Finite Group Databasebeta

← C2×#19139273 #25265690

Subgroups — C2×#19139273 #25265690

Order 11008.

2466 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063319C211yesmaximal, characteristic
2C22×#13063315C211yesmaximal, characteristic, complemented
3#19139273C2116yesmaximal, direct product factor
4C2×#14582834C211yesmaximal, characteristic
5C2×#14582833C211yesmaximal, characteristic, complemented
6C2×#14582833C211yesmaximal, characteristic, complemented
7C2×#14582823C211yesmaximal, characteristic
8C2×#14582795C211yesmaximal, characteristic, complemented
9C2×#14582791C211yesmaximal, characteristic
10C2×#14582791C211yesmaximal, characteristic
11C2×#14582789C211yesmaximal, characteristic
12C2×#14582788C211yesmaximal, characteristic
13C2×#14582763C211yesmaximal, characteristic, complemented
14C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
15C2×#14582750C211yesmaximal, characteristic, complemented
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C2×#13063319—28no—
18C2×#13063319C2218yes—
19C2×#13063315—28no—
20C2×#13063315C2218yescomplemented
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43#14582834C2218yes—
44#14582833C2218yescomplemented
45#14582833C2218yescomplemented
46#14582823C2218yes—
47#14582795C2218yescomplemented
48#14582791C2218yes—
49#14582791C2218yes—
50#14582789C2218yes—
51#14582788C2218yes—
52#14582763C2218yescomplemented
53C4×Dic43⋊C4C2218yescomplemented
54#14582750C2218yescomplemented
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C42×C43C2211yescharacteristic
64C43×#387C2218yescomplemented
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77#13063319—232no—
78#13063315—232no—
79C2×C4⋊Dic43—24no—
80C2×C4⋊Dic43—24no—
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—24no—
89C2×Dic43⋊C4—24no—
90C2×Dic43⋊C4—24no—
91C2×Dic43⋊C4D418yes—
92C2×Dic43⋊C4C2314yes—
93C2×Dic43⋊C4C2314yes—
94C2×Dic43⋊C4C2314yes—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2314yes—
97C2×Dic43⋊C4C2314yes—
98C2×Dic43⋊C4C2314yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×(C2×D43)⋊C4—24no—
102C2×(C2×D43)⋊C4—24no—
103C2×(C2×D43)⋊C4—24no—
104C2×(C2×D43)⋊C4—24no—
105C2×(C2×D43)⋊C4—24no—
106C2×(C2×D43)⋊C4—24no—
107C2×(C2×D43)⋊C4—24no—
108C2×(C2×D43)⋊C4C2314yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×C4×Dic43—24no—
116C2×C4×Dic43—24no—
117C2×C4×Dic43—24no—
118C2×C4×Dic43—24no—
119C2×C4×Dic43C2314yes—
120C2×C4×Dic43C2314yes—
121C2×C4×Dic43C2314yes—
122C2×C4×Dic43C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43—24no—
137C2×C4⋊C4×C43—24no—
138C2×C4⋊C4×C43C2314yes—
139C2×C4⋊C4×C43C2314yes—
140C2×C42×C43—24no—
141C2×C42×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144#95×C43C2314yes—
145#95×C43C2314yes—
146C24×C43C2411yescharacteristic
147C23×D43—22no—
148C23×D43—22no—
149C23×D43—22no—
150C23×D43—22no—
151C23×D43—22no—
152C23×D43—22no—
153C23×D43—22no—
154C23×D43C2412yes—
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×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43C2×D414yes—
175C22×C4×C43#4114yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2412yes—
181C22×C4×C43C2412yes—
182C22×C4×C43C2412yes—
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×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43C2×D414yes—
200C22×Dic43C2×D414yes—
201C22×Dic43#4114yes—
202C22×Dic43#4114yes—
203C22×Dic43#4114yes—
204C22×Dic43C2412yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C22×Dic43C2412yes—
210C22×Dic43C2412yes—
211C4⋊C4×C43—28no—
212C4⋊C4×C43—28no—
213C42×C43—28no—
214(C2×D43)⋊C4—28no—
215(C2×D43)⋊C4—28no—
216(C2×D43)⋊C4—28no—
217(C2×D43)⋊C4—28no—
218(C2×D43)⋊C4—28no—
219(C2×D43)⋊C4—28no—
220(C2×D43)⋊C4—28no—
221C4⋊Dic43—28no—
222C4⋊Dic43—28no—
223Dic43⋊C4—28no—
224Dic43⋊C4—28no—
225Dic43⋊C4—28no—
226Dic43⋊C4—28no—
227Dic43⋊C4—28no—
228Dic43⋊C4—28no—
229Dic43⋊C4—28no—
230Dic43⋊C4—28no—
231Dic43⋊C4C2×D4116yes—
232C4×Dic43—28no—
233C4×Dic43—28no—
234C4×Dic43—28no—
235C4×Dic43—28no—
236C23×C43C22×D412yes—
237C23×C43C2×#4112yes—
238C23×C43C2×#4112yes—
239C23×C43C2×#4112yes—
240C23×C43C2×#4112yes—
241C23×C432−1+412yes—
242C23×C432−1+412yes—
243C23×C43C2511yescharacteristic
244C22×D43—22no—
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—22no—
250C22×D43—22no—
251C22×D43—44no—
252C22×D43—44no—
253C22×D43—44no—
254C22×D43—44no—
255C22×D43—44no—
256C22×D43—44no—
257C22×D43—44no—
258C2×C4×C43—28no—
259C2×C4×C43—28no—
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—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—44no—
280C2×C4×C43—44no—
281C2×C4×C43—44no—
282C2×C4×C43—44no—
283C2×C4×C43—44no—
284C2×C4×C43C22×D414yes—
285C2×C4×C43C2×#4114yes—
286C2×Dic43—28no—
287C2×Dic43—28no—
288C2×Dic43—28no—
289C2×Dic43—28no—
290C2×Dic43—28no—
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—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—44no—
308C2×Dic43—44no—
309C2×Dic43C22×D414yes—
310C2×Dic43C22×D414yes—
311C2×Dic43C2×#4114yes—
312C2×Dic43C2×#4114yes—
313C2×Dic43C2×#4114yes—
314C2×#2519—431nomaximal, Sylow
315C22×C43#52914yes—
316C22×C43#53214yes—
317C22×C43#54114yes—
318C22×C43#54714yes—
319C22×C43#54814yes—
320C22×C43#55214yes—
321C22×C43#55214yes—
322C22×C43C23×D411yescharacteristic
323C22×C43C22×#4111yescharacteristic
324C22×C43C22×#4111yescharacteristic
325C22×C43C22×#4111yescharacteristic
326C22×C43C22×#4111yescharacteristic
327C22×C43C2×2−1+411yescharacteristic
328C22×C43C2×2−1+411yescharacteristic
329C2×D43—42no—
330C2×D43—42no—
331C2×D43—42no—
332C2×D43—42no—
333C2×D43—42no—
334C2×D43—42no—
335C2×D43—42no—
336C2×D43—88no—
337C4×C43—24no—
338C4×C43—24no—
339C4×C43—42no—
340C4×C43—42no—
341C4×C43—42no—
342C4×C43—42no—
343C4×C43—42no—
344Dic43—24no—
345Dic43—24no—
346Dic43—24no—
347Dic43—24no—
348Dic43—24no—
349Dic43—42no—
350Dic43—42no—
351C22×#126—431no—
352C22×#125—431no—
353#2519—4316no—
354C2×#399—431no—
355C2×#398—431no—
356C2×#398—431no—
357C2×#396—431no—
358C2×#389—431no—
359C2×#388—431no—
360C2×#388—431no—
361C2×#388—431no—
362C2×#388—431no—
363C2×#387D4311yescharacteristic, complemented
364C2×#382—431no—
365C2×C4×C4⋊C4—431no—
366C2×C4×C4⋊C4—431no—
367C2×C43#251918yescomplemented
368C2×C43C2×#52911yescharacteristic
369C2×C43C2×#53211yescharacteristic
370C2×C43C2×#54111yescharacteristic
371C2×C43C2×#54711yescharacteristic
372C2×C43C2×#54811yescharacteristic
373C2×C43C2×#55211yescharacteristic
374C2×C43C2×#55211yescharacteristic
375D43—82no—
376C2×#126—438no—
377C2×#126—868no—
378C2×#125—438no—
379C2×#125—868no—
380C22×C4⋊C4—431no—
381C22×C4⋊C4—431no—
382C22×C4⋊C4—431no—
383C22×C4⋊C4—431no—
384C22×C4⋊C4—431no—
385C22×C4⋊C4—431no—
386C22×C4⋊C4—431no—
387C22×C4⋊C4—431no—
388C22×C4⋊C4—431no—
389C22×C4⋊C4—431no—
390C22×C4⋊C4—431no—
391C22×C4⋊C4C2×D4311yescharacteristic
392C22×C4⋊C4C2×D4311yescharacteristic
393C22×C22⋊C4—431no—
394C22×C22⋊C4—431no—
395C22×C22⋊C4—431no—
396C22×C22⋊C4—431no—
397C22×C22⋊C4—431no—
398C22×C22⋊C4—431no—
399C22×C22⋊C4—431no—
400C22×C42—431no—
401C22×C42—431no—
402C22×C42—431no—
403C22×C42—431no—
404C22×C42C2×D4311yescharacteristic
405#399—438no—
406#398—438no—
407#398—438no—
408#396—438no—
409#389—438no—
410#388—438no—
411#388—438no—
412#388—438no—
413#388—438no—
414#387C2×D4318yescomplemented
415#382—438no—
416C4×C4⋊C4—438no—
417C4×C4⋊C4—438no—
418C2×#95—431no—
419C2×#95—431no—
420C2×#95—431no—
421C2×#95—431no—
422C2×#95—431no—
423C2×#95—431no—
424C2×#95C2×D4311yescharacteristic
425C2×#95C2×D4311yescharacteristic
426C2×#95C2×D4311yescharacteristic
427C2×#95C2×D4311yescharacteristic
428C43C2×#251911yescharacteristic, complemented, Sylow
429C25—431no—
430C23×C4—431no—
431C23×C4—431no—
432C23×C4—431no—
433C23×C4—431no—
434C23×C4—431no—
435C23×C4—431no—
436C23×C4—431no—
437C23×C4C22×D4311yescharacteristic
438C23×C4C22×D4311yescharacteristic
439C23×C4C22×D4311yescharacteristic
440C23×C4C22×D4311yescharacteristic
441C23×C4C22×D4311yescharacteristic
442C23×C4C22×D4311yescharacteristic
443C23×C4C22×D4311yescharacteristic
444#126—8632no—
445#125—8632no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—438no—
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—434no—
457C2×C4⋊C4—434no—
458C2×C4⋊C4—434no—
459C2×C4⋊C4—434no—
460C2×C4⋊C4—864no—
461C2×C4⋊C4—864no—
462C2×C4⋊C4—864no—
463C2×C4⋊C4—864no—
464C2×C4⋊C4—864no—
465C2×C4⋊C4—864no—
466C2×C4⋊C4—864no—
467C2×C4⋊C4—864no—
468C2×C4⋊C4—864no—
469C2×C4⋊C4—864no—
470C2×C4⋊C4C22×D4314yes—
471C2×C4⋊C4C22×D4314yes—
472C2×C22⋊C4—434no—
473C2×C22⋊C4—434no—
474C2×C22⋊C4—434no—
475C2×C22⋊C4—434no—
476C2×C22⋊C4—434no—
477C2×C22⋊C4—434no—
478C2×C22⋊C4—434no—
479C2×C22⋊C4—864no—
480C2×C22⋊C4—864no—
481C2×C22⋊C4—864no—
482C2×C22⋊C4—864no—
483C2×C22⋊C4—864no—
484C2×C22⋊C4—864no—
485C2×C22⋊C4—864no—
486C2×C42—24no—
487C2×C42—434no—
488C2×C42—434no—
489C2×C42—434no—
490C2×C42—434no—
491C2×C42—864no—
492C2×C42—864no—
493C2×C42—864no—
494C2×C42—864no—
495C2×C42C22×D4314yes—
496#95—434no—
497#95—434no—
498#95—434no—
499#95—434no—
500#95—434no—
501#95—434no—
502#95C22×D4314yes—
503#95C22×D4314yes—
504#95C22×D4314yes—
505#95C22×D4314yes—
506C24—432no—
507C24—862no—
508C24—862no—
509C24—862no—
510C24—862no—
511C24—862no—
512C24—862no—
513C24—862no—
514C24C23×D4311yescharacteristic
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—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—434no—
535C22×C4—434no—
536C22×C4—434no—
537C22×C4—434no—
538C22×C4—434no—
539C22×C4—432no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—432no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—432no—
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—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4#1062189814yes—
563C22×C4D4×D4314yes—
564C22×C4C23×D4312yes—
565C22×C4C23×D4312yes—
566C22×C4C23×D4312yes—
567C22×C4C23×D4312yes—
568C22×C4C23×D4312yes—
569C22×C4C23×D4312yes—
570C22×C4C23×D4312yes—
571C4⋊C4—28no—
572C4⋊C4—28no—
573C4⋊C4—4316no—
574C4⋊C4—868no—
575C4⋊C4—868no—
576C4⋊C4—868no—
577C4⋊C4—868no—
578C4⋊C4—868no—
579C4⋊C4—868no—
580C4⋊C4—868no—
581C4⋊C4—868no—
582C4⋊C4—868no—
583C4⋊C4—868no—
584C22⋊C4—868no—
585C22⋊C4—868no—
586C22⋊C4—868no—
587C22⋊C4—868no—
588C22⋊C4—868no—
589C22⋊C4—868no—
590C22⋊C4—868no—
591C42—28no—
592C42—868no—
593C42—868no—
594C42—868no—
595C42—868no—
596C23—862no—
597C23—862no—
598C23—862no—
599C23—862no—
600C23—862no—
601C23—862no—
602C23—862no—
603C23—1724no—
604C23—1724no—
605C23—1724no—
606C23—1724no—
607C23—1724no—
608C23—1724no—
609C23—1724no—
610C23C2×D4×D4312yes—
611C23#41×D4312yes—
612C23#41×D4312yes—
613C23#41×D4312yes—
614C23C2×#1062189812yes—
615C23#1306337212yes—
616C23#1306337312yes—
617C23C24×D4311yescharacteristic
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—28no—
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—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—434no—
645C2×C4—434no—
646C2×C4—434no—
647C2×C4—434no—
648C2×C4—434no—
649C2×C4—868no—
650C2×C4—868no—
651C2×C4—868no—
652C2×C4—868no—
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—868no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—1724no—
671C2×C4—1724no—
672C2×C4C2×D4×D4314yes—
673C2×C4C2×#1062189814yes—
674C22—3448no—
675C22—1722no—
676C22—1722no—
677C22—1722no—
678C22—1722no—
679C22—1722no—
680C22—1722no—
681C22—1722no—
682C22#1458343214yes—
683C22#1458344614yes—
684C22#1458350814yes—
685C22#1458354714yes—
686C22#1458355914yes—
687C22#1458358214yes—
688C22#1458359014yes—
689C22C22×D4×D4311yescharacteristic
690C22C2×#41×D4311yescharacteristic
691C22C2×#41×D4311yescharacteristic
692C22C2×#41×D4311yescharacteristic
693C22C22×#1062189811yescharacteristic
694C22C2×#1306337211yescharacteristic
695C22C2×#1306337311yescharacteristic
696C4—24no—
697C4—24no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—864no—
704C4—864no—
705C4—864no—
706C4—864no—
707C4—864no—
708C4—1722no—
709C4—1722no—
710C2—3442no—
711C2#1913927318yesdirect product factor
712C2C2×#1458343211yescharacteristic
713C2C2×#1458344611yescharacteristic
714C2C2×#1458350811yescharacteristic
715C2C2×#1458354711yescharacteristic
716C2C2×#1458355911yescharacteristic
717C2C2×#1458358211yescharacteristic
718C2C2×#1458359011yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#387D43
hypocenterC43C2×#2519
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×#13063315C2semidirect
3. #19139273C2direct (N × H)
5. C2×#14582833C2semidirect
6. C2×#14582833C2semidirect
8. C2×#14582795C2semidirect
13. C2×#14582763C2semidirect
14. C2×C4×Dic43⋊C4C2semidirect
15. C2×#14582750C2semidirect
16. C2×C43×#387C2semidirect
20. C2×#13063315C22semidirect
44. #14582833C22semidirect
45. #14582833C22semidirect
47. #14582795C22semidirect
52. #14582763C22semidirect
53. C4×Dic43⋊C4C22semidirect
54. #14582750C22semidirect
64. C43×#387C22semidirect
363. C2×#387D43semidirect
367. C2×C43#2519semidirect
414. #387C2×D43semidirect
428. C43C2×#2519semidirect
711. C2#19139273direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633192
C22×#130633152
#191392732
C2×#145828342
C2×#145828332
C2×#145828232
C2×#145827952
C2×#145827912
C2×#145827892
C2×#145827882
C2×#145827632
C2×C4×Dic43⋊C42
C2×#145827502
C2×C43×#3872
C2×#251943