Finite Group Databasebeta

← C2×#14542552 #17942498

Subgroups — C2×#14542552 #17942498

Order 4352.

11210 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587694C211yesmaximal, characteristic, complemented
2C22×#10587697C211yesmaximal, characteristic, complemented
3#14542552C2132yesmaximal, direct product factor
4C2×#11763478C211yesmaximal, characteristic, complemented
5C2×#11763477C213yesmaximal, complemented
6C2×Q8×C22⋊D17C211yesmaximal, characteristic, complemented
7C2×#11763472C213yesmaximal, complemented
8C2×#11763471C211yesmaximal, characteristic, complemented
9C2×#11763468C213yesmaximal, complemented
10C2×#11763467C213yesmaximal, complemented
11C2×#11763389C213yesmaximal, complemented
12C2×#11763388C213yesmaximal, complemented
13C2×#11763358C213yesmaximal, complemented
14C2×#11763356C213yesmaximal, complemented
15C2×C4×Q8×D17C211yesmaximal, characteristic, complemented
16C2×C17×#548C211yesmaximal, characteristic, complemented
17C2×#10587694—216no—
18C2×#10587694C22116yescomplemented
19C2×#10587697—216no—
20C2×#10587697C22116yescomplemented
21C22×#63256C2213yes—
22C22×#63256C2211yescharacteristic
23C22×#63252C2213yes—
24C22×#63252C2213yes—
25C22×#63252C2213yes—
26C22×#63254C2213yes—
27C22×#63254C2213yes—
28C23×Dic34C2213yes—
29C22×Q8×D17C2213yes—
30C22×Q8×D17C2211yescharacteristic
31C22×Q8×D17C2211yescharacteristic
32#11763478C22116yescomplemented
33#11763477C22148yescomplemented
34Q8×C22⋊D17C22116yescomplemented
35#11763472C22148yescomplemented
36#11763471C22116yescomplemented
37#11763468C22148yescomplemented
38#11763467C22148yescomplemented
39#11763389C22148yescomplemented
40#11763388C22148yescomplemented
41#11763358C22148yescomplemented
42#11763356C22148yescomplemented
43C2×#10587574C2213yes—
44C2×#10587630C2213yes—
45C2×#10587626C2213yes—
46C2×#10587626C2213yes—
47C2×#10587561C2213yes—
48C2×#10587571C2213yes—
49C2×#10587571C2213yes—
50C2×#10587583C2213yes—
51C2×#10587610C2213yes—
52C2×#10587582C2216yes—
53C2×#10587564C2216yes—
54C2×#10587632C2213yes—
55C2×#10587581C2213yes—
56C2×#10587581C2213yes—
57C2×#10587616C2213yes—
58C2×#10587570C2216yes—
59C2×#10587570C2216yes—
60C2×#10587570C2211yescharacteristic
61C2×#10587570C2213yes—
62C2×#10587625C2216yes—
63C2×#10587624C2213yes—
64C2×#10587624C2213yes—
65C2×Q8×Dic17C2211yescharacteristic
66C2×C4×Dic34C2213yes—
67C2×#10587573C2213yes—
68C4×Q8×D17C22116yescomplemented
69C2×C4×D68C2213yes—
70C2×C4×C22⋊D17C2213yes—
71C2×C4×C22⋊D17C2213yes—
72C2×#10587567C2216yes—
73C2×#10587567C2216yes—
74C2×C4⋊C4×D17C2213yes—
75C2×C42×D17C2213yes—
76C22×#41×C17C2211yescharacteristic
77C23×Q8×C17C2211yescharacteristic
78C17×#548C22116yescomplemented
79C2×C17×#124C2213yes—
80C2×C17×C22⋊Q8C2213yes—
81C2×C17×#121C2213yes—
82C2×C4×Q8×C17C2211yescharacteristic
83C2×C4×D4×C17C2213yes—
84C2×#41×C17—28no—
85C2×#41×C17C2318yes—
86C22×Q8×C17—28no—
87C22×Q8×C17C2318yes—
88C22×Q8×C17C2313yes—
89C22×Q8×C17C2311yescharacteristic
90C22×D4×C17C2313yes—
91C22×D4×C17C2313yes—
92C23×C4×C17C2313yes—
93C23×C4×C17C2313yes—
94C22×C22⋊D17C2313yes—
95C22×C22⋊D17C2311yescharacteristic
96C22×C22⋊D17C2311yescharacteristic
97C22×C22⋊D17C2313yes—
98C22×C22⋊D17C2313yes—
99C22×C22⋊D17C2313yes—
100C22×C22⋊D17C2316yes—
101C23×Dic17C2316yes—
102#10587697—2128no—
103#10587694—2128no—
104C2×#63256—28no—
105C2×#63256—224no—
106C2×#63256C2318yes—
107C2×#63256C23124yes—
108C2×Q8×D17—28no—
109C2×Q8×D17—224no—
110C2×Q8×D17D4116yescomplemented
111C2×Q8×D17C23124yes—
112C2×Q8×D17C2318yes—
113C2×Q8×D17C2318yes—
114C2×#63254—224no—
115C2×#63254—224no—
116C2×#63254C23124yes—
117C2×#63254C23124yes—
118C2×#63252—224no—
119C2×#63252—224no—
120C2×#63252—224no—
121C2×#63252C23124yes—
122C2×#63252C23124yes—
123C2×#63252C23124yes—
124C22×D68C2313yes—
125C22×D68C2311yescharacteristic
126C22×D68C2313yes—
127C22×D68C2313yes—
128C22×C4×D17C2311yescharacteristic
129C22×C4×D17C2316yes—
130C22×C4×D17C2313yes—
131C22×C4×D17C2313yes—
132C22×C4×D17C2313yes—
133C22×C4×D17C2313yes—
134C22×Dic34—224no—
135C22×Dic34C23124yes—
136C22×Dic34C2313yes—
137C22×Dic34C2313yes—
138C22×Dic34C2313yes—
139C22×Dic34C2313yes—
140C17×#124C23124yes—
141C17×C22⋊Q8C23124yes—
142C17×#121C23124yes—
143C4×Q8×C17C2318yes—
144C4×D4×C17C23124yes—
145C2×C4⋊C4×C17C2313yes—
146C2×C4⋊C4×C17C2313yes—
147C2×C22⋊C4×C17C2311yescharacteristic
148C2×C22⋊C4×C17C2313yes—
149C2×C22⋊C4×C17C2316yes—
150C2×C42×C17C2313yes—
151C2×C22⋊Dic17C2313yes—
152C2×C22⋊Dic17C2313yes—
153#10587632C23124yes—
154Q8×Dic17C2318yes—
155#10587630C23124yes—
156#10587626C23124yes—
157#10587626C23124yes—
158#10587625C23148yes—
159#10587624C23124yes—
160#10587624C23124yes—
161#10587616C23124yes—
162C4×C22⋊D17C23124yes—
163C4×C22⋊D17C23124yes—
164C2×#63227C2313yes—
165C2×#63227C2316yes—
166C2×#63227C2313yes—
167C2×#63227C2313yes—
168C2×#63227C2311yescharacteristic
169C2×C4⋊Dic17C2313yes—
170C2×C4⋊Dic17C2313yes—
171#10587610C23124yes—
172C2×#63225C2316yes—
173C2×#63225C2313yes—
174C2×#63225C2316yes—
175C2×#63225C2311yescharacteristic
176C2×C4×Dic17C2313yes—
177C2×C4×Dic17C2313yes—
178C2×C4×Dic17C2313yes—
179#10587583C23124yes—
180#10587582C23148yes—
181#10587581C23124yes—
182#10587581C23124yes—
183C4⋊C4×D17C23124yes—
184#10587574C23124yes—
185#10587573C23124yes—
186#10587571C23124yes—
187#10587571C23124yes—
188#10587570C23148yes—
189#10587570C2318yes—
190#10587570C23124yes—
191#10587570C23148yes—
192#10587567C23148yes—
193#10587567C23148yes—
194#10587564C23148yes—
195#10587561C23124yes—
196C4×D68C23124yes—
197C42×D17C23124yes—
198C4×Dic34C23124yes—
199C24×C17C2413yes—
200C24×C17C2411yescharacteristic
201C23×D17C2413yes—
202C23×D17C2411yescharacteristic
203C23×D17C2411yescharacteristic
204#41×C17—232no—
205C2×Q8×C17—232no—
206C2×Q8×C17—212no—
207C2×Q8×C17C2×D418yes—
208C2×Q8×C17C24112yes—
209C2×Q8×C17C2414yes—
210C2×D4×C17—212no—
211C2×D4×C17—46no—
212C2×D4×C17C24112yes—
213C2×D4×C17C24112yes—
214C22×C4×C17—212no—
215C22×C4×C17—212no—
216C22×C4×C17C24112yes—
217C22×C4×C17C2411yescharacteristic
218C22×C4×C17C2413yes—
219C22×C4×C17C2413yes—
220C22×C4×C17C2411yescharacteristic
221C22×C4×C17C24112yes—
222C22×C4×C17C2413yes—
223C2×C22⋊D17—24no—
224C2×C22⋊D17—212no—
225C2×C22⋊D17—212no—
226C2×C22⋊D17—212no—
227C2×C22⋊D17—212no—
228C2×C22⋊D17—24no—
229C2×C22⋊D17—412no—
230C2×C22⋊D17C2414yes—
231C2×C22⋊D17C24112yes—
232C2×C22⋊D17C24112yes—
233C2×C22⋊D17C24112yes—
234C2×C22⋊D17C24112yes—
235C2×C22⋊D17C2414yes—
236C2×C22⋊D17C24124yes—
237C22×Dic17—224no—
238C22×Dic17C2411yescharacteristic
239C22×Dic17C2413yes—
240C22×Dic17C24124yes—
241C22×Dic17C2413yes—
242C22×Dic17C2413yes—
243C22×Dic17C2411yescharacteristic
244#63256—232no—
245#63256—296no—
246Q8×D17—232no—
247Q8×D17—296no—
248Q8×D17C2×D4164yescomplemented
249#63254—296no—
250#63254—296no—
251#63252—296no—
252#63252—296no—
253#63252—296no—
254C2×D68—24no—
255C2×D68—212no—
256C2×D68—212no—
257C2×D68—46no—
258C2×D68C2414yes—
259C2×D68C24112yes—
260C2×D68C24112yes—
261C2×D68C24112yes—
262C2×C4×D17—212no—
263C2×C4×D17—212no—
264C2×C4×D17—224no—
265C2×C4×D17—24no—
266C2×C4×D17—46no—
267C2×C4×D17C2×D4124yes—
268C2×C4×D17C24112yes—
269C2×C4×D17C24112yes—
270C2×C4×D17C24124yes—
271C2×C4×D17C2414yes—
272C2×C4×D17C24112yes—
273C2×C4×D17C24112yes—
274C2×Dic34—212no—
275C2×Dic34—212no—
276C2×Dic34—212no—
277C2×Dic34—296no—
278C2×Dic34C2×D4124yes—
279C2×Dic34C24112yes—
280C2×Dic34C24112yes—
281C2×Dic34C24112yes—
282C2×Dic34C24112yes—
283C4⋊C4×C17C24112yes—
284C4⋊C4×C17C24112yes—
285C22⋊C4×C17C24124yes—
286C22⋊C4×C17C24112yes—
287C22⋊C4×C17C2414yes—
288C42×C17C24112yes—
289C22⋊Dic17C24112yes—
290C22⋊Dic17C24112yes—
291#63227C2414yes—
292#63227C24112yes—
293#63227C24124yes—
294#63227C24112yes—
295#63227C24112yes—
296C4⋊Dic17C24112yes—
297C4⋊Dic17C24112yes—
298#63225C24124yes—
299#63225C24124yes—
300#63225C24112yes—
301#63225C2414yes—
302C4×Dic17C24112yes—
303C4×Dic17C24112yes—
304C4×Dic17C24112yes—
305C2×#3497—171nomaximal, Sylow
306C23×C17—26no—
307C23×C17—22no—
308C23×C17—26no—
309C23×C17—22no—
310C23×C17—26no—
311C23×C17—22no—
312C23×C17C2512yes—
313C23×C17C2516yes—
314C23×C17C2511yescharacteristic
315C22×D17—22no—
316C22×D17—22no—
317C22×D17—26no—
318C22×D17—22no—
319C22×D17—26no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—26no—
323C22×D17C22×D414yes—
324C22×D17C2516yes—
325C22×D17C2512yes—
326C22×D17C2512yes—
327Q8×C17—224no—
328Q8×C17C22×D4116yes—
329D4×C17—224no—
330D4×C17—412no—
331C2×C4×C17—22no—
332C2×C4×C17—26no—
333C2×C4×C17—22no—
334C2×C4×C17—26no—
335C2×C4×C17—224no—
336C2×C4×C17—224no—
337C2×C4×C17C22×D4112yes—
338C2×C4×C17C2512yes—
339C2×C4×C17C2516yes—
340C2×C4×C17C2516yes—
341C2×C4×C17C2512yes—
342C2×C4×C17C2516yes—
343C22⋊D17—28no—
344C22⋊D17—224no—
345C22⋊D17—224no—
346C22⋊D17—224no—
347C22⋊D17—224no—
348C22⋊D17—28no—
349C22⋊D17—424no—
350C2×Dic17—22no—
351C2×Dic17—26no—
352C2×Dic17—26no—
353C2×Dic17—248no—
354C2×Dic17C22×D4112yes—
355C2×Dic172−1+414yescomplemented
356C2×Dic17C2512yes—
357C2×Dic17C2516yes—
358C2×Dic17C2516yes—
359C2×Dic17C2516yes—
360C2×Dic17C2512yes—
361D68—28no—
362D68—224no—
363D68—224no—
364D68—412no—
365C4×D17—224no—
366C4×D17—224no—
367C4×D17—248no—
368C4×D17—28no—
369C4×D17—412no—
370C4×D17C22×D4148yes—
371Dic34—224no—
372Dic34—224no—
373Dic34—224no—
374Dic34C22×D4148yes—
375C22×2−1+4—171no—
376C22×2−1+4—171no—
377#3497—1732no—
378C2×#550—171no—
379C2×#550—173no—
380C2×D4×Q8—171no—
381C2×D4×Q8—173no—
382C2×#548—173no—
383C2×#548—171no—
384C2×#548—173no—
385C2×#548D1711yescharacteristic, complemented
386C2×#537—173no—
387C2×#537—173no—
388C2×#532—173no—
389C2×#532—173no—
390C22×C4×Q8—171no—
391C22×C17—26no—
392C22×C17—22no—
393C22×C17—22no—
394C22×C17—26no—
395C22×C17—26no—
396C22×C17—22no—
397C22×C17—412no—
398C22×C17—44no—
399C22×C17C23×D412yes—
400C22×C17C2×2−1+412yes—
401C22×C17#58512yes—
402C22×C17C2611yescharacteristic
403C2×D17—22no—
404C2×D17—22no—
405C2×D17—28no—
406C2×D17—26no—
407C2×D17—22no—
408C2×D17—26no—
409C2×D17—22no—
410C2×D17—22no—
411C2×D17—26no—
412C2×D17—412no—
413C2×D17—44no—
414C2×D17C23×D414yes—
415C4×C17—22no—
416C4×C17—26no—
417C4×C17—22no—
418C4×C17—26no—
419C4×C17C23×D4112yes—
420Dic17—22no—
421Dic17—26no—
422Dic17—26no—
423Dic17C23×D4112yes—
424Dic17C2×2−1+414yescomplemented
425C2×2−1+4—1716no—
426C2×2−1+4—1716no—
427C2×2−1+4—3416no—
428C2×2−1+4—3416no—
429C22×#41—173no—
430C22×#41—171no—
431C22×#41—173no—
432C22×#41—173no—
433C22×#41—173no—
434C22×#41—173no—
435C22×#41—173no—
436C22×#41C2×D1711yescharacteristic
437C23×Q8—171no—
438C23×Q8—173no—
439C23×Q8—171no—
440C23×Q8—173no—
441C23×Q8C2×D1711yescharacteristic
442#550—1716no—
443#550—1748no—
444D4×Q8—1716no—
445D4×Q8—1748no—
446#548—1748no—
447#548—1716no—
448#548—1748no—
449#548C2×D17116yescomplemented
450#537—1748no—
451#537—1748no—
452#532—1748no—
453#532—1748no—
454C2×C4⋊Q8—173no—
455C2×C4⋊Q8—173no—
456C2×#127—173no—
457C2×#127—173no—
458C2×#124—173no—
459C2×#124—173no—
460C2×#124—173no—
461C2×#124C2×D1713yes—
462C2×C22⋊Q8—173no—
463C2×C22⋊Q8—173no—
464C2×C22⋊Q8—176no—
465C2×C22⋊Q8—173no—
466C2×C22⋊Q8—176no—
467C2×C22⋊Q8C2×D1713yes—
468C2×#121—173no—
469C2×#121—173no—
470C2×#121—176no—
471C2×#121—173no—
472C2×#121—173no—
473C2×#121—173no—
474C2×#121—173no—
475C2×#121—171no—
476C2×#121—176no—
477C2×#121—176no—
478C2×#121C2×D1713yes—
479C2×C4×Q8—171no—
480C2×C4×Q8—1716no—
481C2×C4×Q8—173no—
482C2×C4×Q8—173no—
483C2×C4×Q8C2×D1711yescharacteristic
484C2×C4×D4—173no—
485C2×C4×D4—173no—
486C2×C4×D4—176no—
487C2×C4×D4—176no—
488C2×C4×D4—173no—
489C2×C4×D4C2×D1713yes—
490C22×C4⋊C4—173no—
491C22×C42—173no—
492C2×C17—46no—
493C2×C17—42no—
494C2×C17#349714yescomplemented
495C2×C17C24×D411yescharacteristic
496C2×C17C22×2−1+411yescharacteristic
497C2×C17C2×#58511yescharacteristic
498D17—24no—
499D17—46no—
500D17—42no—
5012−1+4—34128no—
5022−1+4—34128no—
503C2×#41—28no—
504C2×#41—1724no—
505C2×#41—178no—
506C2×#41—1724no—
507C2×#41—1724no—
508C2×#41—1724no—
509C2×#41—1724no—
510C2×#41—1724no—
511C2×#41—3424no—
512C2×#41—3424no—
513C2×#41—3424no—
514C2×#41—3424no—
515C2×#41—3424no—
516C2×#41—3424no—
517C2×#41—348no—
518C2×#41C22×D1718yes—
519C22×Q8—28no—
520C22×Q8—1716no—
521C22×Q8—178no—
522C22×Q8—1724no—
523C22×Q8—178no—
524C22×Q8—173no—
525C22×Q8—173no—
526C22×Q8—173no—
527C22×Q8—173no—
528C22×Q8—1724no—
529C22×Q8—3424no—
530C22×Q8—3424no—
531C22×Q8—348no—
532C22×Q8C22×D1713yes—
533C22×Q8C22×D1718yes—
534C22×Q8C22×D1711yescharacteristic
535C22×D4—171no—
536C22×D4—173no—
537C22×D4—171no—
538C22×D4—173no—
539C22×D4—173no—
540C22×D4—173no—
541C22×D4—176no—
542C22×D4—171no—
543C22×D4—173no—
544C22×D4—173no—
545C22×D4—173no—
546C22×D4C22×D1713yes—
547C22×D4C22×D1713yes—
548C23×C4—173no—
549C23×C4—176no—
550C23×C4—176no—
551C23×C4—173no—
552C23×C4—173no—
553C23×C4—171no—
554C23×C4—173no—
555C23×C4C22×D1713yes—
556C23×C4C22×D1713yes—
557C4⋊Q8—1724no—
558C4⋊Q8—1724no—
559#127—1724no—
560#127—1724no—
561#124—1724no—
562#124—1724no—
563#124—1724no—
564#124C22×D17124yes—
565C22⋊Q8—1724no—
566C22⋊Q8—1724no—
567C22⋊Q8—1748no—
568C22⋊Q8—1724no—
569C22⋊Q8—1748no—
570C22⋊Q8C22×D17124yes—
571#121—1724no—
572#121—1724no—
573#121—1748no—
574#121—1724no—
575#121—1724no—
576#121—1724no—
577#121—1724no—
578#121—178no—
579#121—1748no—
580#121—1748no—
581#121C22×D17124yes—
582C4×Q8—178no—
583C4×Q8—1724no—
584C4×Q8—1724no—
585C4×Q8C22×D1718yes—
586C4×D4—1724no—
587C4×D4—1724no—
588C4×D4—1748no—
589C4×D4—1748no—
590C4×D4—1724no—
591C4×D4C22×D17124yes—
592C2×C4⋊C4—176no—
593C2×C4⋊C4—173no—
594C2×C4⋊C4—171no—
595C2×C4⋊C4—173no—
596C2×C4⋊C4—176no—
597C2×C4⋊C4—173no—
598C2×C4⋊C4—1724no—
599C2×C4⋊C4C22×D1713yes—
600C2×C4⋊C4C22×D1713yes—
601C2×C22⋊C4—173no—
602C2×C22⋊C4—173no—
603C2×C22⋊C4—173no—
604C2×C22⋊C4—171no—
605C2×C22⋊C4—173no—
606C2×C22⋊C4—173no—
607C2×C22⋊C4—176no—
608C2×C22⋊C4C22×D1713yes—
609C2×C22⋊C4C22×D1716yes—
610C2×C22⋊C4C22×D1711yescharacteristic
611C2×C42—173no—
612C2×C42—173no—
613C2×C42—173no—
614C2×C42—1724no—
615C2×C42C22×D1713yes—
616C17C2×#349711yescharacteristic, complemented, Sylow
617C24—171no—
618C24—171no—
619C24—173no—
620C24C23×D1711yescharacteristic
621C24C23×D1713yes—
622#41—232no—
623#41—3496no—
624#41—3496no—
625#41—3496no—
626#41—3496no—
627#41—3496no—
628#41—3496no—
629#41—3432no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—1764no—
633C2×Q8—1724no—
634C2×Q8—1712no—
635C2×Q8—1712no—
636C2×Q8—1712no—
637C2×Q8—1712no—
638C2×Q8—3412no—
639C2×Q8—3412no—
640C2×Q8—3496no—
641C2×Q8—3496no—
642C2×Q8—3432no—
643C2×Q8—3412no—
644C2×Q8D4×D1718yes—
645C2×Q8C23×D17112yes—
646C2×Q8C23×D1714yes—
647C2×D4—212no—
648C2×D4—46no—
649C2×D4—174no—
650C2×D4—1712no—
651C2×D4—174no—
652C2×D4—1712no—
653C2×D4—1712no—
654C2×D4—1712no—
655C2×D4—1724no—
656C2×D4—174no—
657C2×D4—1712no—
658C2×D4—1712no—
659C2×D4—1712no—
660C2×D4—344no—
661C2×D4—3412no—
662C2×D4—344no—
663C2×D4—3412no—
664C2×D4—3412no—
665C2×D4—3412no—
666C2×D4—344no—
667C2×D4—3412no—
668C2×D4—3412no—
669C2×D4—686no—
670C2×D4—6812no—
671C2×D4C23×D17112yes—
672C2×D4C23×D17112yes—
673C22×C4—212no—
674C22×C4—212no—
675C22×C4—171no—
676C22×C4—173no—
677C22×C4—1724no—
678C22×C4—1712no—
679C22×C4—1724no—
680C22×C4—173no—
681C22×C4—171no—
682C22×C4—173no—
683C22×C4—174no—
684C22×C4—1724no—
685C22×C4—1712no—
686C22×C4—1712no—
687C22×C4—1712no—
688C22×C4—344no—
689C22×C4—3424no—
690C22×C4—3424no—
691C22×C4—3412no—
692C22×C4—3412no—
693C22×C4—686no—
694C22×C4C23×D17112yes—
695C22×C4C23×D17112yes—
696C22×C4C23×D1711yescharacteristic
697C22×C4C23×D1713yes—
698C22×C4C23×D1711yescharacteristic
699C22×C4C23×D1713yes—
700C22×C4C23×D1713yes—
701C4⋊C4—1724no—
702C4⋊C4—1712no—
703C4⋊C4—174no—
704C4⋊C4—1712no—
705C4⋊C4—1724no—
706C4⋊C4—1712no—
707C4⋊C4C23×D17112yes—
708C4⋊C4C23×D17112yes—
709C22⋊C4—1712no—
710C22⋊C4—1712no—
711C22⋊C4—1712no—
712C22⋊C4—174no—
713C22⋊C4—1712no—
714C22⋊C4—1712no—
715C22⋊C4—1724no—
716C22⋊C4C23×D17112yes—
717C22⋊C4C23×D17124yes—
718C22⋊C4C23×D1714yes—
719C42—1712no—
720C42—1712no—
721C42—1712no—
722C42C23×D17112yes—
723C23—22no—
724C23—26no—
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—174no—
730C23—172no—
731C23—172no—
732C23—176no—
733C23—342no—
734C23—342no—
735C23—346no—
736C23—342no—
737C23—342no—
738C23—346no—
739C23—342no—
740C23—346no—
741C23C24×D1712yes—
742C23C24×D1716yes—
743C23C24×D1711yescharacteristic
744Q8—224no—
745Q8—1748no—
746Q8—3424no—
747Q8—3424no—
748Q8—3424no—
749Q8C2×D4×D17116yes—
750D4—224no—
751D4—412no—
752D4—348no—
753D4—3424no—
754D4—3424no—
755D4—3424no—
756D4—348no—
757D4—3424no—
758D4—348no—
759D4—3424no—
760D4—3424no—
761D4—6812no—
762D4—6824no—
763C2×C4—22no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—1712no—
770C2×C4—174no—
771C2×C4—172no—
772C2×C4—176no—
773C2×C4—1748no—
774C2×C4—176no—
775C2×C4—172no—
776C2×C4—176no—
777C2×C4—3448no—
778C2×C4—348no—
779C2×C4—3448no—
780C2×C4—346no—
781C2×C4—342no—
782C2×C4—346no—
783C2×C4—3424no—
784C2×C4—3424no—
785C2×C4—6812no—
786C2×C4C2×D4×D17112yes—
787C2×C4C24×D1712yes—
788C2×C4C24×D1716yes—
789C2×C4C24×D1712yes—
790C2×C4C24×D1716yes—
791C2×C4C24×D1716yes—
792C22—22no—
793C22—26no—
794C22—22no—
795C22—26no—
796C22—22no—
797C22—26no—
798C22—44no—
799C22—412no—
800C22—174no—
801C22—348no—
802C22—342no—
803C22—342no—
804C22—346no—
805C22—342no—
806C22—342no—
807C22—346no—
808C22—342no—
809C22—346no—
810C22—6812no—
811C22—684no—
812C22C22×D4×D1712yes—
813C222−1+4×D1712yes—
814C22#1176364512yes—
815C22C25×D1711yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—1712no—
821C4—174no—
822C4—346no—
823C4—342no—
824C4—346no—
825C4C22×D4×D17112yes—
826C2—42no—
827C2—46no—
828C2—344no—
829C2—686no—
830C2—682no—
831C2#1454255214yesdirect product factor
832C2C23×D4×D1711yescharacteristic
833C2C2×2−1+4×D1711yescharacteristic
834C2C2×#1176364511yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#548C2
socleC23×C17C25
hypercenterC2×#548D17
hypocenterC17C2×#3497
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#10587694C2semidirect
2. C22×#10587697C2semidirect
3. #14542552C2direct (N × H)
4. C2×#11763478C2semidirect
5. C2×#11763477C2semidirect
6. C2×Q8×C22⋊D17C2semidirect
7. C2×#11763472C2semidirect
8. C2×#11763471C2semidirect
9. C2×#11763468C2semidirect
10. C2×#11763467C2semidirect
11. C2×#11763389C2semidirect
12. C2×#11763388C2semidirect
13. C2×#11763358C2semidirect
14. C2×#11763356C2semidirect
15. C2×C4×Q8×D17C2semidirect
16. C2×C17×#548C2semidirect
18. C2×#10587694C22semidirect
20. C2×#10587697C22semidirect
32. #11763478C22semidirect
33. #11763477C22semidirect
34. Q8×C22⋊D17C22semidirect
35. #11763472C22semidirect
36. #11763471C22semidirect
37. #11763468C22semidirect
38. #11763467C22semidirect
39. #11763389C22semidirect
40. #11763388C22semidirect
41. #11763358C22semidirect
42. #11763356C22semidirect
68. C4×Q8×D17C22semidirect
78. C17×#548C22semidirect
110. C2×Q8×D17D4semidirect
248. Q8×D17C2×D4semidirect
355. C2×Dic172−1+4semidirect
385. C2×#548D17semidirect
424. Dic17C2×2−1+4semidirect
449. #548C2×D17semidirect
494. C2×C17#3497semidirect
616. C17C2×#3497semidirect
831. C2#14542552direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876942
C22×#105876972
#145425522
C2×#117634782
C2×#117634772
C2×Q8×C22⋊D172
C2×#117634722
C2×#117634712
C2×#117634682
C2×#117634672
C2×#117633892
C2×#117633882
C2×#117633582
C2×#117633562
C2×C4×Q8×D172
C2×C17×#5482
C2×#349717