescharacteristic
306C8×Dic17C2311yescharacteristic
307C8×Dic17C2311yescharacteristic
308C8×Dic17C2311yescharacteristic
309C8×Dic17C2312yes—
310C8×Dic17C2312yes—
311C8×Dic17C2312yes—
312C4⋊#3622C2312yes—
313C4⋊#3622C2312yes—
314#10587474C2312yes—
315C4×#3622C2312yes—
316C24×C17C22×C411yescharacteristic
317C23×D17C22×C411yescharacteristic
318#41×C17—22no—
319#41×C17—22no—
320C2×Q8×C17C22×C411yescharacteristic
321C2×D4×C17C22×C412yes—
322C2×D4×C17C22×C412yes—
323C2×D4×C17C22×C411yescharacteristic
324C2×D4×C17C22×C412yes—
325C22×C4×C17—22no—
326C22×C4×C17—22no—
327C22×C4×C17C22×C411yescharacteristic
328C22×C4×C17C22×C411yescharacteristic
329C22×C4×C17C22×C411yescharacteristic
330C22×C4×C17C2411yescharacteristic
331C22×C4×C17C2411yescharacteristic
332C22×C4×C17C2412yes—
333C22×C4×C17C2411yescharacteristic
334C2×C22⋊D17—24no—
335C2×C22⋊D17C22×C412yes—
336C2×C22⋊D17C22×C411yescharacteristic
337C2×C22⋊D17C22×C411yescharacteristic
338C2×C22⋊D17C22×C411yescharacteristic
339C2×C22⋊D17C22×C412yes—
340C2×C22⋊D17C22×C411yescharacteristic
341C22×Dic17C22×C411yescharacteristic
342C22×Dic17C22×C412yes—
343C22×Dic17C22×C412yes—
344C22×Dic17C22×C411yescharacteristic
345C22×Dic17C22×C411yescharacteristic
346C22×Dic17C22×C412yes—
347C22×Dic17C22×C412yes—
348#63254—28no—
349C2×C4×D17—22no—
350C2×C4×D17—22no—
351C2×C4×D17C22×C411yescharacteristic
352C2×C4×D17C22×C411yescharacteristic
353C2×C4×D17C22×C412yes—
354C2×C4×D17C22×C412yes—
355C2×C4×D17C2411yescharacteristic
356C2×C4×D17C2411yescharacteristic
357C2×Dic34C22×C412yes—
358C2×Dic34C22×C412yes—
359M16×C17—22no—
360M16×C17—22no—
361M16×C17—42no—
362C2×C8×C17—22no—
363C2×C8×C17—22no—
364C2×C8×C17—41no—
365C2×C8×C17—41no—
366C2×C8×C17—41no—
367C2×C8×C17—41no—
368C2×C8×C17—42no—
369C2×C8×C17C2411yescharacteristic
370C2×C8×C17C2411yescharacteristic
371C2×C8×C17C2411yescharacteristic
372C2×C8×C17C2411yescharacteristic
373C2×C8×C17C2412yes—
374C2×C8×C17C2412yes—
375C4⋊C4×C17C22×C412yes—
376C4⋊C4×C17C22×C412yes—
377C4⋊C4×C17C22×C411yescharacteristic
378C4⋊C4×C17C22×C411yescharacteristic
379C22⋊C4×C17C22×C412yes—
380C22⋊C4×C17C22×C412yes—
381C22⋊C4×C17C22×C412yes—
382C22⋊C4×C17C22×C412yes—
383C22⋊C4×C17C22×C412yes—
384C42×C17C2412yes—
385C22⋊Dic17C22×C411yescharacteristic
386C22⋊Dic17C22×C412yes—
387C22⋊Dic17C22×C412yes—
388C22⋊Dic17C22×C412yes—
389C22⋊Dic17C22×C411yescharacteristic
390C22⋊Dic17C22×C412yes—
391C22⋊Dic17C22×C412yes—
392C22⋊Dic17C22×C411yescharacteristic
393C22⋊Dic17C22×C411yescharacteristic
394C22⋊Dic17C22×C412yes—
395C22⋊Dic17C22×C412yes—
396C22⋊Dic17C22×C412yes—
397#63227C22×C412yes—
398#63227C22×C412yes—
399#63227C22×C411yescharacteristic
400#63227C22×C412yes—
401#63227C22×C411yescharacteristic
402#63227C22×C411yescharacteristic
403#63227C22×C412yes—
404#63227C22×C411yescharacteristic
405C4⋊Dic17C22×C412yes—
406C4⋊Dic17C22×C412yes—
407C4⋊Dic17C22×C412yes—
408C4⋊Dic17C22×C412yes—
409C4⋊Dic17C22×C412yes—
410C4⋊Dic17C22×C412yes—
411C4⋊Dic17C22×C411yescharacteristic
412C4⋊Dic17C22×C411yescharacteristic
413C4⋊Dic17C22×C411yescharacteristic
414C4⋊Dic17C22×C411yescharacteristic
415#63225C22×C412yes—
416#63225C22×C412yes—
417#63225C22×C412yes—
418#63225C22×C412yes—
419#63225C22×C412yes—
420#63225C22×C412yes—
421#63225C22×C411yescharacteristic
422#63225C22×C412yes—
423#63225C22×C411yescharacteristic
424#63225C22×C412yes—
425#63225C22×C411yescharacteristic
426#63225C22×C411yescharacteristic
427C4×Dic17C22×C412yes—
428C4×Dic17C22×C412yes—
429C4×Dic17C22×C412yes—
430C4×Dic17C22×C412yes—
431C4×Dic17C22×C412yes—
432C4×Dic17C22×C412yes—
433C4×Dic17C22×C411yescharacteristic
434C4×Dic17C22×C411yescharacteristic
435C4×Dic17C2411yescharacteristic
436C4×Dic17C2411yescharacteristic
437C4×Dic17C2412yes—
438C4×Dic17C2412yes—
439#63223—22no—
440#63223—22no—
441#63223—42no—
442#63223—42no—
443C2×#3622—22no—
444C2×#3622—22no—
445C2×#3622—42no—
446C2×#3622—42no—
447C2×#3622C2411yescharacteristic
448C2×#3622C2412yes—
449C2×#3622C2411yescharacteristic
450C2×#3622C2411yescharacteristic
451C2×#3622C2412yes—
452C2×#3622C2411yescharacteristic
453#63218—42no—
454C8×D17—41no—
455C8×D17—41no—
456C8×D17—41no—
457C8×D17—41no—
458C8×D17—42no—
459#60271—171nomaximal, Sylow
460C23×C17—22no—
461C23×C17—22no—
462C23×C17—41no—
463C23×C17C23×C411yescharacteristic
464C23×C17C23×C412yes—
465C23×C17C23×C411yescharacteristic
466C23×C17C23×C411yescharacteristic
467C22×D17—22no—
468C22×D17—22no—
469C22×D17—41no—
470C22×D17C23×C411yescharacteristic
471C22×D17C23×C411yescharacteristic
472Q8×C17—22no—
473D4×C17—24no—
474D4×C17—24no—
475D4×C17—22no—
476D4×C17—42no—
477C2×C4×C17—22no—
478C2×C4×C17—22no—
479C2×C4×C17—22no—
480C2×C4×C17—21no—
481C2×C4×C17—21no—
482C2×C4×C17—22no—
483C2×C4×C17—21no—
484C2×C4×C17—21no—
485C2×C4×C17—22no—
486C2×C4×C17C23×C412yes—
487C2×C4×C17C23×C412yes—
488C2×C4×C17C23×C411yescharacteristic
489C2×C4×C17C23×C411yescharacteristic
490C2×C4×C17C23×C412yes—
491C2×C4×C17C23×C411yescharacteristic
492C2×C4×C17H(5,𝔽2)12yes—
493C2×C4×C172−1+412yes—
494C2×C4×C17C2511yescharacteristic
495C22⋊D17—22no—
496C22⋊D17—24no—
497C22⋊D17—22no—
498C22⋊D17—22no—
499C22⋊D17—42no—
500C22⋊D17#13114yescomplemented
501C2×Dic17—22no—
502C2×Dic17—24no—
503C2×Dic17—24no—
504C2×Dic17—22no—
505C2×Dic17—41no—
506C2×Dic17—42no—
507C2×Dic17—42no—
508C2×Dic17C23×C411yescharacteristic
509C2×Dic17C23×C411yescharacteristic
510C2×Dic17C23×C411yescharacteristic
511C2×Dic17C23×C412yes—
512C2×Dic17C23×C412yes—
513C2×Dic17C23×C412yes—
514C2×Dic17C23×C412yes—
515C2×Dic17C23×C411yescharacteristic
516C2×Dic17C23×C411yescharacteristic
517C2×Dic17C23×C411yescharacteristic
518C4×D17—24no—
519C4×D17—22no—
520C4×D17—22no—
521C4×D17—21no—
522C4×D17—21no—
523C4×D17—21no—
524C4×D17—21no—
525C4×D17—42no—
526Dic34—24no—
527Dic34—42no—
528C8×C17—21no—
529C8×C17—21no—
530C8×C17—21no—
531C8×C17—21no—
532C8×C17—22no—
533C8×C17—22no—
534#3622—21no—
535#3622—21no—
536#3622—22no—
537#3622—22no—
538#3622—21no—
539#3622—21no—
540#3475—171no—
541#2994—172no—
542#2994—172no—
543#2994—172no—
544#2993—172no—
545#2992—172no—
546#2992—172no—
547#2990—172no—
548#2988—172no—
549#2962—171no—
550#2960—171no—
551D4×M16—171no—
552#2933—171no—
553#2933—171no—
554#2929—171no—
555#2929D1711yescharacteristic, complemented
556C2×C8×D4—171no—
557#2924—171no—
558#2924—171no—
559#2922—171no—
560#2906—171no—
561C2×#424—171no—
562C2×#424—171no—
563C22×C17—21no—
564C22×C17—21no—
565C22×C17—21no—
566C22×C17—21no—
567C22×C17—21no—
568C22×C17—22no—
569C22×C17—22no—
570C22×C17—21no—
571C22×C17—22no—
572C22×C17—21no—
573C22×C17—44no—
574C22×C17#52012yes—
575C22×C17C2×#13112yes—
576C22×C17C24×C411yescharacteristic
577C2×D17—21no—
578C2×D17—21no—
579C2×D17—21no—
580C2×D17—21no—
581C2×D17—21no—
582C2×D17—44no—
583C2×D17C2×#13112yes—
584C4×C17—21no—
585C4×C17—21no—
586C4×C17—22no—
587C4×C17—22no—
588C4×C17—22no—
589C4×C17#52012yes—
590C4×C17C2×H(5,𝔽2)11yescharacteristic
591C4×C17C2×2−1+411yescharacteristic
592Dic17—21no—
593Dic17—21no—
594Dic17—22no—
595Dic17—22no—
596Dic17—21no—
597Dic17—21no—
598Dic17—22no—
599Dic17—22no—
600Dic17—21no—
601Dic17C2×#13112yes—
602C2×#131—171no—
603C2×#131C2×D1711yescharacteristic
604C22×M16—171no—
605C22×M16—171no—
606C23×C8—171no—
607C23×C8C2×D1711yescharacteristic
608#556—171no—
609#555—171no—
610#554—171no—
611#553—171no—
612#553—171no—
613#552—172no—
614#552—171no—
615#552—171no—
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#525C2×D1711yescharacteristic
626C4×#41—171no—
627C4×#41—172no—
628C2×C4×D4—171no—
629C2×#117—171no—
630C2×#117—171no—
631#446—172no—
632#446—172no—
633#446—172no—
634#446—172no—
635#446—172no—
636C8×Q8—172no—
637C8×Q8—172no—
638C8×Q8—172no—
639#436—172no—
640#436—172no—
641#436—172no—
642#435—172no—
643#435—172no—
644#435—172no—
645#435—172no—
646#435—172no—
647#435—172no—
648#435—172no—
649#435—172no—
650#435C2×D1712yescomplemented
651#435C2×D1712yescomplemented
652C8×D4—171no—
653C8×D4—171no—
654C8×D4—171no—
655C8×D4—171no—
656C8×D4—171no—
657C8×D4—171no—
658C8×D4—171no—
659C8×D4—171no—
660C8×D4—172no—
661C8×D4—172no—
662C8×D4—172no—
663C8×D4—172no—
664C8×D4—172no—
665C8×D4C2×D1712yescomplemented
666C8×D4C2×D1712yescomplemented
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#431—172no—
676#431—172no—
677#431—172no—
678#431—172no—
679#424—171no—
680#424—172no—
681#424—171no—
682#424—171no—
683#424—171no—
684#424—171no—
685#424—171no—
686#424—172no—
687#424—172no—
688#424—172no—
689#424—171no—
690#424—172no—
691#424—172no—
692#424C2×D1711yescharacteristic
693#423—171no—
694#423—172no—
695C2×C4⋊C8—172no—
696C2×C4⋊C8—172no—
697C2×C4⋊C8—171no—
698C2×C4⋊C8—172no—
699C2×C4⋊C8—172no—
700C2×C4⋊C8—172no—
701#408—171no—
702#408C2×D1711yescharacteristic
703#407—171no—
704#407C2×D1711yescharacteristic
705C2×C22⋊C8—171no—
706C2×C22⋊C8—171no—
707#405—171no—
708#405—171no—
709#405—171no—
710#405C2×D1711yescharacteristic
711C4×M16—171no—
712C2×C4×C8—171no—
713C2×C17—22no—
714C2×C17—22no—
715C2×C17—42no—
716C2×C17—41no—
717C2×C17C2×#52011yescharacteristic
718C2×C17C22×#13111yescharacteristic
719C2×C17#357311yescharacteristic
720D17—22no—
721D17—41no—
722C2×#41—172no—
723C2×#41C22×D1711yescharacteristic
724C22×D4—171no—
725C23×C4—171no—
726C23×C4C22×D1711yescharacteristic
727#131—42no—
728#131—682no—
729C2×M16—171no—
730C2×M16—171no—
731C2×M16—172no—
732C2×M16—172no—
733C2×M16—172no—
734C2×M16—682no—
735C2×M16—682no—
736C2×M16C22×D1711yescharacteristic
737C2×M16C22×D1711yescharacteristic
738C2×M16C22×D1712yes—
739C22×C8—42no—
740C22×C8—171no—
741C22×C8—171no—
742C22×C8—172no—
743C22×C8—172no—
744C22×C8—171no—
745C22×C8—171no—
746C22×C8—171no—
747C22×C8—171no—
748C22×C8—172no—
749C22×C8—682no—
750C22×C8C22×D1711yescharacteristic
751C22×C8C22×D1711yescharacteristic
752C22×C8C22×D1711yescharacteristic
753C22×C8C22×D1711yescharacteristic
754C22×C8C22×D1711yescharacteristic
755C22×C8C22×D1711yescharacteristic
756C22×C8C22×D1712yes—
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#123C4×D1712yes—
781C22⋊Q8—171no—
782C22⋊Q8—171no—
783C22⋊Q8—172no—
784C22⋊Q8—172no—
785C22⋊Q8—172no—
786C22⋊Q8—172no—
787C22⋊Q8—172no—
788C22⋊Q8C4×D1711yescharacteristic
789C22⋊Q8C4×D1711yescharacteristic
790#121—171no—
791#121—171no—
792#121—172no—
793#121—172no—
794#121—172no—
795#121C4×D1711yescharacteristic
796#121C4×D1711yescharacteristic
797#120—172no—
798#120C4×D1712yes—
799C4×Q8—171no—
800C4×Q8—171no—
801C4×Q8—172no—
802C4×Q8—172no—
803C4×Q8—172no—
804C4×D4—172no—
805C4×D4—171no—
806C4×D4—172no—
807C4×D4—172no—
808C4×D4—171no—
809C4×D4—171no—
810C4×D4—171no—
811C4×D4—171no—
812C4×D4—171no—
813C4×D4—171no—
814C4×D4—171no—
815C4×D4—171no—
816C4×D4—171no—
817C4×D4—172no—
818C4×D4—172no—
819C4×D4—172no—
820C4×D4—172no—
821C4×D4C22×D1712yes—
822C4×D4C22×D1712yes—
823#117—172no—
824#117—171no—
825#117—171no—
826#117—171no—
827#117—171no—
828#117—172no—
829#117—172no—
830#117—171no—
831#117—171no—
832#117—172no—
833#117—172no—
834#117—172no—
835#117—172no—
836#117—172no—
837#117C22×D1711yescharacteristic
838C2×C4⋊C4—171no—
839C2×C4⋊C4—171no—
840C2×C4⋊C4—171no—
841C2×C4⋊C4—171no—
842C2×C4⋊C4—171no—
843C2×C22⋊C4—172no—
844C2×C22⋊C4—171no—
845C2×C22⋊C4—171no—
846C2×C22⋊C4—172no—
847C2×C42—172no—
848C2×C42—171no—
849C2×C42—172no—
850C2×C42—172no—
851C4⋊C8—171no—
852C4⋊C8—172no—
853C4⋊C8—172no—
854C4⋊C8—172no—
855C4⋊C8—172no—
856C4⋊C8—171no—
857C4⋊C8—172no—
858C4⋊C8—172no—
859C4⋊C8—172no—
860C4⋊C8—171no—
861C4⋊C8—171no—
862C4⋊C8—172no—
863C4⋊C8—172no—
864C4⋊C8—172no—
865C4⋊C8—172no—
866C4⋊C8—172no—
867C4⋊C8—172no—
868C4⋊C8—172no—
869C4⋊C8—172no—
870C4⋊C8—172no—
871C4⋊C8C22×D1712yes—
872C4⋊C8C22×D1712yes—
873C22⋊C8—171no—
874C22⋊C8—171no—
875C22⋊C8—171no—
876C22⋊C8—171no—
877C22⋊C8—172no—
878C22⋊C8—172no—
879C22⋊C8—171no—
880C22⋊C8—171no—
881C22⋊C8—171no—
882C22⋊C8—171no—
883C22⋊C8—172no—
884C22⋊C8—172no—
885C22⋊C8C22×D1712yes—
886C22⋊C8C22×D1712yes—
887C22⋊C8C22×D1712yes—
888C22⋊C8C22×D1712yes—
889#97—172no—
890#97—172no—
891#97—172no—
892#97—172no—
893#97C22×D1712yes—
894C4×C8—171no—
895C4×C8—171no—
896C4×C8—171no—
897C4×C8—171no—
898C4×C8—172no—
899C4×C8—172no—
900C4×C8—172no—
901C4×C8—172no—
902C4×C8C22×D1712yes—
903C17#6027111yescharacteristic, complemented, Sylow
904C24—171no—
905C24C2×C4×D1711yescharacteristic
906#41—22no—
907#41—22no—
908#41—348no—
909C2×Q8—172no—
910C2×Q8—172no—
911C2×Q8C2×C4×D1711yescharacteristic
912C2×D4—171no—
913C2×D4—172no—
914C2×D4—171no—
915C2×D4—171no—
916C2×D4—171no—
917C2×D4—172no—
918C2×D4—344no—
919C2×D4C2×C4×D1712yes—
920C2×D4C2×C4×D1711yescharacteristic
921C2×D4C2×C4×D1712yes—
922C2×D4C2×C4×D1712yes—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—172no—
926C22×C4—171no—
927C22×C4—172no—
928C22×C4—171no—
929C22×C4—171no—
930C22×C4—172no—
931C22×C4—172no—
932C22×C4—172no—
933C22×C4—171no—
934C22×C4—171no—
935C22×C4—171no—
936C22×C4—171no—
937C22×C4—172no—
938C22×C4—342no—
939C22×C4—342no—
940C22×C4C2×C4×D1711yescharacteristic
941C22×C4C2×C4×D1711yescharacteristic
942C22×C4C2×C4×D1711yescharacteristic
943C22×C4C23×D1711yescharacteristic
944C22×C4C23×D1712yes—
945C22×C4C23×D1711yescharacteristic
946C22×C4C23×D1711yescharacteristic
947M16—22no—
948M16—22no—
949M16—42no—
950M16—342no—
951M16—342no—
952M16—682no—
953M16—682no—
954M16—682no—
955C2×C8—22no—
956C2×C8—22no—
957C2×C8—41no—
958C2×C8—41no—
959C2×C8—41no—
960C2×C8—41no—
961C2×C8—42no—
962C2×C8—171no—
963C2×C8—171no—
964C2×C8—171no—
965C2×C8—172no—
966C2×C8—172no—
967C2×C8—171no—
968C2×C8—342no—
969C2×C8—342no—
970C2×C8—681no—
971C2×C8—681no—
972C2×C8—681no—
973C2×C8—681no—
974C2×C8—682no—
975C2×C8—682no—
976C2×C8—682no—
977C2×C8C23×D1712yes—
978C2×C8C23×D1711yescharacteristic
979C2×C8C23×D1711yescharacteristic
980C2×C8C23×D1712yes—
981C2×C8C23×D1711yescharacteristic
982C2×C8C23×D1711yescharacteristic
983C4⋊C4—171no—
984C4⋊C4—171no—
985C4⋊C4—171no—
986C4⋊C4—171no—
987C4⋊C4—171no—
988C4⋊C4—172no—
989C4⋊C4—172no—
990C4⋊C4—172no—
991C4⋊C4—172no—
992C4⋊C4—171no—
993C4⋊C4—171no—
994C4⋊C4—171no—
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×D1712yes—
1008C4⋊C4C2×C4×D1712yes—
1009C22⋊C4—172no—
1010C22⋊C4—171no—
1011C22⋊C4—172no—
1012C22⋊C4—172no—
1013C22⋊C4—172no—
1014C22⋊C4—171no—
1015C22⋊C4—171no—
1016C22⋊C4—171no—
1017C22⋊C4—172no—
1018C22⋊C4—172no—
1019C22⋊C4—172no—
1020C22⋊C4—172no—
1021C22⋊C4—171no—
1022C22⋊C4—172no—
1023C22⋊C4—172no—
1024C22⋊C4—171no—
1025C22⋊C4—171no—
1026C22⋊C4—171no—
1027C22⋊C4—172no—
1028C22⋊C4—172no—
1029C22⋊C4C2×C4×D1712yes—
1030C22⋊C4C2×C4×D1712yes—
1031C22⋊C4C2×C4×D1712yes—
1032C22⋊C4C2×C4×D1712yes—
1033C22⋊C4C2×C4×D1712yes—
1034C42—172no—
1035C42—172no—
1036C42—172no—
1037C42—172no—
1038C42—172no—
1039C42—171no—
1040C42—171no—
1041C42—172no—
1042C42—171no—
1043C42—171no—
1044C42—172no—
1045C42—172no—
1046C42C23×D1712yes—
1047C23—22no—
1048C23—22no—
1049C23—41no—
1050C23—171no—
1051C23—171no—
1052C23—342no—
1053C23—342no—
1054C23—681no—
1055C23C22×C4×D1711yescharacteristic
1056C23C22×C4×D1712yes—
1057C23C22×C4×D1711yescharacteristic
1058C23C22×C4×D1711yescharacteristic
1059Q8—22no—
1060Q8—344no—
1061Q8—682no—
1062D4—24no—
1063D4—24no—
1064D4—22no—
1065D4—42no—
1066D4—174no—
1067D4—342no—
1068D4—342no—
1069D4—344no—
1070D4—342no—
1071D4—682no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—171no—
1082C2×C4—172no—
1083C2×C4—171no—
1084C2×C4—172no—
1085C2×C4—171no—
1086C2×C4—171no—
1087C2×C4—172no—
1088C2×C4—172no—
1089C2×C4—171no—
1090C2×C4—171no—
1091C2×C4—344no—
1092C2×C4—342no—
1093C2×C4—344no—
1094C2×C4—342no—
1095C2×C4—344no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—341no—
1099C2×C4—341no—
1100C2×C4—341no—
1101C2×C4—341no—
1102C2×C4—682no—
1103C2×C4—682no—
1104C2×C4—682no—
1105C2×C4—681no—
1106C2×C4C22×C4×D1711yescharacteristic
1107C2×C4C22×C4×D1712yes—
1108C2×C4C22×C4×D1712yes—
1109C2×C4C22×C4×D1712yes—
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—22no—
1120C8—22no—
1121C8—341no—
1122C8—341no—
1123C8—342no—
1124C8—342no—
1125C8—341no—
1126C8—341no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—22no—
1132C22—21no—
1133C22—22no—
1134C22—21no—
1135C22—21no—
1136C22—22no—
1137C22—44no—
1138C22—172no—
1139C22—341no—
1140C22—341no—
1141C22—341no—
1142C22—341no—
1143C22—341no—
1144C22—684no—
1145C22#1176328812yes—
1146C22#131×D1712yes—
1147C22C23×C4×D1711yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—21no—
1151C4—21no—
1152C4—22no—
1153C4—172no—
1154C4—342no—
1155C4—341no—
1156C4—342no—
1157C4—342no—
1158C4—341no—
1159C4—342no—
1160C4—341no—
1161C4—341no—
1162C4—341no—
1163C4#1176328812yes—
1164C4C2×#1058769111yescharacteristic
1165C4C2×#1058769711yescharacteristic
1166C2—22no—
1167C2—22no—
1168C2—41no—
1169C2—42no—
1170C2—342no—
1171C2—681no—
1172C2C2×#1176328811yescharacteristic
1173C2C2×#131×D1711yescharacteristic
1174C2#1454349511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
FittingC17×#2929C2
prime radical#14542344C2
cosocleC2×C4×C17C25
hypercenter#2929D17
hypocenterC17#60271
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. #14537941C2semidirect
3. #14537939C2semidirect
4. #14537937C2semidirect
5. #14537926C2semidirect
6. #14537919C2semidirect
7. #14537917C2semidirect
8. #14537904C2semidirect
9. #14537891C2semidirect
10. #14537728C2semidirect
11. #14537717C2semidirect
12. #14537516C2semidirect
13. #14537511C2semidirect
14. #14537506C2semidirect
15. #14537481C2semidirect
16. C2×C8×C22⋊D17C2semidirect
17. #14537444C2semidirect
18. #14537439C2semidirect
19. #14537424C2semidirect
20. #14537350C2semidirect
21. C2×#11762835C2semidirect
22. D17×#424C2semidirect
23. C17×#2929C2semidirect
50. #11762939C22semidirect
51. #11762938C22semidirect
52. #11762938C22semidirect
53. #11762937C22semidirect
54. #11762937C22semidirect
55. C8×Dic34C22semidirect
56. #11762933C22semidirect
57. #11762933C22semidirect
58. #11762887C22semidirect
59. #11762885C22semidirect
62. #11762883C22semidirect
63. #11762883C22semidirect
64. #11762881C22semidirect
65. #11762881C22semidirect
66. #11762880C22semidirect
67. #11762878C22semidirect
69. D4×#3622C22semidirect
78. C8×C22⋊D17C22semidirect
80. #11762872C22semidirect
81. #11762872C22semidirect
82. #11762871C22semidirect
83. #11762868C22semidirect
84. #11762867C22semidirect
85. #11762867C22semidirect
86. #11762867C22semidirect
87. #11762867C22semidirect
88. #11762864C22semidirect
89. #11762863C22semidirect
90. #11762860C22semidirect
91. #11762859C22semidirect
92. #11762859C22semidirect
93. #11762859C22semidirect
96. #11762837C22semidirect
102. #11762835C22semidirect
103. #11762835C22semidirect
104. #11762835C22semidirect
105. #11762834C22semidirect
106. #11762834C22semidirect
108. #11762832C22semidirect
110. C2×#10587485C22semidirect
111. C2×#10587485C22semidirect
112. C2×#10587485C22semidirect
113. C4⋊C8×D17C22semidirect
114. C4⋊C8×D17C22semidirect
127. C17×#435C22semidirect
128. C17×#435C22semidirect
129. C8×D4×C17C22semidirect
130. C8×D4×C17C22semidirect
500. C22⋊D17#131semidirect
555. #2929D17semidirect
650. #435C2×D17semidirect
651. #435C2×D17semidirect
665. C8×D4C2×D17semidirect
666. C8×D4C2×D17semidirect
903. C17#60271semidirect

Maximal subgroups

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

subgroupindex
#145423442
#145379412
#145379392
#145379372
#145379262
#145379192
#145379172
#145379042
#145378912
#145377282
#145377172
#145375162
#145375112
#145375062
#145374812
C2×C8×C22⋊D172
#145374442
#145374392
#145374242
#145373502
C2×#117628352
D17×#4242
C17×#29292
#6027117