Finite Group Databasebeta

← #25063449

Subgroups — #25063449

Order 11008.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148022C211yesmaximal, characteristic
2#19143712C211yesmaximal, characteristic, complemented
3#19133069C211yesmaximal, characteristic, complemented
4#19133061C211yesmaximal, characteristic, complemented
5#19133056C211yesmaximal, characteristic, complemented
6#19133051C211yesmaximal, characteristic, complemented
7#19133043C211yesmaximal, characteristic, complemented
8#19133035C211yesmaximal, characteristic, complemented
9#19133030C211yesmaximal, characteristic, complemented
10#19133025C211yesmaximal, characteristic, complemented
11#19133017C211yesmaximal, characteristic, complemented
12#19133009C211yesmaximal, characteristic, complemented
13#19133004C211yesmaximal, characteristic, complemented
14#19132999C211yesmaximal, characteristic, complemented
15C43×#2965C211yesmaximal, characteristic, complemented
16#14583527C411yescharacteristic
17#14583520C411yescharacteristic
18#14583520C411yescharacteristic
19#14583514—21no—
20#14583511C411yescharacteristic
21#14583511C411yescharacteristic
22#14583507—21no—
23#14583491—21no—
24#14583491—21no—
25#14583477C411yescharacteristic
26#14583475C411yescharacteristic
27#14583470C411yescharacteristic
28#14583456C2211yescharacteristic
29#14583456C2211yescharacteristic
30#14583453—21no—
31#14583433C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583431—21no—
34#14583429—21no—
35#14583429—21no—
36C4×#10621898C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38#14583030—21no—
39#14582977—21no—
40#14582971—21no—
41#14582971—21no—
42#14582956C2211yescharacteristic
43#14582956C2211yescharacteristic
44#14582952C2211yescharacteristic
45#14582923C2211yescharacteristic
46#14582923C2211yescharacteristic
47C2×C4⋊(C43⋊C8)C2211yescharacteristic
48#14582631C2211yescharacteristic
49#14582631C2211yescharacteristic
50#14582631C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582631C2211yescharacteristic
55#14582631C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582631C2211yescharacteristic
60#14582628C2211yescharacteristic
61#14582628C2211yescharacteristic
62#14582628C2211yescharacteristic
63#14582628C2211yescharacteristic
64C4×#41×C43C2211yescharacteristic
65C43×#446—21no—
66C43×#436—21no—
67C43×#435—21no—
68C43×#435—21no—
69C43×#431C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×#431C2211yescharacteristic
72C4×M16×C43C2211yescharacteristic
73C4×M16×C43C2211yescharacteristic
74C2×C4×C8×C43C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C2×#10621877—21no—
78C2×#10621877—21no—
79C22×C43⋊C8—21no—
80#13063325C2×C411yescharacteristic
81#13063325C2×C411yescharacteristic
82#13063325C2×C411yescharacteristic
83#13063325C2×C411yescharacteristic
84#13063324—21no—
85#13063323—21no—
86#13063320—21no—
87#13063320—21no—
88#13063319—21no—
89#13063319—21no—
90#13063318—21no—
91#13063318—21no—
92#13063318—21no—
93#13063318—21no—
94#13063317—21no—
95#13063317—21no—
96#13063317C2×C411yescharacteristic
97#13063317C2×C411yescharacteristic
98#13063316—21no—
99#13063315—21no—
100#13063315—21no—
101#13063315—21no—
102#13063315—21no—
103#13063313C2×C411yescharacteristic
104#13063313C2×C411yescharacteristic
105#13063312—21no—
106#13063311—21no—
107#13063311—21no—
108#13063309—21no—
109#13063309—21no—
110#13063308—21no—
111#13063308—21no—
112#13063307—21no—
113#13063307—21no—
114#13063306—21no—
115#13063306—21no—
116#13063305—21no—
117#13063305—21no—
118#13063304—21no—
119#13063304—21no—
120#13063304C2×C411yescharacteristic
121#13063304C2×C411yescharacteristic
122#13063304C2×C411yescharacteristic
123#13063304C2×C411yescharacteristic
124#13063304C2×C411yescharacteristic
125#13063304C2×C411yescharacteristic
126#13063303—21no—
127#13063303—21no—
128#13063302—21no—
129#13063302—21no—
130#13063301—21no—
131#13063299C2×C411yescharacteristic
132#13063299C2×C411yescharacteristic
133#13063297—21no—
134#13063297—21no—
135#13063296—21no—
136C4×Dic86—21no—
137C4×Dic86—21no—
138C4×Dic86—21no—
139C4×Dic86—21no—
140C4×Dic86C2×C411yescharacteristic
141C4×Dic86C2×C411yescharacteristic
142C4×Dic86C2×C411yescharacteristic
143C4×Dic86C2311yescharacteristic
144C4×Dic86C2311yescharacteristic
145C4×Dic86C2311yescharacteristic
146C4×D172C2×C411yescharacteristic
147C4×D172C2311yescharacteristic
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150C4×C22⋊D43—21no—
151C4×C22⋊D43—21no—
152#13063284—21no—
153#13063284—21no—
154#13063284C2×C411yescharacteristic
155#13063282—21no—
156#13063282—21no—
157#13063282—21no—
158C2×C4⋊Dic43C2×C411yescharacteristic
159C2×Dic43⋊C4—21no—
160C2×C4×Dic43—21no—
161C42×D43—21no—
162C4⋊(C43⋊C8)—21no—
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165C4⋊(C43⋊C8)C2311yescharacteristic
166C4⋊(C43⋊C8)C2311yescharacteristic
167C4⋊(C43⋊C8)C2311yescharacteristic
168C4⋊(C43⋊C8)C2311yescharacteristic
169C22⋊(C43⋊C8)—21no—
170C22⋊(C43⋊C8)—21no—
171C22⋊(C43⋊C8)—21no—
172#13063236—21no—
173#13063236—21no—
174C4×C43⋊C8—21no—
175C2×#41×C43C2×C411yescharacteristic
176C2×M16×C43—21no—
177C2×M16×C43—21no—
178C22×C8×C43—21no—
179C4×Q8×C43D411yescharacteristic
180C4×Q8×C43D411yescharacteristic
181C4×D4×C43D411yescharacteristic
182C4×D4×C43D411yescharacteristic
183C4×D4×C43D411yescharacteristic
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186C4×D4×C43D411yescharacteristic
187#117×C43C2×C411yescharacteristic
188#117×C43C2×C411yescharacteristic
189#117×C43C2×C411yescharacteristic
190C2×C42×C43C2311yescharacteristic
191C2×C42×C43C2311yescharacteristic
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43—21no—
194C4⋊C8×C43—21no—
195C4⋊C8×C43—21no—
196C22⋊C8×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43—21no—
199#97×C43—21no—
200#97×C43—21no—
201C4×C8×C43—21no—
202C4×C8×C43C2311yescharacteristic
203C4×C8×C43C2311yescharacteristic
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
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—
225#10621898—42no—
226C2×D172C22×C411yescharacteristic
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—42no—
234C2×Dic86C22×C411yescharacteristic
235C2×Dic86C22×C411yescharacteristic
236C2×Dic86C22×C411yescharacteristic
237M16×C43—42no—
238M16×C43—42no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—42no—
244C4⋊C4×C43C22⋊C411yescharacteristic
245C4⋊C4×C43C22⋊C411yescharacteristic
246C4⋊C4×C43C22⋊C411yescharacteristic
247C4⋊C4×C43C22⋊C411yescharacteristic
248C4⋊C4×C43C22⋊C411yescharacteristic
249C4⋊C4×C43C22⋊C411yescharacteristic
250C22⋊C4×C43C22⋊C411yescharacteristic
251C22⋊C4×C43C22⋊C411yescharacteristic
252C22⋊C4×C43C22⋊C411yescharacteristic
253C22⋊C4×C43C22⋊C411yescharacteristic
254C22⋊C4×C43C22⋊C411yescharacteristic
255C22⋊C4×C43C22⋊C411yescharacteristic
256C42×C43C22×C411yescharacteristic
257C42×C43C22×C411yescharacteristic
258C42×C43C22×C411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C42×C43C2×D411yescharacteristic
262C42×C43C2×D411yescharacteristic
263C42×C43C2×D411yescharacteristic
264C42×C43C2×D411yescharacteristic
265C42×C43C2411yescharacteristic
266C22⋊Dic43—21no—
267C22⋊Dic43—21no—
268C22⋊Dic43—21no—
269C22⋊Dic43—21no—
270C22⋊Dic43—21no—
271C22⋊Dic43—21no—
272C22⋊Dic43—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)⋊C4—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43C22×C411yescharacteristic
289C4⋊Dic43C22×C411yescharacteristic
290C4⋊Dic43C22×C411yescharacteristic
291C4⋊Dic43C22×C411yescharacteristic
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—
313C4×Dic43—21no—
314C4×Dic43—21no—
315#10621877—81no—
316#10621877—81no—
317C2×C43⋊C8—21no—
318C2×C43⋊C8—21no—
319C2×C43⋊C8—21no—
320C2×C43⋊C8—21no—
321C2×C43⋊C8—81no—
322C23×C43C2×C22⋊C411yescharacteristic
323C23×C43C2×C22⋊C411yescharacteristic
324C23×C43C2×C22⋊C411yescharacteristic
325C22×D43—21no—
326Q8×C43—41no—
327D4×C43—41no—
328D4×C43—41no—
329D4×C43—41no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43C2×C22⋊C411yescharacteristic
343C2×C4×C43C2×C22⋊C411yescharacteristic
344C2×C4×C43C2×C22⋊C411yescharacteristic
345C2×C4×C43C2×C22⋊C411yescharacteristic
346C2×C4×C43C2×C22⋊C411yescharacteristic
347C2×C4×C43C2×C22⋊C411yescharacteristic
348C2×C4×C43C2×C22⋊C411yescharacteristic
349C2×C4×C43C2×C22⋊C411yescharacteristic
350C2×C4×C43C2×C22⋊C411yescharacteristic
351C2×C4×C43C23×C411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C22⋊D43—42no—
355C22⋊D43—81no—
356C22⋊D43—81no—
357C2×Dic43—21no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—42no—
365C2×Dic43—81no—
366D172—22no—
367C4×D43—42no—
368C4×D43—41no—
369C4×D43—41no—
370C4×D43—81no—
371Dic86—22no—
372Dic86—22no—
373Dic86—22no—
374Dic86—42no—
375Dic86—81no—
376Dic86—81no—
377C8×C43—22no—
378C8×C43—41no—
379C8×C43—41no—
380C8×C43—41no—
381C43⋊C8—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384C43⋊C8—41no—
385#17506—431nomaximal, Sylow
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—21no—
395C22×C43C22×C22⋊C411yescharacteristic
396C2×D43—41no—
397C2×D43—41no—
398C2×D43—41no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—21no—
404C4×C43—21no—
405C4×C43—21no—
406C4×C43—21no—
407C4×C43—21no—
408C4×C43—21no—
409C4×C43#56812yes—
410C4×C43#57711yescharacteristic
411C4×C43#57811yescharacteristic
412Dic43—41no—
413Dic43—41no—
414Dic43—41no—
415Dic43—41no—
416Dic43—41no—
417Dic43—41no—
418Dic43—41no—
419#3461—431no—
420#2989—431no—
421#2965D4311yescharacteristic, complemented
422#1497—431no—
423#1495—431no—
424#1494—431no—
425#1493—431no—
426#1491—431no—
427#1489—431no—
428#1488—431no—
429#1487—431no—
430#1485—431no—
431#1483—431no—
432#1482—431no—
433#1481—431no—
434C2×C43—41no—
435C2×C43—41no—
436C2×C43—41no—
437C2×C43#287911yescharacteristic
438C2×C43#289811yescharacteristic
439C2×C43#290111yescharacteristic
440D43—81no—
441#544—431no—
442#542—431no—
443#542—431no—
444#542—861no—
445#541—431no—
446#541—431no—
447#541—861no—
448#539—861no—
449#539—861no—
450#537—431no—
451#536—431no—
452#536—431no—
453#533—431no—
454#533—431no—
455#533—861no—
456#529—431no—
457#529—431no—
458#529—861no—
459#529—861no—
460#529—861no—
461C4×#41—431no—
462C4×#41C2×D4311yescharacteristic
463C2×C4×Q8—431no—
464#446—21no—
465#446—861no—
466#436—21no—
467#436—861no—
468#435—21no—
469#435—21no—
470#435—861no—
471#435—861no—
472#432—431no—
473#432—431no—
474#431—431no—
475#431C2×D4311yescharacteristic
476#431C2×D4311yescharacteristic
477#431C2×D4311yescharacteristic
478#423—431no—
479#423—431no—
480C2×C4⋊C8—431no—
481C4×M16C2×D4311yescharacteristic
482C4×M16C2×D4311yescharacteristic
483C2×C4×C8C2×D4311yescharacteristic
484Q8⋊C8—431no—
485Q8⋊C8—431no—
486Q8⋊C8—431no—
487Q8⋊C8—431no—
488Q8⋊C8—431no—
489Q8⋊C8—431no—
490Q8⋊C8—431no—
491Q8⋊C8—431no—
492Q8⋊C8—431no—
493Q8⋊C8—431no—
494Q8⋊C8—431no—
495Q8⋊C8—431no—
496D4⋊C8—431no—
497D4⋊C8—431no—
498D4⋊C8—431no—
499D4⋊C8—431no—
500C43#1750611yescharacteristic, complemented, Sylow
501C2×#41—431no—
502C2×#41C4×D4311yescharacteristic
503C22×Q8—431no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—861no—
507C2×M16—861no—
508C22×C8—21no—
509C22×C8—861no—
510C4⋊Q8—431no—
511C4⋊Q8—431no—
512C4⋊Q8—431no—
513C4⋊Q8—431no—
514C4⋊Q8—861no—
515C4⋊Q8—861no—
516#126—861no—
517#126—861no—
518#126—861no—
519#126—861no—
520#126—861no—
521#126—861no—
522#126—861no—
523#126—861no—
524#125—431no—
525#125—431no—
526#125—861no—
527#125—861no—
528#125—861no—
529#125—861no—
530#125—861no—
531#125—861no—
532#125—861no—
533#124—431no—
534#124—431no—
535#124—861no—
536#124—861no—
537#124—861no—
538#123—861no—
539#123—861no—
540#123—861no—
541#123—861no—
542#123—861no—
543#123—861no—
544#123—861no—
545#123—861no—
546C22⋊Q8—431no—
547C22⋊Q8—431no—
548C22⋊Q8—431no—
549C22⋊Q8—431no—
550C22⋊Q8—431no—
551C22⋊Q8—431no—
552C22⋊Q8—861no—
553C22⋊Q8—861no—
554C22⋊Q8—861no—
555C22⋊Q8—861no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—861no—
561#121—431no—
562#121—431no—
563#121—861no—
564#121—861no—
565#121—861no—
566C4×Q8—431no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8—431no—
571C4×Q8—431no—
572C4×Q8—861no—
573C4×Q8—861no—
574C4×Q8—861no—
575C4×Q8—861no—
576C4×Q8D17211yescharacteristic
577C4×Q8C22⋊D4311yescharacteristic
578C4×D4—431no—
579C4×D4—431no—
580C4×D4—861no—
581C4×D4—861no—
582C4×D4—861no—
583C4×D4—861no—
584C4×D4D17211yescharacteristic
585C4×D4D17211yescharacteristic
586C4×D4D17211yescharacteristic
587C4×D4C22⋊D4311yescharacteristic
588C4×D4C22⋊D4311yescharacteristic
589C4×D4C22⋊D4311yescharacteristic
590#117—431no—
591#117—861no—
592#117—861no—
593#117—861no—
594#117—861no—
595#117—861no—
596#117C4×D4311yescharacteristic
597#117C4×D4311yescharacteristic
598#117C4×D4311yescharacteristic
599C2×C4⋊C4—431no—
600C2×C4⋊C4—861no—
601C2×C42—861no—
602C2×C42—861no—
603C2×C42C22×D4311yescharacteristic
604C2×C42C22×D4311yescharacteristic
605C2×C42C22×D4311yescharacteristic
606C4⋊C8—21no—
607C4⋊C8—21no—
608C4⋊C8—21no—
609C4⋊C8—431no—
610C4⋊C8—431no—
611C4⋊C8—431no—
612C4⋊C8—431no—
613C4⋊C8—861no—
614C4⋊C8—861no—
615C4⋊C8—861no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—861no—
620C22⋊C8—861no—
621C22⋊C8—861no—
622#97—21no—
623#97—21no—
624#97—861no—
625#97—861no—
626C4×C8—21no—
627C4×C8—861no—
628C4×C8C22×D4311yescharacteristic
629C4×C8C22×D4311yescharacteristic
630C4×C8C22×D4311yescharacteristic
631C4×C8C22×D4311yescharacteristic
632#41—42no—
633#41—1722no—
634C2×Q8—431no—
635C2×Q8—431no—
636C2×Q8—431no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8—861no—
640C2×Q8—1722no—
641C2×Q8(C2×D43)⋊C411yescharacteristic
642C2×D4—431no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4(C2×D43)⋊C411yescharacteristic
647C2×D4(C2×D43)⋊C411yescharacteristic
648C2×D4(C2×D43)⋊C411yescharacteristic
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4C2×C4×D4311yescharacteristic
655C22×C4C2×C4×D4311yescharacteristic
656C22×C4C2×C4×D4311yescharacteristic
657C22×C4C2×D17211yescharacteristic
658C22×C4C2×D17211yescharacteristic
659C22×C4C2×D17211yescharacteristic
660C22×C4C2×C22⋊D4311yescharacteristic
661C22×C4C2×C22⋊D4311yescharacteristic
662C22×C4C2×C22⋊D4311yescharacteristic
663M16—42no—
664M16—42no—
665M16—3441no—
666M16—3441no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—42no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—3441no—
677C4⋊C4—431no—
678C4⋊C4—431no—
679C4⋊C4—431no—
680C4⋊C4—431no—
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—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4(C2×D43)⋊C411yescharacteristic
705C4⋊C4(C2×D43)⋊C411yescharacteristic
706C4⋊C4(C2×D43)⋊C411yescharacteristic
707C4⋊C4(C2×D43)⋊C411yescharacteristic
708C4⋊C4(C2×D43)⋊C411yescharacteristic
709C4⋊C4(C2×D43)⋊C411yescharacteristic
710C22⋊C4—861no—
711C22⋊C4—861no—
712C22⋊C4—861no—
713C22⋊C4—861no—
714C22⋊C4—861no—
715C22⋊C4—861no—
716C22⋊C4—861no—
717C22⋊C4—861no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4(C2×D43)⋊C411yescharacteristic
726C22⋊C4(C2×D43)⋊C411yescharacteristic
727C22⋊C4(C2×D43)⋊C411yescharacteristic
728C22⋊C4(C2×D43)⋊C411yescharacteristic
729C22⋊C4(C2×D43)⋊C411yescharacteristic
730C22⋊C4(C2×D43)⋊C411yescharacteristic
731C42—861no—
732C42—861no—
733C42—861no—
734C42—861no—
735C42—861no—
736C42—861no—
737C42—861no—
738C42C2×C4×D4311yescharacteristic
739C42C2×C4×D4311yescharacteristic
740C42C2×C4×D4311yescharacteristic
741C42C2×D17211yescharacteristic
742C42C2×D17211yescharacteristic
743C42C2×D17211yescharacteristic
744C42C2×C22⋊D4311yescharacteristic
745C42C2×C22⋊D4311yescharacteristic
746C42C2×C22⋊D4311yescharacteristic
747C42C23×D4311yescharacteristic
748C23—861no—
749C23C2×(C2×D43)⋊C411yescharacteristic
750C23C2×(C2×D43)⋊C411yescharacteristic
751C23C2×(C2×D43)⋊C411yescharacteristic
752Q8—41no—
753Q8—862no—
754Q8—862no—
755Q8—862no—
756Q8—3441no—
757Q8—3441no—
758Q8—1722no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—862no—
763D4—3441no—
764D4—3441no—
765D4—1722no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—861no—
779C2×C4—861no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—3441no—
786C2×C4—3441no—
787C2×C4—1722no—
788C2×C4—1722no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4C2×(C2×D43)⋊C411yescharacteristic
792C2×C4C2×(C2×D43)⋊C411yescharacteristic
793C2×C4C2×(C2×D43)⋊C411yescharacteristic
794C2×C4C2×(C2×D43)⋊C411yescharacteristic
795C2×C4C2×(C2×D43)⋊C411yescharacteristic
796C2×C4C2×(C2×D43)⋊C411yescharacteristic
797C2×C4C2×(C2×D43)⋊C411yescharacteristic
798C2×C4C2×(C2×D43)⋊C411yescharacteristic
799C2×C4C2×(C2×D43)⋊C411yescharacteristic
800C2×C4C22×C4×D4311yescharacteristic
801C2×C4C22×C22⋊D4311yescharacteristic
802C2×C4C22×D17211yescharacteristic
803C8—22no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—1721no—
808C8—1721no—
809C8—1721no—
810C8—1721no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—1721no—
821C22—1721no—
822C22—1721no—
823C22C22×(C2×D43)⋊C411yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—1721no—
835C4—1721no—
836C4—1721no—
837C4—1721no—
838C4—1721no—
839C4—1721no—
840C4—1721no—
841C4#1458366512yes—
842C4#1458371111yescharacteristic
843C4#1458371611yescharacteristic
844C2—41no—
845C2—41no—
846C2—41no—
847C2—3441no—
848C2#1914303911yescharacteristic
849C2#1914312911yescharacteristic
850C2#1914314311yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2965C2
socleC22×C43C22×C22⋊C4
prime radical#14583477C4
cosocleC42×C43C24
hypercenter#2965D43
hypocenterC43#17506
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #19143712C2semidirect
3. #19133069C2semidirect
4. #19133061C2semidirect
5. #19133056C2semidirect
6. #19133051C2semidirect
7. #19133043C2semidirect
8. #19133035C2semidirect
9. #19133030C2semidirect
10. #19133025C2semidirect
11. #19133017C2semidirect
12. #19133009C2semidirect
13. #19133004C2semidirect
14. #19132999C2semidirect
15. C43×#2965C2semidirect
421. #2965D43semidirect
500. C43#17506semidirect

Maximal subgroups

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

subgroupindex
#191480222
#191437122
#191330692
#191330612
#191330562
#191330512
#191330432
#191330352
#191330302
#191330252
#191330172
#191330092
#191330042
#191329992
C43×#29652
#1750643