Finite Group Databasebeta

← C2×#22600819 #32876025

Subgroups — C2×#22600819 #32876025

Order 18176.

1942 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×#17986695C211yesmaximal, characteristic
2#22600819C2116yesmaximal, direct product factor
3C2×#17986405C211yesmaximal, characteristic, complemented
4C2×#17986332C211yesmaximal, characteristic, complemented
5C2×#17986317C211yesmaximal, characteristic, complemented
6C2×#17986337C211yesmaximal, characteristic, complemented
7C2×#17986312C211yesmaximal, characteristic, complemented
8C2×#17986306C211yesmaximal, characteristic, complemented
9C2×#17986276C211yesmaximal, characteristic, complemented
10C2×#17986247C211yesmaximal, characteristic, complemented
11C2×#17986230C211yesmaximal, characteristic, complemented
12C2×#17986097C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986039C211yesmaximal, characteristic, complemented
15C22×#14556061C211yesmaximal, characteristic, complemented
16C2×#554×C71C211yesmaximal, characteristic, complemented
17C22×#11765852C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19C23×C71⋊C8C2211yescharacteristic
20#17986695—24no—
21#17986695C2218yes—
22C2×#14556123—21no—
23C2×#14556120C2211yescharacteristic
24C2×#14556110—21no—
25C2×#14556102C2211yescharacteristic
26C2×#14556102C2211yescharacteristic
27C2×#14556100—21no—
28C2×C4×D284C2211yescharacteristic
29C2×(C22⋊D71)⋊C4—21no—
30C2×#14556087C2211yescharacteristic
31C22×C4⋊Dic71C2211yescharacteristic
32#17986405C2218yescomplemented
33#17986337C2218yescomplemented
34#17986332C2218yescomplemented
35#17986317C2218yescomplemented
36#17986312C2218yescomplemented
37#17986306C2218yescomplemented
38#17986276C2218yescomplemented
39#17986247C2218yescomplemented
40#17986230C2218yescomplemented
41#17986097C2218yescomplemented
42#17986071C2218yescomplemented
43#17986039C2218yescomplemented
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556061C2211yescharacteristic
50C2×#14556061C2218yescomplemented
51C2×#14556059C2211yescharacteristic
52C2×#14556059C2211yescharacteristic
53C2×#14556059C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556052C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64#554×C71—24no—
65#554×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#125×C71—21no—
68C2×C22⋊Q8×C71—21no—
69C2×C22⋊Q8×C71—21no—
70C2×C22⋊Q8×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×D4×C71—21no—
74C2×C4×D4×C71C2211yescharacteristic
75C22×C4⋊C4×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×D284C2311yescharacteristic
78C22×C22⋊D71—21no—
79C22×C22⋊D71—21no—
80C23×Dic71—21no—
81C22×C4×D71—21no—
82C2×#11765852—24no—
83C2×#11765852C2314yes—
84C2×#11765849—24no—
85C2×#11765849C2314yes—
86C22×C71⋊C8—24no—
87C22×C71⋊C8C2314yes—
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92#14556123—28no—
93#14556120—22no—
94#14556120C2314yes—
95#14556110—28no—
96#14556102—22no—
97#14556102—22no—
98#14556102C2314yes—
99#14556102C2314yes—
100#14556100—28no—
101C4×D284—22no—
102C4×D284C2314yes—
103(C22⋊D71)⋊C4—28no—
104#14556087—22no—
105#14556087C2314yes—
106C2×C4⋊Dic71—22no—
107C2×C4⋊Dic71—21no—
108C2×C4⋊Dic71C2314yes—
109C2×C4⋊Dic71C2311yescharacteristic
110C2×C4⋊Dic71C2311yescharacteristic
111C2×C4⋊Dic71C2311yescharacteristic
112C2×Dic71⋊C4—21no—
113C2×Dic71⋊C4—21no—
114C2×C22⋊Dic71—21no—
115C2×(C2×D71)⋊C4—21no—
116C2×(C2×D71)⋊C4—21no—
117C2×(C2×D71)⋊C4—21no—
118C2×C4×Dic71—21no—
119#14556061C2314yes—
120#14556061C2314yes—
121#14556061C2314yes—
122#14556061C2314yes—
123#14556061C2314yes—
124#14556061C2314yes—
125#14556059C2314yes—
126#14556059C2314yes—
127#14556059C2314yes—
128C4⋊(C71⋊C8)C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131#14556052C2314yes—
132#14556048C2314yes—
133#14556048C2314yes—
134#14556048C2314yes—
135C22⋊(C71⋊C8)C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137#14556039C2314yes—
138C22×Q8×C71—21no—
139C22×Q8×C71C2311yescharacteristic
140C22×D4×C71D411yescharacteristic
141C23×C4×C71—21no—
142C23×C4×C71—21no—
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C4⋊Q8×C71—22no—
146C4⋊Q8×C71C2314yes—
147#125×C71—28no—
148C22⋊Q8×C71—22no—
149C22⋊Q8×C71—22no—
150C22⋊Q8×C71—28no—
151C22⋊Q8×C71—28no—
152C22⋊Q8×C71C2314yes—
153C22⋊Q8×C71C2314yes—
154C4×Q8×C71—22no—
155C4×Q8×C71C2314yes—
156C4×D4×C71—28no—
157C4×D4×C71D414yes—
158C4×D4×C71C2314yes—
159C2×C4⋊C4×C71—21no—
160C2×C4⋊C4×C71—21no—
161C2×C4⋊C4×C71—22no—
162C2×C4⋊C4×C71—22no—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71D411yescharacteristic
168C2×C4⋊C4×C71C2314yes—
169C2×C4⋊C4×C71C2314yes—
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71D411yescharacteristic
176C2×C22⋊C4×C71D411yescharacteristic
177C2×C42×C71—21no—
178C2×C42×C71C2311yescharacteristic
179C23×D71—21no—
180C2×D284—22no—
181C2×D284—22no—
182C2×D284—21no—
183C2×D284C2412yes—
184C2×C22⋊D71—24no—
185C2×C22⋊D71—24no—
186C2×C22⋊D71—44no—
187C2×C22⋊D71—82no—
188C22×Dic71—21no—
189C22×Dic71—21no—
190C22×Dic71—21no—
191C22×Dic71—24no—
192C22×Dic71—82no—
193C2×C4×D71—24no—
194C2×C4×D71—82no—
195#11765852—28no—
196#11765849—28no—
197C2×C71⋊C8—22no—
198C2×C71⋊C8—22no—
199C2×C71⋊C8—22no—
200C2×C71⋊C8—28no—
201C2×C71⋊C8#4114yes—
202C2×C71⋊C8C2412yes—
203C2×C71⋊C8C2412yes—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71—24no—
209C4⋊Dic71—21no—
210C4⋊Dic71C2412yes—
211C4⋊Dic71C2412yes—
212C4⋊Dic71C2412yes—
213Dic71⋊C4—24no—
214Dic71⋊C4—24no—
215C22⋊Dic71—24no—
216(C2×D71)⋊C4—24no—
217(C2×D71)⋊C4—24no—
218(C2×D71)⋊C4—24no—
219C4×Dic71—24no—
220C24×C71C2×D411yescharacteristic
221C24×C71C2×D411yescharacteristic
222C2×Q8×C71—21no—
223C2×Q8×C71—24no—
224C2×Q8×C71—22no—
225C2×Q8×C71—22no—
226C2×Q8×C71—82no—
227C2×Q8×C71C2412yes—
228C2×D4×C71—24no—
229C2×D4×C71C2×D414yes—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71—24no—
239C22×C4×C71—24no—
240C22×C4×C71—82no—
241C22×C4×C71—82no—
242C22×C4×C71C2×D411yescharacteristic
243C22×C4×C71C2×D411yescharacteristic
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D412yes—
247C22×C4×C71C2×D412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2412yes—
250C22×C4×C71C2411yescharacteristic
251C4⋊C4×C71—21no—
252C4⋊C4×C71—24no—
253C4⋊C4×C71—24no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71—21no—
256C4⋊C4×C71—24no—
257C4⋊C4×C71—24no—
258C4⋊C4×C71—24no—
259C4⋊C4×C71—24no—
260C4⋊C4×C71C2×D414yes—
261C4⋊C4×C71C2412yes—
262C4⋊C4×C71C2412yes—
263C4⋊C4×C71C2412yes—
264C22⋊C4×C71—24no—
265C22⋊C4×C71—24no—
266C22⋊C4×C71C2×D414yes—
267C22⋊C4×C71C2×D414yes—
268C42×C71—24no—
269C42×C71C2×D412yes—
270C42×C71C2412yes—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71#13714yes—
277C23×C71C22×D412yes—
278C23×C71C22×D412yes—
279C23×C71C22×D411yescharacteristic
280C22×D71—22no—
281C22×D71—42no—
282C22×D71—42no—
283C22×D71—42no—
284Q8×C71—22no—
285Q8×C71—22no—
286Q8×C71—42no—
287Q8×C71—84no—
288D4×C71—28no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—24no—
294C2×C4×C71—24no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—42no—
304C2×C4×C71—42no—
305C2×C4×C71—42no—
306C2×C4×C71—42no—
307C2×C4×C71—84no—
308C2×C4×C71—84no—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D412yes—
311C2×C4×C71C22×D412yes—
312C2×C4×C71C22×D412yes—
313C2×C4×C71C22×D411yescharacteristic
314C2×C4×C71C2×#4112yes—
315C2×C4×C712−1+412yes—
316C2×C4×C71C2511yescharacteristic
317C22⋊D71—48no—
318C22⋊D71—84no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—42no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325C2×Dic71—84no—
326D284—22no—
327D284—22no—
328D284—42no—
329C4×D71—84no—
330C71⋊C8—22no—
331C71⋊C8—22no—
332C71⋊C8—22no—
333C71⋊C8C2×#4114yes—
334C22×C71—28no—
335C22×C71—22no—
336C22×C71—22no—
337C22×C71—22no—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—44no—
341C22×C71#54712yes—
342C22×C71C2×#13714yes—
343C22×C71C2×#13712yes—
344C22×C71#57612yes—
345C22×C71C23×D411yescharacteristic
346C2×D71—42no—
347C2×D71—42no—
348C2×D71—42no—
349C2×D71—84no—
350C4×C71—22no—
351C4×C71—22no—
352C4×C71—22no—
353C4×C71—22no—
354C4×C71—42no—
355C4×C71—42no—
356C4×C71—42no—
357C4×C71—42no—
358C4×C71#54712yes—
359C4×C71C22×#4111yescharacteristic
360C4×C71C2×2−1+411yescharacteristic
361Dic71—42no—
362Dic71—42no—
363Dic71—42no—
364C2×#3346—711nomaximal, Sylow
365C2×C71—24no—
366C2×C71—42no—
367C2×C71#334614yescomplemented
368C2×C71C2×#54711yescharacteristic
369C2×C71C22×#13711yescharacteristic
370C2×C71C2×#57611yescharacteristic
371D71—82no—
372C2×#554D7111yescharacteristic, complemented
373C2×#553—711no—
374#3346—7116no—
375C2×#501—711no—
376C2×#484—711no—
377C2×#481—711no—
378C2×#485—711no—
379C2×#480—711no—
380C2×#479—711no—
381C2×#474—711no—
382C2×#468—711no—
383C2×#465—711no—
384C2×#440—711no—
385C2×#435—711no—
386C2×#428—711no—
387C22×#107—711no—
388C71C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—711no—
390C22×M16—711no—
391C23×C8—711no—
392#554—24no—
393#554C2×D7118yescomplemented
394#553—718no—
395#553—1424no—
396C2×C4⋊Q8C2×D7111yescharacteristic
397C2×#126—1421no—
398C2×#125—21no—
399C2×#125—711no—
400C2×#123—1421no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403C2×C22⋊Q8C2×D7111yescharacteristic
404C2×C22⋊Q8C2×D7111yescharacteristic
405C2×#121—711no—
406C2×#121—711no—
407C2×#121—1421no—
408C2×C4×Q8C2×D7111yescharacteristic
409C2×C4×D4—21no—
410C2×C4×D4—711no—
411C2×C4×D4—1421no—
412C2×C4×D4C2×D7111yescharacteristic
413C2×#117—711no—
414C22×C4⋊C4—711no—
415C22×C4⋊C4C2×D7111yescharacteristic
416C22×C4⋊C4C2×D7111yescharacteristic
417#501—718no—
418#485—718no—
419#484—718no—
420#481—718no—
421#480—718no—
422#479—718no—
423#474—718no—
424#468—718no—
425#465—718no—
426#440—718no—
427#435—718no—
428#428—718no—
429C2×#107—711no—
430C2×#107—711no—
431C2×#107—711no—
432C2×#107—711no—
433C2×#107—718no—
434C2×#107—711no—
435C2×#107—711no—
436C2×#106—711no—
437C2×#106—711no—
438C2×#106—711no—
439C2×C4⋊C8—711no—
440C2×#103—711no—
441C2×#103—711no—
442C2×#103—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×#102—711no—
446C2×C22⋊C8—711no—
447C2×C22⋊C8—711no—
448C2×#97—711no—
449C22×Q8—21no—
450C22×Q8C22×D7111yescharacteristic
451C22×D4—711no—
452C22×D4—1421no—
453C22×D4—1421no—
454C22×D4C22⋊D7111yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—1421no—
458C23×C4—1421no—
459C23×C4C22×D7111yescharacteristic
460C23×C4C22×D7111yescharacteristic
461C2×SD16—714no—
462C2×SD16—1424no—
463C2×M16—714no—
464C2×M16—1424no—
465C22×C8—711no—
466C22×C8—711no—
467C22×C8—714no—
468C22×C8—711no—
469C22×C8—711no—
470C22×C8—1424no—
471C4⋊Q8—22no—
472C4⋊Q8C22×D7114yes—
473#126—1428no—
474#125—28no—
475#125—714no—
476#125—1422no—
477#123—1428no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8C22×D7114yes—
483C22⋊Q8C22×D7114yes—
484#121—714no—
485#121—714no—
486#121—1428no—
487#121—1422no—
488#121—1422no—
489C4×Q8—22no—
490C4×Q8C22×D7114yes—
491C4×D4—28no—
492C4×D4—714no—
493C4×D4—1428no—
494C4×D4—1422no—
495C4×D4C22⋊D7114yes—
496C4×D4C22×D7114yes—
497#117—714no—
498#117—1422no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—711no—
508C2×C4⋊C4—711no—
509C2×C4⋊C4—714no—
510C2×C4⋊C4—711no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1422no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4C22⋊D7111yescharacteristic
516C2×C4⋊C4C22×D7111yescharacteristic
517C2×C4⋊C4C22×D7111yescharacteristic
518C2×C4⋊C4C22×D7111yescharacteristic
519C2×C4⋊C4C22×D7114yes—
520C2×C4⋊C4C22×D7114yes—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1421no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4C22⋊D7111yescharacteristic
528C2×C22⋊C4C22⋊D7111yescharacteristic
529C2×C42—21no—
530C2×C42—1421no—
531C2×C42C22×D7111yescharacteristic
532#107—714no—
533#107—714no—
534#107—714no—
535#107—714no—
536#107—714no—
537#107—714no—
538#106—714no—
539#106—714no—
540#106—714no—
541C4⋊C8—714no—
542#103—714no—
543#103—714no—
544#103—714no—
545#102—714no—
546#102—714no—
547#102—714no—
548C22⋊C8—714no—
549C22⋊C8—714no—
550#97—714no—
551C24—1421no—
552C24C2×C22⋊D7111yescharacteristic
553C24C2×C22⋊D7111yescharacteristic
554C2×Q8—21no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—82no—
559C2×Q8C23×D7112yes—
560C2×D4—24no—
561C2×D4—2844no—
562C2×D4—5682no—
563C2×D4—712no—
564C2×D4—1424no—
565C2×D4—1424no—
566C2×D4—1421no—
567C2×D4—1422no—
568C2×D4—1422no—
569C2×D4C2×C22⋊D7114yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—5682no—
583C22×C4—5682no—
584C22×C4—1421no—
585C22×C4—1421no—
586C22×C4—1421no—
587C22×C4—1424no—
588C22×C4—1424no—
589C22×C4C2×C22⋊D7112yes—
590C22×C4C2×C22⋊D7112yes—
591C22×C4C2×C22⋊D7111yescharacteristic
592C22×C4C2×C22⋊D7111yescharacteristic
593C22×C4C2×C22⋊D7111yescharacteristic
594C22×C4C2×C22⋊D7111yescharacteristic
595C22×C4C23×D7112yes—
596C22×C4C23×D7112yes—
597C22×C4C23×D7111yescharacteristic
598SD16—1428no—
599M16—1428no—
600C2×C8—714no—
601C2×C8—712no—
602C2×C8—712no—
603C2×C8—712no—
604C2×C8—712no—
605C2×C8—1428no—
606C2×C8—1422no—
607C2×C8—1422no—
608C2×C8—1422no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—712no—
619C4⋊C4—712no—
620C4⋊C4—712no—
621C4⋊C4—1424no—
622C4⋊C4—1424no—
623C4⋊C4—1421no—
624C4⋊C4—1421no—
625C4⋊C4—1424no—
626C4⋊C4—1421no—
627C4⋊C4C2×C22⋊D7114yes—
628C4⋊C4C23×D7112yes—
629C4⋊C4C23×D7112yes—
630C4⋊C4C23×D7112yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1424no—
634C22⋊C4—1424no—
635C22⋊C4—1424no—
636C22⋊C4—1424no—
637C22⋊C4C2×C22⋊D7114yes—
638C22⋊C4C2×C22⋊D7114yes—
639C42—24no—
640C42—1424no—
641C42C2×C22⋊D7112yes—
642C42C23×D7112yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—2842no—
649C23—2842no—
650C23—2842no—
651C23—1422no—
652C23#1455615914yes—
653C23C22×C22⋊D7112yes—
654C23C22×C22⋊D7112yes—
655C23C22×C22⋊D7111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—84no—
660D4—28no—
661D4—2848no—
662D4—2842no—
663D4—5684no—
664D4—1422no—
665D4—1422no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4—2842no—
687C2×C4—2842no—
688C2×C4—2842no—
689C2×C4—5684no—
690C2×C4—5684no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4C22×C22⋊D7112yes—
695C2×C4C22×C22⋊D7112yes—
696C2×C4C22×C22⋊D7112yes—
697C2×C4C22×C22⋊D7112yes—
698C2×C4C22×C22⋊D7111yescharacteristic
699C2×C4#41×D7112yes—
700C2×C4#1455617512yes—
701C2×C4C24×D7111yescharacteristic
702C8—714no—
703C8—1422no—
704C8—1422no—
705C8—1422no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—2842no—
714C22—2842no—
715C22—2842no—
716C22—5684no—
717C22#1798664812yes—
718C22C2×#1455615914yes—
719C22C2×#1455615912yes—
720C22#1798680212yes—
721C22C23×C22⋊D7111yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—2842no—
731C4—2842no—
732C4—2842no—
733C4#1798664812yes—
734C4C2×#41×D7111yescharacteristic
735C4C2×#1455617511yescharacteristic
736C2—24no—
737C2—42no—
738C2—5682no—
739C2#2260081914yesdirect product factor
740C2C2×#1798664811yescharacteristic
741C2C22×#1455615911yescharacteristic
742C2C2×#1798680211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#554×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986695C2
hypercenterC2×#554D71
hypocenterC71C2×#3346
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #22600819C2direct (N × H)
3. C2×#17986405C2semidirect
4. C2×#17986332C2semidirect
5. C2×#17986317C2semidirect
6. C2×#17986337C2semidirect
7. C2×#17986312C2semidirect
8. C2×#17986306C2semidirect
9. C2×#17986276C2semidirect
10. C2×#17986247C2semidirect
11. C2×#17986230C2semidirect
12. C2×#17986097C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986039C2semidirect
15. C22×#14556061C2semidirect
16. C2×#554×C71C2semidirect
32. #17986405C22semidirect
33. #17986337C22semidirect
34. #17986332C22semidirect
35. #17986317C22semidirect
36. #17986312C22semidirect
37. #17986306C22semidirect
38. #17986276C22semidirect
39. #17986247C22semidirect
40. #17986230C22semidirect
41. #17986097C22semidirect
42. #17986071C22semidirect
43. #17986039C22semidirect
50. C2×#14556061C22semidirect
65. #554×C71C22semidirect
367. C2×C71#3346semidirect
372. C2×#554D71semidirect
388. C71C2×#3346semidirect
393. #554C2×D71semidirect
739. C2#22600819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866952
#226008192
C2×#179864052
C2×#179863322
C2×#179863172
C2×#179863372
C2×#179863122
C2×#179863062
C2×#179862762
C2×#179862472
C2×#179862302
C2×#179860972
C2×#179860712
C2×#179860392
C22×#145560612
C2×#554×C712
C2×#334671