Finite Group Databasebeta

← #25064405

Subgroups — #25064405

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148430C211yesmaximal, characteristic
2#19143623C211yesmaximal, characteristic, complemented
3#19137566C211yesmaximal, characteristic, complemented
4#19133150C211yesmaximal, characteristic, complemented
5#19133148C211yesmaximal, characteristic, complemented
6#19133134C211yesmaximal, characteristic, complemented
7#19133133C211yesmaximal, characteristic, complemented
8#19133126C211yesmaximal, characteristic, complemented
9#19133122C211yesmaximal, characteristic, complemented
10#19133118C211yesmaximal, characteristic, complemented
11#19133113C211yesmaximal, characteristic, complemented
12#19133109C211yesmaximal, characteristic, complemented
13#19133085C211yesmaximal, characteristic, complemented
14#19133083C211yesmaximal, characteristic, complemented
15C43×#1509C211yesmaximal, characteristic, complemented
16#14583602C411yescharacteristic, complemented
17#14583600—21no—
18#14583599C411yescharacteristic, complemented
19#14583593—21no—
20#14583590C411yescharacteristic, complemented
21#14583587C411yescharacteristic, complemented
22#14583574—21no—
23#14583573—21no—
24#14583561C411yescharacteristic, complemented
25#14583557C411yescharacteristic, complemented
26#14583544C411yescharacteristic, complemented
27#14583542C411yescharacteristic, complemented
28#14583493—21no—
29#14583482—21no—
30#14583460—21no—
31#14583433C2211yescharacteristic
32#14583412C2211yescharacteristic
33#14583409C2211yescharacteristic
34C22⋊Q8×D43C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583371—21no—
37C2×C4×D172C2211yescharacteristic
38#14582972—21no—
39#14582972—21no—
40#14582969—21no—
41#14582969—21no—
42#14582956C2211yescharacteristic, complemented
43#14582861C2211yescharacteristic
44#14582861C2211yescharacteristic
45C22⋊C8×D43C2211yescharacteristic, complemented
46C22⋊C8×D43C2211yescharacteristic, complemented
47#14582801—21no—
48#14582789—21no—
49#14582789—21no—
50#14582765C2211yescharacteristic, complemented
51#14582761C2211yescharacteristic
52#14582761C2211yescharacteristic, complemented
53C4×C4⋊Dic43—21no—
54#14582746C2211yescharacteristic
55#14582746C2211yescharacteristic, complemented
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582636C2211yescharacteristic, complemented
59#14582636C2211yescharacteristic, complemented
60#14582635C2211yescharacteristic, complemented
61#14582635C2211yescharacteristic, complemented
62#14582634C2211yescharacteristic
63#14582634C2211yescharacteristic
64#14582633C2211yescharacteristic
65#14582633C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C4×C4⋊C4×C43C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621900C2×C411yescharacteristic
77C2×Q8×D43C2×C411yescharacteristic
78C22×D172D411yescharacteristic
79C2×D4×D43—21no—
80C2×D4×D43C2×C411yescharacteristic
81C22×C4×D43C2311yescharacteristic
82C22×C4×D43C2311yescharacteristic
83C2×#10621872—21no—
84C2×#10621872—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87#13063320—21no—
88#13063320—21no—
89#13063319—21no—
90#13063319—21no—
91#13063318—21no—
92#13063317C2×C411yescharacteristic
93#13063316—21no—
94#13063315—21no—
95#13063313—21no—
96#13063313C2×C411yescharacteristic
97#13063311—21no—
98#13063310—21no—
99#13063310—21no—
100#13063310—21no—
101#13063310—21no—
102#13063309—21no—
103#13063308—21no—
104#13063308—21no—
105#13063307—21no—
106#13063307—21no—
107#13063305—21no—
108#13063305C2×C411yescharacteristic
109#13063305C2×C411yescharacteristic
110#13063304C2311yescharacteristic
111#13063303—21no—
112#13063302—21no—
113#13063302—21no—
114#13063301C2×C411yescharacteristic
115#13063301C2×C411yescharacteristic
116#13063300—21no—
117#13063300—21no—
118#13063300C2×C411yescharacteristic
119#13063300C2×C411yescharacteristic
120#13063299—21no—
121#13063299C2311yescharacteristic
122#13063298—21no—
123#13063298—21no—
124#13063298—21no—
125#13063298—21no—
126#13063297—21no—
127#13063296C2×C411yescharacteristic
128#13063296C2×C411yescharacteristic
129#13063295—21no—
130#13063295—21no—
131#13063295—21no—
132#13063293—21no—
133C4×Dic86C2×C411yescharacteristic
134C4×D172—21no—
135C4×D172C2×C411yescharacteristic
136C4×D172C2×C411yescharacteristic
137C4×D172C2×C411yescharacteristic
138C4×D172C2×C411yescharacteristic
139C4×D172C2×C411yescharacteristic
140C4×D172D411yescharacteristic
141C4×D172D411yescharacteristic
142C4×D172D411yescharacteristic
143C4×D172D411yescharacteristic
144D4×Dic43—21no—
145#13063287—21no—
146#13063287—21no—
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152#13063283—21no—
153#13063283C2×C411yescharacteristic
154#13063283C2×C411yescharacteristic
155#13063282—21no—
156#13063282—21no—
157C2×C4⋊Dic43—21no—
158C2×C4⋊Dic43D411yescharacteristic
159C4⋊C4×D43—21no—
160C4⋊C4×D43C2×C411yescharacteristic
161C4⋊C4×D43C2×C411yescharacteristic
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C2×(C2×D43)⋊C4D411yescharacteristic
169C22⋊C4×D43—21no—
170C22⋊C4×D43—21no—
171C22⋊C4×D43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43—21no—
174C4⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063236—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187#126×C43—21no—
188#125×C43C2×C411yescharacteristic
189#124×C43C2×C411yescharacteristic
190#123×C43—21no—
191C22⋊Q8×C43C2311yescharacteristic
192#121×C43C2311yescharacteristic
193C4×Q8×C43C2×C411yescharacteristic
194C4×D4×C43—21no—
195C4×D4×C43C2×C411yescharacteristic
196#117×C43—21no—
197C2×C4⋊C4×C43—21no—
198C2×C42×C43—21no—
199C2×C42×C43C2311yescharacteristic
200C4⋊C8×C43—21no—
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203#97×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C23×D43—21no—
207C23×D43C2×D411yescharacteristic
208C23×D43C2×D411yescharacteristic
209C2×Q8×C43C22×C411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43C22×C411yescharacteristic
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2411yescharacteristic
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228#10621902—81no—
229Q8×D43—81no—
230#10621900—81no—
231D4×D43—42no—
232D4×D43—42no—
233D4×D43—81no—
234C2×D172—21no—
235C2×D172—21no—
236C2×D172—21no—
237C2×D172—41no—
238C2×D172—41no—
239C2×D172C22⋊C411yescharacteristic
240C2×D172C22⋊C411yescharacteristic
241C2×D172C22⋊C411yescharacteristic
242C2×D172C22⋊C411yescharacteristic
243C2×D172C22×C411yescharacteristic
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—81no—
250C2×C4×D43—81no—
251C2×C4×D43C22×C411yescharacteristic
252C2×C4×D43C22×C411yescharacteristic
253C2×C4×D43C22×C411yescharacteristic
254C2×C4×D43C22×C411yescharacteristic
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×C4×D43C2×D411yescharacteristic
259C2×Dic86—21no—
260C2×Dic86C22×C411yescharacteristic
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—42no—
268C4⋊C4×C43C22×C411yescharacteristic
269C4⋊C4×C43C22×C411yescharacteristic
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C42×C43—21no—
276C42×C43—42no—
277C42×C43C22×C411yescharacteristic
278C42×C43C22×C411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—42no—
297(C2×D43)⋊C4—42no—
298(C2×D43)⋊C4—81no—
299(C2×D43)⋊C4—81no—
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301(C2×D43)⋊C4C22⋊C411yescharacteristic
302(C2×D43)⋊C4C22⋊C411yescharacteristic
303(C2×D43)⋊C4C22⋊C411yescharacteristic
304(C2×D43)⋊C4C22⋊C411yescharacteristic
305(C2×D43)⋊C4C22⋊C411yescharacteristic
306(C2×D43)⋊C4C22⋊C411yescharacteristic
307(C2×D43)⋊C4C22⋊C411yescharacteristic
308C4⋊Dic43—21no—
309C4⋊Dic43—21no—
310C4⋊Dic43—42no—
311C4⋊Dic43C22⋊C411yescharacteristic
312C4⋊Dic43C22⋊C411yescharacteristic
313C4⋊Dic43C22⋊C411yescharacteristic
314C4⋊Dic43C22⋊C411yescharacteristic
315C4⋊Dic43C22×C411yescharacteristic
316C4⋊Dic43C22×C411yescharacteristic
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325C4×Dic43—21no—
326C4×Dic43—21no—
327C4×Dic43—21no—
328C4×Dic43—81no—
329C4×Dic43—81no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—21no—
332#10621872—81no—
333#10621872—81no—
334C8×D43—81no—
335C8×D43—81no—
336C23×C43—21no—
337C23×C43C22×D411yescharacteristic
338C22×D43—21no—
339C22×D43—21no—
340C22×D43—21no—
341C22×D43—21no—
342C22×D43—21no—
343C22×D43—41no—
344C22×D43—41no—
345C22×D43—41no—
346C22×D43—41no—
347C22×D43—42no—
348C22×D43—81no—
349C22×D43—81no—
350C22×D43C2×C22⋊C411yescharacteristic
351C22×D43C2×C22⋊C411yescharacteristic
352C22×D43C2×C22⋊C411yescharacteristic
353C22×D43C2×C22⋊C411yescharacteristic
354Q8×C43—41no—
355D4×C43—41no—
356D4×C43—41no—
357D4×C43—41no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—22no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—81no—
372C2×C4×C43C2×C22⋊C411yescharacteristic
373C2×C4×C43C2×C22⋊C411yescharacteristic
374C2×C4×C43C2×C22⋊C411yescharacteristic
375C2×C4×C43C2×C22⋊C411yescharacteristic
376C2×C4×C43C23×C411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C22⋊D43—42no—
379C22⋊D43—41no—
380C22⋊D43—41no—
381C22⋊D43—81no—
382C22⋊D43—81no—
383C22⋊D43—81no—
384C2×Dic43—21no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—81no—
396C2×Dic43C2×C22⋊C411yescharacteristic
397C2×Dic43C2×C22⋊C411yescharacteristic
398C2×Dic43C2×C22⋊C411yescharacteristic
399C2×Dic43C2×C22⋊C411yescharacteristic
400D172—41no—
401D172—41no—
402D172—41no—
403D172—41no—
404D172—41no—
405D172—42no—
406D172—81no—
407D172—81no—
408C4×D43—41no—
409C4×D43—41no—
410C4×D43—41no—
411C4×D43—41no—
412C4×D43—41no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—42no—
417C4×D43—81no—
418C4×D43—81no—
419C4×D43—81no—
420C4×D43—81no—
421Dic86—41no—
422Dic86—81no—
423C8×C43—41no—
424C8×C43—41no—
425C43⋊C8—41no—
426C43⋊C8—41no—
427#17625—431nomaximal, Sylow
428C22×C43—21no—
429C22×C43—21no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43C22×C22⋊C411yescharacteristic
434C22×C43#57511yescharacteristic
435C22×C43#57511yescharacteristic
436C2×D43—21no—
437C2×D43—21no—
438C2×D43—21no—
439C2×D43—21no—
440C2×D43—21no—
441C2×D43—21no—
442C2×D43—21no—
443C2×D43—21no—
444C2×D43—21no—
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—41no—
449C2×D43—41no—
450C2×D43—41no—
451C2×D43—81no—
452C2×D43—81no—
453C2×D43—81no—
454C2×D43—81no—
455C2×D43—162no—
456C4×C43—21no—
457C4×C43—21no—
458C4×C43—21no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—21no—
462C4×C43—42no—
463C4×C43—41no—
464C4×C43—41no—
465C4×C43—41no—
466C4×C43—81no—
467Dic43—21no—
468Dic43—21no—
469Dic43—21no—
470Dic43—21no—
471Dic43—41no—
472Dic43—41no—
473Dic43—41no—
474Dic43—81no—
475Dic43—81no—
476#3505—431no—
477#2973—431no—
478#2357—431no—
479#1516—431no—
480#1516—431no—
481#1512—431no—
482#1512—431no—
483#1511—431no—
484#1510—431no—
485#1509—431no—
486#1509D4311yescharacteristic, complemented
487#1508—431no—
488#1507—431no—
489#1501—431no—
490#1501—431no—
491C2×C43—21no—
492C2×C43—21no—
493C2×C43—81no—
494C2×C43#288311yescharacteristic
495C2×C43#289611yescharacteristic
496C2×C43#290111yescharacteristic
497D43—41no—
498D43—41no—
499D43—41no—
500D43—41no—
501D43—81no—
502#553—431no—
503#553—431no—
504#553—861no—
505#553—861no—
506#552—431no—
507#552—431no—
508#551—861no—
509#551—861no—
510#548—431no—
511#548—431no—
512#546—431no—
513#546—431no—
514#539—861no—
515#538—861no—
516#534—861no—
517#529—431no—
518#529C2×D4311yescharacteristic
519#525—431no—
520#525—431no—
521C2×C22⋊Q8—431no—
522C2×#121—431no—
523#518—861no—
524C2×C4×D4—431no—
525#435—861no—
526#435—861no—
527#435—861no—
528#435—861no—
529#432—431no—
530#432C2×D4311yescharacteristic, complemented
531#407—431no—
532#407—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8—431no—
535#390—861no—
536#388—861no—
537#388—861no—
538#382—431no—
539#381—431no—
540#381—431no—
541C4×C4⋊C4—861no—
542C4×C4⋊C4C2×D4311yescharacteristic, complemented
543C4×C22⋊C4—431no—
544C4×C22⋊C4—431no—
545#328—431no—
546#328—431no—
547#328—431no—
548#328—431no—
549#328—431no—
550#328—431no—
551#328C2×D4311yescharacteristic, complemented
552#328C2×D4311yescharacteristic, complemented
553#327—431no—
554#327—431no—
555#327—431no—
556#327—431no—
557#327—431no—
558#327—431no—
559#327C2×D4311yescharacteristic
560#327C2×D4311yescharacteristic
561C43#1762511yescharacteristic, complemented, Sylow
562C2×#41—431no—
563C2×#41—431no—
564C22×Q8—431no—
565C22×D4—431no—
566C22×D4—431no—
567C22×D4—861no—
568C23×C4—431no—
569C23×C4—431no—
570C2×M16—861no—
571C2×M16—861no—
572C22×C8—861no—
573C22×C8—861no—
574#126—21no—
575#126—861no—
576#126—861no—
577#126—861no—
578#126—861no—
579#126—861no—
580#125—431no—
581#125—861no—
582#125—861no—
583#125C4×D4311yescharacteristic
584#124—431no—
585#124—861no—
586#124—861no—
587#124C4×D4311yescharacteristic
588#123—21no—
589#123—861no—
590#123—861no—
591#123—861no—
592#123—861no—
593#123—861no—
594#123—861no—
595#123—861no—
596#123—861no—
597#123—861no—
598C22⋊Q8—431no—
599C22⋊Q8—431no—
600C22⋊Q8—431no—
601C22⋊Q8—431no—
602C22⋊Q8—431no—
603C22⋊Q8—861no—
604C22⋊Q8—861no—
605C22⋊Q8—861no—
606C22⋊Q8—861no—
607C22⋊Q8C22×D4311yescharacteristic
608#121—431no—
609#121—431no—
610#121—431no—
611#121—431no—
612#121—431no—
613#121—861no—
614#121—861no—
615#121—861no—
616#121—861no—
617#121—861no—
618#121—861no—
619#121—861no—
620#121—861no—
621#121C22×D4311yescharacteristic
622#120—861no—
623#120—861no—
624#120—861no—
625#120—861no—
626C4×Q8—431no—
627C4×Q8C4×D4311yescharacteristic
628C4×D4—21no—
629C4×D4—431no—
630C4×D4—431no—
631C4×D4—431no—
632C4×D4—431no—
633C4×D4—431no—
634C4×D4—431no—
635C4×D4—431no—
636C4×D4—431no—
637C4×D4—431no—
638C4×D4—861no—
639C4×D4—861no—
640C4×D4—861no—
641C4×D4—861no—
642C4×D4—861no—
643C4×D4—861no—
644C4×D4—861no—
645C4×D4—861no—
646C4×D4—861no—
647C4×D4C4×D4311yescharacteristic
648#117—21no—
649#117—431no—
650#117—431no—
651#117—861no—
652#117—861no—
653#117—861no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—431no—
656C2×C4⋊C4—431no—
657C2×C4⋊C4—431no—
658C2×C4⋊C4—861no—
659C2×C4⋊C4—861no—
660C2×C22⋊C4—431no—
661C2×C22⋊C4—431no—
662C2×C22⋊C4—861no—
663C2×C22⋊C4—861no—
664C2×C22⋊C4—861no—
665C2×C22⋊C4—861no—
666C2×C22⋊C4—861no—
667C2×C22⋊C4—861no—
668C2×C22⋊C4—861no—
669C2×C22⋊C4—861no—
670C2×C42—21no—
671C2×C42—861no—
672C2×C42—861no—
673C2×C42C22×D4311yescharacteristic
674C4⋊C8—21no—
675C4⋊C8—861no—
676C22⋊C8—431no—
677C22⋊C8—431no—
678C22⋊C8—861no—
679C22⋊C8—861no—
680C22⋊C8—861no—
681C22⋊C8—861no—
682C22⋊C8C22×D4311yescharacteristic
683C22⋊C8C22×D4311yescharacteristic
684#97—21no—
685#97—861no—
686#95—431no—
687#95—431no—
688#95—861no—
689#95—861no—
690#95—861no—
691#95C22×D4311yescharacteristic
692#95C22×D4311yescharacteristic
693C24—431no—
694C24—431no—
695C24—861no—
696#41—3441no—
697#41—3441no—
698C2×Q8—431no—
699C2×Q8—861no—
700C2×Q8—3441no—
701C2×Q8C2×C4×D4311yescharacteristic
702C2×D4—21no—
703C2×D4—431no—
704C2×D4—431no—
705C2×D4—431no—
706C2×D4—431no—
707C2×D4—431no—
708C2×D4—861no—
709C2×D4—861no—
710C2×D4—861no—
711C2×D4—861no—
712C2×D4—861no—
713C2×D4—861no—
714C2×D4—861no—
715C2×D4—861no—
716C2×D4—3441no—
717C2×D4—1721no—
718C2×D4—1721no—
719C2×D4—1722no—
720C2×D4—1722no—
721C2×D4C2×C4×D4311yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—431no—
726C22×C4—431no—
727C22×C4—431no—
728C22×C4—431no—
729C22×C4—431no—
730C22×C4—431no—
731C22×C4—431no—
732C22×C4—431no—
733C22×C4—431no—
734C22×C4—431no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—3441no—
744C22×C4—3441no—
745C22×C4D4×D4311yescharacteristic
746C22×C4D4×D4311yescharacteristic
747C22×C4C23×D4311yescharacteristic
748M16—3441no—
749M16—3441no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—861no—
753C2×C8—861no—
754C2×C8—3441no—
755C2×C8—3441no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—42no—
761C4⋊C4—431no—
762C4⋊C4—431no—
763C4⋊C4—431no—
764C4⋊C4—431no—
765C4⋊C4—431no—
766C4⋊C4—431no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—861no—
771C4⋊C4—861no—
772C4⋊C4—861no—
773C4⋊C4—861no—
774C4⋊C4—861no—
775C4⋊C4—861no—
776C4⋊C4—861no—
777C4⋊C4—1722no—
778C4⋊C4C2×C4×D4311yescharacteristic
779C4⋊C4C2×C4×D4311yescharacteristic
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—431no—
786C22⋊C4—431no—
787C22⋊C4—431no—
788C22⋊C4—431no—
789C22⋊C4—431no—
790C22⋊C4—431no—
791C22⋊C4—431no—
792C22⋊C4—431no—
793C22⋊C4—861no—
794C22⋊C4—861no—
795C22⋊C4—861no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—861no—
799C22⋊C4—861no—
800C22⋊C4—861no—
801C22⋊C4—861no—
802C22⋊C4—861no—
803C22⋊C4—861no—
804C22⋊C4—861no—
805C22⋊C4—861no—
806C22⋊C4—861no—
807C22⋊C4—861no—
808C22⋊C4—3441no—
809C22⋊C4—3441no—
810C22⋊C4—1722no—
811C22⋊C4—1722no—
812C42—21no—
813C42—42no—
814C42—861no—
815C42—861no—
816C42—861no—
817C42—3441no—
818C42—3441no—
819C42C2×C4×D4311yescharacteristic
820C42C2×C4×D4311yescharacteristic
821C42D4×D4311yescharacteristic
822C42D4×D4311yescharacteristic
823C23—21no—
824C23—431no—
825C23—431no—
826C23—431no—
827C23—431no—
828C23—861no—
829C23—861no—
830C23—861no—
831C23—861no—
832C23—861no—
833C23—3441no—
834C23—3441no—
835C23—1721no—
836C23—1721no—
837C23—1721no—
838C23—1721no—
839C23—1722no—
840C23C2×D4×D4311yescharacteristic
841Q8—41no—
842Q8—3441no—
843Q8—1721no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—3441no—
848D4—3441no—
849D4—3441no—
850D4—3441no—
851D4—3441no—
852D4—1721no—
853D4—1721no—
854D4—1721no—
855D4—1721no—
856D4—1721no—
857D4—1722no—
858D4—1722no—
859D4—1721no—
860D4—1721no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—81no—
875C2×C4—431no—
876C2×C4—431no—
877C2×C4—431no—
878C2×C4—431no—
879C2×C4—861no—
880C2×C4—861no—
881C2×C4—861no—
882C2×C4—3441no—
883C2×C4—3441no—
884C2×C4—3441no—
885C2×C4—3441no—
886C2×C4—3441no—
887C2×C4—1721no—
888C2×C4—1721no—
889C2×C4—1721no—
890C2×C4—1721no—
891C2×C4—1721no—
892C2×C4—1721no—
893C2×C4—1721no—
894C2×C4—1721no—
895C2×C4—1722no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4C22⋊C4×D4311yescharacteristic
905C2×C4C22⋊C4×D4311yescharacteristic
906C2×C4C22⋊C4×D4311yescharacteristic
907C2×C4C22⋊C4×D4311yescharacteristic
908C2×C4C22×C4×D4311yescharacteristic
909C2×C4C2×D4×D4311yescharacteristic
910C8—41no—
911C8—41no—
912C8—1721no—
913C8—1721no—
914C22—21no—
915C22—21no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—861no—
920C22—861no—
921C22—861no—
922C22—861no—
923C22—861no—
924C22—861no—
925C22—861no—
926C22—861no—
927C22—861no—
928C22—861no—
929C22—861no—
930C22—861no—
931C22—3441no—
932C22—3441no—
933C22—3441no—
934C22—3441no—
935C22—1721no—
936C22—1721no—
937C22—1721no—
938C22—6882no—
939C22C2×C22⋊C4×D4311yescharacteristic
940C22#1458369511yescharacteristic
941C22#1458369811yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—42no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—81no—
953C4—861no—
954C4—861no—
955C4—861no—
956C4—861no—
957C4—3441no—
958C4—3441no—
959C4—1721no—
960C4—1721no—
961C4—1721no—
962C2—21no—
963C2—21no—
964C2—81no—
965C2—3441no—
966C2—1721no—
967C2—1721no—
968C2—1721no—
969C2—1721no—
970C2#1914305411yescharacteristic
971C2#1914311111yescharacteristic
972C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#19148430C2
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43#17625
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #19143623C2semidirect
3. #19137566C2semidirect
4. #19133150C2semidirect
5. #19133148C2semidirect
6. #19133134C2semidirect
7. #19133133C2semidirect
8. #19133126C2semidirect
9. #19133122C2semidirect
10. #19133118C2semidirect
11. #19133113C2semidirect
12. #19133109C2semidirect
13. #19133085C2semidirect
14. #19133083C2semidirect
15. C43×#1509C2semidirect
16. #14583602C4semidirect
18. #14583599C4semidirect
20. #14583590C4semidirect
21. #14583587C4semidirect
24. #14583561C4semidirect
25. #14583557C4semidirect
26. #14583544C4semidirect
27. #14583542C4semidirect
42. #14582956C22semidirect
45. C22⋊C8×D43C22semidirect
46. C22⋊C8×D43C22semidirect
50. #14582765C22semidirect
52. #14582761C22semidirect
55. #14582746C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582636C22semidirect
59. #14582636C22semidirect
60. #14582635C22semidirect
61. #14582635C22semidirect
69. C43×#432C22semidirect
70. C4×C4⋊C4×C43C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
486. #1509D43semidirect
530. #432C2×D43semidirect
542. C4×C4⋊C4C2×D43semidirect
551. #328C2×D43semidirect
552. #328C2×D43semidirect
561. C43#17625semidirect

Maximal subgroups

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

subgroupindex
#191484302
#191436232
#191375662
#191331502
#191331482
#191331342
#191331332
#191331262
#191331222
#191331182
#191331132
#191331092
#191330852
#191330832
C43×#15092
#1762543