Finite Group Databasebeta

← C2×#14537768 #17898786

Subgroups — C2×#14537768 #17898786

Order 4352.

1970 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
1C2×#11763346C211yesmaximal, characteristic
2#14537768C2116yesmaximal, direct product factor
3C2×#11762940C211yesmaximal, characteristic, complemented
4C2×#11762888C211yesmaximal, characteristic, complemented
5C2×#11762886C211yesmaximal, characteristic, complemented
6C2×#11762882C211yesmaximal, characteristic, complemented
7C2×#11762882C211yesmaximal, characteristic, complemented
8C2×#11762879C211yesmaximal, characteristic, complemented
9C2×#11762879C211yesmaximal, characteristic, complemented
10C2×#11762869C211yesmaximal, characteristic, complemented
11C2×#11762869C211yesmaximal, characteristic, complemented
12C2×#11762865C211yesmaximal, characteristic, complemented
13C2×#11762766C211yesmaximal, characteristic, complemented
14C2×#11762763C211yesmaximal, characteristic, complemented
15C2×#11762761C211yesmaximal, characteristic, complemented
16C2×C17×#446C211yesmaximal, characteristic, complemented
17C22×#63218C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19C22×#63218C2211yescharacteristic
20C22×#63218C2211yescharacteristic
21C22×C8×D17C2211yescharacteristic
22C22×C8×D17C2211yescharacteristic
23#11763346C418yes—
24#11763346C2218yes—
25C2×#10587584C411yescharacteristic
26C2×#10587584C411yescharacteristic
27C2×#10587576C411yescharacteristic
28C2×#10587633C411yescharacteristic
29C2×#10587580C411yescharacteristic
30C2×#10587580C411yescharacteristic
31C2×#10587632C411yescharacteristic
32C2×#10587581C411yescharacteristic
33C2×C4×D68C2211yescharacteristic
34C2×C4×D68C2211yescharacteristic
35C2×C4×D68C2211yescharacteristic
36C2×#10587558C2211yescharacteristic
37C2×#10587558C2211yescharacteristic
38C2×C42×D17C2211yescharacteristic
39#11762940C2218yescomplemented
40#11762888C2218yescomplemented
41#11762886C2218yescomplemented
42#11762882C2218yescomplemented
43#11762882C2218yescomplemented
44#11762879C2218yescomplemented
45#11762879C2218yescomplemented
46#11762869C2218yescomplemented
47#11762869C2218yescomplemented
48#11762865C2218yescomplemented
49C2×C4⋊#3622C2211yescharacteristic
50C2×C4⋊#3622C2211yescharacteristic
51C2×C4⋊#3622C2211yescharacteristic
52C2×#10587491C2211yescharacteristic
53C2×#10587491C2211yescharacteristic
54C2×#10587491C2211yescharacteristic
55C2×#10587491C2211yescharacteristic
56C2×#10587491C2211yescharacteristic
57C2×#10587491C2211yescharacteristic
58#11762766C2218yescomplemented
59#11762763C2218yescomplemented
60#11762761C2218yescomplemented
61C2×#10587474C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×#10587486C2211yescharacteristic
64C2×#10587486C2211yescharacteristic
65C2×C4×#3622C2211yescharacteristic
66C2×C8×Dic17C2211yescharacteristic
67C2×C8×Dic17C2211yescharacteristic
68C2×C4×Q8×C17C2211yescharacteristic
69C17×#446C2218yescomplemented
70C2×C17×C4⋊C8C2211yescharacteristic
71C2×C17×C4⋊C8C2211yescharacteristic
72C2×C17×C4⋊C8C2211yescharacteristic
73C2×C17×#97C2211yescharacteristic
74C2×C17×#97C2211yescharacteristic
75C2×C4×C8×C17C2211yescharacteristic
76C22×Q8×C17C2×C411yescharacteristic
77C22×D68C2×C411yescharacteristic
78C22×D68C2×C411yescharacteristic
79C22×D68C2×C411yescharacteristic
80C22×C4×D17C2×C411yescharacteristic
81C22×C4×D17C2×C411yescharacteristic
82C22×C4×D17C2311yescharacteristic
83C22×C4×D17C2311yescharacteristic
84C22×C4×D17C2311yescharacteristic
85C22×C8×C17C2311yescharacteristic
86C22×C8×C17C2311yescharacteristic
87C22×C8×C17C2311yescharacteristic
88C22×C8×C17C2311yescharacteristic
89C4×Q8×C17C2×C414yes—
90C4×Q8×C17C2314yes—
91C2×C4⋊C4×C17C2×C411yescharacteristic
92C2×C4⋊C4×C17C2×C411yescharacteristic
93C2×C4⋊C4×C17C2×C411yescharacteristic
94C2×C42×C17C2311yescharacteristic
95C2×C42×C17C2311yescharacteristic
96C2×C42×C17C2311yescharacteristic
97#10587633C2×C418yes—
98#10587632C2×C418yes—
99C2×#63227C2×C411yescharacteristic
100C2×#63227C2×C411yescharacteristic
101C2×#63227C2×C411yescharacteristic
102C2×#63227C2×C411yescharacteristic
103C2×#63227C2×C411yescharacteristic
104C2×#63227C2×C411yescharacteristic
105C2×#63227C2×C411yescharacteristic
106C2×#63227C2×C411yescharacteristic
107C2×#63227C2×C411yescharacteristic
108C2×#63227C2×C411yescharacteristic
109C2×C4⋊Dic17C2×C411yescharacteristic
110C2×C4⋊Dic17C2×C411yescharacteristic
111C2×C4⋊Dic17C2×C411yescharacteristic
112C2×#63225C2×C411yescharacteristic
113C2×#63225C2×C411yescharacteristic
114C2×#63225C2×C411yescharacteristic
115C2×#63225C2×C411yescharacteristic
116C2×C4×Dic17C2×C411yescharacteristic
117C2×C4×Dic17C2×C411yescharacteristic
118C2×C4×Dic17C2311yescharacteristic
119C22×#3622C2311yescharacteristic
120C22×#3622C2311yescharacteristic
121C22×#3622C2311yescharacteristic
122C22×#3622C2311yescharacteristic
123C2×#63218—24no—
124C2×#63218—24no—
125C2×#63218—24no—
126C2×#63218—24no—
127C2×#63218C2314yes—
128C2×#63218C2314yes—
129C2×#63218C2314yes—
130C2×#63218C2314yes—
131C2×C8×D17—24no—
132C2×C8×D17—24no—
133C2×C8×D17C2314yes—
134C2×C8×D17C2314yes—
135#10587584C2×C418yes—
136#10587584C2×C418yes—
137#10587581C2×C418yes—
138#10587580C2×C418yes—
139#10587580C2×C418yes—
140#10587576C2×C418yes—
141C4×D68C2×C414yes—
142C4×D68C2×C414yes—
143C4×D68C2×C414yes—
144C4×D68C2314yes—
145C4×D68C2314yes—
146C4×D68C2314yes—
147#10587558C2×C414yes—
148#10587558C2×C414yes—
149#10587558C2314yes—
150#10587558C2314yes—
151C42×D17C2×C414yes—
152C42×D17C2314yes—
153C17×C4⋊C8C2314yes—
154C17×C4⋊C8C2314yes—
155C17×C4⋊C8C2314yes—
156C17×#97C2314yes—
157C17×#97C2314yes—
158C4×C8×C17C2314yes—
159#10587491C2314yes—
160#10587491C2314yes—
161#10587491C2314yes—
162#10587491C2314yes—
163#10587491C2314yes—
164#10587491C2314yes—
165#10587486C2314yes—
166#10587486C2314yes—
167C8×Dic17C2314yes—
168C8×Dic17C2314yes—
169C4⋊#3622C2314yes—
170C4⋊#3622C2314yes—
171C4⋊#3622C2314yes—
172#10587474C2314yes—
173#10587474C2314yes—
174C4×#3622C2314yes—
175C23×D17C22×C411yescharacteristic
176C23×D17C22×C411yescharacteristic
177C23×D17C22×C411yescharacteristic
178C2×Q8×C17—42no—
179C2×Q8×C17C22×C414yes—
180C22×C4×C17C22×C411yescharacteristic
181C22×C4×C17C22×C411yescharacteristic
182C22×C4×C17C22×C411yescharacteristic
183C22×C4×C17C22×C411yescharacteristic
184C22×C4×C17C22×C411yescharacteristic
185C22×C4×C17C22×C411yescharacteristic
186C22×C4×C17C2411yescharacteristic
187C22×Dic17C22×C411yescharacteristic
188C22×Dic17C22×C411yescharacteristic
189C22×Dic17C22×C411yescharacteristic
190C22×Dic17C22×C411yescharacteristic
191C22×Dic17C22×C411yescharacteristic
192C2×D68—42no—
193C2×D68—42no—
194C2×D68—42no—
195C2×D68C22×C414yes—
196C2×D68C22×C414yes—
197C2×D68C22×C414yes—
198C2×C4×D17—22no—
199C2×C4×D17—22no—
200C2×C4×D17—22no—
201C2×C4×D17—22no—
202C2×C4×D17—22no—
203C2×C4×D17—22no—
204C2×C4×D17—42no—
205C2×C4×D17—42no—
206C2×C4×D17C22×C412yes—
207C2×C4×D17C22×C412yes—
208C2×C4×D17C22×C412yes—
209C2×C4×D17C22×C414yes—
210C2×C4×D17C22×C414yes—
211C2×C4×D17C2412yes—
212C2×C4×D17C2412yes—
213C2×C4×D17C2412yes—
214C2×C8×C17—22no—
215C2×C8×C17—22no—
216C2×C8×C17—22no—
217C2×C8×C17#4114yes—
218C2×C8×C17C2412yes—
219C2×C8×C17C2412yes—
220C2×C8×C17C2412yes—
221C2×C8×C17C2412yes—
222C4⋊C4×C17C22×C414yes—
223C4⋊C4×C17C22×C414yes—
224C4⋊C4×C17C22×C414yes—
225C42×C17C22×C412yes—
226C42×C17C22×C412yes—
227C42×C17C22×C412yes—
228C42×C17C2412yes—
229C42×C17C2412yes—
230C42×C17C2412yes—
231#63227C22×C414yes—
232#63227C22×C414yes—
233#63227C22×C414yes—
234#63227C22×C414yes—
235#63227C22×C414yes—
236#63227C22×C414yes—
237#63227C22×C414yes—
238#63227C22×C414yes—
239#63227C22×C414yes—
240#63227C22×C414yes—
241C4⋊Dic17C22×C414yes—
242C4⋊Dic17C22×C414yes—
243C4⋊Dic17C22×C414yes—
244#63225C22×C414yes—
245#63225C22×C414yes—
246#63225C22×C414yes—
247#63225C22×C414yes—
248C4×Dic17C22×C412yes—
249C4×Dic17C22×C414yes—
250C4×Dic17C22×C414yes—
251C4×Dic17C2412yes—
252C2×#3622—22no—
253C2×#3622—22no—
254C2×#3622—22no—
255C2×#3622#4114yes—
256C2×#3622C2412yes—
257C2×#3622C2412yes—
258C2×#3622C2412yes—
259C2×#3622C2412yes—
260#63218—28no—
261#63218—28no—
262#63218—28no—
263#63218—28no—
264C8×D17—28no—
265C8×D17—28no—
266C2×#2967—171nomaximal, Sylow
267C23×C17C23×C411yescharacteristic
268C22×D17—22no—
269C22×D17—22no—
270C22×D17—22no—
271C22×D17—22no—
272C22×D17—22no—
273C22×D17—22no—
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—22no—
277C22×D17C23×C412yes—
278C22×D17C23×C412yes—
279C22×D17C23×C412yes—
280Q8×C17—44no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17C23×C412yes—
288C2×C4×C17C23×C412yes—
289C2×C4×C17C23×C412yes—
290C2×C4×C17C23×C412yes—
291C2×C4×C17C23×C412yes—
292C2×C4×C17C23×C412yes—
293C2×C4×C17C23×C411yescharacteristic
294C2×C4×C17C2×#4112yes—
295C2×C4×C17C2×#4112yes—
296C2×C4×C17C2511yescharacteristic
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17C23×C412yes—
303C2×Dic17C23×C412yes—
304C2×Dic17C23×C412yes—
305C2×Dic17C23×C412yes—
306C2×Dic17C23×C412yes—
307D68—44no—
308D68—44no—
309D68—44no—
310C4×D17—24no—
311C4×D17—24no—
312C4×D17—24no—
313C4×D17—22no—
314C4×D17—22no—
315C4×D17—22no—
316C4×D17—22no—
317C4×D17—22no—
318C4×D17—22no—
319C4×D17—44no—
320C4×D17—44no—
321C8×C17—22no—
322C8×C17—22no—
323C8×C17—22no—
324C8×C17C2×#4114yes—
325#3622—22no—
326#3622—22no—
327#3622—22no—
328#3622C2×#4114yes—
329C2×#529—171no—
330#2967—1716no—
331C2×#446—171no—
332C2×#446D1711yescharacteristic, complemented
333C2×#436—171no—
334C2×#436—171no—
335C2×#435—171no—
336C2×#435—171no—
337C2×#435—171no—
338C2×#435—171no—
339C2×#433—171no—
340C2×#433—171no—
341C2×#432—171no—
342C2×#405—171no—
343C2×#405—171no—
344C2×C4×M16—171no—
345C22×C17C4×#4112yes—
346C22×C17#56812yes—
347C22×C17#56812yes—
348C22×C17C24×C411yescharacteristic
349C2×D17—22no—
350C2×D17—22no—
351C2×D17—22no—
352C2×D17—22no—
353C2×D17—22no—
354C2×D17—22no—
355C2×D17—22no—
356C2×D17—22no—
357C2×D17—22no—
358C2×D17—44no—
359C2×D17—44no—
360C2×D17—44no—
361C4×C17—22no—
362C4×C17—22no—
363C4×C17—22no—
364C4×C17—22no—
365C4×C17—22no—
366C4×C17—22no—
367C4×C17C4×#4112yes—
368C4×C17C22×#4111yescharacteristic
369C4×C17C22×#4111yescharacteristic
370Dic17—22no—
371Dic17—22no—
372Dic17—22no—
373Dic17—22no—
374Dic17—22no—
375C22×M16—171no—
376C22×M16—171no—
377C22×M16—171no—
378C22×M16—171no—
379C23×C8—171no—
380C23×C8—171no—
381#529—178no—
382#529—178no—
383C2×#126—171no—
384C2×#126—171no—
385C2×#125—171no—
386C2×#124—171no—
387C2×#123—171no—
388C2×#123—171no—
389C2×C22⋊Q8—171no—
390C2×#121—171no—
391C2×C4×Q8C2×D1711yescharacteristic
392C2×C4×D4—171no—
393C2×C4×D4—171no—
394C2×C4×D4—171no—
395C2×#117—171no—
396C2×#117—171no—
397C22×C42—171no—
398#446—178no—
399#446C2×D1718yescomplemented
400#436—178no—
401#436—178no—
402#435—178no—
403#435—178no—
404#435—178no—
405#435—178no—
406#433—178no—
407#433—178no—
408#432—178no—
409C2×C4⋊C8—171no—
410C2×C4⋊C8—171no—
411C2×C4⋊C8—171no—
412C2×C4⋊C8C2×D1711yescharacteristic
413C2×C4⋊C8C2×D1711yescharacteristic
414C2×C4⋊C8C2×D1711yescharacteristic
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—
423C4×M16—178no—
424C2×#97—171no—
425C2×#97—171no—
426C2×#97—171no—
427C2×#97—171no—
428C2×#97C2×D1711yescharacteristic
429C2×#97C2×D1711yescharacteristic
430C2×C4×C8—171no—
431C2×C4×C8—171no—
432C2×C4×C8—171no—
433C2×C4×C8C2×D1711yescharacteristic
434C2×C17#296714yescomplemented
435C2×C17C2×C4×#4111yescharacteristic
436C2×C17C2×#56811yescharacteristic
437C2×C17C2×#56811yescharacteristic
438D17—42no—
439D17—42no—
440D17—42no—
441C22×Q8C4×D1711yescharacteristic
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—174no—
453C2×M16—174no—
454C2×M16—344no—
455C2×M16—344no—
456C2×M16—344no—
457C2×M16—344no—
458C22×C8—171no—
459C22×C8—171no—
460C22×C8—171no—
461C22×C8—171no—
462C22×C8—174no—
463C22×C8—174no—
464C22×C8—344no—
465C22×C8—344no—
466C22×C8C22×D1711yescharacteristic
467C22×C8C22×D1711yescharacteristic
468C22×C8C22×D1711yescharacteristic
469C22×C8C22×D1711yescharacteristic
470#126—178no—
471#126—178no—
472#125—178no—
473#124—178no—
474#123—178no—
475#123—178no—
476C22⋊Q8—178no—
477#121—178no—
478C4×Q8C4×D1714yes—
479C4×Q8C22×D1714yes—
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⋊C4C4×D1711yescharacteristic
498C2×C4⋊C4C4×D1711yescharacteristic
499C2×C4⋊C4C4×D1711yescharacteristic
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⋊C4—171no—
508C2×C22⋊C4—171no—
509C2×C22⋊C4—171no—
510C2×C42—171no—
511C2×C42—171no—
512C2×C42—171no—
513C2×C42—174no—
514C2×C42—174no—
515C2×C42C22×D1711yescharacteristic
516C2×C42C22×D1711yescharacteristic
517C2×C42C22×D1711yescharacteristic
518C4⋊C8—174no—
519C4⋊C8—174no—
520C4⋊C8—174no—
521C4⋊C8C22×D1714yes—
522C4⋊C8C22×D1714yes—
523C4⋊C8C22×D1714yes—
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—
534#97C22×D1714yes—
535#97C22×D1714yes—
536C4×C8—174no—
537C4×C8—174no—
538C4×C8—174no—
539C4×C8C22×D1714yes—
540C17C2×#296711yescharacteristic, complemented, Sylow
541C24—171no—
542C24—171no—
543C24—171no—
544C2×Q8—42no—
545C2×Q8C2×C4×D1714yes—
546C2×D4—174no—
547C2×D4—174no—
548C2×D4—174no—
549C2×D4—682no—
550C2×D4—682no—
551C2×D4—682no—
552C22×C4—171no—
553C22×C4—171no—
554C22×C4—171no—
555C22×C4—171no—
556C22×C4—171no—
557C22×C4—172no—
558C22×C4—172no—
559C22×C4—172no—
560C22×C4—172no—
561C22×C4—172no—
562C22×C4—172no—
563C22×C4—174no—
564C22×C4—174no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—682no—
572C22×C4—682no—
573C22×C4C2×C4×D1711yescharacteristic
574C22×C4C2×C4×D1711yescharacteristic
575C22×C4C2×C4×D1711yescharacteristic
576C22×C4C2×C4×D1711yescharacteristic
577C22×C4C2×C4×D1711yescharacteristic
578C22×C4C2×C4×D1711yescharacteristic
579C22×C4C23×D1711yescharacteristic
580M16—348no—
581M16—348no—
582M16—348no—
583M16—348no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—174no—
588C2×C8—172no—
589C2×C8—172no—
590C2×C8—172no—
591C2×C8—172no—
592C2×C8—348no—
593C2×C8—342no—
594C2×C8—342no—
595C2×C8—342no—
596C2×C8—348no—
597C2×C8#6325614yes—
598C2×C8C23×D1712yes—
599C2×C8C23×D1712yes—
600C2×C8C23×D1712yes—
601C2×C8C23×D1712yes—
602C4⋊C4—174no—
603C4⋊C4—174no—
604C4⋊C4—174no—
605C4⋊C4—174no—
606C4⋊C4—174no—
607C4⋊C4—174no—
608C4⋊C4—174no—
609C4⋊C4C2×C4×D1714yes—
610C4⋊C4C2×C4×D1714yes—
611C4⋊C4C2×C4×D1714yes—
612C22⋊C4—174no—
613C22⋊C4—174no—
614C22⋊C4—174no—
615C22⋊C4—174no—
616C22⋊C4—174no—
617C22⋊C4—174no—
618C22⋊C4—174no—
619C22⋊C4—174no—
620C22⋊C4—174no—
621C22⋊C4—174no—
622C42—172no—
623C42—174no—
624C42—174no—
625C42—172no—
626C42C2×C4×D1712yes—
627C42C2×C4×D1712yes—
628C42C2×C4×D1712yes—
629C42C23×D1712yes—
630C42C23×D1712yes—
631C42C23×D1712yes—
632C23—172no—
633C23—172no—
634C23—172no—
635C23—342no—
636C23—342no—
637C23—342no—
638C23—342no—
639C23—342no—
640C23—342no—
641C23—342no—
642C23—342no—
643C23—342no—
644C23C22×C4×D1711yescharacteristic
645Q8—44no—
646D4—684no—
647D4—684no—
648D4—684no—
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—172no—
658C2×C4—172no—
659C2×C4—172no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—342no—
663C2×C4—342no—
664C2×C4—342no—
665C2×C4—344no—
666C2×C4—344no—
667C2×C4—344no—
668C2×C4—342no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—684no—
675C2×C4—684no—
676C2×C4C22×C4×D1712yes—
677C2×C4C22×C4×D1712yes—
678C2×C4C22×C4×D1712yes—
679C2×C4C22×C4×D1712yes—
680C2×C4C22×C4×D1712yes—
681C2×C4C22×C4×D1712yes—
682C2×C4C22×C4×D1711yescharacteristic
683C2×C4C2×#6325612yes—
684C2×C4#41×D1712yes—
685C2×C4C24×D1711yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—174no—
690C8—342no—
691C8—342no—
692C8—342no—
693C8C2×#6325614yes—
694C22—342no—
695C22—342no—
696C22—342no—
697C22—342no—
698C22—342no—
699C22—342no—
700C22—342no—
701C22—342no—
702C22—342no—
703C22—684no—
704C22—684no—
705C22—684no—
706C22C4×#6325612yes—
707C22#1176357412yes—
708C22#1176357512yes—
709C22C23×C4×D1711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—342no—
717C4—342no—
718C4—342no—
719C4—342no—
720C4—342no—
721C4C4×#6325612yes—
722C4C2×#41×D1711yescharacteristic
723C4C22×#6325611yescharacteristic
724C2—682no—
725C2—682no—
726C2—682no—
727C2#1453776814yesdirect product factor
728C2C2×C4×#6325611yescharacteristic
729C2C2×#1176357411yescharacteristic
730C2C2×#1176357511yescharacteristic
subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#446C2
socleC23×C17C23×C4
prime radicalC2×#10587581C4
cosocleC2×C4×C17C25
hypercenterC2×#446D17
hypocenterC17C2×#2967
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #14537768C2direct (N × H)
3. C2×#11762940C2semidirect
4. C2×#11762888C2semidirect
5. C2×#11762886C2semidirect
6. C2×#11762882C2semidirect
7. C2×#11762882C2semidirect
8. C2×#11762879C2semidirect
9. C2×#11762879C2semidirect
10. C2×#11762869C2semidirect
11. C2×#11762869C2semidirect
12. C2×#11762865C2semidirect
13. C2×#11762766C2semidirect
14. C2×#11762763C2semidirect
15. C2×#11762761C2semidirect
16. C2×C17×#446C2semidirect
39. #11762940C22semidirect
40. #11762888C22semidirect
41. #11762886C22semidirect
42. #11762882C22semidirect
43. #11762882C22semidirect
44. #11762879C22semidirect
45. #11762879C22semidirect
46. #11762869C22semidirect
47. #11762869C22semidirect
48. #11762865C22semidirect
58. #11762766C22semidirect
59. #11762763C22semidirect
60. #11762761C22semidirect
69. C17×#446C22semidirect
332. C2×#446D17semidirect
399. #446C2×D17semidirect
434. C2×C17#2967semidirect
540. C17C2×#2967semidirect
727. C2#14537768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633462
#145377682
C2×#117629402
C2×#117628882
C2×#117628862
C2×#117628822
C2×#117628792
C2×#117628692
C2×#117628652
C2×#117627662
C2×#117627632
C2×#117627612
C2×C17×#4462
C2×#296717