Finite Group Databasebeta

← C2×#548×D79 #35195199

Subgroups — C2×#548×D79 #35195199

Order 20224.

12142 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D79C211yesmaximal, characteristic, complemented
2C23×Q8×D79C211yesmaximal, characteristic, complemented
3C2×#19099225C211yesmaximal, characteristic, complemented
4C2×#19099224C211yesmaximal, characteristic, complemented
5C2×#19099223C213yesmaximal, complemented
6C2×#19099222C213yesmaximal, complemented
7C2×#19099221C213yesmaximal, complemented
8C2×#19099220C211yesmaximal, characteristic, complemented
9C2×#19099219C213yesmaximal, complemented
10#548×D79C2132yesmaximal, direct product factor
11C2×#124×D79C213yesmaximal, complemented
12C2×C22⋊Q8×D79C213yesmaximal, complemented
13C2×#121×D79C213yesmaximal, complemented
14C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
15C2×C4×D4×D79C213yesmaximal, complemented
16C2×#548×C79C211yesmaximal, characteristic, complemented
17C22×#11929625C2211yescharacteristic, complemented
18C22×#11929624C2213yescomplemented
19C22×#11929623C2213yescomplemented
20C2×#41×D79—216no—
21C2×#41×D79C22116yescomplemented
22C23×Dic158C2213yescomplemented
23C22×Q8×D79—216no—
24C22×Q8×D79C2213yes—
25C22×Q8×D79C2211yescharacteristic
26C22×Q8×D79C22116yescomplemented
27C22×Q8×D79C2211yescharacteristic, complemented
28C22×Q8×D79C2213yescomplemented
29C22×D4×D79C2213yes—
30C22×D4×D79C2213yes—
31C23×C4×D79C2213yes—
32C23×C4×D79C2213yes—
33#19099225C22116yescomplemented
34#19099224C22116yescomplemented
35#19099223C22148yescomplemented
36#19099222C22148yescomplemented
37#19099221C22148yescomplemented
38#19099220C22116yescomplemented
39#19099219C22148yescomplemented
40C2×#14579150C2213yescomplemented
41C2×#14579149C2213yescomplemented
42C2×#14579148C2213yescomplemented
43C2×#14579147C2216yescomplemented
44C2×#14579147C2216yescomplemented
45#124×D79C22148yescomplemented
46C2×#14579141C2213yescomplemented
47C2×#14579140C2213yescomplemented
48C2×#14579139C2216yescomplemented
49C2×#14579138C2216yescomplemented
50C2×#14579137C2213yescomplemented
51C22⋊Q8×D79C22148yescomplemented
52C2×#14579136C2213yescomplemented
53C2×#14579135C2213yescomplemented
54C2×#14579134C2216yescomplemented
55C2×#14579133C2216yescomplemented
56C2×#14579132C2213yescomplemented
57#121×D79C22148yescomplemented
58C2×Q8×Dic79C2211yescharacteristic, complemented
59C2×C4×Dic158C2213yescomplemented
60C2×#14579126C2213yescomplemented
61C4×Q8×D79C22116yescomplemented
62C2×C4×D316C2213yescomplemented
63C2×D4×Dic79C2213yescomplemented
64C2×#14579123C2213yescomplemented
65C2×C4×C22⋊D79C2213yescomplemented
66C2×C4×C22⋊D79C2213yescomplemented
67C2×(C22⋊D79)⋊C4C2213yescomplemented
68C2×(C22⋊D79)⋊C4C2213yescomplemented
69C4×D4×D79C22148yescomplemented
70C2×C4⋊C4×D79C2213yes—
71C2×C4⋊C4×D79C2213yes—
72C2×C22⋊C4×D79C2211yescharacteristic
73C2×C22⋊C4×D79C2213yes—
74C2×C22⋊C4×D79C2216yes—
75C2×C42×D79C2213yes—
76C22×#41×C79C2211yescharacteristic, complemented
77C23×Q8×C79C2211yescharacteristic, complemented
78#548×C79C22116yescomplemented
79C2×#124×C79C2213yescomplemented
80C2×C22⋊Q8×C79C2213yescomplemented
81C2×#121×C79C2213yescomplemented
82C2×C4×Q8×C79C2211yescharacteristic, complemented
83C2×C4×D4×C79C2213yescomplemented
84C24×D79C2313yes—
85C24×D79C2311yescharacteristic
86C2×#11929625—28no—
87C2×#11929625C2318yescomplemented
88C2×#11929624—224no—
89C2×#11929624C23124yescomplemented
90C2×#11929623—224no—
91C2×#11929623C23124yescomplemented
92#41×D79—2128no—
93C22×Dic158—224no—
94C22×Dic158C2316yes—
95C22×Dic158C2313yes—
96C22×Dic158C2313yes—
97C22×Dic158C23124yescomplemented
98C2×Q8×D79—28no—
99C2×Q8×D79—224no—
100C2×Q8×D79—2128no—
101C2×Q8×D79—224no—
102C2×Q8×D79D4116yescomplemented
103C2×Q8×D79C23124yes—
104C2×Q8×D79C2318yes—
105C2×Q8×D79C2318yescomplemented
106C2×Q8×D79C23124yescomplemented
107C22×D316C2313yes—
108C22×D316C2313yes—
109C22×C22⋊D79C2313yes—
110C22×C22⋊D79C2313yes—
111C22×C22⋊D79C2316yes—
112C2×D4×D79—224no—
113C2×D4×D79—224no—
114C2×D4×D79C23124yes—
115C2×D4×D79C23124yes—
116C23×Dic79C2313yes—
117C23×Dic79C2313yes—
118C22×C4×D79—224no—
119C22×C4×D79—224no—
120C22×C4×D79C2311yescharacteristic
121C22×C4×D79C2313yes—
122C22×C4×D79C2313yes—
123C22×C4×D79C2311yescharacteristic
124C22×C4×D79C23124yes—
125C22×C4×D79C23124yes—
126C22×C4×D79C2313yes—
127C22×C4×D79C2313yes—
128C22×C4×D79C2313yes—
129C22×C4×D79C2313yes—
130C22×C4×D79C2313yes—
131#14579150C23124yescomplemented
132#14579149C23124yescomplemented
133#14579148C23124yescomplemented
134#14579147C23148yescomplemented
135#14579147C23148yescomplemented
136#14579141C23124yescomplemented
137#14579140C23124yescomplemented
138#14579139C23148yescomplemented
139#14579138C23148yescomplemented
140#14579137C23124yescomplemented
141#14579136C23124yescomplemented
142#14579135C23124yescomplemented
143#14579134C23148yescomplemented
144#14579133C23148yescomplemented
145#14579132C23124yescomplemented
146Q8×Dic79C2318yescomplemented
147C4×Dic158C23124yescomplemented
148#14579126C23124yescomplemented
149C4×D316C23124yescomplemented
150D4×Dic79C23124yescomplemented
151#14579123C23124yescomplemented
152C4×C22⋊D79C23124yescomplemented
153C4×C22⋊D79C23124yescomplemented
154(C22⋊D79)⋊C4C23124yescomplemented
155(C22⋊D79)⋊C4C23124yescomplemented
156C2×C4⋊Dic79C2313yes—
157C2×C4⋊Dic79C2313yes—
158C2×Dic79⋊C4C2313yes—
159C2×Dic79⋊C4C2313yes—
160C2×Dic79⋊C4C2316yes—
161C4⋊C4×D79C23124yes—
162C4⋊C4×D79C23124yes—
163C2×C22⋊Dic79C2311yescharacteristic
164C2×C22⋊Dic79C2313yes—
165C2×C22⋊Dic79C2316yes—
166C2×(C2×D79)⋊C4C2311yescharacteristic
167C2×(C2×D79)⋊C4C2313yes—
168C2×(C2×D79)⋊C4C2311yescharacteristic
169C2×(C2×D79)⋊C4C2313yes—
170C2×(C2×D79)⋊C4C2316yes—
171C2×(C2×D79)⋊C4C2316yes—
172C22⋊C4×D79C2318yes—
173C22⋊C4×D79C23124yes—
174C22⋊C4×D79C23148yes—
175C2×C4×Dic79C2313yes—
176C2×C4×Dic79C2313yes—
177C2×C4×Dic79C2313yes—
178C42×D79C23124yes—
179C2×#41×C79—28no—
180C2×#41×C79C2318yescomplemented
181C22×Q8×C79—28no—
182C22×Q8×C79C2313yes—
183C22×Q8×C79C2311yescharacteristic
184C22×Q8×C79C2318yescomplemented
185C22×D4×C79C2313yes—
186C22×D4×C79C2313yes—
187C23×C4×C79C2313yes—
188C23×C4×C79C2313yes—
189#124×C79C23124yescomplemented
190C22⋊Q8×C79C23124yescomplemented
191#121×C79C23124yescomplemented
192C4×Q8×C79C2318yescomplemented
193C4×D4×C79C23124yescomplemented
194C2×C4⋊C4×C79C2313yes—
195C2×C4⋊C4×C79C2313yes—
196C2×C22⋊C4×C79C2311yescharacteristic
197C2×C22⋊C4×C79C2313yes—
198C2×C22⋊C4×C79C2316yes—
199C2×C42×C79C2313yes—
200C23×D79—24no—
201C23×D79—24no—
202C23×D79—212no—
203C23×D79—212no—
204C23×D79—212no—
205C23×D79#4118yescomplemented
206C23×D79C24112yes—
207C23×D79C2413yes—
208C23×D79C2414yes—
209C23×D79C2411yescharacteristic
210C23×D79C2411yescharacteristic
211#11929625—232no—
212#11929624—296no—
213#11929623—296no—
214C2×Dic158—224no—
215C2×Dic158—296no—
216C2×Dic158—212no—
217C2×Dic158C2×D4124yescomplemented
218C2×Dic158C24124yes—
219C2×Dic158C24112yes—
220C2×Dic158C24112yes—
221Q8×D79—296no—
222Q8×D79—296no—
223Q8×D79—232no—
224Q8×D79C2×D4164yescomplemented
225C2×D316—212no—
226C2×D316—212no—
227C2×D316C24112yes—
228C2×D316C24112yes—
229C2×C22⋊D79—224no—
230C2×C22⋊D79—212no—
231C2×C22⋊D79—212no—
232C2×C22⋊D79C24124yes—
233C2×C22⋊D79C24112yes—
234C2×C22⋊D79C24112yes—
235D4×D79—296no—
236D4×D79—296no—
237C22×Dic79—212no—
238C22×Dic79—212no—
239C22×Dic79C2413yes—
240C22×Dic79C24112yes—
241C22×Dic79C24112yes—
242C22×Dic79C2411yescharacteristic
243C22×Dic79C2413yes—
244C22×Dic79C2411yescharacteristic
245C22×Dic79C2413yes—
246C2×C4×D79—212no—
247C2×C4×D79—212no—
248C2×C4×D79—296no—
249C2×C4×D79—296no—
250C2×C4×D79—212no—
251C2×C4×D79—24no—
252C2×C4×D79—212no—
253C2×C4×D79—24no—
254C2×C4×D79—212no—
255C2×C4×D79—212no—
256C2×C4×D79C2×D4124yes—
257C2×C4×D79C24112yes—
258C2×C4×D79C24112yes—
259C2×C4×D79C24112yes—
260C2×C4×D79C24112yes—
261C2×C4×D79C24112yes—
262C2×C4×D79C2414yes—
263C2×C4×D79C24112yes—
264C2×C4×D79C2414yes—
265C2×C4×D79C24112yes—
266C4⋊Dic79C24112yes—
267C4⋊Dic79C24112yes—
268Dic79⋊C4C24112yes—
269Dic79⋊C4C24112yes—
270Dic79⋊C4C24124yes—
271C22⋊Dic79C2414yes—
272C22⋊Dic79C24112yes—
273C22⋊Dic79C24124yes—
274(C2×D79)⋊C4C2414yes—
275(C2×D79)⋊C4C24112yes—
276(C2×D79)⋊C4C2414yes—
277(C2×D79)⋊C4C24112yes—
278(C2×D79)⋊C4C24124yes—
279(C2×D79)⋊C4C24124yes—
280C4×Dic79C24112yes—
281C4×Dic79C24112yes—
282C4×Dic79C24112yes—
283C24×C79C2413yes—
284C24×C79C2411yescharacteristic
285#41×C79—232no—
286C2×Q8×C79—232no—
287C2×Q8×C79—212no—
288C2×Q8×C79C2×D418yescomplemented
289C2×Q8×C79C24112yes—
290C2×Q8×C79C2414yes—
291C2×D4×C79—212no—
292C2×D4×C79—212no—
293C2×D4×C79C24112yes—
294C2×D4×C79C24112yes—
295C22×C4×C79—212no—
296C22×C4×C79—212no—
297C22×C4×C79C2413yes—
298C22×C4×C79C24112yes—
299C22×C4×C79C24112yes—
300C22×C4×C79C2411yescharacteristic
301C22×C4×C79C2413yes—
302C22×C4×C79C2411yescharacteristic
303C22×C4×C79C2413yes—
304C4⋊C4×C79C24112yes—
305C4⋊C4×C79C24112yes—
306C22⋊C4×C79C2414yes—
307C22⋊C4×C79C24112yes—
308C22⋊C4×C79C24124yes—
309C42×C79C24112yes—
310C23×C79—22no—
311C23×C79—22no—
312C23×C79—26no—
313C23×C79—26no—
314C23×C79—26no—
315C23×C79C2×#4114yescomplemented
316C23×C79C2516yes—
317C23×C79C2512yes—
318C23×C79C2511yescharacteristic
319C22×D79—22no—
320C22×D79—22no—
321C22×D79—232no—
322C22×D79—28no—
323C22×D79—28no—
324C22×D79—26no—
325C22×D79—26no—
326C22×D79—26no—
327C22×D79—224no—
328C22×D79—224no—
329C22×D79—224no—
330C22×D79—448no—
331C22×D79C22×D414yes—
332C22×D79C2×#4114yes—
333C22×D79C2×#41116yescomplemented
334C22×D79C2×#4114yescomplemented
335C22×D792−1+414yes—
336C22×D79C2516yes—
337C22×D79C2512yes—
338C22×D79C2512yes—
339Q8×C79—224no—
340Q8×C79C22×D4116yescomplemented
341D4×C79—224no—
342D4×C79—224no—
343C2×C4×C79—22no—
344C2×C4×C79—26no—
345C2×C4×C79—26no—
346C2×C4×C79—22no—
347C2×C4×C79—224no—
348C2×C4×C79—224no—
349C2×C4×C79C22×D4112yes—
350C2×C4×C79C2512yes—
351C2×C4×C79C2516yes—
352C2×C4×C79C2516yes—
353C2×C4×C79C2512yes—
354C2×C4×C79C2516yes—
355C22⋊D79—224no—
356C22⋊D79—224no—
357C22⋊D79—248no—
358C2×Dic79—22no—
359C2×Dic79—26no—
360C2×Dic79—26no—
361C2×Dic79—22no—
362C2×Dic79—224no—
363C2×Dic79—224no—
364C2×Dic79C22×D4112yes—
365C2×Dic79C2512yes—
366C2×Dic79C2516yes—
367C2×Dic79C2516yes—
368C2×Dic79C2512yes—
369C2×Dic79C2516yes—
370D316—224no—
371D316—224no—
372C4×D79—28no—
373C4×D79—224no—
374C4×D79—224no—
375C4×D79—28no—
376C4×D79—224no—
377C4×D79—224no—
378C4×D79—224no—
379C4×D79—224no—
380C4×D79C22×D4148yes—
381Dic158—224no—
382Dic158—248no—
383Dic158C22×D4148yescomplemented
384C22×C79—22no—
385C22×C79—22no—
386C22×C79—28no—
387C22×C79—26no—
388C22×C79—26no—
389C22×C79—26no—
390C22×C79—412no—
391C22×C79C23×D412yes—
392C22×C79C22×#4112yes—
393C22×C79C22×#4114yescomplemented
394C22×C79C2×2−1+412yes—
395C22×C79C2611yescharacteristic
396C2×D79—22no—
397C2×D79—22no—
398C2×D79—28no—
399C2×D79—232no—
400C2×D79—26no—
401C2×D79—26no—
402C2×D79—26no—
403C2×D79—412no—
404C2×D79—448no—
405C2×D79#548116yesdirect product factor
406C2×D79C23×D414yes—
407C2×D79C22×#4114yes—
408C2×D79C22×#4114yescomplemented
409C2×D79C2×2−1+414yes—
410C4×C79—22no—
411C4×C79—26no—
412C4×C79—26no—
413C4×C79—22no—
414C4×C79C23×D4112yes—
415Dic79—26no—
416Dic79—22no—
417Dic79—26no—
418Dic79—22no—
419Dic79C23×D4112yes—
420C22×#548—791nomaximal, Sylow
421C2×C79—24no—
422C2×C79—46no—
423C2×C79C2×#54814yescomplemented
424C2×C79C24×D411yescharacteristic
425C2×C79C23×#4111yescharacteristic
426C2×C79C22×2−1+411yescharacteristic
427D79—24no—
428D79—46no—
429D79C2×#54818yesdirect product factor
430C23×#41—791no—
431C24×Q8—791no—
432C2×#548—791no—
433C2×#548—791no—
434C2×#548—7932no—
435C2×#548—793no—
436C2×#548—793no—
437C2×#548—793no—
438C2×#548—791no—
439C2×#548—793no—
440C2×#548D7911yescharacteristic, direct product factor
441C22×#124—793no—
442C22×C22⋊Q8—793no—
443C22×#121—793no—
444C22×C4×Q8—791no—
445C22×C4×D4—793no—
446C79C22×#54811yescharacteristic, complemented, Sylow
447C22×#41—7916no—
448C22×#41—791no—
449C22×#41—793no—
450C22×#41—793no—
451C22×#41—15816no—
452C22×#41C2×D7911yescharacteristic, complemented
453C23×Q8—791no—
454C23×Q8—793no—
455C23×Q8—793no—
456C23×Q8—791no—
457C23×Q8—7916no—
458C23×Q8—793no—
459C23×Q8—15816no—
460C23×Q8C2×D7911yescharacteristic, complemented
461C23×D4—793no—
462C23×D4—793no—
463C24×C4—793no—
464C24×C4—793no—
465#548—7916no—
466#548—7916no—
467#548—7948no—
468#548—7948no—
469#548—7948no—
470#548—7916no—
471#548—7948no—
472#548C2×D79116yesdirect product factor
473C2×#124—793no—
474C2×#124—793no—
475C2×#124—7948no—
476C2×#124—796no—
477C2×#124—796no—
478C2×#124—793no—
479C2×#124C2×D7913yescomplemented
480C2×C22⋊Q8—793no—
481C2×C22⋊Q8—793no—
482C2×C22⋊Q8—7948no—
483C2×C22⋊Q8—796no—
484C2×C22⋊Q8—793no—
485C2×C22⋊Q8—796no—
486C2×C22⋊Q8C2×D7913yescomplemented
487C2×#121—793no—
488C2×#121—796no—
489C2×#121—793no—
490C2×#121—7948no—
491C2×#121—793no—
492C2×#121—796no—
493C2×#121C2×D7913yescomplemented
494C2×C4×Q8—791no—
495C2×C4×Q8—7916no—
496C2×C4×Q8—793no—
497C2×C4×Q8—793no—
498C2×C4×Q8C2×D7911yescharacteristic, complemented
499C2×C4×D4—793no—
500C2×C4×D4—793no—
501C2×C4×D4—793no—
502C2×C4×D4—7948no—
503C2×C4×D4—793no—
504C2×C4×D4—793no—
505C2×C4×D4—793no—
506C2×C4×D4—793no—
507C2×C4×D4C2×D7913yescomplemented
508C22×C4⋊C4—793no—
509C22×C4⋊C4—793no—
510C22×C22⋊C4—791no—
511C22×C22⋊C4—793no—
512C22×C22⋊C4—796no—
513C22×C42—793no—
514C25—791no—
515C25—793no—
516C2×#41—28no—
517C2×#41—798no—
518C2×#41—7924no—
519C2×#41—7924no—
520C2×#41—15824no—
521C2×#41—15824no—
522C2×#41—158128no—
523C2×#41—1588no—
524C2×#41C22×D7918yescomplemented
525C22×Q8—28no—
526C22×Q8—7916no—
527C22×Q8—798no—
528C22×Q8—7924no—
529C22×Q8—7924no—
530C22×Q8—798no—
531C22×Q8—793no—
532C22×Q8—796no—
533C22×Q8—793no—
534C22×Q8—7924no—
535C22×Q8—15824no—
536C22×Q8—15824no—
537C22×Q8—158128no—
538C22×Q8—15824no—
539C22×Q8—1588no—
540C22×Q8C22×D7913yes—
541C22×Q8C22×D7911yescharacteristic
542C22×Q8C22×D7918yescomplemented
543C22×D4—793no—
544C22×D4—793no—
545C22×D4—796no—
546C22×D4—7924no—
547C22×D4—7924no—
548C22×D4—793no—
549C22×D4—793no—
550C22×D4—15824no—
551C22×D4—15824no—
552C22×D4C22×D7913yes—
553C22×D4C22×D7913yes—
554C23×C4—793no—
555C23×C4—793no—
556C23×C4—793no—
557C23×C4—791no—
558C23×C4—793no—
559C23×C4—793no—
560C23×C4—791no—
561C23×C4—793no—
562C23×C4—7924no—
563C23×C4—793no—
564C23×C4—793no—
565C23×C4—7924no—
566C23×C4—793no—
567C23×C4—15824no—
568C23×C4—15824no—
569C23×C4C22×D7913yes—
570C23×C4C22×D7913yes—
571#124—7924no—
572#124—7924no—
573#124—7948no—
574#124—7948no—
575#124—7924no—
576#124C22×D79124yescomplemented
577C22⋊Q8—7924no—
578C22⋊Q8—7924no—
579C22⋊Q8—7948no—
580C22⋊Q8—7924no—
581C22⋊Q8—7948no—
582C22⋊Q8C22×D79124yescomplemented
583#121—7924no—
584#121—7948no—
585#121—7924no—
586#121—7924no—
587#121—7948no—
588#121C22×D79124yescomplemented
589C4×Q8—798no—
590C4×Q8—7924no—
591C4×Q8—7924no—
592C4×Q8C22×D7918yescomplemented
593C4×D4—7924no—
594C4×D4—7924no—
595C4×D4—7924no—
596C4×D4—7924no—
597C4×D4—7924no—
598C4×D4—7924no—
599C4×D4—7924no—
600C4×D4C22×D79124yescomplemented
601C2×C4⋊C4—793no—
602C2×C4⋊C4—793no—
603C2×C4⋊C4—793no—
604C2×C4⋊C4—796no—
605C2×C4⋊C4—793no—
606C2×C4⋊C4—7924no—
607C2×C4⋊C4—7924no—
608C2×C4⋊C4C22×D7913yes—
609C2×C4⋊C4C22×D7913yes—
610C2×C22⋊C4—791no—
611C2×C22⋊C4—793no—
612C2×C22⋊C4—796no—
613C2×C22⋊C4—791no—
614C2×C22⋊C4—791no—
615C2×C22⋊C4—793no—
616C2×C22⋊C4—793no—
617C2×C22⋊C4—796no—
618C2×C22⋊C4—796no—
619C2×C22⋊C4—798no—
620C2×C22⋊C4—7924no—
621C2×C22⋊C4—7948no—
622C2×C22⋊C4C22×D7911yescharacteristic
623C2×C22⋊C4C22×D7913yes—
624C2×C22⋊C4C22×D7916yes—
625C2×C42—793no—
626C2×C42—793no—
627C2×C42—793no—
628C2×C42—7924no—
629C2×C42C22×D7913yes—
630C24—791no—
631C24—798no—
632C24—794no—
633C24—791no—
634C24—7912no—
635C24—793no—
636C24—15812no—
637C24—15812no—
638C24—15812no—
639C24—1584no—
640C24—1584no—
641C24C23×D7913yes—
642C24C23×D7911yescharacteristic
643#41—232no—
644#41—15896no—
645#41—15896no—
646#41—15832no—
647C2×Q8—232no—
648C2×Q8—212no—
649C2×Q8—7964no—
650C2×Q8—7912no—
651C2×Q8—7924no—
652C2×Q8—7912no—
653C2×Q8—7924no—
654C2×Q8—15824no—
655C2×Q8—15896no—
656C2×Q8—15896no—
657C2×Q8—15896no—
658C2×Q8—15832no—
659C2×Q8—15812no—
660C2×Q8D4×D7918yescomplemented
661C2×Q8C23×D79112yes—
662C2×Q8C23×D7914yes—
663C2×D4—212no—
664C2×D4—212no—
665C2×D4—7912no—
666C2×D4—7912no—
667C2×D4—7924no—
668C2×D4—7912no—
669C2×D4—7912no—
670C2×D4—15812no—
671C2×D4—15896no—
672C2×D4—15824no—
673C2×D4—15896no—
674C2×D4—15812no—
675C2×D4—15812no—
676C2×D4—15812no—
677C2×D4C23×D79112yes—
678C2×D4C23×D79112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—793no—
682C22×C4—7912no—
683C22×C4—7924no—
684C22×C4—7912no—
685C22×C4—7912no—
686C22×C4—791no—
687C22×C4—793no—
688C22×C4—793no—
689C22×C4—791no—
690C22×C4—794no—
691C22×C4—7912no—
692C22×C4—7912no—
693C22×C4—794no—
694C22×C4—7912no—
695C22×C4—7912no—
696C22×C4—7912no—
697C22×C4—7912no—
698C22×C4—15812no—
699C22×C4—15896no—
700C22×C4—15812no—
701C22×C4—15896no—
702C22×C4—1584no—
703C22×C4—1584no—
704C22×C4—15812no—
705C22×C4—15812no—
706C22×C4—15812no—
707C22×C4—15812no—
708C22×C4—15812no—
709C22×C4—15812no—
710C22×C4C23×D79112yes—
711C22×C4C23×D79112yes—
712C22×C4C23×D7911yescharacteristic
713C22×C4C23×D7913yes—
714C22×C4C23×D7913yes—
715C22×C4C23×D7911yescharacteristic
716C22×C4C23×D7913yes—
717C4⋊C4—7912no—
718C4⋊C4—7912no—
719C4⋊C4—7924no—
720C4⋊C4—7912no—
721C4⋊C4—7912no—
722C4⋊C4C23×D79112yes—
723C4⋊C4C23×D79112yes—
724C22⋊C4—794no—
725C22⋊C4—7912no—
726C22⋊C4—7924no—
727C22⋊C4—794no—
728C22⋊C4—794no—
729C22⋊C4—7912no—
730C22⋊C4—7912no—
731C22⋊C4—7924no—
732C22⋊C4—7924no—
733C22⋊C4C23×D7914yes—
734C22⋊C4C23×D79112yes—
735C22⋊C4C23×D79124yes—
736C42—7912no—
737C42—7912no—
738C42—7912no—
739C42C23×D79112yes—
740C23—22no—
741C23—22no—
742C23—26no—
743C23—26no—
744C23—26no—
745C23—31648no—
746C23—794no—
747C23—792no—
748C23—794no—
749C23—794no—
750C23—792no—
751C23—794no—
752C23—7916no—
753C23—796no—
754C23—15824no—
755C23—15824no—
756C23—15824no—
757C23—1588no—
758C23—15832no—
759C23—1588no—
760C23—1586no—
761C23—1586no—
762C23—1586no—
763C23—1582no—
764C23—1582no—
765C23#41×D7914yescomplemented
766C23C24×D7916yes—
767C23C24×D7912yes—
768C23C24×D7911yescharacteristic
769Q8—224no—
770Q8—7948no—
771Q8—15848no—
772Q8—15824no—
773Q8C2×D4×D79116yescomplemented
774D4—224no—
775D4—224no—
776D4—15824no—
777D4—15848no—
778D4—15824no—
779D4—15824no—
780D4—15824no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—26no—
784C2×C4—26no—
785C2×C4—224no—
786C2×C4—224no—
787C2×C4—796no—
788C2×C4—7912no—
789C2×C4—7948no—
790C2×C4—792no—
791C2×C4—796no—
792C2×C4—796no—
793C2×C4—792no—
794C2×C4—15824no—
795C2×C4—15824no—
796C2×C4—1588no—
797C2×C4—15824no—
798C2×C4—15824no—
799C2×C4—1588no—
800C2×C4—15824no—
801C2×C4—15824no—
802C2×C4—1582no—
803C2×C4—1582no—
804C2×C4—1586no—
805C2×C4—1586no—
806C2×C4—15824no—
807C2×C4—15824no—
808C2×C4C2×D4×D79112yes—
809C2×C4C24×D7912yes—
810C2×C4C24×D7916yes—
811C2×C4C24×D7916yes—
812C2×C4C24×D7912yes—
813C2×C4C24×D7916yes—
814C22—28no—
815C22—22no—
816C22—22no—
817C22—26no—
818C22—26no—
819C22—26no—
820C22—412no—
821C22—31648no—
822C22—31612no—
823C22—7916no—
824C22—794no—
825C22—794no—
826C22—794no—
827C22—794no—
828C22—15832no—
829C22—1586no—
830C22—1586no—
831C22—1586no—
832C22—1588no—
833C22—1582no—
834C22—1582no—
835C22C22×D4×D7912yes—
836C22C2×#41×D7912yes—
837C22C2×#41×D7914yescomplemented
838C222−1+4×D7912yes—
839C22C25×D7911yescharacteristic
840C4—22no—
841C4—26no—
842C4—26no—
843C4—22no—
844C4—7912no—
845C4—1582no—
846C4—1586no—
847C4—1586no—
848C4—1582no—
849C4C22×D4×D79112yes—
850C2—24no—
851C2—46no—
852C2—3166no—
853C2—798no—
854C2—1584no—
855C2#548×D7914yesdirect product factor
856C2C23×D4×D7911yescharacteristic
857C2C22×#41×D7911yescharacteristic
858C2C2×2−1+4×D7911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#548×C79C2
socleC23×C79C25
hypercenterC2×#548D79
hypocenterC79C22×#548
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#41×D79C2semidirect
2. C23×Q8×D79C2semidirect
3. C2×#19099225C2semidirect
4. C2×#19099224C2semidirect
5. C2×#19099223C2semidirect
6. C2×#19099222C2semidirect
7. C2×#19099221C2semidirect
8. C2×#19099220C2semidirect
9. C2×#19099219C2semidirect
10. #548×D79C2direct (N × H)
11. C2×#124×D79C2semidirect
12. C2×C22⋊Q8×D79C2semidirect
13. C2×#121×D79C2semidirect
14. C2×C4×Q8×D79C2semidirect
15. C2×C4×D4×D79C2semidirect
16. C2×#548×C79C2semidirect
17. C22×#11929625C22semidirect
18. C22×#11929624C22semidirect
19. C22×#11929623C22semidirect
21. C2×#41×D79C22semidirect
22. C23×Dic158C22semidirect
26. C22×Q8×D79C22semidirect
27. C22×Q8×D79C22semidirect
28. C22×Q8×D79C22semidirect
33. #19099225C22semidirect
34. #19099224C22semidirect
35. #19099223C22semidirect
36. #19099222C22semidirect
37. #19099221C22semidirect
38. #19099220C22semidirect
39. #19099219C22semidirect
40. C2×#14579150C22semidirect
41. C2×#14579149C22semidirect
42. C2×#14579148C22semidirect
43. C2×#14579147C22semidirect
44. C2×#14579147C22semidirect
45. #124×D79C22semidirect
46. C2×#14579141C22semidirect
47. C2×#14579140C22semidirect
48. C2×#14579139C22semidirect
49. C2×#14579138C22semidirect
50. C2×#14579137C22semidirect
51. C22⋊Q8×D79C22semidirect
52. C2×#14579136C22semidirect
53. C2×#14579135C22semidirect
54. C2×#14579134C22semidirect
55. C2×#14579133C22semidirect
56. C2×#14579132C22semidirect
57. #121×D79C22semidirect
58. C2×Q8×Dic79C22semidirect
59. C2×C4×Dic158C22semidirect
60. C2×#14579126C22semidirect
61. C4×Q8×D79C22semidirect
62. C2×C4×D316C22semidirect
63. C2×D4×Dic79C22semidirect
64. C2×#14579123C22semidirect
65. C2×C4×C22⋊D79C22semidirect
66. C2×C4×C22⋊D79C22semidirect
67. C2×(C22⋊D79)⋊C4C22semidirect
68. C2×(C22⋊D79)⋊C4C22semidirect
69. C4×D4×D79C22semidirect
76. C22×#41×C79C22semidirect
77. C23×Q8×C79C22semidirect
78. #548×C79C22semidirect
79. C2×#124×C79C22semidirect
80. C2×C22⋊Q8×C79C22semidirect
81. C2×#121×C79C22semidirect
82. C2×C4×Q8×C79C22semidirect
83. C2×C4×D4×C79C22semidirect
87. C2×#11929625C23semidirect
89. C2×#11929624C23semidirect
91. C2×#11929623C23semidirect
97. C22×Dic158C23semidirect
102. C2×Q8×D79D4semidirect
105. C2×Q8×D79C23semidirect
106. C2×Q8×D79C23semidirect
131. #14579150C23semidirect
132. #14579149C23semidirect
133. #14579148C23semidirect
134. #14579147C23semidirect
135. #14579147C23semidirect
136. #14579141C23semidirect
137. #14579140C23semidirect
138. #14579139C23semidirect
139. #14579138C23semidirect
140. #14579137C23semidirect
141. #14579136C23semidirect
142. #14579135C23semidirect
143. #14579134C23semidirect
144. #14579133C23semidirect
145. #14579132C23semidirect
146. Q8×Dic79C23semidirect
147. C4×Dic158C23semidirect
148. #14579126C23semidirect
149. C4×D316C23semidirect
150. D4×Dic79C23semidirect
151. #14579123C23semidirect
152. C4×C22⋊D79C23semidirect
153. C4×C22⋊D79C23semidirect
154. (C22⋊D79)⋊C4C23semidirect
155. (C22⋊D79)⋊C4C23semidirect
180. C2×#41×C79C23semidirect
184. C22×Q8×C79C23semidirect
189. #124×C79C23semidirect
190. C22⋊Q8×C79C23semidirect
191. #121×C79C23semidirect
192. C4×Q8×C79C23semidirect
193. C4×D4×C79C23semidirect
205. C23×D79#41semidirect
217. C2×Dic158C2×D4semidirect
224. Q8×D79C2×D4semidirect
288. C2×Q8×C79C2×D4semidirect
315. C23×C79C2×#41semidirect
333. C22×D79C2×#41semidirect
334. C22×D79C2×#41semidirect
340. Q8×C79C22×D4semidirect
383. Dic158C22×D4semidirect
393. C22×C79C22×#41semidirect
405. C2×D79#548direct (N × H)
408. C2×D79C22×#41semidirect
423. C2×C79C2×#548semidirect
429. D79C2×#548direct (N × H)
440. C2×#548D79direct (N × H)
446. C79C22×#548semidirect
452. C22×#41C2×D79semidirect
460. C23×Q8C2×D79semidirect
472. #548C2×D79direct (N × H)
479. C2×#124C2×D79semidirect
486. C2×C22⋊Q8C2×D79semidirect
493. C2×#121C2×D79semidirect
498. C2×C4×Q8C2×D79semidirect
507. C2×C4×D4C2×D79semidirect
524. C2×#41C22×D79semidirect
542. C22×Q8C22×D79semidirect
576. #124C22×D79semidirect
582. C22⋊Q8C22×D79semidirect
588. #121C22×D79semidirect
592. C4×Q8C22×D79semidirect
600. C4×D4C22×D79semidirect
660. C2×Q8D4×D79semidirect
765. C23#41×D79semidirect
773. Q8C2×D4×D79semidirect
837. C22C2×#41×D79semidirect
855. C2#548×D79direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D792
C23×Q8×D792
C2×#190992252
C2×#190992242
C2×#190992232
C2×#190992222
C2×#190992212
C2×#190992202
C2×#190992192
#548×D792
C2×#124×D792
C2×C22⋊Q8×D792
C2×#121×D792
C2×C4×Q8×D792
C2×C4×D4×D792
C2×#548×C792
C22×#54879