Finite Group Databasebeta

← #25064822

Subgroups — #25064822

Order 11008.

902 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148484C211yesmaximal, characteristic
2#19143610C211yesmaximal, characteristic, complemented
3#19143604C211yesmaximal, characteristic, complemented
4#19133225C211yesmaximal, characteristic, complemented
5#19133224C211yesmaximal, characteristic, complemented
6#19133217C211yesmaximal, characteristic, complemented
7#19133215C211yesmaximal, characteristic, complemented
8#19133212C211yesmaximal, characteristic, complemented
9#19133208C211yesmaximal, characteristic, complemented
10#19133208C211yesmaximal, characteristic, complemented
11#19133199C211yesmaximal, characteristic, complemented
12#19133184C211yesmaximal, characteristic, complemented
13#19133182C211yesmaximal, characteristic, complemented
14#329×D43C211yesmaximal, characteristic, complemented
15C43×#1529C211yesmaximal, characteristic, complemented
16#14583633—21no—
17#14583632—21no—
18#14583617—21no—
19#14583616—21no—
20#14583578—21no—
21#14583577—21no—
22#14583574—21no—
23#14583573—21no—
24#14583522C411yescharacteristic
25#14583521C411yescharacteristic
26#14583516C411yescharacteristic
27#14583514C411yescharacteristic
28#14583472C411yescharacteristic
29#14583465C411yescharacteristic
30#14583455C2211yescharacteristic
31#14583434C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583428C2211yescharacteristic
34#124×D43C2211yescharacteristic
35#14583375C411yescharacteristic
36#14583371C411yescharacteristic
37C4×#10621898C2211yescharacteristic
38#14583029—21no—
39#14583028—21no—
40#14582969—21no—
41#14582968—21no—
42#14582968—21no—
43#14582967—21no—
44C8×D172—21no—
45(C22⋊D43)⋊C8—21no—
46#14582956C2211yescharacteristic, complemented
47#14582954C2211yescharacteristic
48#14582954C2211yescharacteristic
49#14582954C2211yescharacteristic, complemented
50#14582954C2211yescharacteristic, complemented
51#14582851C2211yescharacteristic, complemented
52C2×#13063236C2211yescharacteristic, complemented
53#97×D43C2211yescharacteristic
54#97×D43C2211yescharacteristic
55#97×D43C2211yescharacteristic, complemented
56#14582641C2211yescharacteristic, complemented
57#14582641C2211yescharacteristic, complemented
58#14582640C2211yescharacteristic, complemented
59#14582640C2211yescharacteristic, complemented
60#14582640C2211yescharacteristic, complemented
61#14582640C2211yescharacteristic, complemented
62#14582639C2211yescharacteristic
63#14582639C2211yescharacteristic
64#14582638C2211yescharacteristic
65#14582638C2211yescharacteristic
66#14582638C2211yescharacteristic
67#14582638C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C4×M16×C43C2211yescharacteristic, complemented
71C43×#330C2211yescharacteristic, complemented
72C43×#330C2211yescharacteristic, complemented
73C43×#329C2211yescharacteristic
74C43×#329C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C2×Q8×D43C2×C411yescharacteristic
77C2×D4×D43C2×C411yescharacteristic
78C2×#10621872—21no—
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83#13063324—21no—
84#13063324C2×C411yescharacteristic
85#13063324C2×C411yescharacteristic
86#13063321—21no—
87#13063320—21no—
88#13063320—21no—
89#13063319—21no—
90#13063319—21no—
91#13063318—21no—
92#13063318—21no—
93#13063318—21no—
94#13063317C2311yescharacteristic
95#13063314C2×C411yescharacteristic
96#13063313—21no—
97#13063313C2311yescharacteristic
98#13063312—21no—
99#13063312C2×C411yescharacteristic
100#13063311—21no—
101#13063311—21no—
102#13063311—21no—
103#13063311—21no—
104#13063311—21no—
105#13063311—21no—
106#13063310—21no—
107#13063310—21no—
108#13063310—21no—
109#13063308—21no—
110#13063308—21no—
111#13063307—21no—
112#13063307—21no—
113#13063307—21no—
114#13063306—21no—
115#13063305—21no—
116#13063305C2×C411yescharacteristic
117#13063304—21no—
118#13063304C2×C411yescharacteristic
119#13063303—21no—
120#13063303—21no—
121#13063303—21no—
122#13063302—21no—
123#13063301C2×C411yescharacteristic
124#13063300C2×C411yescharacteristic
125#13063299C2×C411yescharacteristic
126#13063296C2×C411yescharacteristic
127#13063295—21no—
128#13063293—21no—
129Q8×Dic43C2×C411yescharacteristic
130C4×Dic86—21no—
131C4×Dic86C2×C411yescharacteristic
132C4×Dic86D411yescharacteristic
133C4×Dic86D411yescharacteristic
134#13063290—21no—
135#13063290—21no—
136#13063290—21no—
137#13063290C2×C411yescharacteristic
138C4×D172C2×C411yescharacteristic
139C4×D172D411yescharacteristic
140C4×D172D411yescharacteristic
141D4×Dic43C2×C411yescharacteristic
142#13063287—21no—
143#13063287C2×C411yescharacteristic
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152#13063284C2×C411yescharacteristic
153#13063283—21no—
154#13063283—21no—
155#13063283C2×C411yescharacteristic
156#13063283C2×C411yescharacteristic
157#13063282—21no—
158#13063282—21no—
159#13063282C2×C411yescharacteristic
160#13063282C2×C411yescharacteristic
161#13063281—21no—
162C2×(C2×D43)⋊C4—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C22⋊C4×D43—21no—
166C42×D43C2311yescharacteristic
167C42×D43C2311yescharacteristic
168C4⋊(C43⋊C8)—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174(C2×D43)⋊C8—21no—
175(C2×D43)⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178#13063236—21no—
179#13063236C2311yescharacteristic
180#13063236C2311yescharacteristic
181#13063236C2311yescharacteristic
182#13063236C2311yescharacteristic
183#13063235—21no—
184#13063235—21no—
185#13063235—21no—
186C8×Dic43—21no—
187C2×M16×C43—21no—
188#126×C43—21no—
189#125×C43C2311yescharacteristic
190#124×C43C2311yescharacteristic
191#123×C43—21no—
192C22⋊Q8×C43C2×C411yescharacteristic
193#121×C43C2×C411yescharacteristic
194C4×Q8×C43C2×C411yescharacteristic
195C4×D4×C43—21no—
196C4×D4×C43C2×C411yescharacteristic
197#117×C43—21no—
198C2×C42×C43C2311yescharacteristic
199C4⋊C8×C43—21no—
200C22⋊C8×C43—21no—
201#97×C43C2311yescharacteristic
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205C4×C8×C43—21no—
206C23×D43—21no—
207C2×Q8×C43C22×C411yescharacteristic
208C2×D4×C43—21no—
209C2×D4×C43C22×C411yescharacteristic
210C22×C4×C43—21no—
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C2×C22⋊D43—21no—
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43C22⋊C411yescharacteristic
218C2×C22⋊D43C22⋊C411yescharacteristic
219C22×Dic43—21no—
220Q8×D43—42no—
221D4×D43—42no—
222#10621898—42no—
223C2×D172—21no—
224C2×D172C22⋊C411yescharacteristic
225C2×D172C22×C411yescharacteristic
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43C22×C411yescharacteristic
230C2×C4×D43C22×C411yescharacteristic
231C2×C4×D43C2×D411yescharacteristic
232C2×C4×D43C2×D411yescharacteristic
233C2×C4×D43C2×D411yescharacteristic
234C2×C4×D43C2×D411yescharacteristic
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86C22⋊C411yescharacteristic
239C2×Dic86C22×C411yescharacteristic
240M16×C43—42no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43C22×C411yescharacteristic
250C4⋊C4×C43C22×C411yescharacteristic
251C22⋊C4×C43—21no—
252C22⋊C4×C43—21no—
253C22⋊C4×C43—21no—
254C22⋊C4×C43—21no—
255C22⋊C4×C43—21no—
256C42×C43—21no—
257C42×C43C22×C411yescharacteristic
258C42×C43C2×D411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C42×C43C2411yescharacteristic
261C22⋊Dic43—21no—
262C22⋊Dic43—21no—
263C22⋊Dic43—21no—
264C22⋊Dic43—21no—
265C22⋊Dic43—21no—
266C22⋊Dic43C22⋊C411yescharacteristic
267C22⋊Dic43C22⋊C411yescharacteristic
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—
276(C2×D43)⋊C4—21no—
277(C2×D43)⋊C4—21no—
278(C2×D43)⋊C4—21no—
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4C22⋊C411yescharacteristic
281(C2×D43)⋊C4C22⋊C411yescharacteristic
282(C2×D43)⋊C4C22⋊C411yescharacteristic
283(C2×D43)⋊C4C22⋊C411yescharacteristic
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43C22⋊C411yescharacteristic
287C4⋊Dic43C22⋊C411yescharacteristic
288C4⋊Dic43C22×C411yescharacteristic
289C4⋊Dic43C22×C411yescharacteristic
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⋊C4C22⋊C411yescharacteristic
299Dic43⋊C4C22⋊C411yescharacteristic
300Dic43⋊C4C22⋊C411yescharacteristic
301Dic43⋊C4C22⋊C411yescharacteristic
302C4×Dic43—21no—
303C4×Dic43—21no—
304C4×Dic43—21no—
305C4×Dic43—21no—
306C4×Dic43—21no—
307C4×Dic43C22×C411yescharacteristic
308C4×Dic43C22×C411yescharacteristic
309C4×Dic43C2×D411yescharacteristic
310C4×Dic43C2×D411yescharacteristic
311C4×Dic43C2×D411yescharacteristic
312C4×Dic43C2×D411yescharacteristic
313C2×C43⋊C8—21no—
314C2×C43⋊C8—21no—
315C2×C43⋊C8—21no—
316C2×C43⋊C8—21no—
317C2×C43⋊C8—42no—
318#10621872—42no—
319C8×D43—42no—
320C8×D43—42no—
321C8×D43—42no—
322C23×C43—21no—
323C23×C43C2×C22⋊C411yescharacteristic
324C22×D43—21no—
325C22×D43—42no—
326C22×D43—81no—
327C22×D43—81no—
328C22×D43C2×C22⋊C411yescharacteristic
329C22×D43C2×C22⋊C411yescharacteristic
330Q8×C43—41no—
331D4×C43—41no—
332D4×C43—81no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—81no—
340C2×C4×C43C2×C22⋊C411yescharacteristic
341C2×C4×C43C2×C22⋊C411yescharacteristic
342C2×C4×C43C2×C22⋊C411yescharacteristic
343C2×C4×C43C23×C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C22⋊D43—22no—
347C22⋊D43—41no—
348C22⋊D43—42no—
349C22⋊D43—81no—
350C22⋊D43—81no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—81no—
355C2×Dic43C2×C22⋊C411yescharacteristic
356C2×Dic43C2×C22⋊C411yescharacteristic
357C2×Dic43C2×C22⋊C411yescharacteristic
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361D172—22no—
362D172—41no—
363D172—81no—
364C4×D43—22no—
365C4×D43—41no—
366C4×D43—41no—
367C4×D43—41no—
368C4×D43—41no—
369C4×D43—41no—
370C4×D43—42no—
371C4×D43—81no—
372C4×D43—81no—
373Dic86—41no—
374Dic86—42no—
375Dic86—41no—
376Dic86—81no—
377Dic86—81no—
378C8×C43—22no—
379C8×C43—41no—
380C8×C43—41no—
381C8×C43—41no—
382C43⋊C8—22no—
383C43⋊C8—41no—
384C43⋊C8—41no—
385C43⋊C8—41no—
386#17686—431nomaximal, Sylow
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43C22×C22⋊C411yescharacteristic
394C2×D43—21no—
395C2×D43—21no—
396C2×D43—21no—
397C2×D43—21no—
398C2×D43—21no—
399C2×D43—41no—
400C2×D43—41no—
401C2×D43—41no—
402C2×D43—162no—
403C2×D43#41312yes—
404C4×C43—21no—
405C4×C43—21no—
406C4×C43—21no—
407C4×C43—21no—
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—41no—
411C4×C43—41no—
412C4×C43—41no—
413Dic43—21no—
414Dic43—21no—
415Dic43—21no—
416Dic43—21no—
417Dic43—21no—
418Dic43—21no—
419Dic43—41no—
420Dic43—41no—
421Dic43—41no—
422#3510—431no—
423#2970—431no—
424#2970—431no—
425#1535—431no—
426#1535—431no—
427#1533—431no—
428#1532—431no—
429#1532—431no—
430#1531—431no—
431#1531—431no—
432#1529—431no—
433#1529D4311yescharacteristic, complemented
434#1524—431no—
435#1524—431no—
436C2×#329—431no—
437C2×C43—41no—
438C2×C43—81no—
439C2×C43C2×#41311yescharacteristic
440C2×C43#290111yescharacteristic
441C2×C43#290111yescharacteristic
442D43—22no—
443D43—41no—
444D43—81no—
445#559—861no—
446#559—861no—
447#556—861no—
448#556—861no—
449#551—861no—
450#551—861no—
451#551—861no—
452#551—861no—
453#542—431no—
454#542—431no—
455#542—431no—
456#542—431no—
457#536—431no—
458#535—431no—
459#533—431no—
460#529—431no—
461#529—431no—
462#529—431no—
463#529C2×D4311yescharacteristic
464C2×#124—431no—
465#519—431no—
466#518—431no—
467C4×#41—431no—
468#446—861no—
469#446—861no—
470#435—861no—
471#435—861no—
472#435—861no—
473#435—861no—
474C8×D4—861no—
475C8×D4—861no—
476#432—431no—
477#432—431no—
478#432—431no—
479#432—431no—
480#432—431no—
481#432C2×D4311yescharacteristic, complemented
482C4×M16—431no—
483C4×M16C2×D4311yescharacteristic, complemented
484C2×#97—431no—
485C2×#97—431no—
486C2×#97—431no—
487C2×#97—431no—
488#330—431no—
489#330—431no—
490#330—431no—
491#330—431no—
492#330—431no—
493#330—431no—
494#330C2×D4311yescharacteristic, complemented
495#330C2×D4311yescharacteristic, complemented
496#329—431no—
497#329—431no—
498#329—431no—
499#329—431no—
500#329—431no—
501#329—431no—
502#329C2×D4311yescharacteristic
503#329C2×D4311yescharacteristic
504C43#1768611yescharacteristic, complemented, Sylow
505C2×#41—431no—
506C22×Q8—431no—
507C22×D4—431no—
508C2×M16—21no—
509C2×M16—861no—
510C22×C8—861no—
511C22×C8—861no—
512C22×C8—861no—
513C22×C8—861no—
514C4⋊Q8—431no—
515C4⋊Q8—431no—
516C4⋊Q8—861no—
517#127—861no—
518#126—21no—
519#126—861no—
520#126—861no—
521#126—861no—
522#126—861no—
523#126—861no—
524#126—861no—
525#126—861no—
526#125—431no—
527#125C22×D4311yescharacteristic
528#124—431no—
529#124—431no—
530#124—431no—
531#124—861no—
532#124—861no—
533#124—861no—
534#124—861no—
535#124—861no—
536#124—861no—
537#124—861no—
538#124—861no—
539#124C22×D4311yescharacteristic
540#123—21no—
541#123—861no—
542#123—861no—
543#123—861no—
544#123—861no—
545#123—861no—
546#123—861no—
547#123—861no—
548#123—861no—
549#123—861no—
550C22⋊Q8—431no—
551C22⋊Q8—431no—
552C22⋊Q8—431no—
553C22⋊Q8—861no—
554C22⋊Q8—861no—
555C22⋊Q8—861no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8C4×D4311yescharacteristic
560#121—431no—
561#121—431no—
562#121—431no—
563#121C4×D4311yescharacteristic
564#120—861no—
565#120—861no—
566C4×Q8—431no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8—431no—
571C4×Q8—861no—
572C4×Q8—861no—
573C4×Q8—861no—
574C4×Q8—861no—
575C4×Q8C4×D4311yescharacteristic
576C4×D4—21no—
577C4×D4—431no—
578C4×D4—431no—
579C4×D4—431no—
580C4×D4—431no—
581C4×D4—431no—
582C4×D4—431no—
583C4×D4—431no—
584C4×D4—431no—
585C4×D4—431no—
586C4×D4—861no—
587C4×D4—861no—
588C4×D4—861no—
589C4×D4—861no—
590C4×D4—861no—
591C4×D4C4×D4311yescharacteristic
592#117—21no—
593#117—431no—
594#117—431no—
595#117—431no—
596#117—431no—
597#117—431no—
598#117—861no—
599#117—861no—
600#117—861no—
601#117—861no—
602#117—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C22⋊C4—861no—
607C2×C42—431no—
608C2×C42—431no—
609C2×C42C22×D4311yescharacteristic
610C4⋊C8—21no—
611C4⋊C8—861no—
612C4⋊C8—861no—
613C4⋊C8—861no—
614C4⋊C8—861no—
615C4⋊C8—861no—
616C22⋊C8—21no—
617C22⋊C8—861no—
618C22⋊C8—861no—
619C22⋊C8—861no—
620C22⋊C8—861no—
621C22⋊C8—861no—
622#97—431no—
623#97—431no—
624#97—431no—
625#97—431no—
626#97—861no—
627#97—861no—
628#97—861no—
629#97—861no—
630#97C22×D4311yescharacteristic
631#97C22×D4311yescharacteristic
632#97C22×D4311yescharacteristic
633#97C22×D4311yescharacteristic
634C4×C8—21no—
635C4×C8—861no—
636C24—861no—
637#41—1722no—
638C2×Q8—431no—
639C2×Q8—431no—
640C2×Q8—861no—
641C2×Q8—861no—
642C2×Q8—861no—
643C2×Q8—1722no—
644C2×Q8C2×C4×D4311yescharacteristic
645C2×D4—21no—
646C2×D4—431no—
647C2×D4—431no—
648C2×D4—431no—
649C2×D4—431no—
650C2×D4—861no—
651C2×D4—861no—
652C2×D4—861no—
653C2×D4—861no—
654C2×D4—1722no—
655C2×D4C2×C4×D4311yescharacteristic
656C22×C4—21no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4C2×C4×D4311yescharacteristic
668C22×C4D4×D4311yescharacteristic
669C22×C4D4×D4311yescharacteristic
670M16—42no—
671M16—1722no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—861no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—1722no—
681C2×C8—1722no—
682C2×C8—1722no—
683C2×C8—1722no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—431no—
689C4⋊C4—431no—
690C4⋊C4—431no—
691C4⋊C4—431no—
692C4⋊C4—431no—
693C4⋊C4—431no—
694C4⋊C4—431no—
695C4⋊C4—431no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4C2×C4×D4311yescharacteristic
707C4⋊C4C2×C4×D4311yescharacteristic
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—431no—
714C22⋊C4—431no—
715C22⋊C4—431no—
716C22⋊C4—431no—
717C22⋊C4—431no—
718C22⋊C4—431no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C22⋊C4—861no—
730C22⋊C4—861no—
731C22⋊C4—861no—
732C22⋊C4—861no—
733C22⋊C4—861no—
734C22⋊C4—861no—
735C22⋊C4—861no—
736C42—21no—
737C42—431no—
738C42—431no—
739C42—431no—
740C42—431no—
741C42—431no—
742C42—431no—
743C42—861no—
744C42—861no—
745C42—861no—
746C42—861no—
747C42—861no—
748C42C2×C4×D4311yescharacteristic
749C42D4×D4311yescharacteristic
750C42D4×D4311yescharacteristic
751C42C23×D4311yescharacteristic
752C23—21no—
753C23—431no—
754C23—431no—
755C23—861no—
756C23—3441no—
757C23—3441no—
758C23—1722no—
759C23C22⋊C4×D4311yescharacteristic
760Q8—41no—
761Q8—3441no—
762Q8—3441no—
763Q8—1721no—
764Q8—1721no—
765Q8—1722no—
766D4—41no—
767D4—81no—
768D4—862no—
769D4—862no—
770D4—3441no—
771D4—3441no—
772D4—3441no—
773D4—1721no—
774D4—1721no—
775D4—1722no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—81no—
783C2×C4—431no—
784C2×C4—431no—
785C2×C4—431no—
786C2×C4—431no—
787C2×C4—431no—
788C2×C4—431no—
789C2×C4—862no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—3441no—
794C2×C4—3441no—
795C2×C4—3441no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1722no—
802C2×C4C22⋊C4×D4311yescharacteristic
803C2×C4C22⋊C4×D4311yescharacteristic
804C2×C4C22⋊C4×D4311yescharacteristic
805C2×C4C22×C4×D4311yescharacteristic
806C2×C4C2×D4×D4311yescharacteristic
807C2×C4C2×D4×D4311yescharacteristic
808C8—22no—
809C8—41no—
810C8—41no—
811C8—41no—
812C8—862no—
813C8—1721no—
814C8—1721no—
815C8—1721no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—432no—
823C22—861no—
824C22—861no—
825C22—861no—
826C22—861no—
827C22—861no—
828C22—1721no—
829C22—1721no—
830C22—1721no—
831C22—6882no—
832C22C2×C22⋊C4×D4311yescharacteristic
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—861no—
843C4—861no—
844C4—861no—
845C4—861no—
846C4—861no—
847C4—861no—
848C4—1721no—
849C4—1721no—
850C4—1721no—
851C2—41no—
852C2—81no—
853C2—862no—
854C2—3441no—
855C2—1721no—
856C2#413×D4311yescharacteristic
857C2#1914313911yescharacteristic
858C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1529C2
socleC22×C43C22×C22⋊C4
prime radical#14583465C4
cosocleC42×C43C24
hypercenter#1529D43
hypocenterC43#17686
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1529

Complements

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

NH ≅ G/Ntype
2. #19143610C2semidirect
3. #19143604C2semidirect
4. #19133225C2semidirect
5. #19133224C2semidirect
6. #19133217C2semidirect
7. #19133215C2semidirect
8. #19133212C2semidirect
9. #19133208C2semidirect
10. #19133208C2semidirect
11. #19133199C2semidirect
12. #19133184C2semidirect
13. #19133182C2semidirect
14. #329×D43C2semidirect
15. C43×#1529C2semidirect
46. #14582956C22semidirect
49. #14582954C22semidirect
50. #14582954C22semidirect
51. #14582851C22semidirect
52. C2×#13063236C22semidirect
55. #97×D43C22semidirect
56. #14582641C22semidirect
57. #14582641C22semidirect
58. #14582640C22semidirect
59. #14582640C22semidirect
60. #14582640C22semidirect
61. #14582640C22semidirect
69. C43×#432C22semidirect
70. C4×M16×C43C22semidirect
71. C43×#330C22semidirect
72. C43×#330C22semidirect
433. #1529D43semidirect
481. #432C2×D43semidirect
483. C4×M16C2×D43semidirect
494. #330C2×D43semidirect
495. #330C2×D43semidirect
504. C43#17686semidirect

Maximal subgroups

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

subgroupindex
#191484842
#191436102
#191436042
#191332252
#191332242
#191332172
#191332152
#191332122
#191332082
#191331992
#191331842
#191331822
#329×D432
C43×#15292
#1768643