Finite Group Databasebeta

← C2×#19148212 #26003689

Subgroups — C2×#19148212 #26003689

Order 11008.

7706 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148212C2132yesmaximal, direct product factor
2C2×#14583625C211yesmaximal, characteristic, complemented
3C2×#14583621C213yesmaximal, complemented
4C2×#14583590C213yesmaximal, complemented
5C2×#14583584C213yesmaximal, complemented
6C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
7C2×#14583561C211yesmaximal, characteristic, complemented
8C2×#14583560C211yesmaximal, characteristic, complemented
9C2×#14583550C213yesmaximal, complemented
10C2×#14583453C213yesmaximal, complemented
11C2×#14583436C213yesmaximal, complemented
12C2×#14583433C213yesmaximal, complemented
13C2×C4×#10621902C211yesmaximal, characteristic, complemented
14C2×C4×#10621898C213yesmaximal, complemented
15C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C43C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621898C2213yes—
19C22×Q8×D43C2211yescharacteristic
20#14583625C22116yescomplemented
21#14583621C22148yescomplemented
22#14583590C22148yescomplemented
23#14583584C22148yescomplemented
24Q8×C22⋊D43C22116yescomplemented
25#14583561C22116yescomplemented
26#14583560C22116yescomplemented
27#14583550C22148yescomplemented
28#14583453C22148yescomplemented
29C2×#13063324C2213yes—
30C2×#13063323C2213yes—
31#14583436C22148yescomplemented
32#14583433C22148yescomplemented
33C2×#13063320C2216yes—
34C2×#13063319C2216yes—
35C2×#13063317C2213yes—
36C2×#13063316C2213yes—
37C2×#13063315C2216yes—
38C2×#13063314C2213yes—
39C2×#13063313C2213yes—
40C2×#13063310C2216yes—
41C2×#13063308C2216yes—
42C2×#13063305C2213yes—
43C2×#13063304C2213yes—
44C2×#13063303C2216yes—
45C2×#13063301C2213yes—
46C2×#13063301C2213yes—
47C2×#13063300C2213yes—
48C2×#13063299C2213yes—
49C4×#10621902C22116yescomplemented
50C4×#10621898C22148yescomplemented
51C2×Q8×Dic43C2211yescharacteristic
52C2×Q8×Dic43C2211yescharacteristic
53C2×C4×Dic86C2213yes—
54C2×C4×Dic86C2213yes—
55C2×C4×Dic86C2213yes—
56C2×#13063290C2213yes—
57C4×Q8×D43C22116yescomplemented
58C2×C4×D172C2213yes—
59C2×C4×D172C2213yes—
60C2×C4×D172C2213yes—
61C2×#13063287C2213yes—
62C2×C4×C22⋊D43C2213yes—
63C2×C4×C22⋊D43C2213yes—
64C2×C4×C22⋊D43C2213yes—
65C2×C4×C22⋊D43C2211yescharacteristic
66C2×#13063284C2213yes—
67C2×#13063283C2213yes—
68C2×#13063282C2213yes—
69C2×#13063282C2216yes—
70C2×#13063282C2213yes—
71C2×C4⋊C4×D43C2213yes—
72C2×C42×D43C2213yes—
73C2×C42×D43C2213yes—
74C23×Q8×C43C2211yescharacteristic
75C2×C4×Q8×C43C2211yescharacteristic
76C2×C4×Q8×C43C2211yescharacteristic
77C2×C4×Q8×C43C2213yes—
78C2×C4×Q8×C43C2213yes—
79C2×C4×Q8×C43C22116yescomplemented
80C22×C4⋊C4×C43C2213yes—
81C22×C42×C43C2213yes—
82C2×#10621902—28no—
83C2×#10621902C2318yes—
84C2×#10621898—224no—
85C2×#10621898C23124yes—
86C22×Dic86C2313yes—
87C22×Dic86C2313yes—
88C2×Q8×D43—28no—
89C2×Q8×D43C2318yes—
90C22×D172C2313yes—
91C22×D172C2313yes—
92C22×C22⋊D43C2313yes—
93C22×C22⋊D43C2311yescharacteristic
94C22×C4×D43C2311yescharacteristic
95C22×C4×D43C2313yes—
96C22×C4×D43C2313yes—
97C22×C4×D43C2313yes—
98C22×C4×D43C2313yes—
99C22×C4×D43C2313yes—
100#13063324C23124yes—
101#13063323C23124yes—
102#13063320C23148yes—
103#13063319C23148yes—
104#13063317C23124yes—
105#13063316C23124yes—
106#13063315C23148yes—
107#13063314C23124yes—
108#13063313C23124yes—
109#13063310C23148yes—
110#13063308C23148yes—
111#13063305C23124yes—
112#13063304C23124yes—
113#13063303C23148yes—
114#13063301C23124yes—
115#13063301C23124yes—
116#13063300C23124yes—
117#13063299C23124yes—
118Q8×Dic43C2318yes—
119Q8×Dic43C2318yes—
120C4×Dic86C23124yes—
121C4×Dic86C23124yes—
122C4×Dic86C23124yes—
123#13063290C23124yes—
124C4×D172C23124yes—
125C4×D172C23124yes—
126C4×D172C23124yes—
127#13063287C23124yes—
128C4×C22⋊D43C23124yes—
129C4×C22⋊D43C23124yes—
130C4×C22⋊D43C2318yes—
131C4×C22⋊D43C23124yes—
132#13063284C23124yes—
133#13063283C23124yes—
134#13063282C23124yes—
135#13063282C23124yes—
136#13063282C23148yes—
137C2×C4⋊Dic43C2313yes—
138C2×C4⋊Dic43C2313yes—
139C2×C4⋊Dic43C2313yes—
140C2×C4⋊Dic43C2313yes—
141C2×Dic43⋊C4C2316yes—
142C2×Dic43⋊C4C2311yescharacteristic
143C2×Dic43⋊C4C2313yes—
144C2×Dic43⋊C4C2313yes—
145C2×Dic43⋊C4C2313yes—
146C2×Dic43⋊C4C2316yes—
147C2×Dic43⋊C4C2316yes—
148C4⋊C4×D43C23124yes—
149C2×C22⋊Dic43C2311yescharacteristic
150C2×C22⋊Dic43C2313yes—
151C2×(C2×D43)⋊C4C2311yescharacteristic
152C2×(C2×D43)⋊C4C2313yes—
153C2×(C2×D43)⋊C4C2313yes—
154C2×(C2×D43)⋊C4C2313yes—
155C2×(C2×D43)⋊C4C2316yes—
156C2×(C2×D43)⋊C4C2316yes—
157C2×(C2×D43)⋊C4C2316yes—
158C2×C4×Dic43C2311yescharacteristic
159C2×C4×Dic43C2313yes—
160C2×C4×Dic43C2313yes—
161C2×C4×Dic43C2313yes—
162C2×C4×Dic43C2313yes—
163C2×C4×Dic43C2313yes—
164C42×D43C23124yes—
165C42×D43C23124yes—
166C22×Q8×C43—28no—
167C22×Q8×C43C2318yes—
168C22×Q8×C43C2313yes—
169C22×Q8×C43C2311yescharacteristic
170C23×C4×C43C2311yescharacteristic
171C23×C4×C43C2313yes—
172C23×C4×C43C2313yes—
173C4×Q8×C43C2318yes—
174C4×Q8×C43C23124yes—
175C4×Q8×C43C2318yes—
176C4×Q8×C43C23124yes—
177C2×C4⋊C4×C43C2313yes—
178C2×C4⋊C4×C43C2313yes—
179C2×C4⋊C4×C43C2316yes—
180C2×C4⋊C4×C43C23124yes—
181C2×C42×C43C2313yes—
182C2×C42×C43C2313yes—
183C2×C42×C43C2313yes—
184C2×C42×C43C2313yes—
185C2×C42×C43C23124yes—
186C24×C43C2411yescharacteristic
187C23×D43C2413yes—
188C23×D43C2411yescharacteristic
189C2×Q8×C43—232no—
190C2×Q8×C43—212no—
191C2×Q8×C43#4118yescomplemented
192C2×Q8×C43C24112yes—
193C2×Q8×C43C2414yes—
194C22×C4×C43—212no—
195C22×C4×C43—24no—
196C22×C4×C43—212no—
197C22×C4×C43C2411yescharacteristic
198C22×C4×C43C2414yes—
199C22×C4×C43C2413yes—
200C22×C4×C43C2413yes—
201C22×C4×C43C24112yes—
202C22×C4×C43C2413yes—
203C22×C4×C43C24112yes—
204C22×C4×C43C2413yes—
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—212no—
207C2×C22⋊D43#4118yescomplemented
208C2×C22⋊D43C24112yes—
209C2×C22⋊D43C2414yes—
210C22×Dic43C2411yescharacteristic
211C22×Dic43C2411yescharacteristic
212C22×Dic43C2413yes—
213C22×Dic43C2413yes—
214C22×Dic43C2413yes—
215C22×Dic43C2411yescharacteristic
216#10621902—232no—
217Q8×D43—232no—
218#10621898—296no—
219C2×D172—212no—
220C2×D172—212no—
221C2×D172C24112yes—
222C2×D172C24112yes—
223C2×C4×D43—212no—
224C2×C4×D43—212no—
225C2×C4×D43—24no—
226C2×C4×D43—212no—
227C2×C4×D43—212no—
228C2×C4×D43—212no—
229C2×C4×D43C2414yes—
230C2×C4×D43C24112yes—
231C2×C4×D43C24112yes—
232C2×C4×D43C24112yes—
233C2×C4×D43C24112yes—
234C2×C4×D43C24112yes—
235C2×Dic86—212no—
236C2×Dic86—212no—
237C2×Dic86C24112yes—
238C2×Dic86C24112yes—
239C4⋊C4×C43C24112yes—
240C4⋊C4×C43C24112yes—
241C4⋊C4×C43C24124yes—
242C42×C43C24112yes—
243C42×C43C24112yes—
244C42×C43C24112yes—
245C42×C43C24112yes—
246C22⋊Dic43C2414yes—
247C22⋊Dic43C24112yes—
248(C2×D43)⋊C4C2414yes—
249(C2×D43)⋊C4C24112yes—
250(C2×D43)⋊C4C24112yes—
251(C2×D43)⋊C4C24112yes—
252(C2×D43)⋊C4C24124yes—
253(C2×D43)⋊C4C24124yes—
254(C2×D43)⋊C4C24124yes—
255C4⋊Dic43C24112yes—
256C4⋊Dic43C24112yes—
257C4⋊Dic43C24112yes—
258C4⋊Dic43C24112yes—
259Dic43⋊C4C24124yes—
260Dic43⋊C4C2414yes—
261Dic43⋊C4C24112yes—
262Dic43⋊C4C24112yes—
263Dic43⋊C4C24112yes—
264Dic43⋊C4C24124yes—
265Dic43⋊C4C24124yes—
266C4×Dic43C2414yes—
267C4×Dic43C24112yes—
268C4×Dic43C24112yes—
269C4×Dic43C24112yes—
270C4×Dic43C24112yes—
271C4×Dic43C24112yes—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43C2×#4114yes—
275C23×C43C2512yes—
276C23×C43C2511yescharacteristic
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—26no—
280C22×D43—26no—
281C22×D43—26no—
282C22×D43C2×#4114yes—
283C22×D43C2516yes—
284C22×D43C2512yes—
285Q8×C43—224no—
286Q8×C43C2×#41116yescomplemented
287C2×C4×C43—26no—
288C2×C4×C43—26no—
289C2×C4×C43—224no—
290C2×C4×C43—26no—
291C2×C4×C43—22no—
292C2×C4×C43—224no—
293C2×C4×C43—28no—
294C2×C4×C43C2×#41112yes—
295C2×C4×C432−1+414yes—
296C2×C4×C43C2516yes—
297C2×C4×C43C2512yes—
298C2×C4×C43C2516yes—
299C2×C4×C43C2516yes—
300C2×C4×C43C2516yes—
301C2×C4×C43C2512yes—
302C22⋊D43—224no—
303C22⋊D43C2×#41116yescomplemented
304C2×Dic43—26no—
305C2×Dic43—26no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—26no—
309C2×Dic43C2×#4114yes—
310C2×Dic43C2512yes—
311C2×Dic43C2512yes—
312C2×Dic43C2516yes—
313C2×Dic43C2516yes—
314C2×Dic43C2516yes—
315C2×Dic43C2512yes—
316D172—224no—
317D172—224no—
318C4×D43—224no—
319C4×D43—224no—
320C4×D43—224no—
321C4×D43—28no—
322C4×D43—224no—
323C4×D43—224no—
324Dic86—224no—
325Dic86—224no—
326C2×#3482—431nomaximal, Sylow
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—28no—
330C22×C43C22×#4114yes—
331C22×C43C22×#4112yes—
332C22×C43C22×#4112yes—
333C22×C43C2×2−1+412yes—
334C22×C43C2611yescharacteristic
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—28no—
338C2×D43—26no—
339C2×D43—26no—
340C2×D43—26no—
341C2×D43—412no—
342C2×D43C22×#4114yes—
343C4×C43—26no—
344C4×C43—26no—
345C4×C43—26no—
346C4×C43—22no—
347C4×C43C22×#41112yes—
348C4×C43C2×2−1+414yes—
349Dic43—26no—
350Dic43—26no—
351Dic43—22no—
352Dic43—22no—
353Dic43—26no—
354Dic43C22×#4114yes—
355#3482—4332no—
356C2×#557—431no—
357C2×#556—433no—
358C2×#552—433no—
359C2×#552—433no—
360C2×D4×Q8—431no—
361C2×#548—431no—
362C2×#548—431no—
363C2×#547—433no—
364C2×#533—433no—
365C2×#529—433no—
366C2×#529—433no—
367C2×C4×#41—433no—
368C2×C4×#41—431no—
369C22×C4×Q8—431no—
370C22×C4×Q8D4311yescharacteristic, complemented
371C2×C43—24no—
372C2×C43#348214yescomplemented
373C2×C43C23×#4111yescharacteristic
374C2×C43C23×#4111yescharacteristic
375C2×C43C22×2−1+411yescharacteristic
376D43—24no—
377D43—46no—
378C22×#41—431no—
379C22×#41—433no—
380C23×Q8—431no—
381C23×Q8C2×D4311yescharacteristic
382#557—4316no—
383#556—4348no—
384#552—4348no—
385#552—4348no—
386D4×Q8—4316no—
387#548—4316no—
388#548—4316no—
389#547—4348no—
390#533—4348no—
391C2×C4⋊Q8—433no—
392C2×C4⋊Q8—433no—
393#529—4348no—
394#529—4348no—
395C2×#126—436no—
396C2×#126—436no—
397C2×#125—433no—
398C2×#125—436no—
399C2×#125—433no—
400C2×#124—433no—
401C2×#124—433no—
402C2×#123—436no—
403C2×#123—436no—
404C2×C22⋊Q8—433no—
405C2×C22⋊Q8—433no—
406C2×C22⋊Q8—433no—
407C2×C22⋊Q8—436no—
408C2×C22⋊Q8—433no—
409C2×#121—433no—
410C2×#121—433no—
411C4×#41—4316no—
412C4×#41—4348no—
413C2×C4×Q8—431no—
414C2×C4×Q8—431no—
415C2×C4×Q8—4316no—
416C2×C4×Q8—433no—
417C2×C4×Q8—433no—
418C2×C4×Q8—433no—
419C2×C4×Q8—433no—
420C2×C4×Q8C2×D4311yescharacteristic
421C2×C4×Q8C2×D4313yes—
422C2×C4×Q8C2×D4311yescharacteristic
423C2×C4×Q8C2×D4313yes—
424C2×C4×Q8C2×D43116yescomplemented
425C2×C4×D4—431no—
426C2×C4×D4—433no—
427C2×C4×D4—433no—
428C2×C4×D4—433no—
429C2×C4×D4—433no—
430C2×C4×D4—433no—
431C2×C4×D4—433no—
432C2×C4×D4—433no—
433C2×#117—433no—
434C2×#117—433no—
435C2×#117—433no—
436C2×#117—433no—
437C2×#117—436no—
438C22×C4⋊C4—433no—
439C22×C4⋊C4C2×D4313yes—
440C22×C42—433no—
441C22×C42—433no—
442C22×C42C2×D4313yes—
443C43C2×#348211yescharacteristic, complemented, Sylow
444C2×#41—438no—
445C2×#41—4324no—
446C2×#41—8624no—
447C2×#41—868no—
448C22×Q8—28no—
449C22×Q8—438no—
450C22×Q8—433no—
451C22×Q8—433no—
452C22×Q8—868no—
453C22×Q8C22×D4313yes—
454C22×Q8C22×D4318yes—
455C22×Q8C22×D4311yescharacteristic
456C22×D4—431no—
457C22×D4—433no—
458C22×D4—433no—
459C22×D4—433no—
460C23×C4—433no—
461C23×C4—433no—
462C23×C4—433no—
463C23×C4—433no—
464C23×C4—433no—
465C23×C4—431no—
466C23×C4C22×D4313yes—
467C23×C4C22×D4313yes—
468C23×C4C22×D4311yescharacteristic
469C4⋊Q8—4324no—
470C4⋊Q8—4324no—
471#126—4348no—
472#126—4348no—
473#125—4324no—
474#125—4348no—
475#125—4324no—
476#124—4324no—
477#124—4324no—
478#123—4348no—
479#123—4348no—
480C22⋊Q8—4324no—
481C22⋊Q8—4324no—
482C22⋊Q8—4324no—
483C22⋊Q8—4348no—
484C22⋊Q8—4324no—
485#121—4324no—
486#121—4324no—
487C4×Q8—438no—
488C4×Q8—438no—
489C4×Q8—4324no—
490C4×Q8—4324no—
491C4×Q8—4324no—
492C4×Q8—4324no—
493C4×Q8C22×D4318yes—
494C4×Q8C22×D43124yes—
495C4×Q8C22×D4318yes—
496C4×Q8C22×D43124yes—
497C4×D4—438no—
498C4×D4—4324no—
499C4×D4—4324no—
500C4×D4—4324no—
501C4×D4—4324no—
502C4×D4—4324no—
503C4×D4—4324no—
504C4×D4—4324no—
505#117—4324no—
506#117—4324no—
507#117—4324no—
508#117—4324no—
509#117—4348no—
510C2×C4⋊C4—433no—
511C2×C4⋊C4—436no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—433no—
514C2×C4⋊C4—433no—
515C2×C4⋊C4—433no—
516C2×C4⋊C4—433no—
517C2×C4⋊C4—433no—
518C2×C4⋊C4—433no—
519C2×C4⋊C4—436no—
520C2×C4⋊C4—436no—
521C2×C4⋊C4—4324no—
522C2×C4⋊C4C22×D4313yes—
523C2×C4⋊C4C22×D4313yes—
524C2×C4⋊C4C22×D4316yes—
525C2×C4⋊C4C22×D43124yes—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—433no—
528C2×C22⋊C4—431no—
529C2×C22⋊C4—433no—
530C2×C22⋊C4—436no—
531C2×C22⋊C4—433no—
532C2×C22⋊C4—433no—
533C2×C22⋊C4—436no—
534C2×C22⋊C4—436no—
535C2×C42—433no—
536C2×C42—433no—
537C2×C42—433no—
538C2×C42—433no—
539C2×C42—433no—
540C2×C42—431no—
541C2×C42—4324no—
542C2×C42—4324no—
543C2×C42C22×D4313yes—
544C2×C42C22×D4313yes—
545C2×C42C22×D43124yes—
546C2×C42C22×D4313yes—
547C2×C42C22×D4313yes—
548C24—431no—
549C24—433no—
550C24C23×D4311yescharacteristic
551#41—8696no—
552#41—8632no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—4312no—
556C2×Q8—4312no—
557C2×Q8—8612no—
558C2×Q8—8632no—
559C2×Q8—8612no—
560C2×Q8#1062189818yescomplemented
561C2×Q8C23×D43112yes—
562C2×Q8C23×D4314yes—
563C2×D4—438no—
564C2×D4—434no—
565C2×D4—4312no—
566C2×D4—4312no—
567C2×D4—4312no—
568C2×D4—8612no—
569C2×D4—8612no—
570C2×D4—8612no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—24no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—433no—
578C22×C4—433no—
579C22×C4—433no—
580C22×C4—434no—
581C22×C4—4312no—
582C22×C4—4312no—
583C22×C4—4312no—
584C22×C4—4312no—
585C22×C4—4312no—
586C22×C4—8612no—
587C22×C4—8612no—
588C22×C4—8612no—
589C22×C4—8612no—
590C22×C4—864no—
591C22×C4—8612no—
592C22×C4C23×D4313yes—
593C22×C4C23×D4311yescharacteristic
594C22×C4C23×D4314yes—
595C22×C4C23×D4313yes—
596C22×C4C23×D4313yes—
597C22×C4C23×D43112yes—
598C22×C4C23×D43112yes—
599C22×C4C23×D4313yes—
600C22×C4C23×D4311yescharacteristic
601C4⋊C4—4312no—
602C4⋊C4—4324no—
603C4⋊C4—434no—
604C4⋊C4—4312no—
605C4⋊C4—4312no—
606C4⋊C4—4312no—
607C4⋊C4—4312no—
608C4⋊C4—4312no—
609C4⋊C4—4312no—
610C4⋊C4—4324no—
611C4⋊C4—4324no—
612C4⋊C4C23×D43112yes—
613C4⋊C4C23×D43112yes—
614C4⋊C4C23×D43124yes—
615C22⋊C4—434no—
616C22⋊C4—4312no—
617C22⋊C4—434no—
618C22⋊C4—4312no—
619C22⋊C4—4324no—
620C22⋊C4—4312no—
621C22⋊C4—4312no—
622C22⋊C4—4324no—
623C22⋊C4—4324no—
624C42—434no—
625C42—4312no—
626C42—4312no—
627C42—4312no—
628C42—4312no—
629C42—4312no—
630C42C23×D43112yes—
631C42C23×D43112yes—
632C42C23×D43112yes—
633C42C23×D43112yes—
634C23—22no—
635C23—22no—
636C23—434no—
637C23—432no—
638C23—436no—
639C23—862no—
640C23—862no—
641C23—866no—
642C23—866no—
643C23—866no—
644C23#41×D4314yes—
645C23C24×D4312yes—
646C23C24×D4311yescharacteristic
647Q8—224no—
648Q8—8624no—
649Q8—8624no—
650Q8C2×#10621898116yescomplemented
651D4—4316no—
652D4—8624no—
653D4—8624no—
654D4—8624no—
655C2×C4—26no—
656C2×C4—26no—
657C2×C4—224no—
658C2×C4—26no—
659C2×C4—22no—
660C2×C4—224no—
661C2×C4—28no—
662C2×C4—434no—
663C2×C4—432no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—436no—
667C2×C4—436no—
668C2×C4—436no—
669C2×C4—8624no—
670C2×C4—8624no—
671C2×C4—866no—
672C2×C4—862no—
673C2×C4—866no—
674C2×C4—862no—
675C2×C4—866no—
676C2×C4—8624no—
677C2×C4—8624no—
678C2×C4—868no—
679C2×C4—8624no—
680C2×C4C2×#10621898112yes—
681C2×C4#1306337314yes—
682C2×C4C24×D4316yes—
683C2×C4C24×D4312yes—
684C2×C4C24×D4316yes—
685C2×C4C24×D4316yes—
686C2×C4C24×D4316yes—
687C2×C4C24×D4312yes—
688C22—22no—
689C22—22no—
690C22—28no—
691C22—434no—
692C22—862no—
693C22—862no—
694C22—868no—
695C22—866no—
696C22—866no—
697C22—866no—
698C22—17212no—
699C22C2×#41×D4314yes—
700C22C2×#41×D4312yes—
701C22C22×#1062189812yes—
702C22C2×#1306337312yes—
703C22C25×D4311yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—434no—
709C4—866no—
710C4—862no—
711C4—866no—
712C4—862no—
713C4—866no—
714C4C22×#10621898112yes—
715C4C2×#1306337314yes—
716C2—24no—
717C2—864no—
718C2—1726no—
719C2#1914821214yesdirect product factor
720C2C22×#41×D4311yescharacteristic
721C2C23×#1062189811yescharacteristic
722C2C22×#1306337311yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC22×C4×Q8×C43C2
socleC23×C43C25
hypercenterC22×C4×Q8D43
hypocenterC43C2×#3482
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #19148212C2direct (N × H)
2. C2×#14583625C2semidirect
3. C2×#14583621C2semidirect
4. C2×#14583590C2semidirect
5. C2×#14583584C2semidirect
6. C2×Q8×C22⋊D43C2semidirect
7. C2×#14583561C2semidirect
8. C2×#14583560C2semidirect
9. C2×#14583550C2semidirect
10. C2×#14583453C2semidirect
11. C2×#14583436C2semidirect
12. C2×#14583433C2semidirect
13. C2×C4×#10621902C2semidirect
14. C2×C4×#10621898C2semidirect
15. C2×C4×Q8×D43C2semidirect
16. C22×C4×Q8×C43C2semidirect
20. #14583625C22semidirect
21. #14583621C22semidirect
22. #14583590C22semidirect
23. #14583584C22semidirect
24. Q8×C22⋊D43C22semidirect
25. #14583561C22semidirect
26. #14583560C22semidirect
27. #14583550C22semidirect
28. #14583453C22semidirect
31. #14583436C22semidirect
32. #14583433C22semidirect
49. C4×#10621902C22semidirect
50. C4×#10621898C22semidirect
57. C4×Q8×D43C22semidirect
79. C2×C4×Q8×C43C22semidirect
191. C2×Q8×C43#41semidirect
207. C2×C22⋊D43#41semidirect
286. Q8×C43C2×#41semidirect
303. C22⋊D43C2×#41semidirect
370. C22×C4×Q8D43semidirect
372. C2×C43#3482semidirect
424. C2×C4×Q8C2×D43semidirect
443. C43C2×#3482semidirect
560. C2×Q8#10621898semidirect
650. Q8C2×#10621898semidirect
719. C2#19148212direct (N × H)

Maximal subgroups

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

subgroupindex
#191482122
C2×#145836252
C2×#145836212
C2×#145835902
C2×#145835842
C2×Q8×C22⋊D432
C2×#145835612
C2×#145835602
C2×#145835502
C2×#145834532
C2×#145834362
C2×#145834332
C2×C4×#106219022
C2×C4×#106218982
C2×C4×Q8×D432
C22×C4×Q8×C432
C2×#348243