Finite Group Databasebeta

← D43×#2365 #25256183

Subgroups — D43×#2365 #25256183

Order 11008.

3158 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
1C2×C4⋊Q8×D43C211yesmaximal, characteristic
2C2×C4×Q8×D43C212yesmaximal
3#19137655C211yesmaximal, characteristic, complemented
4#19137654C212yesmaximal, complemented
5#19137653C211yesmaximal, characteristic, complemented
6#19137652C212yesmaximal, complemented
7#19137651C211yesmaximal, characteristic, complemented
8#19137650C214yesmaximal, complemented
9#19137649C212yesmaximal, complemented
10#19137648C212yesmaximal, complemented
11#391×D43C212yesmaximal
12#389×D43C212yesmaximal
13#387×D43C214yesmaximal
14C4×C4⋊C4×D43C211yesmaximal, characteristic
15C4×C4⋊C4×D43C212yesmaximal
16C4×C4⋊C4×D43C211yesmaximal, characteristic
17C43×#2365C211yesmaximal, characteristic, complemented
18C22×Q8×D43C2212yes—
19C2×#13063325C2211yescharacteristic
20C2×#13063324C2212yes—
21C2×#13063324C2212yes—
22C2×#13063323C2212yes—
23C4⋊Q8×D43C4116yescomplemented
24C2×Q8×Dic43C2212yes—
25C2×C4×Dic86C2214yes—
26C2×C4×Dic86C2212yes—
27C2×#13063290C2214yes—
28C2×#13063290C2212yes—
29C4×Q8×D43—216no—
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2214yes—
32C2×C4⋊C4×D43C2211yescharacteristic
33C2×C4⋊C4×D43C2212yes—
34C2×C4⋊C4×D43C2212yes—
35C2×C4⋊C4×D43C2211yescharacteristic
36C2×C4⋊C4×D43C2211yescharacteristic
37C2×C42×D43C2212yes—
38C2×C42×D43C2212yes—
39C2×C42×D43C2214yes—
40C2×C42×D43C2211yescharacteristic
41#14582806C2212yes—
42#14582805C2212yes—
43#14582804C2212yes—
44#14582803C2214yes—
45#14582803C2214yes—
46#14582798C2212yes—
47#14582797C2212yes—
48#14582796C2214yes—
49#14582795C2212yes—
50#14582794C2214yes—
51#14582786C2214yes—
52#14582785C2214yes—
53#14582784C2214yes—
54#14582783C2214yes—
55#14582782C2214yes—
56#14582781C2214yes—
57#14582780C2214yes—
58C4⋊C4×Dic43C2211yescharacteristic
59C4⋊C4×Dic43C2212yes—
60C4⋊C4×Dic43C2211yescharacteristic
61C4⋊C4×Dic43C2212yes—
62C4⋊C4×Dic43C2211yescharacteristic
63C4⋊C4×Dic43C2211yescharacteristic
64C4×Dic43⋊C4C2212yes—
65C4×Dic43⋊C4C2214yes—
66C4×Dic43⋊C4C2212yes—
67C4×C4⋊Dic43C2212yes—
68C4×C4⋊Dic43C2211yescharacteristic
69C4×C4⋊Dic43C2211yescharacteristic
70#14582750C2212yes—
71#14582750C2212yes—
72#14582750C2214yes—
73#95×D43C2214yes—
74#95×D43C2214yes—
75#95×D43C2212yes—
76#95×D43C2212yes—
77C2×C4⋊Q8×C43C2211yescharacteristic
78C2×C4×Q8×C43C2212yes—
79C43×#391C2212yes—
80C43×#389C2212yes—
81C43×#387C2214yes—
82C4×C4⋊C4×C43C2211yescharacteristic
83C4×C4⋊C4×C43C2211yescharacteristic
84C4×C4⋊C4×C43C2212yes—
85C22×Dic86C2314yes—
86C22×Dic86C2312yes—
87C2×Q8×D43—28no—
88C2×Q8×D43—28no—
89C2×Q8×D43C2×C4116yes—
90C22×C4×D43C2312yes—
91C22×C4×D43C2312yes—
92C22×C4×D43C2314yes—
93C22×C4×D43C2311yescharacteristic
94C22×C4×D43C2312yes—
95C22×C4×D43C2312yes—
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2311yescharacteristic
98#13063325C2×C418yescomplemented
99#13063324C2×C4116yescomplemented
100#13063324C2×C4116yescomplemented
101#13063323C2×C4116yescomplemented
102Q8×Dic43—28no—
103C4×Dic86—28no—
104C4×Dic86—216no—
105#13063290—28no—
106#13063290—216no—
107C2×C4⋊Dic43C2314yes—
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2312yes—
111C2×C4⋊Dic43C2312yes—
112C2×C4⋊Dic43C2311yescharacteristic
113C2×C4⋊Dic43C2311yescharacteristic
114C2×Dic43⋊C4C2314yes—
115C2×Dic43⋊C4C2312yes—
116C2×Dic43⋊C4C2314yes—
117C2×Dic43⋊C4C2312yes—
118C2×Dic43⋊C4C2314yes—
119C2×Dic43⋊C4C2314yes—
120C2×Dic43⋊C4C2312yes—
121C2×Dic43⋊C4C2312yes—
122C4⋊C4×D43—216no—
123C4⋊C4×D43—24no—
124C4⋊C4×D43—24no—
125C4⋊C4×D43C2×C4116yes—
126C4⋊C4×D43C2×C4116yes—
127C4⋊C4×D43D418yes—
128C4⋊C4×D43Q818yescomplemented
129C2×C4×Dic43C2314yes—
130C2×C4×Dic43C2314yes—
131C2×C4×Dic43C2314yes—
132C2×C4×Dic43C2312yes—
133C2×C4×Dic43C2312yes—
134C2×C4×Dic43C2312yes—
135C2×C4×Dic43C2312yes—
136C2×C4×Dic43C2312yes—
137C2×C4×Dic43C2312yes—
138C2×C4×Dic43C2311yescharacteristic
139C2×C4×Dic43C2311yescharacteristic
140C2×C4×Dic43C2311yescharacteristic
141C42×D43—216no—
142C42×D43—28no—
143C42×D43—28no—
144C42×D43C2×C418yes—
145C43⋊#95C2312yes—
146C43⋊#95C2314yes—
147C43⋊#95C2314yes—
148C43⋊#95C2312yes—
149C43⋊#95C2314yes—
150C43⋊#95C2314yes—
151C43⋊#95C2312yes—
152C43⋊#95C2312yes—
153C43⋊#95C2314yes—
154C43⋊#95C2314yes—
155C43⋊#95C2312yes—
156C43⋊#95C2312yes—
157C22×Q8×C43C2312yes—
158C4⋊Q8×C43C2×C418yescomplemented
159C4×Q8×C43—28no—
160C2×C4⋊C4×C43C2314yes—
161C2×C4⋊C4×C43C2311yescharacteristic
162C2×C4⋊C4×C43C2311yescharacteristic
163C2×C4⋊C4×C43C2312yes—
164C2×C4⋊C4×C43C2312yes—
165C2×C4⋊C4×C43C2311yescharacteristic
166C2×C4⋊C4×C43C2311yescharacteristic
167C2×C42×C43C2312yes—
168C2×C42×C43C2312yes—
169C2×C42×C43C2314yes—
170C2×C42×C43C2311yescharacteristic
171#95×C43C2312yes—
172#95×C43C2314yes—
173#95×C43C2314yes—
174#95×C43C2312yes—
175C23×D43C2411yescharacteristic
176C2×Q8×C43—24no—
177C2×Q8×C43—24no—
178C2×Q8×C43C22×C418yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2412yes—
181C22×C4×C43C2411yescharacteristic
182C22×C4×C43C2414yes—
183C22×C4×C43C2412yes—
184C22×C4×C43C2412yes—
185C22×C4×C43C2411yescharacteristic
186C22×C4×C43C2411yescharacteristic
187C22×Dic43C2412yes—
188C22×Dic43C2412yes—
189C22×Dic43C2411yescharacteristic
190C22×Dic43C2414yes—
191C22×Dic43C2412yes—
192C22×Dic43C2412yes—
193C22×Dic43C2411yescharacteristic
194C22×Dic43C2411yescharacteristic
195Q8×D43—264no—
196C2×C4×D43—24no—
197C2×C4×D43—28no—
198C2×C4×D43—24no—
199C2×C4×D43—24no—
200C2×C4×D43—28no—
201C2×C4×D43—24no—
202C2×C4×D43—24no—
203C2×C4×D43—24no—
204C2×C4×D43—22no—
205C2×C4×D43—24no—
206C2×C4×D43—22no—
207C2×C4×D43—24no—
208C2×C4×D43—24no—
209C2×C4×D43—24no—
210C2×C4×D43C22×C414yes—
211C2×C4×D43C22×C4116yes—
212C2×C4×D43C22×C414yes—
213C2×C4×D43C22×C414yes—
214C2×C4×D43C2×D418yes—
215C2×C4×D43C2×D414yes—
216C2×C4×D43C2×Q818yes—
217C2×C4×D43C2×Q814yes—
218C2×C4×D43#4114yes—
219C2×C4×D43#4114yes—
220C2×Dic86—24no—
221C2×Dic86—24no—
222C2×Dic86—28no—
223C2×Dic86—28no—
224C2×Dic86C22×C418yes—
225C2×Dic86C22×C4116yes—
226C4⋊C4×C43—28no—
227C4⋊C4×C43—22no—
228C4⋊C4×C43—22no—
229C4⋊C4×C43C22×C418yes—
230C4⋊C4×C43C22×C418yes—
231C4⋊C4×C43C2×D414yes—
232C4⋊C4×C43C2×Q814yescomplemented
233C42×C43—28no—
234C42×C43—24no—
235C42×C43—24no—
236C42×C43C22×C414yes—
237C4⋊Dic43—22no—
238C4⋊Dic43—22no—
239C4⋊Dic43—28no—
240C4⋊Dic43C22×C418yes—
241C4⋊Dic43C22×C418yes—
242C4⋊Dic43C2×D414yes—
243C4⋊Dic43C2×Q814yescomplemented
244Dic43⋊C4—28no—
245Dic43⋊C4—28no—
246Dic43⋊C4—24no—
247Dic43⋊C4—24no—
248Dic43⋊C4C22×C4116yes—
249Dic43⋊C4C22×C4116yes—
250Dic43⋊C4C2×D418yes—
251Dic43⋊C4C2×Q818yescomplemented
252C4×Dic43—28no—
253C4×Dic43—24no—
254C4×Dic43—24no—
255C4×Dic43—24no—
256C4×Dic43—28no—
257C4×Dic43—28no—
258C4×Dic43—24no—
259C4×Dic43—24no—
260C4×Dic43—24no—
261C4×Dic43C22×C414yes—
262C4×Dic43C22×C414yes—
263C4×Dic43C22×C414yes—
264C23×C43C2511yescharacteristic
265C22×D43C23×C412yes—
266C22×D43C22×D412yes—
267C22×D43C22×Q812yes—
268C22×D43C2×#4112yes—
269C22×D43C2×#4112yes—
270C22×D432−1+412yes—
271C22×D432−1+412yes—
272Q8×C43—216no—
273C2×C4×C43—22no—
274C2×C4×C43—24no—
275C2×C4×C43—22no—
276C2×C4×C43—24no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
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—22no—
286C2×C4×C43—22no—
287C2×C4×C43C23×C412yes—
288C2×C4×C43C23×C418yes—
289C2×C4×C43C23×C412yes—
290C2×C4×C43C23×C412yes—
291C2×C4×C43C22×D414yes—
292C2×C4×C43C22×D412yes—
293C2×C4×C43C22×Q814yes—
294C2×C4×C43C22×Q812yes—
295C2×C4×C43C2×#4112yes—
296C2×C4×C43C2×#4112yes—
297C2×Dic43—22no—
298C2×Dic43—24no—
299C2×Dic43—22no—
300C2×Dic43—24no—
301C2×Dic43—21no—
302C2×Dic43—21no—
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×Dic43C23×C412yes—
312C2×Dic43C23×C418yes—
313C2×Dic43C23×C412yes—
314C2×Dic43C23×C412yes—
315C2×Dic43C22×D414yes—
316C2×Dic43C22×D412yes—
317C2×Dic43C22×Q814yes—
318C2×Dic43C22×Q812yes—
319C2×Dic43C2×#4112yes—
320C2×Dic43C2×#4112yes—
321C4×D43—232no—
322C4×D43—28no—
323C4×D43—216no—
324C4×D43—216no—
325C4×D43—48no—
326C4×D43—48no—
327C4×D43C4×D4116yes—
328C4×D43C4×Q8116yescomplemented
329Dic86—216no—
330Dic86—232no—
331C2×#2365—431nomaximal, Sylow
332C22×C43C24×C411yescharacteristic
333C22×C43C23×D411yescharacteristic
334C22×C43C23×Q811yescharacteristic
335C22×C43C22×#4111yescharacteristic
336C22×C43C22×#4111yescharacteristic
337C22×C43C2×2−1+411yescharacteristic
338C22×C43C2×2−1+411yescharacteristic
339C2×D43C2×C4×D414yes—
340C2×D43C2×C4×Q814yes—
341C2×D43#51914yes—
342C2×D43#54714yes—
343C2×D43D4×Q814yes—
344C2×D43#55614yes—
345C2×D43#55714yes—
346C4×C43—28no—
347C4×C43—22no—
348C4×C43—24no—
349C4×C43—24no—
350C4×C43—42no—
351C4×C43—42no—
352C4×C43C2×C4×D414yes—
353C4×C43C2×C4×Q814yescomplemented
354Dic43—28no—
355Dic43—22no—
356Dic43—24no—
357Dic43—24no—
358Dic43—42no—
359Dic43—42no—
360Dic43C2×C4×D414yes—
361Dic43C2×C4×Q814yescomplemented
362C22×C4⋊Q8—431no—
363C22×C4×Q8—432no—
364#2365—432no—
365#2365—432no—
366#2365—434no—
367#2365—431no—
368#2365—431no—
369#2365—432no—
370#2365—431no—
371#2365—432no—
372#2365D4311yescharacteristic, direct product factor
373C2×#391—432no—
374C2×#389—432no—
375C2×#387—434no—
376C2×C4×C4⋊C4—431no—
377C2×C4×C4⋊C4—432no—
378C2×C4×C4⋊C4—431no—
379C2×C43C22×C4×D411yescharacteristic
380C2×C43C22×C4×Q811yescharacteristic
381C2×C43C2×#51911yescharacteristic
382C2×C43C2×#54711yescharacteristic
383C2×C43C2×D4×Q811yescharacteristic
384C2×C43C2×#55611yescharacteristic
385C2×C43C2×#55711yescharacteristic
386D43#236518yesdirect product factor
387C23×Q8—432no—
388C2×C4⋊Q8—432no—
389C2×C4⋊Q8—4316no—
390C2×C4⋊Q8—432no—
391C2×C4⋊Q8—432no—
392C2×C4⋊Q8—431no—
393C2×C4⋊Q8C2×D4311yescharacteristic
394C2×C4×Q8—432no—
395C2×C4×Q8—434no—
396C2×C4×Q8—432no—
397C2×C4×Q8—432no—
398C2×C4×Q8—434no—
399C2×C4×Q8—8616no—
400C2×C4×Q8C2×D4312yes—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—432no—
403C22×C4⋊C4—432no—
404C22×C4⋊C4—431no—
405C22×C4⋊C4—434no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4—431no—
408C22×C42—431no—
409C22×C42—434no—
410C22×C42—432no—
411C22×C42—432no—
412#391—432no—
413#391—432no—
414#391—432no—
415#391—434no—
416#391—434no—
417#391C2×D4312yes—
418#389—434no—
419#389—432no—
420#389—432no—
421#389—432no—
422#389—434no—
423#389C2×D4312yes—
424#387—434no—
425#387—434no—
426#387—434no—
427#387—434no—
428#387—434no—
429#387—434no—
430#387—434no—
431#387C2×D4314yes—
432C4×C4⋊C4—431no—
433C4×C4⋊C4—431no—
434C4×C4⋊C4—431no—
435C4×C4⋊C4—431no—
436C4×C4⋊C4—432no—
437C4×C4⋊C4—432no—
438C4×C4⋊C4—431no—
439C4×C4⋊C4—431no—
440C4×C4⋊C4—432no—
441C4×C4⋊C4—432no—
442C4×C4⋊C4—432no—
443C4×C4⋊C4—434no—
444C4×C4⋊C4—432no—
445C4×C4⋊C4—432no—
446C4×C4⋊C4—434no—
447C4×C4⋊C4C2×D4311yescharacteristic
448C4×C4⋊C4C2×D4311yescharacteristic
449C4×C4⋊C4C2×D4312yes—
450C2×#95—432no—
451C2×#95—432no—
452C2×#95—434no—
453C2×#95—434no—
454C43C2×#236511yescharacteristic, complemented, Sylow
455C22×Q8—4316no—
456C22×Q8—434no—
457C22×Q8—432no—
458C22×Q8—868no—
459C22×Q8—868no—
460C22×Q8C22×D4312yes—
461C23×C4—431no—
462C23×C4—431no—
463C23×C4—434no—
464C23×C4—432no—
465C23×C4—431no—
466C23×C4—432no—
467C23×C4—432no—
468C23×C4—432no—
469C4⋊Q8—4316no—
470C4⋊Q8—4316no—
471C4⋊Q8—4316no—
472C4⋊Q8—438no—
473C4⋊Q8C4×D4318yescomplemented
474C4×Q8—28no—
475C4×Q8—8616no—
476C4×Q8—868no—
477C4×Q8—8616no—
478C4×Q8—868no—
479C4×Q8—868no—
480C2×C4⋊C4—432no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—434no—
483C2×C4⋊C4—434no—
484C2×C4⋊C4—432no—
485C2×C4⋊C4—432no—
486C2×C4⋊C4—432no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—4316no—
489C2×C4⋊C4—4316no—
490C2×C4⋊C4—438no—
491C2×C4⋊C4—438no—
492C2×C4⋊C4—434no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—434no—
495C2×C4⋊C4—432no—
496C2×C4⋊C4—432no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—8616no—
500C2×C4⋊C4—864no—
501C2×C4⋊C4—864no—
502C2×C4⋊C4C22×D4314yes—
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4312yes—
506C2×C4⋊C4C22×D4312yes—
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C42—431no—
510C2×C42—431no—
511C2×C42—431no—
512C2×C42—438no—
513C2×C42—434no—
514C2×C42—434no—
515C2×C42—434no—
516C2×C42—432no—
517C2×C42—432no—
518C2×C42—432no—
519C2×C42—432no—
520C2×C42—432no—
521C2×C42—432no—
522C2×C42—868no—
523C2×C42—8616no—
524C2×C42—868no—
525C2×C42C22×D4314yes—
526C2×C42C22×D4312yes—
527C2×C42C22×D4312yes—
528C2×C42C22×D4311yescharacteristic
529#95—432no—
530#95—432no—
531#95—432no—
532#95—432no—
533#95—432no—
534#95—432no—
535#95—434no—
536#95—434no—
537#95—434no—
538#95—434no—
539#95—434no—
540#95—434no—
541#95C22×D4312yes—
542#95C22×D4312yes—
543#95C22×D4314yes—
544#95C22×D4314yes—
545C24—431no—
546C2×Q8—24no—
547C2×Q8—24no—
548C2×Q8—4316no—
549C2×Q8—438no—
550C2×Q8—868no—
551C2×Q8—868no—
552C2×Q8—8664no—
553C2×Q8—864no—
554C2×Q8—864no—
555C2×Q8C2×C4×D4318yes—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—434no—
559C22×C4—434no—
560C22×C4—434no—
561C22×C4—434no—
562C22×C4—434no—
563C22×C4—434no—
564C22×C4—431no—
565C22×C4—432no—
566C22×C4—434no—
567C22×C4—432no—
568C22×C4—434no—
569C22×C4—4316no—
570C22×C4—438no—
571C22×C4—438no—
572C22×C4—432no—
573C22×C4—432no—
574C22×C4—864no—
575C22×C4—868no—
576C22×C4—864no—
577C22×C4—868no—
578C22×C4—864no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—864no—
584C22×C4—864no—
585C22×C4—864no—
586C22×C4—864no—
587C22×C4—864no—
588C22×C4C23×D4312yes—
589C22×C4C23×D4312yes—
590C22×C4C23×D4311yescharacteristic
591C22×C4C23×D4314yes—
592C22×C4C23×D4312yes—
593C22×C4C23×D4312yes—
594C22×C4C23×D4311yescharacteristic
595C22×C4C23×D4311yescharacteristic
596C4⋊C4—28no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—4316no—
600C4⋊C4—4316no—
601C4⋊C4—438no—
602C4⋊C4—438no—
603C4⋊C4—438no—
604C4⋊C4—434no—
605C4⋊C4—438no—
606C4⋊C4—434no—
607C4⋊C4—868no—
608C4⋊C4—868no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—868no—
612C4⋊C4—862no—
613C4⋊C4—862no—
614C4⋊C4C2×C4×D4318yes—
615C4⋊C4C2×C4×D4318yes—
616C4⋊C4D4×D4314yes—
617C4⋊C4Q8×D4314yescomplemented
618C42—28no—
619C42—24no—
620C42—24no—
621C42—434no—
622C42—434no—
623C42—434no—
624C42—864no—
625C42—868no—
626C42—868no—
627C42—864no—
628C42—864no—
629C42—864no—
630C42—868no—
631C42—864no—
632C42—864no—
633C42C2×C4×D4314yes—
634C23—432no—
635C23—432no—
636C23—432no—
637C23—432no—
638C23—432no—
639C23—432no—
640C23—432no—
641C23C24×D4311yescharacteristic
642Q8—216no—
643Q8—8632no—
644Q8—8616no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—432no—
662C2×C4—432no—
663C2×C4—432no—
664C2×C4—432no—
665C2×C4—4316no—
666C2×C4—4316no—
667C2×C4—432no—
668C2×C4—438no—
669C2×C4—434no—
670C2×C4—434no—
671C2×C4—8632no—
672C2×C4—868no—
673C2×C4—8616no—
674C2×C4—8616no—
675C2×C4—862no—
676C2×C4—864no—
677C2×C4—862no—
678C2×C4—864no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—1728no—
690C2×C4—1728no—
691C2×C4C22×C4×D4312yes—
692C2×C4C22×C4×D4318yes—
693C2×C4C22×C4×D4312yes—
694C2×C4C22×C4×D4312yes—
695C2×C4C2×D4×D4314yes—
696C2×C4C2×D4×D4312yes—
697C2×C4C2×Q8×D4314yes—
698C2×C4C2×Q8×D4312yes—
699C2×C4#41×D4312yes—
700C2×C4#41×D4312yes—
701C22—434no—
702C22—434no—
703C22—434no—
704C22—434no—
705C22—434no—
706C22—434no—
707C22—434no—
708C22C23×C4×D4311yescharacteristic
709C22C22×D4×D4311yescharacteristic
710C22C22×Q8×D4311yescharacteristic
711C22C2×#41×D4311yescharacteristic
712C22C2×#41×D4311yescharacteristic
713C222−1+4×D4311yescharacteristic
714C222−1+4×D4311yescharacteristic
715C4—22no—
716C4—24no—
717C4—24no—
718C4—28no—
719C4—42no—
720C4—42no—
721C4—434no—
722C4—434no—
723C4—862no—
724C4—864no—
725C4—864no—
726C4—868no—
727C4—1722no—
728C4—1722no—
729C4C4×D4×D4314yes—
730C4C4×Q8×D4314yescomplemented
731C2—438no—
732C2C2×C4×D4×D4311yescharacteristic
733C2C2×C4×Q8×D4311yescharacteristic
734C2#519×D4311yescharacteristic
735C2#547×D4311yescharacteristic
736C2D4×Q8×D4311yescharacteristic
737C2#556×D4311yescharacteristic
738C2#557×D4311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2365C2
socle, cosocleC23×C43C25
prime radicalC23×D43C24
hypercenter#2365D43
hypocenterC43C2×#2365
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
3. #19137655C2semidirect
4. #19137654C2semidirect
5. #19137653C2semidirect
6. #19137652C2semidirect
7. #19137651C2semidirect
8. #19137650C2semidirect
9. #19137649C2semidirect
10. #19137648C2semidirect
17. C43×#2365C2semidirect
23. C4⋊Q8×D43C4semidirect
98. #13063325C2×C4semidirect
99. #13063324C2×C4semidirect
100. #13063324C2×C4semidirect
101. #13063323C2×C4semidirect
128. C4⋊C4×D43Q8semidirect
158. C4⋊Q8×C43C2×C4semidirect
232. C4⋊C4×C43C2×Q8semidirect
243. C4⋊Dic43C2×Q8semidirect
251. Dic43⋊C4C2×Q8semidirect
328. C4×D43C4×Q8semidirect
353. C4×C43C2×C4×Q8semidirect
361. Dic43C2×C4×Q8semidirect
372. #2365D43direct (N × H)
386. D43#2365direct (N × H)
454. C43C2×#2365semidirect
473. C4⋊Q8C4×D43semidirect
617. C4⋊C4Q8×D43semidirect
730. C4C4×Q8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D432
C2×C4×Q8×D432
#191376552
#191376542
#191376532
#191376522
#191376512
#191376502
#191376492
#191376482
#391×D432
#389×D432
#387×D432
C4×C4⋊C4×D432
C43×#23652
C2×#236543