Finite Group Databasebeta

← C2×#19145257 #25966459

Subgroups — C2×#19145257 #25966459

Order 11008.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583511C211yesmaximal, characteristic, complemented
2#19145257C2116yesmaximal, direct product factor
3C2×#14583305C211yesmaximal, characteristic, complemented
4C2×#14583294C211yesmaximal, characteristic, complemented
5C2×#14583253C211yesmaximal, characteristic, complemented
6C2×#14583251C211yesmaximal, characteristic, complemented
7C2×#14583155C211yesmaximal, characteristic, complemented
8C2×#14583143C211yesmaximal, characteristic
9C2×#14583138C211yesmaximal, characteristic, complemented
10C2×#14583126C211yesmaximal, characteristic
11C2×#14583004C211yesmaximal, characteristic, complemented
12C2×#14582999C211yesmaximal, characteristic, complemented
13C2×C4×#10621885C211yesmaximal, characteristic, complemented
14C2×C4×#10621883C211yesmaximal, characteristic, complemented
15C2×#14582855C211yesmaximal, characteristic, complemented
16C2×C43×#542C211yesmaximal, characteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22C23×C43⋊C8C2211yescharacteristic
23#14583511—24no—
24#14583511C2218yescomplemented
25C2×#13063325C2211yescharacteristic
26C2×#13063318—21no—
27C2×#13063318—21no—
28C2×#13063317C2211yescharacteristic
29C2×#13063315—21no—
30C2×#13063315—21no—
31C2×#13063304C2211yescharacteristic
32C2×#13063304C2211yescharacteristic
33C2×C4×Dic86C2211yescharacteristic
34C2×C4×Dic86C2211yescharacteristic
35#14583305C2218yescomplemented
36#14583294C2218yescomplemented
37#14583253C2218yescomplemented
38#14583251C2218yescomplemented
39#14583155C2218yescomplemented
40#14583143C2218yes—
41#14583138C2218yescomplemented
42#14583126C2218yes—
43#14583004C2218yescomplemented
44#14582999C2218yescomplemented
45C4×#10621885C2218yescomplemented
46C4×#10621883C2218yescomplemented
47C2×#13063258C2211yescharacteristic
48C2×#13063258C2211yescharacteristic
49C2×#13063256C2211yescharacteristic
50C2×#13063256C2211yescharacteristic
51C2×#13063249C2211yescharacteristic
52C2×#13063249C2211yescharacteristic
53C2×#13063248C2211yescharacteristic
54C2×#13063248C2211yescharacteristic
55C2×#13063248C2211yescharacteristic
56C2×#13063248C2211yescharacteristic
57C2×#13063246C2211yescharacteristic
58C2×#13063246C2211yescharacteristic
59#14582855C2218yescomplemented
60C2×#13063236C2211yescharacteristic
61C2×#13063236C2211yescharacteristic
62C2×C4×C43⋊C8C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C43×#542—24no—
65C43×#542C2218yes—
66C2×C4⋊Q8×C43C2211yescharacteristic
67C2×#126×C43—21no—
68C2×#124×C43—21no—
69C2×#124×C43C2211yescharacteristic
70C2×#123×C43—21no—
71C2×C22⋊Q8×C43—21no—
72C2×C22⋊Q8×C43C2211yescharacteristic
73C2×#121×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C2×C4×D4×C43C2211yescharacteristic
76C2×#117×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×Dic86C2311yescharacteristic
79C2×#10621885—24no—
80C2×#10621885—24no—
81C2×#10621885C2314yes—
82C2×#10621885C2314yes—
83C2×#10621883—24no—
84C2×#10621883—24no—
85C2×#10621883C2314yes—
86C2×#10621883C2314yes—
87C2×#10621877—24no—
88C2×#10621877C2314yes—
89C22×C43⋊C8—24no—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2314yes—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95#13063325—22no—
96#13063325C2314yes—
97#13063318—28no—
98#13063318—28no—
99#13063317—22no—
100#13063317C2314yes—
101#13063315—28no—
102#13063315—28no—
103#13063304—22no—
104#13063304—22no—
105#13063304C2314yes—
106#13063304C2314yes—
107C4×Dic86—22no—
108C4×Dic86—22no—
109C4×Dic86C2314yes—
110C4×Dic86C2314yes—
111C2×C4⋊Dic43—21no—
112C2×C4⋊Dic43—21no—
113C2×C4⋊Dic43C2311yescharacteristic
114C2×C4⋊Dic43C2311yescharacteristic
115C2×Dic43⋊C4—21no—
116C2×Dic43⋊C4—21no—
117C2×Dic43⋊C4—21no—
118C2×Dic43⋊C4—21no—
119C2×Dic43⋊C4—21no—
120C2×Dic43⋊C4—21no—
121C2×C22⋊Dic43—21no—
122C2×C22⋊Dic43—21no—
123C2×C4×Dic43—21no—
124C2×C4×Dic43—21no—
125#13063258C2314yes—
126#13063258C2314yes—
127#13063256C2314yes—
128#13063256C2314yes—
129#13063249C2314yes—
130#13063249C2314yes—
131#13063248C2314yes—
132#13063248C2314yes—
133#13063248C2314yes—
134#13063248C2314yes—
135#13063246C2314yes—
136#13063246C2314yes—
137#13063236C2314yes—
138#13063236C2314yes—
139C4×C43⋊C8C2314yes—
140C4×C43⋊C8C2314yes—
141C22×Q8×C43—21no—
142C22×Q8×C43C2311yescharacteristic
143C22×D4×C43—21no—
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43—21no—
146C23×C4×C43C2311yescharacteristic
147C4⋊Q8×C43—22no—
148C4⋊Q8×C43C2314yes—
149#126×C43—28no—
150#124×C43—28no—
151#124×C43—22no—
152#124×C43C2314yes—
153#123×C43—28no—
154C22⋊Q8×C43—22no—
155C22⋊Q8×C43—28no—
156C22⋊Q8×C43C2314yes—
157#121×C43—22no—
158#121×C43C2314yes—
159C4×Q8×C43—22no—
160C4×Q8×C43C2314yes—
161C4×D4×C43—22no—
162C4×D4×C43C2314yes—
163#117×C43D414yes—
164#117×C43C2314yes—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43D411yescharacteristic
169C2×C4⋊C4×C43D411yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43D411yescharacteristic
178C2×C22⋊C4×C43D411yescharacteristic
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181C2×C42×C43C2311yescharacteristic
182C24×C43—21no—
183C24×C43C2×D411yescharacteristic
184C2×Q8×C43—21no—
185C2×Q8×C43—24no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43—82no—
189C2×Q8×C43C2412yes—
190C2×D4×C43—21no—
191C2×D4×C43—24no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—82no—
195C2×D4×C43C2412yes—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—24no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—82no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2412yes—
210C22×C4×C43C2411yescharacteristic
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C2×Dic86—22no—
216C2×Dic86—22no—
217C2×Dic86—22no—
218C2×Dic86—22no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86C2412yes—
222C2×Dic86C2412yes—
223C4⋊C4×C43—24no—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43C2×D414yes—
229C4⋊C4×C43C2×D414yes—
230C4⋊C4×C43C2412yes—
231C4⋊C4×C43C2412yes—
232C22⋊C4×C43—24no—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—24no—
235C22⋊C4×C43—24no—
236C22⋊C4×C43—24no—
237C22⋊C4×C43C2×D414yes—
238C22⋊C4×C43C2×D414yes—
239C42×C43—24no—
240C42×C43C2×D412yes—
241C42×C43C2×D412yes—
242C42×C43C2412yes—
243C42×C43C2412yes—
244C22⋊Dic43—24no—
245C22⋊Dic43—24no—
246#10621885—28no—
247#10621885—28no—
248#10621883—28no—
249#10621883—28no—
250C4⋊Dic43—24no—
251C4⋊Dic43—24no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262C4×Dic43—24no—
263C4×Dic43—24no—
264#10621877—28no—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—28no—
268C2×C43⋊C8#4114yes—
269C2×C43⋊C8#4114yes—
270C2×C43⋊C8C2412yes—
271C2×C43⋊C8C2412yes—
272C2×C43⋊C8C2412yes—
273C2×C43⋊C8C2412yes—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43C22×D412yes—
282C23×C43C22×D411yescharacteristic
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—42no—
286Q8×C43—84no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—42no—
290D4×C43—84no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—24no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—84no—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D412yes—
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C2×#4112yes—
313C2×C4×C43C2×#4112yes—
314C2×C4×C43C2511yescharacteristic
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323Dic86—22no—
324Dic86—22no—
325Dic86—22no—
326Dic86—22no—
327Dic86—42no—
328Dic86—42no—
329C43⋊C8—22no—
330C43⋊C8—22no—
331C43⋊C8C2×#4114yes—
332C43⋊C8C2×#4114yes—
333C2×#3178—431nomaximal, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—44no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—84no—
342C22×C43#53212yes—
343C22×C43#57712yes—
344C22×C43#57812yes—
345C22×C43C23×D411yescharacteristic
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43#53212yes—
355C4×C43C22×#4111yescharacteristic
356C4×C43C22×#4111yescharacteristic
357Dic43—42no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#542D4311yescharacteristic
362C2×#541—431no—
363#3178—4316no—
364C2×#501—431no—
365C2×#497—431no—
366C2×#488—431no—
367C2×#487—431no—
368C2×#470—431no—
369C2×#468—431no—
370C2×#467—431no—
371C2×#465—431no—
372C2×#441—431no—
373C2×#440—431no—
374C2×C4×Q16—431no—
375C2×C4×SD16—431no—
376C2×#405—431no—
377C2×C43—42no—
378C2×C43—82no—
379C2×C43#317814yescomplemented
380C2×C43C2×#53211yescharacteristic
381C2×C43C2×#57711yescharacteristic
382C2×C43C2×#57811yescharacteristic
383C22×Q16—431no—
384C22×Q16—431no—
385C22×SD16—431no—
386C22×SD16—431no—
387C22×M16—431no—
388C23×C8—431no—
389#542—24no—
390#542C2×D4318yes—
391#541—438no—
392#541—864no—
393C2×C4⋊Q8—431no—
394C2×C4⋊Q8C2×D4311yescharacteristic
395C2×#126—21no—
396C2×#126—861no—
397C2×#126—861no—
398C2×#125—431no—
399C2×#125—861no—
400C2×#125—861no—
401C2×#124—21no—
402C2×#124C2×D4311yescharacteristic
403C2×#123—21no—
404C2×C22⋊Q8—21no—
405C2×C22⋊Q8—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8C2×D4311yescharacteristic
408C2×#121C2×D4311yescharacteristic
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8C2×D4311yescharacteristic
412C2×C4×D4C2×D4311yescharacteristic
413C2×#117C2×D4311yescharacteristic
414#501—438no—
415#497—438no—
416#488—438no—
417#487—438no—
418#470—438no—
419#468—438no—
420#467—438no—
421#465—438no—
422#441—438no—
423#440—438no—
424C4×Q16—438no—
425C4×SD16—438no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#106—431no—
429C2×#106—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#102—431no—
437C2×#102—431no—
438#405—438no—
439C2×#97—431no—
440C2×#97—431no—
441C2×C4×C8—431no—
442C2×C4×C8—431no—
443C43C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—21no—
445C22×Q8—431no—
446C22×Q8—431no—
447C22×Q8C22×D4311yescharacteristic
448C22×D4—21no—
449C22×D4C22×D4311yescharacteristic
450C23×C4—21no—
451C23×C4C22×D4311yescharacteristic
452C2×Q16—434no—
453C2×Q16—434no—
454C2×Q16—864no—
455C2×Q16—864no—
456C2×SD16—434no—
457C2×SD16—434no—
458C2×SD16—864no—
459C2×SD16—864no—
460C2×M16—434no—
461C2×M16—864no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—431no—
465C22×C8—434no—
466C22×C8—431no—
467C22×C8—864no—
468C4⋊Q8—22no—
469C4⋊Q8—434no—
470C4⋊Q8—862no—
471C4⋊Q8C22×D4314yes—
472#126—28no—
473#126—868no—
474#126—868no—
475#125—434no—
476#125—868no—
477#125—868no—
478#125—862no—
479#124—28no—
480#124—22no—
481#124C22×D4314yes—
482#123—28no—
483C22⋊Q8—22no—
484C22⋊Q8—28no—
485C22⋊Q8—434no—
486C22⋊Q8—434no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489C22⋊Q8C22×D4314yes—
490#121—22no—
491#121C22×D4314yes—
492C4×Q8—22no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8C22×D4314yes—
498C4×D4—22no—
499C4×D4C22×D4314yes—
500#117C22⋊D4314yes—
501#117C22×D4314yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4C22⋊D4311yescharacteristic
516C2×C4⋊C4C22⋊D4311yescharacteristic
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4C22⋊D4311yescharacteristic
527C2×C22⋊C4C22⋊D4311yescharacteristic
528C2×C42—21no—
529C2×C42—861no—
530C2×C42—861no—
531C2×C42C22×D4311yescharacteristic
532C2×C42C22×D4311yescharacteristic
533#107—434no—
534#107—434no—
535#106—434no—
536#106—434no—
537#103—434no—
538#103—434no—
539#103—434no—
540#103—434no—
541#103—434no—
542#103—434no—
543#102—434no—
544#102—434no—
545#97—434no—
546#97—434no—
547C4×C8—434no—
548C4×C8—434no—
549C24—21no—
550C24C2×C22⋊D4311yescharacteristic
551C2×Q8—21no—
552C2×Q8—24no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—82no—
556C2×Q8—432no—
557C2×Q8—432no—
558C2×Q8—861no—
559C2×Q8—861no—
560C2×Q8—862no—
561C2×Q8—862no—
562C2×Q8—862no—
563C2×Q8—862no—
564C2×Q8C23×D4312yes—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—82no—
570C2×D4C23×D4312yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—82no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4C2×C22⋊D4312yes—
583C22×C4C2×C22⋊D4311yescharacteristic
584C22×C4C2×C22⋊D4311yescharacteristic
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C2×C22⋊D4311yescharacteristic
587C22×C4C2×C22⋊D4311yescharacteristic
588C22×C4C23×D4312yes—
589C22×C4C23×D4311yescharacteristic
590Q16—868no—
591Q16—868no—
592SD16—868no—
593SD16—868no—
594M16—868no—
595C2×C8—434no—
596C2×C8—434no—
597C2×C8—432no—
598C2×C8—432no—
599C2×C8—432no—
600C2×C8—432no—
601C2×C8—868no—
602C2×C8—862no—
603C2×C8—862no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—432no—
610C4⋊C4—432no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4C2×C22⋊D4314yes—
622C4⋊C4C2×C22⋊D4314yes—
623C4⋊C4C23×D4312yes—
624C4⋊C4C23×D4312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4C2×C22⋊D4314yes—
633C22⋊C4C2×C22⋊D4314yes—
634C42—24no—
635C42—864no—
636C42—864no—
637C42C2×C22⋊D4312yes—
638C42C2×C22⋊D4312yes—
639C42C23×D4312yes—
640C42C23×D4312yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C22×C22⋊D4312yes—
649C23C22×C22⋊D4311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—84no—
654Q8—862no—
655Q8—862no—
656Q8—862no—
657Q8—862no—
658Q8—1722no—
659Q8—1722no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—1722no—
684C2×C4—1722no—
685C2×C4—1722no—
686C2×C4—1722no—
687C2×C4C22×C22⋊D4312yes—
688C2×C4C22×C22⋊D4312yes—
689C2×C4C22×C22⋊D4312yes—
690C2×C4C22×C22⋊D4312yes—
691C2×C4C22×C22⋊D4312yes—
692C2×C4C22×C22⋊D4311yescharacteristic
693C2×C4#41×D4312yes—
694C2×C4#41×D4312yes—
695C2×C4C24×D4311yescharacteristic
696C8—434no—
697C8—434no—
698C8—862no—
699C8—862no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1458344512yes—
709C22#1458371012yes—
710C22#1458371412yes—
711C22C23×C22⋊D4311yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—1722no—
721C4—1722no—
722C4—1722no—
723C4—1722no—
724C4#1458344512yes—
725C4C2×#41×D4311yescharacteristic
726C4C2×#41×D4311yescharacteristic
727C2—42no—
728C2—82no—
729C2#1914525714yesdirect product factor
730C2C2×#1458344511yescharacteristic
731C2C2×#1458371011yescharacteristic
732C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#542C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenterC2×#542D43
hypocenterC43C2×#3178
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#14583511C2semidirect
2. #19145257C2direct (N × H)
3. C2×#14583305C2semidirect
4. C2×#14583294C2semidirect
5. C2×#14583253C2semidirect
6. C2×#14583251C2semidirect
7. C2×#14583155C2semidirect
9. C2×#14583138C2semidirect
11. C2×#14583004C2semidirect
12. C2×#14582999C2semidirect
13. C2×C4×#10621885C2semidirect
14. C2×C4×#10621883C2semidirect
15. C2×#14582855C2semidirect
24. #14583511C22semidirect
35. #14583305C22semidirect
36. #14583294C22semidirect
37. #14583253C22semidirect
38. #14583251C22semidirect
39. #14583155C22semidirect
41. #14583138C22semidirect
43. #14583004C22semidirect
44. #14582999C22semidirect
45. C4×#10621885C22semidirect
46. C4×#10621883C22semidirect
59. #14582855C22semidirect
379. C2×C43#3178semidirect
443. C43C2×#3178semidirect
729. C2#19145257direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835112
#191452572
C2×#145833052
C2×#145832942
C2×#145832532
C2×#145832512
C2×#145831552
C2×#145831432
C2×#145831382
C2×#145831262
C2×#145830042
C2×#145829992
C2×C4×#106218852
C2×C4×#106218832
C2×#145828552
C2×C43×#5422
C2×#317843