Finite Group Databasebeta

← C4×#19127932 #35410889

Subgroups — C4×#19127932 #35410889

Order 21248.

1138 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
1C2×#19127932C211yesmaximal, characteristic
2C2×C4×#13050577C211yesmaximal, characteristic, complemented
3C22×C4×C83⋊C8C211yesmaximal, characteristic, complemented
4C4×#14581766C211yesmaximal, characteristic
5#24908320C211yesmaximal, characteristic, complemented
6#24908188C211yesmaximal, characteristic, complemented
7#24908145C211yesmaximal, characteristic, complemented
8#24908142C211yesmaximal, characteristic, complemented
9#24907889C211yesmaximal, characteristic
10#24907887C211yesmaximal, characteristic, complemented
11#24907486C211yesmaximal, characteristic, complemented
12C4×#14581723C211yesmaximal, characteristic, complemented
13C4×#14581716C211yesmaximal, characteristic, complemented
14C4×#14581712C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C83C211yesmaximal, characteristic, complemented
16C22×#13050577C2211yescharacteristic
17C23×C83⋊C8C2211yescharacteristic
18C23×C83⋊C8C2211yescharacteristic
19C2×#14581766C2211yescharacteristic
20C2×C4×D332C2211yescharacteristic
21C2×C4×C22⋊D83—21no—
22#19127932C418yesdirect product factor
23C4×#13050577—24no—
24C2×#14581723C2211yescharacteristic
25C2×#14581723C2211yescharacteristic
26C2×#14581723C2211yescharacteristic
27C2×#14581716C2211yescharacteristic
28C2×#14581716C2211yescharacteristic
29C2×#14581716C2211yescharacteristic
30C2×#14581712C2211yescharacteristic
31C2×#14581712C2211yescharacteristic
32C2×#14581712C2211yescharacteristic
33C2×C4×C83⋊C8—24no—
34C2×C4×C83⋊C8C2211yescharacteristic
35C2×C4×C83⋊C8C2211yescharacteristic
36C2×C4×C83⋊C8C2211yescharacteristic
37C2×C4×C83⋊C8C2211yescharacteristic
38#19127603C2211yescharacteristic
39#19127599C2211yescharacteristic
40#19127592—21no—
41#19127580—21no—
42#19127561C2211yescharacteristic
43C4×C4⋊Dic83C2211yescharacteristic
44C4×(C2×D83)⋊C4—21no—
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51C2×C22⋊Q8×C83C2211yescharacteristic
52C2×C4×Q8×C83C2211yescharacteristic
53C22×C42×C83C2211yescharacteristic
54#391×C83C2211yescharacteristic
55#389×C83C2211yescharacteristic
56#387×C83—21no—
57#385×C83—21no—
58#380×C83C2211yescharacteristic
59C4×C4⋊C4×C83—21no—
60C4×C4⋊C4×C83C2211yescharacteristic
61C4×C22⋊C4×C83—21no—
62C22×D332C2311yescharacteristic
63C22×C22⋊D83—21no—
64C22×C4×D83—21no—
65C2×#13050577—22no—
66C2×#13050577—22no—
67C2×#13050577C2×C414yescomplemented
68C22×C83⋊C8—22no—
69C22×C83⋊C8—22no—
70C22×C83⋊C8—22no—
71C22×C83⋊C8—22no—
72C22×C83⋊C8—22no—
73C22×C83⋊C8C2×C414yescomplemented
74C22×C83⋊C8C2311yescharacteristic
75C22×C83⋊C8C2311yescharacteristic
76C22×C83⋊C8C2311yescharacteristic
77C22×C83⋊C8C2311yescharacteristic
78#14581766—22no—
79#14581766C2×C414yes—
80C4×D332—22no—
81C4×D332—22no—
82C4×C22⋊D83—44no—
83C2×C4⋊Dic83C2311yescharacteristic
84C2×C4⋊Dic83C2311yescharacteristic
85C2×C4⋊Dic83C2311yescharacteristic
86C2×Dic83⋊C4—21no—
87C2×C22⋊Dic83—21no—
88C2×(C2×D83)⋊C4—21no—
89C2×(C2×D83)⋊C4—21no—
90C2×(C2×D83)⋊C4—21no—
91C2×(C2×D83)⋊C4—21no—
92C2×C4×Dic83—21no—
93#14581723—22no—
94#14581723—22no—
95#14581723C2×C414yescomplemented
96#14581716—22no—
97#14581716—22no—
98#14581716C2×C414yescomplemented
99#14581712—22no—
100#14581712—22no—
101#14581712C2×C414yescomplemented
102C4×C83⋊C8—22no—
103C4×C83⋊C8—22no—
104C4×C83⋊C8—22no—
105C4×C83⋊C8D414yescomplemented
106C83⋊#95—21no—
107C83⋊#95—21no—
108C83⋊#95—21no—
109C22×Q8×C83C2311yescharacteristic
110C23×C4×C83D411yescharacteristic
111C23×C4×C83D411yescharacteristic
112C23×C4×C83C2311yescharacteristic
113C22⋊Q8×C83—22no—
114C22⋊Q8×C83C2×C414yescomplemented
115C4×Q8×C83—22no—
116C4×Q8×C83—22no—
117C2×C4⋊C4×C83—21no—
118C2×C4⋊C4×C83—21no—
119C2×C4⋊C4×C83—21no—
120C2×C4⋊C4×C83C2311yescharacteristic
121C2×C4⋊C4×C83C2311yescharacteristic
122C2×C4⋊C4×C83C2311yescharacteristic
123C2×C22⋊C4×C83—21no—
124C2×C22⋊C4×C83—21no—
125C2×C42×C83—22no—
126C2×C42×C83—22no—
127C2×C42×C83—21no—
128C2×C42×C83—21no—
129C2×C42×C83D411yescharacteristic
130C2×C42×C83D411yescharacteristic
131C2×C42×C83C2311yescharacteristic
132C2×C42×C83C2311yescharacteristic
133#95×C83—21no—
134#95×C83—21no—
135#95×C83—21no—
136#95×C83—21no—
137#95×C83—21no—
138C23×D83—21no—
139C2×D332—21no—
140C2×D332—21no—
141C2×D332—21no—
142C2×D332—21no—
143C2×D332—21no—
144C2×D332C22×C412yes—
145C2×C22⋊D83—24no—
146C2×C22⋊D83—42no—
147C2×C22⋊D83—42no—
148C22×Dic83—21no—
149C22×Dic83—21no—
150C22×Dic83—21no—
151C2×C4×D83—42no—
152C2×C4×D83—42no—
153C2×C4×D83—42no—
154#13050577—28no—
155C2×C83⋊C8—28no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—28no—
163C2×C83⋊C8C22×C412yes—
164C2×C83⋊C8C22×C412yes—
165C2×C83⋊C8C2×D412yes—
166C2×C83⋊C8C2×D412yes—
167C2×C83⋊C8#4112yes—
168C2×C83⋊C8#4112yes—
169C4⋊Dic83—21no—
170C4⋊Dic83—21no—
171C4⋊Dic83—21no—
172C4⋊Dic83—21no—
173C4⋊Dic83—21no—
174C4⋊Dic83C22×C412yes—
175Dic83⋊C4—42no—
176C22⋊Dic83—42no—
177(C2×D83)⋊C4—24no—
178(C2×D83)⋊C4—42no—
179(C2×D83)⋊C4—42no—
180(C2×D83)⋊C4—42no—
181C4×Dic83—42no—
182C24×C83C2×D411yescharacteristic
183C2×Q8×C83—21no—
184C2×Q8×C83—21no—
185C2×Q8×C83—21no—
186C2×Q8×C83—21no—
187C2×Q8×C83—21no—
188C2×Q8×C83C22×C412yes—
189C22×C4×C83—22no—
190C22×C4×C83—22no—
191C22×C4×C83—22no—
192C22×C4×C83—22no—
193C22×C4×C83—22no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83SD1614yescomplemented
203C22×C4×C83C22×C412yes—
204C22×C4×C83C2×D411yescharacteristic
205C22×C4×C83C2×D411yescharacteristic
206C22×C4×C83C2×D411yescharacteristic
207C22×C4×C83C2×D411yescharacteristic
208C22×C4×C83C2×D411yescharacteristic
209C22×C4×C83#4112yes—
210C22×C4×C83C2411yescharacteristic
211C4⋊C4×C83—24no—
212C4⋊C4×C83—21no—
213C4⋊C4×C83—21no—
214C4⋊C4×C83—21no—
215C4⋊C4×C83—21no—
216C4⋊C4×C83—21no—
217C4⋊C4×C83—42no—
218C4⋊C4×C83—42no—
219C4⋊C4×C83C22×C412yes—
220C22⋊C4×C83—24no—
221C22⋊C4×C83—42no—
222C42×C83—22no—
223C42×C83—22no—
224C42×C83—21no—
225C42×C83—21no—
226C42×C83—42no—
227C42×C83—42no—
228C42×C83C2×D412yes—
229C42×C83#4112yes—
230C23×C83—21no—
231C23×C83—21no—
232C23×C83—21no—
233C23×C83—21no—
234C23×C83C4×D412yes—
235C23×C83C2×SD1612yes—
236C23×C83#13512yes—
237C23×C83C22×D411yescharacteristic
238C22×D83—22no—
239C22×D83—41no—
240C22×D83—41no—
241C22×D83—41no—
242C22×D83—41no—
243C22×D83—41no—
244C22×D83—41no—
245Q8×C83—22no—
246Q8×C83—22no—
247Q8×C83—41no—
248Q8×C83—41no—
249C2×C4×C83—28no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83—21no—
253C2×C4×C83—21no—
254C2×C4×C83—21no—
255C2×C4×C83—21no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—22no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—28no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—41no—
266C2×C4×C83—41no—
267C2×C4×C83—41no—
268C2×C4×C83—41no—
269C2×C4×C83—41no—
270C2×C4×C83—41no—
271C2×C4×C83—41no—
272C2×C4×C83—41no—
273C2×C4×C83—41no—
274C2×C4×C83—41no—
275C2×C4×C83C4×D412yes—
276C2×C4×C83#12112yes—
277C2×C4×C83#12112yes—
278C2×C4×C83C2×SD1612yes—
279C2×C4×C83C2×SD1612yes—
280C2×C4×C83#13512yes—
281C2×C4×C83#13512yes—
282C2×C4×C83C23×C411yescharacteristic
283C2×C4×C83C22×D411yescharacteristic
284C2×C4×C83C2×#4111yescharacteristic
285C2×C4×C83C2×#4111yescharacteristic
286C2×C4×C83C2×#4111yescharacteristic
287C2×C4×C83C2×#4111yescharacteristic
288C22⋊D83—48no—
289C2×Dic83—22no—
290C2×Dic83—41no—
291C2×Dic83—41no—
292C2×Dic83—41no—
293C2×Dic83—41no—
294C2×Dic83—41no—
295C2×Dic83—41no—
296C2×Dic83—41no—
297C2×Dic83—41no—
298D332—22no—
299D332—22no—
300D332—41no—
301D332—41no—
302C4×D83—84no—
303C83⋊C8—22no—
304C83⋊C8—22no—
305C83⋊C8—22no—
306C83⋊C8C4×D414yescomplemented
307C22×C83—22no—
308C22×C83—22no—
309C22×C83—22no—
310C22×C83—22no—
311C22×C83—22no—
312C22×C83—22no—
313C22×C83C4×SD1614yescomplemented
314C22×C83C2×C4×D411yescharacteristic
315C22×C83C2×#12111yescharacteristic
316C22×C83#53211yescharacteristic
317C22×C83C22×SD1611yescharacteristic
318C22×C83C2×#13511yescharacteristic
319C22×C83C2×#13511yescharacteristic
320C22×C83C2×#13511yescharacteristic
321C2×D83—42no—
322C2×D83—42no—
323C2×D83—42no—
324C2×D83—81no—
325C2×D83—81no—
326C2×D83—81no—
327C2×D83—81no—
328C4×C83—22no—
329C4×C83—22no—
330C4×C83—22no—
331C4×C83—22no—
332C4×C83—42no—
333C4×C83—42no—
334C4×C83—81no—
335C4×C83—81no—
336C4×C83#46514yescomplemented
337C4×C83C2×C4×D411yescharacteristic
338C4×C83C4×#4111yescharacteristic
339C4×C83#52511yescharacteristic
340C4×C83#52911yescharacteristic
341Dic83—42no—
342Dic83—81no—
343Dic83—81no—
344C4×#465—831nomaximal, Sylow
345C2×C83—24no—
346C2×C83C4×#12111yescharacteristic
347C2×C83C2×C4×SD1611yescharacteristic
348C2×C83C4×#13511yescharacteristic
349C2×C83C2×#46511yescharacteristic
350C2×C83#305011yescharacteristic
351C2×C83#316711yescharacteristic
352C2×C83#316811yescharacteristic
353D83—82no—
354C2×#465—831no—
355C2×C4×SD16—831no—
356C22×C4×C8—831no—
357C4×C22⋊Q8D8311yescharacteristic, complemented
358C4×#121—831no—
359#1968—831no—
360#1941—831no—
361#1934—831no—
362#1933—831no—
363#1893—831no—
364#1892—831no—
365#1807—831no—
366C4×#106—831no—
367C4×#103—831no—
368C4×#102—831no—
369C83C4×#46511yescharacteristic, complemented, Sylow
370C22×SD16—831no—
371C23×C8—831no—
372C23×C8—831no—
373C2×C22⋊Q8C2×D8311yescharacteristic
374C2×#121—831no—
375C2×C4×Q8C2×D8311yescharacteristic
376C2×C4×D4—831no—
377C2×C4×D4—1661no—
378C22×C42C2×D8311yescharacteristic
379#465—838no—
380C4×SD16—1664no—
381C2×#106—831no—
382C2×#106—831no—
383C2×#106—831no—
384C2×#103—831no—
385C2×#103—831no—
386C2×#103—831no—
387C2×#102—831no—
388C2×#102—831no—
389C2×#102—831no—
390C2×C4×C8—831no—
391C2×C4×C8—831no—
392C2×C4×C8—831no—
393C2×C4×C8—831no—
394C2×C4×C8—1664no—
395#391C2×D8311yescharacteristic
396#390—831no—
397#389—831no—
398#389C2×D8311yescharacteristic
399#388—1661no—
400#387—21no—
401#386—1661no—
402#385—21no—
403#380—831no—
404#380C2×D8311yescharacteristic
405C4×C4⋊C4—21no—
406C4×C4⋊C4—831no—
407C4×C4⋊C4C2×D8311yescharacteristic
408C4×C22⋊C4—21no—
409C4×C22⋊C4—1661no—
410#340—831no—
411#340—831no—
412#340—831no—
413#340—831no—
414#340—831no—
415#340—831no—
416C22×Q8C22×D8311yescharacteristic
417C22×D4—831no—
418C22×D4—1661no—
419C23×C4—1661no—
420C23×C4C22⋊D8311yescharacteristic
421C23×C4C22⋊D8311yescharacteristic
422C23×C4C22×D8311yescharacteristic
423C2×SD16—834no—
424C2×SD16—1662no—
425C2×SD16—1662no—
426C22×C8—831no—
427C22×C8—834no—
428C22×C8—831no—
429C22×C8—831no—
430C22×C8—831no—
431C22×C8—1662no—
432C22×C8—1662no—
433C22×C8—1662no—
434C22×C8—1662no—
435C22×C8—1662no—
436C22⋊Q8—22no—
437C22⋊Q8C4×D8314yescomplemented
438#121—834no—
439#121—1662no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×D4—3324no—
443C4×D4—1662no—
444C4×D4—1662no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—831no—
449C2×C4⋊C4—831no—
450C2×C4⋊C4—831no—
451C2×C4⋊C4—1661no—
452C2×C4⋊C4C22×D8311yescharacteristic
453C2×C4⋊C4C22×D8311yescharacteristic
454C2×C4⋊C4C22×D8311yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—1661no—
458C2×C22⋊C4—1661no—
459C2×C22⋊C4—1661no—
460C2×C22⋊C4—1661no—
461C2×C22⋊C4—1661no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—1661no—
467C2×C42C22⋊D8311yescharacteristic
468C2×C42C22⋊D8311yescharacteristic
469C2×C42C22×D8311yescharacteristic
470C2×C42C22×D8311yescharacteristic
471#106—834no—
472#106—1662no—
473#106—1662no—
474#103—834no—
475#103—1662no—
476#103—1662no—
477#102—834no—
478#102—1662no—
479#102—1662no—
480C4×C8—834no—
481C4×C8—1662no—
482C4×C8—1662no—
483C4×C8—1662no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—1661no—
490#95—1661no—
491#95—1661no—
492C24—1661no—
493C24C2×C22⋊D8311yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4×D8312yes—
500C2×D4—3322no—
501C2×D4—3322no—
502C2×D4—832no—
503C2×D4—1664no—
504C2×D4—1661no—
505C2×D4—1661no—
506C2×D4—1661no—
507C2×D4—1661no—
508C2×D4—1661no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—3322no—
523C22×C4—3322no—
524C22×C4—3322no—
525C22×C4—1661no—
526C22×C4—1661no—
527C22×C4—1661no—
528C22×C4#1305057714yescomplemented
529C22×C4C2×C4×D8312yes—
530C22×C4C2×C22⋊D8311yescharacteristic
531C22×C4C2×C22⋊D8311yescharacteristic
532C22×C4C2×C22⋊D8311yescharacteristic
533C22×C4C2×C22⋊D8311yescharacteristic
534C22×C4C2×C22⋊D8311yescharacteristic
535C22×C4#1305059012yes—
536C22×C4C23×D8311yescharacteristic
537SD16—1668no—
538C2×C8—832no—
539C2×C8—832no—
540C2×C8—832no—
541C2×C8—832no—
542C2×C8—832no—
543C2×C8—832no—
544C2×C8—1668no—
545C2×C8—1668no—
546C2×C8—1661no—
547C2×C8—1661no—
548C2×C8—1661no—
549C2×C8—1661no—
550C2×C8—1661no—
551C2×C8—1661no—
552C4⋊C4—21no—
553C4⋊C4—24no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—3322no—
561C4⋊C4—832no—
562C4⋊C4—1661no—
563C4⋊C4—1661no—
564C4⋊C4—1661no—
565C4⋊C4—1661no—
566C4⋊C4—1661no—
567C4⋊C4C2×C4×D8312yes—
568C22⋊C4—24no—
569C22⋊C4—42no—
570C22⋊C4—3322no—
571C22⋊C4—3322no—
572C22⋊C4—3322no—
573C22⋊C4—3322no—
574C22⋊C4—1664no—
575C42—22no—
576C42—22no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42—3322no—
582C42D4×D8312yes—
583C42#1305058912yes—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—3321no—
589C23—3321no—
590C23—3321no—
591C23—3321no—
592C23—3321no—
593C23—3321no—
594C23—1662no—
595C23C4×C22⋊D8312yes—
596C23C2×#1305057712yes—
597C23#1458181212yes—
598C23C22×C22⋊D8311yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—3328no—
604D4—3321no—
605D4—3321no—
606D4—1662no—
607D4—1662no—
608C2×C4—28no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—3321no—
635C2×C4—3321no—
636C2×C4—3321no—
637C2×C4—3321no—
638C2×C4—3321no—
639C2×C4—3321no—
640C2×C4—3321no—
641C2×C4—3321no—
642C2×C4—6644no—
643C2×C4—1662no—
644C2×C4C4×C22⋊D8312yes—
645C2×C4#1458176412yes—
646C2×C4#1458176412yes—
647C2×C4C2×#1305057712yes—
648C2×C4C2×#1305057712yes—
649C2×C4#1458181212yes—
650C2×C4#1458181212yes—
651C2×C4C22×C4×D8311yescharacteristic
652C2×C4C2×D4×D8311yescharacteristic
653C2×C4#41×D8311yescharacteristic
654C2×C4#41×D8311yescharacteristic
655C2×C4C2×#1305058911yescharacteristic
656C2×C4C2×#1305059011yescharacteristic
657C8—834no—
658C8—1662no—
659C8—1662no—
660C8—1662no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—3322no—
668C22—3322no—
669C22—3322no—
670C22—6641no—
671C22—6641no—
672C22—6641no—
673C22—6641no—
674C22C4×#1305057714yescomplemented
675C22C2×C4×C22⋊D8311yescharacteristic
676C22C2×#1458176411yescharacteristic
677C22#1912824711yescharacteristic
678C22C22×#1305057711yescharacteristic
679C22C2×#1458181211yescharacteristic
680C22C2×#1458181211yescharacteristic
681C22C2×#1458181211yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—42no—
687C4—42no—
688C4—81no—
689C4—81no—
690C4—3322no—
691C4—6641no—
692C4—6641no—
693C4#1912793214yesdirect product factor
694C4C4×D4×D8311yescharacteristic
695C4C4×#1305058911yescharacteristic
696C4#1912821011yescharacteristic
697C4#1912823111yescharacteristic
698C2—24no—
699C2—6642no—
700C2C4×#1458176411yescharacteristic
701C2C2×C4×#1305057711yescharacteristic
702C2C4×#1458181211yescharacteristic
703C2C2×#1912793211yescharacteristic
704C2#2491704111yescharacteristic
705C2#2491802311yescharacteristic
706C2#2491802711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC4×C22⋊Q8×C83C2
socleC23×C83C22×D4
prime radicalC2×#14581766C22
cosocleC22×C4×C83C24
hypercenterC4×C22⋊Q8D83
hypocenterC83C4×#465
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#13050577C2semidirect
3. C22×C4×C83⋊C8C2semidirect
5. #24908320C2semidirect
6. #24908188C2semidirect
7. #24908145C2semidirect
8. #24908142C2semidirect
10. #24907887C2semidirect
11. #24907486C2semidirect
12. C4×#14581723C2semidirect
13. C4×#14581716C2semidirect
14. C4×#14581712C2semidirect
15. C4×C22⋊Q8×C83C2semidirect
22. #19127932C4direct (N × H)
67. C2×#13050577C2×C4semidirect
73. C22×C83⋊C8C2×C4semidirect
95. #14581723C2×C4semidirect
98. #14581716C2×C4semidirect
101. #14581712C2×C4semidirect
105. C4×C83⋊C8D4semidirect
114. C22⋊Q8×C83C2×C4semidirect
202. C22×C4×C83SD16semidirect
306. C83⋊C8C4×D4semidirect
313. C22×C83C4×SD16semidirect
336. C4×C83#465semidirect
357. C4×C22⋊Q8D83semidirect
369. C83C4×#465semidirect
437. C22⋊Q8C4×D83semidirect
528. C22×C4#13050577semidirect
674. C22C4×#13050577semidirect
693. C4#19127932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191279322
C2×C4×#130505772
C22×C4×C83⋊C82
C4×#145817662
#249083202
#249081882
#249081452
#249081422
#249078892
#249078872
#249074862
C4×#145817232
C4×#145817162
C4×#145817122
C4×C22⋊Q8×C832
C4×#46583