Finite Group Databasebeta

← C2×#14539000 #17902589

Subgroups — C2×#14539000 #17902589

Order 4352.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763421C211yesmaximal, characteristic, complemented
2C2×#11763289C211yesmaximal, characteristic
3#14539000C2116yesmaximal, direct product factor
4C2×#11763145C211yesmaximal, characteristic, complemented
5C2×#11763140C211yesmaximal, characteristic, complemented
6C2×#11763117C211yesmaximal, characteristic, complemented
7C2×#11763110C211yesmaximal, characteristic, complemented
8C2×#11763020C211yesmaximal, characteristic, complemented
9C2×#11763015C211yesmaximal, characteristic, complemented
10C2×#11762973C211yesmaximal, characteristic
11C2×#11762973C211yesmaximal, characteristic
12C2×#11762917C211yesmaximal, characteristic, complemented
13C2×#11762911C211yesmaximal, characteristic, complemented
14C2×C4×Dic68C211yesmaximal, characteristic, complemented
15C2×C4×#63219C211yesmaximal, characteristic, complemented
16C2×C17×#433C211yesmaximal, characteristic, complemented
17C22×#63252C2211yescharacteristic
18C22×Dic68C2211yescharacteristic
19C22×Dic68C2211yescharacteristic
20C22×#63219C2211yescharacteristic
21C22×#63219C2211yescharacteristic
22#11763421—24no—
23#11763421C2218yescomplemented
24C2×#10587555C2211yescharacteristic
25C2×#10587565—21no—
26C2×#10587565—21no—
27C2×#10587556C2211yescharacteristic
28C2×#10587575—21no—
29C2×#10587575—21no—
30C2×#10587610C2211yescharacteristic
31C2×#10587610C2211yescharacteristic
32#11763289—24no—
33#11763289C2218yes—
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×Dic34C2211yescharacteristic
36C2×C4×Dic34C2211yescharacteristic
37C2×C4×Dic34C2211yescharacteristic
38C2×C4×D68C2211yescharacteristic
39C2×C4×D68C2211yescharacteristic
40C2×#10587567—21no—
41C2×#10587567—21no—
42C2×#10587578—21no—
43C22×C4⋊Dic17C2211yescharacteristic
44C2×C4⋊C4×D17—21no—
45#11763145C2218yescomplemented
46#11763140C2218yescomplemented
47#11763117C2218yescomplemented
48#11763110C2218yescomplemented
49#11763020C2218yescomplemented
50#11763015C2218yescomplemented
51#11762973C2218yes—
52#11762973C2218yes—
53#11762917C2218yescomplemented
54#11762911C2218yescomplemented
55C4×Dic68C2218yescomplemented
56C4×#63219C2218yescomplemented
57C2×#10587489C2211yescharacteristic
58C2×#10587489C2211yescharacteristic
59C2×#10587488C2211yescharacteristic
60C2×#10587488C2211yescharacteristic
61C2×#10587487C2211yescharacteristic
62C2×#10587487C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587487C2211yescharacteristic
66C2×#10587487C2211yescharacteristic
67C2×#10587492C2211yescharacteristic
68C2×#10587492C2211yescharacteristic
69C2×C17×#117C2211yescharacteristic
70C17×#433C2218yescomplemented
71C2×C17×C4⋊C8C2211yescharacteristic
72C2×C17×C4⋊C8C2211yescharacteristic
73C2×C17×C22⋊C8C2211yescharacteristic
74C2×C17×C22⋊C8C2211yescharacteristic
75C2×C17×#97C2211yescharacteristic
76C2×C4×C8×C17C2211yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C22×C22⋊D17—21no—
79C23×Dic17—21no—
80C2×#63252—22no—
81C2×#63252—24no—
82C2×#63252—24no—
83C2×#63252C2314yes—
84C22×D68C2311yescharacteristic
85C22×C4×D17—21no—
86C22×C4×D17—21no—
87C22×C4×D17—21no—
88C22×Dic34C2311yescharacteristic
89C22×Dic34C2311yescharacteristic
90C22×Dic34C2311yescharacteristic
91C22×C8×C17C2311yescharacteristic
92C22×C8×C17C2311yescharacteristic
93C22×C8×C17C2311yescharacteristic
94C22×C8×C17C2311yescharacteristic
95C17×#117D414yes—
96C17×#117C2314yes—
97C2×C4⋊C4×C17D411yescharacteristic
98C2×C4⋊C4×C17D411yescharacteristic
99C2×C22⋊C4×C17D411yescharacteristic
100C2×C22⋊C4×C17D411yescharacteristic
101C2×C42×C17C2311yescharacteristic
102C2×C42×C17C2311yescharacteristic
103C2×C22⋊Dic17—21no—
104C2×C22⋊Dic17—21no—
105C2×#63227—21no—
106C2×#63227—21no—
107C2×C4⋊Dic17—21no—
108C2×C4⋊Dic17—22no—
109C2×C4⋊Dic17—21no—
110C2×C4⋊Dic17—21no—
111C2×C4⋊Dic17C2311yescharacteristic
112C2×C4⋊Dic17C2311yescharacteristic
113C2×C4⋊Dic17C2314yes—
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116#10587610—22no—
117#10587610—22no—
118#10587610C2314yes—
119#10587610C2314yes—
120C2×#63225—21no—
121C2×#63225—21no—
122C2×#63225—21no—
123C2×#63225—21no—
124C2×#63225—21no—
125C2×#63225—21no—
126C2×#63225—21no—
127C2×#63225—21no—
128C2×C4×Dic17—21no—
129C2×C4×Dic17—21no—
130C2×C4×Dic17—21no—
131C2×C4×Dic17—21no—
132C2×Dic68—24no—
133C2×Dic68—24no—
134C2×Dic68C2314yes—
135C2×Dic68C2314yes—
136C2×#63219—24no—
137C2×#63219—24no—
138C2×#63219C2314yes—
139C2×#63219C2314yes—
140#10587578—28no—
141C4⋊C4×D17—28no—
142#10587575—28no—
143#10587575—28no—
144#10587567—28no—
145#10587567—28no—
146#10587565—28no—
147#10587565—28no—
148C4×D68—22no—
149C4×D68—22no—
150C4×D68C2314yes—
151C4×D68C2314yes—
152#10587556—22no—
153#10587556C2314yes—
154#10587555—22no—
155#10587555C2314yes—
156C4×Dic34—22no—
157C4×Dic34—22no—
158C4×Dic34—22no—
159C4×Dic34—22no—
160C4×Dic34C2314yes—
161C4×Dic34C2314yes—
162C4×Dic34C2314yes—
163C4×Dic34C2314yes—
164C17×C4⋊C8C2314yes—
165C17×C4⋊C8C2314yes—
166C17×C22⋊C8C2314yes—
167C17×C22⋊C8C2314yes—
168C17×#97C2314yes—
169C4×C8×C17C2314yes—
170#10587492C2314yes—
171#10587492C2314yes—
172#10587489C2314yes—
173#10587489C2314yes—
174#10587488C2314yes—
175#10587488C2314yes—
176#10587487C2314yes—
177#10587487C2314yes—
178#10587487C2314yes—
179#10587487C2314yes—
180#10587487C2314yes—
181#10587487C2314yes—
182C24×C17C2×D411yescharacteristic
183C23×D17—21no—
184C22×C4×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17C2×D411yescharacteristic
187C22×C4×C17C2×D411yescharacteristic
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D412yes—
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2412yes—
193C22×C4×C17C2411yescharacteristic
194C2×C22⋊D17—28no—
195C2×C22⋊D17—24no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—24no—
204C22×Dic17—82no—
205#63252—216no—
206#63252—28no—
207#63252—28no—
208C2×D68—21no—
209C2×D68—22no—
210C2×D68#4114yes—
211C2×D68C2412yes—
212C2×C4×D17—28no—
213C2×C4×D17—24no—
214C2×C4×D17—24no—
215C2×C4×D17—24no—
216C2×C4×D17—82no—
217C2×C4×D17—82no—
218C2×Dic34—21no—
219C2×Dic34—22no—
220C2×Dic34—22no—
221C2×Dic34—22no—
222C2×Dic34—22no—
223C2×Dic34—22no—
224C2×Dic34—21no—
225C2×Dic34—21no—
226C2×Dic34#4114yes—
227C2×Dic34C2412yes—
228C2×Dic34C2412yes—
229C2×Dic34C2412yes—
230C2×C8×C17—22no—
231C2×C8×C17—22no—
232C2×C8×C17—22no—
233C2×C8×C17—22no—
234C2×C8×C17C2412yes—
235C2×C8×C17C2412yes—
236C2×C8×C17C2412yes—
237C2×C8×C17C2412yes—
238C4⋊C4×C17C2×D414yes—
239C4⋊C4×C17C2×D414yes—
240C22⋊C4×C17C2×D414yes—
241C22⋊C4×C17C2×D414yes—
242C42×C17C2×D412yes—
243C42×C17C2×D412yes—
244C42×C17C2412yes—
245C42×C17C2412yes—
246C22⋊Dic17—24no—
247C22⋊Dic17—24no—
248#63227—24no—
249#63227—24no—
250C4⋊Dic17—21no—
251C4⋊Dic17—21no—
252C4⋊Dic17—21no—
253C4⋊Dic17—21no—
254C4⋊Dic17—24no—
255C4⋊Dic17—24no—
256C4⋊Dic17—24no—
257C4⋊Dic17C2412yes—
258C4⋊Dic17C2412yes—
259C4⋊Dic17C2412yes—
260C4⋊Dic17C2412yes—
261#63225—24no—
262#63225—24no—
263#63225—24no—
264#63225—24no—
265#63225—24no—
266#63225—24no—
267#63225—24no—
268#63225—24no—
269C4×Dic17—24no—
270C4×Dic17—24no—
271C4×Dic17—24no—
272C4×Dic17—24no—
273Dic68—28no—
274Dic68—28no—
275#63219—28no—
276#63219—28no—
277C2×#3120—171nomaximal, Sylow
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—22no—
281C23×C17C22×D412yes—
282C23×C17C22×D411yescharacteristic
283C22×D17—24no—
284C22×D17—22no—
285C22×D17—42no—
286C22×D17—42no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—24no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
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×C17C2×#4112yes—
302C2×C4×C17C2×#4112yes—
303C2×C4×C17C2511yescharacteristic
304C22⋊D17—216no—
305C2×Dic17—24no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—84no—
320D68—24no—
321D68—22no—
322D68C2×#4114yes—
323C4×D17—216no—
324C4×D17—84no—
325C4×D17—84no—
326Dic34—24no—
327Dic34—22no—
328Dic34—22no—
329Dic34—22no—
330Dic34—22no—
331Dic34—22no—
332Dic34—42no—
333Dic34—42no—
334Dic34C2×#4114yes—
335C8×C17—22no—
336C8×C17—22no—
337C8×C17—22no—
338C8×C17—22no—
339C2×#541—171no—
340C2×#520—171no—
341#3120—1716no—
342C2×#484—171no—
343C2×#483—171no—
344C2×#479—171no—
345C2×#478—171no—
346C2×#462—171no—
347C2×#461—171no—
348C2×#452—171no—
349C2×#452—171no—
350C2×#441—171no—
351C2×#440—171no—
352C2×C4×Q16—171no—
353C2×C4×SD16—171no—
354C2×#433D1711yescharacteristic, complemented
355C22×C17—22no—
356C22×C17—22no—
357C22×C17—22no—
358C22×C17—44no—
359C22×C17#52512yes—
360C22×C17#57712yes—
361C22×C17#57812yes—
362C22×C17C23×D411yescharacteristic
363C2×D17—24no—
364C2×D17—48no—
365C2×D17—42no—
366C2×D17—42no—
367C4×C17—22no—
368C4×C17—22no—
369C4×C17—22no—
370C4×C17—22no—
371C4×C17—22no—
372C4×C17#52512yes—
373C4×C17C22×#4111yescharacteristic
374C4×C17C22×#4111yescharacteristic
375Dic17—24no—
376Dic17—42no—
377Dic17—42no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381Dic17—42no—
382C22×#41—171no—
383C22×Q16—171no—
384C22×Q16—171no—
385C22×SD16—171no—
386C22×SD16—171no—
387#541—178no—
388#541—344no—
389C2×C4⋊Q8—171no—
390C2×#126—341no—
391C2×#126—341no—
392C2×#125—171no—
393C2×#125—341no—
394C2×#125—341no—
395C2×C22⋊Q8—171no—
396C2×C22⋊Q8—171no—
397#520—178no—
398#520—344no—
399C2×C4×Q8—171no—
400C2×C4×Q8—171no—
401C2×C4×Q8—171no—
402C2×C4×Q8—171no—
403C2×C4×D4—171no—
404C2×C4×D4—171no—
405C2×C4×D4—341no—
406C2×C4×D4—341no—
407C2×#117—341no—
408C2×#117C2×D1711yescharacteristic
409C22×C4⋊C4—171no—
410C22×C4⋊C4—341no—
411#484—178no—
412#483—178no—
413#479—178no—
414#478—178no—
415#462—178no—
416#461—178no—
417#452—178no—
418#452—178no—
419#441—178no—
420#440—178no—
421C4×Q16—178no—
422C4×SD16—178no—
423#433C2×D1718yescomplemented
424C2×#107—171no—
425C2×#107—171no—
426C2×#106—171no—
427C2×#106—171no—
428C2×C4⋊C8C2×D1711yescharacteristic
429C2×C4⋊C8C2×D1711yescharacteristic
430C2×#103—171no—
431C2×#103—171no—
432C2×#103—171no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#103—171no—
436C2×#102—171no—
437C2×#102—171no—
438C2×C22⋊C8C2×D1711yescharacteristic
439C2×C22⋊C8C2×D1711yescharacteristic
440C2×#97C2×D1711yescharacteristic
441C2×C4×C8C2×D1711yescharacteristic
442C2×C17—42no—
443C2×C17#312014yescomplemented
444C2×C17C2×#52511yescharacteristic
445C2×C17C2×#57711yescharacteristic
446C2×C17C2×#57811yescharacteristic
447D17—44no—
448C2×#41—174no—
449C2×#41—344no—
450C2×#41—344no—
451C2×#41—342no—
452C22×Q8—171no—
453C22×Q8—171no—
454C22×Q8—171no—
455C22×D4—171no—
456C22×D4—341no—
457C23×C4—341no—
458C23×C4—341no—
459C23×C4—341no—
460C23×C4—341no—
461C23×C4C22×D1711yescharacteristic
462C2×Q16—174no—
463C2×Q16—174no—
464C2×Q16—344no—
465C2×Q16—344no—
466C2×SD16—174no—
467C2×SD16—174no—
468C2×SD16—344no—
469C2×SD16—344no—
470C22×C8C22×D1711yescharacteristic
471C22×C8C22×D1711yescharacteristic
472C22×C8C22×D1711yescharacteristic
473C22×C8C22×D1711yescharacteristic
474C4⋊Q8—174no—
475C4⋊Q8—342no—
476#126—348no—
477#126—348no—
478#125—174no—
479#125—348no—
480#125—348no—
481#125—342no—
482C22⋊Q8—174no—
483C22⋊Q8—174no—
484C22⋊Q8—342no—
485C22⋊Q8—342no—
486C4×Q8—174no—
487C4×Q8—174no—
488C4×Q8—174no—
489C4×Q8—174no—
490C4×Q8—342no—
491C4×Q8—342no—
492C4×Q8—342no—
493C4×Q8—342no—
494C4×D4—174no—
495C4×D4—174no—
496C4×D4—348no—
497C4×D4—348no—
498C4×D4—342no—
499C4×D4—342no—
500#117—348no—
501#117D6814yes—
502#117C22×D1714yes—
503C2×C4⋊C4—171no—
504C2×C4⋊C4—171no—
505C2×C4⋊C4—174no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4—342no—
510C2×C4⋊C4—341no—
511C2×C4⋊C4—341no—
512C2×C4⋊C4—341no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4—341no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4—341no—
519C2×C4⋊C4—341no—
520C2×C4⋊C4—348no—
521C2×C4⋊C4D6811yescharacteristic
522C2×C4⋊C4D6811yescharacteristic
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4D6811yescharacteristic
528C2×C22⋊C4D6811yescharacteristic
529C2×C42—341no—
530C2×C42—341no—
531C2×C42—341no—
532C2×C42—341no—
533C2×C42C22×D1711yescharacteristic
534C2×C42C22×D1711yescharacteristic
535#107—174no—
536#107—174no—
537#106—174no—
538#106—174no—
539C4⋊C8C22×D1714yes—
540C4⋊C8C22×D1714yes—
541#103—174no—
542#103—174no—
543#103—174no—
544#103—174no—
545#103—174no—
546#103—174no—
547#102—174no—
548#102—174no—
549C22⋊C8C22×D1714yes—
550C22⋊C8C22×D1714yes—
551#97C22×D1714yes—
552C4×C8C22×D1714yes—
553C17C2×#312011yescharacteristic, complemented, Sylow
554C24—341no—
555C24C2×D6811yescharacteristic
556#41—348no—
557#41—348no—
558#41—3416no—
559C2×Q8—174no—
560C2×Q8—172no—
561C2×Q8—172no—
562C2×Q8—172no—
563C2×Q8—341no—
564C2×Q8—341no—
565C2×Q8—341no—
566C2×Q8—342no—
567C2×Q8—342no—
568C2×Q8—342no—
569C2×Q8—342no—
570C2×Q8—342no—
571C2×D4—174no—
572C2×D4—172no—
573C2×D4—348no—
574C2×D4—344no—
575C2×D4—341no—
576C2×D4—342no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—348no—
580C22×C4—341no—
581C22×C4—344no—
582C22×C4—341no—
583C22×C4—341no—
584C22×C4—341no—
585C22×C4—341no—
586C22×C4—341no—
587C22×C4—341no—
588C22×C4—344no—
589C22×C4—344no—
590C22×C4—344no—
591C22×C4—1362no—
592C22×C4—1362no—
593C22×C4—1362no—
594C22×C4C2×D6812yes—
595C22×C4C2×D6811yescharacteristic
596C22×C4C2×D6811yescharacteristic
597C22×C4C2×D6811yescharacteristic
598C22×C4C2×D6811yescharacteristic
599C22×C4C2×D6811yescharacteristic
600C22×C4C23×D1712yes—
601C22×C4C23×D1711yescharacteristic
602Q16—348no—
603Q16—348no—
604SD16—348no—
605SD16—348no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8C23×D1712yes—
611C2×C8C23×D1712yes—
612C2×C8C23×D1712yes—
613C2×C8C23×D1712yes—
614C4⋊C4—172no—
615C4⋊C4—172no—
616C4⋊C4—172no—
617C4⋊C4—172no—
618C4⋊C4—344no—
619C4⋊C4—341no—
620C4⋊C4—341no—
621C4⋊C4—341no—
622C4⋊C4—341no—
623C4⋊C4—344no—
624C4⋊C4—344no—
625C4⋊C4—344no—
626C4⋊C4—344no—
627C4⋊C4—344no—
628C4⋊C4—344no—
629C4⋊C4—344no—
630C4⋊C4—344no—
631C4⋊C4—344no—
632C4⋊C4—344no—
633C4⋊C4C2×D6814yes—
634C4⋊C4C2×D6814yes—
635C22⋊C4—344no—
636C22⋊C4—344no—
637C22⋊C4—344no—
638C22⋊C4—344no—
639C22⋊C4C2×D6814yes—
640C22⋊C4C2×D6814yes—
641C42—344no—
642C42—344no—
643C42—344no—
644C42—344no—
645C42C2×D6812yes—
646C42C2×D6812yes—
647C42C23×D1712yes—
648C42C23×D1712yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—344no—
653C23—342no—
654C23—682no—
655C23—682no—
656C23C22×D6812yes—
657C23C22×D6811yescharacteristic
658Q8—174no—
659Q8—344no—
660Q8—342no—
661Q8—342no—
662Q8—342no—
663Q8—342no—
664Q8—342no—
665Q8—682no—
666Q8—682no—
667D4—174no—
668D4—3416no—
669D4—344no—
670D4—342no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—3416no—
680C2×C4—344no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—342no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—682no—
689C2×C4—682no—
690C2×C4—682no—
691C2×C4—682no—
692C2×C4—682no—
693C2×C4—682no—
694C2×C4—1364no—
695C2×C4—1364no—
696C2×C4—1364no—
697C2×C4C22×D6812yes—
698C2×C4C22×D6812yes—
699C2×C4C22×D6812yes—
700C2×C4C22×D6812yes—
701C2×C4C22×D6812yes—
702C2×C4C22×D6811yescharacteristic
703C2×C4#41×D1712yes—
704C2×C4#41×D1712yes—
705C2×C4C24×D1711yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—344no—
715C22—682no—
716C22—682no—
717C22—688no—
718C22#1176332112yes—
719C22#1176362112yes—
720C22#1176362612yes—
721C22C23×D6811yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—344no—
728C4—682no—
729C4—682no—
730C4—682no—
731C4—682no—
732C4—682no—
733C4—682no—
734C4#1176332112yes—
735C4C2×#41×D1711yescharacteristic
736C4C2×#41×D1711yescharacteristic
737C2—42no—
738C2—684no—
739C2#1453900014yesdirect product factor
740C2C2×#1176332111yescharacteristic
741C2C2×#1176362111yescharacteristic
742C2C2×#1176362611yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#433C2
socleC23×C17C22×D4
prime radicalC22×#63252C22
hypercenterC2×#433D17
hypocenterC17C2×#3120
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#11763421C2semidirect
3. #14539000C2direct (N × H)
4. C2×#11763145C2semidirect
5. C2×#11763140C2semidirect
6. C2×#11763117C2semidirect
7. C2×#11763110C2semidirect
8. C2×#11763020C2semidirect
9. C2×#11763015C2semidirect
12. C2×#11762917C2semidirect
13. C2×#11762911C2semidirect
14. C2×C4×Dic68C2semidirect
15. C2×C4×#63219C2semidirect
16. C2×C17×#433C2semidirect
23. #11763421C22semidirect
45. #11763145C22semidirect
46. #11763140C22semidirect
47. #11763117C22semidirect
48. #11763110C22semidirect
49. #11763020C22semidirect
50. #11763015C22semidirect
53. #11762917C22semidirect
54. #11762911C22semidirect
55. C4×Dic68C22semidirect
56. C4×#63219C22semidirect
70. C17×#433C22semidirect
354. C2×#433D17semidirect
423. #433C2×D17semidirect
443. C2×C17#3120semidirect
553. C17C2×#3120semidirect
739. C2#14539000direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634212
C2×#117632892
#145390002
C2×#117631452
C2×#117631402
C2×#117631172
C2×#117631102
C2×#117630202
C2×#117630152
C2×#117629732
C2×#117629172
C2×#117629112
C2×C4×Dic682
C2×C4×#632192
C2×C17×#4332
C2×#312017