Finite Group Databasebeta

← C2×#14533797 #17204366

Subgroups — C2×#14533797 #17204366

Order 4352.

3094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587610C211yesmaximal, characteristic
2C22×#10587564C211yesmaximal, characteristic
3#14533797C2116yesmaximal, direct product factor
4C2×#11762743C211yesmaximal, characteristic, complemented
5C2×#11762742C211yesmaximal, characteristic, complemented
6C2×#11762730C211yesmaximal, characteristic, complemented
7C2×#11762729C211yesmaximal, characteristic, complemented
8C2×#11762713C211yesmaximal, characteristic, complemented
9C2×#11762713C211yesmaximal, characteristic, complemented
10C2×#11762708C211yesmaximal, characteristic, complemented
11C2×#11762705C211yesmaximal, characteristic, complemented
12C2×#11762684C211yesmaximal, characteristic
13C2×#11762667C211yesmaximal, characteristic
14C2×C22⋊C4×Dic17C211yesmaximal, characteristic
15C22×#10587502C211yesmaximal, characteristic
16C2×C17×#385C211yesmaximal, characteristic
17C23×Dic34C2211yescharacteristic
18C23×Dic34C2211yescharacteristic
19C24×Dic17C2211yescharacteristic
20C24×Dic17C2211yescharacteristic
21C2×#10587610—28no—
22C2×#10587610C2218yes—
23C2×#10587564—28no—
24C2×#10587564C2218yes—
25C22×C4⋊Dic17C2211yescharacteristic
26C22×C4⋊Dic17C2211yescharacteristic
27C22×C4⋊Dic17C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63225C2211yescharacteristic
33C22×#63225C2211yescharacteristic
34C22×#63225C2211yescharacteristic
35C22×C22⋊Dic17C2211yescharacteristic
36C22×C22⋊Dic17C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38C22×C4×Dic17C2211yescharacteristic
39#11762743C2218yescomplemented
40#11762742C2218yescomplemented
41#11762730C2218yescomplemented
42#11762729C2218yescomplemented
43#11762713C2218yescomplemented
44#11762713C2218yescomplemented
45#11762708C2218yescomplemented
46#11762705C2218yescomplemented
47#11762684C2218yes—
48#11762667C2218yes—
49C22⋊C4×Dic17C2218yes—
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2218yes—
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61C24×C4×C17C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C22⋊C4×C17C2211yescharacteristic
65C22×C22⋊C4×C17C2211yescharacteristic
66C17×#385C2218yes—
67C2×C17×#95C2211yescharacteristic
68C2×C17×#95C2211yescharacteristic
69C25×C17C2311yescharacteristic
70C23×C4×C17—24no—
71C23×C4×C17—24no—
72C23×C4×C17—42no—
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2314yes—
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×Dic17—24no—
81C23×Dic17—24no—
82C23×Dic17—42no—
83C23×Dic17—42no—
84C23×Dic17—42no—
85C23×Dic17Q818yescomplemented
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2314yes—
90C23×Dic17C2311yescharacteristic
91C23×Dic17C2311yescharacteristic
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C23×Dic17C2311yescharacteristic
95C23×Dic17C2314yes—
96C22×Dic34—24no—
97C22×Dic34—24no—
98C22×Dic34—24no—
99C22×Dic34—24no—
100C22×Dic34—42no—
101C22×Dic34—42no—
102C22×Dic34C2314yes—
103C22×Dic34C2314yes—
104C2×C4⋊C4×C17—24no—
105C2×C4⋊C4×C17—42no—
106C2×C4⋊C4×C17C2314yes—
107C2×C4⋊C4×C17C2314yes—
108C2×C22⋊C4×C17—24no—
109C2×C22⋊C4×C17Q818yescomplemented
110C2×C22⋊C4×C17C2314yes—
111C2×C22⋊C4×C17C2314yes—
112C2×C22⋊Dic17—24no—
113C2×C22⋊Dic17D418yes—
114C2×C22⋊Dic17C2314yes—
115C2×C22⋊Dic17C2314yes—
116C2×C4⋊Dic17—24no—
117C2×C4⋊Dic17—24no—
118C2×C4⋊Dic17—24no—
119C2×C4⋊Dic17—42no—
120C2×C4⋊Dic17C2314yes—
121C2×C4⋊Dic17C2314yes—
122C2×C4⋊Dic17C2314yes—
123C2×C4⋊Dic17C2314yes—
124#10587610—232no—
125C2×#63225—24no—
126C2×#63225—24no—
127C2×#63225—24no—
128C2×#63225—24no—
129C2×#63225—42no—
130C2×#63225—42no—
131C2×#63225C2314yes—
132C2×#63225C2314yes—
133C2×#63225C2314yes—
134C2×#63225C2314yes—
135C2×#63225C2314yes—
136C2×#63225C2314yes—
137C2×C4×Dic17—42no—
138C2×C4×Dic17—42no—
139C2×C4×Dic17C2314yes—
140C2×C4×Dic17C2314yes—
141#10587564—232no—
142C17×#95C2314yes—
143C17×#95C2314yes—
144#10587502C2314yes—
145#10587502C2314yes—
146#10587502C2314yes—
147#10587502C2314yes—
148#10587502C2314yes—
149#10587502C2314yes—
150#10587502C2314yes—
151#10587502C2314yes—
152#10587502C2314yes—
153#10587502C2314yes—
154C24×C17—22no—
155C24×C17—22no—
156C24×C17—22no—
157C24×C17—22no—
158C24×C17C2×D414yes—
159C24×C17C2×Q814yes—
160C24×C17C2×Q814yes—
161C24×C17C2412yes—
162C24×C17C2411yescharacteristic
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—22no—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—28no—
172C22×C4×C17—22no—
173C22×C4×C17—22no—
174C22×C4×C17—22no—
175C22×C4×C17—22no—
176C22×C4×C17—22no—
177C22×C4×C17—22no—
178C22×C4×C17—22no—
179C22×C4×C17—28no—
180C22×C4×C17—44no—
181C22×C4×C17—416no—
182C22×C4×C17C2×Q814yes—
183C22×C4×C17C2×Q814yes—
184C22×C4×C17#4114yes—
185C22×C4×C17C2412yes—
186C22×C4×C17C2412yes—
187C22×C4×C17C2412yes—
188C22×C4×C17C2412yes—
189C22×C4×C17C2412yes—
190C22×C4×C17C2412yes—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—22no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—28no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—28no—
212C22×Dic17—416no—
213C22×Dic17—44no—
214C22×Dic17—44no—
215C22×Dic17—44no—
216C22×Dic17—416no—
217C22×Dic17C2×D414yes—
218C22×Dic17C2×D414yes—
219C22×Dic17C2×Q814yes—
220C22×Dic17C2×Q814yes—
221C22×Dic17C2×Q8116yescomplemented
222C22×Dic17#4114yes—
223C22×Dic17C2412yes—
224C22×Dic17C2412yes—
225C22×Dic17C2412yes—
226C22×Dic17C2412yes—
227C22×Dic17C2412yes—
228C22×Dic17C2412yes—
229C22×Dic17C2412yes—
230C22×Dic17C2412yes—
231C2×Dic34—28no—
232C2×Dic34—28no—
233C2×Dic34—28no—
234C2×Dic34—28no—
235C2×Dic34—44no—
236C2×Dic34—44no—
237C2×Dic34—416no—
238C2×Dic34—416no—
239C4⋊C4×C17—28no—
240C4⋊C4×C17—44no—
241C22⋊C4×C17—28no—
242C22⋊C4×C17C2×Q8116yescomplemented
243C22⋊Dic17—28no—
244C22⋊Dic17C2×D4116yes—
245C4⋊Dic17—28no—
246C4⋊Dic17—28no—
247C4⋊Dic17—28no—
248C4⋊Dic17—44no—
249#63225—28no—
250#63225—28no—
251#63225—28no—
252#63225—28no—
253#63225—44no—
254#63225—44no—
255C4×Dic17—44no—
256C4×Dic17—44no—
257C2×#2549—171nomaximal, Sylow
258C23×C17—28no—
259C23×C17—28no—
260C23×C17—28no—
261C23×C17—28no—
262C23×C17—28no—
263C23×C17—28no—
264C23×C17—22no—
265C23×C17—22no—
266C23×C17—22no—
267C23×C17—22no—
268C23×C17C4⋊Q8116yes—
269C23×C17C22×D414yes—
270C23×C17C22×D412yes—
271C23×C17C22×Q814yes—
272C23×C17C22×Q812yes—
273C23×C17C22×Q814yes—
274C23×C17C22×Q812yes—
275C23×C17C2×#4112yes—
276C23×C17C2×#4112yes—
277C23×C17H(5,𝔽2)12yes—
278C23×C17H(5,𝔽2)12yes—
279C23×C17C2511yescharacteristic
280C2×C4×C17—28no—
281C2×C4×C17—28no—
282C2×C4×C17—28no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—416no—
299C2×C4×C17—44no—
300C2×C4×C17—44no—
301C2×C4×C17—44no—
302C2×C4×C17C22×Q814yes—
303C2×C4×C17C22×Q814yes—
304C2×C4×C17C2×#4114yes—
305C2×Dic17—28no—
306C2×Dic17—28no—
307C2×Dic17—28no—
308C2×Dic17—28no—
309C2×Dic17—28no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—416no—
330C2×Dic17—416no—
331C2×Dic17—44no—
332C2×Dic17—44no—
333C2×Dic17—44no—
334C2×Dic17C22×D414yes—
335C2×Dic17C22×D414yes—
336C2×Dic17C22×Q814yes—
337C2×Dic17C22×Q814yes—
338C2×Dic17C2×#4114yes—
339Dic34—416no—
340Dic34—416no—
341C22×C22⋊Q8—171no—
342C22×C22⋊Q8—171no—
343#2549—1716no—
344C2×#398—171no—
345C2×#398—171no—
346C2×#395—171no—
347C2×#395—171no—
348C2×#391—171no—
349C2×#391—171no—
350C2×#389—171no—
351C2×#389—171no—
352C2×#385—171no—
353C2×#385D1711yescharacteristic
354C2×#380—171no—
355C2×C4×C22⋊C4—171no—
356C22×#95—171no—
357C22×C17—24no—
358C22×C17—24no—
359C22×C17—24no—
360C22×C17—24no—
361C22×C17—24no—
362C22×C17—24no—
363C22×C17—232no—
364C22×C17C2×C4⋊Q818yes—
365C22×C17C2×C4⋊Q814yes—
366C22×C17#53314yes—
367C22×C17#54314yes—
368C22×C17#54614yes—
369C22×C17#54614yes—
370C22×C17#55414yes—
371C22×C17#55414yes—
372C22×C17C23×D411yescharacteristic
373C22×C17C23×Q811yescharacteristic
374C22×C17C23×Q811yescharacteristic
375C22×C17C22×#4111yescharacteristic
376C22×C17C22×#4111yescharacteristic
377C22×C17C2×H(5,𝔽2)11yescharacteristic
378C22×C17C2×H(5,𝔽2)11yescharacteristic
379C4×C17—24no—
380C4×C17—24no—
381C4×C17—24no—
382C4×C17—42no—
383C4×C17—42no—
384C4×C17—42no—
385Dic17—24no—
386Dic17—24no—
387Dic17—24no—
388Dic17—24no—
389Dic17—24no—
390Dic17—42no—
391Dic17—42no—
392Dic17—42no—
393C23×Q8—171no—
394C23×Q8—171no—
395C24×C4—171no—
396C24×C4—171no—
397C24×C4C2×D1711yescharacteristic
398C2×C22⋊Q8—178no—
399C2×C22⋊Q8—178no—
400C2×C22⋊Q8—348no—
401C2×C22⋊Q8—348no—
402C22×C4⋊C4—171no—
403C22×C4⋊C4—171no—
404C22×C4⋊C4—171no—
405C22×C4⋊C4—171no—
406C22×C4⋊C4—171no—
407C22×C4⋊C4—171no—
408C22×C4⋊C4—171no—
409C22×C4⋊C4—171no—
410C22×C4⋊C4—171no—
411C22×C4⋊C4—171no—
412C22×C4⋊C4C2×D1711yescharacteristic
413C22×C4⋊C4C2×D1711yescharacteristic
414C22×C22⋊C4—171no—
415C22×C22⋊C4—171no—
416C22×C22⋊C4C2×D1711yescharacteristic
417C22×C22⋊C4C2×D1711yescharacteristic
418C22×C42—171no—
419C22×C42—171no—
420#398—178no—
421#398—178no—
422#395—178no—
423#395—178no—
424#391—178no—
425#391—178no—
426#389—178no—
427#389—178no—
428#385—178no—
429#385C2×D1718yes—
430#380—178no—
431C4×C22⋊C4—178no—
432C2×#95—171no—
433C2×#95—171no—
434C2×#95—171no—
435C2×#95—171no—
436C2×#95—171no—
437C2×#95—171no—
438C2×#95—171no—
439C2×#95—171no—
440C2×#95—178no—
441C2×#95—171no—
442C2×#95—171no—
443C2×#95C2×D1711yescharacteristic
444C2×#95C2×D1711yescharacteristic
445C2×C17—28no—
446C2×C17#254918yescomplemented
447C2×C17C22×C4⋊Q811yescharacteristic
448C2×C17C2×#53311yescharacteristic
449C2×C17C2×#54311yescharacteristic
450C2×C17C2×#54611yescharacteristic
451C2×C17C2×#54611yescharacteristic
452C2×C17C2×#55411yescharacteristic
453C2×C17C2×#55411yescharacteristic
454C25C22×D1711yescharacteristic
455C22×Q8—174no—
456C22×Q8—174no—
457C22×Q8—344no—
458C22×Q8—344no—
459C22×Q8—344no—
460C22×Q8—344no—
461C22×Q8—682no—
462C22×Q8—682no—
463C23×C4—24no—
464C23×C4—24no—
465C23×C4—42no—
466C23×C4—171no—
467C23×C4—171no—
468C23×C4—171no—
469C23×C4—171no—
470C23×C4—171no—
471C23×C4—178no—
472C23×C4—174no—
473C23×C4—171no—
474C23×C4—171no—
475C23×C4—171no—
476C23×C4—174no—
477C23×C4—344no—
478C23×C4—344no—
479C23×C4—682no—
480C23×C4—682no—
481C23×C4—682no—
482C23×C4C22×D1711yescharacteristic
483C23×C4C22×D1711yescharacteristic
484C23×C4C22×D1711yescharacteristic
485C23×C4C22×D1714yes—
486C23×C4C22×D1711yescharacteristic
487C23×C4C22×D1711yescharacteristic
488C23×C4C22×D1711yescharacteristic
489C22⋊Q8—3432no—
490C22⋊Q8—3432no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4—174no—
494C2×C4⋊C4—174no—
495C2×C4⋊C4—174no—
496C2×C4⋊C4—174no—
497C2×C4⋊C4—174no—
498C2×C4⋊C4—174no—
499C2×C4⋊C4—174no—
500C2×C4⋊C4—174no—
501C2×C4⋊C4—174no—
502C2×C4⋊C4—174no—
503C2×C4⋊C4—344no—
504C2×C4⋊C4—344no—
505C2×C4⋊C4—344no—
506C2×C4⋊C4—344no—
507C2×C4⋊C4—344no—
508C2×C4⋊C4—344no—
509C2×C4⋊C4—344no—
510C2×C4⋊C4—682no—
511C2×C4⋊C4—682no—
512C2×C4⋊C4—682no—
513C2×C4⋊C4C22×D1714yes—
514C2×C4⋊C4C22×D1714yes—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—178no—
517C2×C22⋊C4—174no—
518C2×C22⋊C4—174no—
519C2×C22⋊C4—344no—
520C2×C22⋊C4Dic3418yescomplemented
521C2×C22⋊C4C22×D1714yes—
522C2×C22⋊C4C22×D1714yes—
523C2×C42—174no—
524C2×C42—174no—
525C2×C42—682no—
526C2×C42—682no—
527#95—174no—
528#95—174no—
529#95—174no—
530#95—174no—
531#95—174no—
532#95—174no—
533#95—174no—
534#95—174no—
535#95—174no—
536#95—174no—
537#95C22×D1714yes—
538#95C22×D1714yes—
539C17C2×#254911yescharacteristic, complemented, Sylow
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24C2×Dic3414yes—
545C24D4×D1714yes—
546C24Q8×D1714yes—
547C24C23×D1712yes—
548C24C23×D1711yescharacteristic
549C2×Q8—348no—
550C2×Q8—348no—
551C2×Q8—348no—
552C2×Q8—348no—
553C2×Q8—684no—
554C2×Q8—684no—
555C2×Q8—6816no—
556C2×Q8—6816no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—44no—
575C22×C4—416no—
576C22×C4—174no—
577C22×C4—174no—
578C22×C4—174no—
579C22×C4—174no—
580C22×C4—174no—
581C22×C4—172no—
582C22×C4—172no—
583C22×C4—172no—
584C22×C4—172no—
585C22×C4—172no—
586C22×C4—1716no—
587C22×C4—172no—
588C22×C4—172no—
589C22×C4—172no—
590C22×C4—348no—
591C22×C4—342no—
592C22×C4—342no—
593C22×C4—342no—
594C22×C4—342no—
595C22×C4—342no—
596C22×C4—342no—
597C22×C4—342no—
598C22×C4—342no—
599C22×C4—342no—
600C22×C4—342no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—342no—
604C22×C4—348no—
605C22×C4—342no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—342no—
610C22×C4—342no—
611C22×C4—684no—
612C22×C4—684no—
613C22×C4—684no—
614C22×C4—6816no—
615C22×C4—6816no—
616C22×C4C2×Dic3414yes—
617C22×C4C2×Dic3414yes—
618C22×C4#6325414yes—
619C22×C4C23×D1712yes—
620C22×C4C23×D1712yes—
621C22×C4C23×D1712yes—
622C22×C4C23×D1712yes—
623C22×C4C23×D1712yes—
624C22×C4C23×D1712yes—
625C4⋊C4—28no—
626C4⋊C4—44no—
627C4⋊C4—348no—
628C4⋊C4—348no—
629C4⋊C4—348no—
630C4⋊C4—348no—
631C4⋊C4—348no—
632C4⋊C4—348no—
633C4⋊C4—348no—
634C4⋊C4—684no—
635C4⋊C4—684no—
636C4⋊C4—684no—
637C22⋊C4—28no—
638C22⋊C4—1716no—
639C22⋊C4—348no—
640C22⋊C4C2×Dic34116yescomplemented
641C42—684no—
642C42—684no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—28no—
651C23—28no—
652C23—28no—
653C23#10587574116yes—
654C23C22×Dic3414yes—
655C23C22×Dic3412yes—
656C23C2×D4×D1714yes—
657C23C2×D4×D1712yes—
658C23C2×#6325412yes—
659C23#1058769112yes—
660C23C2×Q8×D1714yes—
661C23C2×Q8×D1712yes—
662C23#41×D1712yes—
663C23#1058769612yes—
664C23C24×D1711yescharacteristic
665Q8—6816no—
666Q8—6816no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—28no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—174no—
690C2×C4—174no—
691C2×C4—174no—
692C2×C4—174no—
693C2×C4—174no—
694C2×C4—342no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—342no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—342no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—342no—
704C2×C4—348no—
705C2×C4—348no—
706C2×C4—348no—
707C2×C4—348no—
708C2×C4—348no—
709C2×C4—342no—
710C2×C4—342no—
711C2×C4—342no—
712C2×C4—342no—
713C2×C4—342no—
714C2×C4—342no—
715C2×C4—342no—
716C2×C4—342no—
717C2×C4—342no—
718C2×C4—6816no—
719C2×C4—6816no—
720C2×C4—684no—
721C2×C4—684no—
722C2×C4—684no—
723C2×C4C22×Dic3414yes—
724C2×C4C22×Dic3414yes—
725C2×C4C2×#6325414yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—232no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22C2×#1058757418yes—
734C22C2×#1058757414yes—
735C22#1176336114yes—
736C22#1176343414yes—
737C22#1176344614yes—
738C22#1176345114yes—
739C22#1176351614yes—
740C22#1176351814yes—
741C22C22×D4×D1711yescharacteristic
742C22C22×Q8×D1711yescharacteristic
743C22C23×Dic3411yescharacteristic
744C22C2×#41×D1711yescharacteristic
745C22C22×#6325411yescharacteristic
746C22C2×#1058769111yescharacteristic
747C22C2×#1058769611yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—344no—
755C4—344no—
756C4—344no—
757C4—344no—
758C4—344no—
759C4—682no—
760C4—682no—
761C4—682no—
762C2—28no—
763C2#1453379718yesdirect product factor
764C2C22×#1058757411yescharacteristic
765C2C2×#1176336111yescharacteristic
766C2C2×#1176343411yescharacteristic
767C2C2×#1176344611yescharacteristic
768C2C2×#1176345111yescharacteristic
769C2C2×#1176351611yescharacteristic
770C2C2×#1176351811yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#385C2
socleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#385D17
hypocenterC17C2×#2549
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. #14533797C2direct (N × H)
4. C2×#11762743C2semidirect
5. C2×#11762742C2semidirect
6. C2×#11762730C2semidirect
7. C2×#11762729C2semidirect
8. C2×#11762713C2semidirect
9. C2×#11762713C2semidirect
10. C2×#11762708C2semidirect
11. C2×#11762705C2semidirect
39. #11762743C22semidirect
40. #11762742C22semidirect
41. #11762730C22semidirect
42. #11762729C22semidirect
43. #11762713C22semidirect
44. #11762713C22semidirect
45. #11762708C22semidirect
46. #11762705C22semidirect
85. C23×Dic17Q8semidirect
109. C2×C22⋊C4×C17Q8semidirect
221. C22×Dic17C2×Q8semidirect
242. C22⋊C4×C17C2×Q8semidirect
446. C2×C17#2549semidirect
520. C2×C22⋊C4Dic34semidirect
539. C17C2×#2549semidirect
640. C22⋊C4C2×Dic34semidirect
763. C2#14533797direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876102
C22×#105875642
#145337972
C2×#117627432
C2×#117627422
C2×#117627302
C2×#117627292
C2×#117627132
C2×#117627082
C2×#117627052
C2×#117626842
C2×#117626672
C2×C22⋊C4×Dic172
C22×#105875022
C2×C17×#3852
C2×#254917