Finite Group Databasebeta

← C2×#23771611 #34494504

Subgroups — C2×#23771611 #34494504

Order 20224.

2110 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23771611C2116yesmaximal, direct product factor
2C2×#19098503C211yesmaximal, characteristic, complemented
3C2×#19098498C211yesmaximal, characteristic, complemented
4C2×#19098498C211yesmaximal, characteristic, complemented
5C2×#19098494C211yesmaximal, characteristic, complemented
6C2×#19098492C211yesmaximal, characteristic, complemented
7C2×#19098492C211yesmaximal, characteristic, complemented
8C2×#19098487C211yesmaximal, characteristic, complemented
9C2×#19098485C211yesmaximal, characteristic, complemented
10C2×#19098481C211yesmaximal, characteristic
11C2×#19098480C211yesmaximal, characteristic
12C2×#19098480C211yesmaximal, characteristic
13C2×#19098458C211yesmaximal, characteristic, complemented
14C2×#19098455C211yesmaximal, characteristic, complemented
15C2×#19098453C211yesmaximal, characteristic, complemented
16C2×#398×C79C211yesmaximal, characteristic, complemented
17C23×D316C2211yescharacteristic
18C22×C4⋊Dic79C2211yescharacteristic
19C22×Dic79⋊C4C2211yescharacteristic
20C22×Dic79⋊C4C2211yescharacteristic
21C22×Dic79⋊C4C2211yescharacteristic
22C22×Dic79⋊C4C2211yescharacteristic
23C22×Dic79⋊C4C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×(C2×D79)⋊C4C2211yescharacteristic
26C22×(C2×D79)⋊C4C2211yescharacteristic
27C22×(C2×D79)⋊C4C2211yescharacteristic
28C22×(C2×D79)⋊C4C2211yescharacteristic
29C22×(C2×D79)⋊C4C2211yescharacteristic
30C22×(C2×D79)⋊C4C2211yescharacteristic
31C22×(C2×D79)⋊C4C2211yescharacteristic
32C22×(C2×D79)⋊C4C2211yescharacteristic
33C22×(C2×D79)⋊C4C2211yescharacteristic
34C22×(C2×D79)⋊C4C2211yescharacteristic
35C22×(C2×D79)⋊C4C2211yescharacteristic
36C22×(C2×D79)⋊C4C2211yescharacteristic
37C22×C4×Dic79C2211yescharacteristic
38#19098503C2218yescomplemented
39#19098498C2218yescomplemented
40#19098498C2218yescomplemented
41#19098494C2218yescomplemented
42#19098492C2218yescomplemented
43#19098492C2218yescomplemented
44#19098487C2218yescomplemented
45#19098485C2218yescomplemented
46#19098481C2218yes—
47#19098480C2218yes—
48#19098480C2218yes—
49#19098458C2218yescomplemented
50#19098455C2218yescomplemented
51#19098453C2218yescomplemented
52C2×C79⋊#95C2211yescharacteristic
53C2×C79⋊#95C2211yescharacteristic
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C22×C4⋊C4×C79C2211yescharacteristic
60C22×C4⋊C4×C79C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C22×C4⋊C4×C79C2211yescharacteristic
63#398×C79C2218yescomplemented
64C2×#95×C79C2211yescharacteristic
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C24×D79C2311yescharacteristic
68C24×D79C2311yescharacteristic
69C22×D316—42no—
70C22×D316—42no—
71C22×D316—42no—
72C22×D316C2314yes—
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C2×C4⋊Dic79—42no—
80C2×C4⋊Dic79C2314yes—
81C2×Dic79⋊C4—24no—
82C2×Dic79⋊C4—42no—
83C2×Dic79⋊C4—42no—
84C2×Dic79⋊C4—42no—
85C2×Dic79⋊C4—42no—
86C2×Dic79⋊C4—42no—
87C2×Dic79⋊C4C2314yes—
88C2×Dic79⋊C4C2314yes—
89C2×Dic79⋊C4C2314yes—
90C2×Dic79⋊C4C2314yes—
91C2×Dic79⋊C4C2314yes—
92C2×Dic79⋊C4C2314yes—
93C2×(C2×D79)⋊C4—24no—
94C2×(C2×D79)⋊C4—24no—
95C2×(C2×D79)⋊C4—42no—
96C2×(C2×D79)⋊C4—42no—
97C2×(C2×D79)⋊C4—42no—
98C2×(C2×D79)⋊C4—42no—
99C2×(C2×D79)⋊C4—42no—
100C2×(C2×D79)⋊C4—42no—
101C2×(C2×D79)⋊C4—42no—
102C2×(C2×D79)⋊C4—42no—
103C2×(C2×D79)⋊C4—42no—
104C2×(C2×D79)⋊C4—42no—
105C2×(C2×D79)⋊C4C2314yes—
106C2×(C2×D79)⋊C4C2314yes—
107C2×(C2×D79)⋊C4C2314yes—
108C2×(C2×D79)⋊C4C2314yes—
109C2×(C2×D79)⋊C4C2314yes—
110C2×(C2×D79)⋊C4C2314yes—
111C2×(C2×D79)⋊C4C2314yes—
112C2×(C2×D79)⋊C4C2314yes—
113C2×(C2×D79)⋊C4C2314yes—
114C2×(C2×D79)⋊C4C2314yes—
115C2×(C2×D79)⋊C4C2314yes—
116C2×(C2×D79)⋊C4C2314yes—
117C2×C4×Dic79—42no—
118C2×C4×Dic79C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C79⋊#95C2314yes—
123C79⋊#95C2314yes—
124C79⋊#95C2314yes—
125C79⋊#95C2314yes—
126C23×C4×C79C2311yescharacteristic
127C23×C4×C79C2311yescharacteristic
128C23×C4×C79C2311yescharacteristic
129C23×C4×C79C2311yescharacteristic
130C23×C4×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C2×C4⋊C4×C79—42no—
134C2×C4⋊C4×C79—42no—
135C2×C4⋊C4×C79—42no—
136C2×C4⋊C4×C79—42no—
137C2×C4⋊C4×C79C2314yes—
138C2×C4⋊C4×C79C2314yes—
139C2×C4⋊C4×C79C2314yes—
140C2×C4⋊C4×C79C2314yes—
141#95×C79C2314yes—
142#95×C79C2314yes—
143#95×C79C2314yes—
144C23×D79—22no—
145C23×D79—22no—
146C23×D79—22no—
147C23×D79—22no—
148C23×D79—22no—
149C23×D79—22no—
150C23×D79—22no—
151C23×D79—22no—
152C23×D79—22no—
153C23×D79—22no—
154C23×D79—22no—
155C23×D79—22no—
156C23×D79—22no—
157C23×D79—22no—
158C23×D79C2412yes—
159C23×D79C2412yes—
160C2×D316—44no—
161C2×D316—44no—
162C2×D316—44no—
163C2×D316—416no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79—22no—
171C22×Dic79—22no—
172C22×Dic79—22no—
173C22×Dic79—22no—
174C22×Dic79—22no—
175C22×Dic79—22no—
176C22×Dic79—22no—
177C22×Dic79—22no—
178C22×Dic79—22no—
179C22×Dic79—22no—
180C22×Dic79—22no—
181C22×Dic79#4114yes—
182C22×Dic79C2412yes—
183C22×Dic79C2412yes—
184C22×Dic79C2412yes—
185C22×Dic79C2412yes—
186C22×Dic79C2412yes—
187C22×Dic79C2412yes—
188C4⋊Dic79—44no—
189Dic79⋊C4—28no—
190Dic79⋊C4—44no—
191Dic79⋊C4—44no—
192Dic79⋊C4—44no—
193Dic79⋊C4—44no—
194Dic79⋊C4—44no—
195(C2×D79)⋊C4—28no—
196(C2×D79)⋊C4—28no—
197(C2×D79)⋊C4—44no—
198(C2×D79)⋊C4—44no—
199(C2×D79)⋊C4—44no—
200(C2×D79)⋊C4—44no—
201(C2×D79)⋊C4—44no—
202(C2×D79)⋊C4—44no—
203(C2×D79)⋊C4—44no—
204(C2×D79)⋊C4—44no—
205(C2×D79)⋊C4—44no—
206(C2×D79)⋊C4—44no—
207C4×Dic79—44no—
208C24×C79C2411yescharacteristic
209C22×C4×C79—22no—
210C22×C4×C79—22no—
211C22×C4×C79—22no—
212C22×C4×C79—22no—
213C22×C4×C79—22no—
214C22×C4×C79—22no—
215C22×C4×C79—22no—
216C22×C4×C79—22no—
217C22×C4×C79—22no—
218C22×C4×C79—22no—
219C22×C4×C79—22no—
220C22×C4×C79—22no—
221C22×C4×C79—22no—
222C22×C4×C79—22no—
223C22×C4×C79—22no—
224C22×C4×C79—22no—
225C22×C4×C79—22no—
226C22×C4×C79—22no—
227C22×C4×C79—22no—
228C22×C4×C79—22no—
229C22×C4×C79—22no—
230C22×C4×C79C2412yes—
231C22×C4×C79C2412yes—
232C22×C4×C79C2412yes—
233C22×C4×C79C2412yes—
234C22×C4×C79C2412yes—
235C22×C4×C79C2412yes—
236C22×C4×C79C2412yes—
237C4⋊C4×C79—44no—
238C4⋊C4×C79—44no—
239C4⋊C4×C79—44no—
240C4⋊C4×C79—44no—
241C23×C79C2×#4112yes—
242C23×C79H(5,𝔽2)12yes—
243C23×C79H(5,𝔽2)12yes—
244C23×C79H(5,𝔽2)12yes—
245C23×C79H(5,𝔽2)12yes—
246C23×C792−1+412yes—
247C23×C792−1+412yes—
248C23×C79C2511yescharacteristic
249C22×D79—22no—
250C22×D79—22no—
251C22×D79—22no—
252C22×D79—22no—
253C22×D79—22no—
254C22×D79—22no—
255C22×D79—22no—
256C22×D79—22no—
257C22×D79—22no—
258C22×D79—22no—
259C22×D79—22no—
260C22×D79—22no—
261C22×D79—22no—
262C22×D79—22no—
263C22×D79—44no—
264C22×D79—44no—
265C22×D79—44no—
266C22×D79—44no—
267C22×D79—44no—
268C22×D79—44no—
269C22×D79—44no—
270C22×D79—44no—
271C22×D79—44no—
272C22×D79—44no—
273C22×D79—44no—
274C22×D79—44no—
275C22×D79—44no—
276C22×D79—44no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—44no—
299C2×C4×C79—44no—
300C2×C4×C79—44no—
301C2×C4×C79—44no—
302C2×C4×C79—44no—
303C2×C4×C79—44no—
304C2×C4×C79—44no—
305C2×Dic79—28no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—22no—
323C2×Dic79—44no—
324C2×Dic79—44no—
325C2×Dic79—44no—
326C2×Dic79—44no—
327C2×Dic79—44no—
328C2×Dic79C2×#4114yes—
329D316—416no—
330C22×C79#53914yes—
331C22×C79#54014yes—
332C22×C79#54214yes—
333C22×C79#56014yes—
334C22×C79#56214yes—
335C22×C79#56214yes—
336C22×C79#56314yes—
337C22×C79C22×#4111yescharacteristic
338C22×C79C2×H(5,𝔽2)11yescharacteristic
339C22×C79C2×H(5,𝔽2)11yescharacteristic
340C22×C79C2×H(5,𝔽2)11yescharacteristic
341C22×C79C2×H(5,𝔽2)11yescharacteristic
342C22×C79C2×2−1+411yescharacteristic
343C22×C79C2×2−1+411yescharacteristic
344C2×D79—42no—
345C2×D79—42no—
346C2×D79—42no—
347C2×D79—42no—
348C2×D79—42no—
349C2×D79—42no—
350C2×D79—42no—
351C2×D79—42no—
352C2×D79—42no—
353C2×D79—42no—
354C2×D79—42no—
355C2×D79—42no—
356C2×D79—42no—
357C2×D79—42no—
358C2×D79—88no—
359C2×D79—88no—
360C4×C79—42no—
361C4×C79—42no—
362C4×C79—42no—
363C4×C79—42no—
364C4×C79—42no—
365C4×C79—42no—
366C4×C79—42no—
367Dic79—24no—
368Dic79—42no—
369Dic79—42no—
370Dic79—42no—
371Dic79—42no—
372Dic79—42no—
373C2×#2837—791nomaximal, Sylow
374C2×C79#283718yescomplemented
375C2×C79C2×#53911yescharacteristic
376C2×C79C2×#54011yescharacteristic
377C2×C79C2×#54211yescharacteristic
378C2×C79C2×#56011yescharacteristic
379C2×C79C2×#56211yescharacteristic
380C2×C79C2×#56211yescharacteristic
381C2×C79C2×#56311yescharacteristic
382D79—82no—
383D79—82no—
384#2837—7916no—
385C2×#400—791no—
386C2×#399—791no—
387C2×#399—791no—
388C2×#398—791no—
389C2×#398D7911yescharacteristic, complemented
390C2×#397—791no—
391C2×#397—791no—
392C2×#396—791no—
393C2×#396—791no—
394C2×#394—791no—
395C2×#394—791no—
396C2×#394—791no—
397C2×#389—791no—
398C2×#388—791no—
399C2×#388—791no—
400C79C2×#283711yescharacteristic, complemented, Sylow
401C23×D4—791no—
402C22×C4⋊C4—791no—
403C22×C4⋊C4—791no—
404C22×C4⋊C4—791no—
405C22×C4⋊C4—791no—
406C22×C4⋊C4—791no—
407C22×C4⋊C4—791no—
408C22×C4⋊C4—791no—
409C22×C4⋊C4C2×D7911yescharacteristic
410C22×C4⋊C4C2×D7911yescharacteristic
411C22×C4⋊C4C2×D7911yescharacteristic
412C22×C4⋊C4C2×D7911yescharacteristic
413C22×C22⋊C4—791no—
414C22×C22⋊C4—791no—
415C22×C22⋊C4—791no—
416C22×C22⋊C4—791no—
417C22×C22⋊C4—791no—
418C22×C22⋊C4—791no—
419C22×C22⋊C4—791no—
420C22×C22⋊C4—791no—
421C22×C22⋊C4—791no—
422C22×C22⋊C4—791no—
423C22×C22⋊C4—791no—
424C22×C22⋊C4—791no—
425C22×C42—791no—
426#400—798no—
427#399—798no—
428#399—798no—
429#398—798no—
430#398C2×D7918yescomplemented
431#397—798no—
432#397—798no—
433#396—798no—
434#396—798no—
435#394—798no—
436#394—798no—
437#394—798no—
438#389—798no—
439#388—798no—
440#388—798no—
441C2×#95—791no—
442C2×#95—791no—
443C2×#95—791no—
444C2×#95—791no—
445C2×#95—791no—
446C2×#95—791no—
447C2×#95—791no—
448C2×#95C2×D7911yescharacteristic
449C2×#95C2×D7911yescharacteristic
450C2×#95C2×D7911yescharacteristic
451C25—791no—
452C25—791no—
453C22×D4—3162no—
454C22×D4—3162no—
455C22×D4—3162no—
456C22×D4—794no—
457C23×C4—791no—
458C23×C4—791no—
459C23×C4—791no—
460C23×C4—791no—
461C23×C4—791no—
462C23×C4—791no—
463C23×C4C22×D7911yescharacteristic
464C23×C4C22×D7911yescharacteristic
465C23×C4C22×D7911yescharacteristic
466C23×C4C22×D7911yescharacteristic
467C23×C4C22×D7911yescharacteristic
468C23×C4C22×D7911yescharacteristic
469C23×C4C22×D7911yescharacteristic
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—3162no—
475C2×C4⋊C4—3162no—
476C2×C4⋊C4—3162no—
477C2×C4⋊C4—3162no—
478C2×C4⋊C4—3162no—
479C2×C4⋊C4—3162no—
480C2×C4⋊C4—794no—
481C2×C4⋊C4—794no—
482C2×C4⋊C4—794no—
483C2×C4⋊C4—794no—
484C2×C4⋊C4—794no—
485C2×C4⋊C4—794no—
486C2×C4⋊C4—794no—
487C2×C4⋊C4—1584no—
488C2×C4⋊C4C22×D7914yes—
489C2×C4⋊C4C22×D7914yes—
490C2×C4⋊C4C22×D7914yes—
491C2×C4⋊C4C22×D7914yes—
492C2×C22⋊C4—3162no—
493C2×C22⋊C4—3162no—
494C2×C22⋊C4—3162no—
495C2×C22⋊C4—3162no—
496C2×C22⋊C4—3162no—
497C2×C22⋊C4—3162no—
498C2×C22⋊C4—3162no—
499C2×C22⋊C4—3162no—
500C2×C22⋊C4—3162no—
501C2×C22⋊C4—3162no—
502C2×C22⋊C4—794no—
503C2×C22⋊C4—794no—
504C2×C22⋊C4—794no—
505C2×C22⋊C4—794no—
506C2×C22⋊C4—794no—
507C2×C22⋊C4—794no—
508C2×C22⋊C4—794no—
509C2×C22⋊C4—794no—
510C2×C22⋊C4—794no—
511C2×C22⋊C4—794no—
512C2×C22⋊C4—794no—
513C2×C22⋊C4—794no—
514C2×C22⋊C4—1584no—
515C2×C22⋊C4—1584no—
516C2×C42—3162no—
517C2×C42—794no—
518#95—794no—
519#95—794no—
520#95—794no—
521#95—794no—
522#95—794no—
523#95—794no—
524#95—794no—
525#95C22×D7914yes—
526#95C22×D7914yes—
527#95C22×D7914yes—
528C24—792no—
529C24—792no—
530C24—1582no—
531C24—1582no—
532C24—1582no—
533C24—1582no—
534C24—1582no—
535C24—1582no—
536C24—1582no—
537C24—1582no—
538C24—1582no—
539C24—1582no—
540C24—1582no—
541C24—1582no—
542C24—1582no—
543C24—1582no—
544C24C23×D7911yescharacteristic
545C2×D4—3164no—
546C2×D4—3164no—
547C2×D4—3164no—
548C2×D4—31616no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—794no—
571C22×C4—792no—
572C22×C4—792no—
573C22×C4—792no—
574C22×C4—792no—
575C22×C4—792no—
576C22×C4—792no—
577C22×C4—1582no—
578C22×C4—1582no—
579C22×C4—1582no—
580C22×C4—1582no—
581C22×C4—1582no—
582C22×C4—1582no—
583C22×C4—1582no—
584C22×C4—1582no—
585C22×C4—1582no—
586C22×C4—1582no—
587C22×C4—1582no—
588C22×C4—1582no—
589C22×C4—1582no—
590C22×C4—1582no—
591C22×C4—1582no—
592C22×C4—1582no—
593C22×C4—1582no—
594C22×C4C23×D7912yes—
595C22×C4C23×D7912yes—
596C22×C4C23×D7912yes—
597C22×C4C23×D7912yes—
598C22×C4C23×D7912yes—
599C22×C4C23×D7912yes—
600C22×C4C23×D7912yes—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—3164no—
606C4⋊C4—3164no—
607C4⋊C4—3164no—
608C4⋊C4—3164no—
609C4⋊C4—3164no—
610C4⋊C4—3164no—
611C4⋊C4—1588no—
612C22⋊C4—3164no—
613C22⋊C4—3164no—
614C22⋊C4—3164no—
615C22⋊C4—3164no—
616C22⋊C4—3164no—
617C22⋊C4—3164no—
618C22⋊C4—3164no—
619C22⋊C4—3164no—
620C22⋊C4—3164no—
621C22⋊C4—3164no—
622C22⋊C4—1588no—
623C22⋊C4—1588no—
624C42—3164no—
625C23—3164no—
626C23—3164no—
627C23—3164no—
628C23—3164no—
629C23—3164no—
630C23—3164no—
631C23—3164no—
632C23—3164no—
633C23—3164no—
634C23—3164no—
635C23—3164no—
636C23—3164no—
637C23—3164no—
638C23—3164no—
639C23—1582no—
640C23—1582no—
641C23—1582no—
642C23—1582no—
643C23—1582no—
644C23—1582no—
645C23—1582no—
646C23—1582no—
647C23—1582no—
648C23—1582no—
649C23—1582no—
650C23—1582no—
651C23—1582no—
652C23—1582no—
653C23#41×D7912yes—
654C23#1457920612yes—
655C23#1457920612yes—
656C23#1457920712yes—
657C23#1457920712yes—
658C23#1457920912yes—
659C23#1457920912yes—
660C23C24×D7911yescharacteristic
661D4—31616no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—3164no—
691C2×C4—3164no—
692C2×C4—3164no—
693C2×C4—3164no—
694C2×C4—3164no—
695C2×C4—794no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4—1582no—
700C2×C4—1582no—
701C2×C4—1582no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1582no—
708C2×C4—1582no—
709C2×C4—1582no—
710C2×C4—1582no—
711C2×C4—1582no—
712C2×C4—1582no—
713C2×C4—1588no—
714C22—3162no—
715C22—3162no—
716C22—3162no—
717C22—3162no—
718C22—3162no—
719C22—3162no—
720C22—3162no—
721C22—3162no—
722C22—3162no—
723C22—3162no—
724C22—3162no—
725C22—3162no—
726C22—3162no—
727C22—3162no—
728C22—6328no—
729C22—6328no—
730C22#1909916114yes—
731C22#1909916514yes—
732C22#1909918314yes—
733C22#1909930114yes—
734C22#1909930914yes—
735C22#1909931114yes—
736C22#1909931214yes—
737C22C2×#41×D7911yescharacteristic
738C22C2×#1457920611yescharacteristic
739C22C2×#1457920611yescharacteristic
740C22C2×#1457920711yescharacteristic
741C22C2×#1457920711yescharacteristic
742C22C2×#1457920911yescharacteristic
743C22C2×#1457920911yescharacteristic
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—3162no—
752C4—3162no—
753C4—3162no—
754C4—3162no—
755C4—3162no—
756C4—1584no—
757C2—6322no—
758C2—6322no—
759C2#2377161118yesdirect product factor
760C2C2×#1909916111yescharacteristic
761C2C2×#1909916511yescharacteristic
762C2C2×#1909918311yescharacteristic
763C2C2×#1909930111yescharacteristic
764C2C2×#1909930911yescharacteristic
765C2C2×#1909931111yescharacteristic
766C2C2×#1909931211yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#398×C79C2
socleC24×C79C24
prime radicalC23×D316C22
hypercenterC2×#398D79
hypocenterC79C2×#2837
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #23771611C2direct (N × H)
2. C2×#19098503C2semidirect
3. C2×#19098498C2semidirect
4. C2×#19098498C2semidirect
5. C2×#19098494C2semidirect
6. C2×#19098492C2semidirect
7. C2×#19098492C2semidirect
8. C2×#19098487C2semidirect
9. C2×#19098485C2semidirect
13. C2×#19098458C2semidirect
14. C2×#19098455C2semidirect
15. C2×#19098453C2semidirect
16. C2×#398×C79C2semidirect
38. #19098503C22semidirect
39. #19098498C22semidirect
40. #19098498C22semidirect
41. #19098494C22semidirect
42. #19098492C22semidirect
43. #19098492C22semidirect
44. #19098487C22semidirect
45. #19098485C22semidirect
49. #19098458C22semidirect
50. #19098455C22semidirect
51. #19098453C22semidirect
63. #398×C79C22semidirect
374. C2×C79#2837semidirect
389. C2×#398D79semidirect
400. C79C2×#2837semidirect
430. #398C2×D79semidirect
759. C2#23771611direct (N × H)

Maximal subgroups

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

subgroupindex
#237716112
C2×#190985032
C2×#190984982
C2×#190984942
C2×#190984922
C2×#190984872
C2×#190984852
C2×#190984812
C2×#190984802
C2×#190984582
C2×#190984552
C2×#190984532
C2×#398×C792
C2×#283779