Finite Group Databasebeta

← D43×#3504 #26005071

Subgroups — D43×#3504 #26005071

Order 11008.

6958 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148421C211yesmaximal, characteristic, complemented
2#19148420C214yesmaximal, complemented
3#19148419C213yesmaximal, complemented
4#19148418C216yesmaximal, complemented
5#19148417C212yesmaximal, complemented
6#19148416C213yesmaximal, complemented
7#19148415C2112yesmaximal, complemented
8#557×D43C214yesmaximal, complemented
9#554×D43C2112yesmaximal, complemented
10#544×D43C216yesmaximal, complemented
11#533×D43C213yesmaximal, complemented
12C2×#125×D43C213yesmaximal, complemented
13#520×D43C212yesmaximal
14C4×#41×D43C211yesmaximal, characteristic
15C43×#3504C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17#14583628C2214yescomplemented
18#14583627C22112yescomplemented
19#14583626C22112yescomplemented
20#14583626C22112yescomplemented
21#14583625C2214yescomplemented
22#14583625C2214yescomplemented
23#14583624C22112yescomplemented
24#14583610C22112yescomplemented
25#14583609C22112yescomplemented
26#14583608C22112yescomplemented
27#14583608C22112yescomplemented
28#14583607C22124yescomplemented
29#14583606C22112yescomplemented
30#14583605C22112yescomplemented
31#14583605C22112yescomplemented
32#14583604C22124yescomplemented
33#14583603C22124yescomplemented
34#14583603C22124yescomplemented
35#14583530C2216yescomplemented
36#14583529C22112yescomplemented
37#14583529C22112yescomplemented
38#14583528C22124yescomplemented
39#14583527C2216yescomplemented
40#14583527C2216yescomplemented
41#14583526C22112yescomplemented
42#14583526C22112yescomplemented
43#14583456C2213yescomplemented
44#14583455C2213yescomplemented
45#14583455C2213yescomplemented
46#14583454C2216yescomplemented
47#14583453C22112yescomplemented
48#14583452C2216yescomplemented
49#14583451C22112yescomplemented
50C4⋊Q8×D43C22112yes—
51C4⋊Q8×D43C2216yes—
52C2×#13063317C2213yescomplemented
53C2×#13063316C2216yescomplemented
54C2×#13063315C22112yescomplemented
55#125×D43C2213yes—
56#125×D43C22112yes—
57#125×D43C2216yes—
58#125×D43C22112yes—
59#125×D43C2211yescharacteristic
60#125×D43C22112yescomplemented
61#125×D43C2216yescomplemented
62#125×D43C2216yescomplemented
63C22⋊Q8×D43C22112yes—
64C22⋊Q8×D43C22124yes—
65#14583382C2212yes—
66#14583381C2214yes—
67#14583380C2216yes—
68#14583379C2216yes—
69#14583378C22112yes—
70#41×Dic43C2211yescharacteristic
71C4×#10621902C2212yes—
72C4×#10621898C2213yes—
73#14583367C2213yes—
74C4×#10621900C2216yes—
75C4×Q8×D43C2214yes—
76C4×Q8×D43C22112yes—
77C4×Q8×D43C2212yes—
78C4×D4×D43C22112yes—
79C4×D4×D43C2216yes—
80#117×D43C2216yes—
81#117×D43C2213yes—
82C2×C4⋊C4×D43C2216yes—
83C2×C4⋊C4×D43C22112yes—
84C2×C42×D43C2213yes—
85C43×#557C2214yescomplemented
86C43×#554C22112yescomplemented
87C43×#544C2216yescomplemented
88C43×#533C2213yescomplemented
89C2×#125×C43C2213yescomplemented
90C43×#520C2212yes—
91C4×#41×C43C2211yescharacteristic
92C2×#10621902C2311yescharacteristic
93C2×#10621898C2313yes—
94C2×#10621900C2313yes—
95#41×D43Q8116yescomplemented
96C2×Q8×D43C23112yes—
97C2×Q8×D43C2311yescharacteristic
98C2×D4×D43C2313yes—
99C22×C4×D43C2316yes—
100C22×C4×D43C23112yes—
101C22×C4×D43C2313yes—
102#13063325C23112yes—
103#13063325C2316yes—
104#13063324C23124yes—
105#13063324C23112yes—
106#13063324C23112yes—
107#13063324C23112yes—
108#13063324C2316yes—
109#13063324C2316yes—
110#13063323C23124yes—
111#13063323C23112yes—
112#13063317C23112yes—
113#13063317C23112yes—
114#13063317C2313yes—
115#13063317C2316yes—
116#13063317C2311yescharacteristic
117#13063316C23112yes—
118#13063316C23112yes—
119#13063316C23112yes—
120#13063316C23112yes—
121#13063316C2316yes—
122#13063316C23112yes—
123#13063316C2312yes—
124#13063315C23124yes—
125#13063315C23124yes—
126#13063315C23124yes—
127#13063315C23124yes—
128#13063315C23112yes—
129#13063315C23124yes—
130#13063315C2314yes—
131#13063305C23124yes—
132#13063305C23112yes—
133#13063304C23124yes—
134#13063304C23112yes—
135#13063303C23124yes—
136#13063303C23112yes—
137#13063303C23124yes—
138#13063303C23112yes—
139#13063302C23112yes—
140#13063302C23124yes—
141#13063302C23124yes—
142#13063302C23112yes—
143#13063301C23112yes—
144#13063301C23124yes—
145Q8×Dic43C23112yes—
146Q8×Dic43C2312yes—
147Q8×Dic43C2314yes—
148C4×Dic86C23112yes—
149C4×Dic86C23112yes—
150C4×Dic86C23112yes—
151C4×Dic86C2316yes—
152C4×Dic86C23112yes—
153#13063290C23112yes—
154#13063290C23112yes—
155#13063290C23112yes—
156#13063290C2316yes—
157#13063290C23112yes—
158C4×D172C2316yes—
159C4×D172C23112yes—
160D4×Dic43C2316yes—
161D4×Dic43C23112yes—
162#13063287C23112yes—
163#13063287C2316yes—
164C4×C22⋊D43C23112yes—
165C4×C22⋊D43C23124yes—
166(C22⋊D43)⋊C4C23124yes—
167(C22⋊D43)⋊C4C23112yes—
168#13063284C2313yes—
169#13063284C2316yes—
170#13063283C2316yes—
171#13063283C2316yes—
172#13063283C2316yes—
173#13063282C2316yes—
174#13063282C23112yes—
175#13063281C2316yes—
176#13063281C23112yes—
177C2×C4⋊Dic43C23112yes—
178C2×C4⋊Dic43C2316yes—
179C2×Dic43⋊C4C23112yes—
180C2×Dic43⋊C4C23112yes—
181C2×Dic43⋊C4C23112yes—
182C4⋊C4×D43C23124yes—
183C4⋊C4×D43C23124yes—
184C4⋊C4×D43C2316yes—
185C4⋊C4×D43C23112yes—
186C4⋊C4×D43C23112yes—
187C4⋊C4×D43C23112yes—
188C4⋊C4×D43C23112yes—
189C4⋊C4×D43C23124yes—
190C4⋊C4×D43C2312yes—
191C4⋊C4×D43C2316yes—
192C4⋊C4×D43C2314yes—
193C4⋊C4×D43C23112yes—
194C22⋊C4×D43C23112yes—
195C22⋊C4×D43C2316yes—
196C2×C4×Dic43C2316yes—
197C2×C4×Dic43C2313yes—
198C42×D43C2311yescharacteristic
199C42×D43C2313yes—
200C42×D43C2316yes—
201C42×D43C2316yes—
202C42×D43C2313yes—
203C42×D43C2313yes—
204C42×D43C23112yes—
205C2×#41×C43C2311yescharacteristic
206C4⋊Q8×C43C2316yes—
207C4⋊Q8×C43C23112yes—
208#125×C43C2313yes—
209#125×C43C2316yes—
210#125×C43C23112yes—
211#125×C43C2311yescharacteristic
212#125×C43C23112yes—
213C22⋊Q8×C43C23112yes—
214C22⋊Q8×C43C23124yes—
215C4×Q8×C43C2312yes—
216C4×Q8×C43C2314yes—
217C4×Q8×C43C23112yes—
218C4×D4×C43C2316yes—
219C4×D4×C43C23112yes—
220#117×C43C2313yes—
221#117×C43C2316yes—
222C2×C4⋊C4×C43C2316yes—
223C2×C4⋊C4×C43C23112yes—
224C2×C42×C43C2313yes—
225C23×D43C2413yes—
226#41×C43C2×Q818yescomplemented
227C2×Q8×C43C24112yes—
228C2×Q8×C43C2411yescharacteristic
229C2×D4×C43C2413yes—
230C22×C4×C43C2416yes—
231C22×C4×C43C24112yes—
232C22×C4×C43C2413yes—
233C2×C22⋊D43C2416yes—
234C22×Dic43C2416yes—
235C22×Dic43C24112yes—
236C22×Dic43C2413yes—
237#10621902C2×Q818yescomplemented
238Q8×D43—424no—
239Q8×D43C2×Q818yes—
240#10621900C2×Q8124yescomplemented
241D4×D43C2×Q8124yes—
242#10621898C2×Q8124yescomplemented
243C2×D172C2413yes—
244C2×C4×D43—412no—
245C2×C4×D43—424no—
246C2×C4×D43C2×Q8124yes—
247C2×C4×D43C2412yes—
248C2×C4×D43C2414yes—
249C2×C4×D43C2416yes—
250C2×C4×D43C24112yes—
251C2×C4×D43C2416yes—
252C2×C4×D43C2416yes—
253C2×C4×D43C24124yes—
254C2×C4×D43C2413yes—
255C2×C4×D43C2411yescharacteristic
256C2×C4×D43C2413yes—
257C2×C4×D43C2413yes—
258C2×Dic86C24112yes—
259C2×Dic86C24112yes—
260C2×Dic86C24112yes—
261C2×Dic86C2413yes—
262C4⋊C4×C43C2416yes—
263C4⋊C4×C43C24112yes—
264C4⋊C4×C43C24112yes—
265C4⋊C4×C43C24124yes—
266C4⋊C4×C43C2412yes—
267C4⋊C4×C43C2416yes—
268C4⋊C4×C43C2414yes—
269C4⋊C4×C43C24112yes—
270C22⋊C4×C43C24112yes—
271C22⋊C4×C43C2416yes—
272C42×C43C2411yescharacteristic
273C42×C43C2413yes—
274C42×C43C2416yes—
275C42×C43C24112yes—
276C22⋊Dic43C24112yes—
277C22⋊Dic43C2416yes—
278(C2×D43)⋊C4C24112yes—
279(C2×D43)⋊C4C24112yes—
280(C2×D43)⋊C4C24112yes—
281C4⋊Dic43C2416yes—
282C4⋊Dic43C24112yes—
283C4⋊Dic43C24112yes—
284C4⋊Dic43C24124yes—
285C4⋊Dic43C2412yes—
286C4⋊Dic43C2416yes—
287C4⋊Dic43C2414yes—
288C4⋊Dic43C24112yes—
289Dic43⋊C4C24112yes—
290Dic43⋊C4C24112yes—
291Dic43⋊C4C24112yes—
292Dic43⋊C4C24124yes—
293Dic43⋊C4C24124yes—
294Dic43⋊C4C24124yes—
295Dic43⋊C4C2414yes—
296Dic43⋊C4C24112yes—
297Dic43⋊C4C2414yes—
298Dic43⋊C4C2414yes—
299Dic43⋊C4C24112yes—
300Dic43⋊C4C24112yes—
301C4×Dic43C2412yes—
302C4×Dic43C2411yescharacteristic
303C4×Dic43C2416yes—
304C4×Dic43C2413yes—
305C4×Dic43C2416yes—
306C4×Dic43C2416yes—
307C4×Dic43C2416yes—
308C4×Dic43C24112yes—
309C4×Dic43C24112yes—
310C4×Dic43C24112yes—
311C23×C43C2513yes—
312C22×D43—212no—
313C22×D43C22×Q8112yes—
314C22×D43C2513yes—
315C22×D43C2511yescharacteristic
316Q8×C43—412no—
317Q8×C43C22×Q814yes—
318D4×C43C22×Q8112yes—
319C2×C4×C43—46no—
320C2×C4×C43—412no—
321C2×C4×C43C22×Q8112yes—
322C2×C4×C43C2512yes—
323C2×C4×C43C2514yes—
324C2×C4×C43C2516yes—
325C2×C4×C43C25112yes—
326C2×C4×C43C2513yes—
327C2×C4×C43C2511yescharacteristic
328C22⋊D43C22×Q8124yes—
329C2×Dic43—46no—
330C2×Dic43—412no—
331C2×Dic43C22×Q8112yes—
332C2×Dic43C2512yes—
333C2×Dic43C2514yes—
334C2×Dic43C2516yes—
335C2×Dic43C25112yes—
336C2×Dic43C2513yes—
337C2×Dic43C2511yescharacteristic
338D172C22×Q8112yes—
339C4×D43—24no—
340C4×D43—224no—
341C4×D43—212no—
342C4×D43—28no—
343C4×D43—46no—
344C4×D43—424no—
345C4×D43—46no—
346C4×D43C22×Q814yes—
347C4×D43C22×Q8112yes—
348C4×D43C22×Q8112yes—
349C4×D43C22×Q8112yes—
350Dic86—412no—
351Dic86—412no—
352Dic86—412no—
353Dic86C22×Q8112yes—
354C2×#3504—431nomaximal, Sylow
355C22×C43—26no—
356C22×C43C23×Q816yes—
357C22×C43C2611yescharacteristic
358C2×D43—26no—
359C2×D43—224no—
360C2×D43C23×Q816yes—
361C2×D43C23×Q812yes—
362C2×D43#58514yes—
363C4×C43—24no—
364C4×C43—26no—
365C4×C43—212no—
366C4×C43—22no—
367C4×C43C23×Q816yes—
368C4×C43C23×Q812yes—
369Dic43—24no—
370Dic43—26no—
371Dic43—212no—
372Dic43—22no—
373Dic43C23×Q816yes—
374Dic43C23×Q812yes—
375#3504—434no—
376#3504—4312no—
377#3504—436no—
378#3504—433no—
379#3504—433no—
380#3504—432no—
381#3504—431no—
382#3504D4311yescharacteristic, direct product factor
383C2×#557—434no—
384C2×#554—4312no—
385C2×#544—436no—
386C2×#533—433no—
387C22×#125—433no—
388C2×#520—432no—
389C2×C4×#41—431no—
390C2×C43—26no—
391C2×C43C24×Q811yescharacteristic
392C2×C43C2×#58512yes—
393D43—26no—
394D43#350414yesdirect product factor
395C22×#41—431no—
396#557—4312no—
397#557—4312no—
398#557—4312no—
399#557—434no—
400#557—434no—
401#557—4312no—
402#557—434no—
403#557C2×D4314yescomplemented
404#554—4312no—
405#554—4312no—
406#554—4312no—
407#554—4324no—
408#554—4324no—
409#554—4324no—
410#554—4312no—
411#554—4312no—
412#554—4312no—
413#554—4312no—
414#554—4324no—
415#554C2×D43112yescomplemented
416#544—4312no—
417#544—4312no—
418#544—4312no—
419#544—4312no—
420#544—4324no—
421#544—436no—
422#544—436no—
423#544—436no—
424#544C2×D4316yescomplemented
425#533—436no—
426#533—433no—
427#533—433no—
428#533—4312no—
429#533—4312no—
430#533—436no—
431#533—433no—
432#533C2×D4313yescomplemented
433C2×C4⋊Q8—436no—
434C2×C4⋊Q8—4312no—
435C2×#125—433no—
436C2×#125—436no—
437C2×#125—4312no—
438C2×#125—4312no—
439C2×#125—436no—
440C2×#125—436no—
441C2×#125—431no—
442C2×#125—4312no—
443C2×#125—4312no—
444C2×#125—436no—
445C2×#125—433no—
446C2×#125C2×D4313yescomplemented
447C2×C22⋊Q8—4312no—
448C2×C22⋊Q8—4324no—
449#520—432no—
450#520—434no—
451#520—4312no—
452#520—436no—
453#520—436no—
454#520C2×D4312yes—
455C4×#41—431no—
456C4×#41—432no—
457C4×#41—436no—
458C4×#41—433no—
459C4×#41—433no—
460C4×#41C2×D4311yescharacteristic
461C2×C4×Q8—432no—
462C2×C4×Q8—434no—
463C2×C4×Q8—4312no—
464C2×C4×D4—436no—
465C2×C4×D4—4312no—
466C2×#117—433no—
467C2×#117—436no—
468C22×C4⋊C4—436no—
469C22×C4⋊C4—4312no—
470C22×C42—433no—
471C43C2×#350411yescharacteristic, complemented, Sylow
472C2×#41—4316no—
473C2×#41—431no—
474C2×#41—433no—
475C2×#41—433no—
476C2×#41C22×D4311yescharacteristic
477C22×Q8—431no—
478C22×Q8—4312no—
479C22×D4—433no—
480C23×C4—433no—
481C23×C4—4312no—
482C23×C4—436no—
483C4⋊Q8—4312no—
484C4⋊Q8—4324no—
485C4⋊Q8—4312no—
486C4⋊Q8—436no—
487C4⋊Q8—436no—
488C4⋊Q8—4324no—
489C4⋊Q8—4312no—
490C4⋊Q8—4312no—
491C4⋊Q8—436no—
492C4⋊Q8—4312no—
493C4⋊Q8C22×D4316yes—
494C4⋊Q8C22×D43112yes—
495#125—4312no—
496#125—436no—
497#125—4324no—
498#125—4312no—
499#125—4324no—
500#125—4324no—
501#125—4312no—
502#125—4312no—
503#125—434no—
504#125—432no—
505#125—4324no—
506#125—4324no—
507#125—4312no—
508#125—4312no—
509#125—433no—
510#125—436no—
511#125—4312no—
512#125—431no—
513#125—4312no—
514#125C22×D4313yes—
515#125C22×D4316yes—
516#125C22×D43112yes—
517#125C22×D4311yescharacteristic
518#125C22×D43112yes—
519C22⋊Q8—4312no—
520C22⋊Q8—4324no—
521C22⋊Q8—4312no—
522C22⋊Q8—4324no—
523C22⋊Q8—4312no—
524C22⋊Q8—4312no—
525C22⋊Q8—4312no—
526C22⋊Q8—4324no—
527C22⋊Q8—4324no—
528C22⋊Q8—4324no—
529C22⋊Q8—4312no—
530C22⋊Q8—4312no—
531C22⋊Q8—4324no—
532C22⋊Q8—4324no—
533C22⋊Q8C22×D43112yes—
534C22⋊Q8C22×D43124yes—
535C4×Q8—432no—
536C4×Q8—434no—
537C4×Q8—4312no—
538C4×Q8—436no—
539C4×Q8—4312no—
540C4×Q8—4312no—
541C4×Q8—4312no—
542C4×Q8—4312no—
543C4×Q8—436no—
544C4×Q8—4312no—
545C4×Q8—4312no—
546C4×Q8—4312no—
547C4×Q8—4312no—
548C4×Q8C22×D4312yes—
549C4×Q8C22×D4314yes—
550C4×Q8C22×D43112yes—
551C4×D4—436no—
552C4×D4—4312no—
553C4×D4—4312no—
554C4×D4—4324no—
555C4×D4—436no—
556C4×D4—4312no—
557C4×D4—4312no—
558C4×D4—4324no—
559C4×D4—436no—
560C4×D4—4312no—
561C4×D4C22×D4316yes—
562C4×D4C22×D43112yes—
563#117—433no—
564#117—436no—
565#117—436no—
566#117—436no—
567#117—436no—
568#117—436no—
569#117—4312no—
570#117—436no—
571#117—4312no—
572#117C22×D4313yes—
573#117C22×D4316yes—
574C2×C4⋊C4—4312no—
575C2×C4⋊C4—436no—
576C2×C4⋊C4—4312no—
577C2×C4⋊C4—4312no—
578C2×C4⋊C4—4312no—
579C2×C4⋊C4—436no—
580C2×C4⋊C4—4312no—
581C2×C4⋊C4—4312no—
582C2×C4⋊C4—4312no—
583C2×C4⋊C4—4312no—
584C2×C4⋊C4—4324no—
585C2×C4⋊C4—4324no—
586C2×C4⋊C4—4324no—
587C2×C4⋊C4—432no—
588C2×C4⋊C4—436no—
589C2×C4⋊C4—434no—
590C2×C4⋊C4—4312no—
591C2×C4⋊C4C22×D4316yes—
592C2×C4⋊C4C22×D43112yes—
593C2×C22⋊C4—4312no—
594C2×C22⋊C4—436no—
595C2×C42—436no—
596C2×C42—433no—
597C2×C42—433no—
598C2×C42—4312no—
599C2×C42—436no—
600C2×C42—436no—
601C2×C42—433no—
602C2×C42—433no—
603C2×C42—431no—
604C2×C42C22×D4313yes—
605C24—433no—
606#41—438no—
607#41—4324no—
608#41—4324no—
609#41Q8×D4318yescomplemented
610C2×Q8—438no—
611C2×Q8—433no—
612C2×Q8—4312no—
613C2×Q8—4312no—
614C2×Q8—4312no—
615C2×Q8—17224no—
616C2×Q8C23×D43112yes—
617C2×Q8C23×D4311yescharacteristic
618C2×D4—436no—
619C2×D4—4324no—
620C2×D4—433no—
621C2×D4C23×D4313yes—
622C22×C4—433no—
623C22×C4—4324no—
624C22×C4—433no—
625C22×C4—431no—
626C22×C4—433no—
627C22×C4—433no—
628C22×C4—436no—
629C22×C4—4312no—
630C22×C4—432no—
631C22×C4—434no—
632C22×C4—436no—
633C22×C4—4312no—
634C22×C4—436no—
635C22×C4—436no—
636C22×C4—4324no—
637C22×C4—17212no—
638C22×C4—17224no—
639C22×C4C23×D4316yes—
640C22×C4C23×D43112yes—
641C22×C4C23×D4313yes—
642C4⋊C4—4312no—
643C4⋊C4—436no—
644C4⋊C4—4312no—
645C4⋊C4—4312no—
646C4⋊C4—4312no—
647C4⋊C4—4324no—
648C4⋊C4—4312no—
649C4⋊C4—4324no—
650C4⋊C4—4324no—
651C4⋊C4—4324no—
652C4⋊C4—434no—
653C4⋊C4—432no—
654C4⋊C4—4312no—
655C4⋊C4—436no—
656C4⋊C4—434no—
657C4⋊C4—434no—
658C4⋊C4—434no—
659C4⋊C4—4312no—
660C4⋊C4—4312no—
661C4⋊C4—4312no—
662C4⋊C4C23×D4316yes—
663C4⋊C4C23×D43112yes—
664C4⋊C4C23×D43112yes—
665C4⋊C4C23×D43124yes—
666C4⋊C4C23×D4312yes—
667C4⋊C4C23×D4316yes—
668C4⋊C4C23×D4314yes—
669C4⋊C4C23×D43112yes—
670C22⋊C4—4312no—
671C22⋊C4—436no—
672C22⋊C4—4312no—
673C22⋊C4—4312no—
674C22⋊C4—4312no—
675C22⋊C4C23×D43112yes—
676C22⋊C4C23×D4316yes—
677C42—432no—
678C42—431no—
679C42—436no—
680C42—433no—
681C42—436no—
682C42—436no—
683C42—436no—
684C42—4312no—
685C42—4312no—
686C42—4312no—
687C42C23×D4311yescharacteristic
688C42C23×D4313yes—
689C42C23×D4316yes—
690C42C23×D43112yes—
691C23—431no—
692C23—4312no—
693C23—433no—
694C23—8612no—
695C23C24×D4313yes—
696Q8—412no—
697Q8—4312no—
698Q8—17212no—
699Q8—17212no—
700Q8—17212no—
701Q8C2×Q8×D4314yes—
702D4—4324no—
703D4—4312no—
704D4C2×Q8×D43112yes—
705C2×C4—46no—
706C2×C4—412no—
707C2×C4—4312no—
708C2×C4—433no—
709C2×C4—431no—
710C2×C4—434no—
711C2×C4—4312no—
712C2×C4—4312no—
713C2×C4—4312no—
714C2×C4—432no—
715C2×C4—434no—
716C2×C4—436no—
717C2×C4—4312no—
718C2×C4—864no—
719C2×C4—8624no—
720C2×C4—8612no—
721C2×C4—868no—
722C2×C4—1726no—
723C2×C4—17224no—
724C2×C4—1726no—
725C2×C4—1726no—
726C2×C4—17212no—
727C2×C4C2×Q8×D43112yes—
728C2×C4C24×D4312yes—
729C2×C4C24×D4314yes—
730C2×C4C24×D4316yes—
731C2×C4C24×D43112yes—
732C2×C4C24×D4313yes—
733C2×C4C24×D4311yescharacteristic
734C22—26no—
735C22—432no—
736C22—434no—
737C22—436no—
738C22—8624no—
739C22—866no—
740C22C22×Q8×D4316yes—
741C22C25×D4311yescharacteristic
742C4—22no—
743C4—212no—
744C4—26no—
745C4—24no—
746C4—432no—
747C4—436no—
748C4—862no—
749C4—8612no—
750C4—866no—
751C4—864no—
752C4C22×Q8×D4312yes—
753C4C22×Q8×D4316yes—
754C2—26no—
755C2—434no—
756C2—866no—
757C2C23×Q8×D4311yescharacteristic
758C2#585×D4312yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3504C2
prime radicalC2×#41×D43C22
hypercenter#3504D43
hypocenterC43C2×#3504
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #19148421C2semidirect
2. #19148420C2semidirect
3. #19148419C2semidirect
4. #19148418C2semidirect
5. #19148417C2semidirect
6. #19148416C2semidirect
7. #19148415C2semidirect
8. #557×D43C2semidirect
9. #554×D43C2semidirect
10. #544×D43C2semidirect
11. #533×D43C2semidirect
12. C2×#125×D43C2semidirect
15. C43×#3504C2semidirect
17. #14583628C22semidirect
18. #14583627C22semidirect
19. #14583626C22semidirect
20. #14583626C22semidirect
21. #14583625C22semidirect
22. #14583625C22semidirect
23. #14583624C22semidirect
24. #14583610C22semidirect
25. #14583609C22semidirect
26. #14583608C22semidirect
27. #14583608C22semidirect
28. #14583607C22semidirect
29. #14583606C22semidirect
30. #14583605C22semidirect
31. #14583605C22semidirect
32. #14583604C22semidirect
33. #14583603C22semidirect
34. #14583603C22semidirect
35. #14583530C22semidirect
36. #14583529C22semidirect
37. #14583529C22semidirect
38. #14583528C22semidirect
39. #14583527C22semidirect
40. #14583527C22semidirect
41. #14583526C22semidirect
42. #14583526C22semidirect
43. #14583456C22semidirect
44. #14583455C22semidirect
45. #14583455C22semidirect
46. #14583454C22semidirect
47. #14583453C22semidirect
48. #14583452C22semidirect
49. #14583451C22semidirect
52. C2×#13063317C22semidirect
53. C2×#13063316C22semidirect
54. C2×#13063315C22semidirect
60. #125×D43C22semidirect
61. #125×D43C22semidirect
62. #125×D43C22semidirect
85. C43×#557C22semidirect
86. C43×#554C22semidirect
87. C43×#544C22semidirect
88. C43×#533C22semidirect
89. C2×#125×C43C22semidirect
95. #41×D43Q8semidirect
226. #41×C43C2×Q8semidirect
237. #10621902C2×Q8semidirect
240. #10621900C2×Q8semidirect
242. #10621898C2×Q8semidirect
382. #3504D43direct (N × H)
394. D43#3504direct (N × H)
403. #557C2×D43semidirect
415. #554C2×D43semidirect
424. #544C2×D43semidirect
432. #533C2×D43semidirect
446. C2×#125C2×D43semidirect
471. C43C2×#3504semidirect
609. #41Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#191484212
#191484202
#191484192
#191484182
#191484172
#191484162
#191484152
#557×D432
#554×D432
#544×D432
#533×D432
C2×#125×D432
#520×D432
C4×#41×D432
C43×#35042
C2×#350443