Finite Group Databasebeta

← C2×#14542434 #17942488

Subgroups — C2×#14542434 #17942488

Order 4352.

11254 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
2C23×Q8×D17C211yesmaximal, characteristic, complemented
3#14542434C2132yesmaximal, direct product factor
4C2×#11763474C213yesmaximal, complemented
5C2×Q8×C22⋊D17C211yesmaximal, characteristic, complemented
6C2×#11763472C213yesmaximal, complemented
7C2×#11763471C211yesmaximal, characteristic, complemented
8C2×#11763470C211yesmaximal, characteristic, complemented
9C2×#11763469C213yesmaximal, complemented
10C2×#11763468C213yesmaximal, complemented
11C2×#11763384C213yesmaximal, complemented
12C2×#11763382C213yesmaximal, complemented
13C2×#11763322C213yesmaximal, complemented
14C2×#11763318C213yesmaximal, complemented
15C2×#11763285C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C17C211yesmaximal, characteristic, complemented
17C2×#10587694—216no—
18C2×#10587694C22116yescomplemented
19C22×#63256C2213yes—
20C22×#63256C2211yescharacteristic, complemented
21C22×#63252C2213yes—
22C22×#63252C2213yescomplemented
23C23×Dic34C2213yes—
24C22×Q8×D17—216no—
25C22×Q8×D17C2213yes—
26C22×Q8×D17C2213yes—
27C22×Q8×D17C2211yescharacteristic
28C22×Q8×D17C2211yescharacteristic
29C22×Q8×D17C22116yescomplemented
30C22×Q8×D17C2213yescomplemented
31C23×C4×D17C2213yes—
32#11763474C22148yescomplemented
33Q8×C22⋊D17C22116yescomplemented
34#11763472C22148yescomplemented
35#11763471C22116yescomplemented
36#11763470C22116yescomplemented
37#11763469C22148yescomplemented
38#11763468C22148yescomplemented
39#11763384C22148yescomplemented
40#11763382C22148yescomplemented
41C2×#10587574C2216yescomplemented
42C2×#10587630C2213yescomplemented
43C2×#10587633C2213yescomplemented
44C2×#10587561C2213yescomplemented
45C2×#10587571C2216yescomplemented
46#11763322C22148yescomplemented
47#11763318C22148yescomplemented
48C2×#10587580C2216yes—
49C2×#10587580C2213yes—
50C2×#10587569C2213yes—
51C2×#10587583C2213yescomplemented
52C2×#10587610C2213yescomplemented
53C2×#10587582C2213yes—
54C2×#10587582C2216yescomplemented
55C2×#10587582C2216yescomplemented
56C2×#10587564C2213yes—
57C2×#10587632C2213yes—
58C2×#10587632C2213yescomplemented
59C2×#10587581C2213yes—
60C2×#10587616C2213yes—
61C2×#10587570C2213yes—
62C2×#10587625C2213yes—
63C2×#10587568C2213yes—
64C2×#10587623C2211yescharacteristic
65#11763285C22116yescomplemented
66C2×Q8×Dic17C2211yescharacteristic, complemented
67C2×C4×Dic34C2213yescomplemented
68C2×#10587573C2213yescomplemented
69C2×C4×D68C2213yes—
70C2×#10587579C2216yes—
71C2×C4×C22⋊D17C2213yes—
72C2×C4×C22⋊D17C2213yes—
73C2×#10587567C2216yes—
74C2×#10587578C2213yes—
75C2×#10587558C2213yes—
76C23×Q8×C17C2211yescharacteristic
77C23×Q8×C17C2211yescharacteristic, complemented
78D4×Q8×C17C22116yescomplemented
79C2×C17×C4⋊Q8C2213yescomplemented
80C2×C17×C22⋊Q8C2213yes—
81C2×C17×C22⋊Q8C2213yescomplemented
82C2×C4×Q8×C17C2211yescharacteristic, complemented
83C2×C4×D4×C17C2213yes—
84C24×D17C2311yescharacteristic
85C22×Q8×C17—28no—
86C22×Q8×C17—28no—
87C22×Q8×C17C2318yes—
88C22×Q8×C17C2313yes—
89C22×Q8×C17C2313yes—
90C22×Q8×C17C2311yescharacteristic
91C22×Q8×C17C2318yescomplemented
92C22×D4×C17C2311yescharacteristic
93C23×C4×C17C2313yes—
94C23×C4×C17C2313yes—
95C22×C22⋊D17C2313yes—
96C22×C22⋊D17C2311yescharacteristic
97C22×C22⋊D17C2311yescharacteristic
98C22×C22⋊D17C2313yes—
99C23×Dic17C2313yes—
100#10587694—2128no—
101C2×#63256—28no—
102C2×#63256—224no—
103C2×#63256C23124yes—
104C2×#63256C2318yescomplemented
105C2×Q8×D17—28no—
106C2×Q8×D17—2128no—
107C2×Q8×D17—224no—
108C2×Q8×D17—224no—
109C2×Q8×D17—224no—
110C2×Q8×D17D4116yescomplemented
111C2×Q8×D17C23124yes—
112C2×Q8×D17C2318yes—
113C2×Q8×D17C23124yes—
114C2×Q8×D17C2318yes—
115C2×Q8×D17C23124yescomplemented
116C2×#63252—224no—
117C2×#63252—224no—
118C2×#63252C23124yes—
119C2×#63252C23124yescomplemented
120C22×D68C2313yes—
121C22×D68C2313yes—
122C22×D68C2313yes—
123C22×C4×D17—224no—
124C22×C4×D17C2316yes—
125C22×C4×D17C2313yes—
126C22×C4×D17C2313yes—
127C22×C4×D17C2313yes—
128C22×C4×D17C2313yes—
129C22×C4×D17C23124yes—
130C22×C4×D17C2313yes—
131C22×Dic34—224no—
132C22×Dic34C23124yes—
133C22×Dic34C2313yes—
134C22×Dic34C2316yes—
135C22×Dic34C2313yes—
136C22×Dic34C2313yes—
137C17×C4⋊Q8C23124yescomplemented
138C17×C22⋊Q8C23124yes—
139C17×C22⋊Q8C23124yescomplemented
140C4×Q8×C17C2318yescomplemented
141C4×D4×C17C23124yes—
142C2×C4⋊C4×C17C2313yes—
143C2×C4⋊C4×C17C2313yes—
144C2×C4⋊C4×C17C2316yes—
145C2×C22⋊C4×C17C2313yes—
146C2×C22⋊C4×C17C2313yes—
147C2×C42×C17C2313yes—
148C2×C22⋊Dic17C2311yescharacteristic
149C2×C22⋊Dic17C2313yes—
150#10587633C23124yescomplemented
151#10587632C23124yes—
152#10587632C23124yescomplemented
153Q8×Dic17C2318yescomplemented
154#10587630C23124yescomplemented
155#10587625C23124yes—
156#10587623C2318yes—
157#10587616C23124yes—
158C4×C22⋊D17C23124yes—
159C4×C22⋊D17C23124yes—
160C2×#63227C2311yescharacteristic
161C2×#63227C2313yes—
162C2×#63227C2316yes—
163C2×#63227C2313yes—
164C2×#63227C2313yes—
165C2×#63227C2316yes—
166C2×#63227C2311yescharacteristic
167C2×#63227C2313yes—
168C2×C4⋊Dic17C2313yes—
169C2×C4⋊Dic17C2313yes—
170#10587610C23124yescomplemented
171C2×#63225C2313yes—
172C2×#63225C2313yes—
173C2×#63225C2316yes—
174C2×#63225C2313yes—
175C2×#63225C2313yes—
176C2×C4×Dic17C2313yes—
177C2×C4×Dic17C2316yes—
178#10587583C23124yescomplemented
179#10587582C23124yes—
180#10587582C23148yescomplemented
181#10587582C23148yescomplemented
182#10587581C23124yes—
183#10587580C23124yes—
184#10587580C23148yes—
185#10587579C23148yes—
186#10587578C23124yes—
187#10587574C23148yescomplemented
188#10587573C23124yescomplemented
189#10587571C23148yescomplemented
190#10587570C23124yes—
191#10587569C23124yes—
192#10587568C23124yes—
193#10587567C23148yes—
194#10587564C23124yes—
195#10587561C23124yescomplemented
196C4×D68C23124yes—
197#10587558C23124yes—
198C4×Dic34C23124yescomplemented
199C24×C17C2411yescharacteristic
200C24×C17C2411yescharacteristic
201C23×D17—24no—
202C23×D17—24no—
203C23×D17—24no—
204C23×D17C2414yes—
205C23×D17C2413yes—
206C23×D17C2411yescharacteristic
207C23×D17C2411yescharacteristic
208C2×Q8×C17—232no—
209C2×Q8×C17—232no—
210C2×Q8×C17—212no—
211C2×Q8×C17—212no—
212C2×Q8×C17C2×D418yes—
213C2×Q8×C17C24112yes—
214C2×Q8×C17C24112yes—
215C2×Q8×C17C2414yes—
216C2×D4×C17—24no—
217C2×D4×C17C2414yes—
218C22×C4×C17—212no—
219C22×C4×C17—212no—
220C22×C4×C17C24112yes—
221C22×C4×C17C24112yes—
222C22×C4×C17C2413yes—
223C22×C4×C17C2413yes—
224C22×C4×C17C2413yes—
225C22×C4×C17C2411yescharacteristic
226C22×C4×C17C2413yes—
227C2×C22⋊D17—212no—
228C2×C22⋊D17—24no—
229C2×C22⋊D17—24no—
230C2×C22⋊D17—212no—
231C2×C22⋊D17C2414yes—
232C2×C22⋊D17C24112yes—
233C2×C22⋊D17C24112yes—
234C2×C22⋊D17C2414yes—
235C22×Dic17—212no—
236C22×Dic17C24112yes—
237C22×Dic17C2413yes—
238C22×Dic17C2411yescharacteristic
239C22×Dic17C2411yescharacteristic
240C22×Dic17C2413yes—
241C22×Dic17C2413yes—
242#63256—232no—
243#63256—296no—
244Q8×D17—232no—
245Q8×D17—296no—
246Q8×D17—296no—
247Q8×D17—296no—
248Q8×D17C2×D4164yescomplemented
249#63252—296no—
250#63252—296no—
251C2×D68—212no—
252C2×D68—212no—
253C2×D68—212no—
254C2×D68C24112yes—
255C2×D68C24112yes—
256C2×D68C24112yes—
257C2×C4×D17—212no—
258C2×C4×D17—212no—
259C2×C4×D17—212no—
260C2×C4×D17—212no—
261C2×C4×D17—224no—
262C2×C4×D17—296no—
263C2×C4×D17C2×D4124yes—
264C2×C4×D17C24112yes—
265C2×C4×D17C24112yes—
266C2×C4×D17C24112yes—
267C2×C4×D17C24112yes—
268C2×C4×D17C24124yes—
269C2×C4×D17C24112yes—
270C2×Dic34—212no—
271C2×Dic34—224no—
272C2×Dic34—212no—
273C2×Dic34—296no—
274C2×Dic34C2×D4124yes—
275C2×Dic34C24112yes—
276C2×Dic34C24124yes—
277C2×Dic34C24112yes—
278C2×Dic34C24112yes—
279C4⋊C4×C17C24124yes—
280C4⋊C4×C17C24112yes—
281C4⋊C4×C17C24112yes—
282C22⋊C4×C17C24112yes—
283C22⋊C4×C17C24112yes—
284C42×C17C24112yes—
285C22⋊Dic17C2414yes—
286C22⋊Dic17C24112yes—
287#63227C2414yes—
288#63227C24112yes—
289#63227C2414yes—
290#63227C24112yes—
291#63227C24124yes—
292#63227C24112yes—
293#63227C24112yes—
294#63227C24124yes—
295C4⋊Dic17C24112yes—
296C4⋊Dic17C24112yes—
297#63225C24112yes—
298#63225C24112yes—
299#63225C24112yes—
300#63225C24124yes—
301#63225C24112yes—
302C4×Dic17C24124yes—
303C4×Dic17C24112yes—
304C2×#3486—171nomaximal, Sylow
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C172−1+414yescomplemented
311C23×C17C2512yes—
312C23×C17C2512yes—
313C23×C17C2511yescharacteristic
314C22×D17—232no—
315C22×D17—22no—
316C22×D17—22no—
317C22×D17—22no—
318C22×D17—22no—
319C22×D17—28no—
320C22×D17—28no—
321C22×D17—28no—
322C22×D17—26no—
323C22×D17—26no—
324C22×D17—26no—
325C22×D17C22×D414yes—
326C22×D172−1+414yescomplemented
327C22×D17C2516yes—
328C22×D17C2512yes—
329C22×D17C2512yes—
330Q8×C17—224no—
331Q8×C17—224no—
332Q8×C17C22×D4116yes—
333D4×C17—28no—
334C2×C4×C17—26no—
335C2×C4×C17—26no—
336C2×C4×C17—26no—
337C2×C4×C17—22no—
338C2×C4×C17—224no—
339C2×C4×C17—224no—
340C2×C4×C17C22×D4112yes—
341C2×C4×C17C2512yes—
342C2×C4×C17C2516yes—
343C2×C4×C17C2516yes—
344C2×C4×C17C2516yes—
345C2×C4×C17C2516yes—
346C22⋊D17—224no—
347C22⋊D17—28no—
348C22⋊D17—28no—
349C22⋊D17—224no—
350C2×Dic17—26no—
351C2×Dic17—22no—
352C2×Dic17—22no—
353C2×Dic17—26no—
354C2×Dic17—224no—
355C2×Dic17C22×D4112yes—
356C2×Dic17C2516yes—
357C2×Dic17C2512yes—
358C2×Dic17C2512yes—
359C2×Dic17C2516yes—
360C2×Dic17C2516yes—
361D68—224no—
362D68—224no—
363D68—224no—
364C4×D17—224no—
365C4×D17—224no—
366C4×D17—224no—
367C4×D17—224no—
368C4×D17—248no—
369C4×D17C22×D4148yes—
370Dic34—224no—
371Dic34—248no—
372Dic34—224no—
373Dic34C22×D4148yes—
374C22×2−1+4—171no—
375C24×Q8—171no—
376#3486—1732no—
377C2×D4×Q8—171no—
378C2×D4×Q8—173no—
379C2×D4×Q8—173no—
380C2×D4×Q8D1711yescharacteristic, complemented
381C2×#548—171no—
382C2×#548—173no—
383C2×#548—171no—
384C2×#548—173no—
385C2×#536—173no—
386C2×#536—173no—
387C2×#525—173no—
388C2×#525—173no—
389C2×#519—171no—
390C22×C17—22no—
391C22×C17—22no—
392C22×C17—28no—
393C22×C17—22no—
394C22×C17—22no—
395C22×C17—22no—
396C22×C17—44no—
397C22×C17C23×D412yes—
398C22×C17C2×2−1+412yes—
399C22×C17C2×2−1+412yes—
400C22×C17C2×2−1+414yescomplemented
401C22×C17C2611yescharacteristic
402C2×D17—232no—
403C2×D17—22no—
404C2×D17—22no—
405C2×D17—22no—
406C2×D17—22no—
407C2×D17—28no—
408C2×D17—28no—
409C2×D17—26no—
410C2×D17—26no—
411C2×D17—26no—
412C2×D17—412no—
413C2×D17C23×D414yes—
414C2×D17C2×2−1+414yescomplemented
415C4×C17—26no—
416C4×C17—26no—
417C4×C17—26no—
418C4×C17—22no—
419C4×C17C23×D4112yes—
420Dic17—26no—
421Dic17—22no—
422Dic17—22no—
423Dic17—26no—
424Dic17C23×D4112yes—
425C2×2−1+4—1716no—
426C2×2−1+4—3416no—
427C22×#41—173no—
428C22×#41—171no—
429C22×#41—173no—
430C22×#41—173no—
431C23×Q8—171no—
432C23×Q8—173no—
433C23×Q8—173no—
434C23×Q8—171no—
435C23×Q8—1716no—
436C23×Q8—173no—
437C23×Q8—173no—
438C23×Q8—3416no—
439C23×Q8C2×D1711yescharacteristic
440C23×Q8C2×D1711yescharacteristic, complemented
441C24×C4—173no—
442D4×Q8—1716no—
443D4×Q8—1748no—
444D4×Q8—1748no—
445D4×Q8C2×D17116yescomplemented
446#548—1716no—
447#548—1748no—
448#548—1716no—
449#548—1748no—
450#536—1748no—
451#536—1748no—
452C2×C4⋊Q8—173no—
453C2×C4⋊Q8—176no—
454C2×C4⋊Q8C2×D1713yescomplemented
455C2×#124—173no—
456C2×#124—176no—
457C2×#124—173no—
458#525—1748no—
459#525—1748no—
460C2×#123—176no—
461C2×#123—173no—
462C2×#123—173no—
463C2×C22⋊Q8—173no—
464C2×C22⋊Q8—173no—
465C2×C22⋊Q8—173no—
466C2×C22⋊Q8—173no—
467C2×C22⋊Q8—176no—
468C2×C22⋊Q8—176no—
469C2×C22⋊Q8—173no—
470C2×C22⋊Q8—173no—
471C2×C22⋊Q8C2×D1713yes—
472C2×C22⋊Q8C2×D1713yescomplemented
473C2×#121—173no—
474C2×#121—173no—
475C2×#121—173no—
476C2×#121—173no—
477C2×#120—171no—
478C2×#120—173no—
479#519—1716no—
480C2×C4×Q8—171no—
481C2×C4×Q8—173no—
482C2×C4×Q8—173no—
483C2×C4×Q8C2×D1711yescharacteristic, complemented
484C2×C4×D4—173no—
485C2×C4×D4—173no—
486C2×C4×D4—176no—
487C2×C4×D4—176no—
488C2×C4×D4—173no—
489C2×C4×D4C2×D1713yes—
490C2×#117—173no—
491C2×#117—173no—
492C2×C17—24no—
493C2×C17—42no—
494C2×C17#348614yescomplemented
495C2×C17C24×D411yescharacteristic
496C2×C17C22×2−1+411yescharacteristic
497C2×C17C22×2−1+411yescharacteristic
498D17—24no—
499D17—24no—
500D17—46no—
501C25—171no—
5022−1+4—34128no—
503C2×#41—1724no—
504C2×#41—178no—
505C2×#41—1724no—
506C2×#41—1724no—
507C2×#41—3424no—
508C2×#41—3424no—
509C2×#41—3424no—
510C2×#41—348no—
511C22×Q8—28no—
512C22×Q8—28no—
513C22×Q8—1716no—
514C22×Q8—178no—
515C22×Q8—1724no—
516C22×Q8—1724no—
517C22×Q8—178no—
518C22×Q8—1724no—
519C22×Q8—173no—
520C22×Q8—176no—
521C22×Q8—173no—
522C22×Q8—173no—
523C22×Q8—1724no—
524C22×Q8—3424no—
525C22×Q8—3424no—
526C22×Q8—34128no—
527C22×Q8—3424no—
528C22×Q8—3424no—
529C22×Q8—348no—
530C22×Q8C22×D1713yes—
531C22×Q8C22×D1713yes—
532C22×Q8C22×D1718yes—
533C22×Q8C22×D1711yescharacteristic
534C22×Q8C22×D1718yescomplemented
535C22×D4—171no—
536C22×D4—173no—
537C22×D4—171no—
538C22×D4—173no—
539C22×D4—173no—
540C22×D4—173no—
541C22×D4—173no—
542C22×D4C22×D1711yescharacteristic
543C23×C4—173no—
544C23×C4—173no—
545C23×C4—173no—
546C23×C4—173no—
547C23×C4—176no—
548C23×C4—173no—
549C23×C4—173no—
550C23×C4—1724no—
551C23×C4—3424no—
552C23×C4C22×D1713yes—
553C23×C4C22×D1713yes—
554C4⋊Q8—1724no—
555C4⋊Q8—1748no—
556C4⋊Q8C22×D17124yescomplemented
557#124—1724no—
558#124—1748no—
559#124—1724no—
560#123—1748no—
561#123—1724no—
562#123—1724no—
563C22⋊Q8—1724no—
564C22⋊Q8—1724no—
565C22⋊Q8—1724no—
566C22⋊Q8—1724no—
567C22⋊Q8—1748no—
568C22⋊Q8—1748no—
569C22⋊Q8—1724no—
570C22⋊Q8—1724no—
571C22⋊Q8C22×D17124yes—
572C22⋊Q8C22×D17124yescomplemented
573#121—1724no—
574#121—1724no—
575#121—1724no—
576#121—1724no—
577#120—178no—
578#120—1724no—
579C4×Q8—178no—
580C4×Q8—1724no—
581C4×Q8—1724no—
582C4×Q8C22×D1718yescomplemented
583C4×D4—1724no—
584C4×D4—1724no—
585C4×D4—1748no—
586C4×D4—1748no—
587C4×D4—1724no—
588C4×D4C22×D17124yes—
589#117—1724no—
590#117—1724no—
591C2×C4⋊C4—173no—
592C2×C4⋊C4—173no—
593C2×C4⋊C4—173no—
594C2×C4⋊C4—173no—
595C2×C4⋊C4—176no—
596C2×C4⋊C4—173no—
597C2×C4⋊C4—173no—
598C2×C4⋊C4C22×D1713yes—
599C2×C4⋊C4C22×D1716yes—
600C2×C4⋊C4C22×D1713yes—
601C2×C22⋊C4—171no—
602C2×C22⋊C4—173no—
603C2×C22⋊C4—173no—
604C2×C22⋊C4—171no—
605C2×C22⋊C4—173no—
606C2×C22⋊C4—171no—
607C2×C22⋊C4—173no—
608C2×C22⋊C4—176no—
609C2×C22⋊C4—176no—
610C2×C22⋊C4—173no—
611C2×C22⋊C4C22×D1713yes—
612C2×C22⋊C4C22×D1713yes—
613C2×C42—176no—
614C2×C42—173no—
615C2×C42C22×D1713yes—
616C17C2×#348611yescharacteristic, complemented, Sylow
617C24—171no—
618C24—171no—
619C24—174no—
620C24—173no—
621C24—344no—
622C24—344no—
623C24—344no—
624C24C23×D1711yescharacteristic
625C24C23×D1711yescharacteristic
626#41—3496no—
627#41—3496no—
628#41—3496no—
629#41—3432no—
630C2×Q8—232no—
631C2×Q8—232no—
632C2×Q8—212no—
633C2×Q8—212no—
634C2×Q8—1764no—
635C2×Q8—1724no—
636C2×Q8—1712no—
637C2×Q8—1724no—
638C2×Q8—1712no—
639C2×Q8—1712no—
640C2×Q8—3424no—
641C2×Q8—3412no—
642C2×Q8—3496no—
643C2×Q8—3496no—
644C2×Q8—3496no—
645C2×Q8—3496no—
646C2×Q8—3432no—
647C2×Q8—3412no—
648C2×Q8D4×D1718yes—
649C2×Q8C23×D17112yes—
650C2×Q8C23×D17112yes—
651C2×Q8C23×D1714yes—
652C2×D4—24no—
653C2×D4—174no—
654C2×D4—1712no—
655C2×D4—174no—
656C2×D4—1712no—
657C2×D4—1712no—
658C2×D4—1712no—
659C2×D4—1712no—
660C2×D4—3412no—
661C2×D4—3412no—
662C2×D4—3412no—
663C2×D4—344no—
664C2×D4—344no—
665C2×D4—3412no—
666C2×D4—3412no—
667C2×D4C23×D1714yes—
668C22×C4—212no—
669C22×C4—212no—
670C22×C4—173no—
671C22×C4—1724no—
672C22×C4—1712no—
673C22×C4—1712no—
674C22×C4—171no—
675C22×C4—173no—
676C22×C4—173no—
677C22×C4—171no—
678C22×C4—1712no—
679C22×C4—1712no—
680C22×C4—1724no—
681C22×C4—1712no—
682C22×C4—1712no—
683C22×C4—3412no—
684C22×C4—3496no—
685C22×C4—3424no—
686C22×C4—3412no—
687C22×C4—3412no—
688C22×C4—3412no—
689C22×C4—3412no—
690C22×C4C23×D17112yes—
691C22×C4C23×D17112yes—
692C22×C4C23×D1713yes—
693C22×C4C23×D1711yescharacteristic
694C22×C4C23×D1713yes—
695C22×C4C23×D1713yes—
696C22×C4C23×D1713yes—
697C4⋊C4—1712no—
698C4⋊C4—1712no—
699C4⋊C4—1712no—
700C4⋊C4—1712no—
701C4⋊C4—1724no—
702C4⋊C4—1712no—
703C4⋊C4—1712no—
704C4⋊C4C23×D17112yes—
705C4⋊C4C23×D17124yes—
706C4⋊C4C23×D17112yes—
707C22⋊C4—174no—
708C22⋊C4—1712no—
709C22⋊C4—1712no—
710C22⋊C4—174no—
711C22⋊C4—1712no—
712C22⋊C4—174no—
713C22⋊C4—1712no—
714C22⋊C4—1724no—
715C22⋊C4—1724no—
716C22⋊C4—1712no—
717C22⋊C4C23×D17112yes—
718C22⋊C4C23×D17112yes—
719C42—1724no—
720C42—1712no—
721C42C23×D17112yes—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—174no—
728C23—174no—
729C23—172no—
730C23—172no—
731C23—176no—
732C23—348no—
733C23—348no—
734C23—3432no—
735C23—342no—
736C23—342no—
737C23—342no—
738C23—342no—
739C23—348no—
740C23—346no—
741C23—346no—
742C23—346no—
743C23#1058769414yescomplemented
744C23C24×D1712yes—
745C23C24×D1712yes—
746C23C24×D1711yescharacteristic
747Q8—224no—
748Q8—224no—
749Q8—1748no—
750Q8—3448no—
751Q8—3424no—
752Q8—3424no—
753Q8C2×D4×D17116yes—
754D4—28no—
755D4—3424no—
756D4—3424no—
757D4—3424no—
758D4—348no—
759D4—348no—
760D4—3424no—
761D4—3424no—
762C2×C4—26no—
763C2×C4—26no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—1712no—
769C2×C4—176no—
770C2×C4—1748no—
771C2×C4—172no—
772C2×C4—176no—
773C2×C4—176no—
774C2×C4—172no—
775C2×C4—3424no—
776C2×C4—3448no—
777C2×C4—3424no—
778C2×C4—3424no—
779C2×C4—342no—
780C2×C4—346no—
781C2×C4—342no—
782C2×C4—346no—
783C2×C4—3424no—
784C2×C4—3424no—
785C2×C4C2×D4×D17112yes—
786C2×C4C24×D1716yes—
787C2×C4C24×D1712yes—
788C2×C4C24×D1716yes—
789C2×C4C24×D1716yes—
790C2×C4C24×D1716yes—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—174no—
799C22—174no—
800C22—3432no—
801C22—348no—
802C22—348no—
803C22—342no—
804C22—342no—
805C22—342no—
806C22—342no—
807C22—346no—
808C22—346no—
809C22—346no—
810C22—6812no—
811C22C22×D4×D1712yes—
812C222−1+4×D1712yes—
813C22C2×#1058769412yes—
814C22C2×#1058769414yescomplemented
815C22C25×D1711yescharacteristic
816C4—26no—
817C4—26no—
818C4—26no—
819C4—22no—
820C4—1712no—
821C4—342no—
822C4—346no—
823C4—342no—
824C4—346no—
825C4C22×D4×D17112yes—
826C2—24no—
827C2—42no—
828C2—344no—
829C2—344no—
830C2—686no—
831C2#1454243414yesdirect product factor
832C2C23×D4×D1711yescharacteristic
833C2C2×2−1+4×D1711yescharacteristic
834C2C22×#1058769411yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×D4×Q8×C17C2
socleC23×C17C25
hypercenterC2×D4×Q8D17
hypocenterC17C2×#3486
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#10587694C2semidirect
2. C23×Q8×D17C2semidirect
3. #14542434C2direct (N × H)
4. C2×#11763474C2semidirect
5. C2×Q8×C22⋊D17C2semidirect
6. C2×#11763472C2semidirect
7. C2×#11763471C2semidirect
8. C2×#11763470C2semidirect
9. C2×#11763469C2semidirect
10. C2×#11763468C2semidirect
11. C2×#11763384C2semidirect
12. C2×#11763382C2semidirect
13. C2×#11763322C2semidirect
14. C2×#11763318C2semidirect
15. C2×#11763285C2semidirect
16. C2×D4×Q8×C17C2semidirect
18. C2×#10587694C22semidirect
20. C22×#63256C22semidirect
22. C22×#63252C22semidirect
29. C22×Q8×D17C22semidirect
30. C22×Q8×D17C22semidirect
32. #11763474C22semidirect
33. Q8×C22⋊D17C22semidirect
34. #11763472C22semidirect
35. #11763471C22semidirect
36. #11763470C22semidirect
37. #11763469C22semidirect
38. #11763468C22semidirect
39. #11763384C22semidirect
40. #11763382C22semidirect
41. C2×#10587574C22semidirect
42. C2×#10587630C22semidirect
43. C2×#10587633C22semidirect
44. C2×#10587561C22semidirect
45. C2×#10587571C22semidirect
46. #11763322C22semidirect
47. #11763318C22semidirect
51. C2×#10587583C22semidirect
52. C2×#10587610C22semidirect
54. C2×#10587582C22semidirect
55. C2×#10587582C22semidirect
58. C2×#10587632C22semidirect
65. #11763285C22semidirect
66. C2×Q8×Dic17C22semidirect
67. C2×C4×Dic34C22semidirect
68. C2×#10587573C22semidirect
77. C23×Q8×C17C22semidirect
78. D4×Q8×C17C22semidirect
79. C2×C17×C4⋊Q8C22semidirect
81. C2×C17×C22⋊Q8C22semidirect
82. C2×C4×Q8×C17C22semidirect
91. C22×Q8×C17C23semidirect
104. C2×#63256C23semidirect
110. C2×Q8×D17D4semidirect
115. C2×Q8×D17C23semidirect
119. C2×#63252C23semidirect
137. C17×C4⋊Q8C23semidirect
139. C17×C22⋊Q8C23semidirect
140. C4×Q8×C17C23semidirect
150. #10587633C23semidirect
152. #10587632C23semidirect
153. Q8×Dic17C23semidirect
154. #10587630C23semidirect
170. #10587610C23semidirect
178. #10587583C23semidirect
180. #10587582C23semidirect
181. #10587582C23semidirect
187. #10587574C23semidirect
188. #10587573C23semidirect
189. #10587571C23semidirect
195. #10587561C23semidirect
198. C4×Dic34C23semidirect
248. Q8×D17C2×D4semidirect
310. C23×C172−1+4semidirect
326. C22×D172−1+4semidirect
380. C2×D4×Q8D17semidirect
400. C22×C17C2×2−1+4semidirect
414. C2×D17C2×2−1+4semidirect
440. C23×Q8C2×D17semidirect
445. D4×Q8C2×D17semidirect
454. C2×C4⋊Q8C2×D17semidirect
472. C2×C22⋊Q8C2×D17semidirect
483. C2×C4×Q8C2×D17semidirect
494. C2×C17#3486semidirect
534. C22×Q8C22×D17semidirect
556. C4⋊Q8C22×D17semidirect
572. C22⋊Q8C22×D17semidirect
582. C4×Q8C22×D17semidirect
616. C17C2×#3486semidirect
743. C23#10587694semidirect
814. C22C2×#10587694semidirect
831. C2#14542434direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876942
C23×Q8×D172
#145424342
C2×#117634742
C2×Q8×C22⋊D172
C2×#117634722
C2×#117634712
C2×#117634702
C2×#117634692
C2×#117634682
C2×#117633842
C2×#117633822
C2×#117633222
C2×#117633182
C2×#117632852
C2×D4×Q8×C172
C2×#348617