Finite Group Databasebeta

← C2×#23771508 #34494459

Subgroups — C2×#23771508 #34494459

Order 20224.

2218 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23771508C2116yesmaximal, direct product factor
2C2×#19098503C211yesmaximal, characteristic, complemented
3C2×#19098501C211yesmaximal, characteristic, complemented
4C2×#19098499C211yesmaximal, characteristic, complemented
5C2×#19098497C211yesmaximal, characteristic, complemented
6C2×#19098496C211yesmaximal, characteristic, complemented
7C2×#19098491C211yesmaximal, characteristic, complemented
8C2×#19098491C211yesmaximal, characteristic, complemented
9C2×#19098488C211yesmaximal, characteristic, complemented
10C2×#19098486C211yesmaximal, characteristic, complemented
11C2×#19098486C211yesmaximal, characteristic, complemented
12C2×#19098477C211yesmaximal, characteristic
13C2×#19098443C211yesmaximal, characteristic
14C2×#19098438C211yesmaximal, characteristic, complemented
15C2×#19098435C211yesmaximal, characteristic, complemented
16C2×#394×C79C211yesmaximal, characteristic
17C24×Dic79C2211yescharacteristic
18C22×C4⋊Dic79C2211yescharacteristic
19C22×C4⋊Dic79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21C22×Dic79⋊C4C2211yescharacteristic
22C22×Dic79⋊C4C2211yescharacteristic
23C22×Dic79⋊C4C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
26C22×Dic79⋊C4C2211yescharacteristic
27C22×C22⋊Dic79C2211yescharacteristic
28C22×C22⋊Dic79C2211yescharacteristic
29C22×C22⋊Dic79C2211yescharacteristic
30C22×C22⋊Dic79C2211yescharacteristic
31C22×C22⋊Dic79C2211yescharacteristic
32C22×C22⋊Dic79C2211yescharacteristic
33C22×C22⋊Dic79C2211yescharacteristic
34#19098503C2218yescomplemented
35#19098501C2218yescomplemented
36#19098499C2218yescomplemented
37#19098497C2218yescomplemented
38#19098496C2218yescomplemented
39#19098491C2218yescomplemented
40#19098491C2218yescomplemented
41#19098488C2218yescomplemented
42#19098486C2218yescomplemented
43#19098486C2218yescomplemented
44#19098477C2218yes—
45#19098443C2218yes—
46#19098438C2218yescomplemented
47#19098435C2218yescomplemented
48C2×C79⋊#95C2211yescharacteristic
49C2×C79⋊#95C2211yescharacteristic
50C2×C79⋊#95C2211yescharacteristic
51C2×C79⋊#95C2211yescharacteristic
52C2×C79⋊#95C2211yescharacteristic
53C2×C79⋊#95C2211yescharacteristic
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C23×D4×C79C2211yescharacteristic
60C22×C4⋊C4×C79C2211yescharacteristic
61C22×C22⋊C4×C79C2211yescharacteristic
62C22×C22⋊C4×C79C2211yescharacteristic
63C22×C22⋊C4×C79C2211yescharacteristic
64C22×C22⋊C4×C79C2211yescharacteristic
65#394×C79C2218yes—
66C2×#95×C79C2211yescharacteristic
67C23×Dic79—42no—
68C23×Dic79—42no—
69C23×Dic79—42no—
70C23×Dic79C2311yescharacteristic
71C23×Dic79C2311yescharacteristic
72C23×Dic79C2311yescharacteristic
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2314yes—
79C2×C4⋊Dic79—42no—
80C2×C4⋊Dic79—42no—
81C2×C4⋊Dic79—42no—
82C2×C4⋊Dic79C2314yes—
83C2×C4⋊Dic79C2314yes—
84C2×C4⋊Dic79C2314yes—
85C2×Dic79⋊C4—42no—
86C2×Dic79⋊C4—42no—
87C2×Dic79⋊C4—42no—
88C2×Dic79⋊C4—42no—
89C2×Dic79⋊C4—42no—
90C2×Dic79⋊C4—42no—
91C2×Dic79⋊C4C2314yes—
92C2×Dic79⋊C4C2314yes—
93C2×Dic79⋊C4C2314yes—
94C2×Dic79⋊C4C2314yes—
95C2×Dic79⋊C4C2314yes—
96C2×Dic79⋊C4C2314yes—
97C2×C22⋊Dic79—24no—
98C2×C22⋊Dic79—42no—
99C2×C22⋊Dic79—42no—
100C2×C22⋊Dic79—42no—
101C2×C22⋊Dic79—42no—
102C2×C22⋊Dic79—42no—
103C2×C22⋊Dic79—42no—
104C2×C22⋊Dic79C2314yes—
105C2×C22⋊Dic79C2314yes—
106C2×C22⋊Dic79C2314yes—
107C2×C22⋊Dic79C2314yes—
108C2×C22⋊Dic79C2314yes—
109C2×C22⋊Dic79C2314yes—
110C2×C22⋊Dic79C2314yes—
111C79⋊#95C2314yes—
112C79⋊#95C2314yes—
113C79⋊#95C2314yes—
114C79⋊#95C2314yes—
115C79⋊#95C2314yes—
116C79⋊#95C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C25×C79C2311yescharacteristic
123C25×C79C2311yescharacteristic
124C22×D4×C79—24no—
125C22×D4×C79—42no—
126C22×D4×C79—42no—
127C22×D4×C79C2314yes—
128C23×C4×C79C2311yescharacteristic
129C23×C4×C79C2311yescharacteristic
130C23×C4×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C2×C4⋊C4×C79—42no—
134C2×C4⋊C4×C79C2314yes—
135C2×C22⋊C4×C79—24no—
136C2×C22⋊C4×C79—42no—
137C2×C22⋊C4×C79—42no—
138C2×C22⋊C4×C79—42no—
139C2×C22⋊C4×C79C2314yes—
140C2×C22⋊C4×C79C2314yes—
141C2×C22⋊C4×C79C2314yes—
142C2×C22⋊C4×C79C2314yes—
143#95×C79C2314yes—
144C22×Dic79—22no—
145C22×Dic79—22no—
146C22×Dic79—22no—
147C22×Dic79—22no—
148C22×Dic79—22no—
149C22×Dic79—22no—
150C22×Dic79—22no—
151C22×Dic79—22no—
152C22×Dic79—22no—
153C22×Dic79—22no—
154C22×Dic79—22no—
155C22×Dic79—22no—
156C22×Dic79—22no—
157C22×Dic79—22no—
158C22×Dic79—22no—
159C22×Dic79—22no—
160C22×Dic79—22no—
161C22×Dic79—22no—
162C22×Dic79—22no—
163C22×Dic79—22no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79—44no—
169C22×Dic79—44no—
170C22×Dic79—44no—
171C22×Dic79—416no—
172C22×Dic79C2412yes—
173C22×Dic79C2412yes—
174C22×Dic79C2412yes—
175C22×Dic79C2412yes—
176C22×Dic79C2412yes—
177C22×Dic79C2412yes—
178C22×Dic79C2412yes—
179C22×Dic79C2412yes—
180C4⋊Dic79—44no—
181C4⋊Dic79—44no—
182C4⋊Dic79—44no—
183Dic79⋊C4—44no—
184Dic79⋊C4—44no—
185Dic79⋊C4—44no—
186Dic79⋊C4—44no—
187Dic79⋊C4—44no—
188Dic79⋊C4—44no—
189C22⋊Dic79—28no—
190C22⋊Dic79—44no—
191C22⋊Dic79—44no—
192C22⋊Dic79—44no—
193C22⋊Dic79—44no—
194C22⋊Dic79—44no—
195C22⋊Dic79—44no—
196C24×C79—22no—
197C24×C79—22no—
198C24×C79—22no—
199C24×C79—22no—
200C24×C79—22no—
201C24×C79—22no—
202C24×C79—22no—
203C24×C79—22no—
204C24×C79—22no—
205C24×C79—22no—
206C24×C79—22no—
207C24×C79—22no—
208C24×C79—22no—
209C24×C79#4114yes—
210C24×C79C2412yes—
211C24×C79C2412yes—
212C24×C79C2411yescharacteristic
213C2×D4×C79—28no—
214C2×D4×C79—44no—
215C2×D4×C79—44no—
216C2×D4×C79—416no—
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×C79—22no—
231C22×C4×C79—22no—
232C22×C4×C79C2412yes—
233C22×C4×C79C2412yes—
234C22×C4×C79C2412yes—
235C22×C4×C79C2412yes—
236C22×C4×C79C2412yes—
237C4⋊C4×C79—44no—
238C22⋊C4×C79—28no—
239C22⋊C4×C79—44no—
240C22⋊C4×C79—44no—
241C22⋊C4×C79—44no—
242C23×C79—28no—
243C23×C79—28no—
244C23×C79—28no—
245C23×C79—22no—
246C23×C79—22no—
247C23×C79—22no—
248C23×C79—22no—
249C23×C79—22no—
250C23×C79—22no—
251C23×C79—22no—
252C23×C79—22no—
253C23×C79—22no—
254C23×C79—22no—
255C23×C79—22no—
256C23×C79—22no—
257C23×C79—22no—
258C23×C79—44no—
259C23×C79—44no—
260C23×C79—44no—
261C23×C79—44no—
262C23×C79—44no—
263C23×C79—44no—
264C23×C79—44no—
265C23×C79—44no—
266C23×C79—44no—
267C23×C79—44no—
268C23×C79—44no—
269C23×C79C2×#4114yes—
270C23×C79C2×#4112yes—
271C23×C79H(5,𝔽2)12yes—
272C23×C79H(5,𝔽2)12yes—
273C23×C79H(5,𝔽2)12yes—
274C23×C79H(5,𝔽2)12yes—
275C23×C792−1+412yes—
276C23×C792−1+412yes—
277C23×C79C2511yescharacteristic
278D4×C79—416no—
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—44no—
295C2×C4×C79—44no—
296C2×C4×C79—44no—
297C2×C4×C79—44no—
298C2×C4×C79—44no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
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—416no—
324C2×Dic79—44no—
325C2×Dic79—44no—
326C2×Dic79—44no—
327C2×Dic79—44no—
328C2×Dic79—44no—
329C2×Dic79—44no—
330C2×Dic79—44no—
331C2×Dic79—44no—
332C22×C79—24no—
333C22×C79—24no—
334C22×C79—24no—
335C22×C79—416no—
336C22×C79—42no—
337C22×C79—42no—
338C22×C79—42no—
339C22×C79—42no—
340C22×C79—42no—
341C22×C79—42no—
342C22×C79—42no—
343C22×C79—42no—
344C22×C79—42no—
345C22×C79—42no—
346C22×C79—42no—
347C22×C79—88no—
348C22×C79#53814yes—
349C22×C79#53914yes—
350C22×C79#53914yes—
351C22×C79#56014yes—
352C22×C79#56214yes—
353C22×C79#56214yes—
354C22×C79#56314yes—
355C22×C79C22×#4111yescharacteristic
356C22×C79C2×H(5,𝔽2)11yescharacteristic
357C22×C79C2×H(5,𝔽2)11yescharacteristic
358C22×C79C2×H(5,𝔽2)11yescharacteristic
359C22×C79C2×H(5,𝔽2)11yescharacteristic
360C22×C79C2×2−1+411yescharacteristic
361C22×C79C2×2−1+411yescharacteristic
362C4×C79—42no—
363C4×C79—42no—
364C4×C79—42no—
365C4×C79—42no—
366C4×C79—42no—
367Dic79—42no—
368Dic79—42no—
369Dic79—42no—
370Dic79—42no—
371Dic79—42no—
372Dic79—42no—
373Dic79—42no—
374Dic79—42no—
375C2×#2827—791nomaximal, Sylow
376C2×C79—44no—
377C2×C79—82no—
378C2×C79#282718yescomplemented
379C2×C79C2×#53811yescharacteristic
380C2×C79C2×#53911yescharacteristic
381C2×C79C2×#53911yescharacteristic
382C2×C79C2×#56011yescharacteristic
383C2×C79C2×#56211yescharacteristic
384C2×C79C2×#56211yescharacteristic
385C2×C79C2×#56311yescharacteristic
386#2827—7916no—
387C2×#400—791no—
388C2×#400—791no—
389C2×#399—791no—
390C2×#398—791no—
391C2×#398—791no—
392C2×#397—791no—
393C2×#397—791no—
394C2×#397—791no—
395C2×#396—791no—
396C2×#396—791no—
397C2×#394—791no—
398C2×#394D7911yescharacteristic
399C2×#386—791no—
400C2×#385—791no—
401C2×#385—791no—
402C79C2×#282711yescharacteristic, complemented, Sylow
403C23×D4C2×D7911yescharacteristic
404C24×C4—791no—
405C22×C4⋊C4—791no—
406C22×C4⋊C4—791no—
407C22×C4⋊C4—791no—
408C22×C4⋊C4—791no—
409C22×C4⋊C4—791no—
410C22×C4⋊C4—791no—
411C22×C4⋊C4—791no—
412C22×C4⋊C4—791no—
413C22×C4⋊C4—791no—
414C22×C4⋊C4C2×D7911yescharacteristic
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⋊C4C2×D7911yescharacteristic
423C22×C22⋊C4C2×D7911yescharacteristic
424C22×C22⋊C4C2×D7911yescharacteristic
425C22×C22⋊C4C2×D7911yescharacteristic
426#400—798no—
427#400—798no—
428#399—798no—
429#398—798no—
430#398—798no—
431#397—798no—
432#397—798no—
433#397—798no—
434#396—798no—
435#396—798no—
436#394—798no—
437#394C2×D7918yes—
438#386—798no—
439#385—798no—
440#385—798no—
441C2×#95—791no—
442C2×#95—791no—
443C2×#95—791no—
444C2×#95—791no—
445C2×#95—791no—
446C2×#95—791no—
447C2×#95—791no—
448C2×#95—791no—
449C2×#95—791no—
450C2×#95—791no—
451C2×#95—791no—
452C2×#95C2×D7911yescharacteristic
453C25C22×D7911yescharacteristic
454C25C22×D7911yescharacteristic
455C22×D4—24no—
456C22×D4—42no—
457C22×D4—42no—
458C22×D4C22×D7914yes—
459C23×C4—3162no—
460C23×C4—3162no—
461C23×C4—3162no—
462C23×C4—794no—
463C23×C4—791no—
464C23×C4—791no—
465C23×C4—791no—
466C23×C4—791no—
467C23×C4—791no—
468C23×C4—791no—
469C23×C4—791no—
470C23×C4—791no—
471C23×C4C22×D7911yescharacteristic
472C23×C4C22×D7911yescharacteristic
473C23×C4C22×D7911yescharacteristic
474C23×C4C22×D7911yescharacteristic
475C23×C4C22×D7911yescharacteristic
476C2×C4⋊C4—42no—
477C2×C4⋊C4—3162no—
478C2×C4⋊C4—3162no—
479C2×C4⋊C4—3162no—
480C2×C4⋊C4—3162no—
481C2×C4⋊C4—3162no—
482C2×C4⋊C4—3162no—
483C2×C4⋊C4—3162no—
484C2×C4⋊C4—3162no—
485C2×C4⋊C4—3162no—
486C2×C4⋊C4—794no—
487C2×C4⋊C4—794no—
488C2×C4⋊C4—794no—
489C2×C4⋊C4—794no—
490C2×C4⋊C4—794no—
491C2×C4⋊C4—794no—
492C2×C4⋊C4—794no—
493C2×C4⋊C4—794no—
494C2×C4⋊C4—794no—
495C2×C4⋊C4C22×D7914yes—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—3162no—
501C2×C22⋊C4—3162no—
502C2×C22⋊C4—3162no—
503C2×C22⋊C4—3162no—
504C2×C22⋊C4—3162no—
505C2×C22⋊C4—3162no—
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—1584no—
514C2×C22⋊C4C22×D7914yes—
515C2×C22⋊C4C22×D7914yes—
516C2×C22⋊C4C22×D7914yes—
517C2×C22⋊C4C22×D7914yes—
518#95—794no—
519#95—794no—
520#95—794no—
521#95—794no—
522#95—794no—
523#95—794no—
524#95—794no—
525#95—794no—
526#95—794no—
527#95—794no—
528#95—794no—
529#95C22×D7914yes—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24#1192962314yes—
544C24C23×D7912yes—
545C24C23×D7912yes—
546C24C23×D7911yescharacteristic
547C2×D4—28no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—416no—
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—31616no—
567C22×C4—3164no—
568C22×C4—3164no—
569C22×C4—3164no—
570C22×C4—792no—
571C22×C4—792no—
572C22×C4—792no—
573C22×C4—792no—
574C22×C4—792no—
575C22×C4—792no—
576C22×C4—792no—
577C22×C4—792no—
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×C4—1582no—
595C22×C4—1582no—
596C22×C4—1582no—
597C22×C4—1582no—
598C22×C4—1582no—
599C22×C4—1582no—
600C22×C4—1582no—
601C22×C4—1582no—
602C22×C4C23×D7912yes—
603C22×C4C23×D7912yes—
604C22×C4C23×D7912yes—
605C22×C4C23×D7912yes—
606C22×C4C23×D7912yes—
607C4⋊C4—44no—
608C4⋊C4—3164no—
609C4⋊C4—3164no—
610C4⋊C4—3164no—
611C4⋊C4—3164no—
612C4⋊C4—3164no—
613C4⋊C4—3164no—
614C4⋊C4—3164no—
615C4⋊C4—3164no—
616C4⋊C4—3164no—
617C22⋊C4—28no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—3164no—
622C22⋊C4—3164no—
623C22⋊C4—3164no—
624C22⋊C4—3164no—
625C22⋊C4—3164no—
626C22⋊C4—3164no—
627C22⋊C4—1588no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23C2×#1192962314yes—
656C23C2×#1192962312yes—
657C23#1457920612yes—
658C23#1457920612yes—
659C23#1457920612yes—
660C23#1457920712yes—
661C23#1457920812yes—
662C23#1457920812yes—
663C23C24×D7911yescharacteristic
664D4—416no—
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—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—31616no—
686C2×C4—3164no—
687C2×C4—3164no—
688C2×C4—3164no—
689C2×C4—3164no—
690C2×C4—3164no—
691C2×C4—3164no—
692C2×C4—3164no—
693C2×C4—3164no—
694C2×C4—1582no—
695C2×C4—1582no—
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—1582no—
714C2×C4—1582no—
715C2×C4—1582no—
716C2×C4—1582no—
717C2×C4—1582no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—416no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—88no—
734C22#1909914814yes—
735C22#1909915714yes—
736C22#1909915814yes—
737C22#1909930114yes—
738C22#1909930714yes—
739C22#1909930814yes—
740C22#1909931614yes—
741C22C22×#1192962311yescharacteristic
742C22C2×#1457920611yescharacteristic
743C22C2×#1457920611yescharacteristic
744C22C2×#1457920611yescharacteristic
745C22C2×#1457920711yescharacteristic
746C22C2×#1457920811yescharacteristic
747C22C2×#1457920811yescharacteristic
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—3162no—
754C4—3162no—
755C4—3162no—
756C4—3162no—
757C4—3162no—
758C4—3162no—
759C4—3162no—
760C4—3162no—
761C2—44no—
762C2—82no—
763C2#2377150818yesdirect product factor
764C2C2×#1909914811yescharacteristic
765C2C2×#1909915711yescharacteristic
766C2C2×#1909915811yescharacteristic
767C2C2×#1909930111yescharacteristic
768C2C2×#1909930711yescharacteristic
769C2C2×#1909930811yescharacteristic
770C2C2×#1909931611yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#394×C79C2
socleC24×C79C24
prime radicalC23×D4×C79C22
hypercenterC2×#394D79
hypocenterC79C2×#2827
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #23771508C2direct (N × H)
2. C2×#19098503C2semidirect
3. C2×#19098501C2semidirect
4. C2×#19098499C2semidirect
5. C2×#19098497C2semidirect
6. C2×#19098496C2semidirect
7. C2×#19098491C2semidirect
8. C2×#19098491C2semidirect
9. C2×#19098488C2semidirect
10. C2×#19098486C2semidirect
11. C2×#19098486C2semidirect
14. C2×#19098438C2semidirect
15. C2×#19098435C2semidirect
34. #19098503C22semidirect
35. #19098501C22semidirect
36. #19098499C22semidirect
37. #19098497C22semidirect
38. #19098496C22semidirect
39. #19098491C22semidirect
40. #19098491C22semidirect
41. #19098488C22semidirect
42. #19098486C22semidirect
43. #19098486C22semidirect
46. #19098438C22semidirect
47. #19098435C22semidirect
378. C2×C79#2827semidirect
402. C79C2×#2827semidirect
763. C2#23771508direct (N × H)

Maximal subgroups

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

subgroupindex
#237715082
C2×#190985032
C2×#190985012
C2×#190984992
C2×#190984972
C2×#190984962
C2×#190984912
C2×#190984882
C2×#190984862
C2×#190984772
C2×#190984432
C2×#190984382
C2×#190984352
C2×#394×C792
C2×#282779