Finite Group Databasebeta

← C2×#22600498 #32874140

Subgroups — C2×#22600498 #32874140

Order 18176.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986714C211yesmaximal, characteristic, complemented
2C2×#17986645C211yesmaximal, characteristic, complemented
3#22600498C2116yesmaximal, direct product factor
4C2×#17986359C211yesmaximal, characteristic, complemented
5C2×#17986341C211yesmaximal, characteristic, complemented
6C2×#17986324C211yesmaximal, characteristic, complemented
7C2×#17986280C211yesmaximal, characteristic, complemented
8C2×#17986245C211yesmaximal, characteristic, complemented
9C2×#17986235C211yesmaximal, characteristic, complemented
10C2×#17986215C211yesmaximal, characteristic, complemented
11C2×#17986146C211yesmaximal, characteristic, complemented
12C2×#17986135C211yesmaximal, characteristic, complemented
13C2×#17986112C211yesmaximal, characteristic, complemented
14C2×#17986005C211yesmaximal, characteristic, complemented
15C2×#17985996C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C22×#11765854C2211yescharacteristic, complemented
20C22×D568C2211yescharacteristic
21C22×D568C2211yescharacteristic
22#17986714—24no—
23#17986714C2218yescomplemented
24#17986645—24no—
25#17986645C2218yescomplemented
26C2×#14556128C2211yescharacteristic, complemented
27C2×#14556116C2211yescharacteristic
28C2×#14556114—21no—
29C2×#14556114—21no—
30C2×#14556113—21no—
31C2×#14556107C2211yescharacteristic
32C2×#14556102C2211yescharacteristic
33C2×#14556102C2211yescharacteristic
34C2×#14556102C2211yescharacteristic, complemented
35C2×#14556101—21no—
36C2×#14556099—21no—
37C2×#14556096—21no—
38C2×C4×D284C2211yescharacteristic
39C2×C4×D284C2211yescharacteristic, complemented
40C2×#14556087C2211yescharacteristic
41C2×#14556087C2211yescharacteristic, complemented
42C2×#14556086—21no—
43C2×C22⋊C4×D71—21no—
44#17986359C2218yescomplemented
45#17986341C2218yescomplemented
46#17986324C2218yescomplemented
47#17986280C2218yescomplemented
48#17986245C2218yescomplemented
49#17986235C2218yescomplemented
50#17986215C2218yescomplemented
51#17986146C2218yescomplemented
52#17986135C2218yescomplemented
53#17986112C2218yescomplemented
54C2×#14556062C2211yescharacteristic, complemented
55C2×#14556062C2211yescharacteristic, complemented
56C2×#14556060C2211yescharacteristic, complemented
57#17986005C2218yescomplemented
58#17985996C2218yescomplemented
59C2×#14556053C2211yescharacteristic, complemented
60C2×#14556053C2211yescharacteristic, complemented
61C2×#14556053C2211yescharacteristic, complemented
62C2×#14556050C2211yescharacteristic
63C2×#14556050C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556050C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2211yescharacteristic, complemented
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×D284—24no—
85C22×D284—22no—
86C22×D284—21no—
87C22×D284—42no—
88C22×D284C2311yescharacteristic
89C22×D284C2311yescharacteristic
90C22×D284C2314yes—
91C22×D284C2311yescharacteristic
92C22×C22⋊D71—21no—
93C22×C22⋊D71—21no—
94C22×C22⋊D71—21no—
95C22×C22⋊D71—21no—
96C22×C4×D71—21no—
97C22×C4×D71—21no—
98C22×C4×D71—21no—
99C2×#11765854—42no—
100C2×#11765854C2314yescomplemented
101C2×D568—24no—
102C2×D568—42no—
103C2×D568C2314yes—
104C2×D568C2314yes—
105#14556128—22no—
106#14556128C2314yescomplemented
107#14556116—22no—
108#14556116C2314yes—
109#14556114—28no—
110#14556114—28no—
111#14556113—28no—
112#14556107—22no—
113#14556107C2314yes—
114#14556102—22no—
115#14556102—22no—
116#14556102—22no—
117#14556102C2314yes—
118#14556102C2314yes—
119#14556102C2314yescomplemented
120#14556101—28no—
121#14556099—28no—
122#14556096—28no—
123C4×D284—22no—
124C4×D284—22no—
125C4×D284C2314yes—
126C4×D284C2314yescomplemented
127#14556087—22no—
128#14556087—22no—
129#14556087C2314yes—
130#14556087C2314yescomplemented
131#14556086—28no—
132C2×C4⋊Dic71—21no—
133C2×C4⋊Dic71C2311yescharacteristic
134C2×C4⋊Dic71C2311yescharacteristic
135C2×C4⋊Dic71C2311yescharacteristic
136C2×C4⋊Dic71C2311yescharacteristic
137C2×Dic71⋊C4—21no—
138C2×C22⋊Dic71—21no—
139C2×C22⋊Dic71—21no—
140C2×C22⋊Dic71—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4—21no—
144C2×(C2×D71)⋊C4—21no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4—21no—
147C2×(C2×D71)⋊C4—21no—
148C22⋊C4×D71—28no—
149C2×C4×Dic71—21no—
150C2×C4×Dic71—21no—
151#14556062C2314yescomplemented
152#14556062C2314yescomplemented
153#14556060C2314yescomplemented
154#14556053C2314yescomplemented
155#14556053C2314yescomplemented
156#14556053C2314yescomplemented
157#14556050C2314yes—
158#14556050C2314yes—
159#14556050C2314yes—
160#14556050C2314yes—
161#14556050C2314yes—
162#14556050C2314yes—
163#14556050C2314yescomplemented
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—21no—
188C23×D71—24no—
189C23×D71—44no—
190C23×D71—44no—
191C23×D71—82no—
192#11765865—28no—
193#11765865—44no—
194#11765865—48no—
195C2×Dic142—22no—
196C2×Dic142—22no—
197C2×Dic142—21no—
198C2×Dic142—24no—
199C2×Dic142—82no—
200C2×Dic142C2412yes—
201C2×D284—21no—
202C2×D284—22no—
203C2×D284—22no—
204C2×D284—22no—
205C2×D284—22no—
206C2×D284—22no—
207C2×D284—28no—
208C2×D284—24no—
209C2×D284—21no—
210C2×D284—21no—
211C2×D284—44no—
212C2×D284—48no—
213C2×D284—44no—
214C2×D284#4114yes—
215C2×D284C2412yes—
216C2×D284C2412yes—
217C2×D284C2412yes—
218C2×C22⋊D71—24no—
219C2×C22⋊D71—24no—
220C2×C22⋊D71—24no—
221C2×C22⋊D71—24no—
222C2×C22⋊D71—44no—
223C2×C22⋊D71—82no—
224C2×C22⋊D71—82no—
225C2×C22⋊D71—82no—
226C22×Dic71—21no—
227C22×Dic71—21no—
228C22×Dic71—21no—
229C22×Dic71—21no—
230C22×Dic71—21no—
231C2×C4×D71—24no—
232C2×C4×D71—24no—
233C2×C4×D71—24no—
234C2×C4×D71—44no—
235C2×C4×D71—44no—
236C2×C4×D71—82no—
237#11765854—44no—
238D568—28no—
239D568—44no—
240C4⋊Dic71—24no—
241C4⋊Dic71—21no—
242C4⋊Dic71—21no—
243C4⋊Dic71—21no—
244C4⋊Dic71—21no—
245C4⋊Dic71C2412yes—
246C4⋊Dic71C2412yes—
247C4⋊Dic71C2412yes—
248C4⋊Dic71C2412yes—
249Dic71⋊C4—24no—
250C22⋊Dic71—24no—
251C22⋊Dic71—24no—
252C22⋊Dic71—24no—
253(C2×D71)⋊C4—24no—
254(C2×D71)⋊C4—24no—
255(C2×D71)⋊C4—24no—
256(C2×D71)⋊C4—24no—
257(C2×D71)⋊C4—24no—
258(C2×D71)⋊C4—24no—
259(C2×D71)⋊C4—24no—
260C4×Dic71—24no—
261C4×Dic71—24no—
262C24×C71C2×D411yescharacteristic
263C24×C71C2×D411yescharacteristic
264C2×D4×C71—42no—
265C2×D4×C71C2×D414yes—
266C22×C4×C71—22no—
267C22×C4×C71—22no—
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D411yescharacteristic
273C22×C4×C71C2×D411yescharacteristic
274C22×C4×C71C2×D412yes—
275C22×C4×C71C2×D412yes—
276C22×C4×C71C2412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2411yescharacteristic
279M16×C71—44no—
280C2×C8×C71—22no—
281C2×C8×C71—22no—
282C2×C8×C71—22no—
283C2×C8×C71—22no—
284C2×C8×C71—44no—
285C2×C8×C71C2412yes—
286C2×C8×C71C2412yes—
287C2×C8×C71C2412yes—
288C2×C8×C71C2412yes—
289C4⋊C4×C71C2×D414yes—
290C22⋊C4×C71C2×D414yes—
291C22⋊C4×C71C2×D414yes—
292C42×C71C2×D412yes—
293C42×C71C2412yes—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—22no—
300C23×C71C22×D412yes—
301C23×C71C22×D412yes—
302C23×C71C22×D411yescharacteristic
303C22×D71—24no—
304C22×D71—22no—
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—48no—
308C22×D71—42no—
309C22×D71—42no—
310C22×D71—48no—
311C22×D71—42no—
312C22×D71—42no—
313C22×D71—42no—
314C22×D71—42no—
315C22×D71—42no—
316C22×D71—42no—
317C22×D71—84no—
318C22×D71—816no—
319D4×C71—44no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—24no—
325C2×C4×C71—24no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71C22×D412yes—
331C2×C4×C71C22×D412yes—
332C2×C4×C71C22×D412yes—
333C2×C4×C71C22×D412yes—
334C2×C4×C71C22×D411yescharacteristic
335C2×C4×C71C2×#4112yes—
336C2×C4×C71H(5,𝔽2)12yes—
337C2×C4×C71C2511yescharacteristic
338C22⋊D71—48no—
339C22⋊D71—84no—
340C22⋊D71—84no—
341C22⋊D71—84no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—42no—
348C2×Dic71—42no—
349C2×Dic71—42no—
350C2×Dic71—42no—
351C2×Dic71—42no—
352D284—24no—
353D284—22no—
354D284—22no—
355D284—22no—
356D284—22no—
357D284—22no—
358D284—48no—
359D284—42no—
360D284—42no—
361D284C2×#4114yes—
362C4×D71—48no—
363C4×D71—48no—
364C4×D71—84no—
365Dic142—22no—
366Dic142—22no—
367Dic142—42no—
368Dic142—84no—
369C8×C71—22no—
370C8×C71—22no—
371C8×C71—22no—
372C8×C71—22no—
373C22×C71—22no—
374C22×C71—22no—
375C22×C71—22no—
376C22×C71—22no—
377C22×C71—22no—
378C22×C71—22no—
379C22×C71—44no—
380C22×C71—44no—
381C22×C71#54612yes—
382C22×C71#57512yes—
383C22×C71#57612yes—
384C22×C71C23×D411yescharacteristic
385C2×D71—24no—
386C2×D71—48no—
387C2×D71—42no—
388C2×D71—42no—
389C2×D71—42no—
390C2×D71—42no—
391C2×D71—42no—
392C2×D71—42no—
393C2×D71—42no—
394C2×D71—42no—
395C2×D71—816no—
396C2×D71—84no—
397C2×D71—84no—
398C4×C71—22no—
399C4×C71—22no—
400C4×C71—22no—
401C4×C71—22no—
402C4×C71#54612yes—
403C4×C71C22×#4111yescharacteristic
404C4×C71C2×H(5,𝔽2)11yescharacteristic
405Dic71—42no—
406Dic71—42no—
407Dic71—42no—
408Dic71—42no—
409Dic71—42no—
410C2×#3319—711nomaximal, Sylow
411C2×C71—42no—
412C2×C71—42no—
413C2×C71#331914yescomplemented
414C2×C71C2×#54611yescharacteristic
415C2×C71C2×#57511yescharacteristic
416C2×C71C2×#57611yescharacteristic
417D71—44no—
418D71—82no—
419D71—82no—
420C2×#555—711no—
421C2×#546—711no—
422#3319—7116no—
423C2×#489—711no—
424C2×#485—711no—
425C2×#482—711no—
426C2×#474—711no—
427C2×#468—711no—
428C2×#466—711no—
429C2×#463—711no—
430C2×#449—711no—
431C2×#447—711no—
432C2×#442—711no—
433C2×#435D7111yescharacteristic, complemented
434C2×#418—711no—
435C2×#416—711no—
436C71C2×#331911yescharacteristic, complemented, Sylow
437C22×#41—711no—
438C23×D4—711no—
439C22×SD16—711no—
440C22×D8—711no—
441C22×D8—711no—
442C22×M16C2×D7111yescharacteristic
443C23×C8C2×D7111yescharacteristic, complemented
444#555—718no—
445#555—1424no—
446#546—718no—
447#546—1424no—
448C2×C4⋊Q8—711no—
449C2×#124—711no—
450C2×#124—1421no—
451C2×#124—1421no—
452C2×#123—1421no—
453C2×C22⋊Q8—711no—
454C2×#121—711no—
455C2×#121—711no—
456C2×#121—711no—
457C2×#121—1421no—
458C2×#121—1421no—
459C2×#120—1421no—
460C2×C4×D4—711no—
461C2×C4×D4—711no—
462C2×C4×D4C2×D7111yescharacteristic
463C2×#117—711no—
464C2×#117—711no—
465C2×#117—1421no—
466C22×C22⋊C4—1421no—
467#489—718no—
468#485—718no—
469#482—718no—
470#474—718no—
471#468—718no—
472#466—718no—
473#463—718no—
474#449—718no—
475#447—718no—
476#442—718no—
477#435C2×D7118yescomplemented
478C2×#107—711no—
479C2×#107—711no—
480C2×#106—711no—
481C2×C4⋊C8C2×D7111yescharacteristic, complemented
482#418—718no—
483#416—718no—
484C2×#103—711no—
485C2×#103—711no—
486C2×#103—711no—
487C2×#102—711no—
488C2×#102—711no—
489C2×#102—711no—
490C2×#102—711no—
491C2×#102—711no—
492C2×#102—711no—
493C2×#102—711no—
494C2×C22⋊C8C2×D7111yescharacteristic
495C2×C22⋊C8C2×D7111yescharacteristic, complemented
496C2×#97C2×D7111yescharacteristic, complemented
497C25—1421no—
498C2×#41—2842no—
499C2×#41—714no—
500C2×#41—1424no—
501C2×#41—1422no—
502C22×Q8—711no—
503C22×Q8—1421no—
504C22×D4—2842no—
505C22×D4—714no—
506C22×D4—711no—
507C22×D4—711no—
508C22×D4—711no—
509C22×D4—1424no—
510C22×D4—1421no—
511C22×D4—1421no—
512C22×D4—1421no—
513C22×D4—1421no—
514C22×D4—1421no—
515C22×D4—1422no—
516C22×D4D28411yescharacteristic
517C23×C4—1421no—
518C23×C4—1421no—
519C23×C4—1421no—
520C23×C4C22×D7111yescharacteristic
521C23×C4C22×D7111yescharacteristic
522C2×SD16—2842no—
523C2×SD16—714no—
524C2×D8—2842no—
525C2×D8—714no—
526C2×D8—714no—
527C2×D8—1424no—
528C2×M16—42no—
529C2×M16C22×D7114yes—
530C22×C8—42no—
531C22×C8C22×D7111yescharacteristic
532C22×C8C22×D7111yescharacteristic
533C22×C8C22×D7111yescharacteristic
534C22×C8C22×D7111yescharacteristic
535C22×C8C22×D7114yescomplemented
536C4⋊Q8—714no—
537C4⋊Q8—1422no—
538#124—714no—
539#124—1428no—
540#124—1428no—
541#124—1422no—
542#123—1428no—
543C22⋊Q8—714no—
544C22⋊Q8—1422no—
545#121—714no—
546#121—714no—
547#121—714no—
548#121—1428no—
549#121—1422no—
550#121—1422no—
551#121—1422no—
552#121—1428no—
553#120—1428no—
554C4×D4—714no—
555C4×D4—714no—
556C4×D4—1422no—
557C4×D4—1422no—
558C4×D4D28414yes—
559C4×D4C22×D7114yes—
560#117—714no—
561#117—714no—
562#117—1422no—
563#117—1422no—
564#117—1428no—
565C2×C4⋊C4—711no—
566C2×C4⋊C4—711no—
567C2×C4⋊C4—711no—
568C2×C4⋊C4—711no—
569C2×C4⋊C4—1421no—
570C2×C4⋊C4—1421no—
571C2×C4⋊C4D28411yescharacteristic
572C2×C22⋊C4—1421no—
573C2×C22⋊C4—1421no—
574C2×C22⋊C4—1421no—
575C2×C22⋊C4—1421no—
576C2×C22⋊C4—1421no—
577C2×C22⋊C4—1421no—
578C2×C22⋊C4—1421no—
579C2×C22⋊C4—1421no—
580C2×C22⋊C4—1421no—
581C2×C22⋊C4—1421no—
582C2×C22⋊C4—1428no—
583C2×C22⋊C4D28411yescharacteristic
584C2×C22⋊C4D28411yescharacteristic
585C2×C42—1421no—
586C2×C42—1421no—
587C2×C42C22×D7111yescharacteristic
588#107—714no—
589#107—714no—
590#106—714no—
591C4⋊C8C22×D7114yescomplemented
592#103—714no—
593#103—714no—
594#103—714no—
595#102—714no—
596#102—714no—
597#102—714no—
598#102—714no—
599#102—714no—
600#102—714no—
601#102—714no—
602C22⋊C8C22×D7114yes—
603C22⋊C8C22×D7114yescomplemented
604#97C22×D7114yescomplemented
605C24—2844no—
606C24—2844no—
607C24—5682no—
608C24—1421no—
609C24—1421no—
610C24—1424no—
611C24—1421no—
612C24C2×D28411yescharacteristic
613C24C2×D28411yescharacteristic
614#41—2848no—
615#41—2844no—
616#41—1428no—
617C2×Q8—5682no—
618C2×Q8—712no—
619C2×Q8—1422no—
620C2×Q8—1422no—
621C2×Q8—1421no—
622C2×Q8—1424no—
623C2×D4—42no—
624C2×D4—2844no—
625C2×D4—2848no—
626C2×D4—2844no—
627C2×D4—2844no—
628C2×D4—5682no—
629C2×D4—5682no—
630C2×D4—5682no—
631C2×D4—714no—
632C2×D4—712no—
633C2×D4—712no—
634C2×D4—712no—
635C2×D4—1428no—
636C2×D4—1424no—
637C2×D4—1424no—
638C2×D4—1424no—
639C2×D4—1424no—
640C2×D4—1421no—
641C2×D4—1424no—
642C2×D4—1421no—
643C2×D4—1421no—
644C2×D4—1422no—
645C2×D4—1422no—
646C2×D4—1422no—
647C2×D4—1422no—
648C2×D4—1422no—
649C2×D4C2×D28414yes—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—2844no—
655C22×C4—2844no—
656C22×C4—5682no—
657C22×C4—1421no—
658C22×C4—1421no—
659C22×C4—1421no—
660C22×C4—1421no—
661C22×C4—1421no—
662C22×C4—1424no—
663C22×C4—1424no—
664C22×C4—1424no—
665C22×C4C2×D28412yes—
666C22×C4C2×D28412yes—
667C22×C4C2×D28411yescharacteristic
668C22×C4C2×D28411yescharacteristic
669C22×C4C2×D28411yescharacteristic
670C22×C4C2×D28411yescharacteristic
671C22×C4C23×D7112yes—
672C22×C4C23×D7112yes—
673C22×C4C23×D7111yescharacteristic
674SD16—2844no—
675D8—2844no—
676D8—1428no—
677M16—44no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—44no—
683C2×C8C23×D7112yes—
684C2×C8C23×D7112yes—
685C2×C8C23×D7112yes—
686C2×C8C23×D7112yes—
687C4⋊C4—712no—
688C4⋊C4—712no—
689C4⋊C4—712no—
690C4⋊C4—712no—
691C4⋊C4—1424no—
692C4⋊C4—1421no—
693C4⋊C4—1421no—
694C4⋊C4—1421no—
695C4⋊C4—1421no—
696C4⋊C4—1424no—
697C4⋊C4C2×D28414yes—
698C22⋊C4—1424no—
699C22⋊C4—1424no—
700C22⋊C4—1424no—
701C22⋊C4—1424no—
702C22⋊C4—1424no—
703C22⋊C4—1424no—
704C22⋊C4—1424no—
705C22⋊C4—1424no—
706C22⋊C4—1424no—
707C22⋊C4—1424no—
708C22⋊C4C2×D28414yes—
709C22⋊C4C2×D28414yes—
710C42—1424no—
711C42—1424no—
712C42C2×D28412yes—
713C42C23×D7112yes—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—2848no—
721C23—2848no—
722C23—2842no—
723C23—2842no—
724C23—2842no—
725C23—2842no—
726C23—2842no—
727C23—2842no—
728C23—2842no—
729C23—2842no—
730C23—5684no—
731C23—56816no—
732C23—1422no—
733C23—1422no—
734C23—1422no—
735C23—1424no—
736C23C22×D28412yes—
737C23C22×D28412yes—
738C23C22×D28411yescharacteristic
739Q8—2842no—
740Q8—5684no—
741Q8—1422no—
742Q8—1422no—
743D4—44no—
744D4—2848no—
745D4—2848no—
746D4—2842no—
747D4—2842no—
748D4—5684no—
749D4—5684no—
750D4—5684no—
751D4—714no—
752D4—1422no—
753D4—1422no—
754D4—1422no—
755D4—1422no—
756D4—1422no—
757D4—1424no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—2848no—
769C2×C4—2848no—
770C2×C4—2842no—
771C2×C4—2842no—
772C2×C4—2842no—
773C2×C4—2842no—
774C2×C4—2842no—
775C2×C4—5684no—
776C2×C4—1422no—
777C2×C4—1422no—
778C2×C4—1422no—
779C2×C4—1422no—
780C2×C4—1422no—
781C2×C4C22×D28412yes—
782C2×C4C22×D28412yes—
783C2×C4C22×D28412yes—
784C2×C4C22×D28412yes—
785C2×C4C22×D28411yescharacteristic
786C2×C4#41×D7112yes—
787C2×C4#1455617312yes—
788C2×C4C24×D7111yescharacteristic
789C8—22no—
790C8—22no—
791C8—22no—
792C8—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—2848no—
802C22—2842no—
803C22—2842no—
804C22—2842no—
805C22—2842no—
806C22—2842no—
807C22—2842no—
808C22—2842no—
809C22—2842no—
810C22—56816no—
811C22—5684no—
812C22—5684no—
813C22—1424no—
814C22#1798664412yes—
815C22#1798679912yes—
816C22#1798680412yes—
817C22C23×D28411yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—2842no—
823C4—2842no—
824C4—2842no—
825C4—2842no—
826C4—2842no—
827C4#1798664412yes—
828C4C2×#41×D7111yescharacteristic
829C4C2×#1455617311yescharacteristic
830C2—42no—
831C2—42no—
832C2—2844no—
833C2—5682no—
834C2—5682no—
835C2#2260049814yesdirect product factor
836C2C2×#1798664411yescharacteristic
837C2C2×#1798679911yescharacteristic
838C2C2×#1798680411yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#435×C71C2
socleC23×C71C22×D4
hypercenterC2×#435D71
hypocenterC71C2×#3319
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×#17986714C2semidirect
2. C2×#17986645C2semidirect
3. #22600498C2direct (N × H)
4. C2×#17986359C2semidirect
5. C2×#17986341C2semidirect
6. C2×#17986324C2semidirect
7. C2×#17986280C2semidirect
8. C2×#17986245C2semidirect
9. C2×#17986235C2semidirect
10. C2×#17986215C2semidirect
11. C2×#17986146C2semidirect
12. C2×#17986135C2semidirect
13. C2×#17986112C2semidirect
14. C2×#17986005C2semidirect
15. C2×#17985996C2semidirect
16. C2×#435×C71C2semidirect
19. C22×#11765854C22semidirect
23. #17986714C22semidirect
25. #17986645C22semidirect
26. C2×#14556128C22semidirect
34. C2×#14556102C22semidirect
39. C2×C4×D284C22semidirect
41. C2×#14556087C22semidirect
44. #17986359C22semidirect
45. #17986341C22semidirect
46. #17986324C22semidirect
47. #17986280C22semidirect
48. #17986245C22semidirect
49. #17986235C22semidirect
50. #17986215C22semidirect
51. #17986146C22semidirect
52. #17986135C22semidirect
53. #17986112C22semidirect
54. C2×#14556062C22semidirect
55. C2×#14556062C22semidirect
56. C2×#14556060C22semidirect
57. #17986005C22semidirect
58. #17985996C22semidirect
59. C2×#14556053C22semidirect
60. C2×#14556053C22semidirect
61. C2×#14556053C22semidirect
68. C2×#14556050C22semidirect
70. C23×C8×C71C22semidirect
72. #435×C71C22semidirect
73. C2×C4⋊C8×C71C22semidirect
75. C2×C22⋊C8×C71C22semidirect
76. C2×#97×C71C22semidirect
100. C2×#11765854C23semidirect
106. #14556128C23semidirect
119. #14556102C23semidirect
126. C4×D284C23semidirect
130. #14556087C23semidirect
151. #14556062C23semidirect
152. #14556062C23semidirect
153. #14556060C23semidirect
154. #14556053C23semidirect
155. #14556053C23semidirect
156. #14556053C23semidirect
163. #14556050C23semidirect
174. C22×C8×C71C23semidirect
181. C4⋊C8×C71C23semidirect
183. C22⋊C8×C71C23semidirect
184. #97×C71C23semidirect
413. C2×C71#3319semidirect
433. C2×#435D71semidirect
436. C71C2×#3319semidirect
443. C23×C8C2×D71semidirect
477. #435C2×D71semidirect
481. C2×C4⋊C8C2×D71semidirect
495. C2×C22⋊C8C2×D71semidirect
496. C2×#97C2×D71semidirect
535. C22×C8C22×D71semidirect
591. C4⋊C8C22×D71semidirect
603. C22⋊C8C22×D71semidirect
604. #97C22×D71semidirect
835. C2#22600498direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867142
C2×#179866452
#226004982
C2×#179863592
C2×#179863412
C2×#179863242
C2×#179862802
C2×#179862452
C2×#179862352
C2×#179862152
C2×#179861462
C2×#179861352
C2×#179861122
C2×#179860052
C2×#179859962
C2×#435×C712
C2×#331971