Finite Group Databasebeta

← C2×#22599751 #32870362

Subgroups — C2×#22599751 #32870362

Order 18176.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986604C211yesmaximal, characteristic, complemented
2#22599751C2116yesmaximal, direct product factor
3C2×#17986306C211yesmaximal, characteristic, complemented
4C2×#17986299C211yesmaximal, characteristic, complemented
5C2×#17986286C211yesmaximal, characteristic, complemented
6C2×#17986276C211yesmaximal, characteristic, complemented
7C2×#17986250C211yesmaximal, characteristic, complemented
8C2×#17986247C211yesmaximal, characteristic, complemented
9C2×#17986233C211yesmaximal, characteristic, complemented
10C2×#17986230C211yesmaximal, characteristic, complemented
11C2×#17986199C211yesmaximal, characteristic, complemented
12C2×#17986211C211yesmaximal, characteristic, complemented
13C2×#17986211C211yesmaximal, characteristic, complemented
14C2×#17986194C211yesmaximal, characteristic, complemented
15C2×#17986026C211yesmaximal, characteristic, complemented
16C2×#542×C71C211yesmaximal, characteristic, complemented
17C22×#11765852C2211yescharacteristic
18C22×#11765852C2211yescharacteristic
19C22×#11765850C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765849C2211yescharacteristic
22C23×C71⋊C8C2211yescharacteristic
23#17986604—24no—
24#17986604C2218yescomplemented
25C2×#14556125C2211yescharacteristic
26C2×#14556120C2211yescharacteristic
27C2×#14556113—21no—
28C2×#14556113—21no—
29C2×#14556102C2211yescharacteristic
30C2×#14556102C2211yescharacteristic
31C2×#14556101—21no—
32C2×#14556101—21no—
33C2×C4×D284C2211yescharacteristic
34C2×C4×D284C2211yescharacteristic
35#17986306C2218yescomplemented
36#17986299C2218yescomplemented
37#17986286C2218yescomplemented
38#17986276C2218yescomplemented
39#17986250C2218yescomplemented
40#17986247C2218yescomplemented
41#17986233C2218yescomplemented
42#17986230C2218yescomplemented
43#17986211C2218yescomplemented
44#17986211C2218yescomplemented
45#17986199C2218yescomplemented
46#17986194C2218yescomplemented
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51#17986026C2218yescomplemented
52C2×C4⋊(C71⋊C8)C2211yescharacteristic
53C2×C4⋊(C71⋊C8)C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×C4⋊(C71⋊C8)C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556052C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×#14556048C2211yescharacteristic
62C2×#14556048C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64#542×C71—24no—
65#542×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#126×C71—21no—
68C2×#124×C71—21no—
69C2×#124×C71C2211yescharacteristic
70C2×#123×C71—21no—
71C2×C22⋊Q8×C71—21no—
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×D4×C71C2211yescharacteristic
76C2×#117×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—
85C2×#11765852—42no—
86C2×#11765852—42no—
87C2×#11765852C2314yes—
88C2×#11765852C2314yes—
89C2×#11765850—42no—
90C2×#11765850—42no—
91C2×#11765850C2314yes—
92C2×#11765850C2314yes—
93C2×#11765849—42no—
94C2×#11765849C2314yes—
95C22×C71⋊C8—42no—
96C22×C71⋊C8C2311yescharacteristic
97C22×C71⋊C8C2311yescharacteristic
98C22×C71⋊C8C2311yescharacteristic
99C22×C71⋊C8C2311yescharacteristic
100C22×C71⋊C8C2314yes—
101#14556125—22no—
102#14556125C2314yes—
103#14556120—22no—
104#14556120C2314yes—
105#14556113—28no—
106#14556113—28no—
107#14556102—22no—
108#14556102—22no—
109#14556102C2314yes—
110#14556102C2314yes—
111#14556101—28no—
112#14556101—28no—
113C4×D284—22no—
114C4×D284—22no—
115C4×D284C2314yes—
116C4×D284C2314yes—
117C2×C4⋊Dic71C2311yescharacteristic
118C2×C4⋊Dic71C2311yescharacteristic
119C2×Dic71⋊C4—21no—
120C2×Dic71⋊C4—21no—
121C2×(C2×D71)⋊C4—21no—
122C2×(C2×D71)⋊C4—21no—
123C2×(C2×D71)⋊C4—21no—
124C2×(C2×D71)⋊C4—21no—
125#14556061C2314yes—
126#14556061C2314yes—
127#14556059C2314yes—
128#14556059C2314yes—
129C4⋊(C71⋊C8)C2314yes—
130C4⋊(C71⋊C8)C2314yes—
131C4⋊(C71⋊C8)C2314yes—
132C4⋊(C71⋊C8)C2314yes—
133#14556052C2314yes—
134#14556052C2314yes—
135#14556049C2314yes—
136#14556049C2314yes—
137#14556048C2314yes—
138#14556048C2314yes—
139#14556048C2314yes—
140#14556048C2314yes—
141C22×Q8×C71—21no—
142C22×Q8×C71C2311yescharacteristic
143C22×D4×C71—21no—
144C22×D4×C71C2311yescharacteristic
145C23×C4×C71—21no—
146C23×C4×C71C2311yescharacteristic
147C4⋊Q8×C71—22no—
148C4⋊Q8×C71C2314yes—
149#126×C71—28no—
150#124×C71—28no—
151#124×C71—22no—
152#124×C71C2314yes—
153#123×C71—28no—
154C22⋊Q8×C71—22no—
155C22⋊Q8×C71—28no—
156C22⋊Q8×C71C2314yes—
157#121×C71—22no—
158#121×C71C2314yes—
159C4×Q8×C71—22no—
160C4×Q8×C71C2314yes—
161C4×D4×C71—22no—
162C4×D4×C71C2314yes—
163#117×C71D414yes—
164#117×C71C2314yes—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71D411yescharacteristic
169C2×C4⋊C4×C71D411yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71D411yescharacteristic
178C2×C22⋊C4×C71D411yescharacteristic
179C2×C42×C71—21no—
180C2×C42×C71C2311yescharacteristic
181C2×C42×C71C2311yescharacteristic
182C23×D71—21no—
183C23×D71—21no—
184C2×D284—22no—
185C2×D284—22no—
186C2×D284—22no—
187C2×D284—22no—
188C2×D284—21no—
189C2×D284—21no—
190C2×D284—24no—
191C2×D284—24no—
192C2×D284—82no—
193C2×D284—82no—
194C2×D284C2412yes—
195C2×D284C2412yes—
196C2×C22⋊D71—24no—
197C2×C22⋊D71—24no—
198C2×C22⋊D71—82no—
199C2×C22⋊D71—82no—
200C22×Dic71—21no—
201C22×Dic71—21no—
202C2×C4×D71—24no—
203C2×C4×D71—24no—
204C2×C4×D71—82no—
205C2×C4×D71—82no—
206#11765852—44no—
207#11765852—44no—
208#11765850—44no—
209#11765850—44no—
210#11765849—44no—
211C2×C71⋊C8—22no—
212C2×C71⋊C8—22no—
213C2×C71⋊C8—22no—
214C2×C71⋊C8—22no—
215C2×C71⋊C8—44no—
216C2×C71⋊C8C2412yes—
217C2×C71⋊C8C2412yes—
218C2×C71⋊C8C2412yes—
219C2×C71⋊C8C2412yes—
220C4⋊Dic71—21no—
221C4⋊Dic71—21no—
222C4⋊Dic71C2412yes—
223C4⋊Dic71C2412yes—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226(C2×D71)⋊C4—24no—
227(C2×D71)⋊C4—24no—
228(C2×D71)⋊C4—24no—
229(C2×D71)⋊C4—24no—
230C24×C71—21no—
231C24×C71C2×D411yescharacteristic
232C2×Q8×C71—21no—
233C2×Q8×C71—24no—
234C2×Q8×C71—22no—
235C2×Q8×C71—22no—
236C2×Q8×C71—82no—
237C2×Q8×C71C2412yes—
238C2×D4×C71—24no—
239C2×D4×C71—21no—
240C2×D4×C71—22no—
241C2×D4×C71—22no—
242C2×D4×C71—82no—
243C2×D4×C71C2412yes—
244C22×C4×C71—22no—
245C22×C4×C71—22no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—24no—
250C22×C4×C71—82no—
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D412yes—
257C22×C4×C71C2412yes—
258C22×C4×C71C2411yescharacteristic
259C4⋊C4×C71—24no—
260C4⋊C4×C71—24no—
261C4⋊C4×C71—24no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71C2×D414yes—
265C4⋊C4×C71C2×D414yes—
266C4⋊C4×C71C2412yes—
267C4⋊C4×C71C2412yes—
268C22⋊C4×C71—24no—
269C22⋊C4×C71—24no—
270C22⋊C4×C71—24no—
271C22⋊C4×C71—24no—
272C22⋊C4×C71—24no—
273C22⋊C4×C71C2×D414yes—
274C22⋊C4×C71C2×D414yes—
275C42×C71—24no—
276C42×C71C2×D412yes—
277C42×C71C2×D412yes—
278C42×C71C2412yes—
279C42×C71C2412yes—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—42no—
285C23×C71—42no—
286C23×C71—42no—
287C23×C71C22×D412yes—
288C23×C71C22×D411yescharacteristic
289C22×D71—22no—
290C22×D71—22no—
291C22×D71—42no—
292C22×D71—42no—
293C22×D71—42no—
294C22×D71—42no—
295C22×D71—42no—
296C22×D71—42no—
297Q8×C71—22no—
298Q8×C71—22no—
299Q8×C71—42no—
300Q8×C71—84no—
301D4×C71—22no—
302D4×C71—22no—
303D4×C71—42no—
304D4×C71—84no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—24no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—42no—
317C2×C4×C71—42no—
318C2×C4×C71—42no—
319C2×C4×C71—84no—
320C2×C4×C71C22×D412yes—
321C2×C4×C71C22×D412yes—
322C2×C4×C71C22×D412yes—
323C2×C4×C71C22×D412yes—
324C2×C4×C71C22×D412yes—
325C2×C4×C71C22×D411yescharacteristic
326C2×C4×C71H(5,𝔽2)12yes—
327C2×C4×C712−1+412yes—
328C2×C4×C71C2511yescharacteristic
329C22⋊D71—84no—
330C22⋊D71—84no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—42no—
334C2×Dic71—42no—
335D284—22no—
336D284—22no—
337D284—22no—
338D284—22no—
339D284—42no—
340D284—42no—
341D284—84no—
342D284—84no—
343C4×D71—84no—
344C4×D71—84no—
345C71⋊C8—22no—
346C71⋊C8—22no—
347C71⋊C8—22no—
348C71⋊C8—22no—
349C22×C71—22no—
350C22×C71—22no—
351C22×C71—22no—
352C22×C71—44no—
353C22×C71—42no—
354C22×C71—42no—
355C22×C71—42no—
356C22×C71—84no—
357C22×C71#53712yes—
358C22×C71#57612yes—
359C22×C71#57712yes—
360C22×C71C23×D411yescharacteristic
361C2×D71—42no—
362C2×D71—42no—
363C2×D71—42no—
364C2×D71—42no—
365C2×D71—42no—
366C2×D71—42no—
367C2×D71—84no—
368C2×D71—84no—
369C4×C71—22no—
370C4×C71—22no—
371C4×C71—22no—
372C4×C71—22no—
373C4×C71—22no—
374C4×C71—42no—
375C4×C71—42no—
376C4×C71—42no—
377C4×C71#53712yes—
378C4×C71C2×H(5,𝔽2)11yescharacteristic
379C4×C71C2×2−1+411yescharacteristic
380Dic71—42no—
381Dic71—42no—
382C2×#3257—711nomaximal, Sylow
383C2×C71—42no—
384C2×C71—82no—
385C2×C71#325714yescomplemented
386C2×C71C2×#53711yescharacteristic
387C2×C71C2×#57611yescharacteristic
388C2×C71C2×#57711yescharacteristic
389D71—82no—
390D71—82no—
391C2×#542D7111yescharacteristic, complemented
392C2×#540—711no—
393#3257—7116no—
394C2×#479—711no—
395C2×#478—711no—
396C2×#476—711no—
397C2×#474—711no—
398C2×#469—711no—
399C2×#468—711no—
400C2×#466—711no—
401C2×#465—711no—
402C2×#460—711no—
403C2×#463—711no—
404C2×#463—711no—
405C2×#459—711no—
406C2×#424—711no—
407C71C2×#325711yescharacteristic, complemented, Sylow
408C22×SD16—711no—
409C22×SD16—711no—
410C22×D8—711no—
411C22×D8—711no—
412C22×M16—711no—
413C23×C8—711no—
414#542—24no—
415#542C2×D7118yescomplemented
416#540—718no—
417#540—1424no—
418C2×C4⋊Q8C2×D7111yescharacteristic
419C2×#127—711no—
420C2×#126—21no—
421C2×#125—711no—
422C2×#124—21no—
423C2×#124C2×D7111yescharacteristic
424C2×#123—21no—
425C2×#123—1421no—
426C2×#123—1421no—
427C2×C22⋊Q8—21no—
428C2×C22⋊Q8C2×D7111yescharacteristic
429C2×#121—711no—
430C2×#121—711no—
431C2×#121—1421no—
432C2×#121—1421no—
433C2×#121C2×D7111yescharacteristic
434C2×C4×Q8C2×D7111yescharacteristic
435C2×C4×D4—711no—
436C2×C4×D4—711no—
437C2×C4×D4C2×D7111yescharacteristic
438C2×#117C2×D7111yescharacteristic
439#479—718no—
440#478—718no—
441#476—718no—
442#474—718no—
443#469—718no—
444#468—718no—
445#466—718no—
446#465—718no—
447#463—718no—
448#463—718no—
449#460—718no—
450#459—718no—
451C2×#107—711no—
452C2×#107—711no—
453C2×#106—711no—
454C2×#106—711no—
455#424—718no—
456C2×C4⋊C8—711no—
457C2×C4⋊C8—711no—
458C2×C4⋊C8—711no—
459C2×C4⋊C8—711no—
460C2×#103—711no—
461C2×#103—711no—
462C2×#102—711no—
463C2×#102—711no—
464C2×#102—711no—
465C2×#102—711no—
466C2×#102—711no—
467C2×#102—711no—
468C22×Q8—21no—
469C22×Q8C22×D7111yescharacteristic
470C22×D4—21no—
471C22×D4—711no—
472C22×D4—711no—
473C22×D4—1421no—
474C22×D4—1421no—
475C22×D4—1421no—
476C22×D4—1421no—
477C22×D4C22×D7111yescharacteristic
478C23×C4—21no—
479C23×C4—1421no—
480C23×C4—1421no—
481C23×C4C22×D7111yescharacteristic
482C2×SD16—2842no—
483C2×SD16—2842no—
484C2×SD16—714no—
485C2×SD16—714no—
486C2×D8—2842no—
487C2×D8—2842no—
488C2×D8—714no—
489C2×D8—714no—
490C2×M16—2842no—
491C2×M16—714no—
492C22×C8—2842no—
493C22×C8—714no—
494C22×C8—711no—
495C22×C8—711no—
496C22×C8—711no—
497C22×C8—711no—
498C4⋊Q8—22no—
499C4⋊Q8C22×D7114yes—
500#127—714no—
501#127—1422no—
502#126—28no—
503#125—714no—
504#125—1422no—
505#124—28no—
506#124—22no—
507#124C22×D7114yes—
508#123—28no—
509#123—1428no—
510#123—1428no—
511C22⋊Q8—22no—
512C22⋊Q8—28no—
513C22⋊Q8C22×D7114yes—
514#121—22no—
515#121—714no—
516#121—714no—
517#121—1422no—
518#121—1422no—
519#121—1428no—
520#121—1428no—
521#121C22×D7114yes—
522C4×Q8—22no—
523C4×Q8C22×D7114yes—
524C4×D4—22no—
525C4×D4—714no—
526C4×D4—714no—
527C4×D4—1422no—
528C4×D4—1422no—
529C4×D4C22×D7114yes—
530#117C22⋊D7114yes—
531#117C22×D7114yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—711no—
536C2×C4⋊C4—711no—
537C2×C4⋊C4—1421no—
538C2×C4⋊C4—1421no—
539C2×C4⋊C4C22⋊D7111yescharacteristic
540C2×C4⋊C4C22⋊D7111yescharacteristic
541C2×C4⋊C4C22×D7111yescharacteristic
542C2×C4⋊C4C22×D7111yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—1421no—
549C2×C22⋊C4—1421no—
550C2×C22⋊C4—1421no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4C22⋊D7111yescharacteristic
553C2×C22⋊C4C22⋊D7111yescharacteristic
554C2×C42—21no—
555C2×C42C22×D7111yescharacteristic
556C2×C42C22×D7111yescharacteristic
557#107—714no—
558#107—714no—
559#106—714no—
560#106—714no—
561C4⋊C8—714no—
562C4⋊C8—714no—
563C4⋊C8—714no—
564C4⋊C8—714no—
565#103—714no—
566#103—714no—
567#102—714no—
568#102—714no—
569#102—714no—
570#102—714no—
571#102—714no—
572#102—714no—
573C24—21no—
574C24—1421no—
575C24—1421no—
576C24C2×C22⋊D7111yescharacteristic
577C2×Q8—21no—
578C2×Q8—24no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—82no—
582C2×Q8C23×D7112yes—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—82no—
588C2×D4—5682no—
589C2×D4—5682no—
590C2×D4—5682no—
591C2×D4—5682no—
592C2×D4—712no—
593C2×D4—712no—
594C2×D4—1424no—
595C2×D4—1424no—
596C2×D4—1421no—
597C2×D4—1421no—
598C2×D4—1424no—
599C2×D4—1424no—
600C2×D4—1422no—
601C2×D4—1422no—
602C2×D4—1422no—
603C2×D4—1422no—
604C2×D4C23×D7112yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—5682no—
613C22×C4—5682no—
614C22×C4—1421no—
615C22×C4—1421no—
616C22×C4—1424no—
617C22×C4—1424no—
618C22×C4C2×C22⋊D7112yes—
619C22×C4C2×C22⋊D7111yescharacteristic
620C22×C4C2×C22⋊D7111yescharacteristic
621C22×C4C2×C22⋊D7111yescharacteristic
622C22×C4C2×C22⋊D7111yescharacteristic
623C22×C4C2×C22⋊D7111yescharacteristic
624C22×C4C23×D7112yes—
625C22×C4C23×D7111yescharacteristic
626SD16—2844no—
627SD16—2844no—
628D8—2844no—
629D8—2844no—
630M16—2844no—
631C2×C8—2844no—
632C2×C8—712no—
633C2×C8—712no—
634C2×C8—712no—
635C2×C8—712no—
636C2×C8—1422no—
637C2×C8—1422no—
638C2×C8—1422no—
639C2×C8—1422no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—712no—
646C4⋊C4—712no—
647C4⋊C4—1424no—
648C4⋊C4—1424no—
649C4⋊C4—1421no—
650C4⋊C4—1421no—
651C4⋊C4C2×C22⋊D7114yes—
652C4⋊C4C2×C22⋊D7114yes—
653C4⋊C4C23×D7112yes—
654C4⋊C4C23×D7112yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1424no—
661C22⋊C4—1424no—
662C22⋊C4—1424no—
663C22⋊C4—1424no—
664C22⋊C4C2×C22⋊D7114yes—
665C22⋊C4C2×C22⋊D7114yes—
666C42—24no—
667C42C2×C22⋊D7112yes—
668C42C2×C22⋊D7112yes—
669C42C23×D7112yes—
670C42C23×D7112yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—2842no—
679C23—2842no—
680C23—2842no—
681C23—2842no—
682C23—2842no—
683C23—2842no—
684C23—1422no—
685C23—1422no—
686C23C22×C22⋊D7112yes—
687C23C22×C22⋊D7111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—84no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—84no—
696D4—2842no—
697D4—2842no—
698D4—5684no—
699D4—5684no—
700D4—5684no—
701D4—5684no—
702D4—1422no—
703D4—1422no—
704D4—1422no—
705D4—1422no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—84no—
721C2×C4—2842no—
722C2×C4—2842no—
723C2×C4—5684no—
724C2×C4—5684no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4C22×C22⋊D7112yes—
728C2×C4C22×C22⋊D7112yes—
729C2×C4C22×C22⋊D7112yes—
730C2×C4C22×C22⋊D7112yes—
731C2×C4C22×C22⋊D7112yes—
732C2×C4C22×C22⋊D7111yescharacteristic
733C2×C4#1455617412yes—
734C2×C4#1455617512yes—
735C2×C4C24×D7111yescharacteristic
736C8—1422no—
737C8—1422no—
738C8—1422no—
739C8—1422no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—2842no—
749C22—2842no—
750C22—2842no—
751C22—2842no—
752C22—2842no—
753C22—2842no—
754C22—5684no—
755C22—5684no—
756C22#1798657712yes—
757C22#1798680212yes—
758C22#1798680712yes—
759C22C23×C22⋊D7111yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—2842no—
769C4—2842no—
770C4#1798657712yes—
771C4C2×#1455617411yescharacteristic
772C4C2×#1455617511yescharacteristic
773C2—42no—
774C2—82no—
775C2—5682no—
776C2—5682no—
777C2#2259975114yesdirect product factor
778C2C2×#1798657711yescharacteristic
779C2C2×#1798680211yescharacteristic
780C2C2×#1798680711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#542×C71C2
socleC23×C71C22×D4
hypercenterC2×#542D71
hypocenterC71C2×#3257
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#17986604C2semidirect
2. #22599751C2direct (N × H)
3. C2×#17986306C2semidirect
4. C2×#17986299C2semidirect
5. C2×#17986286C2semidirect
6. C2×#17986276C2semidirect
7. C2×#17986250C2semidirect
8. C2×#17986247C2semidirect
9. C2×#17986233C2semidirect
10. C2×#17986230C2semidirect
11. C2×#17986199C2semidirect
12. C2×#17986211C2semidirect
13. C2×#17986211C2semidirect
14. C2×#17986194C2semidirect
15. C2×#17986026C2semidirect
16. C2×#542×C71C2semidirect
24. #17986604C22semidirect
35. #17986306C22semidirect
36. #17986299C22semidirect
37. #17986286C22semidirect
38. #17986276C22semidirect
39. #17986250C22semidirect
40. #17986247C22semidirect
41. #17986233C22semidirect
42. #17986230C22semidirect
43. #17986211C22semidirect
44. #17986211C22semidirect
45. #17986199C22semidirect
46. #17986194C22semidirect
51. #17986026C22semidirect
65. #542×C71C22semidirect
385. C2×C71#3257semidirect
391. C2×#542D71semidirect
407. C71C2×#3257semidirect
415. #542C2×D71semidirect
777. C2#22599751direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866042
#225997512
C2×#179863062
C2×#179862992
C2×#179862862
C2×#179862762
C2×#179862502
C2×#179862472
C2×#179862332
C2×#179862302
C2×#179861992
C2×#179862112
C2×#179861942
C2×#179860262
C2×#542×C712
C2×#325771