Finite Group Databasebeta

← C2×#22600378 #32874124

Subgroups — C2×#22600378 #32874124

Order 18176.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986719C211yesmaximal, characteristic, complemented
2C2×#17986645C211yesmaximal, characteristic
3#22600378C2116yesmaximal, direct product factor
4C2×#17986359C211yesmaximal, characteristic, complemented
5C2×#17986341C211yesmaximal, characteristic, complemented
6C2×#17986324C211yesmaximal, characteristic, complemented
7C2×#17986290C211yesmaximal, characteristic, complemented
8C2×#17986257C211yesmaximal, characteristic, complemented
9C2×#17986228C211yesmaximal, characteristic, complemented
10C2×#17986222C211yesmaximal, characteristic, complemented
11C2×#17986163C211yesmaximal, characteristic, complemented
12C2×#17986152C211yesmaximal, characteristic, complemented
13C2×#17986101C211yesmaximal, characteristic, complemented
14C2×#17986005C211yesmaximal, characteristic, complemented
15C2×#17985996C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C22×Dic284C2211yescharacteristic, complemented
20C22×#11765854C2211yescharacteristic
21C22×#11765854C2211yescharacteristic
22#17986719—24no—
23#17986719C2218yescomplemented
24#17986645—24no—
25#17986645C2218yes—
26C2×#14556128C2211yescharacteristic, complemented
27C2×#14556121—21no—
28C2×#14556121—21no—
29C2×#14556116C2211yescharacteristic
30C2×#14556115—21no—
31C2×#14556113—21no—
32C2×#14556107C2211yescharacteristic
33C2×#14556107C2211yescharacteristic
34C2×#14556107C2211yescharacteristic, complemented
35C2×#14556102C2211yescharacteristic
36C2×#14556101—21no—
37C2×#14556096—21no—
38C2×C4×Dic142C2211yescharacteristic, complemented
39C2×#14556093—21no—
40C2×C4×D284C2211yescharacteristic
41C2×#14556087C2211yescharacteristic
42C2×#14556087C2211yescharacteristic, complemented
43C2×C22⋊C4×D71—21no—
44#17986359C2218yescomplemented
45#17986341C2218yescomplemented
46#17986324C2218yescomplemented
47#17986290C2218yescomplemented
48#17986257C2218yescomplemented
49#17986228C2218yescomplemented
50#17986222C2218yescomplemented
51#17986163C2218yescomplemented
52#17986152C2218yescomplemented
53#17986101C2218yescomplemented
54C2×#14556062C2211yescharacteristic, complemented
55C2×#14556060C2211yescharacteristic, complemented
56C2×#14556060C2211yescharacteristic, complemented
57#17986005C2218yescomplemented
58#17985996C2218yescomplemented
59C2×#14556053C2211yescharacteristic, complemented
60C2×#14556053C2211yescharacteristic, complemented
61C2×#14556053C2211yescharacteristic, complemented
62C2×#14556053C2211yescharacteristic, complemented
63C2×#14556050C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556050C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2211yescharacteristic
69C22×M16×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic, complemented
71C2×C4×D4×C71C2211yescharacteristic
72#435×C71C2218yescomplemented
73C2×C4⋊C8×C71C2211yescharacteristic, complemented
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic, complemented
76C2×#97×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C2×#11765865—24no—
79C2×#11765865—22no—
80C2×#11765865—42no—
81C2×#11765865C2314yes—
82C22×Dic142—21no—
83C22×Dic142C2311yescharacteristic
84C22×Dic142C2311yescharacteristic
85C22×D284—24no—
86C22×D284—22no—
87C22×D284—21no—
88C22×D284—42no—
89C22×D284C2311yescharacteristic
90C22×D284C2314yes—
91C22×D284C2311yescharacteristic
92C22×C22⋊D71—21no—
93C22×C22⋊D71—21no—
94C22×C4×D71—21no—
95C22×C4×D71—21no—
96C2×Dic284—42no—
97C2×Dic284C2314yescomplemented
98C2×#11765854—24no—
99C2×#11765854—42no—
100C2×#11765854C2314yes—
101C2×#11765854C2314yes—
102#14556128—22no—
103#14556128C2314yescomplemented
104#14556121—28no—
105#14556121—28no—
106#14556116—22no—
107#14556116C2314yes—
108#14556115—28no—
109#14556113—28no—
110#14556107—22no—
111#14556107—22no—
112#14556107—22no—
113#14556107C2314yes—
114#14556107C2314yes—
115#14556107C2314yescomplemented
116#14556102—22no—
117#14556102C2314yes—
118#14556101—28no—
119#14556096—28no—
120C4×Dic142—22no—
121C4×Dic142C2314yescomplemented
122#14556093—28no—
123C4×D284—22no—
124C4×D284C2314yes—
125#14556087—22no—
126#14556087—22no—
127#14556087C2314yes—
128#14556087C2314yescomplemented
129C2×C4⋊Dic71—21no—
130C2×C4⋊Dic71C2311yescharacteristic
131C2×C4⋊Dic71C2311yescharacteristic
132C2×C4⋊Dic71C2311yescharacteristic
133C2×C4⋊Dic71C2311yescharacteristic
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4—21no—
137C2×Dic71⋊C4—21no—
138C2×C22⋊Dic71—21no—
139C2×C22⋊Dic71—21no—
140C2×C22⋊Dic71—21no—
141C2×C22⋊Dic71—21no—
142C2×C22⋊Dic71—21no—
143C2×(C2×D71)⋊C4—21no—
144C2×(C2×D71)⋊C4—21no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4—21no—
147C22⋊C4×D71—28no—
148C2×C4×Dic71—21no—
149C2×C4×Dic71—21no—
150C2×C4×Dic71—21no—
151#14556062C2314yescomplemented
152#14556060C2314yescomplemented
153#14556060C2314yescomplemented
154#14556053C2314yescomplemented
155#14556053C2314yescomplemented
156#14556053C2314yescomplemented
157#14556053C2314yescomplemented
158#14556050C2314yes—
159#14556050C2314yes—
160#14556050C2314yes—
161#14556050C2314yes—
162#14556050C2314yes—
163#14556050C2314yes—
164C22×D4×C71D411yescharacteristic
165C23×C4×C71C2311yescharacteristic
166C23×C4×C71C2311yescharacteristic
167C2×M16×C71—42no—
168C2×M16×C71C2314yes—
169C22×C8×C71—42no—
170C22×C8×C71C2311yescharacteristic
171C22×C8×C71C2311yescharacteristic
172C22×C8×C71C2311yescharacteristic
173C22×C8×C71C2311yescharacteristic
174C22×C8×C71C2314yescomplemented
175C4×D4×C71D414yes—
176C4×D4×C71C2314yes—
177C2×C4⋊C4×C71D411yescharacteristic
178C2×C22⋊C4×C71D411yescharacteristic
179C2×C22⋊C4×C71D411yescharacteristic
180C2×C42×C71C2311yescharacteristic
181C4⋊C8×C71C2314yescomplemented
182C22⋊C8×C71C2314yes—
183C22⋊C8×C71C2314yescomplemented
184#97×C71C2314yescomplemented
185C23×D71—21no—
186C23×D71—21no—
187C23×D71—24no—
188C23×D71—44no—
189C23×D71—44no—
190C23×D71—82no—
191#11765865—28no—
192#11765865—44no—
193#11765865—48no—
194C2×Dic142—22no—
195C2×Dic142—22no—
196C2×Dic142—22no—
197C2×Dic142—22no—
198C2×Dic142—24no—
199C2×Dic142—21no—
200C2×Dic142—21no—
201C2×Dic142—44no—
202C2×Dic142C2412yes—
203C2×Dic142C2412yes—
204C2×D284—21no—
205C2×D284—22no—
206C2×D284—22no—
207C2×D284—22no—
208C2×D284—28no—
209C2×D284—24no—
210C2×D284—21no—
211C2×D284—44no—
212C2×D284—48no—
213C2×D284—44no—
214C2×D284#4114yes—
215C2×D284C2412yes—
216C2×D284C2412yes—
217C2×C22⋊D71—24no—
218C2×C22⋊D71—24no—
219C2×C22⋊D71—44no—
220C2×C22⋊D71—82no—
221C22×Dic71—21no—
222C22×Dic71—21no—
223C22×Dic71—21no—
224C22×Dic71—21no—
225C22×Dic71—21no—
226C22×Dic71—21no—
227C2×C4×D71—24no—
228C2×C4×D71—24no—
229C2×C4×D71—44no—
230C2×C4×D71—82no—
231Dic284—44no—
232#11765854—28no—
233#11765854—44no—
234C4⋊Dic71—24no—
235C4⋊Dic71—21no—
236C4⋊Dic71—21no—
237C4⋊Dic71—21no—
238C4⋊Dic71—21no—
239C4⋊Dic71C2412yes—
240C4⋊Dic71C2412yes—
241C4⋊Dic71C2412yes—
242C4⋊Dic71C2412yes—
243Dic71⋊C4—24no—
244Dic71⋊C4—24no—
245Dic71⋊C4—24no—
246Dic71⋊C4—24no—
247C22⋊Dic71—24no—
248C22⋊Dic71—24no—
249C22⋊Dic71—24no—
250C22⋊Dic71—24no—
251C22⋊Dic71—24no—
252(C2×D71)⋊C4—24no—
253(C2×D71)⋊C4—24no—
254(C2×D71)⋊C4—24no—
255(C2×D71)⋊C4—24no—
256C4×Dic71—24no—
257C4×Dic71—24no—
258C4×Dic71—24no—
259C24×C71C2×D411yescharacteristic
260C24×C71C2×D411yescharacteristic
261C2×D4×C71—42no—
262C2×D4×C71C2×D414yes—
263C22×C4×C71—22no—
264C22×C4×C71—22no—
265C22×C4×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D412yes—
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D412yes—
273C22×C4×C71C2412yes—
274C22×C4×C71C2412yes—
275C22×C4×C71C2411yescharacteristic
276M16×C71—44no—
277C2×C8×C71—22no—
278C2×C8×C71—22no—
279C2×C8×C71—22no—
280C2×C8×C71—22no—
281C2×C8×C71—44no—
282C2×C8×C71C2412yes—
283C2×C8×C71C2412yes—
284C2×C8×C71C2412yes—
285C2×C8×C71C2412yes—
286C4⋊C4×C71C2×D414yes—
287C22⋊C4×C71C2×D414yes—
288C22⋊C4×C71C2×D414yes—
289C42×C71C2×D412yes—
290C42×C71C2412yes—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71C22×D412yes—
298C23×C71C22×D412yes—
299C23×C71C22×D411yescharacteristic
300C22×D71—24no—
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—48no—
304C22×D71—42no—
305C22×D71—42no—
306C22×D71—48no—
307C22×D71—42no—
308C22×D71—42no—
309C22×D71—42no—
310C22×D71—84no—
311C22×D71—816no—
312D4×C71—44no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—24no—
318C2×C4×C71—24no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71C22×D412yes—
324C2×C4×C71C22×D412yes—
325C2×C4×C71C22×D412yes—
326C2×C4×C71C22×D412yes—
327C2×C4×C71C22×D411yescharacteristic
328C2×C4×C71C2×#4112yes—
329C2×C4×C71H(5,𝔽2)12yes—
330C2×C4×C71C2511yescharacteristic
331C22⋊D71—48no—
332C22⋊D71—84no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—42no—
340C2×Dic71—42no—
341C2×Dic71—42no—
342C2×Dic71—42no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345D284—24no—
346D284—22no—
347D284—22no—
348D284—22no—
349D284—48no—
350D284—42no—
351D284C2×#4114yes—
352C4×D71—48no—
353C4×D71—84no—
354Dic142—22no—
355Dic142—22no—
356Dic142—22no—
357Dic142—22no—
358Dic142—48no—
359Dic142—42no—
360Dic142—42no—
361C8×C71—22no—
362C8×C71—22no—
363C8×C71—22no—
364C8×C71—22no—
365C22×C71—22no—
366C22×C71—22no—
367C22×C71—22no—
368C22×C71—22no—
369C22×C71—22no—
370C22×C71—22no—
371C22×C71—44no—
372C22×C71—44no—
373C22×C71#54612yes—
374C22×C71#57512yes—
375C22×C71#57712yes—
376C22×C71C23×D411yescharacteristic
377C2×D71—24no—
378C2×D71—48no—
379C2×D71—42no—
380C2×D71—42no—
381C2×D71—42no—
382C2×D71—42no—
383C2×D71—42no—
384C2×D71—816no—
385C2×D71—84no—
386C4×C71—22no—
387C4×C71—22no—
388C4×C71—22no—
389C4×C71—22no—
390C4×C71#54612yes—
391C4×C71C22×#4111yescharacteristic
392C4×C71C2×H(5,𝔽2)11yescharacteristic
393Dic71—42no—
394Dic71—42no—
395Dic71—42no—
396Dic71—42no—
397Dic71—42no—
398Dic71—42no—
399C2×#3311—711nomaximal, Sylow
400C2×C71—42no—
401C2×C71—42no—
402C2×C71#331114yescomplemented
403C2×C71C2×#54611yescharacteristic
404C2×C71C2×#57511yescharacteristic
405C2×C71C2×#57711yescharacteristic
406D71—44no—
407D71—82no—
408C2×#556—711no—
409C2×#546—711no—
410#3311—7116no—
411C2×#489—711no—
412C2×#485—711no—
413C2×#482—711no—
414C2×#476—711no—
415C2×#470—711no—
416C2×#465—711no—
417C2×#464—711no—
418C2×#452—711no—
419C2×#450—711no—
420C2×#440—711no—
421C2×#435D7111yescharacteristic, complemented
422C2×#418—711no—
423C2×#416—711no—
424C71C2×#331111yescharacteristic, complemented, Sylow
425C22×#41—711no—
426C23×D4—711no—
427C22×Q16—711no—
428C22×SD16—711no—
429C22×SD16—711no—
430C22×M16C2×D7111yescharacteristic
431C23×C8C2×D7111yescharacteristic, complemented
432#556—718no—
433#556—1424no—
434#546—718no—
435#546—1424no—
436C2×C4⋊Q8—711no—
437C2×#126—1421no—
438C2×#126—1421no—
439C2×#124—711no—
440C2×#124—1421no—
441C2×#123—1421no—
442C2×C22⋊Q8—711no—
443C2×C22⋊Q8—711no—
444C2×C22⋊Q8—711no—
445C2×#121—711no—
446C2×#121—1421no—
447C2×#120—1421no—
448C2×C4×Q8—711no—
449C2×C4×Q8—1421no—
450C2×C4×D4—711no—
451C2×C4×D4C2×D7111yescharacteristic
452C2×#117—711no—
453C2×#117—711no—
454C22×C22⋊C4—1421no—
455#489—718no—
456#485—718no—
457#482—718no—
458#476—718no—
459#470—718no—
460#465—718no—
461#464—718no—
462#452—718no—
463#450—718no—
464#440—718no—
465#435C2×D7118yescomplemented
466C2×#107—711no—
467C2×#106—711no—
468C2×#106—711no—
469C2×C4⋊C8C2×D7111yescharacteristic, complemented
470#418—718no—
471#416—718no—
472C2×#103—711no—
473C2×#103—711no—
474C2×#103—711no—
475C2×#103—711no—
476C2×#102—711no—
477C2×#102—711no—
478C2×#102—711no—
479C2×#102—711no—
480C2×#102—711no—
481C2×#102—711no—
482C2×C22⋊C8C2×D7111yescharacteristic
483C2×C22⋊C8C2×D7111yescharacteristic, complemented
484C2×#97C2×D7111yescharacteristic, complemented
485C25—1421no—
486C2×#41—2842no—
487C2×#41—714no—
488C2×#41—1424no—
489C2×#41—1422no—
490C22×Q8—711no—
491C22×Q8—711no—
492C22×Q8—1421no—
493C22×D4—2842no—
494C22×D4—714no—
495C22×D4—711no—
496C22×D4—711no—
497C22×D4—1424no—
498C22×D4—1421no—
499C22×D4—1421no—
500C22×D4—1421no—
501C22×D4—1422no—
502C22×D4D28411yescharacteristic
503C23×C4—1421no—
504C23×C4—1421no—
505C23×C4C22×D7111yescharacteristic
506C23×C4C22×D7111yescharacteristic
507C2×Q16—2842no—
508C2×Q16—714no—
509C2×SD16—2842no—
510C2×SD16—714no—
511C2×SD16—714no—
512C2×SD16—1424no—
513C2×M16—42no—
514C2×M16C22×D7114yes—
515C22×C8—42no—
516C22×C8C22×D7111yescharacteristic
517C22×C8C22×D7111yescharacteristic
518C22×C8C22×D7111yescharacteristic
519C22×C8C22×D7111yescharacteristic
520C22×C8C22×D7114yescomplemented
521C4⋊Q8—714no—
522C4⋊Q8—1422no—
523#126—1428no—
524#126—1428no—
525#124—714no—
526#124—1428no—
527#124—1422no—
528#123—1428no—
529C22⋊Q8—714no—
530C22⋊Q8—714no—
531C22⋊Q8—714no—
532C22⋊Q8—1422no—
533C22⋊Q8—1422no—
534C22⋊Q8—1422no—
535#121—714no—
536#121—1422no—
537#121—1428no—
538#120—1428no—
539C4×Q8—714no—
540C4×Q8—1428no—
541C4×Q8—1422no—
542C4×D4—714no—
543C4×D4—1422no—
544C4×D4D28414yes—
545C4×D4C22×D7114yes—
546#117—714no—
547#117—714no—
548#117—1422no—
549#117—1422no—
550C2×C4⋊C4—711no—
551C2×C4⋊C4—711no—
552C2×C4⋊C4—711no—
553C2×C4⋊C4—711no—
554C2×C4⋊C4—1421no—
555C2×C4⋊C4—1421no—
556C2×C4⋊C4—1421no—
557C2×C4⋊C4—1421no—
558C2×C4⋊C4—1421no—
559C2×C4⋊C4D28411yescharacteristic
560C2×C22⋊C4—1421no—
561C2×C22⋊C4—1421no—
562C2×C22⋊C4—1421no—
563C2×C22⋊C4—1421no—
564C2×C22⋊C4—1421no—
565C2×C22⋊C4—1421no—
566C2×C22⋊C4—1421no—
567C2×C22⋊C4—1421no—
568C2×C22⋊C4—1421no—
569C2×C22⋊C4—1428no—
570C2×C22⋊C4D28411yescharacteristic
571C2×C22⋊C4D28411yescharacteristic
572C2×C42—1421no—
573C2×C42—1421no—
574C2×C42—1421no—
575C2×C42C22×D7111yescharacteristic
576#107—714no—
577#106—714no—
578#106—714no—
579C4⋊C8C22×D7114yescomplemented
580#103—714no—
581#103—714no—
582#103—714no—
583#103—714no—
584#102—714no—
585#102—714no—
586#102—714no—
587#102—714no—
588#102—714no—
589#102—714no—
590C22⋊C8C22×D7114yes—
591C22⋊C8C22×D7114yescomplemented
592#97C22×D7114yescomplemented
593C24—2844no—
594C24—2844no—
595C24—5682no—
596C24—1421no—
597C24—1424no—
598C24—1421no—
599C24C2×D28411yescharacteristic
600C24C2×D28411yescharacteristic
601#41—2848no—
602#41—2844no—
603#41—1428no—
604C2×Q8—2844no—
605C2×Q8—712no—
606C2×Q8—712no—
607C2×Q8—1422no—
608C2×Q8—1422no—
609C2×Q8—1422no—
610C2×Q8—1422no—
611C2×Q8—1421no—
612C2×Q8—1424no—
613C2×Q8—1421no—
614C2×D4—42no—
615C2×D4—2844no—
616C2×D4—2848no—
617C2×D4—2844no—
618C2×D4—2844no—
619C2×D4—5682no—
620C2×D4—714no—
621C2×D4—712no—
622C2×D4—712no—
623C2×D4—1428no—
624C2×D4—1424no—
625C2×D4—1424no—
626C2×D4—1424no—
627C2×D4—1421no—
628C2×D4—1421no—
629C2×D4—1422no—
630C2×D4—1422no—
631C2×D4—1422no—
632C2×D4C2×D28414yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—2844no—
638C22×C4—5682no—
639C22×C4—1421no—
640C22×C4—1421no—
641C22×C4—1421no—
642C22×C4—1421no—
643C22×C4—1421no—
644C22×C4—1421no—
645C22×C4—1424no—
646C22×C4—1424no—
647C22×C4C2×D28412yes—
648C22×C4C2×D28412yes—
649C22×C4C2×D28411yescharacteristic
650C22×C4C2×D28411yescharacteristic
651C22×C4C2×D28411yescharacteristic
652C22×C4C2×D28411yescharacteristic
653C22×C4C23×D7112yes—
654C22×C4C23×D7112yes—
655C22×C4C23×D7111yescharacteristic
656Q16—2844no—
657SD16—2844no—
658SD16—1428no—
659M16—44no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—44no—
665C2×C8C23×D7112yes—
666C2×C8C23×D7112yes—
667C2×C8C23×D7112yes—
668C2×C8C23×D7112yes—
669C4⋊C4—712no—
670C4⋊C4—712no—
671C4⋊C4—712no—
672C4⋊C4—712no—
673C4⋊C4—1424no—
674C4⋊C4—1424no—
675C4⋊C4—1424no—
676C4⋊C4—1424no—
677C4⋊C4—1421no—
678C4⋊C4—1421no—
679C4⋊C4—1421no—
680C4⋊C4—1421no—
681C4⋊C4—1424no—
682C4⋊C4C2×D28414yes—
683C22⋊C4—1424no—
684C22⋊C4—1424no—
685C22⋊C4—1424no—
686C22⋊C4—1424no—
687C22⋊C4—1424no—
688C22⋊C4—1424no—
689C22⋊C4—1424no—
690C22⋊C4—1424no—
691C22⋊C4—1424no—
692C22⋊C4C2×D28414yes—
693C22⋊C4C2×D28414yes—
694C42—1424no—
695C42—1424no—
696C42—1424no—
697C42C2×D28412yes—
698C42C23×D7112yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—2848no—
706C23—2848no—
707C23—2842no—
708C23—2842no—
709C23—2842no—
710C23—2842no—
711C23—2842no—
712C23—5684no—
713C23—56816no—
714C23—1422no—
715C23—1422no—
716C23—1424no—
717C23C22×D28412yes—
718C23C22×D28412yes—
719C23C22×D28411yescharacteristic
720Q8—2848no—
721Q8—2842no—
722Q8—2842no—
723Q8—1422no—
724Q8—1422no—
725Q8—1422no—
726Q8—1422no—
727D4—44no—
728D4—2848no—
729D4—2848no—
730D4—2842no—
731D4—5684no—
732D4—714no—
733D4—1422no—
734D4—1422no—
735D4—1422no—
736D4—1424no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—2848no—
748C2×C4—2842no—
749C2×C4—2842no—
750C2×C4—2842no—
751C2×C4—2842no—
752C2×C4—2842no—
753C2×C4—2842no—
754C2×C4—5684no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1422no—
760C2×C4—1422no—
761C2×C4C22×D28412yes—
762C2×C4C22×D28412yes—
763C2×C4C22×D28412yes—
764C2×C4C22×D28412yes—
765C2×C4C22×D28411yescharacteristic
766C2×C4#41×D7112yes—
767C2×C4#1455617312yes—
768C2×C4C24×D7111yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—2842no—
782C22—2842no—
783C22—2848no—
784C22—2842no—
785C22—2842no—
786C22—2842no—
787C22—56816no—
788C22—5684no—
789C22—1424no—
790C22#1798664412yes—
791C22#1798679912yes—
792C22#1798681112yes—
793C22C23×D28411yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—2842no—
799C4—2842no—
800C4—2842no—
801C4—2842no—
802C4—2842no—
803C4—2842no—
804C4#1798664412yes—
805C4C2×#41×D7111yescharacteristic
806C4C2×#1455617311yescharacteristic
807C2—42no—
808C2—42no—
809C2—2844no—
810C2—5682no—
811C2#2260037814yesdirect product factor
812C2C2×#1798664411yescharacteristic
813C2C2×#1798679911yescharacteristic
814C2C2×#1798681111yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#435×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986645C2
hypercenterC2×#435D71
hypocenterC71C2×#3311
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#17986719C2semidirect
3. #22600378C2direct (N × H)
4. C2×#17986359C2semidirect
5. C2×#17986341C2semidirect
6. C2×#17986324C2semidirect
7. C2×#17986290C2semidirect
8. C2×#17986257C2semidirect
9. C2×#17986228C2semidirect
10. C2×#17986222C2semidirect
11. C2×#17986163C2semidirect
12. C2×#17986152C2semidirect
13. C2×#17986101C2semidirect
14. C2×#17986005C2semidirect
15. C2×#17985996C2semidirect
16. C2×#435×C71C2semidirect
19. C22×Dic284C22semidirect
23. #17986719C22semidirect
26. C2×#14556128C22semidirect
34. C2×#14556107C22semidirect
38. C2×C4×Dic142C22semidirect
42. C2×#14556087C22semidirect
44. #17986359C22semidirect
45. #17986341C22semidirect
46. #17986324C22semidirect
47. #17986290C22semidirect
48. #17986257C22semidirect
49. #17986228C22semidirect
50. #17986222C22semidirect
51. #17986163C22semidirect
52. #17986152C22semidirect
53. #17986101C22semidirect
54. C2×#14556062C22semidirect
55. C2×#14556060C22semidirect
56. C2×#14556060C22semidirect
57. #17986005C22semidirect
58. #17985996C22semidirect
59. C2×#14556053C22semidirect
60. C2×#14556053C22semidirect
61. C2×#14556053C22semidirect
62. C2×#14556053C22semidirect
70. C23×C8×C71C22semidirect
72. #435×C71C22semidirect
73. C2×C4⋊C8×C71C22semidirect
75. C2×C22⋊C8×C71C22semidirect
76. C2×#97×C71C22semidirect
97. C2×Dic284C23semidirect
103. #14556128C23semidirect
115. #14556107C23semidirect
121. C4×Dic142C23semidirect
128. #14556087C23semidirect
151. #14556062C23semidirect
152. #14556060C23semidirect
153. #14556060C23semidirect
154. #14556053C23semidirect
155. #14556053C23semidirect
156. #14556053C23semidirect
157. #14556053C23semidirect
174. C22×C8×C71C23semidirect
181. C4⋊C8×C71C23semidirect
183. C22⋊C8×C71C23semidirect
184. #97×C71C23semidirect
402. C2×C71#3311semidirect
421. C2×#435D71semidirect
424. C71C2×#3311semidirect
431. C23×C8C2×D71semidirect
465. #435C2×D71semidirect
469. C2×C4⋊C8C2×D71semidirect
483. C2×C22⋊C8C2×D71semidirect
484. C2×#97C2×D71semidirect
520. C22×C8C22×D71semidirect
579. C4⋊C8C22×D71semidirect
591. C22⋊C8C22×D71semidirect
592. #97C22×D71semidirect
811. C2#22600378direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867192
C2×#179866452
#226003782
C2×#179863592
C2×#179863412
C2×#179863242
C2×#179862902
C2×#179862572
C2×#179862282
C2×#179862222
C2×#179861632
C2×#179861522
C2×#179861012
C2×#179860052
C2×#179859962
C2×#435×C712
C2×#331171