Finite Group Databasebeta

← C2×#19148685 #26004816

Subgroups — C2×#19148685 #26004816

Order 11008.

7022 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148685C2132yesmaximal, direct product factor
2C2×#14583627C213yesmaximal, complemented
3C2×#14583625C211yesmaximal, characteristic, complemented
4C2×#14583617C213yesmaximal, complemented
5C2×#14583590C213yesmaximal, complemented
6C2×#14583588C213yesmaximal, complemented
7C2×Q8×D172C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
9C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
10C2×#14583511C213yesmaximal, complemented
11C2×#14583507C213yesmaximal, complemented
12C2×#14583453C213yesmaximal, complemented
13C2×#14583427C213yesmaximal
14C2×#14583375C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
16C2×C43×#519C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19#14583627C22148yescomplemented
20#14583625C22116yescomplemented
21#14583617C22148yescomplemented
22#14583590C22148yescomplemented
23#14583588C22148yescomplemented
24Q8×D172C22116yescomplemented
25Q8×C22⋊D43C22116yescomplemented
26Q8×C22⋊D43C22116yescomplemented
27#14583511C22148yescomplemented
28#14583507C22148yescomplemented
29#14583453C22148yescomplemented
30C2×#13063325C2213yes—
31C2×#13063324C2213yes—
32C2×#13063323C2213yes—
33C2×#13063323C2213yes—
34#14583427C22148yes—
35C2×#13063320C2213yes—
36C2×#13063319C2216yes—
37C2×#13063318C2216yes—
38C2×#13063318C2213yes—
39C2×#13063317C2216yes—
40C2×#13063317C2213yes—
41C2×#13063316C2213yes—
42C2×#13063315C2216yes—
43C2×#13063315C2213yes—
44C2×#13063315C2216yes—
45C2×#13063311C2213yes—
46C2×#13063310C2213yes—
47C2×#13063307C2213yes—
48C2×#13063305C2213yes—
49C2×#13063305C2213yes—
50C2×#13063304C2213yes—
51C2×#13063304C2213yes—
52C2×#13063303C2213yes—
53C2×#13063301C2213yes—
54C2×#13063301C2213yes—
55C2×#13063298C2211yescharacteristic
56#14583375C22116yescomplemented
57C2×Q8×Dic43C2211yescharacteristic
58C2×Q8×Dic43C2211yescharacteristic
59C2×C4×Dic86C2213yes—
60C2×C4×Dic86C2213yes—
61C2×C4×Dic86C2216yes—
62C2×C4×Dic86C2213yes—
63C2×#13063290C2213yes—
64C2×#13063290C2213yes—
65C4×Q8×D43C22116yescomplemented
66C2×C4×D172C2213yes—
67C2×C4×C22⋊D43C2213yes—
68C2×C4×C22⋊D43C2213yes—
69C2×#13063283C2213yes—
70C2×#13063282C2213yes—
71C2×#13063282C2216yes—
72C2×C4⋊C4×D43C2213yes—
73C2×C42×D43C2213yes—
74C23×Q8×C43C2211yescharacteristic
75C43×#519C22116yescomplemented
76C2×C4×Q8×C43C2211yescharacteristic
77C2×C4×Q8×C43C2211yescharacteristic
78C2×C4×Q8×C43C2213yes—
79C2×C4×Q8×C43C2213yes—
80C2×#117×C43C2213yes—
81C2×#117×C43C2213yes—
82C22×Dic86C2313yes—
83C22×Dic86C2313yes—
84C22×Dic86C2313yes—
85C2×Q8×D43—28no—
86C2×Q8×D43—28no—
87C2×Q8×D43C2318yes—
88C2×Q8×D43C2318yes—
89C22×D172C2311yescharacteristic
90C22×C22⋊D43C2311yescharacteristic
91C22×C22⋊D43C2311yescharacteristic
92C22×C4×D43C2311yescharacteristic
93C22×C4×D43C2313yes—
94C22×C4×D43C2313yes—
95C22×C4×D43C2313yes—
96#13063325C23124yes—
97#13063324C23124yes—
98#13063323C23124yes—
99#13063323C23124yes—
100#13063320C23124yes—
101#13063319C23148yes—
102#13063318C23148yes—
103#13063318C23124yes—
104#13063317C23148yes—
105#13063317C23124yes—
106#13063316C23124yes—
107#13063315C23148yes—
108#13063315C23124yes—
109#13063315C23148yes—
110#13063311C23124yes—
111#13063310C23124yes—
112#13063307C23124yes—
113#13063305C23124yes—
114#13063305C23124yes—
115#13063304C23124yes—
116#13063304C23124yes—
117#13063303C23124yes—
118#13063301C23124yes—
119#13063301C23124yes—
120#13063298C2318yes—
121Q8×Dic43C2318yes—
122Q8×Dic43C2318yes—
123C4×Dic86C23148yes—
124C4×Dic86C23124yes—
125C4×Dic86C23124yes—
126C4×Dic86C23124yes—
127#13063290C23124yes—
128#13063290C23124yes—
129C4×D172C23124yes—
130C4×C22⋊D43C23124yes—
131C4×C22⋊D43C23124yes—
132#13063283C23124yes—
133#13063282C23148yes—
134#13063282C23124yes—
135C2×C4⋊Dic43C2313yes—
136C2×C4⋊Dic43C2313yes—
137C2×C4⋊Dic43C2313yes—
138C2×C4⋊Dic43C2316yes—
139C2×C4⋊Dic43C2313yes—
140C2×Dic43⋊C4C2316yes—
141C2×Dic43⋊C4C2313yes—
142C2×Dic43⋊C4C2313yes—
143C2×Dic43⋊C4C2316yes—
144C2×Dic43⋊C4C2316yes—
145C2×Dic43⋊C4C2313yes—
146C2×Dic43⋊C4C2313yes—
147C2×Dic43⋊C4C2311yescharacteristic
148C2×Dic43⋊C4C2316yes—
149C2×Dic43⋊C4C2313yes—
150C4⋊C4×D43C23124yes—
151C2×C22⋊Dic43C2313yes—
152C2×C22⋊Dic43C2313yes—
153C2×(C2×D43)⋊C4C2311yescharacteristic
154C2×(C2×D43)⋊C4C2313yes—
155C2×(C2×D43)⋊C4C2313yes—
156C2×(C2×D43)⋊C4C2313yes—
157C2×(C2×D43)⋊C4C2313yes—
158C2×(C2×D43)⋊C4C2313yes—
159C2×C4×Dic43C2313yes—
160C2×C4×Dic43C2313yes—
161C2×C4×Dic43C2313yes—
162C2×C4×Dic43C2316yes—
163C2×C4×Dic43C2313yes—
164C42×D43C23124yes—
165C22×Q8×C43—28no—
166C22×Q8×C43C2318yes—
167C22×Q8×C43C2313yes—
168C22×Q8×C43C2311yescharacteristic
169C23×C4×C43C2313yes—
170C4×Q8×C43C2318yes—
171C4×Q8×C43C23124yes—
172C4×Q8×C43C2318yes—
173C4×Q8×C43C23124yes—
174#117×C43C23124yes—
175#117×C43C23124yes—
176C2×C4⋊C4×C43C2313yes—
177C2×C4⋊C4×C43C2313yes—
178C2×C4⋊C4×C43C2313yes—
179C2×C4⋊C4×C43C2313yes—
180C2×C22⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43C2313yes—
182C2×C42×C43C2313yes—
183C2×C42×C43C2316yes—
184C2×C42×C43C2313yes—
185C24×C43C2411yescharacteristic
186C23×D43C2411yescharacteristic
187C23×D43C2411yescharacteristic
188C2×Q8×C43—232no—
189C2×Q8×C43—212no—
190C2×Q8×C43#4118yes—
191C2×Q8×C43C24112yes—
192C2×Q8×C43C2414yes—
193C22×C4×C43—212no—
194C22×C4×C43C2411yescharacteristic
195C22×C4×C43C2413yes—
196C22×C4×C43C2413yes—
197C22×C4×C43C2411yescharacteristic
198C22×C4×C43C2413yes—
199C22×C4×C43C24112yes—
200C22×C4×C43C2413yes—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43C2414yes—
204C2×C22⋊D43C2414yes—
205C22×Dic43C2413yes—
206C22×Dic43C2411yescharacteristic
207C22×Dic43C2413yes—
208C22×Dic43C2413yes—
209C22×Dic43C2413yes—
210C22×Dic43C2411yescharacteristic
211Q8×D43—232no—
212Q8×D43—232no—
213C2×D172—24no—
214C2×D172C2414yes—
215C2×C4×D43—212no—
216C2×C4×D43—212no—
217C2×C4×D43—24no—
218C2×C4×D43—212no—
219C2×C4×D43C2414yes—
220C2×C4×D43C24112yes—
221C2×C4×D43C24112yes—
222C2×C4×D43C24112yes—
223C2×Dic86—212no—
224C2×Dic86—212no—
225C2×Dic86—212no—
226C2×Dic86C24112yes—
227C2×Dic86C24112yes—
228C2×Dic86C24112yes—
229C4⋊C4×C43C24112yes—
230C4⋊C4×C43C24112yes—
231C4⋊C4×C43C24112yes—
232C4⋊C4×C43C24112yes—
233C22⋊C4×C43C2414yes—
234C22⋊C4×C43C24112yes—
235C42×C43C24112yes—
236C42×C43C24124yes—
237C42×C43C24112yes—
238C22⋊Dic43C24112yes—
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)⋊C4C24112yes—
246C4⋊Dic43C24112yes—
247C4⋊Dic43C24112yes—
248C4⋊Dic43C24112yes—
249C4⋊Dic43C24124yes—
250C4⋊Dic43C24112yes—
251Dic43⋊C4C24124yes—
252Dic43⋊C4C24112yes—
253Dic43⋊C4C24112yes—
254Dic43⋊C4C24124yes—
255Dic43⋊C4C24124yes—
256Dic43⋊C4C24112yes—
257Dic43⋊C4C24112yes—
258Dic43⋊C4C2414yes—
259Dic43⋊C4C24124yes—
260Dic43⋊C4C24112yes—
261C4×Dic43C24112yes—
262C4×Dic43C24112yes—
263C4×Dic43C24112yes—
264C4×Dic43C24124yes—
265C4×Dic43C24112yes—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43C2512yes—
270C23×C43C2511yescharacteristic
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D432−1+414yes—
277C22×D43C2512yes—
278C22×D43C2512yes—
279Q8×C43—224no—
280Q8×C43C2×#41116yes—
281C2×C4×C43—26no—
282C2×C4×C43—26no—
283C2×C4×C43—22no—
284C2×C4×C43—26no—
285C2×C4×C43—22no—
286C2×C4×C43—224no—
287C2×C4×C43C2×#41112yes—
288C2×C4×C43C2516yes—
289C2×C4×C43C2512yes—
290C2×C4×C43C2516yes—
291C2×C4×C43C2512yes—
292C2×C4×C43C2516yes—
293C2×C4×C43C2516yes—
294C22⋊D43—28no—
295C22⋊D43—28no—
296C2×Dic43—26no—
297C2×Dic43—26no—
298C2×Dic43—26no—
299C2×Dic43—26no—
300C2×Dic43—22no—
301C2×Dic432−1+414yes—
302C2×Dic43C2512yes—
303C2×Dic43C2516yes—
304C2×Dic43C2516yes—
305C2×Dic43C2516yes—
306C2×Dic43C2516yes—
307C2×Dic43C2512yes—
308D172—28no—
309C4×D43—224no—
310C4×D43—224no—
311C4×D43—224no—
312C4×D43—28no—
313Dic86—224no—
314Dic86—224no—
315Dic86—224no—
316C2×#3523—431nomaximal, Sylow
317C22×C43—22no—
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—44no—
321C22×C43C22×#4112yes—
322C22×C43C2×2−1+412yes—
323C22×C43C2×2−1+412yes—
324C22×C43C2611yescharacteristic
325C2×D43—22no—
326C2×D43—22no—
327C2×D43—28no—
328C2×D43—22no—
329C2×D43—22no—
330C2×D43—22no—
331C2×D43—44no—
332C2×D43C2×2−1+414yes—
333C4×C43—26no—
334C4×C43—26no—
335C4×C43—26no—
336C4×C43—22no—
337C4×C43—22no—
338C4×C43C22×#41112yes—
339Dic43—26no—
340Dic43—26no—
341Dic43—26no—
342Dic43—26no—
343Dic43—22no—
344Dic43C2×2−1+414yes—
345#3523—4332no—
346C2×#557—431no—
347C2×#557—433no—
348C2×#556—433no—
349C2×#552—433no—
350C2×#552—433no—
351C2×D4×Q8—431no—
352C2×D4×Q8—431no—
353C2×D4×Q8—431no—
354C2×#541—433no—
355C2×#541—433no—
356C2×#533—433no—
357C2×#529—433no—
358C2×#519—431no—
359C2×#519D4311yescharacteristic, complemented
360C22×C4×Q8—431no—
361C2×C43—42no—
362C2×C43#352314yescomplemented
363C2×C43C23×#4111yescharacteristic
364C2×C43C22×2−1+411yescharacteristic
365C2×C43C22×2−1+411yescharacteristic
366D43—24no—
367D43—42no—
368C23×Q8—431no—
369C23×Q8—431no—
370C23×Q8C2×D4311yescharacteristic
371#557—4316no—
372#557—4348no—
373#556—4348no—
374#552—4348no—
375#552—4348no—
376D4×Q8—4316no—
377D4×Q8—4316no—
378D4×Q8—4316no—
379#541—4348no—
380#541—4348no—
381#533—4348no—
382C2×C4⋊Q8—433no—
383C2×C4⋊Q8—433no—
384C2×C4⋊Q8—433no—
385C2×C4⋊Q8—433no—
386#529—4348no—
387C2×#126—433no—
388C2×#126—433no—
389C2×#126—436no—
390C2×#126—436no—
391C2×#125—433no—
392C2×#125—436no—
393C2×#125—436no—
394C2×#125—433no—
395C2×#125—436no—
396C2×#125—433no—
397C2×#124—433no—
398C2×#123—433no—
399C2×#123—433no—
400C2×C22⋊Q8—433no—
401C2×C22⋊Q8—433no—
402C2×C22⋊Q8—433no—
403C2×C22⋊Q8—433no—
404C2×C22⋊Q8—433no—
405C2×C22⋊Q8—433no—
406C2×C22⋊Q8—433no—
407C2×#121—431no—
408#519—4316no—
409#519C2×D43116yescomplemented
410C2×C4×Q8—431no—
411C2×C4×Q8—431no—
412C2×C4×Q8—4316no—
413C2×C4×Q8—433no—
414C2×C4×Q8—433no—
415C2×C4×Q8—433no—
416C2×C4×Q8—433no—
417C2×C4×Q8—433no—
418C2×C4×Q8—436no—
419C2×C4×Q8C2×D4311yescharacteristic
420C2×C4×Q8C2×D4313yes—
421C2×C4×Q8C2×D4311yescharacteristic
422C2×C4×Q8C2×D4313yes—
423C2×C4×D4—433no—
424C2×C4×D4—433no—
425C2×C4×D4—433no—
426C2×#117—433no—
427C2×#117—433no—
428C2×#117—436no—
429C2×#117C2×D4313yes—
430C2×#117C2×D4313yes—
431C22×C4⋊C4—433no—
432C22×C42—433no—
433C43C2×#352311yescharacteristic, complemented, Sylow
434C22×Q8—28no—
435C22×Q8—438no—
436C22×Q8—438no—
437C22×Q8—433no—
438C22×Q8—433no—
439C22×Q8—433no—
440C22×Q8—868no—
441C22×Q8—868no—
442C22×Q8C22×D4313yes—
443C22×Q8C22×D4318yes—
444C22×Q8C22×D4311yescharacteristic
445C22×D4—431no—
446C22×D4—431no—
447C22×D4—431no—
448C23×C4—433no—
449C23×C4—433no—
450C23×C4—433no—
451C23×C4—431no—
452C23×C4C22×D4313yes—
453C4⋊Q8—4324no—
454C4⋊Q8—4324no—
455C4⋊Q8—4324no—
456C4⋊Q8—4324no—
457#126—4324no—
458#126—4324no—
459#126—4348no—
460#126—4348no—
461#125—4324no—
462#125—4348no—
463#125—4348no—
464#125—4324no—
465#125—4348no—
466#125—4324no—
467#124—4324no—
468#123—4324no—
469#123—4324no—
470C22⋊Q8—4324no—
471C22⋊Q8—4324no—
472C22⋊Q8—4324no—
473C22⋊Q8—4324no—
474C22⋊Q8—4324no—
475C22⋊Q8—4324no—
476C22⋊Q8—4324no—
477#121—438no—
478C4×Q8—438no—
479C4×Q8—438no—
480C4×Q8—4324no—
481C4×Q8—4324no—
482C4×Q8—4324no—
483C4×Q8—4324no—
484C4×Q8—4324no—
485C4×Q8—4348no—
486C4×Q8C22×D4318yes—
487C4×Q8C22×D43124yes—
488C4×Q8C22×D4318yes—
489C4×Q8C22×D43124yes—
490C4×D4—4324no—
491C4×D4—4324no—
492C4×D4—4324no—
493#117—4324no—
494#117—4324no—
495#117—4348no—
496#117C22×D43124yes—
497#117C22×D43124yes—
498C2×C4⋊C4—433no—
499C2×C4⋊C4—436no—
500C2×C4⋊C4—433no—
501C2×C4⋊C4—433no—
502C2×C4⋊C4—433no—
503C2×C4⋊C4—436no—
504C2×C4⋊C4—436no—
505C2×C4⋊C4—433no—
506C2×C4⋊C4—433no—
507C2×C4⋊C4—433no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—436no—
510C2×C4⋊C4—436no—
511C2×C4⋊C4—433no—
512C2×C4⋊C4—433no—
513C2×C4⋊C4—4324no—
514C2×C4⋊C4C22×D4313yes—
515C2×C4⋊C4C22×D4313yes—
516C2×C4⋊C4C22×D4313yes—
517C2×C4⋊C4C22×D4313yes—
518C2×C22⋊C4—433no—
519C2×C22⋊C4—433no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—433no—
522C2×C22⋊C4—433no—
523C2×C22⋊C4—433no—
524C2×C22⋊C4—433no—
525C2×C22⋊C4—433no—
526C2×C22⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4C22×D4313yes—
528C2×C42—436no—
529C2×C42—433no—
530C2×C42—433no—
531C2×C42—433no—
532C2×C42—433no—
533C2×C42—4324no—
534C2×C42C22×D4313yes—
535C2×C42C22×D4316yes—
536C2×C42C22×D4313yes—
537C24—431no—
538C24—431no—
539C24C23×D4311yescharacteristic
540C2×Q8—232no—
541C2×Q8—212no—
542C2×Q8—4312no—
543C2×Q8—4312no—
544C2×Q8—4312no—
545C2×Q8—8612no—
546C2×Q8—8632no—
547C2×Q8—8632no—
548C2×Q8—8612no—
549C2×Q8—8612no—
550C2×Q8#1062189818yes—
551C2×Q8C23×D43112yes—
552C2×Q8C23×D4314yes—
553C2×D4—434no—
554C2×D4—434no—
555C2×D4—434no—
556C2×D4—864no—
557C2×D4—864no—
558C2×D4—864no—
559C22×C4—212no—
560C22×C4—431no—
561C22×C4—433no—
562C22×C4—431no—
563C22×C4—433no—
564C22×C4—433no—
565C22×C4—433no—
566C22×C4—434no—
567C22×C4—4312no—
568C22×C4—4312no—
569C22×C4—4312no—
570C22×C4—864no—
571C22×C4—8612no—
572C22×C4—8612no—
573C22×C4—8612no—
574C22×C4C23×D43112yes—
575C22×C4C23×D4313yes—
576C22×C4C23×D4311yescharacteristic
577C22×C4C23×D4313yes—
578C22×C4C23×D4311yescharacteristic
579C22×C4C23×D4313yes—
580C22×C4C23×D4313yes—
581C4⋊C4—4312no—
582C4⋊C4—4324no—
583C4⋊C4—4312no—
584C4⋊C4—4312no—
585C4⋊C4—4312no—
586C4⋊C4—4324no—
587C4⋊C4—4324no—
588C4⋊C4—4312no—
589C4⋊C4—4312no—
590C4⋊C4—4312no—
591C4⋊C4—434no—
592C4⋊C4—4324no—
593C4⋊C4—4324no—
594C4⋊C4—4312no—
595C4⋊C4—4312no—
596C4⋊C4C23×D43112yes—
597C4⋊C4C23×D43112yes—
598C4⋊C4C23×D43112yes—
599C4⋊C4C23×D43112yes—
600C22⋊C4—4312no—
601C22⋊C4—4312no—
602C22⋊C4—434no—
603C22⋊C4—4312no—
604C22⋊C4—4312no—
605C22⋊C4—4312no—
606C22⋊C4—4312no—
607C22⋊C4—4312no—
608C22⋊C4C23×D4314yes—
609C22⋊C4C23×D43112yes—
610C42—4312no—
611C42—4312no—
612C42—4312no—
613C42—4324no—
614C42—4312no—
615C42C23×D43112yes—
616C42C23×D43124yes—
617C42C23×D43112yes—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—434no—
622C23—432no—
623C23—432no—
624C23—862no—
625C23—862no—
626C23—862no—
627C23—862no—
628C23—862no—
629C23C24×D4312yes—
630C23C24×D4311yescharacteristic
631Q8—224no—
632Q8—8624no—
633Q8—8624no—
634Q8—8624no—
635Q8C2×#10621898116yes—
636D4—868no—
637D4—868no—
638D4—868no—
639C2×C4—26no—
640C2×C4—22no—
641C2×C4—26no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—224no—
645C2×C4—434no—
646C2×C4—432no—
647C2×C4—436no—
648C2×C4—432no—
649C2×C4—436no—
650C2×C4—436no—
651C2×C4—436no—
652C2×C4—868no—
653C2×C4—8624no—
654C2×C4—866no—
655C2×C4—866no—
656C2×C4—866no—
657C2×C4—862no—
658C2×C4—866no—
659C2×C4—8624no—
660C2×C4—8624no—
661C2×C4C2×#10621898112yes—
662C2×C4C24×D4316yes—
663C2×C4C24×D4312yes—
664C2×C4C24×D4316yes—
665C2×C4C24×D4312yes—
666C2×C4C24×D4316yes—
667C2×C4C24×D4316yes—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—434no—
673C22—862no—
674C22—862no—
675C22—868no—
676C22—862no—
677C22—862no—
678C22—862no—
679C22—1724no—
680C22C22×#1062189812yes—
681C222−1+4×D4312yes—
682C222−1+4×D4312yes—
683C22C25×D4311yescharacteristic
684C4—26no—
685C4—22no—
686C4—26no—
687C4—22no—
688C4—26no—
689C4—434no—
690C4—866no—
691C4—866no—
692C4—866no—
693C4—862no—
694C4—866no—
695C4C22×#10621898112yes—
696C2—42no—
697C2—864no—
698C2—1722no—
699C2#1914868514yesdirect product factor
700C2C23×#1062189811yescharacteristic
701C2C2×2−1+4×D4311yescharacteristic
702C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#519C2
socleC23×C43C25
prime radicalC2×#13063298C22
hypercenterC2×#519D43
hypocenterC43C2×#3523
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. #19148685C2direct (N × H)
2. C2×#14583627C2semidirect
3. C2×#14583625C2semidirect
4. C2×#14583617C2semidirect
5. C2×#14583590C2semidirect
6. C2×#14583588C2semidirect
7. C2×Q8×D172C2semidirect
8. C2×Q8×C22⋊D43C2semidirect
9. C2×Q8×C22⋊D43C2semidirect
10. C2×#14583511C2semidirect
11. C2×#14583507C2semidirect
12. C2×#14583453C2semidirect
14. C2×#14583375C2semidirect
15. C2×C4×Q8×D43C2semidirect
16. C2×C43×#519C2semidirect
19. #14583627C22semidirect
20. #14583625C22semidirect
21. #14583617C22semidirect
22. #14583590C22semidirect
23. #14583588C22semidirect
24. Q8×D172C22semidirect
25. Q8×C22⋊D43C22semidirect
26. Q8×C22⋊D43C22semidirect
27. #14583511C22semidirect
28. #14583507C22semidirect
29. #14583453C22semidirect
56. #14583375C22semidirect
65. C4×Q8×D43C22semidirect
75. C43×#519C22semidirect
359. C2×#519D43semidirect
362. C2×C43#3523semidirect
409. #519C2×D43semidirect
433. C43C2×#3523semidirect
699. C2#19148685direct (N × H)

Maximal subgroups

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

subgroupindex
#191486852
C2×#145836272
C2×#145836252
C2×#145836172
C2×#145835902
C2×#145835882
C2×Q8×D1722
C2×Q8×C22⋊D432
C2×#145835112
C2×#145835072
C2×#145834532
C2×#145834272
C2×#145833752
C2×C4×Q8×D432
C2×C43×#5192
C2×#352343