Finite Group Databasebeta

← C2×#22599593 #32869641

Subgroups — C2×#22599593 #32869641

Order 18176.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986604C211yesmaximal, characteristic
2#22599593C2116yesmaximal, direct product factor
3C2×#17986405C211yesmaximal, characteristic, complemented
4C2×#17986398C211yesmaximal, characteristic, complemented
5C2×#17986365C211yesmaximal, characteristic, complemented
6C2×#17986347C211yesmaximal, characteristic, complemented
7C2×#17986317C211yesmaximal, characteristic, complemented
8C2×#17986323C211yesmaximal, characteristic, complemented
9C2×#17986323C211yesmaximal, characteristic, complemented
10C2×#17986312C211yesmaximal, characteristic, complemented
11C2×#17986296C211yesmaximal, characteristic, complemented
12C2×#17986296C211yesmaximal, characteristic, complemented
13C2×#17986286C211yesmaximal, characteristic, complemented
14C2×#17986276C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#544×C71C211yesmaximal, characteristic, complemented
17#17986604—24no—
18#17986604C2218yes—
19C2×#14556125C2211yescharacteristic
20C2×#14556120C2211yescharacteristic
21C2×#14556113—21no—
22C2×#14556113—21no—
23C2×#14556102C2211yescharacteristic
24C2×#14556102C2211yescharacteristic
25C2×#14556101—21no—
26C2×#14556101—21no—
27C2×C4×D284C2211yescharacteristic
28C2×C4×D284C2211yescharacteristic
29#17986405C2218yescomplemented
30#17986398C2218yescomplemented
31#17986365C2218yescomplemented
32#17986347C2218yescomplemented
33#17986323C2218yescomplemented
34#17986323C2218yescomplemented
35#17986317C2218yescomplemented
36#17986312C2218yescomplemented
37#17986296C2218yescomplemented
38#17986296C2218yescomplemented
39#17986286C2218yescomplemented
40#17986276C2218yescomplemented
41#17986060C2218yescomplemented
42C2×#14556061C2211yescharacteristic
43C2×#14556061C2211yescharacteristic
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556059C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×C4⋊(C71⋊C8)C2211yescharacteristic
52C2×#14556048C2211yescharacteristic
53C2×#14556048C2211yescharacteristic
54C2×#14556048C2211yescharacteristic
55C2×#14556048C2211yescharacteristic
56C2×#14556048C2211yescharacteristic
57C2×#14556048C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#544×C71—24no—
65#544×C71C2218yescomplemented
66C2×C4⋊Q8×C71—21no—
67C2×C4⋊Q8×C71C2211yescharacteristic
68C2×C4⋊Q8×C71C2211yescharacteristic
69C2×#125×C71—21no—
70C2×#125×C71C2211yescharacteristic
71C2×#125×C71C2211yescharacteristic
72C2×C22⋊Q8×C71—21no—
73C2×C22⋊Q8×C71—21no—
74C2×#117×C71C2211yescharacteristic
75C2×#117×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×D284—21no—
78C22×D284—21no—
79C22×D284C2311yescharacteristic
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C22×C22⋊D71—21no—
83C22×C4×D71—21no—
84C22×C4×D71—21no—
85C22×C71⋊C8C2311yescharacteristic
86C22×C71⋊C8C2311yescharacteristic
87C22×C71⋊C8C2311yescharacteristic
88C22×C71⋊C8C2311yescharacteristic
89#14556125—22no—
90#14556125C2314yes—
91#14556120—22no—
92#14556120C2314yes—
93#14556113—28no—
94#14556113—28no—
95#14556102—22no—
96#14556102—22no—
97#14556102C2314yes—
98#14556102C2314yes—
99#14556101—28no—
100#14556101—28no—
101C4×D284—22no—
102C4×D284—22no—
103C4×D284C2314yes—
104C4×D284C2314yes—
105C2×C4⋊Dic71C2311yescharacteristic
106C2×C4⋊Dic71C2311yescharacteristic
107C2×Dic71⋊C4—21no—
108C2×Dic71⋊C4—21no—
109C2×(C2×D71)⋊C4—21no—
110C2×(C2×D71)⋊C4—21no—
111C2×(C2×D71)⋊C4—21no—
112C2×(C2×D71)⋊C4—21no—
113#14556061C2314yes—
114#14556061C2314yes—
115#14556061C2314yes—
116#14556061C2314yes—
117#14556059C2314yes—
118#14556059C2314yes—
119#14556059C2314yes—
120#14556059C2314yes—
121C4⋊(C71⋊C8)C2314yes—
122C4⋊(C71⋊C8)C2314yes—
123#14556048C2314yes—
124#14556048C2314yes—
125#14556048C2314yes—
126#14556048C2314yes—
127#14556048C2314yes—
128#14556048C2314yes—
129#14556048C2314yes—
130#14556048C2314yes—
131C22⋊(C71⋊C8)C2314yes—
132C22⋊(C71⋊C8)C2314yes—
133#14556039C2314yes—
134C4×C71⋊C8C2314yes—
135C22×Q8×C71—21no—
136C22×Q8×C71—21no—
137C23×C4×C71—21no—
138C23×C4×C71C2311yescharacteristic
139C4⋊Q8×C71—28no—
140C4⋊Q8×C71—22no—
141C4⋊Q8×C71—22no—
142C4⋊Q8×C71C2314yes—
143C4⋊Q8×C71C2314yes—
144#125×C71—28no—
145#125×C71—22no—
146#125×C71—22no—
147#125×C71C2314yes—
148#125×C71C2314yes—
149C22⋊Q8×C71—28no—
150C22⋊Q8×C71—28no—
151#117×C71—22no—
152#117×C71D414yes—
153#117×C71C2314yes—
154#117×C71C2314yes—
155C2×C4⋊C4×C71—21no—
156C2×C4⋊C4×C71—22no—
157C2×C4⋊C4×C71—21no—
158C2×C4⋊C4×C71—21no—
159C2×C4⋊C4×C71—21no—
160C2×C4⋊C4×C71—21no—
161C2×C4⋊C4×C71—21no—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71D411yescharacteristic
164C2×C4⋊C4×C71D411yescharacteristic
165C2×C4⋊C4×C71C2314yes—
166C2×C4⋊C4×C71C2311yescharacteristic
167C2×C4⋊C4×C71C2311yescharacteristic
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C22⋊C4×C71—21no—
171C2×C22⋊C4×C71D411yescharacteristic
172C2×C22⋊C4×C71D411yescharacteristic
173C2×C42×C71—21no—
174C2×C42×C71C2311yescharacteristic
175C2×C42×C71C2311yescharacteristic
176C23×D71—21no—
177C23×D71—21no—
178C2×D284—22no—
179C2×D284—22no—
180C2×D284—22no—
181C2×D284—22no—
182C2×D284—21no—
183C2×D284—21no—
184C2×D284—24no—
185C2×D284—24no—
186C2×D284—82no—
187C2×D284—82no—
188C2×D284C2412yes—
189C2×D284C2412yes—
190C2×C22⋊D71—24no—
191C2×C22⋊D71—24no—
192C2×C22⋊D71—82no—
193C2×C22⋊D71—82no—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C2×C4×D71—24no—
197C2×C4×D71—24no—
198C2×C4×D71—82no—
199C2×C4×D71—82no—
200C2×C71⋊C8—22no—
201C2×C71⋊C8—22no—
202C2×C71⋊C8—22no—
203C2×C71⋊C8—22no—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C2×C71⋊C8C2412yes—
207C2×C71⋊C8C2412yes—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71C2412yes—
211C4⋊Dic71C2412yes—
212Dic71⋊C4—24no—
213Dic71⋊C4—24no—
214(C2×D71)⋊C4—24no—
215(C2×D71)⋊C4—24no—
216(C2×D71)⋊C4—24no—
217(C2×D71)⋊C4—24no—
218C24×C71C2×D411yescharacteristic
219C2×Q8×C71—24no—
220C2×Q8×C71—24no—
221C2×Q8×C71—82no—
222C2×Q8×C71—82no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—21no—
226C22×C4×C71—21no—
227C22×C4×C71—21no—
228C22×C4×C71—21no—
229C22×C4×C71—24no—
230C22×C4×C71—82no—
231C22×C4×C71C2×D411yescharacteristic
232C22×C4×C71C2×D411yescharacteristic
233C22×C4×C71C2×D411yescharacteristic
234C22×C4×C71C2×D411yescharacteristic
235C22×C4×C71C2×D411yescharacteristic
236C22×C4×C71C2×D412yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2411yescharacteristic
239C4⋊C4×C71—24no—
240C4⋊C4×C71—21no—
241C4⋊C4×C71—21no—
242C4⋊C4×C71—24no—
243C4⋊C4×C71—24no—
244C4⋊C4×C71—24no—
245C4⋊C4×C71—24no—
246C4⋊C4×C71—24no—
247C4⋊C4×C71—24no—
248C4⋊C4×C71—21no—
249C4⋊C4×C71—21no—
250C4⋊C4×C71C2×D414yes—
251C4⋊C4×C71C2×D414yes—
252C4⋊C4×C71C2412yes—
253C4⋊C4×C71C2412yes—
254C4⋊C4×C71C2412yes—
255C4⋊C4×C71C2412yes—
256C22⋊C4×C71—24no—
257C22⋊C4×C71C2×D414yes—
258C22⋊C4×C71C2×D414yes—
259C42×C71—24no—
260C42×C71C2×D412yes—
261C42×C71C2×D412yes—
262C42×C71C2412yes—
263C42×C71C2412yes—
264C23×C71—22no—
265C23×C71—22no—
266C23×C71—22no—
267C23×C71C22×D412yes—
268C23×C71C22×D411yescharacteristic
269C22×D71—22no—
270C22×D71—22no—
271C22×D71—42no—
272C22×D71—42no—
273C22×D71—42no—
274C22×D71—42no—
275C22×D71—42no—
276C22×D71—42no—
277Q8×C71—84no—
278Q8×C71—84no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—24no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—42no—
292C2×C4×C71—42no—
293C2×C4×C71—42no—
294C2×C4×C71—42no—
295C2×C4×C71—84no—
296C2×C4×C71C22×D412yes—
297C2×C4×C71C22×D412yes—
298C2×C4×C71C22×D412yes—
299C2×C4×C71C22×D412yes—
300C2×C4×C71C22×D412yes—
301C2×C4×C71C22×D411yescharacteristic
302C2×C4×C712−1+412yes—
303C2×C4×C712−1+412yes—
304C2×C4×C71C2511yescharacteristic
305C22⋊D71—84no—
306C22⋊D71—84no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—42no—
310C2×Dic71—42no—
311D284—22no—
312D284—22no—
313D284—22no—
314D284—22no—
315D284—42no—
316D284—42no—
317D284—84no—
318D284—84no—
319C4×D71—84no—
320C4×D71—84no—
321C71⋊C8—22no—
322C71⋊C8—22no—
323C71⋊C8—22no—
324C71⋊C8—22no—
325C22×C71—22no—
326C22×C71—22no—
327C22×C71—22no—
328C22×C71—44no—
329C22×C71#53612yes—
330C22×C71#57612yes—
331C22×C71#57712yes—
332C22×C71C23×D411yescharacteristic
333C2×D71—42no—
334C2×D71—42no—
335C2×D71—42no—
336C2×D71—42no—
337C2×D71—42no—
338C2×D71—42no—
339C2×D71—84no—
340C2×D71—84no—
341C4×C71—22no—
342C4×C71—22no—
343C4×C71—22no—
344C4×C71—22no—
345C4×C71—22no—
346C4×C71—42no—
347C4×C71—42no—
348C4×C71—42no—
349C4×C71—42no—
350C4×C71#53612yes—
351C4×C71C2×2−1+411yescharacteristic
352C4×C71C2×2−1+411yescharacteristic
353Dic71—42no—
354Dic71—42no—
355C2×#3241—711nomaximal, Sylow
356C2×C71—42no—
357C2×C71#324114yescomplemented
358C2×C71C2×#53611yescharacteristic
359C2×C71C2×#57611yescharacteristic
360C2×C71C2×#57711yescharacteristic
361D71—82no—
362D71—82no—
363C2×#544D7111yescharacteristic, complemented
364C2×#540—711no—
365#3241—7116no—
366C2×#501—711no—
367C2×#499—711no—
368C2×#490—711no—
369C2×#486—711no—
370C2×#481—711no—
371C2×#482—711no—
372C2×#482—711no—
373C2×#480—711no—
374C2×#478—711no—
375C2×#478—711no—
376C2×#476—711no—
377C2×#474—711no—
378C2×#433—711no—
379C71C2×#324111yescharacteristic, complemented, Sylow
380#544—24no—
381#544C2×D7118yescomplemented
382#540—718no—
383#540—1424no—
384C2×C4⋊Q8—21no—
385C2×C4⋊Q8C2×D7111yescharacteristic
386C2×C4⋊Q8C2×D7111yescharacteristic
387C2×#127—711no—
388C2×#125—21no—
389C2×#125—711no—
390C2×#125C2×D7111yescharacteristic
391C2×#125C2×D7111yescharacteristic
392C2×#123—1421no—
393C2×#123—1421no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8—21no—
396C2×#121—711no—
397C2×#121—711no—
398C2×#121—1421no—
399C2×#121—1421no—
400C2×C4×D4—711no—
401C2×C4×D4—711no—
402C2×#117C2×D7111yescharacteristic
403C2×#117C2×D7111yescharacteristic
404C22×C4⋊C4C2×D7111yescharacteristic
405#501—718no—
406#499—718no—
407#490—718no—
408#486—718no—
409#482—718no—
410#482—718no—
411#481—718no—
412#480—718no—
413#478—718no—
414#478—718no—
415#476—718no—
416#474—718no—
417#433—718no—
418C2×#107—711no—
419C2×#107—711no—
420C2×#107—711no—
421C2×#107—711no—
422C2×#106—711no—
423C2×#106—711no—
424C2×#106—711no—
425C2×#106—711no—
426C2×C4⋊C8—711no—
427C2×C4⋊C8—711no—
428C2×#102—711no—
429C2×#102—711no—
430C2×#102—711no—
431C2×#102—711no—
432C2×#102—711no—
433C2×#102—711no—
434C2×#102—711no—
435C2×#102—711no—
436C2×C22⋊C8—711no—
437C2×C22⋊C8—711no—
438C2×#97—711no—
439C2×C4×C8—711no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×D4—711no—
443C22×D4—711no—
444C22×D4—1421no—
445C22×D4—1421no—
446C22×D4—1421no—
447C22×D4—1421no—
448C23×C4—21no—
449C23×C4—1421no—
450C23×C4—1421no—
451C23×C4C22×D7111yescharacteristic
452C22×C8—711no—
453C22×C8—711no—
454C22×C8—711no—
455C22×C8—711no—
456C4⋊Q8—28no—
457C4⋊Q8—22no—
458C4⋊Q8—22no—
459C4⋊Q8C22×D7114yes—
460C4⋊Q8C22×D7114yes—
461#127—714no—
462#127—1422no—
463#125—28no—
464#125—22no—
465#125—22no—
466#125—714no—
467#125—1422no—
468#125C22×D7114yes—
469#125C22×D7114yes—
470#123—1428no—
471#123—1428no—
472C22⋊Q8—28no—
473C22⋊Q8—28no—
474#121—714no—
475#121—714no—
476#121—1422no—
477#121—1422no—
478#121—1428no—
479#121—1428no—
480C4×D4—714no—
481C4×D4—714no—
482C4×D4—1422no—
483C4×D4—1422no—
484#117—22no—
485#117C22⋊D7114yes—
486#117C22×D7114yes—
487#117C22×D7114yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—711no—
497C2×C4⋊C4—711no—
498C2×C4⋊C4—1421no—
499C2×C4⋊C4—1421no—
500C2×C4⋊C4C22⋊D7111yescharacteristic
501C2×C4⋊C4C22⋊D7111yescharacteristic
502C2×C4⋊C4C22×D7111yescharacteristic
503C2×C4⋊C4C22×D7111yescharacteristic
504C2×C4⋊C4C22×D7114yes—
505C2×C4⋊C4C22×D7111yescharacteristic
506C2×C4⋊C4C22×D7111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1421no—
509C2×C22⋊C4—1421no—
510C2×C22⋊C4—1421no—
511C2×C22⋊C4—1421no—
512C2×C22⋊C4C22⋊D7111yescharacteristic
513C2×C22⋊C4C22⋊D7111yescharacteristic
514C2×C42—21no—
515C2×C42C22×D7111yescharacteristic
516C2×C42C22×D7111yescharacteristic
517#107—714no—
518#107—714no—
519#107—714no—
520#107—714no—
521#106—714no—
522#106—714no—
523#106—714no—
524#106—714no—
525C4⋊C8—714no—
526C4⋊C8—714no—
527#102—714no—
528#102—714no—
529#102—714no—
530#102—714no—
531#102—714no—
532#102—714no—
533#102—714no—
534#102—714no—
535C22⋊C8—714no—
536C22⋊C8—714no—
537#97—714no—
538C4×C8—714no—
539C24—1421no—
540C24—1421no—
541C24C2×C22⋊D7111yescharacteristic
542C2×Q8—24no—
543C2×Q8—24no—
544C2×Q8—82no—
545C2×Q8—82no—
546C2×D4—5682no—
547C2×D4—5682no—
548C2×D4—5682no—
549C2×D4—5682no—
550C2×D4—712no—
551C2×D4—712no—
552C2×D4—1424no—
553C2×D4—1424no—
554C2×D4—1421no—
555C2×D4—1421no—
556C2×D4—1424no—
557C2×D4—1424no—
558C2×D4—1422no—
559C2×D4—1422no—
560C2×D4—1422no—
561C2×D4—1422no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—82no—
570C22×C4—5682no—
571C22×C4—5682no—
572C22×C4—1421no—
573C22×C4—1421no—
574C22×C4—1424no—
575C22×C4—1424no—
576C22×C4C2×C22⋊D7112yes—
577C22×C4C2×C22⋊D7111yescharacteristic
578C22×C4C2×C22⋊D7111yescharacteristic
579C22×C4C2×C22⋊D7111yescharacteristic
580C22×C4C2×C22⋊D7111yescharacteristic
581C22×C4C2×C22⋊D7111yescharacteristic
582C22×C4C23×D7112yes—
583C22×C4C23×D7111yescharacteristic
584C2×C8—712no—
585C2×C8—712no—
586C2×C8—712no—
587C2×C8—712no—
588C2×C8—1422no—
589C2×C8—1422no—
590C2×C8—1422no—
591C2×C8—1422no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—712no—
604C4⋊C4—712no—
605C4⋊C4—1424no—
606C4⋊C4—1424no—
607C4⋊C4—1421no—
608C4⋊C4—1421no—
609C4⋊C4C2×C22⋊D7114yes—
610C4⋊C4C2×C22⋊D7114yes—
611C4⋊C4C23×D7112yes—
612C4⋊C4C23×D7112yes—
613C4⋊C4C23×D7112yes—
614C4⋊C4C23×D7112yes—
615C22⋊C4—24no—
616C22⋊C4—1424no—
617C22⋊C4—1424no—
618C22⋊C4—1424no—
619C22⋊C4—1424no—
620C22⋊C4C2×C22⋊D7114yes—
621C22⋊C4C2×C22⋊D7114yes—
622C42—24no—
623C42C2×C22⋊D7112yes—
624C42C2×C22⋊D7112yes—
625C42C23×D7112yes—
626C42C23×D7112yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—2842no—
631C23—2842no—
632C23—2842no—
633C23—2842no—
634C23—2842no—
635C23—2842no—
636C23—1422no—
637C23—1422no—
638C23C22×C22⋊D7112yes—
639C23C22×C22⋊D7111yescharacteristic
640Q8—84no—
641Q8—84no—
642D4—2842no—
643D4—2842no—
644D4—5684no—
645D4—5684no—
646D4—5684no—
647D4—5684no—
648D4—1422no—
649D4—1422no—
650D4—1422no—
651D4—1422no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—2842no—
670C2×C4—2842no—
671C2×C4—5684no—
672C2×C4—5684no—
673C2×C4—1422no—
674C2×C4—1422no—
675C2×C4C22×C22⋊D7112yes—
676C2×C4C22×C22⋊D7112yes—
677C2×C4C22×C22⋊D7112yes—
678C2×C4C22×C22⋊D7112yes—
679C2×C4C22×C22⋊D7112yes—
680C2×C4C22×C22⋊D7111yescharacteristic
681C2×C4#1455617612yes—
682C2×C4#1455617612yes—
683C2×C4C24×D7111yescharacteristic
684C8—1422no—
685C8—1422no—
686C8—1422no—
687C8—1422no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—2842no—
693C22—2842no—
694C22—2842no—
695C22—2842no—
696C22—2842no—
697C22—2842no—
698C22—5684no—
699C22—5684no—
700C22#1798657312yes—
701C22#1798680212yes—
702C22#1798680712yes—
703C22C23×C22⋊D7111yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—2842no—
714C4—2842no—
715C4#1798657312yes—
716C4C2×#1455617611yescharacteristic
717C4C2×#1455617611yescharacteristic
718C2—42no—
719C2—5682no—
720C2—5682no—
721C2#2259959314yesdirect product factor
722C2C2×#1798657311yescharacteristic
723C2C2×#1798680211yescharacteristic
724C2C2×#1798680711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#544×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986604C2
hypercenterC2×#544D71
hypocenterC71C2×#3241
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #22599593C2direct (N × H)
3. C2×#17986405C2semidirect
4. C2×#17986398C2semidirect
5. C2×#17986365C2semidirect
6. C2×#17986347C2semidirect
7. C2×#17986317C2semidirect
8. C2×#17986323C2semidirect
9. C2×#17986323C2semidirect
10. C2×#17986312C2semidirect
11. C2×#17986296C2semidirect
12. C2×#17986296C2semidirect
13. C2×#17986286C2semidirect
14. C2×#17986276C2semidirect
15. C2×#17986060C2semidirect
16. C2×#544×C71C2semidirect
29. #17986405C22semidirect
30. #17986398C22semidirect
31. #17986365C22semidirect
32. #17986347C22semidirect
33. #17986323C22semidirect
34. #17986323C22semidirect
35. #17986317C22semidirect
36. #17986312C22semidirect
37. #17986296C22semidirect
38. #17986296C22semidirect
39. #17986286C22semidirect
40. #17986276C22semidirect
41. #17986060C22semidirect
65. #544×C71C22semidirect
357. C2×C71#3241semidirect
363. C2×#544D71semidirect
379. C71C2×#3241semidirect
381. #544C2×D71semidirect
721. C2#22599593direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866042
#225995932
C2×#179864052
C2×#179863982
C2×#179863652
C2×#179863472
C2×#179863172
C2×#179863232
C2×#179863122
C2×#179862962
C2×#179862862
C2×#179862762
C2×#179860602
C2×#544×C712
C2×#324171