Finite Group Databasebeta

← C2×#23777488 #35196484

Subgroups — C2×#23777488 #35196484

Order 20224.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777488C2132yesmaximal, direct product factor
2C2×#19099289C212yesmaximal, complemented
3C2×#19099288C211yesmaximal, characteristic, complemented
4C2×#19099288C211yesmaximal, characteristic, complemented
5C2×#19099287C211yesmaximal, characteristic, complemented
6C2×#19099285C212yesmaximal, complemented
7C2×#19099255C212yesmaximal, complemented
8C2×#19099246C214yesmaximal, complemented
9C2×#19099228C211yesmaximal, characteristic, complemented
10C2×#19099226C212yesmaximal, complemented
11C2×#19099172C214yesmaximal, complemented
12C2×#19099171C212yesmaximal, complemented
13C2×#19099115C212yesmaximal, complemented
14C2×#19099099C212yesmaximal
15C2×#19099097C211yesmaximal, characteristic
16C2×#19099039C212yesmaximal, complemented
17C22×C4×Dic158C211yesmaximal, characteristic, complemented
18C2×#533×C79C211yesmaximal, characteristic, complemented
19C23×Dic158C2211yescharacteristic
20C22×Q8×D79C2212yes—
21#19099289C22132yescomplemented
22#19099288C22116yescomplemented
23#19099288C22116yescomplemented
24#19099287C22116yescomplemented
25#19099285C22132yescomplemented
26#19099255C22132yescomplemented
27#19099246C22164yescomplemented
28#19099228C22116yescomplemented
29#19099226C22132yescomplemented
30#19099172C22164yescomplemented
31#19099171C22132yescomplemented
32#19099115C22132yescomplemented
33C2×#14579160C2214yes—
34C2×#14579160C2212yes—
35C2×#14579159C2212yes—
36C2×#14579159C2212yes—
37#19099099C22132yes—
38#19099097C22116yes—
39C2×#14579156C2214yes—
40C2×#14579156C2214yes—
41C2×#14579156C2214yes—
42C2×#14579155C2214yes—
43C2×#14579155C2212yes—
44C2×#14579153C2214yes—
45C2×#14579153C2211yescharacteristic
46C2×#14579152C2212yes—
47C2×#14579152C2214yes—
48C2×#14579152C2212yes—
49C2×#14579151C2214yes—
50C2×#14579151C2214yes—
51C2×#14579151C2214yes—
52C2×#14579150C2212yes—
53C2×#14579149C2211yescharacteristic
54C2×#14579145C2214yes—
55C2×#14579144C2212yes—
56C2×#14579141C2212yes—
57C2×#14579140C2211yescharacteristic
58C2×#14579139C2214yes—
59C2×#14579139C2214yes—
60C2×#14579138C2214yes—
61C2×#14579137C2212yes—
62C2×#14579135C2211yescharacteristic
63#19099039C22132yescomplemented
64C2×Q8×Dic79C2212yes—
65C2×Q8×Dic79C2212yes—
66C2×Q8×Dic79C2212yes—
67C2×C4×Dic158C2211yescharacteristic
68C2×C4×Dic158C2211yescharacteristic
69C2×C4×Dic158C2212yes—
70C2×C4×Dic158C2211yescharacteristic
71C2×C4×Dic158C2211yescharacteristic
72C2×C4×Dic158C2212yes—
73C2×C4×Dic158C2214yes—
74C2×C4×Dic158C2211yescharacteristic
75C2×C4×Dic158C22116yescomplemented
76C2×#14579126C2212yes—
77C2×#14579126C2214yes—
78C2×#14579126C2212yes—
79C2×C4×D316C2211yescharacteristic
80C2×#14579123C2212yes—
81C2×C4×C22⋊D79C2212yes—
82C2×(C22⋊D79)⋊C4C2214yes—
83C2×#14579119C2212yes—
84C2×#14579119C2214yes—
85C2×#14579118C2214yes—
86C2×#14579118C2212yes—
87C2×#14579117C2214yes—
88C22×C4⋊Dic79C2211yescharacteristic
89C22×Dic79⋊C4C2212yes—
90C22×C4×Dic79C2212yes—
91#533×C79C22116yescomplemented
92C2×C4⋊Q8×C79C2211yescharacteristic
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×#125×C79C2212yes—
95C2×C22⋊Q8×C79C2212yes—
96C2×C22⋊Q8×C79C2212yes—
97C2×C4×Q8×C79C2212yes—
98C2×C4×Q8×C79C2212yes—
99C2×#117×C79C2212yes—
100C22×C42×C79C2211yescharacteristic
101C22×Dic158—28no—
102C22×Dic158C2318yes—
103C22×Dic158C2311yescharacteristic
104C22×Dic158C2314yes—
105C22×Dic158C2312yes—
106C22×Dic158C2311yescharacteristic
107C22×Dic158C2311yescharacteristic
108C2×Q8×D79—216no—
109C2×Q8×D79C23116yes—
110C22×D316C2311yescharacteristic
111C22×C22⋊D79C2312yes—
112C23×Dic79C2312yes—
113C23×Dic79C2312yes—
114C22×C4×D79C2314yes—
115C22×C4×D79C2312yes—
116#14579160C23132yes—
117#14579160C23116yes—
118#14579159C23116yes—
119#14579159C23116yes—
120#14579156C23132yes—
121#14579156C23132yes—
122#14579156C23132yes—
123#14579155C23132yes—
124#14579155C23116yes—
125#14579153C23132yes—
126#14579153C2318yes—
127#14579152C23116yes—
128#14579152C23132yes—
129#14579152C23116yes—
130#14579151C23132yes—
131#14579151C23132yes—
132#14579151C23132yes—
133#14579150C23116yes—
134#14579149C2318yes—
135#14579145C23132yes—
136#14579144C23116yes—
137#14579141C23116yes—
138#14579140C2318yes—
139#14579139C23132yes—
140#14579139C23132yes—
141#14579138C23132yes—
142#14579137C23116yes—
143#14579135C2318yes—
144Q8×Dic79C23116yes—
145Q8×Dic79C23116yes—
146Q8×Dic79C23116yes—
147C4×Dic158C2318yes—
148C4×Dic158C23116yes—
149C4×Dic158C2318yes—
150C4×Dic158C23132yes—
151C4×Dic158C23116yes—
152C4×Dic158C2318yes—
153C4×Dic158C2318yes—
154C4×Dic158C2318yes—
155#14579126C23132yes—
156#14579126C23116yes—
157#14579126C23116yes—
158C4×D316C2318yes—
159#14579123C23116yes—
160C4×C22⋊D79C23116yes—
161(C22⋊D79)⋊C4C23132yes—
162#14579119C23132yes—
163#14579119C23116yes—
164#14579118C23116yes—
165#14579118C23132yes—
166#14579117C23132yes—
167C2×C4⋊Dic79C2318yes—
168C2×C4⋊Dic79C2311yescharacteristic
169C2×C4⋊Dic79C2311yescharacteristic
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2314yes—
172C2×C4⋊Dic79C2311yescharacteristic
173C2×C4⋊Dic79C2311yescharacteristic
174C2×C4⋊Dic79C2314yes—
175C2×C4⋊Dic79C2314yes—
176C2×Dic79⋊C4C23116yes—
177C2×Dic79⋊C4C2312yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2314yes—
187C2×Dic79⋊C4C2312yes—
188C2×Dic79⋊C4C2314yes—
189C2×Dic79⋊C4C2312yes—
190C2×C22⋊Dic79C2312yes—
191C2×(C2×D79)⋊C4C2312yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2314yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2312yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×C4×Dic79C2312yes—
199C2×C4×Dic79C2312yes—
200C2×C4×Dic79C2312yes—
201C2×C4×Dic79C2312yes—
202C2×C4×Dic79C23116yes—
203C2×C4×Dic79C2314yes—
204C2×C4×Dic79C2314yes—
205C2×C4×Dic79C2312yes—
206C2×C4×Dic79C2314yes—
207C22×Q8×C79C2312yes—
208C22×Q8×C79C2312yes—
209C23×C4×C79C2311yescharacteristic
210C23×C4×C79C2311yescharacteristic
211C23×C4×C79C2311yescharacteristic
212C4⋊Q8×C79C2318yes—
213C4⋊Q8×C79C2318yes—
214#125×C79C23116yes—
215C22⋊Q8×C79C23116yes—
216C22⋊Q8×C79C23116yes—
217C4×Q8×C79C23116yes—
218C4×Q8×C79C23116yes—
219#117×C79C23116yes—
220C2×C4⋊C4×C79C2312yes—
221C2×C4⋊C4×C79C2312yes—
222C2×C4⋊C4×C79C2314yes—
223C2×C4⋊C4×C79C2314yes—
224C2×C4⋊C4×C79C2312yes—
225C2×C4⋊C4×C79C2312yes—
226C2×C22⋊C4×C79C2314yes—
227C2×C42×C79C2311yescharacteristic
228C2×C42×C79C2311yescharacteristic
229C2×C42×C79C2311yescharacteristic
230C2×C42×C79C2311yescharacteristic
231C2×C42×C79C2318yes—
232C2×C42×C79C2314yes—
233C23×D79C2412yes—
234C2×Dic158—216no—
235C2×Dic158—28no—
236C2×Dic158—232no—
237C2×Dic158—24no—
238C2×Dic158—24no—
239C2×Dic158#4118yes—
240C2×Dic158C24116yes—
241C2×Dic158C2418yes—
242C2×Dic158C2414yes—
243C2×Dic158C2414yes—
244C2×Dic158C2414yes—
245Q8×D79—264no—
246C2×D316—24no—
247C2×D316C2414yes—
248C2×C22⋊D79—28no—
249C2×C22⋊D79C2418yes—
250C22×Dic79—28no—
251C22×Dic79—28no—
252C22×Dic79C2412yes—
253C22×Dic79C2412yes—
254C22×Dic79C2418yes—
255C22×Dic79C2412yes—
256C22×Dic79C2412yes—
257C22×Dic79C2412yes—
258C22×Dic79C2412yes—
259C22×Dic79C2418yes—
260C22×Dic79C2412yes—
261C2×C4×D79—216no—
262C2×C4×D79—28no—
263C2×C4×D79C24116yes—
264C2×C4×D79C2418yes—
265C4⋊Dic79C2414yes—
266C4⋊Dic79C2414yes—
267C4⋊Dic79C2418yes—
268C4⋊Dic79C24116yes—
269C4⋊Dic79C2414yes—
270C4⋊Dic79C2414yes—
271C4⋊Dic79C24116yes—
272C4⋊Dic79C24116yes—
273Dic79⋊C4C2418yes—
274Dic79⋊C4C2418yes—
275Dic79⋊C4C2418yes—
276Dic79⋊C4C2418yes—
277Dic79⋊C4C24116yes—
278Dic79⋊C4C24116yes—
279Dic79⋊C4C24116yes—
280Dic79⋊C4C2418yes—
281Dic79⋊C4C2418yes—
282Dic79⋊C4C24116yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C24116yes—
285Dic79⋊C4C2418yes—
286C22⋊Dic79C2418yes—
287(C2×D79)⋊C4C2418yes—
288(C2×D79)⋊C4C2418yes—
289(C2×D79)⋊C4C24116yes—
290(C2×D79)⋊C4C24116yes—
291(C2×D79)⋊C4C2418yes—
292(C2×D79)⋊C4C24116yes—
293(C2×D79)⋊C4C2418yes—
294C4×Dic79C2418yes—
295C4×Dic79C2418yes—
296C4×Dic79C2418yes—
297C4×Dic79C2418yes—
298C4×Dic79C24116yes—
299C4×Dic79C24116yes—
300C4×Dic79C2418yes—
301C4×Dic79C24116yes—
302C24×C79C2411yescharacteristic
303C2×Q8×C79—28no—
304C2×Q8×C79—28no—
305C2×Q8×C79C2418yes—
306C2×Q8×C79C2418yes—
307C22×C4×C79—24no—
308C22×C4×C79—24no—
309C22×C4×C79—24no—
310C22×C4×C79C2411yescharacteristic
311C22×C4×C79C2414yes—
312C22×C4×C79C2414yes—
313C22×C4×C79C2411yescharacteristic
314C22×C4×C79C2411yescharacteristic
315C22×C4×C79C2411yescharacteristic
316C22×C4×C79C2414yes—
317C22×C4×C79C2414yes—
318C22×C4×C79C2414yes—
319C22×C4×C79C2411yescharacteristic
320C22×C4×C79C2411yescharacteristic
321C4⋊C4×C79C2418yes—
322C4⋊C4×C79C2418yes—
323C4⋊C4×C79C24116yes—
324C4⋊C4×C79C24116yes—
325C4⋊C4×C79C2418yes—
326C4⋊C4×C79C2418yes—
327C22⋊C4×C79C24116yes—
328C42×C79C2414yes—
329C42×C79C2414yes—
330C42×C79C2414yes—
331C42×C79C2414yes—
332C42×C79C24116yes—
333C23×C79—22no—
334C23×C79—22no—
335C23×C792−1+414yes—
336C23×C79C2512yes—
337C23×C79C2511yescharacteristic
338C22×D79—24no—
339C22×D79—24no—
340C22×D79—24no—
341C22×D79C2514yes—
342Q8×C79—216no—
343Q8×C79—216no—
344C2×C4×C79—28no—
345C2×C4×C79—22no—
346C2×C4×C79—22no—
347C2×C4×C79—28no—
348C2×C4×C79—22no—
349C2×C4×C79—22no—
350C2×C4×C79—28no—
351C2×C4×C79—28no—
352C2×C4×C79—28no—
353C2×C4×C79C2×#4114yes—
354C2×C4×C792−1+414yes—
355C2×C4×C79C2512yes—
356C2×C4×C79C2518yes—
357C2×C4×C79C2518yes—
358C2×C4×C79C2512yes—
359C2×C4×C79C2512yes—
360C2×C4×C79C2512yes—
361C2×C4×C79C2512yes—
362C2×C4×C79C2512yes—
363C22⋊D79—216no—
364C2×Dic79—24no—
365C2×Dic79—24no—
366C2×Dic79—216no—
367C2×Dic79—24no—
368C2×Dic79—24no—
369C2×Dic79—24no—
370C2×Dic79—24no—
371C2×Dic79—216no—
372C2×Dic79C2×#4118yes—
373C2×Dic79C2514yes—
374C2×Dic79C2514yes—
375C2×Dic79C2514yes—
376C2×Dic79C2514yes—
377C2×Dic79C2514yes—
378C2×Dic79C2514yes—
379C2×Dic79C2514yes—
380D316—28no—
381C4×D79—216no—
382C4×D79—232no—
383Dic158—28no—
384Dic158—28no—
385Dic158—232no—
386Dic158—216no—
387Dic158C2×#41116yes—
388C22×C79—22no—
389C22×C79—22no—
390C22×C79—28no—
391C22×C79C22×#4112yes—
392C22×C79C2×2−1+412yes—
393C22×C79C2×2−1+414yes—
394C22×C79C2×2−1+412yes—
395C22×C79C2611yescharacteristic
396C2×D79—24no—
397C2×D79—24no—
398C2×D79—24no—
399C2×D79—48no—
400C4×C79—22no—
401C4×C79—28no—
402C4×C79—22no—
403C4×C79—22no—
404C4×C79—22no—
405C4×C79—28no—
406C4×C79C22×#4114yes—
407C4×C79C2×2−1+414yes—
408Dic79—24no—
409Dic79—24no—
410Dic79—24no—
411Dic79—24no—
412Dic79—24no—
413Dic79—24no—
414Dic79C22×#4118yes—
415C2×#3523—791nomaximal, Sylow
416C2×C79—24no—
417C2×C79#352314yescomplemented
418C2×C79C23×#4111yescharacteristic
419C2×C79C22×2−1+411yescharacteristic
420C2×C79C22×2−1+411yescharacteristic
421D79—44no—
422#3523—7932no—
423C2×#557—791no—
424C2×#557—791no—
425C2×#557—792no—
426C2×#556—791no—
427C2×#556—792no—
428C2×#552—792no—
429C2×#552—794no—
430C2×D4×Q8—791no—
431C2×D4×Q8—792no—
432C2×#541—794no—
433C2×#541—792no—
434C2×#533—792no—
435C2×#533D7911yescharacteristic, complemented
436C2×#529—791no—
437C2×#529—792no—
438C2×#519—792no—
439C22×C4×Q8—791no—
440C79C2×#352311yescharacteristic, complemented, Sylow
441C23×Q8—792no—
442C23×Q8—791no—
443#557—7916no—
444#557—7916no—
445#557—7932no—
446#556—7916no—
447#556—7932no—
448#552—7932no—
449#552—7964no—
450D4×Q8—7916no—
451D4×Q8—7932no—
452#541—7964no—
453#541—7932no—
454#533—7932no—
455#533C2×D79116yescomplemented
456C2×C4⋊Q8—792no—
457C2×C4⋊Q8—792no—
458C2×C4⋊Q8—792no—
459C2×C4⋊Q8—794no—
460C2×C4⋊Q8C2×D7911yescharacteristic
461C2×C4⋊Q8C2×D7911yescharacteristic
462#529—7932no—
463#529—7916no—
464C2×#126—794no—
465C2×#126—794no—
466C2×#126—794no—
467C2×#126—792no—
468C2×#126—794no—
469C2×#125—792no—
470C2×#125—794no—
471C2×#125—794no—
472C2×#125—794no—
473C2×#125—794no—
474C2×#125—792no—
475C2×#125—791no—
476C2×#125—794no—
477C2×#125C2×D7912yes—
478C2×#124—792no—
479C2×#124—791no—
480C2×#123—792no—
481C2×#123—794no—
482C2×C22⋊Q8—792no—
483C2×C22⋊Q8—791no—
484C2×C22⋊Q8—794no—
485C2×C22⋊Q8—794no—
486C2×C22⋊Q8—792no—
487C2×C22⋊Q8—794no—
488C2×C22⋊Q8C2×D7912yes—
489C2×C22⋊Q8C2×D7912yes—
490C2×#121—791no—
491#519—7932no—
492C2×C4×Q8—792no—
493C2×C4×Q8—792no—
494C2×C4×Q8—792no—
495C2×C4×Q8—794no—
496C2×C4×Q8—792no—
497C2×C4×Q8—792no—
498C2×C4×Q8—791no—
499C2×C4×Q8—792no—
500C2×C4×Q8—791no—
501C2×C4×Q8—791no—
502C2×C4×Q8—792no—
503C2×C4×Q8—791no—
504C2×C4×Q8—7916no—
505C2×C4×Q8—794no—
506C2×C4×Q8—791no—
507C2×C4×Q8C2×D7912yes—
508C2×C4×Q8C2×D7912yes—
509C2×C4×D4—792no—
510C2×C4×D4—792no—
511C2×C4×D4—794no—
512C2×C4×D4—791no—
513C2×#117—794no—
514C2×#117—792no—
515C2×#117—794no—
516C2×#117—792no—
517C2×#117—794no—
518C2×#117C2×D7912yes—
519C22×C4⋊C4—792no—
520C22×C4⋊C4—791no—
521C22×C42—792no—
522C22×C42C2×D7911yescharacteristic
523C22×Q8—7916no—
524C22×Q8—791no—
525C22×Q8—791no—
526C22×Q8—794no—
527C22×Q8—792no—
528C22×Q8—791no—
529C22×Q8—798no—
530C22×Q8—1588no—
531C22×Q8—15816no—
532C22×Q8C22×D7912yes—
533C22×Q8C22×D7912yes—
534C22×D4—792no—
535C22×D4—791no—
536C23×C4—792no—
537C23×C4—792no—
538C23×C4—794no—
539C23×C4—792no—
540C23×C4C22×D7911yescharacteristic
541C23×C4C22×D7911yescharacteristic
542C23×C4C22×D7911yescharacteristic
543C4⋊Q8—7916no—
544C4⋊Q8—7916no—
545C4⋊Q8—7916no—
546C4⋊Q8—7932no—
547C4⋊Q8C22×D7918yes—
548C4⋊Q8C22×D7918yes—
549#126—7932no—
550#126—7932no—
551#126—7932no—
552#126—7916no—
553#126—7932no—
554#125—7916no—
555#125—7932no—
556#125—7932no—
557#125—7932no—
558#125—7932no—
559#125—7916no—
560#125—798no—
561#125—7932no—
562#125C22×D79116yes—
563#124—7916no—
564#124—798no—
565#123—7916no—
566#123—7932no—
567C22⋊Q8—7916no—
568C22⋊Q8—798no—
569C22⋊Q8—7932no—
570C22⋊Q8—7932no—
571C22⋊Q8—7916no—
572C22⋊Q8—7932no—
573C22⋊Q8C22×D79116yes—
574C22⋊Q8C22×D79116yes—
575#121—798no—
576C4×Q8—7916no—
577C4×Q8—7916no—
578C4×Q8—7916no—
579C4×Q8—7932no—
580C4×Q8—7916no—
581C4×Q8—7916no—
582C4×Q8—798no—
583C4×Q8—7916no—
584C4×Q8—798no—
585C4×Q8—798no—
586C4×Q8—7916no—
587C4×Q8—798no—
588C4×Q8—7932no—
589C4×Q8—798no—
590C4×Q8C22×D79116yes—
591C4×Q8C22×D79116yes—
592C4×D4—7916no—
593C4×D4—7916no—
594C4×D4—7932no—
595C4×D4—798no—
596#117—7932no—
597#117—7916no—
598#117—7932no—
599#117—7916no—
600#117—7932no—
601#117C22×D79116yes—
602C2×C4⋊C4—792no—
603C2×C4⋊C4—791no—
604C2×C4⋊C4—792no—
605C2×C4⋊C4—791no—
606C2×C4⋊C4—792no—
607C2×C4⋊C4—792no—
608C2×C4⋊C4—792no—
609C2×C4⋊C4—7916no—
610C2×C4⋊C4—798no—
611C2×C4⋊C4—794no—
612C2×C4⋊C4—792no—
613C2×C4⋊C4—792no—
614C2×C4⋊C4—794no—
615C2×C4⋊C4—794no—
616C2×C4⋊C4—794no—
617C2×C4⋊C4—791no—
618C2×C4⋊C4—794no—
619C2×C4⋊C4—792no—
620C2×C4⋊C4—791no—
621C2×C4⋊C4—794no—
622C2×C4⋊C4—794no—
623C2×C4⋊C4—792no—
624C2×C4⋊C4—794no—
625C2×C4⋊C4C22×D7912yes—
626C2×C4⋊C4C22×D7914yes—
627C2×C4⋊C4C22×D7912yes—
628C2×C4⋊C4C22×D7912yes—
629C2×C4⋊C4C22×D7912yes—
630C2×C4⋊C4C22×D7914yes—
631C2×C22⋊C4—792no—
632C2×C22⋊C4—792no—
633C2×C22⋊C4—794no—
634C2×C22⋊C4—792no—
635C2×C22⋊C4—794no—
636C2×C22⋊C4—792no—
637C2×C22⋊C4—792no—
638C2×C22⋊C4—794no—
639C2×C22⋊C4C22×D7914yes—
640C2×C42—792no—
641C2×C42—794no—
642C2×C42—794no—
643C2×C42—794no—
644C2×C42—792no—
645C2×C42—792no—
646C2×C42—792no—
647C2×C42—792no—
648C2×C42—7916no—
649C2×C42C22×D7911yescharacteristic
650C2×C42C22×D7914yes—
651C2×C42C22×D7911yescharacteristic
652C2×C42C22×D7911yescharacteristic
653C2×C42C22×D7911yescharacteristic
654C2×C42C22×D7918yes—
655C24—792no—
656C24C23×D7911yescharacteristic
657C2×Q8—28no—
658C2×Q8—28no—
659C2×Q8—798no—
660C2×Q8—794no—
661C2×Q8—794no—
662C2×Q8—7916no—
663C2×Q8—798no—
664C2×Q8—794no—
665C2×Q8—1588no—
666C2×Q8—15816no—
667C2×Q8—15832no—
668C2×Q8—15864no—
669C2×Q8—1584no—
670C2×Q8—1584no—
671C2×Q8C23×D7918yes—
672C2×Q8C23×D7918yes—
673C2×D4—798no—
674C2×D4—794no—
675C2×D4—1588no—
676C2×D4—1584no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—792no—
681C22×C4—798no—
682C22×C4—798no—
683C22×C4—792no—
684C22×C4—792no—
685C22×C4—792no—
686C22×C4—792no—
687C22×C4—792no—
688C22×C4—792no—
689C22×C4—7916no—
690C22×C4—798no—
691C22×C4—15816no—
692C22×C4—1588no—
693C22×C4—1588no—
694C22×C4—1588no—
695C22×C4C23×D7914yes—
696C22×C4C23×D7914yes—
697C22×C4C23×D7914yes—
698C22×C4C23×D7911yescharacteristic
699C22×C4C23×D7914yes—
700C22×C4C23×D7914yes—
701C22×C4C23×D7911yescharacteristic
702C22×C4C23×D7911yescharacteristic
703C22×C4C23×D7911yescharacteristic
704C22×C4C23×D7911yescharacteristic
705C22×C4C23×D7911yescharacteristic
706C4⋊C4—798no—
707C4⋊C4—798no—
708C4⋊C4—798no—
709C4⋊C4—798no—
710C4⋊C4—7916no—
711C4⋊C4—798no—
712C4⋊C4—798no—
713C4⋊C4—7916no—
714C4⋊C4—7916no—
715C4⋊C4—7916no—
716C4⋊C4—798no—
717C4⋊C4—7916no—
718C4⋊C4—798no—
719C4⋊C4—794no—
720C4⋊C4—794no—
721C4⋊C4—798no—
722C4⋊C4—7916no—
723C4⋊C4—794no—
724C4⋊C4—794no—
725C4⋊C4—7916no—
726C4⋊C4—7916no—
727C4⋊C4C23×D7918yes—
728C4⋊C4C23×D79116yes—
729C4⋊C4C23×D7918yes—
730C4⋊C4C23×D7918yes—
731C4⋊C4C23×D7918yes—
732C4⋊C4C23×D79116yes—
733C22⋊C4—798no—
734C22⋊C4—798no—
735C22⋊C4—7916no—
736C22⋊C4—798no—
737C22⋊C4—7916no—
738C22⋊C4—798no—
739C22⋊C4—798no—
740C22⋊C4—7916no—
741C22⋊C4C23×D79116yes—
742C42—798no—
743C42—798no—
744C42—798no—
745C42—798no—
746C42—7916no—
747C42—7916no—
748C42—7916no—
749C42—798no—
750C42C23×D7914yes—
751C42C23×D7914yes—
752C42C23×D7914yes—
753C42C23×D7914yes—
754C42C23×D79116yes—
755C23—22no—
756C23—22no—
757C23—794no—
758C23—1584no—
759C23—1584no—
760C23—1584no—
761C23#1457920914yes—
762C23C24×D7912yes—
763C23C24×D7911yescharacteristic
764Q8—216no—
765Q8—216no—
766Q8—7916no—
767Q8—15816no—
768Q8—15832no—
769Q8—1588no—
770Q8—1588no—
771D4—15816no—
772D4—1588no—
773C2×C4—22no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—794no—
783C2×C4—798no—
784C2×C4—794no—
785C2×C4—794no—
786C2×C4—794no—
787C2×C4—794no—
788C2×C4—794no—
789C2×C4—794no—
790C2×C4—15832no—
791C2×C4—15816no—
792C2×C4—1584no—
793C2×C4—15816no—
794C2×C4—1584no—
795C2×C4—1584no—
796C2×C4—1584no—
797C2×C4—1584no—
798C2×C4—1584no—
799C2×C4—15816no—
800C2×C4#41×D7914yes—
801C2×C4#1457920814yes—
802C2×C4C24×D7912yes—
803C2×C4C24×D7918yes—
804C2×C4C24×D7918yes—
805C2×C4C24×D7912yes—
806C2×C4C24×D7912yes—
807C2×C4C24×D7912yes—
808C2×C4C24×D7912yes—
809C2×C4C24×D7912yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—3168no—
814C22—1584no—
815C22—1584no—
816C22—1584no—
817C22C2×#41×D7912yes—
818C22C2×#1457920812yes—
819C22C2×#1457920914yes—
820C22C2×#1457920912yes—
821C22C25×D7911yescharacteristic
822C4—22no—
823C4—28no—
824C4—22no—
825C4—28no—
826C4—22no—
827C4—22no—
828C4—798no—
829C4—1584no—
830C4—1584no—
831C4—1584no—
832C4—1584no—
833C4—1584no—
834C4—1584no—
835C4C2×#41×D7914yes—
836C4C2×#1457920814yes—
837C2—24no—
838C2—3164no—
839C2#2377748814yesdirect product factor
840C2C22×#41×D7911yescharacteristic
841C2C22×#1457920811yescharacteristic
842C2C22×#1457920911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#533×C79C2
socleC23×C79C25
prime radicalC2×#14579135C22
hypercenterC2×#533D79
hypocenterC79C2×#3523
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #23777488C2direct (N × H)
2. C2×#19099289C2semidirect
3. C2×#19099288C2semidirect
4. C2×#19099288C2semidirect
5. C2×#19099287C2semidirect
6. C2×#19099285C2semidirect
7. C2×#19099255C2semidirect
8. C2×#19099246C2semidirect
9. C2×#19099228C2semidirect
10. C2×#19099226C2semidirect
11. C2×#19099172C2semidirect
12. C2×#19099171C2semidirect
13. C2×#19099115C2semidirect
16. C2×#19099039C2semidirect
17. C22×C4×Dic158C2semidirect
18. C2×#533×C79C2semidirect
21. #19099289C22semidirect
22. #19099288C22semidirect
23. #19099288C22semidirect
24. #19099287C22semidirect
25. #19099285C22semidirect
26. #19099255C22semidirect
27. #19099246C22semidirect
28. #19099228C22semidirect
29. #19099226C22semidirect
30. #19099172C22semidirect
31. #19099171C22semidirect
32. #19099115C22semidirect
63. #19099039C22semidirect
75. C2×C4×Dic158C22semidirect
91. #533×C79C22semidirect
417. C2×C79#3523semidirect
435. C2×#533D79semidirect
440. C79C2×#3523semidirect
455. #533C2×D79semidirect
839. C2#23777488direct (N × H)

Maximal subgroups

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

subgroupindex
#237774882
C2×#190992892
C2×#190992882
C2×#190992872
C2×#190992852
C2×#190992552
C2×#190992462
C2×#190992282
C2×#190992262
C2×#190991722
C2×#190991712
C2×#190991152
C2×#190990992
C2×#190990972
C2×#190990392
C22×C4×Dic1582
C2×#533×C792
C2×#352379