Finite Group Databasebeta

← C2×#14541738 #17914861

Subgroups — C2×#14541738 #17914861

Order 4352.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763519C211yesmaximal, characteristic, complemented
2#14541738C2116yesmaximal, direct product factor
3C2×#11763219C211yesmaximal, characteristic, complemented
4C2×#11763215C211yesmaximal, characteristic, complemented
5C2×#11763208C211yesmaximal, characteristic, complemented
6C2×#11763109C211yesmaximal, characteristic, complemented
7C2×#11763109C211yesmaximal, characteristic, complemented
8C2×#11763106C211yesmaximal, characteristic, complemented
9C2×#11763106C211yesmaximal, characteristic, complemented
10C2×#11763089C211yesmaximal, characteristic, complemented
11C2×#11763086C211yesmaximal, characteristic, complemented
12C2×#11762940C211yesmaximal, characteristic, complemented
13C2×#11762919C211yesmaximal, characteristic
14C2×#11762919C211yesmaximal, characteristic
15C2×C4×#63228C211yesmaximal, characteristic
16C2×C17×#554C211yesmaximal, characteristic, complemented
17C22×#63228C2211yescharacteristic
18#11763519—24no—
19#11763519C2218yescomplemented
20C2×#10587555C2211yescharacteristic
21C2×#10587556C2211yescharacteristic
22C2×#10587556C2211yescharacteristic
23C2×#10587582—21no—
24C2×#10587582—21no—
25C2×#10587632—21no—
26C2×C4×D68C2211yescharacteristic
27C2×C4×D68C2211yescharacteristic
28C2×C4×D68C2211yescharacteristic
29C2×C4⋊C4×D17—21no—
30#11763219C2218yescomplemented
31#11763215C2218yescomplemented
32#11763208C2218yescomplemented
33#11763109C2218yescomplemented
34#11763109C2218yescomplemented
35#11763106C2218yescomplemented
36#11763106C2218yescomplemented
37#11763089C2218yescomplemented
38#11763086C2218yescomplemented
39#11762940C2218yescomplemented
40#11762919C2218yes—
41#11762919C2218yes—
42C4×#63228C2218yes—
43C2×#10587478C2211yescharacteristic
44C2×#10587478C2211yescharacteristic
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51C2×#10587479C2211yescharacteristic
52C2×C4⋊#3622C2211yescharacteristic
53C2×C4⋊#3622C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587503C2211yescharacteristic
56C2×#10587503C2211yescharacteristic
57C2×#10587503C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×#10587474C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#554—24no—
65C17×#554C2218yescomplemented
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#125C2211yescharacteristic
68C2×C17×#125C2211yescharacteristic
69C2×C17×C22⋊Q8—21no—
70C2×C17×C22⋊Q8—21no—
71C2×C17×C22⋊Q8—21no—
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×D4×C17C2211yescharacteristic
74C2×C4×D4×C17C2211yescharacteristic
75C2×C4×D4×C17C2211yescharacteristic
76C22×C4⋊C4×C17—21no—
77C22×Q8×C17—21no—
78C22×Q8×C17D411yescharacteristic
79C22×D4×C17C2311yescharacteristic
80C23×C4×C17—21no—
81C23×C4×C17—21no—
82C23×C4×C17—21no—
83C22×D68C2311yescharacteristic
84C22×C4×D17—21no—
85C22×C4×D17—21no—
86C22×C4×D17—21no—
87C22×Dic34—21no—
88C17×C4⋊Q8—22no—
89C17×C4⋊Q8C2314yes—
90C17×#125—22no—
91C17×#125—22no—
92C17×#125C2314yes—
93C17×#125C2314yes—
94C17×C22⋊Q8—28no—
95C17×C22⋊Q8—28no—
96C17×C22⋊Q8—28no—
97C4×Q8×C17D414yes—
98C4×Q8×C17C2314yes—
99C4×D4×C17—22no—
100C4×D4×C17—22no—
101C4×D4×C17—22no—
102C4×D4×C17C2314yes—
103C4×D4×C17C2314yes—
104C4×D4×C17C2314yes—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17—28no—
111C2×C4⋊C4×C17D411yescharacteristic
112C2×C4⋊C4×C17D411yescharacteristic
113C2×C4⋊C4×C17D411yescharacteristic
114C2×C4⋊C4×C17C2311yescharacteristic
115C2×C4⋊C4×C17C2311yescharacteristic
116C2×C4⋊C4×C17C2311yescharacteristic
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17—21no—
119C2×C22⋊C4×C17—21no—
120C2×C42×C17C2311yescharacteristic
121C2×C42×C17C2311yescharacteristic
122C2×C42×C17C2311yescharacteristic
123#10587632—28no—
124C2×#63228Q818yescomplemented
125C2×#63228C2314yes—
126C2×#63227—21no—
127C2×#63227—21no—
128C2×#63227—21no—
129C2×C4⋊Dic17—21no—
130C2×C4⋊Dic17C2311yescharacteristic
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133C2×#63225—21no—
134C2×#63225—21no—
135C2×#63225—21no—
136C2×#63225—21no—
137C22×#3622C2311yescharacteristic
138C22×#3622C2311yescharacteristic
139C22×#3622C2311yescharacteristic
140C22×#3622C2311yescharacteristic
141#10587582—28no—
142#10587582—28no—
143C4⋊C4×D17—28no—
144C4×D68—22no—
145C4×D68—22no—
146C4×D68—22no—
147C4×D68C2314yes—
148C4×D68C2314yes—
149C4×D68C2314yes—
150#10587556—22no—
151#10587556—22no—
152#10587556C2314yes—
153#10587556C2314yes—
154#10587555—22no—
155#10587555C2314yes—
156#10587503C2314yes—
157#10587503C2314yes—
158#10587503C2314yes—
159#10587480C2314yes—
160#10587480C2314yes—
161#10587480C2314yes—
162#10587479C2314yes—
163#10587479C2314yes—
164#10587479C2314yes—
165#10587479C2314yes—
166#10587478C2314yes—
167#10587478C2314yes—
168#10587478C2314yes—
169#10587478C2314yes—
170#10587478C2314yes—
171C4⋊#3622C2314yes—
172C4⋊#3622C2314yes—
173C4⋊#3622C2314yes—
174#10587474C2314yes—
175#10587474C2314yes—
176C4×#3622C2314yes—
177C24×C17—21no—
178C23×D17—21no—
179C2×Q8×C17—24no—
180C2×Q8×C17—42no—
181C2×Q8×C17—82no—
182C2×Q8×C17C2×D414yes—
183C2×D4×C17—21no—
184C2×D4×C17—22no—
185C2×D4×C17C2×Q814yes—
186C2×D4×C17C2412yes—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—24no—
191C22×C4×C17—24no—
192C22×C4×C17—24no—
193C22×C4×C17—44no—
194C22×C4×C17—82no—
195C22×C4×C17—82no—
196C22×C4×C17C2×D411yescharacteristic
197C22×C4×C17C2×D411yescharacteristic
198C22×C4×C17C2×D411yescharacteristic
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2×D411yescharacteristic
201C22×C4×C17C2×D411yescharacteristic
202C22×C4×C17C2411yescharacteristic
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C2×D68—21no—
207C2×D68—22no—
208C2×D68C2×Q814yes—
209C2×D68C2412yes—
210C2×C4×D17—24no—
211C2×C4×D17—24no—
212C2×C4×D17—24no—
213C2×C4×D17—44no—
214C2×C4×D17—82no—
215C2×C4×D17—82no—
216C2×Dic34—24no—
217C2×Dic34—82no—
218C4⋊C4×C17—24no—
219C4⋊C4×C17—24no—
220C4⋊C4×C17—24no—
221C4⋊C4×C17—24no—
222C4⋊C4×C17—24no—
223C4⋊C4×C17—21no—
224C4⋊C4×C17—21no—
225C4⋊C4×C17—21no—
226C4⋊C4×C17C2×D414yes—
227C4⋊C4×C17C2×D414yes—
228C4⋊C4×C17C2×D414yes—
229C4⋊C4×C17C2412yes—
230C4⋊C4×C17C2412yes—
231C4⋊C4×C17C2412yes—
232C22⋊C4×C17—24no—
233C22⋊C4×C17—24no—
234C22⋊C4×C17—24no—
235C42×C17C2×D412yes—
236C42×C17C2×D412yes—
237C42×C17C2×D412yes—
238C42×C17C2412yes—
239C42×C17C2412yes—
240C42×C17C2412yes—
241#63228C2×Q8116yescomplemented
242#63227—24no—
243#63227—24no—
244#63227—24no—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—24no—
248C4⋊Dic17—21no—
249C4⋊Dic17C2412yes—
250C4⋊Dic17C2412yes—
251C4⋊Dic17C2412yes—
252#63225—24no—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256C2×#3622—22no—
257C2×#3622—22no—
258C2×#3622—22no—
259C2×#3622C2×Q814yes—
260C2×#3622C2412yes—
261C2×#3622C2412yes—
262C2×#3622C2412yes—
263C2×#3622C2412yes—
264C2×#3389—171nomaximal, Sylow
265C23×C17—24no—
266C23×C17—22no—
267C23×C17—42no—
268C23×C17—42no—
269C23×C17C22×D411yescharacteristic
270C22×D17—24no—
271C22×D17—22no—
272C22×D17—42no—
273C22×D17—42no—
274Q8×C17—44no—
275Q8×C17—84no—
276D4×C17—24no—
277D4×C17—22no—
278D4×C17C22×Q814yes—
279C2×C4×C17—22no—
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×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—48no—
289C2×C4×C17—42no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—84no—
293C2×C4×C17—84no—
294C2×C4×C17C22×D412yes—
295C2×C4×C17C22×D412yes—
296C2×C4×C17C22×D412yes—
297C2×C4×C17C22×D412yes—
298C2×C4×C17C22×D412yes—
299C2×C4×C17C22×D412yes—
300C2×C4×C17C22×D411yescharacteristic
301C2×C4×C17C22×Q812yes—
302C2×C4×C172−1+412yes—
303C2×C4×C17C2511yescharacteristic
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—42no—
308C2×Dic17—42no—
309C2×Dic17—42no—
310D68—24no—
311D68—22no—
312D68C22×Q814yes—
313C4×D17—48no—
314C4×D17—84no—
315C4×D17—84no—
316Dic34—84no—
317#3622—22no—
318#3622—22no—
319#3622—22no—
320#3622C22×Q814yes—
321C2×#554—171no—
322C2×#554D1711yescharacteristic, complemented
323#3389—1716no—
324C2×#501—171no—
325C2×#501—171no—
326C2×#499—171no—
327C2×#478—171no—
328C2×#478—171no—
329C2×#478—171no—
330C2×#478—171no—
331C2×#474—171no—
332C2×#474—171no—
333C2×#446—171no—
334C2×#442—171no—
335C2×#442—171no—
336C2×C4×D8—171no—
337C22×C17—24no—
338C22×C17—48no—
339C22×C17—42no—
340C22×C17—42no—
341C22×C17D4×Q812yes—
342C22×C17#57512yes—
343C22×C17#57612yes—
344C22×C17C23×D411yescharacteristic
345C2×D17—24no—
346C2×D17—48no—
347C2×D17—42no—
348C2×D17—42no—
349C4×C17—22no—
350C4×C17—22no—
351C4×C17—22no—
352C4×C17—22no—
353C4×C17—22no—
354C4×C17—22no—
355C4×C17—42no—
356C4×C17—42no—
357C4×C17—42no—
358C4×C17D4×Q812yes—
359C4×C17C23×Q811yescharacteristic
360C4×C17C2×2−1+411yescharacteristic
361Dic17—42no—
362Dic17—42no—
363Dic17—42no—
364C22×D8—171no—
365#554—24no—
366#554—178no—
367#554—344no—
368#554C2×D1718yescomplemented
369C2×C4⋊Q8—171no—
370C2×C4⋊Q8C2×D1711yescharacteristic
371C2×#125—171no—
372C2×#125—171no—
373C2×#125C2×D1711yescharacteristic
374C2×#125C2×D1711yescharacteristic
375C2×C22⋊Q8—21no—
376C2×C22⋊Q8—21no—
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8—341no—
379C2×C22⋊Q8—341no—
380C2×C22⋊Q8—341no—
381C2×C4×Q8C2×D1711yescharacteristic
382C2×C4×D4—171no—
383C2×C4×D4—171no—
384C2×C4×D4—171no—
385C2×C4×D4C2×D1711yescharacteristic
386C2×C4×D4C2×D1711yescharacteristic
387C2×C4×D4C2×D1711yescharacteristic
388C22×C4⋊C4—21no—
389C22×C4⋊C4—341no—
390#501—178no—
391#501—178no—
392#499—178no—
393#478—178no—
394#478—178no—
395#478—178no—
396#478—178no—
397#474—178no—
398#474—178no—
399#446—178no—
400#442—178no—
401#442—178no—
402C4×D8—178no—
403C2×#107—171no—
404C2×#107—171no—
405C2×#107—171no—
406C2×#107—171no—
407C2×#107—171no—
408C2×#106—171no—
409C2×#106—171no—
410C2×#106—171no—
411C2×#106—171no—
412C2×C4⋊C8—171no—
413C2×C4⋊C8—171no—
414C2×C4⋊C8—171no—
415C2×#102—171no—
416C2×#102—171no—
417C2×#102—171no—
418C2×#102—171no—
419C2×#102—171no—
420C2×#102—171no—
421C2×#97—171no—
422C2×#97—171no—
423C2×C4×C8—171no—
424C2×C17—44no—
425C2×C17#338914yescomplemented
426C2×C17C2×D4×Q811yescharacteristic
427C2×C17C2×#57511yescharacteristic
428C2×C17C2×#57611yescharacteristic
429D17—44no—
430C22×Q8—21no—
431C22×Q8—341no—
432C22×Q8C22⋊D1711yescharacteristic
433C22×D4—171no—
434C22×D4C22×D1711yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—341no—
439C23×C4—341no—
440C23×C4—341no—
441C2×D8—178no—
442C2×D8—174no—
443C22×C8—171no—
444C22×C8—171no—
445C22×C8—171no—
446C22×C8—171no—
447C4⋊Q8—22no—
448C4⋊Q8—174no—
449C4⋊Q8—342no—
450C4⋊Q8C22×D1714yes—
451#125—22no—
452#125—22no—
453#125—174no—
454#125—174no—
455#125—342no—
456#125—342no—
457#125C22×D1714yes—
458#125C22×D1714yes—
459C22⋊Q8—28no—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—348no—
463C22⋊Q8—348no—
464C22⋊Q8—348no—
465C4×Q8C22⋊D1714yes—
466C4×Q8C22×D1714yes—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—174no—
471C4×D4—174no—
472C4×D4—174no—
473C4×D4—342no—
474C4×D4—342no—
475C4×D4—342no—
476C4×D4C22×D1714yes—
477C4×D4C22×D1714yes—
478C4×D4C22×D1714yes—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—28no—
485C2×C4⋊C4—171no—
486C2×C4⋊C4—171no—
487C2×C4⋊C4—171no—
488C2×C4⋊C4—341no—
489C2×C4⋊C4—341no—
490C2×C4⋊C4—341no—
491C2×C4⋊C4—341no—
492C2×C4⋊C4—341no—
493C2×C4⋊C4—348no—
494C2×C4⋊C4C22⋊D1711yescharacteristic
495C2×C4⋊C4C22⋊D1711yescharacteristic
496C2×C4⋊C4C22⋊D1711yescharacteristic
497C2×C4⋊C4C22×D1711yescharacteristic
498C2×C4⋊C4C22×D1711yescharacteristic
499C2×C4⋊C4C22×D1711yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—341no—
504C2×C22⋊C4—341no—
505C2×C22⋊C4—341no—
506C2×C42C22×D1711yescharacteristic
507C2×C42C22×D1711yescharacteristic
508C2×C42C22×D1711yescharacteristic
509#107—174no—
510#107—174no—
511#107—174no—
512#107—174no—
513#107—174no—
514#106—174no—
515#106—174no—
516#106—174no—
517#106—174no—
518C4⋊C8—174no—
519C4⋊C8—174no—
520C4⋊C8—174no—
521#102—174no—
522#102—174no—
523#102—174no—
524#102—174no—
525#102—174no—
526#102—174no—
527#97—174no—
528#97—174no—
529C4×C8—174no—
530C17C2×#338911yescharacteristic, complemented, Sylow
531C24—21no—
532C24—341no—
533C2×Q8—24no—
534C2×Q8—42no—
535C2×Q8—82no—
536C2×Q8—344no—
537C2×Q8—1362no—
538C2×Q8C2×C22⋊D1714yes—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—174no—
542C2×D4—172no—
543C2×D4—342no—
544C2×D4—341no—
545C2×D4Q8×D1714yes—
546C2×D4C23×D1712yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—44no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—341no—
557C22×C4—341no—
558C22×C4—341no—
559C22×C4—344no—
560C22×C4—344no—
561C22×C4—344no—
562C22×C4—684no—
563C22×C4—1362no—
564C22×C4—1362no—
565C22×C4C2×C22⋊D1711yescharacteristic
566C22×C4C2×C22⋊D1711yescharacteristic
567C22×C4C2×C22⋊D1711yescharacteristic
568C22×C4C2×C22⋊D1711yescharacteristic
569C22×C4C2×C22⋊D1711yescharacteristic
570C22×C4C2×C22⋊D1711yescharacteristic
571C22×C4C23×D1711yescharacteristic
572D8—1716no—
573C2×C8—174no—
574C2×C8—172no—
575C2×C8—172no—
576C2×C8—172no—
577C2×C8—172no—
578C2×C8—342no—
579C2×C8—342no—
580C2×C8—342no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—172no—
590C4⋊C4—172no—
591C4⋊C4—172no—
592C4⋊C4—341no—
593C4⋊C4—341no—
594C4⋊C4—341no—
595C4⋊C4—344no—
596C4⋊C4—344no—
597C4⋊C4—344no—
598C4⋊C4—344no—
599C4⋊C4—344no—
600C4⋊C4C2×C22⋊D1714yes—
601C4⋊C4C2×C22⋊D1714yes—
602C4⋊C4C2×C22⋊D1714yes—
603C4⋊C4C23×D1712yes—
604C4⋊C4C23×D1712yes—
605C4⋊C4C23×D1712yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—344no—
610C22⋊C4—344no—
611C22⋊C4—344no—
612C42C2×C22⋊D1712yes—
613C42C2×C22⋊D1712yes—
614C42C2×C22⋊D1712yes—
615C42C23×D1712yes—
616C42C23×D1712yes—
617C42C23×D1712yes—
618C23—24no—
619C23—22no—
620C23—42no—
621C23—42no—
622C23—344no—
623C23—342no—
624C23—682no—
625C23—682no—
626C23C22×C22⋊D1711yescharacteristic
627Q8—44no—
628Q8—84no—
629Q8—1364no—
630D4—24no—
631D4—22no—
632D4—174no—
633D4—344no—
634D4—342no—
635D4C2×Q8×D1714yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—342no—
652C2×C4—342no—
653C2×C4—342no—
654C2×C4—688no—
655C2×C4—682no—
656C2×C4—682no—
657C2×C4—682no—
658C2×C4—1364no—
659C2×C4—1364no—
660C2×C4C2×Q8×D1712yes—
661C2×C4#1058769412yes—
662C2×C4C22×C22⋊D1712yes—
663C2×C4C22×C22⋊D1712yes—
664C2×C4C22×C22⋊D1712yes—
665C2×C4C22×C22⋊D1712yes—
666C2×C4C22×C22⋊D1712yes—
667C2×C4C22×C22⋊D1712yes—
668C2×C4C22×C22⋊D1711yescharacteristic
669C2×C4C24×D1711yescharacteristic
670C8—174no—
671C8—342no—
672C8—342no—
673C8—342no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—344no—
679C22—682no—
680C22—688no—
681C22—682no—
682C22Q8×C22⋊D1712yes—
683C22#1176360712yes—
684C22#1176361212yes—
685C22C23×C22⋊D1711yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—682no—
696C4—682no—
697C4—682no—
698C4Q8×C22⋊D1712yes—
699C4C22×Q8×D1711yescharacteristic
700C4C2×#1058769411yescharacteristic
701C2—44no—
702C2—684no—
703C2#1454173814yesdirect product factor
704C2C2×Q8×C22⋊D1711yescharacteristic
705C2C2×#1176360711yescharacteristic
706C2C2×#1176361211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#554C2
socleC23×C17C22×D4
prime radicalC22×#63228C22
hypercenterC2×#554D17
hypocenterC17C2×#3389
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11763519C2semidirect
2. #14541738C2direct (N × H)
3. C2×#11763219C2semidirect
4. C2×#11763215C2semidirect
5. C2×#11763208C2semidirect
6. C2×#11763109C2semidirect
7. C2×#11763109C2semidirect
8. C2×#11763106C2semidirect
9. C2×#11763106C2semidirect
10. C2×#11763089C2semidirect
11. C2×#11763086C2semidirect
12. C2×#11762940C2semidirect
16. C2×C17×#554C2semidirect
19. #11763519C22semidirect
30. #11763219C22semidirect
31. #11763215C22semidirect
32. #11763208C22semidirect
33. #11763109C22semidirect
34. #11763109C22semidirect
35. #11763106C22semidirect
36. #11763106C22semidirect
37. #11763089C22semidirect
38. #11763086C22semidirect
39. #11762940C22semidirect
65. C17×#554C22semidirect
124. C2×#63228Q8semidirect
241. #63228C2×Q8semidirect
322. C2×#554D17semidirect
368. #554C2×D17semidirect
425. C2×C17#3389semidirect
530. C17C2×#3389semidirect
703. C2#14541738direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635192
#145417382
C2×#117632192
C2×#117632152
C2×#117632082
C2×#117631092
C2×#117631062
C2×#117630892
C2×#117630862
C2×#117629402
C2×#117629192
C2×C4×#632282
C2×C17×#5542
C2×#338917