Finite Group Databasebeta

← #25065538

Subgroups — #25065538

Order 11008.

870 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148481C211yesmaximal, characteristic
2#19143720C211yesmaximal, characteristic
3#19133326C211yesmaximal, characteristic, complemented
4#19133323C211yesmaximal, characteristic, complemented
5#19133320C211yesmaximal, characteristic, complemented
6#19133306C211yesmaximal, characteristic, complemented
7#19133303C211yesmaximal, characteristic, complemented
8#19133296C211yesmaximal, characteristic, complemented
9#19133293C211yesmaximal, characteristic, complemented
10#19133286C211yesmaximal, characteristic, complemented
11#19133283C211yesmaximal, characteristic, complemented
12#19133253C211yesmaximal, characteristic, complemented
13#19133250C211yesmaximal, characteristic, complemented
14C2×#14582647C211yesmaximal, characteristic, complemented
15C43×#2990C211yesmaximal, characteristic
16#14583627—21no—
17#14583627—21no—
18#14583619—21no—
19#14583619—21no—
20#14583589—21no—
21#14583589—21no—
22#14583589—21no—
23#14583589—21no—
24#14583511C412yes—
25#14583511C412yes—
26#14583470C412yes—
27#14583456C2211yescharacteristic
28#14583456C2211yescharacteristic
29#14583456C2211yescharacteristic
30#14583456C2211yescharacteristic
31#14583456C2211yescharacteristic
32C2×#13063325C2211yescharacteristic
33#14583376C412yes—
34#14583030—21no—
35#14582971—21no—
36#14582971—21no—
37D4×C43⋊C8—21no—
38#14582956C2211yescharacteristic
39#14582956C2211yescharacteristic
40#14582952C2211yescharacteristic
41#14582923C2211yescharacteristic
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582647C2211yescharacteristic
45#14582647C2211yescharacteristic
46#14582647C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C4×#41×C43C2211yescharacteristic
61C43×#446—21no—
62C43×#435—21no—
63C43×#435—21no—
64C8×D4×C43—21no—
65C43×#432C2211yescharacteristic
66C43×#432C2211yescharacteristic
67C43×#431C2211yescharacteristic
68C43×#423C2211yescharacteristic
69C2×C4⋊C8×C43C2211yescharacteristic
70C2×C4⋊C8×C43C2211yescharacteristic
71C22×Dic86C2×C412yes—
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75#13063325—21no—
76#13063325—21no—
77#13063325C2×C412yes—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063323—22no—
83#13063318—22no—
84#13063318—22no—
85#13063318—22no—
86#13063318—22no—
87#13063317—21no—
88#13063317—21no—
89#13063317—21no—
90#13063317—21no—
91#13063317C2×C412yes—
92#13063315—22no—
93#13063315—22no—
94#13063315—22no—
95#13063315—22no—
96#13063312—22no—
97#13063306—22no—
98#13063306—22no—
99#13063304—21no—
100#13063304—21no—
101#13063304—21no—
102#13063304—21no—
103#13063304—21no—
104#13063304—21no—
105#13063304C2×C412yes—
106#13063304C2×C412yes—
107#13063304C2×C412yes—
108#13063304C2×C412yes—
109C4×Dic86—21no—
110C4×Dic86—21no—
111C4×Dic86—21no—
112C4×Dic86—21no—
113C4×Dic86—21no—
114C4×Dic86—21no—
115C4×Dic86C2×C412yes—
116C4×Dic86C2×C412yes—
117C4×Dic86C2×C412yes—
118C4×Dic86C2×C412yes—
119#13063290—22no—
120#13063290—22no—
121#13063284—21no—
122#13063284—21no—
123#13063284—21no—
124#13063284—21no—
125#13063284C2×C412yes—
126#13063281—22no—
127#13063281—22no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C4⋊(C43⋊C8)—21no—
131C4⋊(C43⋊C8)—21no—
132C4⋊(C43⋊C8)—21no—
133C4⋊(C43⋊C8)C2311yescharacteristic
134C4⋊(C43⋊C8)C2311yescharacteristic
135C4⋊(C43⋊C8)C2311yescharacteristic
136C4⋊(C43⋊C8)C2311yescharacteristic
137C22⋊(C43⋊C8)—21no—
138C22⋊(C43⋊C8)—21no—
139C22⋊(C43⋊C8)—21no—
140#13063236—21no—
141#13063236—21no—
142C4×C43⋊C8—21no—
143C2×#41×C43C2×C411yescharacteristic
144C2×M16×C43—21no—
145C22×C8×C43—21no—
146C22×C8×C43—21no—
147C4×Q8×C43D411yescharacteristic
148C4×Q8×C43D411yescharacteristic
149C4×D4×C43D411yescharacteristic
150C4×D4×C43D411yescharacteristic
151C4×D4×C43D411yescharacteristic
152C4×D4×C43D411yescharacteristic
153C4×D4×C43D411yescharacteristic
154C4×D4×C43D411yescharacteristic
155#117×C43C2×C411yescharacteristic
156#117×C43C2×C411yescharacteristic
157#117×C43C2×C411yescharacteristic
158C2×C42×C43C2311yescharacteristic
159C2×C42×C43C2311yescharacteristic
160C2×C42×C43C2311yescharacteristic
161C4⋊C8×C43—21no—
162C4⋊C8×C43—21no—
163C4⋊C8×C43—21no—
164C4⋊C8×C43C2311yescharacteristic
165C4⋊C8×C43C2311yescharacteristic
166C4⋊C8×C43C2311yescharacteristic
167C4⋊C8×C43C2311yescharacteristic
168C22⋊C8×C43—21no—
169C22⋊C8×C43—21no—
170C22⋊C8×C43—21no—
171#97×C43—21no—
172#97×C43—21no—
173C4×C8×C43—21no—
174#41×C43—42no—
175C2×Q8×C43C22⋊C411yescharacteristic
176C2×D4×C43C22⋊C411yescharacteristic
177C2×D4×C43C22⋊C411yescharacteristic
178C2×D4×C43C22⋊C411yescharacteristic
179C22×C4×C43C22×C411yescharacteristic
180C22×C4×C43C22×C411yescharacteristic
181C22×C4×C43C22×C411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×Dic43—22no—
189C2×Dic86—22no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—44no—
193C2×Dic86C22×C412yes—
194C2×Dic86C22×C412yes—
195M16×C43—81no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—81no—
201C2×C8×C43—81no—
202C4⋊C4×C43C22⋊C411yescharacteristic
203C4⋊C4×C43C22⋊C411yescharacteristic
204C4⋊C4×C43C22⋊C411yescharacteristic
205C4⋊C4×C43C22⋊C411yescharacteristic
206C4⋊C4×C43C22⋊C411yescharacteristic
207C4⋊C4×C43C22⋊C411yescharacteristic
208C22⋊C4×C43C22⋊C411yescharacteristic
209C22⋊C4×C43C22⋊C411yescharacteristic
210C22⋊C4×C43C22⋊C411yescharacteristic
211C22⋊C4×C43C22⋊C411yescharacteristic
212C22⋊C4×C43C22⋊C411yescharacteristic
213C22⋊C4×C43C22⋊C411yescharacteristic
214C42×C43C22×C411yescharacteristic
215C42×C43C22×C411yescharacteristic
216C42×C43C22×C411yescharacteristic
217C42×C43C2×D411yescharacteristic
218C42×C43C2×D411yescharacteristic
219C42×C43C2×D411yescharacteristic
220C42×C43C2×D411yescharacteristic
221C42×C43C2×D411yescharacteristic
222C42×C43C2×D411yescharacteristic
223C42×C43C2411yescharacteristic
224C22⋊Dic43—22no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—22no—
228C22⋊Dic43—22no—
229C4⋊Dic43—22no—
230C4⋊Dic43—22no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43C22×C412yes—
238C4⋊Dic43C22×C412yes—
239Dic43⋊C4—22no—
240Dic43⋊C4—22no—
241Dic43⋊C4—22no—
242Dic43⋊C4—22no—
243Dic43⋊C4—22no—
244Dic43⋊C4—22no—
245Dic43⋊C4—22no—
246Dic43⋊C4—22no—
247Dic43⋊C4—22no—
248Dic43⋊C4—22no—
249C4×Dic43—22no—
250C4×Dic43—22no—
251C4×Dic43—22no—
252C4×Dic43—22no—
253C4×Dic43—22no—
254#10621877—81no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—81no—
260C2×C43⋊C8—81no—
261C23×C43C2×C22⋊C411yescharacteristic
262C23×C43C2×C22⋊C411yescharacteristic
263C23×C43C2×C22⋊C411yescharacteristic
264Q8×C43—41no—
265D4×C43—22no—
266D4×C43—22no—
267D4×C43—41no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43C2×C22⋊C411yescharacteristic
284C2×C4×C43C2×C22⋊C411yescharacteristic
285C2×C4×C43C2×C22⋊C411yescharacteristic
286C2×C4×C43C2×C22⋊C411yescharacteristic
287C2×C4×C43C2×C22⋊C411yescharacteristic
288C2×C4×C43C2×C22⋊C411yescharacteristic
289C2×C4×C43C2×C22⋊C411yescharacteristic
290C2×C4×C43C2×C22⋊C411yescharacteristic
291C2×C4×C43C2×C22⋊C411yescharacteristic
292C2×C4×C43C23×C411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—44no—
300Dic86—44no—
301Dic86—41no—
302Dic86—41no—
303Dic86—41no—
304Dic86—41no—
305Dic86—42no—
306Dic86—42no—
307C8×C43—41no—
308C8×C43—41no—
309C8×C43—41no—
310C8×C43—41no—
311C43⋊C8—41no—
312C43⋊C8—41no—
313C43⋊C8—41no—
314C43⋊C8—41no—
315#17780—431nomaximal, Sylow
316C22×C43—21no—
317C22×C43—21no—
318C22×C43—21no—
319C22×C43—21no—
320C22×C43—21no—
321C22×C43—21no—
322C22×C43—21no—
323C22×C43—21no—
324C22×C43#41312yes—
325C22×C43C22×C22⋊C411yescharacteristic
326C4×C43—21no—
327C4×C43—21no—
328C4×C43—21no—
329C4×C43—21no—
330C4×C43—21no—
331C4×C43—21no—
332C4×C43—21no—
333C4×C43—21no—
334C4×C43—21no—
335C4×C43—21no—
336C4×C43#57711yescharacteristic
337C4×C43#57711yescharacteristic
338C4×C43#57811yescharacteristic
339C4×C43#57811yescharacteristic
340Dic43—42no—
341Dic43—42no—
342Dic43—42no—
343Dic43—42no—
344#3509—431no—
345#2990—431no—
346#2990D4311yescharacteristic
347#1559—431no—
348#1559—431no—
349#1558—431no—
350#1554—431no—
351#1554—431no—
352#1552—431no—
353#1552—431no—
354#1550—431no—
355#1550—431no—
356#1542—431no—
357#1542—431no—
358C2×#333—431no—
359C2×C43—22no—
360C2×C43—41no—
361C2×C43—41no—
362C2×C43C2×#41311yescharacteristic
363C2×C43#289811yescharacteristic
364C2×C43#289811yescharacteristic
365#557—861no—
366#557—861no—
367#556—861no—
368#556—861no—
369#552—861no—
370#552—861no—
371#552—861no—
372#552—861no—
373#541—432no—
374#541—432no—
375#536—432no—
376#533—431no—
377#533—431no—
378#533—431no—
379#533—431no—
380#533—431no—
381C2×C4⋊Q8—431no—
382#519—432no—
383C4×#41C2×D4311yescharacteristic
384#446—21no—
385#446—861no—
386#435—21no—
387#435—21no—
388#435—861no—
389#435—861no—
390C8×D4—21no—
391C8×D4—861no—
392#432—431no—
393#432—431no—
394#432C2×D4311yescharacteristic
395#432C2×D4311yescharacteristic
396#431—431no—
397#431C2×D4311yescharacteristic
398#423—431no—
399#423C2×D4311yescharacteristic
400C2×C4⋊C8—431no—
401C2×C4⋊C8—431no—
402C2×C4⋊C8C2×D4311yescharacteristic
403C2×C4⋊C8C2×D4311yescharacteristic
404#333—431no—
405#333—431no—
406#333—431no—
407#333—431no—
408#333—431no—
409#333—431no—
410#333—431no—
411#333—431no—
412#332—431no—
413#332—431no—
414#332—431no—
415#332—431no—
416#332—431no—
417#332—431no—
418#332—431no—
419#332—431no—
420C43#1778011yescharacteristic, complemented, Sylow
421C2×#41C4×D4311yescharacteristic
422C22×Q8—432no—
423C2×M16—21no—
424C2×M16—861no—
425C22×C8—21no—
426C22×C8—21no—
427C22×C8—861no—
428C22×C8—861no—
429C4⋊Q8—432no—
430C4⋊Q8—431no—
431C4⋊Q8—431no—
432C4⋊Q8—431no—
433C4⋊Q8—431no—
434C4⋊Q8—862no—
435C4⋊Q8—861no—
436C4⋊Q8—861no—
437#126—862no—
438#126—862no—
439#126—862no—
440#126—862no—
441#125—432no—
442#125—862no—
443#125—862no—
444#125—862no—
445#125—862no—
446#125—861no—
447#125—861no—
448#125—861no—
449#125—861no—
450#124—862no—
451#123—862no—
452#123—862no—
453C22⋊Q8—432no—
454C22⋊Q8—432no—
455C22⋊Q8—432no—
456C22⋊Q8—432no—
457C22⋊Q8—861no—
458C22⋊Q8—861no—
459C22⋊Q8—861no—
460C22⋊Q8—861no—
461C22⋊Q8—861no—
462C22⋊Q8—861no—
463C4×Q8—432no—
464C4×Q8—432no—
465C4×Q8—432no—
466C4×Q8—432no—
467C4×Q8—862no—
468C4×Q8—862no—
469C4×Q8—861no—
470C4×Q8—861no—
471C4×Q8—861no—
472C4×Q8—861no—
473C4×Q8—861no—
474C4×Q8—861no—
475C4×Q8D17211yescharacteristic
476C4×Q8C22⋊D4311yescharacteristic
477C4×D4D17211yescharacteristic
478C4×D4D17211yescharacteristic
479C4×D4D17211yescharacteristic
480C4×D4C22⋊D4311yescharacteristic
481C4×D4C22⋊D4311yescharacteristic
482C4×D4C22⋊D4311yescharacteristic
483#117—432no—
484#117—861no—
485#117—861no—
486#117—861no—
487#117—861no—
488#117—862no—
489#117—862no—
490#117C4×D4311yescharacteristic
491#117C4×D4311yescharacteristic
492#117C4×D4311yescharacteristic
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C42C22×D4311yescharacteristic
496C2×C42C22×D4311yescharacteristic
497C2×C42C22×D4311yescharacteristic
498C4⋊C8—21no—
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—431no—
502C4⋊C8—431no—
503C4⋊C8—431no—
504C4⋊C8—431no—
505C4⋊C8—861no—
506C4⋊C8—861no—
507C4⋊C8—861no—
508C4⋊C8C22×D4311yescharacteristic
509C4⋊C8C22×D4311yescharacteristic
510C4⋊C8C22×D4311yescharacteristic
511C4⋊C8C22×D4311yescharacteristic
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—861no—
516C22⋊C8—861no—
517C22⋊C8—861no—
518#97—21no—
519#97—21no—
520#97—861no—
521#97—861no—
522C4×C8—21no—
523C4×C8—861no—
524#41—42no—
525C2×Q8—432no—
526C2×Q8—432no—
527C2×Q8—862no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—1724no—
531C2×Q8(C2×D43)⋊C411yescharacteristic
532C2×D4(C2×D43)⋊C411yescharacteristic
533C2×D4(C2×D43)⋊C411yescharacteristic
534C2×D4(C2×D43)⋊C411yescharacteristic
535C22×C4—862no—
536C22×C4C2×C4×D4311yescharacteristic
537C22×C4C2×C4×D4311yescharacteristic
538C22×C4C2×C4×D4311yescharacteristic
539C22×C4C2×D17211yescharacteristic
540C22×C4C2×D17211yescharacteristic
541C22×C4C2×D17211yescharacteristic
542C22×C4C2×C22⋊D4311yescharacteristic
543C22×C4C2×C22⋊D4311yescharacteristic
544C22×C4C2×C22⋊D4311yescharacteristic
545M16—81no—
546M16—3441no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—81no—
552C2×C8—81no—
553C2×C8—861no—
554C2×C8—861no—
555C2×C8—861no—
556C2×C8—861no—
557C2×C8—3441no—
558C2×C8—3441no—
559C4⋊C4—432no—
560C4⋊C4—432no—
561C4⋊C4—862no—
562C4⋊C4—862no—
563C4⋊C4—862no—
564C4⋊C4—862no—
565C4⋊C4—862no—
566C4⋊C4—862no—
567C4⋊C4—862no—
568C4⋊C4—862no—
569C4⋊C4—862no—
570C4⋊C4—862no—
571C4⋊C4—862no—
572C4⋊C4—862no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4(C2×D43)⋊C411yescharacteristic
580C4⋊C4(C2×D43)⋊C411yescharacteristic
581C4⋊C4(C2×D43)⋊C411yescharacteristic
582C4⋊C4(C2×D43)⋊C411yescharacteristic
583C4⋊C4(C2×D43)⋊C411yescharacteristic
584C4⋊C4(C2×D43)⋊C411yescharacteristic
585C22⋊C4—862no—
586C22⋊C4—862no—
587C22⋊C4—862no—
588C22⋊C4—862no—
589C22⋊C4—862no—
590C22⋊C4(C2×D43)⋊C411yescharacteristic
591C22⋊C4(C2×D43)⋊C411yescharacteristic
592C22⋊C4(C2×D43)⋊C411yescharacteristic
593C22⋊C4(C2×D43)⋊C411yescharacteristic
594C22⋊C4(C2×D43)⋊C411yescharacteristic
595C22⋊C4(C2×D43)⋊C411yescharacteristic
596C42—862no—
597C42—862no—
598C42—862no—
599C42—862no—
600C42—862no—
601C42C2×C4×D4311yescharacteristic
602C42C2×C4×D4311yescharacteristic
603C42C2×C4×D4311yescharacteristic
604C42C2×D17211yescharacteristic
605C42C2×D17211yescharacteristic
606C42C2×D17211yescharacteristic
607C42C2×C22⋊D4311yescharacteristic
608C42C2×C22⋊D4311yescharacteristic
609C42C2×C22⋊D4311yescharacteristic
610C42C23×D4311yescharacteristic
611C23C2×(C2×D43)⋊C411yescharacteristic
612C23C2×(C2×D43)⋊C411yescharacteristic
613C23C2×(C2×D43)⋊C411yescharacteristic
614Q8—41no—
615Q8—1722no—
616Q8—1722no—
617Q8—1724no—
618Q8—1721no—
619Q8—1721no—
620Q8—1721no—
621Q8—1721no—
622D4—22no—
623D4—22no—
624D4—41no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—862no—
643C2×C4—862no—
644C2×C4—1724no—
645C2×C4C2×(C2×D43)⋊C411yescharacteristic
646C2×C4C2×(C2×D43)⋊C411yescharacteristic
647C2×C4C2×(C2×D43)⋊C411yescharacteristic
648C2×C4C2×(C2×D43)⋊C411yescharacteristic
649C2×C4C2×(C2×D43)⋊C411yescharacteristic
650C2×C4C2×(C2×D43)⋊C411yescharacteristic
651C2×C4C2×(C2×D43)⋊C411yescharacteristic
652C2×C4C2×(C2×D43)⋊C411yescharacteristic
653C2×C4C2×(C2×D43)⋊C411yescharacteristic
654C2×C4C22×C4×D4311yescharacteristic
655C2×C4C22×C22⋊D4311yescharacteristic
656C2×C4C22×D17211yescharacteristic
657C8—41no—
658C8—41no—
659C8—41no—
660C8—41no—
661C8—1721no—
662C8—1721no—
663C8—1721no—
664C8—1721no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22#1458288112yes—
674C22C22×(C2×D43)⋊C411yescharacteristic
675C4—21no—
676C4—21no—
677C4—21no—
678C4—21no—
679C4—21no—
680C4—21no—
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—1722no—
686C4—1722no—
687C4—1722no—
688C4—1722no—
689C4#1458371011yescharacteristic
690C4#1458371111yescharacteristic
691C4#1458371411yescharacteristic
692C4#1458371611yescharacteristic
693C2—22no—
694C2—41no—
695C2—41no—
696C2C2×#1458288111yescharacteristic
697C2#1914312511yescharacteristic
698C2#1914312911yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2990C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#41×C43C2×C4
cosocleC42×C43C24
hypercenter#2990D43
hypocenterC43#17780
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
3. #19133326C2semidirect
4. #19133323C2semidirect
5. #19133320C2semidirect
6. #19133306C2semidirect
7. #19133303C2semidirect
8. #19133296C2semidirect
9. #19133293C2semidirect
10. #19133286C2semidirect
11. #19133283C2semidirect
12. #19133253C2semidirect
13. #19133250C2semidirect
14. C2×#14582647C2semidirect
420. C43#17780semidirect

Maximal subgroups

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

subgroupindex
#191484812
#191437202
#191333262
#191333232
#191333202
#191333062
#191333032
#191332962
#191332932
#191332862
#191332832
#191332532
#191332502
C2×#145826472
C43×#29902
#1778043