Finite Group Databasebeta

← C2×#19148588 #26004794

Subgroups — C2×#19148588 #26004794

Order 11008.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148588C2132yesmaximal, direct product factor
2C2×#14583625C211yesmaximal, characteristic, complemented
3C2×#14583621C213yesmaximal, complemented
4C2×#14583604C213yesmaximal, complemented
5C2×#14583597C213yesmaximal, complemented
6C2×#14583590C213yesmaximal, complemented
7C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
8C2×#14583561C211yesmaximal, characteristic, complemented
9C2×#14583560C211yesmaximal, characteristic, complemented
10C2×#14583521C213yesmaximal, complemented
11C2×#14583507C213yesmaximal, complemented
12C2×#14583433C213yesmaximal, complemented
13C2×#14583433C213yesmaximal, complemented
14C2×#14583381C211yesmaximal, characteristic, complemented
15C2×#14583375C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C43C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19#14583625C22116yescomplemented
20#14583621C22148yescomplemented
21#14583604C22148yescomplemented
22#14583597C22148yescomplemented
23#14583590C22148yescomplemented
24Q8×C22⋊D43C22116yescomplemented
25#14583561C22116yescomplemented
26#14583560C22116yescomplemented
27#14583521C22148yescomplemented
28#14583507C22148yescomplemented
29C2×#13063324C2213yes—
30C2×#13063323C2213yes—
31#14583433C22148yescomplemented
32#14583433C22148yescomplemented
33C2×#13063320C2216yes—
34C2×#13063319C2213yes—
35C2×#13063319C2213yes—
36C2×#13063319C2216yes—
37C2×#13063317C2213yes—
38C2×#13063317C2213yes—
39C2×#13063316C2213yes—
40C2×#13063315C2216yes—
41C2×#13063314C2213yes—
42C2×#13063313C2213yes—
43C2×#13063313C2213yes—
44C2×#13063310C2216yes—
45C2×#13063308C2211yescharacteristic
46C2×#13063308C2213yes—
47C2×#13063305C2213yes—
48C2×#13063304C2213yes—
49C2×#13063304C2213yes—
50C2×#13063303C2216yes—
51C2×#13063301C2213yes—
52C2×#13063301C2213yes—
53C2×#13063300C2213yes—
54C2×#13063299C2213yes—
55C2×#13063299C2213yes—
56#14583381C22116yescomplemented
57#14583375C22116yescomplemented
58C2×Q8×Dic43C2211yescharacteristic
59C2×Q8×Dic43C2211yescharacteristic
60C2×C4×Dic86C2213yes—
61C2×C4×Dic86C2213yes—
62C2×#13063290C2213yes—
63C2×C4×D172C2213yes—
64C2×C4×D172C2213yes—
65C2×#13063287C2213yes—
66C2×C4×C22⋊D43C2213yes—
67C2×C4×C22⋊D43C2213yes—
68C2×C4×C22⋊D43C2216yes—
69C2×#13063283C2213yes—
70C2×#13063282C2213yes—
71C2×#13063282C2213yes—
72C2×#13063282C2216yes—
73C2×C4⋊C4×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—
84C22×Dic86C2313yes—
85C22×Dic86C2313yes—
86C2×Q8×D43—28no—
87C2×Q8×D43C2318yes—
88C22×D172C2313yes—
89C22×D172C2313yes—
90C22×C22⋊D43C2313yes—
91C22×C22⋊D43C2311yescharacteristic
92C22×C4×D43C2313yes—
93C22×C4×D43C2313yes—
94C22×C4×D43C2316yes—
95#13063324C23124yes—
96#13063323C23124yes—
97#13063320C23148yes—
98#13063319C23124yes—
99#13063319C23124yes—
100#13063319C23148yes—
101#13063317C23124yes—
102#13063317C23124yes—
103#13063316C23124yes—
104#13063315C23148yes—
105#13063314C23124yes—
106#13063313C23124yes—
107#13063313C23124yes—
108#13063310C23148yes—
109#13063308C2318yes—
110#13063308C23124yes—
111#13063305C23124yes—
112#13063304C23124yes—
113#13063304C23124yes—
114#13063303C23148yes—
115#13063301C23124yes—
116#13063301C23124yes—
117#13063300C23124yes—
118#13063299C23124yes—
119#13063299C23124yes—
120Q8×Dic43C2318yes—
121Q8×Dic43C2318yes—
122C4×Dic86C23124yes—
123C4×Dic86C23124yes—
124#13063290C23124yes—
125C4×D172C23124yes—
126C4×D172C23124yes—
127#13063287C23124yes—
128C4×C22⋊D43C23124yes—
129C4×C22⋊D43C23124yes—
130C4×C22⋊D43C23148yes—
131#13063283C23124yes—
132#13063282C23148yes—
133#13063282C23124yes—
134#13063282C23124yes—
135C2×C4⋊Dic43C2313yes—
136C2×C4⋊Dic43C2313yes—
137C2×C4⋊Dic43C2313yes—
138C2×C4⋊Dic43C2313yes—
139C2×Dic43⋊C4C2313yes—
140C2×Dic43⋊C4C2311yescharacteristic
141C2×Dic43⋊C4C2313yes—
142C2×Dic43⋊C4C2313yes—
143C2×Dic43⋊C4C2313yes—
144C2×Dic43⋊C4C2316yes—
145C2×Dic43⋊C4C2313yes—
146C2×Dic43⋊C4C2316yes—
147C2×Dic43⋊C4C2313yes—
148C2×Dic43⋊C4C2311yescharacteristic
149C4⋊C4×D43C23124yes—
150C2×C22⋊Dic43C2311yescharacteristic
151C2×C22⋊Dic43C2313yes—
152C2×(C2×D43)⋊C4C2311yescharacteristic
153C2×(C2×D43)⋊C4C2313yes—
154C2×(C2×D43)⋊C4C2313yes—
155C2×(C2×D43)⋊C4C2313yes—
156C2×(C2×D43)⋊C4C2313yes—
157C2×(C2×D43)⋊C4C2316yes—
158C2×(C2×D43)⋊C4C2316yes—
159C2×(C2×D43)⋊C4C2313yes—
160C2×(C2×D43)⋊C4C2313yes—
161C2×(C2×D43)⋊C4C2311yescharacteristic
162C2×C4×Dic43C2316yes—
163C2×C4×Dic43C2313yes—
164C2×C4×Dic43C2313yes—
165C22×Q8×C43—28no—
166C22×Q8×C43C2318yes—
167C22×Q8×C43C2313yes—
168C22×Q8×C43C2311yescharacteristic
169C23×C4×C43C2311yescharacteristic
170C23×C4×C43C2313yes—
171C23×C4×C43C2313yes—
172C4×Q8×C43C2318yes—
173C4×Q8×C43C23124yes—
174C4×Q8×C43C2318yes—
175C4×Q8×C43C23124yes—
176C2×C4⋊C4×C43C2313yes—
177C2×C4⋊C4×C43C2313yes—
178C2×C4⋊C4×C43C2316yes—
179C2×C4⋊C4×C43C23124yes—
180C2×C42×C43C2313yes—
181C2×C42×C43C2313yes—
182C2×C42×C43C2313yes—
183C2×C42×C43C2313yes—
184C2×C42×C43C23124yes—
185C24×C43C2411yescharacteristic
186C23×D43C2411yescharacteristic
187C23×D43C2413yes—
188C2×Q8×C43—232no—
189C2×Q8×C43—212no—
190C2×Q8×C43#4118yes—
191C2×Q8×C43C24112yes—
192C2×Q8×C43C2414yes—
193C22×C4×C43—212no—
194C22×C4×C43—24no—
195C22×C4×C43—46no—
196C22×C4×C43C2411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C22×C4×C43C2414yes—
199C22×C4×C43C2413yes—
200C22×C4×C43C2413yes—
201C22×C4×C43C2413yes—
202C22×C4×C43C24112yes—
203C22×C4×C43C24112yes—
204C22×C4×C43C2413yes—
205C2×C22⋊D43—212no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43C24112yes—
208C2×C22⋊D43C2414yes—
209C22×Dic43C2411yescharacteristic
210C22×Dic43C2413yes—
211C22×Dic43C2411yescharacteristic
212C22×Dic43C2413yes—
213C22×Dic43C2413yes—
214C22×Dic43C2411yescharacteristic
215#10621902—232no—
216Q8×D43—232no—
217C2×D172—212no—
218C2×D172—46no—
219C2×D172C24112yes—
220C2×D172C24112yes—
221C2×C4×D43—212no—
222C2×C4×D43—212no—
223C2×C4×D43—412no—
224C2×C4×D43C24112yes—
225C2×C4×D43C24112yes—
226C2×C4×D43C24124yes—
227C2×Dic86—212no—
228C2×Dic86—46no—
229C2×Dic86C24112yes—
230C2×Dic86C24112yes—
231C4⋊C4×C43C24112yes—
232C4⋊C4×C43C24112yes—
233C4⋊C4×C43C24124yes—
234C42×C43C24112yes—
235C42×C43C24112yes—
236C42×C43C24112yes—
237C42×C43C24112yes—
238C22⋊Dic43C2414yes—
239C22⋊Dic43C24112yes—
240(C2×D43)⋊C4C2414yes—
241(C2×D43)⋊C4C24112yes—
242(C2×D43)⋊C4C24112yes—
243(C2×D43)⋊C4C24112yes—
244(C2×D43)⋊C4C24112yes—
245(C2×D43)⋊C4C24124yes—
246(C2×D43)⋊C4C24124yes—
247(C2×D43)⋊C4C24112yes—
248(C2×D43)⋊C4C24112yes—
249(C2×D43)⋊C4C2414yes—
250C4⋊Dic43C24112yes—
251C4⋊Dic43C24112yes—
252C4⋊Dic43C24112yes—
253C4⋊Dic43C24112yes—
254Dic43⋊C4C24112yes—
255Dic43⋊C4C2414yes—
256Dic43⋊C4C24112yes—
257Dic43⋊C4C24112yes—
258Dic43⋊C4C24112yes—
259Dic43⋊C4C24124yes—
260Dic43⋊C4C24112yes—
261Dic43⋊C4C24124yes—
262Dic43⋊C4C24112yes—
263Dic43⋊C4C2414yes—
264C4×Dic43C24124yes—
265C4×Dic43C24112yes—
266C4×Dic43C24112yes—
267C23×C43—22no—
268C23×C43—22no—
269C23×C432−1+414yes—
270C23×C43C2512yes—
271C23×C43C2511yescharacteristic
272C22×D43—22no—
273C22×D43—26no—
274C22×D43—22no—
275C22×D43—26no—
276C22×D43—26no—
277C22×D43—22no—
278C22×D43C2512yes—
279C22×D43C2516yes—
280Q8×C43—224no—
281Q8×C43C2×#41116yes—
282C2×C4×C43—26no—
283C2×C4×C43—28no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—26no—
287C2×C4×C43—26no—
288C2×C4×C43—224no—
289C2×C4×C43—412no—
290C2×C4×C43C2×#41112yes—
291C2×C4×C43C2516yes—
292C2×C4×C43C2512yes—
293C2×C4×C43C2512yes—
294C2×C4×C43C2516yes—
295C2×C4×C43C2516yes—
296C2×C4×C43C2516yes—
297C22⋊D43—224no—
298C22⋊D43—28no—
299C2×Dic43—26no—
300C2×Dic43—22no—
301C2×Dic43—26no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—26no—
305C2×Dic43C2516yes—
306C2×Dic43C2512yes—
307C2×Dic43C2512yes—
308C2×Dic43C2516yes—
309C2×Dic43C2516yes—
310C2×Dic43C2512yes—
311D172—224no—
312D172—412no—
313C4×D43—224no—
314C4×D43—224no—
315C4×D43—424no—
316Dic86—224no—
317Dic86—412no—
318C2×#3516—431nomaximal, Sylow
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—28no—
322C22×C43C22×#4112yes—
323C22×C43C2×2−1+414yes—
324C22×C43C2×2−1+412yes—
325C22×C43#58512yes—
326C22×C43C2611yescharacteristic
327C2×D43—22no—
328C2×D43—26no—
329C2×D43—22no—
330C2×D43—26no—
331C2×D43—26no—
332C2×D43—22no—
333C2×D43—44no—
334C2×D43—412no—
335C4×C43—26no—
336C4×C43—22no—
337C4×C43—22no—
338C4×C43—26no—
339C4×C43—26no—
340C4×C43C22×#41112yes—
341Dic43—26no—
342Dic43—22no—
343Dic43—26no—
344Dic43—22no—
345Dic43—22no—
346Dic43—26no—
347#3516—4332no—
348C2×#557—431no—
349C2×#556—433no—
350C2×#554—433no—
351C2×#553—433no—
352C2×#552—433no—
353C2×D4×Q8—431no—
354C2×#548—431no—
355C2×#548—431no—
356C2×#542—433no—
357C2×#541—433no—
358C2×#529—433no—
359C2×#529—433no—
360C2×#520—431no—
361C2×#519—431no—
362C22×C4×Q8D4311yescharacteristic, complemented
363C2×C43—24no—
364C2×C43#351614yescomplemented
365C2×C43C23×#4111yescharacteristic
366C2×C43C22×2−1+411yescharacteristic
367C2×C43C2×#58511yescharacteristic
368D43—42no—
369D43—46no—
370C22×#41—431no—
371C23×Q8—431no—
372C23×Q8C2×D4311yescharacteristic
373#557—4316no—
374#556—4348no—
375#554—4348no—
376#553—4348no—
377#552—4348no—
378D4×Q8—4316no—
379#548—4316no—
380#548—4316no—
381#542—4348no—
382#541—4348no—
383C2×C4⋊Q8—433no—
384C2×C4⋊Q8—433no—
385#529—4348no—
386#529—4348no—
387C2×#126—436no—
388C2×#126—436no—
389C2×#126—433no—
390C2×#126—433no—
391C2×#125—436no—
392C2×#125—433no—
393C2×#125—433no—
394C2×#125—433no—
395C2×#124—433no—
396C2×#124—433no—
397C2×#124—433no—
398C2×#123—431no—
399C2×#123—433no—
400C2×#123—436no—
401C2×C22⋊Q8—433no—
402C2×C22⋊Q8—433no—
403C2×C22⋊Q8—433no—
404C2×C22⋊Q8—433no—
405C2×C22⋊Q8—436no—
406C2×C22⋊Q8—433no—
407C2×#121—433no—
408C2×#121—433no—
409C2×#121—433no—
410#520—4316no—
411#519—4316no—
412C2×C4×Q8—431no—
413C2×C4×Q8—431no—
414C2×C4×Q8—433no—
415C2×C4×Q8—433no—
416C2×C4×Q8—433no—
417C2×C4×Q8C2×D4311yescharacteristic
418C2×C4×Q8C2×D4313yes—
419C2×C4×Q8C2×D4311yescharacteristic
420C2×C4×Q8C2×D4313yes—
421C2×C4×Q8C2×D43116yescomplemented
422C2×C4×D4—433no—
423C2×C4×D4—433no—
424C2×C4×D4—436no—
425C2×C4×D4—433no—
426C2×C4×D4—433no—
427C2×C4×D4—433no—
428C2×#117—433no—
429C2×#117—433no—
430C2×#117—433no—
431C2×#117—436no—
432C22×C4⋊C4—433no—
433C22×C4⋊C4C2×D4313yes—
434C22×C42C2×D4313yes—
435C43C2×#351611yescharacteristic, complemented, Sylow
436C2×#41—438no—
437C2×#41—868no—
438C22×Q8—28no—
439C22×Q8—438no—
440C22×Q8—433no—
441C22×Q8—433no—
442C22×Q8—868no—
443C22×Q8C22×D4313yes—
444C22×Q8C22×D4318yes—
445C22×Q8C22×D4311yescharacteristic
446C22×D4—433no—
447C22×D4—431no—
448C22×D4—433no—
449C22×D4—433no—
450C23×C4—433no—
451C23×C4—433no—
452C23×C4—436no—
453C23×C4C22×D4313yes—
454C23×C4C22×D4311yescharacteristic
455C23×C4C22×D4313yes—
456C4⋊Q8—4324no—
457C4⋊Q8—4324no—
458#126—4348no—
459#126—4348no—
460#126—4324no—
461#126—4324no—
462#125—4348no—
463#125—4324no—
464#125—4324no—
465#125—4324no—
466#124—4324no—
467#124—4324no—
468#124—4324no—
469#123—438no—
470#123—4324no—
471#123—4348no—
472C22⋊Q8—4324no—
473C22⋊Q8—4324no—
474C22⋊Q8—4324no—
475C22⋊Q8—4324no—
476C22⋊Q8—4324no—
477C22⋊Q8—4348no—
478#121—4324no—
479#121—4324no—
480#121—4324no—
481C4×Q8—438no—
482C4×Q8—438no—
483C4×Q8—4324no—
484C4×Q8—4324no—
485C4×Q8—4324no—
486C4×Q8C22×D4318yes—
487C4×Q8C22×D43124yes—
488C4×Q8C22×D4318yes—
489C4×Q8C22×D43124yes—
490C4×D4—4324no—
491C4×D4—4324no—
492C4×D4—4348no—
493C4×D4—4324no—
494C4×D4—4324no—
495C4×D4—4324no—
496#117—4324no—
497#117—4324no—
498#117—4324no—
499#117—4348no—
500C2×C4⋊C4—433no—
501C2×C4⋊C4—433no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—433no—
504C2×C4⋊C4—433no—
505C2×C4⋊C4—433no—
506C2×C4⋊C4—433no—
507C2×C4⋊C4—436no—
508C2×C4⋊C4—433no—
509C2×C4⋊C4—433no—
510C2×C4⋊C4—436no—
511C2×C4⋊C4—433no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—433no—
514C2×C4⋊C4—4324no—
515C2×C4⋊C4C22×D4313yes—
516C2×C4⋊C4C22×D4313yes—
517C2×C4⋊C4C22×D4316yes—
518C2×C4⋊C4C22×D43124yes—
519C2×C22⋊C4—431no—
520C2×C22⋊C4—433no—
521C2×C22⋊C4—433no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—433no—
524C2×C22⋊C4—433no—
525C2×C22⋊C4—433no—
526C2×C22⋊C4—436no—
527C2×C22⋊C4—431no—
528C2×C22⋊C4—436no—
529C2×C22⋊C4—433no—
530C2×C22⋊C4—433no—
531C2×C42—436no—
532C2×C42—433no—
533C2×C42—433no—
534C2×C42C22×D4313yes—
535C2×C42C22×D4313yes—
536C2×C42C22×D4313yes—
537C2×C42C22×D4313yes—
538C2×C42C22×D43124yes—
539C24—431no—
540C24—433no—
541C24C23×D4311yescharacteristic
542#41—8632no—
543C2×Q8—232no—
544C2×Q8—212no—
545C2×Q8—4312no—
546C2×Q8—4312no—
547C2×Q8—8632no—
548C2×Q8—8612no—
549C2×Q8—1726no—
550C2×Q8#1062189818yes—
551C2×Q8C23×D43112yes—
552C2×Q8C23×D4314yes—
553C2×D4—4312no—
554C2×D4—434no—
555C2×D4—4312no—
556C2×D4—4312no—
557C2×D4—8612no—
558C2×D4—864no—
559C2×D4—8612no—
560C2×D4—1726no—
561C22×C4—24no—
562C22×C4—212no—
563C22×C4—46no—
564C22×C4—431no—
565C22×C4—433no—
566C22×C4—431no—
567C22×C4—433no—
568C22×C4—433no—
569C22×C4—431no—
570C22×C4—4312no—
571C22×C4—4312no—
572C22×C4—4324no—
573C22×C4—8612no—
574C22×C4—8612no—
575C22×C4—17212no—
576C22×C4C23×D4314yes—
577C22×C4C23×D43112yes—
578C22×C4C23×D4313yes—
579C22×C4C23×D4311yescharacteristic
580C22×C4C23×D4311yescharacteristic
581C22×C4C23×D4313yes—
582C22×C4C23×D4313yes—
583C22×C4C23×D43112yes—
584C22×C4C23×D4313yes—
585C4⋊C4—4312no—
586C4⋊C4—4312no—
587C4⋊C4—434no—
588C4⋊C4—4312no—
589C4⋊C4—4312no—
590C4⋊C4—4312no—
591C4⋊C4—4312no—
592C4⋊C4—4324no—
593C4⋊C4—4312no—
594C4⋊C4—4312no—
595C4⋊C4—4324no—
596C4⋊C4—4312no—
597C4⋊C4—434no—
598C4⋊C4—4312no—
599C4⋊C4C23×D43112yes—
600C4⋊C4C23×D43112yes—
601C4⋊C4C23×D43124yes—
602C22⋊C4—434no—
603C22⋊C4—4312no—
604C22⋊C4—4312no—
605C22⋊C4—434no—
606C22⋊C4—4312no—
607C22⋊C4—4312no—
608C22⋊C4—4312no—
609C22⋊C4—4324no—
610C22⋊C4—434no—
611C22⋊C4—4324no—
612C22⋊C4—4312no—
613C22⋊C4—4312no—
614C42—4324no—
615C42—4312no—
616C42—4312no—
617C42C23×D43112yes—
618C42C23×D43112yes—
619C42C23×D43112yes—
620C42C23×D43112yes—
621C23—22no—
622C23—22no—
623C23—432no—
624C23—436no—
625C23—862no—
626C23—866no—
627C23—862no—
628C23—866no—
629C23—866no—
630C23—862no—
631C23#1306337314yes—
632C23C24×D4312yes—
633C23C24×D4311yescharacteristic
634Q8—224no—
635Q8—8624no—
636Q8—17212no—
637Q8C2×#10621898116yes—
638D4—8624no—
639D4—868no—
640D4—8624no—
641D4—17212no—
642C2×C4—26no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—26no—
647C2×C4—26no—
648C2×C4—224no—
649C2×C4—412no—
650C2×C4—432no—
651C2×C4—436no—
652C2×C4—432no—
653C2×C4—436no—
654C2×C4—436no—
655C2×C4—432no—
656C2×C4—862no—
657C2×C4—866no—
658C2×C4—866no—
659C2×C4—862no—
660C2×C4—866no—
661C2×C4—862no—
662C2×C4—8624no—
663C2×C4—8624no—
664C2×C4—17224no—
665C2×C4C2×#10621898112yes—
666C2×C4C24×D4316yes—
667C2×C4C24×D4312yes—
668C2×C4C24×D4312yes—
669C2×C4C24×D4316yes—
670C2×C4C24×D4316yes—
671C2×C4C24×D4316yes—
672C22—28no—
673C22—22no—
674C22—22no—
675C22—862no—
676C22—866no—
677C22—862no—
678C22—866no—
679C22—866no—
680C22—862no—
681C22—1724no—
682C22—17212no—
683C22C22×#1062189812yes—
684C22C2×#1306337314yes—
685C22C2×#1306337312yes—
686C22#1458373512yes—
687C22C25×D4311yescharacteristic
688C4—26no—
689C4—22no—
690C4—22no—
691C4—26no—
692C4—26no—
693C4—862no—
694C4—866no—
695C4—866no—
696C4—862no—
697C4—866no—
698C4—862no—
699C4C22×#10621898112yes—
700C2—24no—
701C2—1722no—
702C2—1726no—
703C2#1914858814yesdirect product factor
704C2C23×#1062189811yescharacteristic
705C2C22×#1306337311yescharacteristic
706C2C2×#1458373511yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC22×C4×Q8×C43C2
socleC23×C43C25
hypercenterC22×C4×Q8D43
hypocenterC43C2×#3516
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #19148588C2direct (N × H)
2. C2×#14583625C2semidirect
3. C2×#14583621C2semidirect
4. C2×#14583604C2semidirect
5. C2×#14583597C2semidirect
6. C2×#14583590C2semidirect
7. C2×Q8×C22⋊D43C2semidirect
8. C2×#14583561C2semidirect
9. C2×#14583560C2semidirect
10. C2×#14583521C2semidirect
11. C2×#14583507C2semidirect
12. C2×#14583433C2semidirect
13. C2×#14583433C2semidirect
14. C2×#14583381C2semidirect
15. C2×#14583375C2semidirect
16. C22×C4×Q8×C43C2semidirect
19. #14583625C22semidirect
20. #14583621C22semidirect
21. #14583604C22semidirect
22. #14583597C22semidirect
23. #14583590C22semidirect
24. Q8×C22⋊D43C22semidirect
25. #14583561C22semidirect
26. #14583560C22semidirect
27. #14583521C22semidirect
28. #14583507C22semidirect
31. #14583433C22semidirect
32. #14583433C22semidirect
56. #14583381C22semidirect
57. #14583375C22semidirect
79. C2×C4×Q8×C43C22semidirect
362. C22×C4×Q8D43semidirect
364. C2×C43#3516semidirect
421. C2×C4×Q8C2×D43semidirect
435. C43C2×#3516semidirect
703. C2#19148588direct (N × H)

Maximal subgroups

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

subgroupindex
#191485882
C2×#145836252
C2×#145836212
C2×#145836042
C2×#145835972
C2×#145835902
C2×Q8×C22⋊D432
C2×#145835612
C2×#145835602
C2×#145835212
C2×#145835072
C2×#145834332
C2×#145833812
C2×#145833752
C22×C4×Q8×C432
C2×#351643