Finite Group Databasebeta

← C2×#19148477 #26005038

Subgroups — C2×#19148477 #26005038

Order 11008.

7022 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148477C2132yesmaximal, direct product factor
2C2×#14583626C214yesmaximal, complemented
3C2×#14583616C214yesmaximal, complemented
4C2×#14583585C214yesmaximal, complemented
5C2×#14583581C214yesmaximal, complemented
6C2×#14583512C211yesmaximal, characteristic, complemented
7C2×#14583511C211yesmaximal, characteristic, complemented
8C2×#14583510C211yesmaximal, characteristic, complemented
9C2×#14583472C212yesmaximal
10C2×#14583455C211yesmaximal, characteristic, complemented
11C2×#14583453C212yesmaximal, complemented
12C2×#14583451C212yesmaximal, complemented
13C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
14C2×#14583375C212yesmaximal, complemented
15C2×#14583367C211yesmaximal, characteristic
16C2×C43×#541C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Q8×D43C2212yes—
19#14583626C22164yescomplemented
20#14583616C22164yescomplemented
21#14583585C22164yescomplemented
22#14583581C22164yescomplemented
23#14583512C22116yescomplemented
24#14583511C22116yescomplemented
25#14583510C22116yescomplemented
26#14583472C22132yes—
27#14583455C22116yescomplemented
28#14583453C22132yescomplemented
29#14583451C22132yescomplemented
30C2×#13063325C2211yescharacteristic
31C2×#13063324C2214yes—
32C2×#13063324C2212yes—
33C2×#13063324C2214yes—
34C2×#13063323C2212yes—
35C4⋊Q8×D43C22116yescomplemented
36C2×#13063320C2214yes—
37C2×#13063320C2214yes—
38C2×#13063318C2214yes—
39C2×#13063317C2211yescharacteristic
40C2×#13063316C2214yes—
41C2×#13063315C2214yes—
42C2×#13063315C2214yes—
43C2×#13063315C2214yes—
44C2×#13063315C2214yes—
45C2×#13063311C2214yes—
46C2×#13063310C2214yes—
47C2×#13063307C2214yes—
48C2×#13063305C2212yes—
49C2×#13063304C2212yes—
50C2×#13063303C2214yes—
51C2×#13063303C2214yes—
52C2×#13063302C2214yes—
53C2×#13063301C2212yes—
54#14583375C22132yescomplemented
55#14583367C22116yes—
56C2×Q8×Dic43C2212yes—
57C2×C4×Dic86C2214yes—
58C2×C4×Dic86C2212yes—
59C2×C4×Dic86C2214yes—
60C2×#13063290C2212yes—
61C2×#13063290C2214yes—
62C2×#13063290C2214yes—
63C2×#13063290C2214yes—
64C2×#13063290C2212yes—
65C2×#13063287C2212yes—
66C2×(C22⋊D43)⋊C4C2212yes—
67C2×(C22⋊D43)⋊C4C2212yes—
68C2×#13063283C2214yes—
69C2×#13063283C2212yes—
70C2×#13063282C2211yescharacteristic
71C2×#13063282C2214yes—
72C2×#13063282C2214yes—
73C2×#13063282C2211yescharacteristic
74C2×#13063281C2214yes—
75C2×C4⋊C4×D43C2214yes—
76C22×C4×Dic43C2211yescharacteristic
77C2×C42×D43C2211yescharacteristic
78C2×C42×D43C2211yescharacteristic
79C43×#541C22116yescomplemented
80C2×C4⋊Q8×C43C2211yescharacteristic
81C2×#126×C43C2214yes—
82C2×#125×C43C2214yes—
83C2×#125×C43C2211yescharacteristic
84C2×C22⋊Q8×C43C2212yes—
85C2×C4×Q8×C43C2212yes—
86C2×#117×C43C2211yescharacteristic
87C2×#10621898—28no—
88C2×#10621898C2318yes—
89C22×Dic86C2314yes—
90C22×Dic86C2311yescharacteristic
91C22×Dic86C2312yes—
92C22×Dic86C2314yes—
93C2×Q8×D43—216no—
94C2×Q8×D43C23116yes—
95C22×D172C2311yescharacteristic
96C22×C22⋊D43C2311yescharacteristic
97C22×C22⋊D43C2311yescharacteristic
98C23×Dic43C2312yes—
99C22×C4×D43C2312yes—
100C22×C4×D43C2312yes—
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2314yes—
103C22×C4×D43C2311yescharacteristic
104#13063325C2318yes—
105#13063324C23132yes—
106#13063324C23132yes—
107#13063324C23116yes—
108#13063323C23116yes—
109#13063320C23132yes—
110#13063320C23132yes—
111#13063318C23132yes—
112#13063317C2318yes—
113#13063316C23132yes—
114#13063315C23132yes—
115#13063315C23132yes—
116#13063315C23132yes—
117#13063315C23132yes—
118#13063311C23132yes—
119#13063310C23132yes—
120#13063307C23132yes—
121#13063305C23116yes—
122#13063304C23116yes—
123#13063303C23132yes—
124#13063303C23132yes—
125#13063302C23132yes—
126#13063301C23116yes—
127Q8×Dic43C23116yes—
128C4×Dic86C23132yes—
129C4×Dic86C23132yes—
130C4×Dic86C23116yes—
131#13063290C23132yes—
132#13063290C23132yes—
133#13063290C23132yes—
134#13063290C23116yes—
135#13063290C23116yes—
136#13063287C23116yes—
137(C22⋊D43)⋊C4C23116yes—
138(C22⋊D43)⋊C4C23116yes—
139#13063283C23132yes—
140#13063283C23116yes—
141#13063282C23132yes—
142#13063282C23132yes—
143#13063282C2318yes—
144#13063282C2318yes—
145#13063281C23132yes—
146C2×C4⋊Dic43C2314yes—
147C2×C4⋊Dic43C2312yes—
148C2×C4⋊Dic43C2314yes—
149C2×C4⋊Dic43C2314yes—
150C2×Dic43⋊C4C2314yes—
151C2×Dic43⋊C4C2314yes—
152C2×Dic43⋊C4C2314yes—
153C2×Dic43⋊C4C2312yes—
154C2×Dic43⋊C4C2312yes—
155C2×Dic43⋊C4C2314yes—
156C2×Dic43⋊C4C2314yes—
157C2×Dic43⋊C4C2314yes—
158C2×Dic43⋊C4C2314yes—
159C2×Dic43⋊C4C2314yes—
160C4⋊C4×D43C23132yes—
161C2×C22⋊Dic43C2314yes—
162C2×(C2×D43)⋊C4C2312yes—
163C2×(C2×D43)⋊C4C2314yes—
164C2×(C2×D43)⋊C4C2312yes—
165C2×(C2×D43)⋊C4C2314yes—
166C2×(C2×D43)⋊C4C2314yes—
167C2×C4×Dic43C2311yescharacteristic
168C2×C4×Dic43C2312yes—
169C2×C4×Dic43C2312yes—
170C2×C4×Dic43C2311yescharacteristic
171C2×C4×Dic43C2312yes—
172C2×C4×Dic43C2318yes—
173C2×C4×Dic43C2314yes—
174C2×C4×Dic43C2314yes—
175C2×C4×Dic43C2314yes—
176C2×C4×Dic43C2314yes—
177C42×D43C2318yes—
178C42×D43C2318yes—
179C22×Q8×C43C2312yes—
180C23×C4×C43C2311yescharacteristic
181C4⋊Q8×C43C2318yes—
182#126×C43C23132yes—
183#125×C43C23132yes—
184#125×C43C2318yes—
185C22⋊Q8×C43C23116yes—
186C4×Q8×C43C23116yes—
187#117×C43C2318yes—
188C2×C4⋊C4×C43C2312yes—
189C2×C4⋊C4×C43C2312yes—
190C2×C4⋊C4×C43C2314yes—
191C2×C4⋊C4×C43C2314yes—
192C2×C4⋊C4×C43C2314yes—
193C2×C4⋊C4×C43C2314yes—
194C2×C22⋊C4×C43C2312yes—
195C2×C22⋊C4×C43C2314yes—
196C2×C42×C43C2311yescharacteristic
197C2×C42×C43C2311yescharacteristic
198C2×C42×C43C2314yes—
199C24×C43C2411yescharacteristic
200C23×D43C2411yescharacteristic
201C23×D43C2411yescharacteristic
202C2×Q8×C43—28no—
203C2×Q8×C43C2418yes—
204C22×C4×C43—24no—
205C22×C4×C43C2412yes—
206C22×C4×C43C2414yes—
207C22×C4×C43C2412yes—
208C22×C4×C43C2414yes—
209C22×C4×C43C2411yescharacteristic
210C22×C4×C43C2414yes—
211C22×C4×C43C2411yescharacteristic
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43C2414yes—
215C2×C22⋊D43C2414yes—
216C22×Dic43—28no—
217C22×Dic43C2412yes—
218C22×Dic43C2414yes—
219C22×Dic43C2414yes—
220C22×Dic43C2411yescharacteristic
221C22×Dic43C2418yes—
222C22×Dic43C2411yescharacteristic
223C22×Dic43C2412yes—
224Q8×D43—264no—
225#10621898—232no—
226C2×D172—24no—
227C2×D172C2414yes—
228C2×C4×D43—24no—
229C2×C4×D43—28no—
230C2×C4×D43—28no—
231C2×C4×D43—216no—
232C2×C4×D43#4118yes—
233C2×C4×D43C2418yes—
234C2×C4×D43C2418yes—
235C2×C4×D43C2414yes—
236C2×C4×D43C24116yes—
237C2×C4×D43C2414yes—
238C2×Dic86—28no—
239C2×Dic86—216no—
240C2×Dic86—24no—
241C2×Dic86—216no—
242C2×Dic86C24116yes—
243C2×Dic86C2414yes—
244C2×Dic86C2418yes—
245C2×Dic86C24116yes—
246C4⋊C4×C43C2418yes—
247C4⋊C4×C43C2418yes—
248C4⋊C4×C43C24116yes—
249C4⋊C4×C43C24116yes—
250C4⋊C4×C43C24116yes—
251C4⋊C4×C43C24116yes—
252C22⋊C4×C43C2418yes—
253C22⋊C4×C43C24116yes—
254C42×C43C2414yes—
255C42×C43C2414yes—
256C42×C43C24116yes—
257C22⋊Dic43C24116yes—
258(C2×D43)⋊C4C2418yes—
259(C2×D43)⋊C4C24116yes—
260(C2×D43)⋊C4C2418yes—
261(C2×D43)⋊C4C24116yes—
262(C2×D43)⋊C4C24116yes—
263C4⋊Dic43C24116yes—
264C4⋊Dic43C2418yes—
265C4⋊Dic43C24116yes—
266C4⋊Dic43C24116yes—
267Dic43⋊C4C24116yes—
268Dic43⋊C4C24116yes—
269Dic43⋊C4C24116yes—
270Dic43⋊C4C2418yes—
271Dic43⋊C4C2418yes—
272Dic43⋊C4C24116yes—
273Dic43⋊C4C24116yes—
274Dic43⋊C4C24116yes—
275Dic43⋊C4C24116yes—
276Dic43⋊C4C24116yes—
277C4×Dic43C2414yes—
278C4×Dic43C2418yes—
279C4×Dic43C2418yes—
280C4×Dic43C2414yes—
281C4×Dic43C2418yes—
282C4×Dic43C24116yes—
283C4×Dic43C24116yes—
284C4×Dic43C24116yes—
285C4×Dic43C24116yes—
286C23×C43—22no—
287C23×C43—24no—
288C23×C43C2512yes—
289C23×C43C2511yescharacteristic
290C22×D43—24no—
291C22×D43—22no—
292C22×D43—24no—
293C22×D43C2×#4114yes—
294C22×D43C2512yes—
295C22×D43C2512yes—
296Q8×C43—216no—
297C2×C4×C43—28no—
298C2×C4×C43—22no—
299C2×C4×C43—28no—
300C2×C4×C43—24no—
301C2×C4×C43—24no—
302C2×C4×C43—28no—
303C2×C4×C43C2×#4114yes—
304C2×C4×C43C2514yes—
305C2×C4×C43C2512yes—
306C2×C4×C43C2518yes—
307C2×C4×C43C2514yes—
308C2×C4×C43C2518yes—
309C2×C4×C43C2512yes—
310C22⋊D43—28no—
311C22⋊D43—28no—
312C2×Dic43—28no—
313C2×Dic43—22no—
314C2×Dic43—28no—
315C2×Dic43—24no—
316C2×Dic43—216no—
317C2×Dic43C2×#4114yes—
318C2×Dic432−1+418yes—
319C2×Dic43C2514yes—
320C2×Dic43C2518yes—
321C2×Dic43C2512yes—
322C2×Dic43C2518yes—
323C2×Dic43C2512yes—
324C2×Dic43C2514yes—
325D172—28no—
326C4×D43—232no—
327C4×D43—28no—
328C4×D43—216no—
329C4×D43—216no—
330C4×D43C2×#41116yes—
331Dic86—216no—
332Dic86—28no—
333Dic86—232no—
334Dic86—232no—
335C2×#3509—431nomaximal, Sylow
336C22×C43—22no—
337C22×C43—24no—
338C22×C43—44no—
339C22×C43C22×#4112yes—
340C22×C43C2×2−1+414yes—
341C22×C43C2611yescharacteristic
342C2×D43—24no—
343C2×D43—28no—
344C2×D43—22no—
345C2×D43—24no—
346C2×D43—44no—
347C2×D43C22×#4114yes—
348C4×C43—28no—
349C4×C43—22no—
350C4×C43—28no—
351C4×C43—24no—
352C4×C43—24no—
353C4×C43C22×#4114yes—
354Dic43—28no—
355Dic43—22no—
356Dic43—28no—
357Dic43—24no—
358Dic43C22×#4114yes—
359Dic43C2×2−1+418yes—
360#3509—4332no—
361C2×#557—434no—
362C2×#556—434no—
363C2×#552—434no—
364C2×#552—434no—
365C2×#541—431no—
366C2×#541—431no—
367C2×#541—431no—
368C2×#541D4311yescharacteristic, complemented
369C2×#536—432no—
370C2×#533—431no—
371C2×#533—432no—
372C2×#533—432no—
373C22×C4⋊Q8—431no—
374C2×#519—432no—
375C2×C4×#41—431no—
376C2×C43—42no—
377C2×C43#350914yescomplemented
378C2×C43C23×#4111yescharacteristic
379C2×C43C22×2−1+412yes—
380D43—24no—
381D43—42no—
382C22×#41—431no—
383C23×Q8—432no—
384#557—4364no—
385#556—4364no—
386#552—4364no—
387#552—4364no—
388#541—4316no—
389#541—4316no—
390#541—4316no—
391#541C2×D43116yescomplemented
392#536—4332no—
393#533—4316no—
394#533—4332no—
395#533—4332no—
396C2×C4⋊Q8—432no—
397C2×C4⋊Q8—4316no—
398C2×C4⋊Q8—434no—
399C2×C4⋊Q8—432no—
400C2×C4⋊Q8—434no—
401C2×C4⋊Q8—431no—
402C2×C4⋊Q8C2×D4311yescharacteristic
403C2×#126—434no—
404C2×#126—434no—
405C2×#126—434no—
406C2×#126C2×D4314yes—
407C2×#125—434no—
408C2×#125—434no—
409C2×#125—434no—
410C2×#125—434no—
411C2×#125—434no—
412C2×#125—431no—
413C2×#125C2×D4311yescharacteristic
414C2×#125C2×D4314yes—
415C2×#124—434no—
416C2×#123—434no—
417C2×#123—434no—
418C2×C22⋊Q8—432no—
419C2×C22⋊Q8—432no—
420C2×C22⋊Q8—434no—
421C2×C22⋊Q8—434no—
422C2×C22⋊Q8—432no—
423C2×C22⋊Q8—434no—
424C2×C22⋊Q8C2×D4312yes—
425#519—4332no—
426C4×#41—4316no—
427C2×C4×Q8—432no—
428C2×C4×Q8—432no—
429C2×C4×Q8—432no—
430C2×C4×Q8—434no—
431C2×C4×Q8—434no—
432C2×C4×Q8—434no—
433C2×C4×Q8—432no—
434C2×C4×Q8—434no—
435C2×C4×Q8—434no—
436C2×C4×Q8C2×D4312yes—
437C2×C4×D4—432no—
438C2×C4×D4—432no—
439C2×C4×D4—432no—
440C2×#117—432no—
441C2×#117—434no—
442C2×#117—434no—
443C2×#117—431no—
444C2×#117—431no—
445C2×#117—434no—
446C2×#117—434no—
447C2×#117C2×D4311yescharacteristic
448C22×C4⋊C4—434no—
449C22×C42—431no—
450C22×C42—431no—
451C22×C42—431no—
452C43C2×#350911yescharacteristic, complemented, Sylow
453C2×#41—438no—
454C2×#41—868no—
455C22×Q8—4316no—
456C22×Q8—434no—
457C22×Q8—432no—
458C22×Q8—434no—
459C22×Q8—431no—
460C22×Q8—8616no—
461C22×Q8C22×D4312yes—
462C22×D4—431no—
463C22×D4—431no—
464C22×D4—431no—
465C23×C4—431no—
466C23×C4—432no—
467C23×C4—434no—
468C23×C4—432no—
469C23×C4—432no—
470C23×C4—431no—
471C23×C4C22×D4311yescharacteristic
472C4⋊Q8—4316no—
473C4⋊Q8—4332no—
474C4⋊Q8—4316no—
475C4⋊Q8—4332no—
476C4⋊Q8—438no—
477C4⋊Q8C22×D4318yes—
478#126—4332no—
479#126—4332no—
480#126—4332no—
481#126C22×D43132yes—
482#125—4332no—
483#125—4332no—
484#125—4332no—
485#125—4332no—
486#125—4332no—
487#125—438no—
488#125C22×D4318yes—
489#125C22×D43132yes—
490#124—4332no—
491#123—4332no—
492#123—4332no—
493C22⋊Q8—4316no—
494C22⋊Q8—4316no—
495C22⋊Q8—4316no—
496C22⋊Q8—4332no—
497C22⋊Q8—4332no—
498C22⋊Q8—4332no—
499C22⋊Q8C22×D43116yes—
500C4×Q8—4316no—
501C4×Q8—4316no—
502C4×Q8—4316no—
503C4×Q8—4332no—
504C4×Q8—4332no—
505C4×Q8—4332no—
506C4×Q8—4316no—
507C4×Q8—4332no—
508C4×Q8—4332no—
509C4×Q8C22×D43116yes—
510C4×D4—4316no—
511C4×D4—4316no—
512C4×D4—4316no—
513#117—4316no—
514#117—4332no—
515#117—4332no—
516#117—438no—
517#117—438no—
518#117—4332no—
519#117—4332no—
520#117C22×D4318yes—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—432no—
526C2×C4⋊C4—432no—
527C2×C4⋊C4—432no—
528C2×C4⋊C4—434no—
529C2×C4⋊C4—434no—
530C2×C4⋊C4—434no—
531C2×C4⋊C4—434no—
532C2×C4⋊C4—434no—
533C2×C4⋊C4—434no—
534C2×C4⋊C4—434no—
535C2×C4⋊C4—4332no—
536C2×C4⋊C4C22×D4314yes—
537C2×C4⋊C4C22×D4312yes—
538C2×C4⋊C4C22×D4314yes—
539C2×C4⋊C4C22×D4312yes—
540C2×C4⋊C4C22×D4314yes—
541C2×C4⋊C4C22×D4314yes—
542C2×C22⋊C4—434no—
543C2×C22⋊C4—432no—
544C2×C22⋊C4—434no—
545C2×C22⋊C4—432no—
546C2×C22⋊C4—434no—
547C2×C22⋊C4—434no—
548C2×C22⋊C4C22×D4314yes—
549C2×C22⋊C4C22×D4312yes—
550C2×C42—431no—
551C2×C42—434no—
552C2×C42—434no—
553C2×C42—434no—
554C2×C42—434no—
555C2×C42—432no—
556C2×C42—432no—
557C2×C42—432no—
558C2×C42—438no—
559C2×C42—431no—
560C2×C42—438no—
561C2×C42—438no—
562C2×C42C22×D4314yes—
563C2×C42C22×D4311yescharacteristic
564C2×C42C22×D4311yescharacteristic
565C24—431no—
566C24—431no—
567C24C23×D4311yescharacteristic
568#41—8632no—
569C2×Q8—28no—
570C2×Q8—4316no—
571C2×Q8—438no—
572C2×Q8—4316no—
573C2×Q8—434no—
574C2×Q8—8616no—
575C2×Q8—864no—
576C2×Q8—8616no—
577C2×Q8—8664no—
578C2×Q8—868no—
579C2×Q8C23×D4318yes—
580C2×D4—434no—
581C2×D4—434no—
582C2×D4—434no—
583C2×D4—864no—
584C2×D4—864no—
585C2×D4—864no—
586C22×C4—24no—
587C22×C4—431no—
588C22×C4—432no—
589C22×C4—438no—
590C22×C4—434no—
591C22×C4—438no—
592C22×C4—432no—
593C22×C4—434no—
594C22×C4—434no—
595C22×C4—431no—
596C22×C4—438no—
597C22×C4—438no—
598C22×C4—434no—
599C22×C4—4316no—
600C22×C4—868no—
601C22×C4—868no—
602C22×C4—8616no—
603C22×C4—868no—
604C22×C4—864no—
605C22×C4C23×D4314yes—
606C22×C4C23×D4312yes—
607C22×C4C23×D4314yes—
608C22×C4C23×D4311yescharacteristic
609C22×C4C23×D4312yes—
610C22×C4C23×D4314yes—
611C22×C4C23×D4311yescharacteristic
612C4⋊C4—4316no—
613C4⋊C4—4316no—
614C4⋊C4—4316no—
615C4⋊C4—4316no—
616C4⋊C4—438no—
617C4⋊C4—438no—
618C4⋊C4—438no—
619C4⋊C4—4316no—
620C4⋊C4—4316no—
621C4⋊C4—4316no—
622C4⋊C4—4316no—
623C4⋊C4—4316no—
624C4⋊C4—4316no—
625C4⋊C4—4316no—
626C4⋊C4C23×D43116yes—
627C4⋊C4C23×D4318yes—
628C4⋊C4C23×D43116yes—
629C4⋊C4C23×D4318yes—
630C4⋊C4C23×D43116yes—
631C4⋊C4C23×D43116yes—
632C22⋊C4—4316no—
633C22⋊C4—438no—
634C22⋊C4—4316no—
635C22⋊C4—438no—
636C22⋊C4—4316no—
637C22⋊C4—4316no—
638C22⋊C4C23×D43116yes—
639C22⋊C4C23×D4318yes—
640C42—434no—
641C42—434no—
642C42—438no—
643C42—438no—
644C42—438no—
645C42—4316no—
646C42—4316no—
647C42—4316no—
648C42—4316no—
649C42C23×D4314yes—
650C42C23×D4314yes—
651C42C23×D43116yes—
652C23—22no—
653C23—24no—
654C23—434no—
655C23—432no—
656C23—432no—
657C23—864no—
658C23—862no—
659C23—864no—
660C23C24×D4312yes—
661C23C24×D4311yescharacteristic
662Q8—216no—
663Q8—8632no—
664Q8—868no—
665Q8—8632no—
666Q8—8616no—
667D4—868no—
668D4—868no—
669D4—868no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—434no—
677C2×C4—438no—
678C2×C4—432no—
679C2×C4—434no—
680C2×C4—4316no—
681C2×C4—434no—
682C2×C4—438no—
683C2×C4—438no—
684C2×C4—432no—
685C2×C4—8616no—
686C2×C4—8616no—
687C2×C4—8632no—
688C2×C4—8616no—
689C2×C4—862no—
690C2×C4—868no—
691C2×C4—864no—
692C2×C4—868no—
693C2×C4—868no—
694C2×C4#41×D4314yes—
695C2×C4C24×D4314yes—
696C2×C4C24×D4318yes—
697C2×C4C24×D4312yes—
698C2×C4C24×D4314yes—
699C2×C4C24×D4318yes—
700C2×C4C24×D4312yes—
701C22—22no—
702C22—24no—
703C22—44no—
704C22—434no—
705C22—864no—
706C22—868no—
707C22—862no—
708C22—864no—
709C22—1724no—
710C22C2×#41×D4312yes—
711C222−1+4×D4314yes—
712C22C25×D4311yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—434no—
719C4—438no—
720C4—862no—
721C4—868no—
722C4—864no—
723C4—868no—
724C4C2×#41×D4314yes—
725C2—42no—
726C2—864no—
727C2—1722no—
728C2#1914847714yesdirect product factor
729C2C22×#41×D4311yescharacteristic
730C2C2×2−1+4×D4312yes—
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#541C2
socleC23×C43C25
prime radicalC22×#10621898C22
hypercenterC2×#541D43
hypocenterC43C2×#3509
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #19148477C2direct (N × H)
2. C2×#14583626C2semidirect
3. C2×#14583616C2semidirect
4. C2×#14583585C2semidirect
5. C2×#14583581C2semidirect
6. C2×#14583512C2semidirect
7. C2×#14583511C2semidirect
8. C2×#14583510C2semidirect
10. C2×#14583455C2semidirect
11. C2×#14583453C2semidirect
12. C2×#14583451C2semidirect
13. C2×C4⋊Q8×D43C2semidirect
14. C2×#14583375C2semidirect
16. C2×C43×#541C2semidirect
19. #14583626C22semidirect
20. #14583616C22semidirect
21. #14583585C22semidirect
22. #14583581C22semidirect
23. #14583512C22semidirect
24. #14583511C22semidirect
25. #14583510C22semidirect
27. #14583455C22semidirect
28. #14583453C22semidirect
29. #14583451C22semidirect
35. C4⋊Q8×D43C22semidirect
54. #14583375C22semidirect
79. C43×#541C22semidirect
368. C2×#541D43semidirect
377. C2×C43#3509semidirect
391. #541C2×D43semidirect
452. C43C2×#3509semidirect
728. C2#19148477direct (N × H)

Maximal subgroups

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

subgroupindex
#191484772
C2×#145836262
C2×#145836162
C2×#145835852
C2×#145835812
C2×#145835122
C2×#145835112
C2×#145835102
C2×#145834722
C2×#145834552
C2×#145834532
C2×#145834512
C2×C4⋊Q8×D432
C2×#145833752
C2×#145833672
C2×C43×#5412
C2×#350943