Finite Group Databasebeta

← C2×#19140018 #25266884

Subgroups — C2×#19140018 #25266884

Order 11008.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140018C2116yesmaximal, direct product factor
2C2×#14582839C211yesmaximal, characteristic, complemented
3C2×#14582830C211yesmaximal, characteristic, complemented
4C2×#14582823C211yesmaximal, characteristic
5C2×#14582821C211yesmaximal, characteristic
6C2×#14582796C211yesmaximal, characteristic, complemented
7C2×#14582796C211yesmaximal, characteristic, complemented
8C2×#14582794C211yesmaximal, characteristic, complemented
9C2×#14582788C211yesmaximal, characteristic
10C2×#14582788C211yesmaximal, characteristic
11C2×#14582782C211yesmaximal, characteristic, complemented
12C2×#14582773C211yesmaximal, characteristic
13C2×#14582770C211yesmaximal, characteristic
14C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×C4×D43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582839C2218yescomplemented
38#14582830C2218yescomplemented
39#14582823C2218yes—
40#14582821C2218yes—
41#14582796C2218yescomplemented
42#14582796C2218yescomplemented
43#14582794C2218yescomplemented
44#14582788C2218yes—
45#14582788C2218yes—
46#14582782C2218yescomplemented
47#14582773C2218yes—
48#14582770C2218yes—
49C4×Dic43⋊C4C2218yescomplemented
50C4×(C2×D43)⋊C4C2218yes—
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C22×C4⋊C4×C43C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C42×C43C2211yescharacteristic
62C43×#387C2218yescomplemented
63C2×#95×C43C2211yescharacteristic
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C24×D43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C22×C4×D43—24no—
76C22×C4×D43—42no—
77C22×C4×D43—42no—
78C22×C4×D43C2314yes—
79C2×C4⋊Dic43—24no—
80C2×C4⋊Dic43—42no—
81C2×C4⋊Dic43C2314yes—
82C2×C4⋊Dic43C2314yes—
83C2×Dic43⋊C4—24no—
84C2×Dic43⋊C4—24no—
85C2×Dic43⋊C4—24no—
86C2×Dic43⋊C4—24no—
87C2×Dic43⋊C4—24no—
88C2×Dic43⋊C4—42no—
89C2×Dic43⋊C4—42no—
90C2×Dic43⋊C4—42no—
91C2×Dic43⋊C4C2314yes—
92C2×Dic43⋊C4C2314yes—
93C2×Dic43⋊C4C2314yes—
94C2×Dic43⋊C4C2314yes—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2314yes—
97C2×Dic43⋊C4C2314yes—
98C2×Dic43⋊C4C2314yes—
99C2×(C2×D43)⋊C4—24no—
100C2×(C2×D43)⋊C4—24no—
101C2×(C2×D43)⋊C4—24no—
102C2×(C2×D43)⋊C4—42no—
103C2×(C2×D43)⋊C4—42no—
104C2×(C2×D43)⋊C4Q818yes—
105C2×(C2×D43)⋊C4C2314yes—
106C2×(C2×D43)⋊C4C2314yes—
107C2×(C2×D43)⋊C4C2314yes—
108C2×(C2×D43)⋊C4C2314yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×C4×Dic43—24no—
112C2×C4×Dic43—42no—
113C2×C4×Dic43—42no—
114C2×C4×Dic43C2314yes—
115C2×C4×Dic43C2314yes—
116C2×C4×Dic43C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—24no—
133C2×C4⋊C4×C43—42no—
134C2×C4⋊C4×C43C2314yes—
135C2×C4⋊C4×C43C2314yes—
136C2×C42×C43—42no—
137C2×C42×C43C2314yes—
138#95×C43C2314yes—
139#95×C43C2314yes—
140#95×C43C2314yes—
141#95×C43C2314yes—
142C24×C43C2411yescharacteristic
143C23×D43—22no—
144C23×D43—22no—
145C23×D43—22no—
146C23×D43—22no—
147C23×D43—22no—
148C23×D43—22no—
149C23×D43C2×Q814yes—
150C23×D43C2412yes—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43C2×Q814yes—
171C22×C4×C43#4114yes—
172C22×C4×C43C2412yes—
173C22×C4×C43C2412yes—
174C22×C4×C43C2412yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43C2×Q814yes—
197C22×Dic43#4114yes—
198C22×Dic43#4114yes—
199C22×Dic43#4114yes—
200C22×Dic43C2412yes—
201C22×Dic43C2412yes—
202C22×Dic43C2412yes—
203C22×Dic43C2412yes—
204C22×Dic43C2412yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C2×C4×D43—28no—
208C2×C4×D43—44no—
209C2×C4×D43—44no—
210C2×C4×D43—416no—
211C4⋊C4×C43—28no—
212C4⋊C4×C43—44no—
213C42×C43—44no—
214(C2×D43)⋊C4—28no—
215(C2×D43)⋊C4—28no—
216(C2×D43)⋊C4—28no—
217(C2×D43)⋊C4—44no—
218(C2×D43)⋊C4—44no—
219(C2×D43)⋊C4C2×Q8116yes—
220C4⋊Dic43—28no—
221C4⋊Dic43—44no—
222Dic43⋊C4—28no—
223Dic43⋊C4—28no—
224Dic43⋊C4—28no—
225Dic43⋊C4—28no—
226Dic43⋊C4—28no—
227Dic43⋊C4—44no—
228Dic43⋊C4—44no—
229Dic43⋊C4—44no—
230C4×Dic43—28no—
231C4×Dic43—44no—
232C4×Dic43—44no—
233C23×C43C22×Q812yes—
234C23×C43C2×#4112yes—
235C23×C43C2×#4112yes—
236C23×C43C2×#4112yes—
237C23×C43C2×#4112yes—
238C23×C43H(5,𝔽2)12yes—
239C23×C43H(5,𝔽2)12yes—
240C23×C43C2511yescharacteristic
241C22×D43—28no—
242C22×D43—28no—
243C22×D43—28no—
244C22×D43—22no—
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—22no—
250C22×D43—44no—
251C22×D43—44no—
252C22×D43—44no—
253C22×D43—44no—
254C22×D43C22×Q814yes—
255C2×C4×C43—28no—
256C2×C4×C43—28no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—44no—
277C2×C4×C43—44no—
278C2×C4×C43—44no—
279C2×C4×C43—44no—
280C2×C4×C43—44no—
281C2×C4×C43C22×Q814yes—
282C2×C4×C43C2×#4114yes—
283C2×Dic43—28no—
284C2×Dic43—28no—
285C2×Dic43—28no—
286C2×Dic43—28no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—44no—
305C2×Dic43—44no—
306C2×Dic43—44no—
307C2×Dic43C22×Q814yes—
308C2×Dic43C2×#4114yes—
309C2×Dic43C2×#4114yes—
310C2×Dic43C2×#4114yes—
311C4×D43—416no—
312C2×#2587—431nomaximal, Sylow
313C22×C43#52914yes—
314C22×C43#53314yes—
315C22×C43#53814yes—
316C22×C43#55314yes—
317C22×C43#55314yes—
318C22×C43#55414yes—
319C22×C43#55414yes—
320C22×C43C23×Q811yescharacteristic
321C22×C43C22×#4111yescharacteristic
322C22×C43C22×#4111yescharacteristic
323C22×C43C22×#4111yescharacteristic
324C22×C43C22×#4111yescharacteristic
325C22×C43C2×H(5,𝔽2)11yescharacteristic
326C22×C43C2×H(5,𝔽2)11yescharacteristic
327C2×D43—24no—
328C2×D43—24no—
329C2×D43—24no—
330C2×D43—416no—
331C2×D43—42no—
332C2×D43—42no—
333C2×D43—42no—
334C2×D43—42no—
335C4×C43—24no—
336C4×C43—24no—
337C4×C43—42no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43—42no—
341C4×C43—42no—
342Dic43—24no—
343Dic43—24no—
344Dic43—24no—
345Dic43—24no—
346Dic43—42no—
347Dic43—42no—
348Dic43—42no—
349#2587—4316no—
350C2×#400—431no—
351C2×#398—431no—
352C2×#396—431no—
353C2×#396—431no—
354C2×#389—431no—
355C2×#389—431no—
356C2×#389—431no—
357C2×#388—431no—
358C2×#388—431no—
359C2×#387—431no—
360C2×#387D4311yescharacteristic, complemented
361C2×#385—431no—
362C2×#385—431no—
363C2×C4×C4⋊C4—431no—
364C2×C4×C22⋊C4—431no—
365C2×C43#258718yescomplemented
366C2×C43C2×#52911yescharacteristic
367C2×C43C2×#53311yescharacteristic
368C2×C43C2×#53811yescharacteristic
369C2×C43C2×#55311yescharacteristic
370C2×C43C2×#55311yescharacteristic
371C2×C43C2×#55411yescharacteristic
372C2×C43C2×#55411yescharacteristic
373D43—44no—
374C24×C4—431no—
375C22×C4⋊C4—431no—
376C22×C4⋊C4—431no—
377C22×C4⋊C4—431no—
378C22×C4⋊C4—431no—
379C22×C4⋊C4—431no—
380C22×C4⋊C4—431no—
381C22×C4⋊C4—431no—
382C22×C4⋊C4—431no—
383C22×C4⋊C4—431no—
384C22×C4⋊C4—431no—
385C22×C4⋊C4C2×D4311yescharacteristic
386C22×C4⋊C4C2×D4311yescharacteristic
387C22×C22⋊C4—431no—
388C22×C22⋊C4—431no—
389C22×C22⋊C4—431no—
390C22×C22⋊C4—431no—
391C22×C22⋊C4—431no—
392C22×C22⋊C4—431no—
393C22×C42—431no—
394C22×C42—431no—
395C22×C42—431no—
396C22×C42C2×D4311yescharacteristic
397#400—438no—
398#398—438no—
399#396—438no—
400#396—438no—
401#389—438no—
402#389—438no—
403#389—438no—
404#388—438no—
405#388—438no—
406#387—438no—
407#387C2×D4318yescomplemented
408#385—438no—
409#385—438no—
410C4×C4⋊C4—438no—
411C4×C22⋊C4—438no—
412C2×#95—431no—
413C2×#95—431no—
414C2×#95—431no—
415C2×#95—431no—
416C2×#95—431no—
417C2×#95—431no—
418C2×#95—431no—
419C2×#95—431no—
420C2×#95C2×D4311yescharacteristic
421C2×#95C2×D4311yescharacteristic
422C2×#95C2×D4311yescharacteristic
423C2×#95C2×D4311yescharacteristic
424C43C2×#258711yescharacteristic, complemented, Sylow
425C25—431no—
426C23×C4—431no—
427C23×C4—431no—
428C23×C4—431no—
429C23×C4—431no—
430C23×C4—431no—
431C23×C4—431no—
432C23×C4—431no—
433C23×C4—434no—
434C23×C4—864no—
435C23×C4—1722no—
436C23×C4—1722no—
437C23×C4C22×D4311yescharacteristic
438C23×C4C22×D4311yescharacteristic
439C23×C4C22×D4311yescharacteristic
440C23×C4C22×D4311yescharacteristic
441C23×C4C22×D4311yescharacteristic
442C23×C4C22×D4311yescharacteristic
443C23×C4C22×D4311yescharacteristic
444C2×C4⋊C4—24no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—434no—
447C2×C4⋊C4—434no—
448C2×C4⋊C4—434no—
449C2×C4⋊C4—434no—
450C2×C4⋊C4—434no—
451C2×C4⋊C4—434no—
452C2×C4⋊C4—434no—
453C2×C4⋊C4—434no—
454C2×C4⋊C4—434no—
455C2×C4⋊C4—434no—
456C2×C4⋊C4—864no—
457C2×C4⋊C4—864no—
458C2×C4⋊C4—864no—
459C2×C4⋊C4—864no—
460C2×C4⋊C4—864no—
461C2×C4⋊C4—864no—
462C2×C4⋊C4—1722no—
463C2×C4⋊C4—1722no—
464C2×C4⋊C4—1722no—
465C2×C4⋊C4—1722no—
466C2×C4⋊C4C22×D4314yes—
467C2×C4⋊C4C22×D4314yes—
468C2×C22⋊C4—438no—
469C2×C22⋊C4—434no—
470C2×C22⋊C4—434no—
471C2×C22⋊C4—434no—
472C2×C22⋊C4—434no—
473C2×C22⋊C4—434no—
474C2×C22⋊C4—434no—
475C2×C22⋊C4—864no—
476C2×C22⋊C4—864no—
477C2×C22⋊C4—864no—
478C2×C22⋊C4—1722no—
479C2×C22⋊C4—1722no—
480C2×C42—42no—
481C2×C42—434no—
482C2×C42—434no—
483C2×C42—434no—
484C2×C42—864no—
485C2×C42—1722no—
486C2×C42—1722no—
487C2×C42C22×D4314yes—
488#95—434no—
489#95—434no—
490#95—434no—
491#95—434no—
492#95—434no—
493#95—434no—
494#95—434no—
495#95—434no—
496#95C22×D4314yes—
497#95C22×D4314yes—
498#95C22×D4314yes—
499#95C22×D4314yes—
500C24—434no—
501C24—432no—
502C24—862no—
503C24—862no—
504C24—862no—
505C24—862no—
506C24—862no—
507C24—862no—
508C24C23×D4311yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—434no—
529C22×C4—434no—
530C22×C4—434no—
531C22×C4—434no—
532C22×C4—432no—
533C22×C4—432no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—432no—
537C22×C4—432no—
538C22×C4—432no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—868no—
557C22×C4—1724no—
558C22×C4—1724no—
559C22×C4—17216no—
560C22×C4#1062189814yes—
561C22×C4Q8×D4314yes—
562C22×C4C23×D4312yes—
563C22×C4C23×D4312yes—
564C22×C4C23×D4312yes—
565C22×C4C23×D4312yes—
566C22×C4C23×D4312yes—
567C22×C4C23×D4312yes—
568C22×C4C23×D4312yes—
569C4⋊C4—28no—
570C4⋊C4—44no—
571C4⋊C4—868no—
572C4⋊C4—868no—
573C4⋊C4—868no—
574C4⋊C4—868no—
575C4⋊C4—868no—
576C4⋊C4—868no—
577C4⋊C4—1724no—
578C4⋊C4—1724no—
579C4⋊C4—1724no—
580C4⋊C4—1724no—
581C22⋊C4—4316no—
582C22⋊C4—868no—
583C22⋊C4—868no—
584C22⋊C4—868no—
585C22⋊C4—1724no—
586C22⋊C4—1724no—
587C42—44no—
588C42—868no—
589C42—1724no—
590C42—1724no—
591C23—434no—
592C23—868no—
593C23—868no—
594C23—868no—
595C23—862no—
596C23—862no—
597C23—862no—
598C23—862no—
599C23—862no—
600C23—862no—
601C23—1724no—
602C23—1724no—
603C23—1724no—
604C23—1724no—
605C23C2×Q8×D4312yes—
606C23#41×D4312yes—
607C23#41×D4312yes—
608C23#41×D4312yes—
609C23C2×#1062189812yes—
610C23#1306337012yes—
611C23#1306337112yes—
612C23C24×D4311yescharacteristic
613C2×C4—28no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—434no—
640C2×C4—434no—
641C2×C4—434no—
642C2×C4—434no—
643C2×C4—868no—
644C2×C4—868no—
645C2×C4—868no—
646C2×C4—868no—
647C2×C4—862no—
648C2×C4—862no—
649C2×C4—862no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—17216no—
665C2×C4—1724no—
666C2×C4—1724no—
667C2×C4—1724no—
668C2×C4C2×Q8×D4314yes—
669C2×C4C2×#1062189814yes—
670C22—864no—
671C22—864no—
672C22—864no—
673C22—1722no—
674C22—1722no—
675C22—1722no—
676C22—1722no—
677C22—17216no—
678C22#1458342714yes—
679C22#1458345314yes—
680C22#1458348214yes—
681C22#1458359414yes—
682C22#1458360014yes—
683C22#1458360314yes—
684C22#1458360514yes—
685C22C22×Q8×D4311yescharacteristic
686C22C2×#41×D4311yescharacteristic
687C22C2×#41×D4311yescharacteristic
688C22C2×#41×D4311yescharacteristic
689C22C22×#1062189811yescharacteristic
690C22C2×#1306337011yescharacteristic
691C22C2×#1306337111yescharacteristic
692C4—24no—
693C4—24no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—864no—
700C4—864no—
701C4—864no—
702C4—864no—
703C4—1722no—
704C4—1722no—
705C4—1722no—
706C2—1724no—
707C2#1914001818yesdirect product factor
708C2C2×#1458342711yescharacteristic
709C2C2×#1458345311yescharacteristic
710C2C2×#1458348211yescharacteristic
711C2C2×#1458359411yescharacteristic
712C2C2×#1458360011yescharacteristic
713C2C2×#1458360311yescharacteristic
714C2C2×#1458360511yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#387D43
hypocenterC43C2×#2587
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #19140018C2direct (N × H)
2. C2×#14582839C2semidirect
3. C2×#14582830C2semidirect
6. C2×#14582796C2semidirect
7. C2×#14582796C2semidirect
8. C2×#14582794C2semidirect
11. C2×#14582782C2semidirect
14. C2×C4×Dic43⋊C4C2semidirect
16. C2×C43×#387C2semidirect
37. #14582839C22semidirect
38. #14582830C22semidirect
41. #14582796C22semidirect
42. #14582796C22semidirect
43. #14582794C22semidirect
46. #14582782C22semidirect
49. C4×Dic43⋊C4C22semidirect
62. C43×#387C22semidirect
360. C2×#387D43semidirect
365. C2×C43#2587semidirect
407. #387C2×D43semidirect
424. C43C2×#2587semidirect
707. C2#19140018direct (N × H)

Maximal subgroups

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

subgroupindex
#191400182
C2×#145828392
C2×#145828302
C2×#145828232
C2×#145828212
C2×#145827962
C2×#145827942
C2×#145827882
C2×#145827822
C2×#145827732
C2×#145827702
C2×C4×Dic43⋊C42
C2×C4×(C2×D43)⋊C42
C2×C43×#3872
C2×#258743