Finite Group Databasebeta

← C2×#387×D43 #25254912

Subgroups — C2×#387×D43 #25254912

Order 11008.

4286 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D43C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic
3C22×C42×D43C211yesmaximal, characteristic
4C2×#14582786C211yesmaximal, characteristic, complemented
5C2×#14582785C211yesmaximal, characteristic, complemented
6C2×#14582784C211yesmaximal, characteristic, complemented
7C2×#14582783C211yesmaximal, characteristic, complemented
8C2×#14582782C211yesmaximal, characteristic, complemented
9C2×#14582781C211yesmaximal, characteristic, complemented
10C2×#14582780C211yesmaximal, characteristic, complemented
11#387×D43C2116yesmaximal, direct product factor
12C2×#95×D43C211yesmaximal, characteristic
13C2×#95×D43C211yesmaximal, characteristic
14C2×#95×D43C211yesmaximal, characteristic
15C2×#95×D43C211yesmaximal, characteristic
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C23×C4×D43C2211yescharacteristic
23C23×C4×D43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C2×C4⋊C4×D43—28no—
31C2×C4⋊C4×D43C4116yescomplemented
32C2×C4⋊C4×D43C2218yes—
33C2×C4⋊C4×D43C2218yes—
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37C2×C42×D43—28no—
38C2×C42×D43C2218yes—
39#14582786C2218yescomplemented
40#14582785C2218yescomplemented
41#14582784C2218yescomplemented
42#14582783C2218yescomplemented
43#14582782C2218yescomplemented
44#14582781C2218yescomplemented
45#14582780C2218yescomplemented
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58#95×D43C2218yes—
59#95×D43C2218yes—
60#95×D43C2218yes—
61#95×D43C2218yes—
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C42×C43C2211yescharacteristic
65C43×#387C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C22×C4×D43—24no—
79C22×C4×D43—24no—
80C22×C4×D43—24no—
81C22×C4×D43—24no—
82C22×C4×D43—24no—
83C22×C4×D43—24no—
84C22×C4×D43—24no—
85C22×C4×D43—24no—
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43—24no—
90C22×C4×D43—24no—
91C22×C4×D43—24no—
92C22×C4×D43—24no—
93C22×C4×D43—24no—
94C22×C4×D43C2×C418yes—
95C22×C4×D43C2×C418yes—
96C22×C4×D43C2×C418yes—
97C22×C4×D43D418yes—
98C22×C4×D43Q818yes—
99C22×C4×D43C2314yes—
100C22×C4×D43C2314yes—
101C22×C4×D43C2314yes—
102C22×C4×D43C2314yes—
103C22×C4×D43C2314yes—
104C22×C4×D43C2314yes—
105C22×C4×D43C2314yes—
106C2×C4⋊Dic43—24no—
107C2×C4⋊Dic43C2×C418yescomplemented
108C2×C4⋊Dic43C2314yes—
109C2×C4⋊Dic43C2314yes—
110C2×Dic43⋊C4—24no—
111C2×Dic43⋊C4—24no—
112C2×Dic43⋊C4C2×C418yescomplemented
113C2×Dic43⋊C4C2×C418yescomplemented
114C2×Dic43⋊C4C2314yes—
115C2×Dic43⋊C4C2314yes—
116C2×Dic43⋊C4C2314yes—
117C2×Dic43⋊C4C2314yes—
118C4⋊C4×D43—232no—
119C4⋊C4×D43C2×C4164yescomplemented
120C2×C4×Dic43—24no—
121C2×C4×Dic43—24no—
122C2×C4×Dic43—24no—
123C2×C4×Dic43C2314yes—
124C2×C4×Dic43C2314yes—
125C2×C4×Dic43C2314yes—
126C42×D43—232no—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43—24no—
147C2×C4⋊C4×C43C2×C418yescomplemented
148C2×C4⋊C4×C43C2314yes—
149C2×C4⋊C4×C43C2314yes—
150C2×C42×C43—24no—
151C2×C42×C43C2314yes—
152#95×C43C2314yes—
153#95×C43C2314yes—
154#95×C43C2314yes—
155#95×C43C2314yes—
156C24×C43C2411yescharacteristic
157C23×D43C22×C414yes—
158C23×D43C2×D414yes—
159C23×D43C2×Q814yes—
160C23×D43#4114yes—
161C23×D43#4114yes—
162C23×D43#4114yes—
163C23×D43#4114yes—
164C23×D43C2412yes—
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×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43C22×C414yes—
182C22×C4×C43C22×C414yes—
183C22×C4×C43C22×C414yes—
184C22×C4×C43C2×D414yes—
185C22×C4×C43C2×Q814yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
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×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43C22×C414yes—
210C22×Dic43C22×C414yes—
211C22×Dic43C22×C414yes—
212C22×Dic43C2×D414yes—
213C22×Dic43C2×Q814yes—
214C22×Dic43C2412yes—
215C22×Dic43C2412yes—
216C22×Dic43C2412yes—
217C22×Dic43C2412yes—
218C22×Dic43C2412yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C2×C4×D43—232no—
222C2×C4×D43—232no—
223C2×C4×D43—232no—
224C2×C4×D43—232no—
225C2×C4×D43—232no—
226C2×C4×D43—28no—
227C2×C4×D43—28no—
228C2×C4×D43—28no—
229C2×C4×D43—28no—
230C2×C4×D43—28no—
231C2×C4×D43—28no—
232C2×C4×D43—28no—
233C2×C4×D43—28no—
234C2×C4×D43—28no—
235C2×C4×D43—28no—
236C2×C4×D43—28no—
237C2×C4×D43—28no—
238C2×C4×D43—28no—
239C2×C4×D43—28no—
240C2×C4×D43—28no—
241C2×C4×D43—28no—
242C2×C4×D43—416no—
243C2×C4×D43—416no—
244C2×C4×D43C22×C4116yes—
245C2×C4×D43C22×C4116yes—
246C2×C4×D43C22×C4116yes—
247C2×C4×D43C2×D4116yes—
248C2×C4×D43C2×Q8116yes—
249C4⋊C4×C43—28no—
250C4⋊C4×C43C22×C4116yescomplemented
251C42×C43—28no—
252C4⋊Dic43—28no—
253C4⋊Dic43C22×C4116yescomplemented
254Dic43⋊C4—28no—
255Dic43⋊C4—28no—
256Dic43⋊C4C22×C4116yescomplemented
257Dic43⋊C4C22×C4116yescomplemented
258C4×Dic43—28no—
259C4×Dic43—28no—
260C4×Dic43—28no—
261C23×C43C23×C412yes—
262C23×C43C22×D412yes—
263C23×C43C22×Q812yes—
264C23×C43C2×#4112yes—
265C23×C43C2×#4112yes—
266C23×C43C2×#4112yes—
267C23×C43C2×#4112yes—
268C23×C43C2511yescharacteristic
269C22×D43#117116yes—
270C22×D43C4×D4116yes—
271C22×D43C4×Q8116yes—
272C22×D43C22⋊Q8116yes—
273C22×D43#123116yes—
274C22×D43#125116yes—
275C22×D43#126116yes—
276C22×D43C23×C414yes—
277C22×D43C22×D414yes—
278C22×D43C22×Q814yes—
279C22×D43C2×#4114yes—
280C22×D43C2×#4114yes—
281C22×D43C2×#4114yes—
282C22×D43C2×#4114yes—
283C2×C4×C43—28no—
284C2×C4×C43—28no—
285C2×C4×C43—28no—
286C2×C4×C43—28no—
287C2×C4×C43—28no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—44no—
305C2×C4×C43—44no—
306C2×C4×C43C23×C414yes—
307C2×C4×C43C23×C414yes—
308C2×C4×C43C23×C414yes—
309C2×C4×C43C22×D414yes—
310C2×C4×C43C22×Q814yes—
311C2×Dic43—28no—
312C2×Dic43—28no—
313C2×Dic43—28no—
314C2×Dic43—28no—
315C2×Dic43—28no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—44no—
333C2×Dic43—44no—
334C2×Dic43C23×C414yes—
335C2×Dic43C23×C414yes—
336C2×Dic43C23×C414yes—
337C2×Dic43C22×D414yes—
338C2×Dic43C22×Q814yes—
339C4×D43—232no—
340C4×D43—232no—
341C4×D43—232no—
342C4×D43—232no—
343C4×D43—232no—
344C4×D43—416no—
345C4×D43—416no—
346C22×#387—431nomaximal, Sylow
347C22×C43C2×#11714yes—
348C22×C43C2×C4×D414yes—
349C22×C43C2×C4×Q814yes—
350C22×C43C2×C22⋊Q814yes—
351C22×C43C2×#12314yes—
352C22×C43C2×#12514yes—
353C22×C43C2×#12614yes—
354C22×C43C24×C411yescharacteristic
355C22×C43C23×D411yescharacteristic
356C22×C43C23×Q811yescharacteristic
357C22×C43C22×#4111yescharacteristic
358C22×C43C22×#4111yescharacteristic
359C22×C43C22×#4111yescharacteristic
360C22×C43C22×#4111yescharacteristic
361C2×D43#387164yesdirect product factor
362C2×D43C2×#11718yes—
363C2×D43C2×C4×D418yes—
364C2×D43C2×C4×Q818yes—
365C2×D43C2×C22⋊Q818yes—
366C2×D43C2×#12318yes—
367C2×D43C2×#12518yes—
368C2×D43C2×#12618yes—
369C4×C43—24no—
370C4×C43—24no—
371C4×C43—24no—
372C4×C43—24no—
373C4×C43—24no—
374C4×C43—42no—
375C4×C43—42no—
376Dic43—24no—
377Dic43—24no—
378Dic43—24no—
379Dic43—24no—
380Dic43—24no—
381Dic43—42no—
382Dic43—42no—
383C23×C4⋊C4—431no—
384C23×C4⋊C4—431no—
385C23×C42—431no—
386C2×#387—431no—
387C2×#387—4316no—
388C2×#387—431no—
389C2×#387—431no—
390C2×#387—431no—
391C2×#387—431no—
392C2×#387—431no—
393C2×#387—431no—
394C2×#387D4311yescharacteristic, direct product factor
395C22×#95—431no—
396C22×#95—431no—
397C22×#95—431no—
398C22×#95—431no—
399C2×C43C2×#38718yescomplemented
400C2×C43C22×#11711yescharacteristic
401C2×C43C22×C4×D411yescharacteristic
402C2×C43C22×C4×Q811yescharacteristic
403C2×C43C22×C22⋊Q811yescharacteristic
404C2×C43C22×#12311yescharacteristic
405C2×C43C22×#12511yescharacteristic
406C2×C43C22×#12611yescharacteristic
407D43C2×#387116yesdirect product factor
408C24×C4—431no—
409C24×C4—431no—
410C24×C4—431no—
411C24×C4—431no—
412C24×C4—431no—
413C24×C4—431no—
414C24×C4—431no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—431no—
418C22×C4⋊C4—438no—
419C22×C4⋊C4—4316no—
420C22×C4⋊C4—431no—
421C22×C4⋊C4—431no—
422C22×C4⋊C4—431no—
423C22×C4⋊C4—438no—
424C22×C4⋊C4—868no—
425C22×C4⋊C4C2×D4311yescharacteristic
426C22×C4⋊C4C2×D4311yescharacteristic
427C22×C42—431no—
428C22×C42—431no—
429C22×C42—431no—
430C22×C42—438no—
431C22×C42—868no—
432C22×C42C2×D4311yescharacteristic
433#387—438no—
434#387—438no—
435#387—438no—
436#387—438no—
437#387—438no—
438#387—438no—
439#387—438no—
440#387C2×D4318yesdirect product factor
441C2×#95—431no—
442C2×#95—431no—
443C2×#95—431no—
444C2×#95—431no—
445C2×#95—431no—
446C2×#95—431no—
447C2×#95—431no—
448C2×#95—431no—
449C2×#95—431no—
450C2×#95—431no—
451C2×#95—431no—
452C2×#95—431no—
453C2×#95—438no—
454C2×#95—438no—
455C2×#95—438no—
456C2×#95—438no—
457C2×#95C2×D4311yescharacteristic
458C2×#95C2×D4311yescharacteristic
459C2×#95C2×D4311yescharacteristic
460C2×#95C2×D4311yescharacteristic
461C43C22×#38711yescharacteristic, complemented, Sylow
462C25—431no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—438no—
469C23×C4—438no—
470C23×C4—438no—
471C23×C4—438no—
472C23×C4—438no—
473C23×C4—434no—
474C23×C4—434no—
475C23×C4—434no—
476C23×C4—434no—
477C23×C4—434no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—434no—
481C23×C4—434no—
482C23×C4—864no—
483C23×C4—864no—
484C23×C4—864no—
485C23×C4—864no—
486C23×C4—864no—
487C23×C4—864no—
488C23×C4—864no—
489C23×C4—864no—
490C23×C4—864no—
491C23×C4—864no—
492C23×C4—864no—
493C23×C4—864no—
494C23×C4—864no—
495C23×C4—864no—
496C23×C4—864no—
497C23×C4—864no—
498C23×C4C22×D4311yescharacteristic
499C23×C4C22×D4311yescharacteristic
500C23×C4C22×D4311yescharacteristic
501C23×C4C22×D4311yescharacteristic
502C23×C4C22×D4311yescharacteristic
503C23×C4C22×D4311yescharacteristic
504C23×C4C22×D4311yescharacteristic
505C2×C4⋊C4—24no—
506C2×C4⋊C4—438no—
507C2×C4⋊C4—438no—
508C2×C4⋊C4—438no—
509C2×C4⋊C4—434no—
510C2×C4⋊C4—434no—
511C2×C4⋊C4—434no—
512C2×C4⋊C4—4364no—
513C2×C4⋊C4—434no—
514C2×C4⋊C4—434no—
515C2×C4⋊C4—434no—
516C2×C4⋊C4—8632no—
517C2×C4⋊C4—864no—
518C2×C4⋊C4—864no—
519C2×C4⋊C4—864no—
520C2×C4⋊C4C4×D4318yescomplemented
521C2×C4⋊C4C22×D4314yes—
522C2×C4⋊C4C22×D4314yes—
523C2×C42—24no—
524C2×C42—434no—
525C2×C42—434no—
526C2×C42—434no—
527C2×C42—8632no—
528C2×C42—864no—
529C2×C42—864no—
530C2×C42—864no—
531C2×C42C22×D4314yes—
532#95—434no—
533#95—434no—
534#95—434no—
535#95—434no—
536#95—434no—
537#95—434no—
538#95—434no—
539#95—434no—
540#95—434no—
541#95—434no—
542#95—434no—
543#95—434no—
544#95C22×D4314yes—
545#95C22×D4314yes—
546#95C22×D4314yes—
547#95C22×D4314yes—
548C24—434no—
549C24—434no—
550C24—434no—
551C24—434no—
552C24—434no—
553C24—434no—
554C24—434no—
555C24—432no—
556C24C23×D4311yescharacteristic
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—434no—
574C22×C4—434no—
575C22×C4—434no—
576C22×C4—434no—
577C22×C4—434no—
578C22×C4—432no—
579C22×C4—432no—
580C22×C4—432no—
581C22×C4—432no—
582C22×C4—432no—
583C22×C4—4316no—
584C22×C4—4316no—
585C22×C4—4316no—
586C22×C4—4316no—
587C22×C4—4316no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—868no—
591C22×C4—868no—
592C22×C4—868no—
593C22×C4—8632no—
594C22×C4—8632no—
595C22×C4—8632no—
596C22×C4—8632no—
597C22×C4—8632no—
598C22×C4—868no—
599C22×C4—868no—
600C22×C4—868no—
601C22×C4—868no—
602C22×C4—868no—
603C22×C4—868no—
604C22×C4—868no—
605C22×C4—868no—
606C22×C4—868no—
607C22×C4—868no—
608C22×C4—868no—
609C22×C4—868no—
610C22×C4—868no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—17216no—
628C22×C4—17216no—
629C22×C4C2×C4×D4314yes—
630C22×C4C2×C4×D4314yes—
631C22×C4C2×C4×D4314yes—
632C22×C4D4×D4314yes—
633C22×C4Q8×D4314yes—
634C22×C4C23×D4312yes—
635C22×C4C23×D4312yes—
636C22×C4C23×D4312yes—
637C22×C4C23×D4312yes—
638C22×C4C23×D4312yes—
639C22×C4C23×D4312yes—
640C22×C4C23×D4312yes—
641C4⋊C4—28no—
642C4⋊C4—4316no—
643C4⋊C4—4316no—
644C4⋊C4—4316no—
645C4⋊C4—868no—
646C4⋊C4—868no—
647C4⋊C4—868no—
648C4⋊C4C2×C4×D43116yescomplemented
649C42—28no—
650C42—868no—
651C42—868no—
652C42—868no—
653C23—4316no—
654C23—4316no—
655C23—4316no—
656C23—4316no—
657C23—4316no—
658C23—4316no—
659C23—4316no—
660C23—434no—
661C23—434no—
662C23—434no—
663C23—434no—
664C23—434no—
665C23—434no—
666C23—434no—
667C23C22×C4×D4312yes—
668C23C2×D4×D4312yes—
669C23C2×Q8×D4312yes—
670C23#41×D4312yes—
671C23#41×D4312yes—
672C23#41×D4312yes—
673C23#41×D4312yes—
674C23C24×D4311yescharacteristic
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—434no—
699C2×C4—434no—
700C2×C4—434no—
701C2×C4—434no—
702C2×C4—434no—
703C2×C4—8632no—
704C2×C4—8632no—
705C2×C4—8632no—
706C2×C4—8632no—
707C2×C4—8632no—
708C2×C4—868no—
709C2×C4—868no—
710C2×C4—868no—
711C2×C4—868no—
712C2×C4—868no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—17216no—
730C2×C4—17216no—
731C2×C4—1724no—
732C2×C4—1724no—
733C2×C4C22×C4×D4314yes—
734C2×C4C22×C4×D4314yes—
735C2×C4C22×C4×D4314yes—
736C2×C4C2×D4×D4314yes—
737C2×C4C2×Q8×D4314yes—
738C22—438no—
739C22—438no—
740C22—438no—
741C22—438no—
742C22—438no—
743C22—438no—
744C22—4364no—
745C22—438no—
746C22#117×D4314yes—
747C22C4×D4×D4314yes—
748C22C4×Q8×D4314yes—
749C22C22⋊Q8×D4314yes—
750C22#123×D4314yes—
751C22#125×D4314yes—
752C22#126×D4314yes—
753C22C23×C4×D4311yescharacteristic
754C22C22×D4×D4311yescharacteristic
755C22C22×Q8×D4311yescharacteristic
756C22C2×#41×D4311yescharacteristic
757C22C2×#41×D4311yescharacteristic
758C22C2×#41×D4311yescharacteristic
759C22C2×#41×D4311yescharacteristic
760C4—24no—
761C4—24no—
762C4—24no—
763C4—24no—
764C4—24no—
765C4—42no—
766C4—42no—
767C4—864no—
768C4—864no—
769C4—864no—
770C4—864no—
771C4—864no—
772C4—1722no—
773C4—1722no—
774C2—4316no—
775C2#387×D4318yesdirect product factor
776C2C2×#117×D4311yescharacteristic
777C2C2×C4×D4×D4311yescharacteristic
778C2C2×C4×Q8×D4311yescharacteristic
779C2C2×C22⋊Q8×D4311yescharacteristic
780C2C2×#123×D4311yescharacteristic
781C2C2×#125×D4311yescharacteristic
782C2C2×#126×D4311yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC24×D43C23
cosocleC23×C43C25
hypercenterC2×#387D43
hypocenterC43C22×#387
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
4. C2×#14582786C2semidirect
5. C2×#14582785C2semidirect
6. C2×#14582784C2semidirect
7. C2×#14582783C2semidirect
8. C2×#14582782C2semidirect
9. C2×#14582781C2semidirect
10. C2×#14582780C2semidirect
11. #387×D43C2direct (N × H)
16. C2×C43×#387C2semidirect
31. C2×C4⋊C4×D43C4semidirect
39. #14582786C22semidirect
40. #14582785C22semidirect
41. #14582784C22semidirect
42. #14582783C22semidirect
43. #14582782C22semidirect
44. #14582781C22semidirect
45. #14582780C22semidirect
65. C43×#387C22semidirect
107. C2×C4⋊Dic43C2×C4semidirect
112. C2×Dic43⋊C4C2×C4semidirect
113. C2×Dic43⋊C4C2×C4semidirect
119. C4⋊C4×D43C2×C4semidirect
147. C2×C4⋊C4×C43C2×C4semidirect
250. C4⋊C4×C43C22×C4semidirect
253. C4⋊Dic43C22×C4semidirect
256. Dic43⋊C4C22×C4semidirect
257. Dic43⋊C4C22×C4semidirect
361. C2×D43#387direct (N × H)
394. C2×#387D43direct (N × H)
399. C2×C43C2×#387semidirect
407. D43C2×#387direct (N × H)
440. #387C2×D43direct (N × H)
461. C43C22×#387semidirect
520. C2×C4⋊C4C4×D43semidirect
648. C4⋊C4C2×C4×D43semidirect
775. C2#387×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D432
C22×C42×D432
C2×#145827862
C2×#145827852
C2×#145827842
C2×#145827832
C2×#145827822
C2×#145827812
C2×#145827802
#387×D432
C2×#95×D432
C2×C43×#3872
C22×#38743