Finite Group Databasebeta

← C2×#19142854 #25303016

Subgroups — C2×#19142854 #25303016

Order 11008.

2110 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
1#19142854C2116yesmaximal, direct product factor
2C2×#14582840C211yesmaximal, characteristic, complemented
3C2×#14582836C211yesmaximal, characteristic
4C2×#14582833C211yesmaximal, characteristic, complemented
5C2×#14582832C211yesmaximal, characteristic, complemented
6C2×#14582832C211yesmaximal, characteristic, complemented
7C2×#14582831C211yesmaximal, characteristic, complemented
8C2×#14582823C211yesmaximal, characteristic
9C2×#14582821C211yesmaximal, characteristic
10C2×#14582820C211yesmaximal, characteristic, complemented
11C2×#14582820C211yesmaximal, characteristic, complemented
12C2×#14582812C211yesmaximal, characteristic
13C2×#14582761C211yesmaximal, characteristic
14C2×#14582758C211yesmaximal, characteristic
15C2×#14582756C211yesmaximal, characteristic
16C2×C43×#400C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36#14582840C2218yescomplemented
37#14582836C2218yes—
38#14582833C2218yescomplemented
39#14582832C2218yescomplemented
40#14582832C2218yescomplemented
41#14582831C2218yescomplemented
42#14582823C2218yes—
43#14582821C2218yes—
44#14582820C2218yescomplemented
45#14582820C2218yescomplemented
46#14582812C2218yes—
47#14582761C2218yes—
48#14582758C2218yes—
49#14582756C2218yes—
50C2×C43⋊#95C2211yescharacteristic
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
61C43×#400C2218yescomplemented
62C2×#95×C43C2211yescharacteristic
63C2×#95×C43C2211yescharacteristic
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C24×D43C2311yescharacteristic
68C22×Dic86—42no—
69C22×Dic86—42no—
70C22×Dic86—42no—
71C22×Dic86C2314yes—
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C22×C4×D43—42no—
80C22×C4×D43—42no—
81C22×C4×D43Q818yescomplemented
82C22×C4×D43C2314yes—
83C2×C4⋊Dic43—42no—
84C2×C4⋊Dic43—42no—
85C2×C4⋊Dic43—42no—
86C2×C4⋊Dic43—42no—
87C2×C4⋊Dic43—42no—
88C2×C4⋊Dic43C2314yes—
89C2×C4⋊Dic43C2314yes—
90C2×C4⋊Dic43C2314yes—
91C2×C4⋊Dic43C2314yes—
92C2×C4⋊Dic43C2314yes—
93C2×Dic43⋊C4—42no—
94C2×Dic43⋊C4—42no—
95C2×Dic43⋊C4—42no—
96C2×Dic43⋊C4—42no—
97C2×Dic43⋊C4—42no—
98C2×Dic43⋊C4—42no—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×(C2×D43)⋊C4—42no—
106C2×(C2×D43)⋊C4—42no—
107C2×(C2×D43)⋊C4—42no—
108C2×(C2×D43)⋊C4—42no—
109C2×(C2×D43)⋊C4—42no—
110C2×(C2×D43)⋊C4—42no—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43—42no—
134C2×C4⋊C4×C43—42no—
135C2×C4⋊C4×C43C2314yes—
136C2×C4⋊C4×C43C2314yes—
137#95×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×C43—22no—
171C22×C4×C43C2×Q814yes—
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×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43C2×Q814yes—
200C22×Dic43C2412yes—
201C22×Dic43C2412yes—
202C22×Dic43C2412yes—
203C22×Dic43C2412yes—
204C22×Dic43C2412yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C2×C4×D43—416no—
208C2×C4×D43—44no—
209C2×C4×D43—44no—
210C2×C4×D43C2×Q8116yescomplemented
211C2×Dic86—44no—
212C2×Dic86—44no—
213C2×Dic86—44no—
214C2×Dic86—416no—
215C4⋊C4×C43—44no—
216C4⋊C4×C43—44no—
217(C2×D43)⋊C4—44no—
218(C2×D43)⋊C4—44no—
219(C2×D43)⋊C4—44no—
220(C2×D43)⋊C4—44no—
221(C2×D43)⋊C4—44no—
222(C2×D43)⋊C4—44no—
223C4⋊Dic43—44no—
224C4⋊Dic43—44no—
225C4⋊Dic43—44no—
226C4⋊Dic43—44no—
227C4⋊Dic43—44no—
228Dic43⋊C4—44no—
229Dic43⋊C4—44no—
230Dic43⋊C4—44no—
231Dic43⋊C4—44no—
232Dic43⋊C4—44no—
233Dic43⋊C4—44no—
234C23×C43C22×Q812yes—
235C23×C43H(5,𝔽2)12yes—
236C23×C43H(5,𝔽2)12yes—
237C23×C43H(5,𝔽2)12yes—
238C23×C43H(5,𝔽2)12yes—
239C23×C432−1+412yes—
240C23×C432−1+412yes—
241C23×C43C2511yescharacteristic
242C22×D43—28no—
243C22×D43—28no—
244C22×D43—28no—
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×D43C22×Q814yes—
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—22no—
277C2×C4×C43—44no—
278C2×C4×C43—44no—
279C2×C4×C43—44no—
280C2×C4×C43—44no—
281C2×C4×C43—44no—
282C2×C4×C43—44no—
283C2×C4×C43C22×Q814yes—
284C2×Dic43—28no—
285C2×Dic43—22no—
286C2×Dic43—22no—
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—22no—
305C2×Dic43—44no—
306C2×Dic43—44no—
307C2×Dic43—44no—
308C2×Dic43—44no—
309C2×Dic43—44no—
310C2×Dic43—44no—
311C2×Dic43C22×Q814yes—
312C4×D43—416no—
313Dic86—416no—
314C2×#2841—431nomaximal, Sylow
315C22×C43#54314yes—
316C22×C43#54414yes—
317C22×C43#54414yes—
318C22×C43#56014yes—
319C22×C43#56214yes—
320C22×C43#56214yes—
321C22×C43#56314yes—
322C22×C43C23×Q811yescharacteristic
323C22×C43C2×H(5,𝔽2)11yescharacteristic
324C22×C43C2×H(5,𝔽2)11yescharacteristic
325C22×C43C2×H(5,𝔽2)11yescharacteristic
326C22×C43C2×H(5,𝔽2)11yescharacteristic
327C22×C43C2×2−1+411yescharacteristic
328C22×C43C2×2−1+411yescharacteristic
329C2×D43—24no—
330C2×D43—24no—
331C2×D43—24no—
332C2×D43—416no—
333C2×D43—42no—
334C2×D43—42no—
335C2×D43—42no—
336C2×D43—42no—
337C4×C43—24no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43—42no—
341C4×C43—42no—
342C4×C43—42no—
343C4×C43—42no—
344Dic43—24no—
345Dic43—42no—
346Dic43—42no—
347Dic43—42no—
348Dic43—42no—
349Dic43—42no—
350Dic43—42no—
351#2841—4316no—
352C2×#400—431no—
353C2×#400D4311yescharacteristic, complemented
354C2×#399—431no—
355C2×#398—431no—
356C2×#398—431no—
357C2×#398—431no—
358C2×#398—431no—
359C2×#396—431no—
360C2×#396—431no—
361C2×#395—431no—
362C2×#395—431no—
363C2×#393—431no—
364C2×#381—431no—
365C2×#380—431no—
366C2×#380—431no—
367C2×C43#284118yescomplemented
368C2×C43C2×#54311yescharacteristic
369C2×C43C2×#54411yescharacteristic
370C2×C43C2×#54411yescharacteristic
371C2×C43C2×#56011yescharacteristic
372C2×C43C2×#56211yescharacteristic
373C2×C43C2×#56211yescharacteristic
374C2×C43C2×#56311yescharacteristic
375D43—44no—
376C23×Q8—431no—
377C24×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⋊C4—431no—
386C22×C4⋊C4—431no—
387C22×C4⋊C4—431no—
388C22×C4⋊C4—431no—
389C22×C4⋊C4C2×D4311yescharacteristic
390C22×C4⋊C4C2×D4311yescharacteristic
391C22×C22⋊C4—431no—
392C22×C22⋊C4—431no—
393C22×C22⋊C4—431no—
394C22×C22⋊C4—431no—
395C22×C22⋊C4—431no—
396C22×C22⋊C4—431no—
397#400—438no—
398#400C2×D4318yescomplemented
399#399—438no—
400#398—438no—
401#398—438no—
402#398—438no—
403#398—438no—
404#396—438no—
405#396—438no—
406#395—438no—
407#395—438no—
408#393—438no—
409#381—438no—
410#380—438no—
411#380—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×#95—431no—
421C2×#95C2×D4311yescharacteristic
422C2×#95C2×D4311yescharacteristic
423C2×#95C2×D4311yescharacteristic
424C2×#95C2×D4311yescharacteristic
425C2×#95C2×D4311yescharacteristic
426C43C2×#284111yescharacteristic, complemented, Sylow
427C25—431no—
428C22×Q8—434no—
429C22×Q8—1722no—
430C22×Q8—1722no—
431C22×Q8—1722no—
432C23×C4—431no—
433C23×C4—438no—
434C23×C4—434no—
435C23×C4—431no—
436C23×C4—431no—
437C23×C4—431no—
438C23×C4—431no—
439C23×C4—431no—
440C23×C4—431no—
441C23×C4—1722no—
442C23×C4—1722no—
443C23×C4C22×D4311yescharacteristic
444C23×C4C22×D4311yescharacteristic
445C23×C4C22×D4311yescharacteristic
446C23×C4C22×D4311yescharacteristic
447C23×C4C22×D4311yescharacteristic
448C23×C4C22×D4311yescharacteristic
449C23×C4C22×D4311yescharacteristic
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
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—434no—
461C2×C4⋊C4—434no—
462C2×C4⋊C4—434no—
463C2×C4⋊C4—1722no—
464C2×C4⋊C4—1722no—
465C2×C4⋊C4—1722no—
466C2×C4⋊C4—1722no—
467C2×C4⋊C4—1722no—
468C2×C4⋊C4—1722no—
469C2×C4⋊C4—1722no—
470C2×C4⋊C4—1722no—
471C2×C4⋊C4—1722no—
472C2×C4⋊C4—1722no—
473C2×C4⋊C4—1722no—
474C2×C4⋊C4C22×D4314yes—
475C2×C4⋊C4C22×D4314yes—
476C2×C22⋊C4—434no—
477C2×C22⋊C4—434no—
478C2×C22⋊C4—434no—
479C2×C22⋊C4—434no—
480C2×C22⋊C4—434no—
481C2×C22⋊C4—434no—
482C2×C22⋊C4—1722no—
483C2×C22⋊C4—1722no—
484C2×C22⋊C4—1722no—
485C2×C22⋊C4—1722no—
486C2×C22⋊C4—1722no—
487C2×C22⋊C4—1722no—
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#95—434no—
497#95C22×D4314yes—
498#95C22×D4314yes—
499#95C22×D4314yes—
500#95C22×D4314yes—
501#95C22×D4314yes—
502C24—434no—
503C24—432no—
504C24—862no—
505C24—862no—
506C24—862no—
507C24—862no—
508C24—862no—
509C24—862no—
510C24C23×D4311yescharacteristic
511C2×Q8—1724no—
512C2×Q8—1724no—
513C2×Q8—1724no—
514C2×Q8—17216no—
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—22no—
535C22×C4—434no—
536C22×C4—432no—
537C22×C4—4316no—
538C22×C4—432no—
539C22×C4—432no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—432no—
543C22×C4—432no—
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—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—1724no—
565C22×C4—1724no—
566C22×C4—17216no—
567C22×C4Q8×D4314yes—
568C22×C4C23×D4312yes—
569C22×C4C23×D4312yes—
570C22×C4C23×D4312yes—
571C22×C4C23×D4312yes—
572C22×C4C23×D4312yes—
573C22×C4C23×D4312yes—
574C22×C4C23×D4312yes—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—1724no—
578C4⋊C4—1724no—
579C4⋊C4—1724no—
580C4⋊C4—1724no—
581C4⋊C4—1724no—
582C4⋊C4—1724no—
583C4⋊C4—1724no—
584C4⋊C4—1724no—
585C4⋊C4—1724no—
586C4⋊C4—1724no—
587C4⋊C4—1724no—
588C22⋊C4—1724no—
589C22⋊C4—1724no—
590C22⋊C4—1724no—
591C22⋊C4—1724no—
592C22⋊C4—1724no—
593C22⋊C4—1724no—
594C23—434no—
595C23—862no—
596C23—862no—
597C23—862no—
598C23—862no—
599C23—862no—
600C23—862no—
601C23—868no—
602C23—868no—
603C23—868no—
604C23—1724no—
605C23—1724no—
606C23—1724no—
607C23—1724no—
608C23C2×Q8×D4312yes—
609C23#1306337012yes—
610C23#1306337112yes—
611C23#1306337112yes—
612C23#1306337112yes—
613C23#1306337212yes—
614C23#1306337212yes—
615C23C24×D4311yescharacteristic
616Q8—17216no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—28no—
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—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—434no—
645C2×C4—862no—
646C2×C4—862no—
647C2×C4—868no—
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—862no—
665C2×C4—862no—
666C2×C4—17216no—
667C2×C4—1724no—
668C2×C4—1724no—
669C2×C4—1724no—
670C2×C4—1724no—
671C2×C4—1724no—
672C2×C4—1724no—
673C2×C4C2×Q8×D4314yes—
674C22—864no—
675C22—864no—
676C22—864no—
677C22—1722no—
678C22—1722no—
679C22—1722no—
680C22—1722no—
681C22—17216no—
682C22#1458352414yes—
683C22#1458352914yes—
684C22#1458352914yes—
685C22#1458364014yes—
686C22#1458364314yes—
687C22#1458364614yes—
688C22#1458365114yes—
689C22C22×Q8×D4311yescharacteristic
690C22C2×#1306337011yescharacteristic
691C22C2×#1306337111yescharacteristic
692C22C2×#1306337111yescharacteristic
693C22C2×#1306337111yescharacteristic
694C22C2×#1306337211yescharacteristic
695C22C2×#1306337211yescharacteristic
696C4—24no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—864no—
704C4—1722no—
705C4—1722no—
706C4—1722no—
707C4—1722no—
708C4—1722no—
709C4—1722no—
710C2—1724no—
711C2#1914285418yesdirect product factor
712C2C2×#1458352411yescharacteristic
713C2C2×#1458352911yescharacteristic
714C2C2×#1458352911yescharacteristic
715C2C2×#1458364011yescharacteristic
716C2C2×#1458364311yescharacteristic
717C2C2×#1458364611yescharacteristic
718C2C2×#1458365111yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#400C2
socleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#400D43
hypocenterC43C2×#2841
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #19142854C2direct (N × H)
2. C2×#14582840C2semidirect
4. C2×#14582833C2semidirect
5. C2×#14582832C2semidirect
6. C2×#14582832C2semidirect
7. C2×#14582831C2semidirect
10. C2×#14582820C2semidirect
11. C2×#14582820C2semidirect
16. C2×C43×#400C2semidirect
36. #14582840C22semidirect
38. #14582833C22semidirect
39. #14582832C22semidirect
40. #14582832C22semidirect
41. #14582831C22semidirect
44. #14582820C22semidirect
45. #14582820C22semidirect
61. C43×#400C22semidirect
81. C22×C4×D43Q8semidirect
210. C2×C4×D43C2×Q8semidirect
353. C2×#400D43semidirect
367. C2×C43#2841semidirect
398. #400C2×D43semidirect
426. C43C2×#2841semidirect
711. C2#19142854direct (N × H)

Maximal subgroups

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

subgroupindex
#191428542
C2×#145828402
C2×#145828362
C2×#145828332
C2×#145828322
C2×#145828312
C2×#145828232
C2×#145828212
C2×#145828202
C2×#145828122
C2×#145827612
C2×#145827582
C2×#145827562
C2×C43×#4002
C2×#284143