Finite Group Databasebeta

← #25064753

Subgroups — #25064753

Order 11008.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148573C211yesmaximal, characteristic
2#19143609C211yesmaximal, characteristic, complemented
3#19133232C211yesmaximal, characteristic, complemented
4#19133227C211yesmaximal, characteristic, complemented
5#19133224C211yesmaximal, characteristic, complemented
6#19133221C211yesmaximal, characteristic, complemented
7#19133216C211yesmaximal, characteristic, complemented
8#19133213C211yesmaximal, characteristic, complemented
9#19133211C211yesmaximal, characteristic, complemented
10#19133203C211yesmaximal, characteristic, complemented
11#19133198C211yesmaximal, characteristic, complemented
12#19133196C211yesmaximal, characteristic, complemented
13#19133184C211yesmaximal, characteristic, complemented
14C2×#14582640C211yesmaximal, characteristic, complemented
15C43×#2923C211yesmaximal, characteristic, complemented
16#14583627C411yescharacteristic
17#14583609C411yescharacteristic
18#14583606C411yescharacteristic
19#14583595C411yescharacteristic
20#14583595C411yescharacteristic
21#14583589C411yescharacteristic
22#14583589C411yescharacteristic
23#14583588—21no—
24#14583582—21no—
25#14583582—21no—
26#14583553C411yescharacteristic
27#14583548—21no—
28#14583507—21no—
29#14583491—21no—
30#14583491—21no—
31#14583456C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583433C2211yescharacteristic
34#14583433C2211yescharacteristic
35C2×#13063317C2211yescharacteristic
36C2×#13063317C2211yescharacteristic
37#14583378—21no—
38#14583030—21no—
39#14582971—21no—
40#14582971—21no—
41D4×C43⋊C8—21no—
42#14582956C2211yescharacteristic
43#14582956C2211yescharacteristic
44#14582956C2211yescharacteristic
45C4×#10621877C2211yescharacteristic
46C2×#13063236C2211yescharacteristic
47C2×#13063236C2211yescharacteristic
48#14582640C2211yescharacteristic
49#14582640C2211yescharacteristic
50#14582640C2211yescharacteristic
51#14582640C2211yescharacteristic
52#14582640C2211yescharacteristic
53#14582640C2211yescharacteristic
54#14582640C2211yescharacteristic
55#14582640C2211yescharacteristic
56#14582640C2211yescharacteristic
57#14582640C2211yescharacteristic
58#14582640C2211yescharacteristic
59#14582640C2211yescharacteristic
60#14582638C2211yescharacteristic
61#14582638C2211yescharacteristic
62#14582638C2211yescharacteristic
63#14582638C2211yescharacteristic
64C4×#41×C43C2211yescharacteristic
65C43×#433—21no—
66C43×#433—21no—
67C43×#432C2211yescharacteristic
68C43×#432C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#432C2211yescharacteristic
71C43×#424—21no—
72C43×#408—21no—
73C4×M16×C43C2211yescharacteristic
74C2×#97×C43C2211yescharacteristic
75C2×#10621900—21no—
76C2×#10621877—21no—
77C22×C43⋊C8—21no—
78C22×C43⋊C8—21no—
79#13063325C2×C411yescharacteristic
80#13063325C2×C411yescharacteristic
81#13063323—21no—
82#13063320—21no—
83#13063320—21no—
84#13063319—21no—
85#13063319—21no—
86#13063319—21no—
87#13063318—21no—
88#13063318—21no—
89#13063317—21no—
90#13063317—21no—
91#13063317—21no—
92#13063317—21no—
93#13063317C2×C411yescharacteristic
94#13063317C2×C411yescharacteristic
95#13063317C2×C411yescharacteristic
96#13063317C2×C411yescharacteristic
97#13063317C2311yescharacteristic
98#13063317C2311yescharacteristic
99#13063317C2311yescharacteristic
100#13063316—21no—
101#13063315—21no—
102#13063315—21no—
103#13063315—21no—
104#13063315—21no—
105#13063313C2311yescharacteristic
106#13063309—21no—
107#13063309—21no—
108#13063308—21no—
109#13063308—21no—
110#13063308—21no—
111#13063307—21no—
112#13063307—21no—
113#13063306—21no—
114#13063306—21no—
115#13063305—21no—
116#13063304—21no—
117#13063304—21no—
118#13063304C2×C411yescharacteristic
119#13063304C2×C411yescharacteristic
120#13063304C2×C411yescharacteristic
121#13063303—21no—
122#13063303—21no—
123#13063302—21no—
124#13063302—21no—
125#13063301—21no—
126#13063299C2×C411yescharacteristic
127#13063299C2×C411yescharacteristic
128#13063299C2×C411yescharacteristic
129#13063297—21no—
130#13063297—21no—
131C4×Dic86—21no—
132C4×Dic86—21no—
133C4×Dic86C2×C411yescharacteristic
134C4×Dic86C2×C411yescharacteristic
135C4×Dic86C2×C411yescharacteristic
136#13063290—21no—
137C4×D172C2×C411yescharacteristic
138C4×D172C2×C411yescharacteristic
139C4×D172C2×C411yescharacteristic
140D4×Dic43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144(C22⋊D43)⋊C4—21no—
145(C22⋊D43)⋊C4—21no—
146#13063284C2×C411yescharacteristic
147#13063284C2×C411yescharacteristic
148#13063282—21no—
149#13063282—21no—
150#13063282—21no—
151#13063281—21no—
152#13063281—21no—
153C2×C4⋊Dic43C2×C411yescharacteristic
154C2×C4⋊Dic43C2×C411yescharacteristic
155C2×C4⋊Dic43C2×C411yescharacteristic
156C2×C4⋊Dic43C2×C411yescharacteristic
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C4⋊C4×D43—21no—
162C4⋊(C43⋊C8)—21no—
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165C22⋊(C43⋊C8)—21no—
166C22⋊(C43⋊C8)—21no—
167C22⋊(C43⋊C8)—21no—
168#13063236—21no—
169#13063236—21no—
170#13063236C2311yescharacteristic
171#13063236C2311yescharacteristic
172#13063236C2311yescharacteristic
173#13063236C2311yescharacteristic
174C4×C43⋊C8—21no—
175C2×#41×C43D411yescharacteristic
176C2×M16×C43—21no—
177C22×C8×C43—21no—
178C4×Q8×C43C2×C411yescharacteristic
179C4×Q8×C43D411yescharacteristic
180C4×D4×C43C2×C411yescharacteristic
181C4×D4×C43C2×C411yescharacteristic
182C4×D4×C43C2×C411yescharacteristic
183C4×D4×C43D411yescharacteristic
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186#117×C43D411yescharacteristic
187#117×C43D411yescharacteristic
188#117×C43D411yescharacteristic
189C2×C42×C43C2311yescharacteristic
190C2×C42×C43C2311yescharacteristic
191C2×C42×C43C2311yescharacteristic
192C4⋊C8×C43—21no—
193C4⋊C8×C43—21no—
194C4⋊C8×C43—21no—
195C4⋊C8×C43—21no—
196C22⋊C8×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43—21no—
199C22⋊C8×C43—21no—
200#97×C43—21no—
201#97×C43C2311yescharacteristic
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205C4×C8×C43—21no—
206#41×C43—42no—
207C2×Q8×C43C22⋊C411yescharacteristic
208C2×D4×C43C22⋊C411yescharacteristic
209C2×D4×C43C22⋊C411yescharacteristic
210C2×D4×C43C22⋊C411yescharacteristic
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227#10621900—44no—
228C2×D172C22×C411yescharacteristic
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86C22×C411yescharacteristic
235M16×C43—42no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—42no—
241C4⋊C4×C43C22⋊C411yescharacteristic
242C4⋊C4×C43C22⋊C411yescharacteristic
243C4⋊C4×C43C22⋊C411yescharacteristic
244C4⋊C4×C43C22⋊C411yescharacteristic
245C4⋊C4×C43C22⋊C411yescharacteristic
246C4⋊C4×C43C22⋊C411yescharacteristic
247C22⋊C4×C43C22⋊C411yescharacteristic
248C22⋊C4×C43C22⋊C411yescharacteristic
249C22⋊C4×C43C22⋊C411yescharacteristic
250C22⋊C4×C43C22⋊C411yescharacteristic
251C22⋊C4×C43C22⋊C411yescharacteristic
252C22⋊C4×C43C22⋊C411yescharacteristic
253C42×C43C22×C411yescharacteristic
254C42×C43C22×C411yescharacteristic
255C42×C43C22×C411yescharacteristic
256C42×C43C2×D411yescharacteristic
257C42×C43C2×D411yescharacteristic
258C42×C43C2×D411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C42×C43C2×D411yescharacteristic
262C42×C43C2411yescharacteristic
263C22⋊Dic43—21no—
264C22⋊Dic43—21no—
265C22⋊Dic43—21no—
266C22⋊Dic43—21no—
267C22⋊Dic43—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4—21no—
275(C2×D43)⋊C4—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43C22×C411yescharacteristic
283C4⋊Dic43C22×C411yescharacteristic
284C4⋊Dic43C22×C411yescharacteristic
285C4⋊Dic43C22×C411yescharacteristic
286C4⋊Dic43C22×C411yescharacteristic
287C4⋊Dic43C22×C411yescharacteristic
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290Dic43⋊C4—21no—
291Dic43⋊C4—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308C4×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313#10621877—42no—
314C2×C43⋊C8—21no—
315C2×C43⋊C8—21no—
316C2×C43⋊C8—21no—
317C2×C43⋊C8—21no—
318C2×C43⋊C8—42no—
319C2×C43⋊C8—42no—
320C23×C43C2×C22⋊C411yescharacteristic
321C23×C43C2×C22⋊C411yescharacteristic
322C23×C43C2×C22⋊C411yescharacteristic
323C22×D43—21no—
324Q8×C43—41no—
325D4×C43—22no—
326D4×C43—22no—
327D4×C43—41no—
328C2×C4×C43—22no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43C2×C22⋊C411yescharacteristic
338C2×C4×C43C2×C22⋊C411yescharacteristic
339C2×C4×C43C2×C22⋊C411yescharacteristic
340C2×C4×C43C2×C22⋊C411yescharacteristic
341C2×C4×C43C2×C22⋊C411yescharacteristic
342C2×C4×C43C2×C22⋊C411yescharacteristic
343C2×C4×C43C2×C22⋊C411yescharacteristic
344C2×C4×C43C2×C22⋊C411yescharacteristic
345C2×C4×C43C2×C22⋊C411yescharacteristic
346C2×C4×C43C23×C411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C22⋊D43—42no—
350C22⋊D43—42no—
351C22⋊D43—81no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—21no—
359C2×Dic43—42no—
360C2×Dic43—42no—
361C2×Dic43—81no—
362C2×Dic43—81no—
363D172—41no—
364C4×D43—42no—
365C4×D43—81no—
366C4×D43—81no—
367Dic86—42no—
368Dic86—41no—
369Dic86—81no—
370C8×C43—41no—
371C8×C43—41no—
372C8×C43—41no—
373C8×C43—41no—
374C43⋊C8—22no—
375C43⋊C8—41no—
376C43⋊C8—41no—
377C43⋊C8—41no—
378#17680—431nomaximal, Sylow
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—21no—
385C22×C43—21no—
386C22×C43—21no—
387C22×C43#42112yes—
388C22×C43C22×C22⋊C411yescharacteristic
389C2×D43—41no—
390C2×D43—41no—
391C2×D43—41no—
392C4×C43—21no—
393C4×C43—21no—
394C4×C43—21no—
395C4×C43—21no—
396C4×C43—21no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—21no—
404Dic43—41no—
405Dic43—41no—
406Dic43—41no—
407Dic43—41no—
408Dic43—41no—
409Dic43—41no—
410Dic43—41no—
411#3515—431no—
412#2970—431no—
413#2923D4311yescharacteristic, complemented
414#1537—431no—
415#1535—431no—
416#1535—431no—
417#1534—431no—
418#1532—431no—
419#1532—431no—
420#1531—431no—
421#1529—431no—
422#1528—431no—
423#1528—431no—
424#1524—431no—
425C2×#330—431no—
426C2×C43—22no—
427C2×C43—41no—
428C2×C43—41no—
429C2×C43#288911yescharacteristic
430C2×C43C2×#42111yescharacteristic
431C2×C43#290111yescharacteristic
432D43—81no—
433#557—431no—
434#554—431no—
435#554—431no—
436#553—431no—
437#553—431no—
438#552—431no—
439#552—431no—
440#552—861no—
441#552—861no—
442#552—861no—
443#547—431no—
444#547—861no—
445#541—861no—
446#539—861no—
447#539—861no—
448#533—431no—
449#529—431no—
450#529—431no—
451#529—431no—
452C2×#125—431no—
453C2×#125—431no—
454#520—861no—
455C4×#41C2×D4311yescharacteristic
456#446—861no—
457#435—861no—
458#435—861no—
459C8×D4—861no—
460#433—21no—
461#433—21no—
462#432—431no—
463#432—431no—
464#432—431no—
465#432C2×D4311yescharacteristic
466#432C2×D4311yescharacteristic
467#432C2×D4311yescharacteristic
468#432C2×D4311yescharacteristic
469#424—21no—
470#408—21no—
471C4×M16—431no—
472C4×M16C2×D4311yescharacteristic
473C2×#97—431no—
474C2×#97—431no—
475C2×#97C2×D4311yescharacteristic
476#330—431no—
477#330—431no—
478#330—431no—
479#330—431no—
480#330—431no—
481#330—431no—
482#330—431no—
483#330—431no—
484#330—431no—
485#330—431no—
486#330—431no—
487#330—431no—
488#329—431no—
489#329—431no—
490#329—431no—
491#329—431no—
492C43#1768011yescharacteristic, complemented, Sylow
493C2×#41—861no—
494C2×#41C22⋊D4311yescharacteristic
495C2×M16—21no—
496C2×M16—861no—
497C22×C8—21no—
498C22×C8—861no—
499C22×C8—861no—
500C4⋊Q8—431no—
501C4⋊Q8—431no—
502C4⋊Q8—861no—
503#126—861no—
504#126—861no—
505#126—861no—
506#126—861no—
507#126—861no—
508#126—861no—
509#126—861no—
510#125—431no—
511#125—431no—
512#125—431no—
513#125—431no—
514#125—431no—
515#125—431no—
516#125—431no—
517#125—861no—
518#125—861no—
519#125—861no—
520#125—861no—
521#125—861no—
522#125—861no—
523#125—861no—
524#125—861no—
525#125—861no—
526#124—431no—
527#123—861no—
528#123—861no—
529#123—861no—
530#123—861no—
531#123—861no—
532#123—861no—
533#123—861no—
534#123—861no—
535#123—861no—
536C22⋊Q8—431no—
537C22⋊Q8—431no—
538C22⋊Q8—431no—
539C22⋊Q8—861no—
540C22⋊Q8—861no—
541C22⋊Q8—861no—
542C22⋊Q8—861no—
543C22⋊Q8—861no—
544C22⋊Q8—861no—
545C22⋊Q8—861no—
546C22⋊Q8—861no—
547#121—431no—
548#121—431no—
549#121—431no—
550#121—861no—
551#121—861no—
552C4×Q8—431no—
553C4×Q8—431no—
554C4×Q8—431no—
555C4×Q8—861no—
556C4×Q8—861no—
557C4×Q8—861no—
558C4×Q8C4×D4311yescharacteristic
559C4×Q8D17211yescharacteristic
560C4×D4—431no—
561C4×D4—431no—
562C4×D4—431no—
563C4×D4—861no—
564C4×D4—861no—
565C4×D4—861no—
566C4×D4—861no—
567C4×D4—861no—
568C4×D4—861no—
569C4×D4C4×D4311yescharacteristic
570C4×D4C4×D4311yescharacteristic
571C4×D4C4×D4311yescharacteristic
572C4×D4D17211yescharacteristic
573C4×D4D17211yescharacteristic
574C4×D4D17211yescharacteristic
575#117—431no—
576#117—431no—
577#117—861no—
578#117—861no—
579#117—861no—
580#117—861no—
581#117—861no—
582#117C22⋊D4311yescharacteristic
583#117C22⋊D4311yescharacteristic
584#117C22⋊D4311yescharacteristic
585C2×C4⋊C4—431no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4—861no—
594C2×C42C22×D4311yescharacteristic
595C2×C42C22×D4311yescharacteristic
596C2×C42C22×D4311yescharacteristic
597C4⋊C8—21no—
598C4⋊C8—21no—
599C4⋊C8—21no—
600C4⋊C8—21no—
601C4⋊C8—861no—
602C4⋊C8—861no—
603C4⋊C8—861no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8—21no—
608C22⋊C8—861no—
609C22⋊C8—861no—
610C22⋊C8—861no—
611#97—21no—
612#97—431no—
613#97—431no—
614#97—431no—
615#97—431no—
616#97—861no—
617#97—861no—
618#97C22×D4311yescharacteristic
619#97C22×D4311yescharacteristic
620#97C22×D4311yescharacteristic
621#97C22×D4311yescharacteristic
622C4×C8—21no—
623C4×C8—861no—
624#41—42no—
625#41—1724no—
626C2×Q8—431no—
627C2×Q8—861no—
628C2×Q8—861no—
629C2×Q8(C2×D43)⋊C411yescharacteristic
630C2×D4—431no—
631C2×D4—861no—
632C2×D4—861no—
633C2×D4—861no—
634C2×D4(C2×D43)⋊C411yescharacteristic
635C2×D4(C2×D43)⋊C411yescharacteristic
636C2×D4(C2×D43)⋊C411yescharacteristic
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4C2×C4×D4311yescharacteristic
645C22×C4C2×C4×D4311yescharacteristic
646C22×C4C2×C4×D4311yescharacteristic
647C22×C4C2×D17211yescharacteristic
648C22×C4C2×D17211yescharacteristic
649C22×C4C2×D17211yescharacteristic
650C22×C4C2×C22⋊D4311yescharacteristic
651C22×C4C2×C22⋊D4311yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653M16—42no—
654M16—1722no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—42no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—1722no—
665C2×C8—1722no—
666C4⋊C4—431no—
667C4⋊C4—431no—
668C4⋊C4—431no—
669C4⋊C4—431no—
670C4⋊C4—431no—
671C4⋊C4—431no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4(C2×D43)⋊C411yescharacteristic
699C4⋊C4(C2×D43)⋊C411yescharacteristic
700C4⋊C4(C2×D43)⋊C411yescharacteristic
701C4⋊C4(C2×D43)⋊C411yescharacteristic
702C4⋊C4(C2×D43)⋊C411yescharacteristic
703C4⋊C4(C2×D43)⋊C411yescharacteristic
704C22⋊C4—861no—
705C22⋊C4—861no—
706C22⋊C4—861no—
707C22⋊C4—861no—
708C22⋊C4—861no—
709C22⋊C4—861no—
710C22⋊C4—861no—
711C22⋊C4—861no—
712C22⋊C4—861no—
713C22⋊C4—861no—
714C22⋊C4—861no—
715C22⋊C4—861no—
716C22⋊C4—861no—
717C22⋊C4(C2×D43)⋊C411yescharacteristic
718C22⋊C4(C2×D43)⋊C411yescharacteristic
719C22⋊C4(C2×D43)⋊C411yescharacteristic
720C22⋊C4(C2×D43)⋊C411yescharacteristic
721C22⋊C4(C2×D43)⋊C411yescharacteristic
722C22⋊C4(C2×D43)⋊C411yescharacteristic
723C42—861no—
724C42—861no—
725C42—861no—
726C42—861no—
727C42—861no—
728C42C2×C4×D4311yescharacteristic
729C42C2×C4×D4311yescharacteristic
730C42C2×C4×D4311yescharacteristic
731C42C2×D17211yescharacteristic
732C42C2×D17211yescharacteristic
733C42C2×D17211yescharacteristic
734C42C2×C22⋊D4311yescharacteristic
735C42C2×C22⋊D4311yescharacteristic
736C42C2×C22⋊D4311yescharacteristic
737C42C23×D4311yescharacteristic
738C23—861no—
739C23C2×(C2×D43)⋊C411yescharacteristic
740C23C2×(C2×D43)⋊C411yescharacteristic
741C23C2×(C2×D43)⋊C411yescharacteristic
742Q8—41no—
743Q8—3441no—
744Q8—1721no—
745Q8—1722no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—3441no—
750D4—1721no—
751D4—1722no—
752D4—1722no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—861no—
766C2×C4—861no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—3441no—
770C2×C4—3441no—
771C2×C4—3441no—
772C2×C4—3441no—
773C2×C4—1722no—
774C2×C4—1722no—
775C2×C4—1722no—
776C2×C4C2×(C2×D43)⋊C411yescharacteristic
777C2×C4C2×(C2×D43)⋊C411yescharacteristic
778C2×C4C2×(C2×D43)⋊C411yescharacteristic
779C2×C4C2×(C2×D43)⋊C411yescharacteristic
780C2×C4C2×(C2×D43)⋊C411yescharacteristic
781C2×C4C2×(C2×D43)⋊C411yescharacteristic
782C2×C4C2×(C2×D43)⋊C411yescharacteristic
783C2×C4C2×(C2×D43)⋊C411yescharacteristic
784C2×C4C2×(C2×D43)⋊C411yescharacteristic
785C2×C4C22×C4×D4311yescharacteristic
786C2×C4C22×C22⋊D4311yescharacteristic
787C2×C4C22×D17211yescharacteristic
788C8—41no—
789C8—41no—
790C8—41no—
791C8—41no—
792C8—862no—
793C8—1721no—
794C8—1721no—
795C8—1721no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—1721no—
805C22—1721no—
806C22—1721no—
807C22#1458291712yes—
808C22C22×(C2×D43)⋊C411yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—1721no—
822C4—1721no—
823C4—1721no—
824C4—1721no—
825C4—1721no—
826C4—1721no—
827C4—1721no—
828C2—22no—
829C2—41no—
830C2—41no—
831C2—3441no—
832C2#1914307711yescharacteristic
833C2C2×#1458291711yescharacteristic
834C2#1914314011yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2923C2
socleC22×C43C22×C22⋊C4
prime radical#19148573C2
cosocleC42×C43C24
hypercenter#2923D43
hypocenterC43#17680
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #19143609C2semidirect
3. #19133232C2semidirect
4. #19133227C2semidirect
5. #19133224C2semidirect
6. #19133221C2semidirect
7. #19133216C2semidirect
8. #19133213C2semidirect
9. #19133211C2semidirect
10. #19133203C2semidirect
11. #19133198C2semidirect
12. #19133196C2semidirect
13. #19133184C2semidirect
14. C2×#14582640C2semidirect
15. C43×#2923C2semidirect
413. #2923D43semidirect
492. C43#17680semidirect

Maximal subgroups

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

subgroupindex
#191485732
#191436092
#191332322
#191332272
#191332242
#191332212
#191332162
#191332132
#191332112
#191332032
#191331982
#191331962
#191331842
C2×#145826402
C43×#29232
#1768043