Finite Group Databasebeta

← C2×#24921553 #36312623

Subgroups — C2×#24921553 #36312623

Order 21248.

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#24921553C2132yesmaximal, direct product factor
2C2×#19128429C213yesmaximal, complemented
3C2×#19128427C211yesmaximal, characteristic, complemented
4C2×#19128419C213yesmaximal, complemented
5C2×#19128392C213yesmaximal, complemented
6C2×#19128390C213yesmaximal, complemented
7C2×Q8×D332C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D83C211yesmaximal, characteristic, complemented
9C2×Q8×C22⋊D83C211yesmaximal, characteristic, complemented
10C2×#19128313C213yesmaximal, complemented
11C2×#19128309C213yesmaximal, complemented
12C2×#19128255C213yesmaximal, complemented
13C2×#19128229C213yesmaximal
14C2×#19128177C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
16C2×#519×C83C211yesmaximal, characteristic, complemented
17C22×Q8×D83C2211yescharacteristic
18C22×Q8×D83C2211yescharacteristic
19#19128429C22148yescomplemented
20#19128427C22116yescomplemented
21#19128419C22148yescomplemented
22#19128392C22148yescomplemented
23#19128390C22148yescomplemented
24Q8×D332C22116yescomplemented
25Q8×C22⋊D83C22116yescomplemented
26Q8×C22⋊D83C22116yescomplemented
27#19128313C22148yescomplemented
28#19128309C22148yescomplemented
29#19128255C22148yescomplemented
30C2×#14581792C2213yes—
31C2×#14581791C2213yes—
32C2×#14581790C2213yes—
33C2×#14581790C2213yes—
34#19128229C22148yes—
35C2×#14581787C2213yes—
36C2×#14581786C2216yes—
37C2×#14581785C2216yes—
38C2×#14581785C2213yes—
39C2×#14581784C2216yes—
40C2×#14581784C2213yes—
41C2×#14581783C2213yes—
42C2×#14581782C2216yes—
43C2×#14581782C2213yes—
44C2×#14581782C2216yes—
45C2×#14581778C2213yes—
46C2×#14581777C2213yes—
47C2×#14581774C2213yes—
48C2×#14581772C2213yes—
49C2×#14581772C2213yes—
50C2×#14581771C2213yes—
51C2×#14581771C2213yes—
52C2×#14581770C2213yes—
53C2×#14581768C2213yes—
54C2×#14581768C2213yes—
55C2×#14581765C2211yescharacteristic
56#19128177C22116yescomplemented
57C2×Q8×Dic83C2211yescharacteristic
58C2×Q8×Dic83C2211yescharacteristic
59C2×C4×Dic166C2213yes—
60C2×C4×Dic166C2213yes—
61C2×C4×Dic166C2213yes—
62C2×C4×Dic166C2216yes—
63C2×#14581757C2213yes—
64C2×#14581757C2213yes—
65C4×Q8×D83C22116yescomplemented
66C2×C4×D332C2213yes—
67C2×C4×C22⋊D83C2213yes—
68C2×C4×C22⋊D83C2213yes—
69C2×#14581750C2213yes—
70C2×#14581749C2213yes—
71C2×#14581749C2216yes—
72C2×C4⋊C4×D83C2213yes—
73C2×C42×D83C2213yes—
74C23×Q8×C83C2211yescharacteristic
75#519×C83C22116yescomplemented
76C2×C4×Q8×C83C2211yescharacteristic
77C2×C4×Q8×C83C2211yescharacteristic
78C2×C4×Q8×C83C2213yes—
79C2×C4×Q8×C83C2213yes—
80C2×#117×C83C2213yes—
81C2×#117×C83C2213yes—
82C22×Dic166C2313yes—
83C22×Dic166C2313yes—
84C22×Dic166C2313yes—
85C2×Q8×D83—28no—
86C2×Q8×D83—28no—
87C2×Q8×D83C2318yes—
88C2×Q8×D83C2318yes—
89C22×D332C2311yescharacteristic
90C22×C22⋊D83C2311yescharacteristic
91C22×C22⋊D83C2311yescharacteristic
92C22×C4×D83C2311yescharacteristic
93C22×C4×D83C2313yes—
94C22×C4×D83C2313yes—
95C22×C4×D83C2313yes—
96#14581792C23124yes—
97#14581791C23124yes—
98#14581790C23124yes—
99#14581790C23124yes—
100#14581787C23124yes—
101#14581786C23148yes—
102#14581785C23148yes—
103#14581785C23124yes—
104#14581784C23148yes—
105#14581784C23124yes—
106#14581783C23124yes—
107#14581782C23148yes—
108#14581782C23124yes—
109#14581782C23148yes—
110#14581778C23124yes—
111#14581777C23124yes—
112#14581774C23124yes—
113#14581772C23124yes—
114#14581772C23124yes—
115#14581771C23124yes—
116#14581771C23124yes—
117#14581770C23124yes—
118#14581768C23124yes—
119#14581768C23124yes—
120#14581765C2318yes—
121Q8×Dic83C2318yes—
122Q8×Dic83C2318yes—
123C4×Dic166C23148yes—
124C4×Dic166C23124yes—
125C4×Dic166C23124yes—
126C4×Dic166C23124yes—
127#14581757C23124yes—
128#14581757C23124yes—
129C4×D332C23124yes—
130C4×C22⋊D83C23124yes—
131C4×C22⋊D83C23124yes—
132#14581750C23124yes—
133#14581749C23148yes—
134#14581749C23124yes—
135C2×C4⋊Dic83C2313yes—
136C2×C4⋊Dic83C2313yes—
137C2×C4⋊Dic83C2313yes—
138C2×C4⋊Dic83C2316yes—
139C2×C4⋊Dic83C2313yes—
140C2×Dic83⋊C4C2316yes—
141C2×Dic83⋊C4C2313yes—
142C2×Dic83⋊C4C2313yes—
143C2×Dic83⋊C4C2316yes—
144C2×Dic83⋊C4C2316yes—
145C2×Dic83⋊C4C2313yes—
146C2×Dic83⋊C4C2313yes—
147C2×Dic83⋊C4C2311yescharacteristic
148C2×Dic83⋊C4C2316yes—
149C2×Dic83⋊C4C2313yes—
150C4⋊C4×D83C23124yes—
151C2×C22⋊Dic83C2313yes—
152C2×C22⋊Dic83C2313yes—
153C2×(C2×D83)⋊C4C2311yescharacteristic
154C2×(C2×D83)⋊C4C2313yes—
155C2×(C2×D83)⋊C4C2313yes—
156C2×(C2×D83)⋊C4C2313yes—
157C2×(C2×D83)⋊C4C2313yes—
158C2×(C2×D83)⋊C4C2313yes—
159C2×C4×Dic83C2313yes—
160C2×C4×Dic83C2313yes—
161C2×C4×Dic83C2313yes—
162C2×C4×Dic83C2316yes—
163C2×C4×Dic83C2313yes—
164C42×D83C23124yes—
165C22×Q8×C83—28no—
166C22×Q8×C83C2318yes—
167C22×Q8×C83C2313yes—
168C22×Q8×C83C2311yescharacteristic
169C23×C4×C83C2313yes—
170C4×Q8×C83C2318yes—
171C4×Q8×C83C23124yes—
172C4×Q8×C83C2318yes—
173C4×Q8×C83C23124yes—
174#117×C83C23124yes—
175#117×C83C23124yes—
176C2×C4⋊C4×C83C2313yes—
177C2×C4⋊C4×C83C2313yes—
178C2×C4⋊C4×C83C2313yes—
179C2×C4⋊C4×C83C2313yes—
180C2×C22⋊C4×C83C2311yescharacteristic
181C2×C22⋊C4×C83C2313yes—
182C2×C42×C83C2313yes—
183C2×C42×C83C2316yes—
184C2×C42×C83C2313yes—
185C23×D83C2411yescharacteristic
186C23×D83C2411yescharacteristic
187C2×Dic166—212no—
188C2×Dic166—212no—
189C2×Dic166—212no—
190C2×Dic166C24112yes—
191C2×Dic166C24112yes—
192C2×Dic166C24112yes—
193Q8×D83—232no—
194Q8×D83—232no—
195C2×D332—24no—
196C2×D332C2414yes—
197C2×C22⋊D83—24no—
198C2×C22⋊D83—24no—
199C2×C22⋊D83C2414yes—
200C2×C22⋊D83C2414yes—
201C22×Dic83C2413yes—
202C22×Dic83C2413yes—
203C22×Dic83C2413yes—
204C22×Dic83C2411yescharacteristic
205C22×Dic83C2413yes—
206C22×Dic83C2411yescharacteristic
207C2×C4×D83—212no—
208C2×C4×D83—212no—
209C2×C4×D83—212no—
210C2×C4×D83—24no—
211C2×C4×D83C2414yes—
212C2×C4×D83C24112yes—
213C2×C4×D83C24112yes—
214C2×C4×D83C24112yes—
215C4⋊Dic83C24112yes—
216C4⋊Dic83C24112yes—
217C4⋊Dic83C24124yes—
218C4⋊Dic83C24112yes—
219C4⋊Dic83C24112yes—
220Dic83⋊C4C2414yes—
221Dic83⋊C4C24124yes—
222Dic83⋊C4C24124yes—
223Dic83⋊C4C24112yes—
224Dic83⋊C4C24112yes—
225Dic83⋊C4C24112yes—
226Dic83⋊C4C24112yes—
227Dic83⋊C4C24124yes—
228Dic83⋊C4C24112yes—
229Dic83⋊C4C24124yes—
230C22⋊Dic83C24112yes—
231C22⋊Dic83C24112yes—
232(C2×D83)⋊C4C2414yes—
233(C2×D83)⋊C4C24112yes—
234(C2×D83)⋊C4C24112yes—
235(C2×D83)⋊C4C24112yes—
236(C2×D83)⋊C4C24112yes—
237(C2×D83)⋊C4C24112yes—
238C4×Dic83C24112yes—
239C4×Dic83C24112yes—
240C4×Dic83C24124yes—
241C4×Dic83C24112yes—
242C4×Dic83C24112yes—
243C24×C83C2411yescharacteristic
244C2×Q8×C83—232no—
245C2×Q8×C83—212no—
246C2×Q8×C83#4118yes—
247C2×Q8×C83C24112yes—
248C2×Q8×C83C2414yes—
249C22×C4×C83—212no—
250C22×C4×C83C24112yes—
251C22×C4×C83C2411yescharacteristic
252C22×C4×C83C2413yes—
253C22×C4×C83C2411yescharacteristic
254C22×C4×C83C2413yes—
255C22×C4×C83C2413yes—
256C22×C4×C83C2413yes—
257C4⋊C4×C83C24112yes—
258C4⋊C4×C83C24112yes—
259C4⋊C4×C83C24112yes—
260C4⋊C4×C83C24112yes—
261C22⋊C4×C83C2414yes—
262C22⋊C4×C83C24112yes—
263C42×C83C24124yes—
264C42×C83C24112yes—
265C42×C83C24112yes—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83C2512yes—
270C23×C83C2511yescharacteristic
271C22×D83—22no—
272C22×D83—22no—
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—22no—
276C22×D832−1+414yes—
277C22×D83C2512yes—
278C22×D83C2512yes—
279Q8×C83—224no—
280Q8×C83C2×#41116yes—
281C2×C4×C83—26no—
282C2×C4×C83—26no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—26no—
286C2×C4×C83—224no—
287C2×C4×C83C2×#41112yes—
288C2×C4×C83C2516yes—
289C2×C4×C83C2512yes—
290C2×C4×C83C2516yes—
291C2×C4×C83C2512yes—
292C2×C4×C83C2516yes—
293C2×C4×C83C2516yes—
294C22⋊D83—28no—
295C22⋊D83—28no—
296C2×Dic83—26no—
297C2×Dic83—26no—
298C2×Dic83—26no—
299C2×Dic83—22no—
300C2×Dic83—26no—
301C2×Dic832−1+414yes—
302C2×Dic83C2516yes—
303C2×Dic83C2512yes—
304C2×Dic83C2516yes—
305C2×Dic83C2516yes—
306C2×Dic83C2516yes—
307C2×Dic83C2512yes—
308D332—28no—
309C4×D83—224no—
310C4×D83—224no—
311C4×D83—224no—
312C4×D83—28no—
313Dic166—224no—
314Dic166—224no—
315Dic166—224no—
316C22×C83—22no—
317C22×C83—22no—
318C22×C83—22no—
319C22×C83—44no—
320C22×C83C22×#4112yes—
321C22×C83C2×2−1+412yes—
322C22×C83C2×2−1+412yes—
323C22×C83C2611yescharacteristic
324C2×D83—22no—
325C2×D83—22no—
326C2×D83—28no—
327C2×D83—22no—
328C2×D83—22no—
329C2×D83—22no—
330C2×D83—44no—
331C2×D83C2×2−1+414yes—
332C4×C83—26no—
333C4×C83—26no—
334C4×C83—26no—
335C4×C83—22no—
336C4×C83—22no—
337C4×C83C22×#41112yes—
338Dic83—26no—
339Dic83—26no—
340Dic83—26no—
341Dic83—26no—
342Dic83—22no—
343Dic83C2×2−1+414yes—
344C2×#3523—831nomaximal, Sylow
345C2×C83—42no—
346C2×C83#352314yescomplemented
347C2×C83C23×#4111yescharacteristic
348C2×C83C22×2−1+411yescharacteristic
349C2×C83C22×2−1+411yescharacteristic
350D83—24no—
351D83—42no—
352#3523—8332no—
353C2×#557—831no—
354C2×#557—833no—
355C2×#556—833no—
356C2×#552—833no—
357C2×#552—833no—
358C2×D4×Q8—831no—
359C2×D4×Q8—831no—
360C2×D4×Q8—831no—
361C2×#541—833no—
362C2×#541—833no—
363C2×#533—833no—
364C2×#529—833no—
365C2×#519—831no—
366C2×#519D8311yescharacteristic, complemented
367C22×C4×Q8—831no—
368C83C2×#352311yescharacteristic, complemented, Sylow
369C23×Q8—831no—
370C23×Q8—831no—
371C23×Q8C2×D8311yescharacteristic
372#557—8316no—
373#557—8348no—
374#556—8348no—
375#552—8348no—
376#552—8348no—
377D4×Q8—8316no—
378D4×Q8—8316no—
379D4×Q8—8316no—
380#541—8348no—
381#541—8348no—
382#533—8348no—
383C2×C4⋊Q8—833no—
384C2×C4⋊Q8—833no—
385C2×C4⋊Q8—833no—
386C2×C4⋊Q8—833no—
387#529—8348no—
388C2×#126—833no—
389C2×#126—833no—
390C2×#126—836no—
391C2×#126—836no—
392C2×#125—833no—
393C2×#125—836no—
394C2×#125—836no—
395C2×#125—833no—
396C2×#125—836no—
397C2×#125—833no—
398C2×#124—833no—
399C2×#123—833no—
400C2×#123—833no—
401C2×C22⋊Q8—833no—
402C2×C22⋊Q8—833no—
403C2×C22⋊Q8—833no—
404C2×C22⋊Q8—833no—
405C2×C22⋊Q8—833no—
406C2×C22⋊Q8—833no—
407C2×C22⋊Q8—833no—
408C2×#121—831no—
409#519—8316no—
410#519C2×D83116yescomplemented
411C2×C4×Q8—831no—
412C2×C4×Q8—831no—
413C2×C4×Q8—8316no—
414C2×C4×Q8—833no—
415C2×C4×Q8—833no—
416C2×C4×Q8—833no—
417C2×C4×Q8—833no—
418C2×C4×Q8—833no—
419C2×C4×Q8—836no—
420C2×C4×Q8C2×D8311yescharacteristic
421C2×C4×Q8C2×D8313yes—
422C2×C4×Q8C2×D8311yescharacteristic
423C2×C4×Q8C2×D8313yes—
424C2×C4×D4—833no—
425C2×C4×D4—833no—
426C2×C4×D4—833no—
427C2×#117—833no—
428C2×#117—833no—
429C2×#117—836no—
430C2×#117C2×D8313yes—
431C2×#117C2×D8313yes—
432C22×C4⋊C4—833no—
433C22×C42—833no—
434C22×Q8—28no—
435C22×Q8—838no—
436C22×Q8—838no—
437C22×Q8—833no—
438C22×Q8—833no—
439C22×Q8—833no—
440C22×Q8—1668no—
441C22×Q8—1668no—
442C22×Q8C22×D8313yes—
443C22×Q8C22×D8318yes—
444C22×Q8C22×D8311yescharacteristic
445C22×D4—831no—
446C22×D4—831no—
447C22×D4—831no—
448C23×C4—833no—
449C23×C4—833no—
450C23×C4—833no—
451C23×C4—831no—
452C23×C4C22×D8313yes—
453C4⋊Q8—8324no—
454C4⋊Q8—8324no—
455C4⋊Q8—8324no—
456C4⋊Q8—8324no—
457#126—8324no—
458#126—8324no—
459#126—8348no—
460#126—8348no—
461#125—8324no—
462#125—8348no—
463#125—8348no—
464#125—8324no—
465#125—8348no—
466#125—8324no—
467#124—8324no—
468#123—8324no—
469#123—8324no—
470C22⋊Q8—8324no—
471C22⋊Q8—8324no—
472C22⋊Q8—8324no—
473C22⋊Q8—8324no—
474C22⋊Q8—8324no—
475C22⋊Q8—8324no—
476C22⋊Q8—8324no—
477#121—838no—
478C4×Q8—838no—
479C4×Q8—838no—
480C4×Q8—8324no—
481C4×Q8—8324no—
482C4×Q8—8324no—
483C4×Q8—8324no—
484C4×Q8—8324no—
485C4×Q8—8348no—
486C4×Q8C22×D8318yes—
487C4×Q8C22×D83124yes—
488C4×Q8C22×D8318yes—
489C4×Q8C22×D83124yes—
490C4×D4—8324no—
491C4×D4—8324no—
492C4×D4—8324no—
493#117—8324no—
494#117—8324no—
495#117—8348no—
496#117C22×D83124yes—
497#117C22×D83124yes—
498C2×C4⋊C4—833no—
499C2×C4⋊C4—836no—
500C2×C4⋊C4—833no—
501C2×C4⋊C4—833no—
502C2×C4⋊C4—833no—
503C2×C4⋊C4—836no—
504C2×C4⋊C4—836no—
505C2×C4⋊C4—833no—
506C2×C4⋊C4—833no—
507C2×C4⋊C4—833no—
508C2×C4⋊C4—831no—
509C2×C4⋊C4—836no—
510C2×C4⋊C4—836no—
511C2×C4⋊C4—833no—
512C2×C4⋊C4—833no—
513C2×C4⋊C4—8324no—
514C2×C4⋊C4C22×D8313yes—
515C2×C4⋊C4C22×D8313yes—
516C2×C4⋊C4C22×D8313yes—
517C2×C4⋊C4C22×D8313yes—
518C2×C22⋊C4—833no—
519C2×C22⋊C4—833no—
520C2×C22⋊C4—831no—
521C2×C22⋊C4—833no—
522C2×C22⋊C4—833no—
523C2×C22⋊C4—833no—
524C2×C22⋊C4—833no—
525C2×C22⋊C4—833no—
526C2×C22⋊C4C22×D8311yescharacteristic
527C2×C22⋊C4C22×D8313yes—
528C2×C42—836no—
529C2×C42—833no—
530C2×C42—833no—
531C2×C42—833no—
532C2×C42—833no—
533C2×C42—8324no—
534C2×C42C22×D8313yes—
535C2×C42C22×D8316yes—
536C2×C42C22×D8313yes—
537C24—831no—
538C24—831no—
539C24C23×D8311yescharacteristic
540C2×Q8—232no—
541C2×Q8—212no—
542C2×Q8—8312no—
543C2×Q8—8312no—
544C2×Q8—8312no—
545C2×Q8—16612no—
546C2×Q8—16632no—
547C2×Q8—16632no—
548C2×Q8—16612no—
549C2×Q8—16612no—
550C2×Q8#1305059018yes—
551C2×Q8C23×D83112yes—
552C2×Q8C23×D8314yes—
553C2×D4—834no—
554C2×D4—834no—
555C2×D4—834no—
556C2×D4—1664no—
557C2×D4—1664no—
558C2×D4—1664no—
559C22×C4—212no—
560C22×C4—831no—
561C22×C4—833no—
562C22×C4—831no—
563C22×C4—833no—
564C22×C4—833no—
565C22×C4—833no—
566C22×C4—834no—
567C22×C4—8312no—
568C22×C4—8312no—
569C22×C4—8312no—
570C22×C4—1664no—
571C22×C4—16612no—
572C22×C4—16612no—
573C22×C4—16612no—
574C22×C4C23×D83112yes—
575C22×C4C23×D8313yes—
576C22×C4C23×D8311yescharacteristic
577C22×C4C23×D8313yes—
578C22×C4C23×D8311yescharacteristic
579C22×C4C23×D8313yes—
580C22×C4C23×D8313yes—
581C4⋊C4—8312no—
582C4⋊C4—8324no—
583C4⋊C4—8312no—
584C4⋊C4—8312no—
585C4⋊C4—8312no—
586C4⋊C4—8324no—
587C4⋊C4—8324no—
588C4⋊C4—8312no—
589C4⋊C4—8312no—
590C4⋊C4—8312no—
591C4⋊C4—834no—
592C4⋊C4—8324no—
593C4⋊C4—8324no—
594C4⋊C4—8312no—
595C4⋊C4—8312no—
596C4⋊C4C23×D83112yes—
597C4⋊C4C23×D83112yes—
598C4⋊C4C23×D83112yes—
599C4⋊C4C23×D83112yes—
600C22⋊C4—8312no—
601C22⋊C4—8312no—
602C22⋊C4—834no—
603C22⋊C4—8312no—
604C22⋊C4—8312no—
605C22⋊C4—8312no—
606C22⋊C4—8312no—
607C22⋊C4—8312no—
608C22⋊C4C23×D8314yes—
609C22⋊C4C23×D83112yes—
610C42—8312no—
611C42—8312no—
612C42—8312no—
613C42—8324no—
614C42—8312no—
615C42C23×D83112yes—
616C42C23×D83124yes—
617C42C23×D83112yes—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—834no—
622C23—832no—
623C23—832no—
624C23—1662no—
625C23—1662no—
626C23—1662no—
627C23—1662no—
628C23—1662no—
629C23C24×D8312yes—
630C23C24×D8311yescharacteristic
631Q8—224no—
632Q8—16624no—
633Q8—16624no—
634Q8—16624no—
635Q8C2×#13050590116yes—
636D4—1668no—
637D4—1668no—
638D4—1668no—
639C2×C4—26no—
640C2×C4—22no—
641C2×C4—26no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—224no—
645C2×C4—834no—
646C2×C4—832no—
647C2×C4—836no—
648C2×C4—832no—
649C2×C4—836no—
650C2×C4—836no—
651C2×C4—836no—
652C2×C4—1668no—
653C2×C4—16624no—
654C2×C4—1666no—
655C2×C4—1666no—
656C2×C4—1666no—
657C2×C4—1662no—
658C2×C4—1666no—
659C2×C4—16624no—
660C2×C4—16624no—
661C2×C4C2×#13050590112yes—
662C2×C4C24×D8316yes—
663C2×C4C24×D8312yes—
664C2×C4C24×D8316yes—
665C2×C4C24×D8312yes—
666C2×C4C24×D8316yes—
667C2×C4C24×D8316yes—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—3324no—
673C22—834no—
674C22—1662no—
675C22—1662no—
676C22—1662no—
677C22—1662no—
678C22—1662no—
679C22—1668no—
680C22C22×#1305059012yes—
681C222−1+4×D8312yes—
682C222−1+4×D8312yes—
683C22C25×D8311yescharacteristic
684C4—26no—
685C4—22no—
686C4—26no—
687C4—22no—
688C4—26no—
689C4—834no—
690C4—1666no—
691C4—1666no—
692C4—1666no—
693C4—1662no—
694C4—1666no—
695C4C22×#13050590112yes—
696C2—42no—
697C2—3322no—
698C2—1664no—
699C2#2492155314yesdirect product factor
700C2C23×#1305059011yescharacteristic
701C2C2×2−1+4×D8311yescharacteristic
702C2C2×2−1+4×D8311yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#519×C83C2
socleC23×C83C25
prime radicalC2×#14581765C22
hypercenterC2×#519D83
hypocenterC83C2×#3523
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. #24921553C2direct (N × H)
2. C2×#19128429C2semidirect
3. C2×#19128427C2semidirect
4. C2×#19128419C2semidirect
5. C2×#19128392C2semidirect
6. C2×#19128390C2semidirect
7. C2×Q8×D332C2semidirect
8. C2×Q8×C22⋊D83C2semidirect
9. C2×Q8×C22⋊D83C2semidirect
10. C2×#19128313C2semidirect
11. C2×#19128309C2semidirect
12. C2×#19128255C2semidirect
14. C2×#19128177C2semidirect
15. C2×C4×Q8×D83C2semidirect
16. C2×#519×C83C2semidirect
19. #19128429C22semidirect
20. #19128427C22semidirect
21. #19128419C22semidirect
22. #19128392C22semidirect
23. #19128390C22semidirect
24. Q8×D332C22semidirect
25. Q8×C22⋊D83C22semidirect
26. Q8×C22⋊D83C22semidirect
27. #19128313C22semidirect
28. #19128309C22semidirect
29. #19128255C22semidirect
56. #19128177C22semidirect
65. C4×Q8×D83C22semidirect
75. #519×C83C22semidirect
346. C2×C83#3523semidirect
366. C2×#519D83semidirect
368. C83C2×#3523semidirect
410. #519C2×D83semidirect
699. C2#24921553direct (N × H)

Maximal subgroups

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

subgroupindex
#249215532
C2×#191284292
C2×#191284272
C2×#191284192
C2×#191283922
C2×#191283902
C2×Q8×D3322
C2×Q8×C22⋊D832
C2×#191283132
C2×#191283092
C2×#191282552
C2×#191282292
C2×#191281772
C2×C4×Q8×D832
C2×#519×C832
C2×#352383