Finite Group Databasebeta

← C2×#14545650 #17980050

Subgroups — C2×#14545650 #17980050

Order 4352.

2306 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545650C2116yesmaximal, direct product factor
2C2×#11763844C211yesmaximal, characteristic, complemented
3C2×#11763842C211yesmaximal, characteristic, complemented
4C2×#11763841C211yesmaximal, characteristic, complemented
5C2×#11763840C211yesmaximal, characteristic, complemented
6C2×#11763840C211yesmaximal, characteristic, complemented
7C2×#11763838C211yesmaximal, characteristic, complemented
8C2×#11763836C211yesmaximal, characteristic, complemented
9C2×D4×#3624C211yesmaximal, characteristic, complemented
10C2×#11763833C211yesmaximal, characteristic, complemented
11C2×#11763833C211yesmaximal, characteristic, complemented
12C2×#11763783C211yesmaximal, characteristic, complemented
13C2×#11763782C211yesmaximal, characteristic, complemented
14C2×#11763779C211yesmaximal, characteristic, complemented
15C22×C22⋊#3624C211yesmaximal, characteristic, complemented
16C2×#11763315C211yesmaximal, characteristic
17C22×#63243C2211yescharacteristic, complemented
18C22×#63247C2211yescharacteristic
19C22×#63247C2211yescharacteristic
20C22×#63247C2211yescharacteristic, complemented
21C22×#63242C2211yescharacteristic, complemented
22C23×#3624C2211yescharacteristic
23C23×#3624C2211yescharacteristic
24C23×#3624C2211yescharacteristic, complemented
25#11763844C2218yescomplemented
26#11763842C2218yescomplemented
27#11763841C2218yescomplemented
28#11763840C2218yescomplemented
29#11763840C2218yescomplemented
30#11763838C2218yescomplemented
31#11763836C2218yescomplemented
32D4×#3624C2218yescomplemented
33#11763833C2218yescomplemented
34#11763833C2218yescomplemented
35C2×#10587544C2211yescharacteristic, complemented
36C2×#10587544C2211yescharacteristic, complemented
37C2×C4⋊#3624C2211yescharacteristic, complemented
38C2×C4⋊#3624C2211yescharacteristic, complemented
39#11763783C2218yescomplemented
40#11763782C2218yescomplemented
41#11763779C2218yescomplemented
42C2×#10587543C2211yescharacteristic, complemented
43C2×#10587543C2211yescharacteristic, complemented
44C2×C22⋊#3624C2211yescharacteristic
45C2×C22⋊#3624C2211yescharacteristic
46C2×C22⋊#3624C2211yescharacteristic
47C2×C22⋊#3624C2211yescharacteristic
48C2×C22⋊#3624C2211yescharacteristic
49C2×C22⋊#3624C2211yescharacteristic
50C2×C22⋊#3624C2211yescharacteristic
51C2×C22⋊#3624C2211yescharacteristic
52C2×C22⋊#3624C2218yescomplemented
53C2×C22⋊#3624C2211yescharacteristic, complemented
54C2×C22⋊#3624C2211yescharacteristic, complemented
55C2×#10587542C2211yescharacteristic, complemented
56C2×#10587542C2211yescharacteristic, complemented
57C2×C4×#3624C2211yescharacteristic, complemented
58C2×C4×#3624C2211yescharacteristic, complemented
59C22×#63254C2211yescharacteristic
60C24×Dic17C2211yescharacteristic
61#11763315C418yes—
62#11763315C2218yes—
63C2×#10587572C411yescharacteristic
64C2×#10587621C411yescharacteristic
65C2×#10587564C411yescharacteristic
66C2×#10587564C411yescharacteristic
67C2×#10587625C411yescharacteristic
68C2×#10587625C411yescharacteristic
69C2×#10587639C411yescharacteristic
70C2×D4×Dic17C2211yescharacteristic
71C2×D4×Dic17C2211yescharacteristic
72C2×#10587567C2211yescharacteristic
73C2×#10587567C2211yescharacteristic
74C2×#10587563C2211yescharacteristic
75C2×C17×#120C411yescharacteristic
76C25×C17C2×C411yescharacteristic
77C22×D4×C17C2×C411yescharacteristic
78C22×D4×C17C2×C411yescharacteristic
79C22×D4×C17C2×C411yescharacteristic
80C22×C22⋊D17C2×C411yescharacteristic
81C22×C22⋊D17C2×C411yescharacteristic
82C22×C22⋊D17C2×C411yescharacteristic
83C22×C22⋊D17C2×C411yescharacteristic
84C23×Dic17—42no—
85C23×Dic17—42no—
86C23×Dic17C2×C411yescharacteristic
87C23×Dic17C2×C411yescharacteristic
88C23×Dic17C2×C411yescharacteristic
89C23×Dic17C2×C414yes—
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C23×Dic17C2314yes—
95C2×#63254—42no—
96C2×#63254—42no—
97C2×#63254C2×C414yes—
98C2×#63254C2314yes—
99C22×C4×D17C2311yescharacteristic
100C22×Dic34C2×C411yescharacteristic
101C2×#63247—42no—
102C2×#63247—42no—
103C2×#63247—42no—
104C2×#63247C2314yes—
105C2×#63247C2314yes—
106C2×#63247C2314yescomplemented
107C22×#3624—42no—
108C22×#3624—42no—
109C22×#3624—42no—
110C22×#3624C2311yescharacteristic
111C22×#3624C2311yescharacteristic
112C22×#3624C2311yescharacteristic
113C22×#3624C2311yescharacteristic
114C22×#3624C2311yescharacteristic
115C22×#3624C2311yescharacteristic
116C22×#3624C2311yescharacteristic
117C22×#3624C2311yescharacteristic
118C22×#3624C2314yes—
119C22×#3624C2314yes—
120C22×#3624C2314yescomplemented
121C2×#63243—42no—
122C2×#63243C2314yescomplemented
123C2×#63242—42no—
124C2×#63242C2314yescomplemented
125C17×#120C2×C418yes—
126C2×C22⋊C4×C17C2×C411yescharacteristic
127C2×C22⋊C4×C17C2×C411yescharacteristic
128C2×C22⋊C4×C17C2×C411yescharacteristic
129#10587639C2×C418yes—
130C2×C22⋊Dic17C2×C411yescharacteristic
131C2×C22⋊Dic17C2×C411yescharacteristic
132C2×C22⋊Dic17C2×C411yescharacteristic
133C2×C22⋊Dic17C2×C411yescharacteristic
134C2×C22⋊Dic17C2×C411yescharacteristic
135#10587625C2×C418yes—
136#10587625C2×C418yes—
137#10587621C2×C418yes—
138D4×Dic17C2×C414yes—
139D4×Dic17C2×C414yes—
140D4×Dic17C2314yes—
141D4×Dic17C2314yes—
142C2×#63227C2×C411yescharacteristic
143C2×#63227C2×C411yescharacteristic
144C2×C4⋊Dic17C2×C411yescharacteristic
145C2×C4⋊Dic17C2×C411yescharacteristic
146C2×#63225C2×C411yescharacteristic
147C2×#63225C2×C411yescharacteristic
148C2×#63225C2×C411yescharacteristic
149C2×#63225C2×C411yescharacteristic
150C2×C4×Dic17C2311yescharacteristic
151C2×C4×Dic17C2311yescharacteristic
152#10587572C2×C418yes—
153#10587567C2×C414yes—
154#10587567C2×C414yes—
155#10587567C2314yes—
156#10587567C2314yes—
157#10587564C2×C418yes—
158#10587564C2×C418yes—
159#10587563C2×C414yes—
160#10587563C2314yes—
161C22⋊#3624C2314yes—
162C22⋊#3624C2314yes—
163C22⋊#3624C2314yes—
164C22⋊#3624C2314yes—
165C22⋊#3624C2314yes—
166C22⋊#3624C2314yes—
167C22⋊#3624C2314yes—
168C22⋊#3624C2314yes—
169C22⋊#3624C2314yescomplemented
170C22⋊#3624C2314yescomplemented
171#10587544C2314yescomplemented
172#10587544C2314yescomplemented
173#10587543C2314yescomplemented
174#10587543C2314yescomplemented
175#10587542C2314yescomplemented
176#10587542C2314yescomplemented
177C4⋊#3624C2314yescomplemented
178C4⋊#3624C2314yescomplemented
179C4×#3624C2314yescomplemented
180C4×#3624C2314yescomplemented
181C24×C17—24no—
182C24×C17—42no—
183C24×C17—42no—
184C24×C17C22×C411yescharacteristic
185C24×C17C22×C411yescharacteristic
186C24×C17C22×C411yescharacteristic
187C24×C17C22×C411yescharacteristic
188C24×C17C22×C414yes—
189C23×D17C22×C411yescharacteristic
190C2×D4×C17—24no—
191C2×D4×C17—42no—
192C2×D4×C17—42no—
193C2×D4×C17C22×C414yes—
194C2×D4×C17C22×C414yes—
195C2×D4×C17C22×C414yes—
196C22×C4×C17C22×C411yescharacteristic
197C22×C4×C17C22×C411yescharacteristic
198C22×C4×C17C22×C411yescharacteristic
199C2×C22⋊D17—24no—
200C2×C22⋊D17—42no—
201C2×C22⋊D17—42no—
202C2×C22⋊D17—42no—
203C2×C22⋊D17C22×C414yes—
204C2×C22⋊D17C22×C414yes—
205C2×C22⋊D17C22×C414yes—
206C2×C22⋊D17C22×C414yes—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—22no—
212C22×Dic17—22no—
213C22×Dic17—22no—
214C22×Dic17—22no—
215C22×Dic17—48no—
216C22×Dic17—44no—
217C22×Dic17—44no—
218C22×Dic17—42no—
219C22×Dic17—42no—
220C22×Dic17—42no—
221C22×Dic17C22×C411yescharacteristic
222C22×Dic17C22×C411yescharacteristic
223C22×Dic17C22×C412yes—
224C22×Dic17C22×C412yes—
225C22×Dic17C22×C412yes—
226C22×Dic17C22×C412yes—
227C22×Dic17C22×C411yescharacteristic
228C22×Dic17C22×C411yescharacteristic
229C22×Dic17C22×C411yescharacteristic
230C22×Dic17C22×C411yescharacteristic
231C22×Dic17C22×C414yes—
232C22×Dic17C22×C414yes—
233C22×Dic17C22×C414yes—
234C22×Dic17C2412yes—
235C22×Dic17C2412yes—
236C22×Dic17C2412yes—
237C22×Dic17C2412yes—
238C22×Dic17C2411yescharacteristic
239#63254—48no—
240#63254—44no—
241#63254—44no—
242C2×C4×D17—22no—
243C2×C4×D17—22no—
244C2×C4×D17C22×C412yes—
245C2×C4×D17C2412yes—
246C2×Dic34—42no—
247C2×Dic34C22×C414yes—
248#63247—44no—
249#63247—44no—
250#63247—44no—
251C2×#3624—22no—
252C2×#3624—22no—
253C2×#3624—22no—
254C2×#3624—22no—
255C2×#3624—22no—
256C2×#3624—22no—
257C2×#3624—22no—
258C2×#3624—22no—
259C2×#3624—44no—
260C2×#3624—44no—
261C2×#3624—44no—
262C2×#3624C2412yes—
263C2×#3624C2412yes—
264C2×#3624C2412yes—
265C2×#3624C2412yes—
266C2×#3624C2412yes—
267C2×#3624C2412yes—
268C2×#3624C2412yes—
269C2×#3624C2412yes—
270#63243—44no—
271#63242—44no—
272C22⋊C4×C17C22×C414yes—
273C22⋊C4×C17C22×C414yes—
274C22⋊C4×C17C22×C414yes—
275C22⋊Dic17C22×C414yes—
276C22⋊Dic17C22×C414yes—
277C22⋊Dic17C22×C414yes—
278C22⋊Dic17C22×C414yes—
279C22⋊Dic17C22×C414yes—
280#63227C22×C414yes—
281#63227C22×C414yes—
282C4⋊Dic17C22×C414yes—
283C4⋊Dic17C22×C414yes—
284#63225C22×C414yes—
285#63225C22×C414yes—
286#63225C22×C414yes—
287#63225C22×C414yes—
288C4×Dic17C22×C412yes—
289C4×Dic17C22×C412yes—
290C4×Dic17C2412yes—
291C4×Dic17C2412yes—
292C2×#2976—171nomaximal, Sylow
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—22no—
298C23×C17—22no—
299C23×C17—28no—
300C23×C17—22no—
301C23×C17—22no—
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
305C23×C17—44no—
306C23×C17—44no—
307C23×C17—416no—
308C23×C17#13114yes—
309C23×C17C23×C412yes—
310C23×C17C23×C412yes—
311C23×C17C23×C412yes—
312C23×C17C23×C412yes—
313C23×C17C23×C411yescharacteristic
314C22×D17—22no—
315C22×D17—22no—
316C22×D17—22no—
317C22×D17C23×C412yes—
318D4×C17—28no—
319D4×C17—44no—
320D4×C17—44no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17C23×C412yes—
325C2×C4×C17C23×C412yes—
326C2×C4×C17C23×C412yes—
327C22⋊D17—28no—
328C22⋊D17—44no—
329C22⋊D17—44no—
330C22⋊D17—44no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—22no—
336C2×Dic17—22no—
337C2×Dic17—24no—
338C2×Dic17—24no—
339C2×Dic17—24no—
340C2×Dic17—24no—
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—22no—
344C2×Dic17—22no—
345C2×Dic17—22no—
346C2×Dic17—22no—
347C2×Dic17—22no—
348C2×Dic17—22no—
349C2×Dic17—44no—
350C2×Dic17—44no—
351C2×Dic17—44no—
352C2×Dic17C23×C412yes—
353C2×Dic17C23×C412yes—
354C2×Dic17C23×C412yes—
355C2×Dic17C23×C412yes—
356C2×Dic17C23×C412yes—
357C2×Dic17C23×C412yes—
358C2×Dic17C23×C411yescharacteristic
359C2×Dic17H(5,𝔽2)12yes—
360C2×Dic17H(5,𝔽2)12yes—
361C2×Dic17C2511yescharacteristic
362C4×D17—24no—
363C4×D17—22no—
364C4×D17—22no—
365Dic34—44no—
366#3624—22no—
367#3624—22no—
368#3624—22no—
369#3624—22no—
370#3624—22no—
371#3624—22no—
372#3624—22no—
373#3624—22no—
374C2×#525—171no—
375#2976—1716no—
376C2×#436—171no—
377C2×#436—171no—
378C2×#435—171no—
379C2×#435—171no—
380C2×#435—171no—
381C2×#435—171no—
382C2×C8×D4—171no—
383C2×C8×D4—171no—
384C2×#433—171no—
385C2×#433—171no—
386C2×#408—171no—
387C2×#408—171no—
388C2×#407—171no—
389C22×C22⋊C8—171no—
390C22×C17—22no—
391C22×C17—28no—
392C22×C17—22no—
393C22×C17—22no—
394C22×C17—22no—
395C22×C17—22no—
396C22×C17—22no—
397C22×C17—22no—
398C22×C17—22no—
399C22×C17—22no—
400C22×C17—22no—
401C22×C17—22no—
402C22×C17—416no—
403C22×C17—44no—
404C22×C17—44no—
405C22×C17—44no—
406C22×C17#51812yes—
407C22×C17C2×#13114yes—
408C22×C17C2×#13112yes—
409C22×C17#56812yes—
410C22×C17C24×C411yescharacteristic
411C2×D17—22no—
412C2×D17—22no—
413C2×D17—22no—
414C2×D17—44no—
415C4×C17—22no—
416C4×C17—22no—
417C4×C17—22no—
418Dic17—22no—
419Dic17—22no—
420Dic17—22no—
421Dic17—22no—
422Dic17—22no—
423Dic17—22no—
424Dic17#51812yes—
425Dic17C2×H(5,𝔽2)11yescharacteristic
426Dic17C2×H(5,𝔽2)11yescharacteristic
427C22×#41—171no—
428C24×C4—171no—
429C22×M16—171no—
430C22×M16—171no—
431C22×M16—171no—
432C22×M16—171no—
433C23×C8—171no—
434C23×C8—171no—
435C23×C8—171no—
436C23×C8—171no—
437#525—178no—
438#525—178no—
439C2×#123—171no—
440C2×#123—171no—
441C2×C22⋊Q8—171no—
442C2×C22⋊Q8—171no—
443C2×#121—171no—
444C2×#121—171no—
445C2×#120—171no—
446C2×#120#59511yescharacteristic
447C2×C4×D4—171no—
448C2×C4×D4—171no—
449C2×C4×D4—171no—
450C2×C4×D4—171no—
451C2×#117—171no—
452#436—178no—
453#436—178no—
454#435—178no—
455#435—178no—
456#435—178no—
457#435—178no—
458C8×D4—178no—
459C8×D4—178no—
460#433—178no—
461#433—178no—
462C2×C4⋊C8—171no—
463C2×C4⋊C8—171no—
464C2×C4⋊C8—171no—
465C2×C4⋊C8—171no—
466#408—178no—
467#408—178no—
468#407—178no—
469C2×C22⋊C8—171no—
470C2×C22⋊C8—171no—
471C2×C22⋊C8—171no—
472C2×C22⋊C8—171no—
473C2×C22⋊C8—178no—
474C2×C22⋊C8—171no—
475C2×C22⋊C8—171no—
476C2×C22⋊C8—171no—
477C2×C22⋊C8—171no—
478C2×C22⋊C8—171no—
479C2×C22⋊C8—171no—
480C2×C22⋊C8—171no—
481C2×C22⋊C8—171no—
482C2×#97—171no—
483C2×#97—171no—
484C2×C4×C8—171no—
485C2×C4×C8—171no—
486C2×C17—24no—
487C2×C17—42no—
488C2×C17—42no—
489C2×C17—42no—
490C2×C17#297614yescomplemented
491C2×C17C2×#51811yescharacteristic
492C2×C17C22×#13111yescharacteristic
493C2×C17C2×#56811yescharacteristic
494D17—42no—
495C25C2×#59511yescharacteristic
496C2×#41—174no—
497C2×#41—174no—
498C2×#41—682no—
499C2×#41—682no—
500C22×Q8—171no—
501C22×D4—171no—
502C22×D4—171no—
503C22×D4—171no—
504C22×D4—171no—
505C22×D4C2×#59511yescharacteristic
506C22×D4C2×#59511yescharacteristic
507C22×D4C2×#59511yescharacteristic
508C23×C4—171no—
509C23×C4—171no—
510C23×C4—171no—
511C23×C4—171no—
512C23×C4—171no—
513C23×C4—171no—
514C23×C4—171no—
515C23×C4—174no—
516C23×C4—174no—
517C23×C4—171no—
518C23×C4—682no—
519C23×C4—682no—
520C2×M16—174no—
521C2×M16—174no—
522C2×M16—174no—
523C2×M16—174no—
524C2×M16—682no—
525C2×M16—682no—
526C2×M16—682no—
527C2×M16—682no—
528C22×C8—171no—
529C22×C8—171no—
530C22×C8—171no—
531C22×C8—171no—
532C22×C8—171no—
533C22×C8—171no—
534C22×C8—171no—
535C22×C8—171no—
536C22×C8—174no—
537C22×C8—174no—
538C22×C8—174no—
539C22×C8—174no—
540C22×C8—682no—
541C22×C8—682no—
542C22×C8—682no—
543C22×C8—682no—
544#123—178no—
545#123—178no—
546C22⋊Q8—178no—
547C22⋊Q8—178no—
548#121—178no—
549#121—178no—
550#120—178no—
551#120C2×#59518yes—
552C4×D4—174no—
553C4×D4—174no—
554C4×D4—174no—
555C4×D4—174no—
556C4×D4—174no—
557C4×D4—174no—
558C4×D4—174no—
559C4×D4—174no—
560#117—174no—
561#117—174no—
562C2×C4⋊C4—171no—
563C2×C4⋊C4—171no—
564C2×C4⋊C4—171no—
565C2×C4⋊C4—171no—
566C2×C4⋊C4—171no—
567C2×C4⋊C4—171no—
568C2×C22⋊C4—171no—
569C2×C22⋊C4—171no—
570C2×C22⋊C4—171no—
571C2×C22⋊C4—171no—
572C2×C22⋊C4—171no—
573C2×C22⋊C4—171no—
574C2×C22⋊C4—171no—
575C2×C22⋊C4C2×#59511yescharacteristic
576C2×C22⋊C4C2×#59511yescharacteristic
577C2×C22⋊C4C2×#59511yescharacteristic
578C2×C42—171no—
579C2×C42—171no—
580C4⋊C8—174no—
581C4⋊C8—174no—
582C4⋊C8—174no—
583C4⋊C8—174no—
584C22⋊C8—174no—
585C22⋊C8—174no—
586C22⋊C8—174no—
587C22⋊C8—174no—
588C22⋊C8—174no—
589C22⋊C8—174no—
590C22⋊C8—174no—
591C22⋊C8—174no—
592C22⋊C8—174no—
593C22⋊C8—174no—
594C22⋊C8—174no—
595C22⋊C8—174no—
596#97—174no—
597#97—174no—
598C4×C8—174no—
599C4×C8—174no—
600C17C2×#297611yescharacteristic, complemented, Sylow
601C24—24no—
602C24—42no—
603C24—42no—
604C24—171no—
605C24C22×#59511yescharacteristic
606C24C22×#59511yescharacteristic
607C24C22×#59511yescharacteristic
608C24C22×#59511yescharacteristic
609C24C22×#59514yes—
610#41—684no—
611#41—684no—
612#41—688no—
613C2×Q8—174no—
614C2×Q8—682no—
615C2×D4—24no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—174no—
619C2×D4—174no—
620C2×D4—174no—
621C2×D4—174no—
622C2×D4—344no—
623C2×D4—682no—
624C2×D4—682no—
625C2×D4—682no—
626C2×D4C22×#59514yes—
627C2×D4C22×#59514yes—
628C2×D4C22×#59514yes—
629C22×C4—171no—
630C22×C4—172no—
631C22×C4—172no—
632C22×C4—172no—
633C22×C4—172no—
634C22×C4—172no—
635C22×C4—172no—
636C22×C4—172no—
637C22×C4—172no—
638C22×C4—171no—
639C22×C4—171no—
640C22×C4—171no—
641C22×C4—171no—
642C22×C4—171no—
643C22×C4—171no—
644C22×C4—174no—
645C22×C4—174no—
646C22×C4—174no—
647C22×C4—172no—
648C22×C4—172no—
649C22×C4—342no—
650C22×C4—342no—
651C22×C4—342no—
652C22×C4—342no—
653C22×C4—342no—
654C22×C4—342no—
655C22×C4—342no—
656C22×C4—342no—
657C22×C4—342no—
658C22×C4—342no—
659C22×C4—684no—
660C22×C4—684no—
661C22×C4—688no—
662C22×C4—682no—
663C22×C4—682no—
664C22×C4—682no—
665C22×C4C22×#59511yescharacteristic
666C22×C4C22×#59511yescharacteristic
667C22×C4C22×#59511yescharacteristic
668M16—684no—
669M16—684no—
670M16—684no—
671M16—684no—
672C2×C8—172no—
673C2×C8—172no—
674C2×C8—172no—
675C2×C8—172no—
676C2×C8—172no—
677C2×C8—172no—
678C2×C8—172no—
679C2×C8—172no—
680C2×C8—342no—
681C2×C8—342no—
682C2×C8—342no—
683C2×C8—342no—
684C2×C8—342no—
685C2×C8—342no—
686C2×C8—342no—
687C2×C8—342no—
688C2×C8—684no—
689C2×C8—684no—
690C2×C8—684no—
691C2×C8—684no—
692C4⋊C4—174no—
693C4⋊C4—174no—
694C4⋊C4—174no—
695C4⋊C4—174no—
696C4⋊C4—174no—
697C4⋊C4—174no—
698C22⋊C4—174no—
699C22⋊C4—174no—
700C22⋊C4—174no—
701C22⋊C4—174no—
702C22⋊C4—174no—
703C22⋊C4—174no—
704C22⋊C4—174no—
705C22⋊C4C22×#59514yes—
706C22⋊C4C22×#59514yes—
707C22⋊C4C22×#59514yes—
708C42—172no—
709C42—172no—
710C42—172no—
711C42—172no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—44no—
725C23—44no—
726C23—416no—
727C23—172no—
728C23—342no—
729C23—342no—
730C23—342no—
731C23#1058767814yes—
732C23C23×#59512yes—
733C23C23×#59512yes—
734C23C23×#59512yes—
735C23C23×#59512yes—
736C23C23×#59511yescharacteristic
737Q8—684no—
738D4—28no—
739D4—44no—
740D4—44no—
741D4—348no—
742D4—684no—
743D4—684no—
744D4—684no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—172no—
749C2×C4—172no—
750C2×C4—171no—
751C2×C4—171no—
752C2×C4—172no—
753C2×C4—172no—
754C2×C4—172no—
755C2×C4—172no—
756C2×C4—172no—
757C2×C4—172no—
758C2×C4—342no—
759C2×C4—342no—
760C2×C4—344no—
761C2×C4—342no—
762C2×C4—342no—
763C2×C4—342no—
764C2×C4—342no—
765C2×C4—342no—
766C2×C4—342no—
767C2×C4—342no—
768C2×C4—342no—
769C2×C4—344no—
770C2×C4—344no—
771C2×C4—344no—
772C2×C4—344no—
773C2×C4—342no—
774C2×C4—342no—
775C2×C4—342no—
776C2×C4—342no—
777C2×C4—342no—
778C2×C4—342no—
779C2×C4—684no—
780C2×C4—684no—
781C2×C4—684no—
782C2×C4C23×#59512yes—
783C2×C4C23×#59512yes—
784C2×C4C23×#59512yes—
785C8—342no—
786C8—342no—
787C8—342no—
788C8—342no—
789C8—342no—
790C8—342no—
791C8—342no—
792C8—342no—
793C22—22no—
794C22—22no—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—416no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—342no—
810C22—342no—
811C22—342no—
812C22—684no—
813C22#1176387612yes—
814C22C2×#1058767814yes—
815C22C2×#1058767812yes—
816C22#1176388712yes—
817C22C24×#59511yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—171no—
822C4—171no—
823C4—172no—
824C4—342no—
825C4—342no—
826C4—342no—
827C4—342no—
828C4—342no—
829C4—342no—
830C2—24no—
831C2—42no—
832C2—42no—
833C2—42no—
834C2—682no—
835C2#1454565014yesdirect product factor
836C2C2×#1176387611yescharacteristic
837C2C22×#1058767811yescharacteristic
838C2C2×#1176388711yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#120C4
socleC23×C17C23×C4
prime radicalC2×#11763315C2
cosocleC2×Dic17C25
hypercenterC2×#120#595
hypocenterC17C2×#2976
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #14545650C2direct (N × H)
2. C2×#11763844C2semidirect
3. C2×#11763842C2semidirect
4. C2×#11763841C2semidirect
5. C2×#11763840C2semidirect
6. C2×#11763840C2semidirect
7. C2×#11763838C2semidirect
8. C2×#11763836C2semidirect
9. C2×D4×#3624C2semidirect
10. C2×#11763833C2semidirect
11. C2×#11763833C2semidirect
12. C2×#11763783C2semidirect
13. C2×#11763782C2semidirect
14. C2×#11763779C2semidirect
15. C22×C22⋊#3624C2semidirect
17. C22×#63243C22semidirect
20. C22×#63247C22semidirect
21. C22×#63242C22semidirect
24. C23×#3624C22semidirect
25. #11763844C22semidirect
26. #11763842C22semidirect
27. #11763841C22semidirect
28. #11763840C22semidirect
29. #11763840C22semidirect
30. #11763838C22semidirect
31. #11763836C22semidirect
32. D4×#3624C22semidirect
33. #11763833C22semidirect
34. #11763833C22semidirect
35. C2×#10587544C22semidirect
36. C2×#10587544C22semidirect
37. C2×C4⋊#3624C22semidirect
38. C2×C4⋊#3624C22semidirect
39. #11763783C22semidirect
40. #11763782C22semidirect
41. #11763779C22semidirect
42. C2×#10587543C22semidirect
43. C2×#10587543C22semidirect
52. C2×C22⋊#3624C22semidirect
53. C2×C22⋊#3624C22semidirect
54. C2×C22⋊#3624C22semidirect
55. C2×#10587542C22semidirect
56. C2×#10587542C22semidirect
57. C2×C4×#3624C22semidirect
58. C2×C4×#3624C22semidirect
106. C2×#63247C23semidirect
120. C22×#3624C23semidirect
122. C2×#63243C23semidirect
124. C2×#63242C23semidirect
169. C22⋊#3624C23semidirect
170. C22⋊#3624C23semidirect
171. #10587544C23semidirect
172. #10587544C23semidirect
173. #10587543C23semidirect
174. #10587543C23semidirect
175. #10587542C23semidirect
176. #10587542C23semidirect
177. C4⋊#3624C23semidirect
178. C4⋊#3624C23semidirect
179. C4×#3624C23semidirect
180. C4×#3624C23semidirect
490. C2×C17#2976semidirect
600. C17C2×#2976semidirect
835. C2#14545650direct (N × H)

Maximal subgroups

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

subgroupindex
#145456502
C2×#117638442
C2×#117638422
C2×#117638412
C2×#117638402
C2×#117638382
C2×#117638362
C2×D4×#36242
C2×#117638332
C2×#117637832
C2×#117637822
C2×#117637792
C22×C22⋊#36242
C2×#117633152
C2×#297617