Finite Group Databasebeta

← C2×#19138303 #25265085

Subgroups — C2×#19138303 #25265085

Order 11008.

2726 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063315C211yesmaximal, characteristic, complemented
2C22×#13063281C211yesmaximal, characteristic
3#19138303C2116yesmaximal, direct product factor
4C2×#14582835C211yesmaximal, characteristic
5C2×#14582835C211yesmaximal, characteristic
6C2×#14582822C211yesmaximal, characteristic
7C2×#14582798C211yesmaximal, characteristic, complemented
8C2×#14582796C211yesmaximal, characteristic, complemented
9C2×#14582794C211yesmaximal, characteristic, complemented
10C2×#14582794C211yesmaximal, characteristic, complemented
11C2×#14582781C211yesmaximal, characteristic, complemented
12C2×#14582780C211yesmaximal, characteristic, complemented
13C2×#14582768C211yesmaximal, characteristic, complemented
14C2×#14582757C211yesmaximal, characteristic
15C2×C22⋊C4×Dic43C211yesmaximal, characteristic
16C2×C43×#396C211yesmaximal, characteristic
17C24×Dic43C2211yescharacteristic
18C2×#13063315—28no—
19C2×#13063315C2218yescomplemented
20C2×#13063281—28no—
21C2×#13063281C2218yes—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C22×Dic43⋊C4C2211yescharacteristic
35C22×C22⋊Dic43C2211yescharacteristic
36C22×C22⋊Dic43C2211yescharacteristic
37C22×C22⋊Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42#14582835C2218yes—
43#14582835C2218yes—
44#14582822C2218yes—
45#14582798C2218yescomplemented
46#14582796C2218yescomplemented
47#14582794C2218yescomplemented
48#14582794C2218yescomplemented
49#14582781C2218yescomplemented
50#14582780C2218yescomplemented
51#14582768C2218yescomplemented
52#14582757C2218yes—
53C22⋊C4×Dic43C2218yes—
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C43×#396C2218yes—
68C2×#95×C43C2211yescharacteristic
69C23×Dic43—24no—
70C23×Dic43—24no—
71C23×Dic43Q818yes—
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2314yes—
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81#13063315—232no—
82#13063281—232no—
83C2×C4⋊Dic43—24no—
84C2×C4⋊Dic43—42no—
85C2×C4⋊Dic43—42no—
86C2×C4⋊Dic43C2314yes—
87C2×C4⋊Dic43C2314yes—
88C2×C4⋊Dic43C2314yes—
89C2×Dic43⋊C4—24no—
90C2×Dic43⋊C4—24no—
91C2×Dic43⋊C4—24no—
92C2×Dic43⋊C4—24no—
93C2×Dic43⋊C4—24no—
94C2×Dic43⋊C4—24no—
95C2×Dic43⋊C4—24no—
96C2×Dic43⋊C4—24no—
97C2×Dic43⋊C4—42no—
98C2×Dic43⋊C4D418yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×C22⋊Dic43—24no—
110C2×C22⋊Dic43—24no—
111C2×C22⋊Dic43—42no—
112C2×C22⋊Dic43C2314yes—
113C2×C22⋊Dic43C2314yes—
114C2×C22⋊Dic43C2314yes—
115C2×C4×Dic43—24no—
116C2×C4×Dic43—24no—
117C2×C4×Dic43—24no—
118C2×C4×Dic43—24no—
119C2×C4×Dic43C2314yes—
120C2×C4×Dic43C2314yes—
121C2×C4×Dic43C2314yes—
122C2×C4×Dic43C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C25×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43—24no—
138C2×C4⋊C4×C43—24no—
139C2×C4⋊C4×C43—42no—
140C2×C4⋊C4×C43C2314yes—
141C2×C4⋊C4×C43C2314yes—
142C2×C4⋊C4×C43C2314yes—
143C2×C22⋊C4×C43—24no—
144C2×C22⋊C4×C43—24no—
145C2×C22⋊C4×C43—42no—
146C2×C22⋊C4×C43C2314yes—
147C2×C22⋊C4×C43C2314yes—
148C2×C22⋊C4×C43C2314yes—
149#95×C43C2314yes—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43C2×Q814yes—
157C24×C43C2412yes—
158C24×C43C2411yescharacteristic
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43C2×D414yes—
176C22×C4×C43#4114yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2412yes—
181C22×C4×C43C2412yes—
182C22×C4×C43C2412yes—
183C22×Dic43—232no—
184C22×Dic43—28no—
185C22×Dic43—28no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43C2×D414yes—
205C22×Dic43C2×D414yes—
206C22×Dic43C2×Q8116yes—
207C22×Dic43C2×Q814yes—
208C22×Dic43C2×Q814yes—
209C22×Dic43#4114yes—
210C22×Dic43#4114yes—
211C22×Dic43C2412yes—
212C22×Dic43C2412yes—
213C22×Dic43C2412yes—
214C22×Dic43C2412yes—
215C22×Dic43C2412yes—
216C22×Dic43C2412yes—
217C22×Dic43C2412yes—
218C22×Dic43C2412yes—
219C4⋊C4×C43—28no—
220C4⋊C4×C43—28no—
221C4⋊C4×C43—44no—
222C22⋊C4×C43—28no—
223C22⋊C4×C43—28no—
224C22⋊C4×C43—44no—
225C22⋊Dic43—28no—
226C22⋊Dic43—28no—
227C22⋊Dic43—44no—
228C4⋊Dic43—28no—
229C4⋊Dic43—44no—
230C4⋊Dic43—44no—
231Dic43⋊C4—28no—
232Dic43⋊C4—28no—
233Dic43⋊C4—28no—
234Dic43⋊C4—28no—
235Dic43⋊C4—28no—
236Dic43⋊C4—28no—
237Dic43⋊C4—28no—
238Dic43⋊C4—28no—
239Dic43⋊C4—44no—
240Dic43⋊C4C2×D4116yes—
241C4×Dic43—28no—
242C4×Dic43—28no—
243C4×Dic43—28no—
244C4×Dic43—28no—
245C23×C43—28no—
246C23×C43—28no—
247C23×C43—28no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—22no—
254C23×C43—44no—
255C23×C43—44no—
256C23×C43—44no—
257C23×C43—44no—
258C23×C43C22×D412yes—
259C23×C43C22×Q814yes—
260C23×C43C22×Q812yes—
261C23×C43C2×#4112yes—
262C23×C43C2×#4112yes—
263C23×C43C2×#4112yes—
264C23×C43H(5,𝔽2)12yes—
265C23×C432−1+412yes—
266C23×C43C2511yescharacteristic
267C2×C4×C43—28no—
268C2×C4×C43—28no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—44no—
286C2×C4×C43—44no—
287C2×C4×C43—44no—
288C2×C4×C43—44no—
289C2×C4×C43C22×D414yes—
290C2×C4×C43C2×#4114yes—
291C2×Dic43—28no—
292C2×Dic43—28no—
293C2×Dic43—28no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—232no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—44no—
314C2×Dic43—44no—
315C2×Dic43—44no—
316C2×Dic43—44no—
317C2×Dic43C22⋊Q8116yes—
318C2×Dic43C22×D414yes—
319C2×Dic43C22×D414yes—
320C2×Dic43C22×Q814yes—
321C2×Dic43C22×Q814yes—
322C2×Dic43C2×#4114yes—
323C2×Dic43C2×#4114yes—
324C2×#2441—431nomaximal, Sylow
325C22×C43—24no—
326C22×C43—24no—
327C22×C43—24no—
328C22×C43—42no—
329C22×C43—416no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43C2×C22⋊Q814yes—
334C22×C43#53314yes—
335C22×C43#54414yes—
336C22×C43#54714yes—
337C22×C43#55014yes—
338C22×C43#55214yes—
339C22×C43#55314yes—
340C22×C43C23×D411yescharacteristic
341C22×C43C23×Q811yescharacteristic
342C22×C43C22×#4111yescharacteristic
343C22×C43C22×#4111yescharacteristic
344C22×C43C22×#4111yescharacteristic
345C22×C43C2×H(5,𝔽2)11yescharacteristic
346C22×C43C2×2−1+411yescharacteristic
347C4×C43—24no—
348C4×C43—24no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43—42no—
352C4×C43—42no—
353Dic43—24no—
354Dic43—24no—
355Dic43—24no—
356Dic43—42no—
357Dic43—42no—
358Dic43—42no—
359Dic43—42no—
360Dic43C2×C22⋊Q818yes—
361C22×#125—431no—
362C22×#117—431no—
363#2441—4316no—
364C2×#399—431no—
365C2×#399—431no—
366C2×#396—431no—
367C2×#396D4311yescharacteristic
368C2×#389—431no—
369C2×#389—431no—
370C2×#389—431no—
371C2×#389—431no—
372C2×#387—431no—
373C2×#387—431no—
374C2×#384—431no—
375C2×#380—431no—
376C2×C4×C22⋊C4—431no—
377C2×C43—44no—
378C2×C43#244118yescomplemented
379C2×C43C22×C22⋊Q811yescharacteristic
380C2×C43C2×#53311yescharacteristic
381C2×C43C2×#54411yescharacteristic
382C2×C43C2×#54711yescharacteristic
383C2×C43C2×#55011yescharacteristic
384C2×C43C2×#55211yescharacteristic
385C2×C43C2×#55311yescharacteristic
386C24×C4—431no—
387C2×#125—438no—
388C2×#125—868no—
389C2×#117—438no—
390C2×#117—868no—
391C22×C4⋊C4—431no—
392C22×C4⋊C4—431no—
393C22×C4⋊C4—431no—
394C22×C4⋊C4—431no—
395C22×C4⋊C4—431no—
396C22×C4⋊C4—431no—
397C22×C4⋊C4—431no—
398C22×C4⋊C4—431no—
399C22×C4⋊C4—431no—
400C22×C4⋊C4—431no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—431no—
403C22×C4⋊C4—431no—
404C22×C4⋊C4C2×D4311yescharacteristic
405C22×C4⋊C4C2×D4311yescharacteristic
406C22×C4⋊C4C2×D4311yescharacteristic
407C22×C22⋊C4—431no—
408C22×C22⋊C4—431no—
409C22×C22⋊C4—431no—
410C22×C22⋊C4C2×D4311yescharacteristic
411C22×C22⋊C4C2×D4311yescharacteristic
412C22×C22⋊C4C2×D4311yescharacteristic
413C22×C42—431no—
414C22×C42—431no—
415C22×C42—431no—
416C22×C42—431no—
417#399—438no—
418#399—438no—
419#396—438no—
420#396C2×D4318yes—
421#389—438no—
422#389—438no—
423#389—438no—
424#389—438no—
425#387—438no—
426#387—438no—
427#384—438no—
428#380—438no—
429C4×C22⋊C4—438no—
430C2×#95—431no—
431C2×#95—431no—
432C2×#95—431no—
433C2×#95—431no—
434C2×#95—431no—
435C2×#95—431no—
436C2×#95—431no—
437C2×#95C2×D4311yescharacteristic
438C43C2×#244111yescharacteristic, complemented, Sylow
439C25C22×D4311yescharacteristic
440C23×C4—431no—
441C23×C4—438no—
442C23×C4—434no—
443C23×C4—431no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—431no—
447C23×C4—431no—
448C23×C4—431no—
449C23×C4—431no—
450C23×C4—864no—
451C23×C4—864no—
452C23×C4C22×D4311yescharacteristic
453C23×C4C22×D4311yescharacteristic
454C23×C4C22×D4311yescharacteristic
455C23×C4C22×D4311yescharacteristic
456C23×C4C22×D4311yescharacteristic
457C23×C4C22×D4311yescharacteristic
458#125—8632no—
459#117—8632no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—438no—
464C2×C4⋊C4—434no—
465C2×C4⋊C4—434no—
466C2×C4⋊C4—434no—
467C2×C4⋊C4—434no—
468C2×C4⋊C4—434no—
469C2×C4⋊C4—434no—
470C2×C4⋊C4—434no—
471C2×C4⋊C4—434no—
472C2×C4⋊C4—434no—
473C2×C4⋊C4—434no—
474C2×C4⋊C4—434no—
475C2×C4⋊C4—434no—
476C2×C4⋊C4—434no—
477C2×C4⋊C4—864no—
478C2×C4⋊C4—864no—
479C2×C4⋊C4—864no—
480C2×C4⋊C4—864no—
481C2×C4⋊C4—864no—
482C2×C4⋊C4—864no—
483C2×C4⋊C4—864no—
484C2×C4⋊C4—864no—
485C2×C4⋊C4—864no—
486C2×C4⋊C4—1722no—
487C2×C4⋊C4—1722no—
488C2×C4⋊C4—1722no—
489C2×C4⋊C4C22×D4314yes—
490C2×C4⋊C4C22×D4314yes—
491C2×C4⋊C4C22×D4314yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—434no—
496C2×C22⋊C4—434no—
497C2×C22⋊C4—434no—
498C2×C22⋊C4—864no—
499C2×C22⋊C4—864no—
500C2×C22⋊C4—1722no—
501C2×C22⋊C4C22×D4314yes—
502C2×C22⋊C4C22×D4314yes—
503C2×C22⋊C4C22×D4314yes—
504C2×C42—434no—
505C2×C42—434no—
506C2×C42—434no—
507C2×C42—434no—
508C2×C42—864no—
509C2×C42—864no—
510C2×C42—864no—
511C2×C42—864no—
512#95—434no—
513#95—434no—
514#95—434no—
515#95—434no—
516#95—434no—
517#95—434no—
518#95—434no—
519#95C22×D4314yes—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24Q8×D4314yes—
527C24C23×D4312yes—
528C24C23×D4311yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—434no—
546C22×C4—434no—
547C22×C4—434no—
548C22×C4—432no—
549C22×C4—434no—
550C22×C4—4316no—
551C22×C4—434no—
552C22×C4—434no—
553C22×C4—432no—
554C22×C4—432no—
555C22×C4—432no—
556C22×C4—432no—
557C22×C4—432no—
558C22×C4—432no—
559C22×C4—432no—
560C22×C4—868no—
561C22×C4—8632no—
562C22×C4—868no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4D4×D4314yes—
582C22×C4#1062190014yes—
583C22×C4C23×D4312yes—
584C22×C4C23×D4312yes—
585C22×C4C23×D4312yes—
586C22×C4C23×D4312yes—
587C22×C4C23×D4312yes—
588C22×C4C23×D4312yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—44no—
592C4⋊C4—4316no—
593C4⋊C4—868no—
594C4⋊C4—868no—
595C4⋊C4—868no—
596C4⋊C4—868no—
597C4⋊C4—868no—
598C4⋊C4—868no—
599C4⋊C4—868no—
600C4⋊C4—868no—
601C4⋊C4—868no—
602C4⋊C4—1724no—
603C4⋊C4—1724no—
604C4⋊C4—1724no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—44no—
608C22⋊C4—868no—
609C22⋊C4—868no—
610C22⋊C4—1724no—
611C42—868no—
612C42—868no—
613C42—868no—
614C42—868no—
615C23—28no—
616C23—28no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—28no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23C2×D4×D4312yes—
629C23C2×Q8×D4314yes—
630C23C2×Q8×D4312yes—
631C23#41×D4312yes—
632C23#41×D4312yes—
633C23C2×#1062190012yes—
634C23#1306337012yes—
635C23#1306337212yes—
636C23C24×D4311yescharacteristic
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—28no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—4316no—
660C2×C4—434no—
661C2×C4—434no—
662C2×C4—434no—
663C2×C4—434no—
664C2×C4—434no—
665C2×C4—434no—
666C2×C4—8632no—
667C2×C4—868no—
668C2×C4—868no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—868no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—1724no—
689C2×C4—1724no—
690C2×C4—1724no—
691C2×C4—1724no—
692C2×C4C2×D4×D4314yes—
693C2×C4C2×#1062190014yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—416no—
702C22C22⋊Q8×D4314yes—
703C22#1458345114yes—
704C22#1458352814yes—
705C22#1458354914yes—
706C22#1458356714yes—
707C22#1458358514yes—
708C22#1458359214yes—
709C22C22×D4×D4311yescharacteristic
710C22C22×Q8×D4311yescharacteristic
711C22C2×#41×D4311yescharacteristic
712C22C2×#41×D4311yescharacteristic
713C22C22×#1062190011yescharacteristic
714C22C2×#1306337011yescharacteristic
715C22C2×#1306337211yescharacteristic
716C4—24no—
717C4—24no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—438no—
723C4—864no—
724C4—864no—
725C4—864no—
726C4—1722no—
727C4—1722no—
728C4—1722no—
729C4—1722no—
730C2—44no—
731C2#1913830318yesdirect product factor
732C2C2×C22⋊Q8×D4311yescharacteristic
733C2C2×#1458345111yescharacteristic
734C2C2×#1458352811yescharacteristic
735C2C2×#1458354911yescharacteristic
736C2C2×#1458356711yescharacteristic
737C2C2×#1458358511yescharacteristic
738C2C2×#1458359211yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#396C2
socleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#396D43
hypocenterC43C2×#2441
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13063315C2semidirect
3. #19138303C2direct (N × H)
7. C2×#14582798C2semidirect
8. C2×#14582796C2semidirect
9. C2×#14582794C2semidirect
10. C2×#14582794C2semidirect
11. C2×#14582781C2semidirect
12. C2×#14582780C2semidirect
13. C2×#14582768C2semidirect
19. C2×#13063315C22semidirect
45. #14582798C22semidirect
46. #14582796C22semidirect
47. #14582794C22semidirect
48. #14582794C22semidirect
49. #14582781C22semidirect
50. #14582780C22semidirect
51. #14582768C22semidirect
378. C2×C43#2441semidirect
438. C43C2×#2441semidirect
731. C2#19138303direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633152
C22×#130632812
#191383032
C2×#145828352
C2×#145828222
C2×#145827982
C2×#145827962
C2×#145827942
C2×#145827812
C2×#145827802
C2×#145827682
C2×#145827572
C2×C22⋊C4×Dic432
C2×C43×#3962
C2×#244143