Finite Group Databasebeta

← C2×#22600824 #32876030

Subgroups — C2×#22600824 #32876030

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×#17986710C211yesmaximal, characteristic, complemented
2C2×#17986702C211yesmaximal, characteristic
3#22600824C2116yesmaximal, direct product factor
4C2×#17986336C211yesmaximal, characteristic, complemented
5C2×#17986319C211yesmaximal, characteristic, complemented
6C2×#17986343C211yesmaximal, characteristic, complemented
7C2×#17986314C211yesmaximal, characteristic, complemented
8C2×#17986303C211yesmaximal, characteristic, complemented
9C2×#17986276C211yesmaximal, characteristic, complemented
10C2×#17986246C211yesmaximal, characteristic, complemented
11C2×#17986229C211yesmaximal, characteristic, complemented
12C2×#17986101C211yesmaximal, characteristic, complemented
13C2×#17986072C211yesmaximal, characteristic, complemented
14C2×#17986038C211yesmaximal, characteristic, complemented
15C2×#107×D71C211yesmaximal, characteristic, complemented
16C2×#501×C71C211yesmaximal, characteristic, complemented
17C22×#11765854C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20#17986710—24no—
21#17986710C2218yescomplemented
22#17986702—24no—
23#17986702C2218yes—
24C2×#14556123—21no—
25C2×#14556119—21no—
26C2×#14556113—21no—
27C2×#14556108C2211yescharacteristic
28C2×#14556108C2211yescharacteristic
29C2×#14556104—21no—
30C2×#14556104—21no—
31C2×#14556103—21no—
32C2×#14556103C2211yescharacteristic
33C2×#14556103C2211yescharacteristic
34C2×C4×Dic142C2211yescharacteristic
35C2×C4×D284C2211yescharacteristic
36C2×C4×D284C2211yescharacteristic
37C2×#14556090—21no—
38C2×#14556090—21no—
39C2×#14556086C2211yescharacteristic
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic
43#17986343C2218yescomplemented
44#17986336C2218yescomplemented
45#17986319C2218yescomplemented
46#17986314C2218yescomplemented
47#17986303C2218yescomplemented
48#17986276C2218yescomplemented
49#17986246C2218yescomplemented
50#17986229C2218yescomplemented
51#17986101C2218yescomplemented
52#17986072C2218yescomplemented
53#17986038C2218yescomplemented
54C2×#14556062C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556061C2211yescharacteristic
58#107×D71C2218yescomplemented
59C2×#14556059C2211yescharacteristic
60C2×C4⋊(C71⋊C8)C2211yescharacteristic
61C2×#14556053C2211yescharacteristic
62C2×#14556051C2211yescharacteristic
63C2×#14556051C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×#14556048C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×(C2×D71)⋊C8C2211yescharacteristic
69C2×C4⋊Q8×C71C2211yescharacteristic
70C2×#125×C71C2211yescharacteristic
71#501×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic
73C2×#107×C71C2211yescharacteristic
74C2×#106×C71C2211yescharacteristic
75C2×#106×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C22×D284—21no—
79C22×D284—21no—
80C22×D284D411yescharacteristic
81C22×D284C2311yescharacteristic
82C22×C4×D71—21no—
83C22×C4×D71—21no—
84C22×C4×D71—21no—
85C22×C4×D71—21no—
86C22×C4×D71C2311yescharacteristic
87C22×C4×D71C2311yescharacteristic
88C2×#11765854—24no—
89C2×#11765854C2314yes—
90C2×#11765848—24no—
91C2×#11765848C2314yes—
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C2×C8×D71—24no—
95C2×C8×D71C2314yes—
96#14556123—28no—
97#14556119—28no—
98#14556113—28no—
99#14556108—22no—
100#14556108—22no—
101#14556108C2314yes—
102#14556108C2314yes—
103#14556104—28no—
104#14556104—28no—
105#14556103—28no—
106#14556103—22no—
107#14556103—22no—
108#14556103C2314yes—
109#14556103C2314yes—
110C4×Dic142—22no—
111C4×Dic142C2314yes—
112C4×D284—22no—
113C4×D284D414yes—
114C4×D284C2314yes—
115C4×D284C2314yes—
116#14556090—28no—
117#14556090—28no—
118#14556086—22no—
119#14556086C2314yes—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71D411yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C4⋊C4×D71—22no—
130C4⋊C4×D71—22no—
131C4⋊C4×D71—22no—
132C4⋊C4×D71C2314yes—
133C4⋊C4×D71C2314yes—
134C4⋊C4×D71C2314yes—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4D411yescharacteristic
142C2×(C2×D71)⋊C4D411yescharacteristic
143C2×C4×Dic71—21no—
144C2×C4×Dic71—21no—
145#14556062C2314yes—
146#14556061C2314yes—
147#14556061C2314yes—
148#14556061C2314yes—
149#14556059C2314yes—
150C4⋊(C71⋊C8)C2314yes—
151#14556053C2314yes—
152#14556051C2314yes—
153#14556051C2314yes—
154#14556050C2314yes—
155#14556048C2314yes—
156#14556048C2314yes—
157(C2×D71)⋊C8C2314yes—
158(C2×D71)⋊C8C2314yes—
159C22×Q8×C71—21no—
160C22×C8×C71C2311yescharacteristic
161C22×C8×C71C2311yescharacteristic
162C4⋊Q8×C71—22no—
163C4⋊Q8×C71C2314yes—
164#125×C71—22no—
165#125×C71C2314yes—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C42×C71C2311yescharacteristic
174#107×C71C2314yes—
175#107×C71C2314yes—
176#106×C71C2314yes—
177#106×C71C2314yes—
178#97×C71C2314yes—
179C23×D71—21no—
180C23×D71C2×D411yescharacteristic
181C23×D71C2×D411yescharacteristic
182C2×Dic142—22no—
183C2×Dic142—22no—
184C2×Dic142—21no—
185C2×Dic142C2412yes—
186C2×D284—24no—
187C2×D284—22no—
188C2×D284—22no—
189C2×D284—24no—
190C2×D284—21no—
191C2×D284—24no—
192C2×D284—44no—
193C2×D284—82no—
194C2×D284C2×D414yes—
195C2×D284C2412yes—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C22×Dic71C2×D411yescharacteristic
200C22×Dic71C2×D411yescharacteristic
201C2×C4×D71—22no—
202C2×C4×D71—22no—
203C2×C4×D71—22no—
204C2×C4×D71—22no—
205C2×C4×D71—24no—
206C2×C4×D71—24no—
207C2×C4×D71—24no—
208C2×C4×D71—24no—
209C2×C4×D71—82no—
210C2×C4×D71—82no—
211C2×C4×D71—82no—
212C2×C4×D71—82no—
213C2×C4×D71C2×D412yes—
214C2×C4×D71C2×D412yes—
215C2×C4×D71C2412yes—
216C2×C4×D71C2412yes—
217#11765854—28no—
218#11765848—28no—
219C2×C71⋊C8—22no—
220C2×C71⋊C8—22no—
221C2×C71⋊C8C2412yes—
222C2×C71⋊C8C2412yes—
223C8×D71—28no—
224C4⋊Dic71—21no—
225C4⋊Dic71—21no—
226C4⋊Dic71—24no—
227C4⋊Dic71—24no—
228C4⋊Dic71C2×D414yes—
229C4⋊Dic71C2412yes—
230C4⋊Dic71C2412yes—
231Dic71⋊C4—24no—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234Dic71⋊C4—24no—
235(C2×D71)⋊C4—24no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4—24no—
238(C2×D71)⋊C4—24no—
239(C2×D71)⋊C4—24no—
240(C2×D71)⋊C4—24no—
241(C2×D71)⋊C4C2×D414yes—
242(C2×D71)⋊C4C2×D414yes—
243C4×Dic71—24no—
244C4×Dic71—24no—
245C2×Q8×C71—24no—
246C2×Q8×C71—82no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2411yescharacteristic
254C2×C8×C71—22no—
255C2×C8×C71#4114yes—
256C2×C8×C71C2412yes—
257C2×C8×C71C2412yes—
258C4⋊C4×C71—24no—
259C4⋊C4×C71—24no—
260C4⋊C4×C71—24no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71C2412yes—
266C4⋊C4×C71C2412yes—
267C4⋊C4×C71C2412yes—
268C4⋊C4×C71C2412yes—
269C42×C71C2×D412yes—
270C42×C71C2412yes—
271C23×C71C22×D411yescharacteristic
272C22×D71—22no—
273C22×D71—22no—
274C22×D71—22no—
275C22×D71—22no—
276C22×D71—22no—
277C22×D71—22no—
278C22×D71—42no—
279C22×D71—42no—
280C22×D71—42no—
281C22×D71#13714yes—
282C22×D71C22×D412yes—
283C22×D71C22×D412yes—
284Q8×C71—84no—
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×C71C22×D412yes—
296C2×C4×C71C22×D412yes—
297C2×C4×C71C22×D411yescharacteristic
298C2×C4×C71C2×#4112yes—
299C2×C4×C712−1+412yes—
300C2×C4×C71C2511yescharacteristic
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—42no—
307C2×Dic71—42no—
308C2×Dic71—42no—
309C2×Dic71C22×D412yes—
310C2×Dic71C22×D412yes—
311D284—28no—
312D284—22no—
313D284—22no—
314D284—48no—
315D284—42no—
316D284—84no—
317C4×D71—24no—
318C4×D71—24no—
319C4×D71—22no—
320C4×D71—22no—
321C4×D71—22no—
322C4×D71—22no—
323C4×D71—84no—
324C4×D71—84no—
325C4×D71—84no—
326C4×D71—84no—
327Dic142—22no—
328Dic142—22no—
329Dic142—42no—
330C8×C71—22no—
331C8×C71C2×#4114yes—
332C71⋊C8—22no—
333C71⋊C8—22no—
334C22×C71#54712yes—
335C22×C71C2×#13712yes—
336C22×C71#57612yes—
337C22×C71C23×D411yescharacteristic
338C2×D71—28no—
339C2×D71—22no—
340C2×D71—22no—
341C2×D71—22no—
342C2×D71—22no—
343C2×D71—22no—
344C2×D71—44no—
345C2×D71—42no—
346C2×D71—42no—
347C2×D71—42no—
348C2×D71—84no—
349C2×D71C2×#13714yes—
350C4×C71—22no—
351C4×C71—22no—
352C4×C71—42no—
353C4×C71—42no—
354C4×C71—42no—
355C4×C71—42no—
356C4×C71#54712yes—
357C4×C71C22×#4111yescharacteristic
358C4×C71C2×2−1+411yescharacteristic
359Dic71—22no—
360Dic71—22no—
361Dic71—42no—
362Dic71—42no—
363Dic71—42no—
364C2×#3346—711nomaximal, Sylow
365C2×C71#334614yescomplemented
366C2×C71C2×#54711yescharacteristic
367C2×C71C22×#13711yescharacteristic
368C2×C71C2×#57611yescharacteristic
369D71—24no—
370D71—42no—
371D71—82no—
372C2×#554—711no—
373C2×#553—711no—
374#3346—7116no—
375C2×#501D7111yescharacteristic, complemented
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—718no—
393#554—1424no—
394#553—718no—
395#553—1424no—
396C2×C4⋊Q8C2×D7111yescharacteristic
397C2×#126—1421no—
398C2×#125—1421no—
399C2×#125C2×D7111yescharacteristic
400C2×#123—1421no—
401C2×C22⋊Q8—711no—
402C2×C22⋊Q8—711no—
403C2×C22⋊Q8—1421no—
404C2×C22⋊Q8—1421no—
405C2×#121—711no—
406C2×#121—711no—
407C2×#121—1421no—
408C2×C4×Q8—711no—
409C2×C4×D4—711no—
410C2×C4×D4—711no—
411C2×C4×D4—1421no—
412C2×C4×D4—1421no—
413C2×#117—711no—
414C22×C4⋊C4—711no—
415C22×C4⋊C4—711no—
416C22×C4⋊C4—711no—
417#501C2×D7118yescomplemented
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×#107C2×D7111yescharacteristic
435C2×#107C2×D7111yescharacteristic
436C2×#106—711no—
437C2×#106C2×D7111yescharacteristic
438C2×#106C2×D7111yescharacteristic
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×#97C2×D7111yescharacteristic
449C22×Q8—21no—
450C22×Q8—711no—
451C22×D4—711no—
452C22×D4—711no—
453C22×D4—1421no—
454C22×D4—1421no—
455C23×C4—711no—
456C23×C4—711no—
457C23×C4—1421no—
458C23×C4—1421no—
459C23×C4—1421no—
460C23×C4—1421no—
461C2×SD16—714no—
462C2×SD16—1424no—
463C2×M16—714no—
464C2×M16—1424no—
465C22×C8—711no—
466C22×C8—711no—
467C22×C8—714no—
468C22×C8—1424no—
469C22×C8C22×D7111yescharacteristic
470C22×C8C22×D7111yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8C22×D7114yes—
473#126—1428no—
474#125—22no—
475#125—1428no—
476#125C22×D7114yes—
477#123—1428no—
478C22⋊Q8—714no—
479C22⋊Q8—714no—
480C22⋊Q8—1428no—
481C22⋊Q8—1428no—
482C22⋊Q8—1422no—
483C22⋊Q8—1422no—
484#121—714no—
485#121—714no—
486#121—1422no—
487#121—1422no—
488#121—1428no—
489C4×Q8—714no—
490C4×Q8—1422no—
491C4×D4—714no—
492C4×D4—714no—
493C4×D4—714no—
494C4×D4—1428no—
495C4×D4—1428no—
496C4×D4—1422no—
497#117—714no—
498#117—1422no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—711no—
503C2×C4⋊C4—711no—
504C2×C4⋊C4—711no—
505C2×C4⋊C4—714no—
506C2×C4⋊C4—714no—
507C2×C4⋊C4—714no—
508C2×C4⋊C4—1422no—
509C2×C4⋊C4—1422no—
510C2×C4⋊C4—1422no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1421no—
517C2×C4⋊C4C22×D7111yescharacteristic
518C2×C4⋊C4C22×D7111yescharacteristic
519C2×C4⋊C4C22×D7111yescharacteristic
520C2×C4⋊C4C22×D7111yescharacteristic
521C2×C22⋊C4—711no—
522C2×C22⋊C4—711no—
523C2×C22⋊C4—1421no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4—1421no—
529C2×C42—1421no—
530C2×C42—1421no—
531C2×C42C22×D7111yescharacteristic
532#107—714no—
533#107—714no—
534#107—714no—
535#107—714no—
536#107C22×D7114yes—
537#107C22×D7114yes—
538#106—714no—
539#106C22×D7114yes—
540#106C22×D7114yes—
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#97C22×D7114yes—
551C24—711no—
552C24—711no—
553C24—1421no—
554C2×Q8—24no—
555C2×Q8—82no—
556C2×Q8—712no—
557C2×Q8—1422no—
558C2×Q8—1422no—
559C2×Q8—1421no—
560C2×D4—2844no—
561C2×D4—5682no—
562C2×D4—714no—
563C2×D4—712no—
564C2×D4—1424no—
565C2×D4—1424no—
566C2×D4—1424no—
567C2×D4—1421no—
568C2×D4—1422no—
569C2×D4—1422no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—5682no—
575C22×C4—5682no—
576C22×C4—5682no—
577C22×C4—5682no—
578C22×C4—711no—
579C22×C4—711no—
580C22×C4—712no—
581C22×C4—712no—
582C22×C4—712no—
583C22×C4—712no—
584C22×C4—1424no—
585C22×C4—1424no—
586C22×C4—1424no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1421no—
590C22×C4—1424no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1422no—
595C22×C4D4×D7111yescharacteristic
596C22×C4D4×D7111yescharacteristic
597C22×C4C23×D7111yescharacteristic
598SD16—1428no—
599M16—1428no—
600C2×C8—22no—
601C2×C8—712no—
602C2×C8—712no—
603C2×C8—1422no—
604C2×C8—1422no—
605C2×C8—1428no—
606C2×C8#1176586614yes—
607C2×C8C23×D7112yes—
608C2×C8C23×D7112yes—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—714no—
617C4⋊C4—712no—
618C4⋊C4—712no—
619C4⋊C4—1424no—
620C4⋊C4—1424no—
621C4⋊C4—1424no—
622C4⋊C4—1424no—
623C4⋊C4—1424no—
624C4⋊C4—1424no—
625C4⋊C4—1421no—
626C4⋊C4—1421no—
627C4⋊C4C23×D7112yes—
628C4⋊C4C23×D7112yes—
629C4⋊C4C23×D7112yes—
630C4⋊C4C23×D7112yes—
631C22⋊C4—714no—
632C22⋊C4—714no—
633C22⋊C4—1424no—
634C22⋊C4—1424no—
635C22⋊C4—1424no—
636C22⋊C4—1424no—
637C22⋊C4—1424no—
638C22⋊C4—1424no—
639C42—1424no—
640C42—1424no—
641C42D4×D7112yes—
642C42C23×D7112yes—
643C23—2842no—
644C23—2842no—
645C23—2842no—
646C23—712no—
647C23—714no—
648C23—712no—
649C23—1422no—
650C23—1422no—
651C23—1422no—
652C23—1422no—
653C23—1422no—
654C23—1422no—
655C23C2×D4×D7111yescharacteristic
656Q8—84no—
657Q8—2842no—
658Q8—1422no—
659Q8—1422no—
660D4—2848no—
661D4—2842no—
662D4—5684no—
663D4—1428no—
664D4—1422no—
665D4—1422no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—2842no—
677C2×C4—2842no—
678C2×C4—2842no—
679C2×C4—5684no—
680C2×C4—5684no—
681C2×C4—5684no—
682C2×C4—5684no—
683C2×C4—712no—
684C2×C4—712no—
685C2×C4—1422no—
686C2×C4—1422no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1424no—
695C2×C4—1424no—
696C2×C4C2×D4×D7112yes—
697C2×C4C2×D4×D7112yes—
698C2×C4C2×D4×D7111yescharacteristic
699C2×C4C2×#1176586612yes—
700C2×C4#1455617612yes—
701C2×C4C24×D7111yescharacteristic
702C8—22no—
703C8—1422no—
704C8—1422no—
705C8C2×#1176586614yes—
706C22—2844no—
707C22—2842no—
708C22—2842no—
709C22—2842no—
710C22—5684no—
711C22—714no—
712C22—1422no—
713C22—1422no—
714C22—1422no—
715C22—1422no—
716C22—1422no—
717C22—1428no—
718C22#1798665212yes—
719C22#137×D7112yes—
720C22#1798680312yes—
721C22C22×D4×D7111yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—2842no—
729C4—2842no—
730C4—2842no—
731C4—1422no—
732C4—1422no—
733C4#1798665212yes—
734C4C22×#1176586611yescharacteristic
735C4C2×#1455617611yescharacteristic
736C2—2842no—
737C2—5682no—
738C2—1424no—
739C2#2260082414yesdirect product factor
740C2C2×#1798665211yescharacteristic
741C2C2×#137×D7111yescharacteristic
742C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#501×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986702C2
hypercenterC2×#501D71
hypocenterC71C2×#3346
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#17986710C2semidirect
3. #22600824C2direct (N × H)
4. C2×#17986336C2semidirect
5. C2×#17986319C2semidirect
6. C2×#17986343C2semidirect
7. C2×#17986314C2semidirect
8. C2×#17986303C2semidirect
9. C2×#17986276C2semidirect
10. C2×#17986246C2semidirect
11. C2×#17986229C2semidirect
12. C2×#17986101C2semidirect
13. C2×#17986072C2semidirect
14. C2×#17986038C2semidirect
15. C2×#107×D71C2semidirect
16. C2×#501×C71C2semidirect
21. #17986710C22semidirect
43. #17986343C22semidirect
44. #17986336C22semidirect
45. #17986319C22semidirect
46. #17986314C22semidirect
47. #17986303C22semidirect
48. #17986276C22semidirect
49. #17986246C22semidirect
50. #17986229C22semidirect
51. #17986101C22semidirect
52. #17986072C22semidirect
53. #17986038C22semidirect
58. #107×D71C22semidirect
71. #501×C71C22semidirect
365. C2×C71#3346semidirect
375. C2×#501D71semidirect
388. C71C2×#3346semidirect
417. #501C2×D71semidirect
739. C2#22600824direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867102
C2×#179867022
#226008242
C2×#179863362
C2×#179863192
C2×#179863432
C2×#179863142
C2×#179863032
C2×#179862762
C2×#179862462
C2×#179862292
C2×#179861012
C2×#179860722
C2×#179860382
C2×#107×D712
C2×#501×C712
C2×#334671