Finite Group Databasebeta

← C2×#19148671 #26004805

Subgroups — C2×#19148671 #26004805

Order 11008.

7758 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#19148671C2132yesmaximal, direct product factor
2C2×#14583631C213yesmaximal, complemented
3C2×Q8×Dic86C211yesmaximal, characteristic, complemented
4C2×#14583607C213yesmaximal, complemented
5C2×#14583568C211yesmaximal, characteristic, complemented
6C2×#14583560C211yesmaximal, characteristic, complemented
7C2×#14583553C213yesmaximal, complemented
8C2×#14583549C213yesmaximal, complemented
9C2×#14583522C213yesmaximal, complemented
10C2×#14583518C213yesmaximal, complemented
11C2×#14583444C213yesmaximal, complemented
12C2×#14583429C213yesmaximal, complemented
13C2×#14583382C211yesmaximal, characteristic, complemented
14C2×#14583381C211yesmaximal, characteristic, complemented
15C22×Q8×Dic43C211yesmaximal, characteristic, complemented
16C2×C43×#548C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2216yes—
19#14583631C22148yescomplemented
20Q8×Dic86C22116yescomplemented
21#14583607C22148yescomplemented
22#14583568C22116yescomplemented
23#14583560C22116yescomplemented
24#14583553C22148yescomplemented
25#14583549C22148yescomplemented
26#14583522C22148yescomplemented
27#14583518C22148yescomplemented
28#14583444C22148yescomplemented
29C2×#13063325C2213yes—
30C2×#13063324C2213yes—
31C2×#13063324C2213yes—
32C2×#13063321C2213yes—
33#14583429C22148yescomplemented
34C2×#13063320C2213yes—
35C2×#13063318C2213yes—
36C2×#13063315C2213yes—
37C2×#13063314C2213yes—
38C2×#13063311C2213yes—
39C2×#13063311C2216yes—
40C2×#13063309C2213yes—
41C2×#13063309C2216yes—
42C2×#13063307C2216yes—
43C2×#13063306C2213yes—
44C2×#13063305C2216yes—
45C2×#13063302C2216yes—
46C2×#13063302C2211yescharacteristic
47C2×#13063301C2213yes—
48C2×#13063299C2213yes—
49C2×#13063299C2213yes—
50C2×#13063297C2213yes—
51C2×#13063296C2213yes—
52#14583382C22116yescomplemented
53#14583381C22116yescomplemented
54C2×Q8×Dic43C2211yescharacteristic
55C2×Q8×Dic43C2211yescharacteristic
56C2×Q8×Dic43C2211yescharacteristic
57C2×Q8×Dic43C2213yes—
58C2×Q8×Dic43C2213yes—
59C2×Q8×Dic43C22116yescomplemented
60C2×C4×Dic86C2213yes—
61C2×C4×D172C2213yes—
62C2×D4×Dic43C2213yes—
63C2×D4×Dic43C2213yes—
64C2×#13063287C2213yes—
65C2×C4×C22⋊D43C2213yes—
66C2×C4×C22⋊D43C2213yes—
67C2×(C22⋊D43)⋊C4C2216yes—
68C2×#13063284C2213yes—
69C2×#13063282C2213yes—
70C22×C4⋊Dic43C2213yes—
71C22×C4⋊Dic43C2213yes—
72C2×C4⋊C4×D43C2213yes—
73C22×C4×Dic43C2213yes—
74C22×#41×C43C2211yescharacteristic
75C23×Q8×C43C2211yescharacteristic
76C43×#548C22116yescomplemented
77C2×#124×C43C2213yes—
78C2×C22⋊Q8×C43C2213yes—
79C2×#121×C43C2213yes—
80C2×C4×Q8×C43C2211yescharacteristic
81C2×C4×D4×C43C2213yes—
82C2×#10621902—28no—
83C2×#10621902C2318yes—
84C2×#10621900—424no—
85C2×#10621900C23148yes—
86C22×Dic86C2311yescharacteristic
87C22×Dic86C2316yes—
88C22×D172C2313yes—
89C22×C22⋊D43C2313yes—
90C22×C22⋊D43C2313yes—
91C22×C22⋊D43C2316yes—
92C23×Dic43C2311yescharacteristic
93C23×Dic43C2313yes—
94C23×Dic43C2316yes—
95C22×C4×D43C2313yes—
96C22×C4×D43C2316yes—
97#13063325C23124yes—
98#13063324C23124yes—
99#13063324C23124yes—
100#13063321C23124yes—
101#13063320C23124yes—
102#13063318C23124yes—
103#13063315C23124yes—
104#13063314C23124yes—
105#13063311C23124yes—
106#13063311C23148yes—
107#13063309C23124yes—
108#13063309C23148yes—
109#13063307C23148yes—
110#13063306C23124yes—
111#13063305C23148yes—
112#13063302C23148yes—
113#13063302C2318yes—
114#13063301C23124yes—
115#13063299C23124yes—
116#13063299C23124yes—
117#13063297C23124yes—
118#13063296C23124yes—
119Q8×Dic43C2318yes—
120Q8×Dic43C2318yes—
121Q8×Dic43C23124yes—
122Q8×Dic43C2318yes—
123Q8×Dic43C23124yes—
124C4×Dic86C23124yes—
125C4×D172C23124yes—
126D4×Dic43C23124yes—
127D4×Dic43C23124yes—
128#13063287C23124yes—
129C4×C22⋊D43C23124yes—
130C4×C22⋊D43C23124yes—
131(C22⋊D43)⋊C4C23148yes—
132#13063284C23124yes—
133#13063282C23124yes—
134C2×C4⋊Dic43C23124yes—
135C2×C4⋊Dic43C23124yes—
136C2×C4⋊Dic43C2313yes—
137C2×C4⋊Dic43C2313yes—
138C2×C4⋊Dic43C2313yes—
139C2×C4⋊Dic43C2313yes—
140C2×C4⋊Dic43C2316yes—
141C2×C4⋊Dic43C2311yescharacteristic
142C2×C4⋊Dic43C2313yes—
143C2×Dic43⋊C4C2313yes—
144C2×Dic43⋊C4C2311yescharacteristic
145C2×Dic43⋊C4C2313yes—
146C2×Dic43⋊C4C2311yescharacteristic
147C2×Dic43⋊C4C2313yes—
148C2×Dic43⋊C4C2313yes—
149C4⋊C4×D43C23124yes—
150C2×C22⋊Dic43C2313yes—
151C2×C22⋊Dic43C2313yes—
152C2×C22⋊Dic43C2311yescharacteristic
153C2×C22⋊Dic43C2313yes—
154C2×(C2×D43)⋊C4C2313yes—
155C2×(C2×D43)⋊C4C2313yes—
156C2×(C2×D43)⋊C4C2316yes—
157C2×(C2×D43)⋊C4C2313yes—
158C2×(C2×D43)⋊C4C2313yes—
159C2×C4×Dic43C2313yes—
160C2×C4×Dic43C2313yes—
161C2×C4×Dic43C2313yes—
162C2×C4×Dic43C2313yes—
163C2×C4×Dic43C23124yes—
164C2×C4×Dic43C2313yes—
165C2×#41×C43—28no—
166C2×#41×C43C2318yes—
167C22×Q8×C43—28no—
168C22×Q8×C43C2318yes—
169C22×Q8×C43C2313yes—
170C22×Q8×C43C2311yescharacteristic
171C22×D4×C43C2313yes—
172C22×D4×C43C2313yes—
173C23×C4×C43C2313yes—
174C23×C4×C43C2313yes—
175#124×C43C23124yes—
176C22⋊Q8×C43C23124yes—
177#121×C43C23124yes—
178C4×Q8×C43C2318yes—
179C4×D4×C43C23124yes—
180C2×C4⋊C4×C43C2313yes—
181C2×C4⋊C4×C43C2313yes—
182C2×C22⋊C4×C43C2311yescharacteristic
183C2×C22⋊C4×C43C2313yes—
184C2×C22⋊C4×C43C2316yes—
185C2×C42×C43C2313yes—
186C24×C43C2413yes—
187C24×C43C2411yescharacteristic
188C23×D43C2413yes—
189#41×C43—232no—
190C2×Q8×C43—232no—
191C2×Q8×C43—212no—
192C2×Q8×C43#4118yescomplemented
193C2×Q8×C43C24112yes—
194C2×Q8×C43C2414yes—
195C2×D4×C43—212no—
196C2×D4×C43—212no—
197C2×D4×C43C24112yes—
198C2×D4×C43C24112yes—
199C22×C4×C43—212no—
200C22×C4×C43—212no—
201C22×C4×C43C2411yescharacteristic
202C22×C4×C43C2413yes—
203C22×C4×C43C2413yes—
204C22×C4×C43C2411yescharacteristic
205C22×C4×C43C24112yes—
206C22×C4×C43C24112yes—
207C22×C4×C43C2413yes—
208C2×C22⋊D43—212no—
209C2×C22⋊D43—212no—
210C2×C22⋊D43—412no—
211C2×C22⋊D43C24112yes—
212C2×C22⋊D43C24112yes—
213C2×C22⋊D43C24124yes—
214C22×Dic43—24no—
215C22×Dic43—212no—
216C22×Dic43—412no—
217C22×Dic43C2411yescharacteristic
218C22×Dic43C2414yes—
219C22×Dic43C2411yescharacteristic
220C22×Dic43C2413yes—
221C22×Dic43C2413yes—
222C22×Dic43C24112yes—
223C22×Dic43C2413yes—
224C22×Dic43C2411yescharacteristic
225C22×Dic43C24124yes—
226C22×Dic43C2411yescharacteristic
227#10621902—232no—
228#10621900—496no—
229C2×D172—212no—
230C2×D172C24112yes—
231C2×C4×D43—212no—
232C2×C4×D43—412no—
233C2×C4×D43C24112yes—
234C2×C4×D43C24124yes—
235C2×Dic86—24no—
236C2×Dic86—412no—
237C2×Dic86C2414yes—
238C2×Dic86C24124yes—
239C4⋊C4×C43C24112yes—
240C4⋊C4×C43C24112yes—
241C22⋊C4×C43C2414yes—
242C22⋊C4×C43C24112yes—
243C22⋊C4×C43C24124yes—
244C42×C43C24112yes—
245C22⋊Dic43C24112yes—
246C22⋊Dic43C24112yes—
247C22⋊Dic43C2414yes—
248C22⋊Dic43C24112yes—
249(C2×D43)⋊C4C24112yes—
250(C2×D43)⋊C4C24112yes—
251(C2×D43)⋊C4C24124yes—
252(C2×D43)⋊C4C24112yes—
253(C2×D43)⋊C4C24112yes—
254C4⋊Dic43C24112yes—
255C4⋊Dic43C24112yes—
256C4⋊Dic43C24112yes—
257C4⋊Dic43C24112yes—
258C4⋊Dic43C24124yes—
259C4⋊Dic43C2414yes—
260C4⋊Dic43C24112yes—
261Dic43⋊C4C24112yes—
262Dic43⋊C4C2414yes—
263Dic43⋊C4C24112yes—
264Dic43⋊C4C2414yes—
265Dic43⋊C4C24112yes—
266Dic43⋊C4C24112yes—
267C4×Dic43C24112yes—
268C4×Dic43C24112yes—
269C4×Dic43C24112yes—
270C4×Dic43C24112yes—
271C4×Dic43C24112yes—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—26no—
275C23×C43—26no—
276C23×C43—26no—
277C23×C43H(5,𝔽2)14yes—
278C23×C43C2516yes—
279C23×C43C2512yes—
280C23×C43C2511yescharacteristic
281C22×D43—26no—
282C22×D43—26no—
283C22×D43—26no—
284C22×D43C2516yes—
285Q8×C43—224no—
286Q8×C43C2×#41116yescomplemented
287D4×C43—224no—
288D4×C43—224no—
289C2×C4×C43—22no—
290C2×C4×C43—26no—
291C2×C4×C43—26no—
292C2×C4×C43—22no—
293C2×C4×C43—224no—
294C2×C4×C43—224no—
295C2×C4×C43C2×#41112yes—
296C2×C4×C43C2516yes—
297C2×C4×C43C2516yes—
298C2×C4×C43C2512yes—
299C2×C4×C43C2512yes—
300C2×C4×C43C2516yes—
301C22⋊D43—224no—
302C22⋊D43—224no—
303C22⋊D43—424no—
304C2×Dic43—22no—
305C2×Dic43—26no—
306C2×Dic43—26no—
307C2×Dic43—26no—
308C2×Dic43—224no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—28no—
312C2×Dic43—424no—
313C2×Dic432−1+414yes—
314C2×Dic43C2512yes—
315C2×Dic43C2512yes—
316C2×Dic43C2516yes—
317C2×Dic43C2516yes—
318C2×Dic43C2516yes—
319C2×Dic43C2512yes—
320C2×Dic43C2512yes—
321D172—224no—
322C4×D43—224no—
323C4×D43—424no—
324Dic86—28no—
325Dic86—424no—
326C2×#3522—431nomaximal, Sylow
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—28no—
330C22×C43—26no—
331C22×C43—26no—
332C22×C43—26no—
333C22×C43—412no—
334C22×C43C22×#4112yes—
335C22×C43C2×H(5,𝔽2)14yes—
336C22×C43C2×H(5,𝔽2)12yes—
337C22×C43C2×2−1+412yes—
338C22×C43C2611yescharacteristic
339C2×D43—26no—
340C2×D43—26no—
341C2×D43—26no—
342C2×D43—412no—
343C4×C43—22no—
344C4×C43—26no—
345C4×C43—26no—
346C4×C43—22no—
347C4×C43C22×#41112yes—
348Dic43—22no—
349Dic43—26no—
350Dic43—26no—
351Dic43—26no—
352Dic43—22no—
353Dic43—22no—
354Dic43C2×2−1+414yes—
355#3522—4332no—
356C2×#559—433no—
357C2×Q82—431no—
358C2×#554—433no—
359C2×#550—431no—
360C2×#548—431no—
361C2×#548D4311yescharacteristic, complemented
362C2×#547—433no—
363C2×#547—433no—
364C2×#542—433no—
365C2×#542—433no—
366C2×#532—433no—
367C2×#529—433no—
368C2×#520—431no—
369C2×#520—431no—
370C22×C4×Q8—431no—
371C2×C43—24no—
372C2×C43—46no—
373C2×C43#352214yescomplemented
374C2×C43C23×#4111yescharacteristic
375C2×C43C22×H(5,𝔽2)11yescharacteristic
376C2×C43C22×2−1+411yescharacteristic
377D43—46no—
378C22×#41—431no—
379C22×#41—436no—
380C22×#41C2×D4311yescharacteristic
381C23×Q8C2×D4311yescharacteristic
382#559—4348no—
383Q82—4316no—
384#554—4348no—
385#550—4316no—
386#548—4316no—
387#548C2×D43116yescomplemented
388#547—4348no—
389#547—4348no—
390#542—4348no—
391#542—4348no—
392#532—4348no—
393C2×C4⋊Q8—433no—
394C2×C4⋊Q8—433no—
395C2×C4⋊Q8—433no—
396C2×#127—433no—
397#529—4348no—
398C2×#126—433no—
399C2×#126—433no—
400C2×#125—433no—
401C2×#124—433no—
402C2×#124—433no—
403C2×#124—436no—
404C2×#124C2×D4313yes—
405C2×#123—433no—
406C2×#123—436no—
407C2×#123—433no—
408C2×#123—436no—
409C2×C22⋊Q8—433no—
410C2×C22⋊Q8—436no—
411C2×C22⋊Q8—431no—
412C2×C22⋊Q8—436no—
413C2×C22⋊Q8C2×D4313yes—
414C2×#121—433no—
415C2×#121—433no—
416C2×#121—433no—
417C2×#121—433no—
418C2×#121C2×D4313yes—
419#520—4316no—
420#520—4316no—
421C2×C4×Q8—431no—
422C2×C4×Q8—433no—
423C2×C4×Q8—431no—
424C2×C4×Q8—433no—
425C2×C4×Q8—431no—
426C2×C4×Q8—4316no—
427C2×C4×Q8—433no—
428C2×C4×Q8C2×D4311yescharacteristic
429C2×C4×D4—433no—
430C2×C4×D4—433no—
431C2×C4×D4—433no—
432C2×C4×D4—433no—
433C2×C4×D4—433no—
434C2×C4×D4—436no—
435C2×C4×D4—433no—
436C2×C4×D4C2×D4313yes—
437C2×#117—433no—
438C2×#117—433no—
439C22×C4⋊C4—433no—
440C22×C4⋊C4—433no—
441C22×C4⋊C4—433no—
442C22×C42—433no—
443C43C2×#352211yescharacteristic, complemented, Sylow
444C2×#41—28no—
445C2×#41—438no—
446C2×#41—4348no—
447C2×#41—868no—
448C2×#41—17224no—
449C2×#41C22×D4318yes—
450C22×Q8—28no—
451C22×Q8—431no—
452C22×Q8—436no—
453C22×Q8C22×D4313yes—
454C22×Q8C22×D4318yes—
455C22×Q8C22×D4311yescharacteristic
456C22×D4—433no—
457C22×D4—433no—
458C22×D4—436no—
459C22×D4—433no—
460C22×D4C22×D4313yes—
461C22×D4C22×D4313yes—
462C23×C4—433no—
463C23×C4—431no—
464C23×C4—436no—
465C23×C4—433no—
466C23×C4—436no—
467C23×C4C22×D4313yes—
468C23×C4C22×D4313yes—
469C4⋊Q8—4324no—
470C4⋊Q8—4324no—
471C4⋊Q8—4324no—
472#127—4324no—
473#126—4324no—
474#126—4324no—
475#125—4324no—
476#124—4324no—
477#124—4324no—
478#124—4348no—
479#124C22×D43124yes—
480#123—4324no—
481#123—4324no—
482#123—4348no—
483#123—4348no—
484C22⋊Q8—4324no—
485C22⋊Q8—4348no—
486C22⋊Q8—438no—
487C22⋊Q8—4348no—
488C22⋊Q8C22×D43124yes—
489#121—4324no—
490#121—4324no—
491#121—4324no—
492#121—4324no—
493#121C22×D43124yes—
494C4×Q8—438no—
495C4×Q8—4324no—
496C4×Q8—438no—
497C4×Q8—4324no—
498C4×Q8—438no—
499C4×Q8—4324no—
500C4×Q8C22×D4318yes—
501C4×D4—4324no—
502C4×D4—4324no—
503C4×D4—4324no—
504C4×D4—4324no—
505C4×D4—4324no—
506C4×D4—4348no—
507C4×D4—4324no—
508C4×D4C22×D43124yes—
509#117—4324no—
510#117—4324no—
511C2×C4⋊C4—433no—
512C2×C4⋊C4—433no—
513C2×C4⋊C4—433no—
514C2×C4⋊C4—433no—
515C2×C4⋊C4—433no—
516C2×C4⋊C4—436no—
517C2×C4⋊C4—4324no—
518C2×C4⋊C4—4324no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—433no—
523C2×C4⋊C4—433no—
524C2×C4⋊C4—433no—
525C2×C4⋊C4—433no—
526C2×C4⋊C4—4324no—
527C2×C4⋊C4C22×D4313yes—
528C2×C4⋊C4C22×D4313yes—
529C2×C22⋊C4—433no—
530C2×C22⋊C4—433no—
531C2×C22⋊C4—431no—
532C2×C22⋊C4—433no—
533C2×C22⋊C4—433no—
534C2×C22⋊C4—433no—
535C2×C22⋊C4—433no—
536C2×C22⋊C4—436no—
537C2×C22⋊C4—433no—
538C2×C22⋊C4C22×D4316yes—
539C2×C22⋊C4C22×D4311yescharacteristic
540C2×C22⋊C4C22×D4313yes—
541C2×C42—433no—
542C2×C42—433no—
543C2×C42—433no—
544C2×C42—433no—
545C2×C42—433no—
546C2×C42—4324no—
547C2×C42C22×D4313yes—
548C24—433no—
549C24C23×D4313yes—
550C24C23×D4311yescharacteristic
551#41—232no—
552#41—8632no—
553#41—17296no—
554C2×Q8—232no—
555C2×Q8—212no—
556C2×Q8—434no—
557C2×Q8—4324no—
558C2×Q8—864no—
559C2×Q8—17212no—
560C2×Q8#1062190018yescomplemented
561C2×Q8C23×D43112yes—
562C2×Q8C23×D4314yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—4312no—
566C2×D4—4312no—
567C2×D4—4324no—
568C2×D4—4312no—
569C2×D4—8612no—
570C2×D4—8612no—
571C2×D4—8612no—
572C2×D4—17212no—
573C2×D4C23×D43112yes—
574C2×D4C23×D43112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—431no—
578C22×C4—434no—
579C22×C4—4312no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—433no—
583C22×C4—433no—
584C22×C4—433no—
585C22×C4—431no—
586C22×C4—4324no—
587C22×C4—4312no—
588C22×C4—4324no—
589C22×C4—864no—
590C22×C4—8612no—
591C22×C4—8612no—
592C22×C4—17212no—
593C22×C4—17212no—
594C22×C4C23×D43112yes—
595C22×C4C23×D43112yes—
596C22×C4C23×D4313yes—
597C22×C4C23×D4311yescharacteristic
598C22×C4C23×D4313yes—
599C22×C4C23×D4311yescharacteristic
600C22×C4C23×D4313yes—
601C4⋊C4—4312no—
602C4⋊C4—4312no—
603C4⋊C4—4312no—
604C4⋊C4—4312no—
605C4⋊C4—4312no—
606C4⋊C4—4324no—
607C4⋊C4—434no—
608C4⋊C4—434no—
609C4⋊C4—434no—
610C4⋊C4—4312no—
611C4⋊C4—4312no—
612C4⋊C4—4312no—
613C4⋊C4—4312no—
614C4⋊C4C23×D43112yes—
615C4⋊C4C23×D43112yes—
616C22⋊C4—4312no—
617C22⋊C4—4312no—
618C22⋊C4—434no—
619C22⋊C4—4312no—
620C22⋊C4—4312no—
621C22⋊C4—4312no—
622C22⋊C4—4312no—
623C22⋊C4—4324no—
624C22⋊C4—4312no—
625C22⋊C4C23×D43124yes—
626C22⋊C4C23×D4314yes—
627C22⋊C4C23×D43112yes—
628C42—4312no—
629C42—4312no—
630C42—4312no—
631C42—4312no—
632C42—4312no—
633C42C23×D43112yes—
634C23—22no—
635C23—22no—
636C23—26no—
637C23—26no—
638C23—26no—
639C23—436no—
640C23—866no—
641C23—866no—
642C23—866no—
643C23#1306337114yes—
644C23C24×D4316yes—
645C23C24×D4312yes—
646C23C24×D4311yescharacteristic
647Q8—224no—
648Q8—868no—
649Q8—17224no—
650Q8C2×#10621900116yescomplemented
651D4—224no—
652D4—224no—
653D4—8624no—
654D4—8624no—
655D4—8624no—
656D4—17224no—
657C2×C4—22no—
658C2×C4—26no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—434no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—432no—
667C2×C4—436no—
668C2×C4—436no—
669C2×C4—436no—
670C2×C4—432no—
671C2×C4—868no—
672C2×C4—862no—
673C2×C4—866no—
674C2×C4—866no—
675C2×C4—8624no—
676C2×C4—866no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—8624no—
680C2×C4—17224no—
681C2×C4—17224no—
682C2×C4C2×#10621900112yes—
683C2×C4C24×D4316yes—
684C2×C4C24×D4312yes—
685C2×C4C24×D4316yes—
686C2×C4C24×D4312yes—
687C2×C4C24×D4316yes—
688C22—22no—
689C22—22no—
690C22—28no—
691C22—26no—
692C22—26no—
693C22—26no—
694C22—412no—
695C22—866no—
696C22—866no—
697C22—866no—
698C22—17212no—
699C22C22×#1062190012yes—
700C22C2×#1306337114yes—
701C22C2×#1306337112yes—
702C222−1+4×D4312yes—
703C22C25×D4311yescharacteristic
704C4—22no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—434no—
709C4—862no—
710C4—866no—
711C4—866no—
712C4—866no—
713C4—862no—
714C4—862no—
715C4C22×#10621900112yes—
716C2—24no—
717C2—46no—
718C2—1726no—
719C2#1914867114yesdirect product factor
720C2C23×#1062190011yescharacteristic
721C2C22×#1306337111yescharacteristic
722C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#548C2
socleC23×C43C25
hypercenterC2×#548D43
hypocenterC43C2×#3522
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #19148671C2direct (N × H)
2. C2×#14583631C2semidirect
3. C2×Q8×Dic86C2semidirect
4. C2×#14583607C2semidirect
5. C2×#14583568C2semidirect
6. C2×#14583560C2semidirect
7. C2×#14583553C2semidirect
8. C2×#14583549C2semidirect
9. C2×#14583522C2semidirect
10. C2×#14583518C2semidirect
11. C2×#14583444C2semidirect
12. C2×#14583429C2semidirect
13. C2×#14583382C2semidirect
14. C2×#14583381C2semidirect
15. C22×Q8×Dic43C2semidirect
16. C2×C43×#548C2semidirect
19. #14583631C22semidirect
20. Q8×Dic86C22semidirect
21. #14583607C22semidirect
22. #14583568C22semidirect
23. #14583560C22semidirect
24. #14583553C22semidirect
25. #14583549C22semidirect
26. #14583522C22semidirect
27. #14583518C22semidirect
28. #14583444C22semidirect
33. #14583429C22semidirect
52. #14583382C22semidirect
53. #14583381C22semidirect
59. C2×Q8×Dic43C22semidirect
76. C43×#548C22semidirect
192. C2×Q8×C43#41semidirect
286. Q8×C43C2×#41semidirect
361. C2×#548D43semidirect
373. C2×C43#3522semidirect
387. #548C2×D43semidirect
443. C43C2×#3522semidirect
560. C2×Q8#10621900semidirect
650. Q8C2×#10621900semidirect
719. C2#19148671direct (N × H)

Maximal subgroups

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

subgroupindex
#191486712
C2×#145836312
C2×Q8×Dic862
C2×#145836072
C2×#145835682
C2×#145835602
C2×#145835532
C2×#145835492
C2×#145835222
C2×#145835182
C2×#145834442
C2×#145834292
C2×#145833822
C2×#145833812
C22×Q8×Dic432
C2×C43×#5482
C2×#352243