Finite Group Databasebeta

← C2×#14545602 #17979874

Subgroups — C2×#14545602 #17979874

Order 4352.

2070 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545602C2116yesmaximal, direct product factor
2C2×#11763861C211yesmaximal, characteristic, complemented
3C2×#11763858C211yesmaximal, characteristic, complemented
4C2×#11763842C211yesmaximal, characteristic, complemented
5C2×#11763841C211yesmaximal, characteristic, complemented
6C2×#11763839C211yesmaximal, characteristic, complemented
7C2×#11763837C211yesmaximal, characteristic, complemented
8C2×#11763836C211yesmaximal, characteristic, complemented
9C2×#11763836C211yesmaximal, characteristic, complemented
10C2×#11763834C211yesmaximal, characteristic, complemented
11C2×#11763833C211yesmaximal, characteristic, complemented
12C2×#11763832C211yesmaximal, characteristic, complemented
13C2×#11763774C211yesmaximal, characteristic, complemented
14C2×#11763773C211yesmaximal, characteristic, complemented
15C2×C4×#63242C211yesmaximal, characteristic, complemented
16C2×#11763342C211yesmaximal, characteristic
17C22×#63243C2211yescharacteristic
18C22×#63247C2211yescharacteristic
19C22×#63242C2211yescharacteristic
20C22×#63242C2211yescharacteristic
21C22×#63242C2211yescharacteristic
22C23×#3624C2211yescharacteristic
23#11763861C2218yescomplemented
24#11763858C2218yescomplemented
25#11763842C2218yescomplemented
26#11763841C2218yescomplemented
27#11763839C2218yescomplemented
28#11763837C2218yescomplemented
29#11763836C2218yescomplemented
30#11763836C2218yescomplemented
31#11763834C2218yescomplemented
32#11763833C2218yescomplemented
33#11763832C2218yescomplemented
34C2×#10587544C2211yescharacteristic
35C2×#10587544C2211yescharacteristic
36C2×#10587544C2211yescharacteristic
37C2×#10587544C2211yescharacteristic
38C2×C4⋊#3624C2211yescharacteristic
39C2×C4⋊#3624C2211yescharacteristic
40C2×#10587543C2211yescharacteristic
41C2×#10587543C2211yescharacteristic
42C2×#10587543C2211yescharacteristic
43C2×#10587543C2211yescharacteristic
44C2×C22⋊#3624C2211yescharacteristic
45C2×C22⋊#3624C2211yescharacteristic
46#11763774C2218yescomplemented
47#11763773C2218yescomplemented
48C2×#10587542C2211yescharacteristic
49C2×#10587542C2211yescharacteristic
50C2×#10587542C2211yescharacteristic
51C2×#10587542C2211yescharacteristic
52C4×#63242C2218yescomplemented
53C2×C4×#3624C2211yescharacteristic
54C2×C4×#3624C2211yescharacteristic
55C2×C4×#3624C2211yescharacteristic
56C2×C4×#3624C2211yescharacteristic
57C2×C4×#3624C2211yescharacteristic
58C2×C4×#3624C2211yescharacteristic
59#11763342C418yes—
60#11763342C2218yes—
61C2×#10587562C411yescharacteristic
62C2×#10587575C411yescharacteristic
63C2×#10587571C411yescharacteristic
64C2×#10587580C411yescharacteristic
65C2×#10587569C411yescharacteristic
66C2×#10587582C411yescharacteristic
67C2×#10587570C411yescharacteristic
68C2×#10587573C2211yescharacteristic
69C2×#10587579C2211yescharacteristic
70C2×#10587567C2211yescharacteristic
71C2×#10587567C2211yescharacteristic
72C2×#10587578C2211yescharacteristic
73C2×#10587563C2211yescharacteristic
74C2×C42×D17C2211yescharacteristic
75C2×C17×#126C411yescharacteristic
76C22×C22⋊D17C2×C411yescharacteristic
77C22×C22⋊D17C2×C411yescharacteristic
78C23×Dic17C2311yescharacteristic
79C22×D68C2×C411yescharacteristic
80C22×C4×D17C2×C411yescharacteristic
81C22×C4×D17C2×C411yescharacteristic
82C22×C4×D17C2311yescharacteristic
83C22×C4×D17C2311yescharacteristic
84C22×Dic34C2×C411yescharacteristic
85C2×#63247—24no—
86C2×#63247C2314yes—
87C22×#3624—24no—
88C22×#3624C2311yescharacteristic
89C22×#3624C2311yescharacteristic
90C22×#3624C2311yescharacteristic
91C22×#3624C2311yescharacteristic
92C22×#3624C2311yescharacteristic
93C22×#3624C2311yescharacteristic
94C22×#3624C2314yes—
95C22×#3624C2311yescharacteristic
96C22×#3624C2311yescharacteristic
97C2×#63243—24no—
98C2×#63243C2314yes—
99C2×#63242—24no—
100C2×#63242—24no—
101C2×#63242—24no—
102C2×#63242C2314yes—
103C2×#63242C2314yes—
104C2×#63242C2314yes—
105C17×#126C2×C418yes—
106C2×C4⋊C4×C17C2×C411yescharacteristic
107C2×C4⋊C4×C17C2×C411yescharacteristic
108C2×C4⋊C4×C17C2×C411yescharacteristic
109C2×C22⋊C4×C17C2×C411yescharacteristic
110C2×C22⋊C4×C17C2×C411yescharacteristic
111C2×C22⋊C4×C17C2×C411yescharacteristic
112C2×C42×C17C2×C411yescharacteristic
113C2×C22⋊Dic17C2×C411yescharacteristic
114C2×#63227C2×C411yescharacteristic
115C2×#63227C2×C411yescharacteristic
116C2×#63227C2×C411yescharacteristic
117C2×#63227C2×C411yescharacteristic
118C2×#63227C2×C411yescharacteristic
119C2×#63227C2×C411yescharacteristic
120C2×C4⋊Dic17C2×C411yescharacteristic
121C2×#63225C2×C411yescharacteristic
122C2×#63225C2×C411yescharacteristic
123C2×#63225C2×C411yescharacteristic
124C2×#63225C2×C411yescharacteristic
125C2×#63225C2×C411yescharacteristic
126C2×#63225C2×C411yescharacteristic
127C2×C4×Dic17C2×C411yescharacteristic
128C2×C4×Dic17C2311yescharacteristic
129C2×C4×Dic17C2311yescharacteristic
130C2×C4×Dic17C2311yescharacteristic
131C2×C4×Dic17C2311yescharacteristic
132#10587582C2×C418yes—
133#10587580C2×C418yes—
134#10587579C2×C414yes—
135#10587579C2314yes—
136#10587578C2×C414yes—
137#10587578C2314yes—
138#10587575C2×C418yes—
139#10587573C2×C414yes—
140#10587573C2314yes—
141#10587571C2×C418yes—
142#10587570C2×C418yes—
143#10587569C2×C418yes—
144#10587567C2×C414yes—
145#10587567C2×C414yes—
146#10587567C2314yes—
147#10587567C2314yes—
148#10587563C2×C414yes—
149#10587563C2314yes—
150#10587562C2×C418yes—
151C42×D17C2×C414yes—
152C42×D17C2314yes—
153C22⋊#3624C2314yes—
154C22⋊#3624C2314yes—
155#10587544C2314yes—
156#10587544C2314yes—
157#10587544C2314yes—
158#10587544C2314yes—
159#10587543C2314yes—
160#10587543C2314yes—
161#10587543C2314yes—
162#10587543C2314yes—
163#10587542C2314yes—
164#10587542C2314yes—
165#10587542C2314yes—
166#10587542C2314yes—
167C4⋊#3624C2314yes—
168C4⋊#3624C2314yes—
169C4×#3624C2314yes—
170C4×#3624C2314yes—
171C4×#3624C2314yes—
172C4×#3624C2314yes—
173C4×#3624C2314yes—
174C4×#3624C2314yes—
175C24×C17C22×C411yescharacteristic
176C23×D17C22×C411yescharacteristic
177C23×D17C22×C411yescharacteristic
178C22×C4×C17C22×C411yescharacteristic
179C22×C4×C17C22×C411yescharacteristic
180C22×C4×C17C22×C411yescharacteristic
181C22×C4×C17C22×C411yescharacteristic
182C22×C4×C17C22×C411yescharacteristic
183C22×C4×C17C22×C411yescharacteristic
184C2×C22⋊D17—24no—
185C2×C22⋊D17—24no—
186C2×C22⋊D17C22×C414yes—
187C2×C22⋊D17C22×C414yes—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17C22×C411yescharacteristic
191C22×Dic17C22×C411yescharacteristic
192C22×Dic17C22×C412yes—
193C22×Dic17C22×C411yescharacteristic
194C22×Dic17C22×C411yescharacteristic
195C22×Dic17C22×C411yescharacteristic
196C22×Dic17C2412yes—
197C22×Dic17C2411yescharacteristic
198C2×D68—24no—
199C2×D68C22×C414yes—
200C2×C4×D17—24no—
201C2×C4×D17—24no—
202C2×C4×D17—22no—
203C2×C4×D17—22no—
204C2×C4×D17—22no—
205C2×C4×D17—22no—
206C2×C4×D17C22×C414yes—
207C2×C4×D17C22×C414yes—
208C2×C4×D17C22×C412yes—
209C2×C4×D17C22×C412yes—
210C2×C4×D17C2412yes—
211C2×C4×D17C2412yes—
212C2×Dic34—24no—
213C2×Dic34C22×C414yes—
214#63247—28no—
215C2×#3624—22no—
216C2×#3624—22no—
217C2×#3624—22no—
218C2×#3624—22no—
219C2×#3624—22no—
220C2×#3624—22no—
221C2×#3624—28no—
222C2×#3624#4114yes—
223C2×#3624#4114yes—
224C2×#3624C2412yes—
225C2×#3624C2412yes—
226C2×#3624C2412yes—
227C2×#3624C2412yes—
228C2×#3624C2412yes—
229C2×#3624C2412yes—
230C2×#3624C2412yes—
231C2×#3624C2412yes—
232#63243—28no—
233#63242—28no—
234#63242—28no—
235#63242—28no—
236C4⋊C4×C17C22×C414yes—
237C4⋊C4×C17C22×C414yes—
238C4⋊C4×C17C22×C414yes—
239C22⋊C4×C17C22×C414yes—
240C22⋊C4×C17C22×C414yes—
241C22⋊C4×C17C22×C414yes—
242C42×C17C22×C414yes—
243C22⋊Dic17C22×C414yes—
244#63227C22×C414yes—
245#63227C22×C414yes—
246#63227C22×C414yes—
247#63227C22×C414yes—
248#63227C22×C414yes—
249#63227C22×C414yes—
250C4⋊Dic17C22×C414yes—
251#63225C22×C414yes—
252#63225C22×C414yes—
253#63225C22×C414yes—
254#63225C22×C414yes—
255#63225C22×C414yes—
256#63225C22×C414yes—
257C4×Dic17C22×C412yes—
258C4×Dic17C22×C412yes—
259C4×Dic17C22×C414yes—
260C4×Dic17C22×C412yes—
261C4×Dic17C22×C412yes—
262C4×Dic17C2412yes—
263C4×Dic17C2412yes—
264C4×Dic17C2412yes—
265C4×Dic17C2412yes—
266C2×#2966—171nomaximal, Sylow
267C23×C17—22no—
268C23×C17—22no—
269C23×C17—22no—
270C23×C17C23×C412yes—
271C23×C17C23×C411yescharacteristic
272C22×D17—22no—
273C22×D17—22no—
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—22no—
277C22×D17#13114yes—
278C22×D17C23×C412yes—
279C22×D17C23×C412yes—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17C23×C412yes—
287C2×C4×C17C23×C412yes—
288C2×C4×C17C23×C412yes—
289C2×C4×C17C23×C412yes—
290C2×C4×C17C23×C412yes—
291C2×C4×C17C23×C412yes—
292C22⋊D17—28no—
293C22⋊D17—28no—
294C2×Dic17—22no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—24no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17#13114yes—
302C2×Dic17C23×C412yes—
303C2×Dic17C23×C412yes—
304C2×Dic17C23×C412yes—
305C2×Dic17C23×C412yes—
306C2×Dic17C23×C411yescharacteristic
307C2×Dic17C23×C412yes—
308C2×Dic17C2×#4112yes—
309C2×Dic17C2×#4112yes—
310C2×Dic17C2511yescharacteristic
311D68—28no—
312C4×D17—28no—
313C4×D17—24no—
314C4×D17—24no—
315C4×D17—28no—
316C4×D17—22no—
317C4×D17—22no—
318C4×D17—22no—
319C4×D17—22no—
320Dic34—28no—
321#3624—22no—
322#3624—22no—
323#3624—22no—
324#3624—22no—
325#3624—22no—
326#3624—22no—
327#3624C2×#4114yes—
328#3624C2×#4114yes—
329C2×#529—171no—
330#2966—1716no—
331C2×#446—171no—
332C2×C8×Q8—171no—
333C2×#436—171no—
334C2×#435—171no—
335C2×#435—171no—
336C2×C8×D4—171no—
337C2×C8×D4—171no—
338C2×C8×D4—171no—
339C2×#433—171no—
340C2×#433—171no—
341C2×#432—171no—
342C2×#405—171no—
343C2×#405—171no—
344C22×C4×C8—171no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—22no—
348C22×C17—44no—
349C22×C17C4×#4112yes—
350C22×C17C2×#13112yes—
351C22×C17C2×#13112yes—
352C22×C17C24×C411yescharacteristic
353C2×D17—22no—
354C2×D17—28no—
355C2×D17—22no—
356C2×D17—22no—
357C2×D17—22no—
358C2×D17—22no—
359C2×D17—44no—
360C2×D17C2×#13114yes—
361C4×C17—22no—
362C4×C17—22no—
363C4×C17—22no—
364C4×C17—22no—
365C4×C17—22no—
366C4×C17—22no—
367Dic17—22no—
368Dic17—22no—
369Dic17—22no—
370Dic17—22no—
371Dic17C4×#4112yes—
372Dic17C2×#13114yes—
373Dic17C22×#4111yescharacteristic
374Dic17C22×#4111yescharacteristic
375C22×M16—171no—
376C22×M16—171no—
377C23×C8—171no—
378C23×C8—171no—
379C23×C8—171no—
380C23×C8—171no—
381#529—178no—
382#529—178no—
383C2×#126—171no—
384C2×#126#59511yescharacteristic
385C2×#125—171no—
386C2×#124—171no—
387C2×#123—171no—
388C2×#123—171no—
389C2×C22⋊Q8—171no—
390C2×#121—171no—
391C2×C4×Q8—171no—
392C2×C4×D4—171no—
393C2×C4×D4—171no—
394C2×C4×D4—171no—
395C2×#117—171no—
396C2×#117—171no—
397C22×C42—171no—
398#446—178no—
399C8×Q8—178no—
400#436—178no—
401#435—178no—
402#435—178no—
403C8×D4—178no—
404C8×D4—178no—
405C8×D4—178no—
406#433—178no—
407#433—178no—
408#432—178no—
409C2×C4⋊C8—171no—
410C2×C4⋊C8—171no—
411C2×C4⋊C8—171no—
412C2×C4⋊C8—171no—
413C2×C4⋊C8—171no—
414C2×C4⋊C8—171no—
415C2×C22⋊C8—171no—
416C2×C22⋊C8—171no—
417C2×C22⋊C8—171no—
418C2×C22⋊C8—171no—
419C2×C22⋊C8—171no—
420C2×C22⋊C8—171no—
421#405—178no—
422#405—178no—
423C2×#97—171no—
424C2×#97—171no—
425C2×#97—171no—
426C2×#97—171no—
427C2×C4×C8—171no—
428C2×C4×C8—171no—
429C2×C4×C8—171no—
430C2×C4×C8—171no—
431C2×C4×C8—171no—
432C2×C4×C8—171no—
433C2×C4×C8—178no—
434C2×C17—42no—
435C2×C17#296614yescomplemented
436C2×C17C2×C4×#4111yescharacteristic
437C2×C17C22×#13111yescharacteristic
438C2×C17C22×#13111yescharacteristic
439D17—24no—
440D17—42no—
441C22×Q8—171no—
442C22×D4—171no—
443C22×D4—171no—
444C22×D4—171no—
445C23×C4—171no—
446C23×C4—171no—
447C23×C4—171no—
448C23×C4—171no—
449C23×C4—171no—
450C2×M16—174no—
451C2×M16—174no—
452C2×M16—344no—
453C2×M16—344no—
454C22×C8—171no—
455C22×C8—171no—
456C22×C8—174no—
457C22×C8—174no—
458C22×C8—174no—
459C22×C8—171no—
460C22×C8—171no—
461C22×C8—171no—
462C22×C8—171no—
463C22×C8—174no—
464C22×C8—171no—
465C22×C8—171no—
466C22×C8—344no—
467C22×C8—344no—
468C22×C8—344no—
469C22×C8—344no—
470#126—178no—
471#126C2×#59518yes—
472#125—178no—
473#124—178no—
474#123—178no—
475#123—178no—
476C22⋊Q8—178no—
477#121—178no—
478C4×Q8—174no—
479C4×Q8—174no—
480C4×D4—174no—
481C4×D4—174no—
482C4×D4—174no—
483C4×D4—174no—
484C4×D4—174no—
485C4×D4—174no—
486#117—174no—
487#117—174no—
488#117—174no—
489#117—174no—
490C2×C4⋊C4—171no—
491C2×C4⋊C4—171no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—171no—
495C2×C4⋊C4—171no—
496C2×C4⋊C4—171no—
497C2×C4⋊C4C2×#59511yescharacteristic
498C2×C4⋊C4C2×#59511yescharacteristic
499C2×C4⋊C4C2×#59511yescharacteristic
500C2×C22⋊C4—171no—
501C2×C22⋊C4—171no—
502C2×C22⋊C4—171no—
503C2×C22⋊C4—171no—
504C2×C22⋊C4—171no—
505C2×C22⋊C4—171no—
506C2×C22⋊C4—171no—
507C2×C22⋊C4C2×#59511yescharacteristic
508C2×C22⋊C4C2×#59511yescharacteristic
509C2×C22⋊C4C2×#59511yescharacteristic
510C2×C42—171no—
511C2×C42—171no—
512C2×C42—171no—
513C2×C42—171no—
514C2×C42—171no—
515C2×C42—174no—
516C2×C42—174no—
517C2×C42C2×#59511yescharacteristic
518C4⋊C8—174no—
519C4⋊C8—174no—
520C4⋊C8—174no—
521C4⋊C8—174no—
522C4⋊C8—174no—
523C4⋊C8—174no—
524C22⋊C8—174no—
525C22⋊C8—174no—
526C22⋊C8—174no—
527C22⋊C8—174no—
528C22⋊C8—174no—
529C22⋊C8—174no—
530#97—174no—
531#97—174no—
532#97—174no—
533#97—174no—
534C4×C8—174no—
535C4×C8—174no—
536C4×C8—174no—
537C4×C8—174no—
538C4×C8—174no—
539C4×C8—174no—
540C17C2×#296611yescharacteristic, complemented, Sylow
541C24—171no—
542C24—171no—
543C24C22×#59511yescharacteristic
544C2×Q8—174no—
545C2×Q8—344no—
546C2×D4—174no—
547C2×D4—174no—
548C2×D4—174no—
549C2×D4—344no—
550C2×D4—344no—
551C2×D4—344no—
552C22×C4—171no—
553C22×C4—171no—
554C22×C4—172no—
555C22×C4—172no—
556C22×C4—171no—
557C22×C4—171no—
558C22×C4—171no—
559C22×C4—171no—
560C22×C4—172no—
561C22×C4—174no—
562C22×C4—174no—
563C22×C4—172no—
564C22×C4—172no—
565C22×C4—172no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—344no—
571C22×C4—344no—
572C22×C4—342no—
573C22×C4—342no—
574C22×C4C22×#59511yescharacteristic
575C22×C4C22×#59511yescharacteristic
576C22×C4C22×#59511yescharacteristic
577C22×C4C22×#59511yescharacteristic
578C22×C4C22×#59511yescharacteristic
579C22×C4C22×#59511yescharacteristic
580M16—348no—
581M16—348no—
582C2×C8—174no—
583C2×C8—174no—
584C2×C8—172no—
585C2×C8—172no—
586C2×C8—172no—
587C2×C8—172no—
588C2×C8—172no—
589C2×C8—172no—
590C2×C8—172no—
591C2×C8—172no—
592C2×C8—348no—
593C2×C8—348no—
594C2×C8—348no—
595C2×C8—348no—
596C2×C8—342no—
597C2×C8—342no—
598C2×C8—342no—
599C2×C8—342no—
600C2×C8—342no—
601C2×C8—342no—
602C4⋊C4—174no—
603C4⋊C4—174no—
604C4⋊C4—174no—
605C4⋊C4—174no—
606C4⋊C4—174no—
607C4⋊C4—174no—
608C4⋊C4—174no—
609C4⋊C4C22×#59514yes—
610C4⋊C4C22×#59514yes—
611C4⋊C4C22×#59514yes—
612C22⋊C4—174no—
613C22⋊C4—174no—
614C22⋊C4—174no—
615C22⋊C4—174no—
616C22⋊C4—174no—
617C22⋊C4—174no—
618C22⋊C4—174no—
619C22⋊C4C22×#59514yes—
620C22⋊C4C22×#59514yes—
621C22⋊C4C22×#59514yes—
622C42—172no—
623C42—172no—
624C42—172no—
625C42—172no—
626C42—172no—
627C42—172no—
628C42—174no—
629C42—172no—
630C42—172no—
631C42C22×#59514yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—174no—
636C23—172no—
637C23—172no—
638C23—342no—
639C23—342no—
640C23—342no—
641C23—342no—
642C23—342no—
643C23C23×#59512yes—
644C23C23×#59511yescharacteristic
645Q8—348no—
646D4—348no—
647D4—348no—
648D4—348no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—172no—
656C2×C4—172no—
657C2×C4—174no—
658C2×C4—171no—
659C2×C4—171no—
660C2×C4—172no—
661C2×C4—172no—
662C2×C4—172no—
663C2×C4—172no—
664C2×C4—172no—
665C2×C4—342no—
666C2×C4—342no—
667C2×C4—342no—
668C2×C4—342no—
669C2×C4—344no—
670C2×C4—344no—
671C2×C4—348no—
672C2×C4—348no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—344no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4C23×#59512yes—
681C2×C4C23×#59512yes—
682C2×C4C23×#59512yes—
683C2×C4C23×#59512yes—
684C2×C4C23×#59512yes—
685C2×C4C23×#59512yes—
686C8—174no—
687C8—174no—
688C8—342no—
689C8—342no—
690C8—342no—
691C8—342no—
692C8—342no—
693C8—342no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—174no—
699C22—342no—
700C22—342no—
701C22—348no—
702C22—342no—
703C22—342no—
704C22—342no—
705C22—684no—
706C22#41×#59512yes—
707C22D17⋊#13112yes—
708C22D17⋊#13112yes—
709C22C24×#59511yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—171no—
717C4—171no—
718C4—172no—
719C4—174no—
720C4—342no—
721C4—342no—
722C4—342no—
723C4—342no—
724C2—42no—
725C2—344no—
726C2—682no—
727C2#1454560214yesdirect product factor
728C2C2×#41×#59511yescharacteristic
729C2C2×D17⋊#13111yescharacteristic
730C2C2×D17⋊#13111yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#126C4
socleC23×C17C23×C4
prime radicalC2×#10587570C4
cosocleC2×Dic17C25
hypercenterC2×#126#595
hypocenterC17C2×#2966
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #14545602C2direct (N × H)
2. C2×#11763861C2semidirect
3. C2×#11763858C2semidirect
4. C2×#11763842C2semidirect
5. C2×#11763841C2semidirect
6. C2×#11763839C2semidirect
7. C2×#11763837C2semidirect
8. C2×#11763836C2semidirect
9. C2×#11763836C2semidirect
10. C2×#11763834C2semidirect
11. C2×#11763833C2semidirect
12. C2×#11763832C2semidirect
13. C2×#11763774C2semidirect
14. C2×#11763773C2semidirect
15. C2×C4×#63242C2semidirect
23. #11763861C22semidirect
24. #11763858C22semidirect
25. #11763842C22semidirect
26. #11763841C22semidirect
27. #11763839C22semidirect
28. #11763837C22semidirect
29. #11763836C22semidirect
30. #11763836C22semidirect
31. #11763834C22semidirect
32. #11763833C22semidirect
33. #11763832C22semidirect
46. #11763774C22semidirect
47. #11763773C22semidirect
52. C4×#63242C22semidirect
435. C2×C17#2966semidirect
540. C17C2×#2966semidirect
727. C2#14545602direct (N × H)

Maximal subgroups

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

subgroupindex
#145456022
C2×#117638612
C2×#117638582
C2×#117638422
C2×#117638412
C2×#117638392
C2×#117638372
C2×#117638362
C2×#117638342
C2×#117638332
C2×#117638322
C2×#117637742
C2×#117637732
C2×C4×#632422
C2×#117633422
C2×#296617