Finite Group Databasebeta

← #35158906

Subgroups — #35158906

Order 20224.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099074C211yesmaximal, characteristic, complemented
2#23774237C214yesmaximal, complemented
3#23774230C212yesmaximal, complemented
4#23774226C212yesmaximal, complemented
5#23774221C211yesmaximal, characteristic, complemented
6#23774214C212yesmaximal, complemented
7#23774210C212yesmaximal, complemented
8#23774206C211yesmaximal, characteristic, complemented
9#23774202C211yesmaximal, characteristic, complemented
10#23774197C211yesmaximal, characteristic, complemented
11#23773313C212yesmaximal, complemented
12#23773309C212yesmaximal, complemented
13#23773006C214yesmaximal, complemented
14#23772618C212yesmaximal, complemented
15#23772616C212yesmaximal, complemented
16C2×#19098527C211yesmaximal, characteristic, complemented
17C2×#525×C79C211yesmaximal, characteristic, complemented
18C22×#11929624C2211yescharacteristic, complemented
19C2×#14579181C2214yescomplemented
20C22×#11929608C2212yescomplemented
21#19099074—21no—
22#19099074—21no—
23#19099074—21no—
24#19099074—21no—
25#19099074C2212yes—
26#19099074C2212yes—
27#19099074C2212yescomplemented
28#19099074C2212yescomplemented
29C2×#14579144—21no—
30C2×#14579140C2211yescharacteristic
31C2×#14579140C2211yescharacteristic, complemented
32C2×#14579135C2211yescharacteristic
33C2×#14579135C2211yescharacteristic, complemented
34C2×#14579130—21no—
35C2×C4×C22⋊D79—21no—
36C2×C4×C22⋊D79—21no—
37C2×#14579120C2211yescharacteristic, complemented
38#19098904C2214yescomplemented
39#19098901C2214yescomplemented
40#19098898C2212yescomplemented
41#19098896C2212yescomplemented
42#19098893C2212yescomplemented
43#19098891C2212yescomplemented
44#19098887C2214yescomplemented
45#19098884C2214yescomplemented
46#19098881C2212yescomplemented
47#19098879C2212yescomplemented
48#19098876C2212yescomplemented
49#19098874C2212yescomplemented
50#19098819C2214yescomplemented
51#19098819C2214yescomplemented
52#19098814C2214yescomplemented
53#19098814C2214yescomplemented
54#19098811C2214yescomplemented
55#19098811C2214yescomplemented
56#19098807C2214yescomplemented
57#19098807C2214yescomplemented
58#19098725C2214yescomplemented
59#19098723C2214yescomplemented
60#19098719C2212yescomplemented
61#19098718C2212yescomplemented
62#19098714C2212yescomplemented
63#19098713C2212yescomplemented
64#19098708C2214yescomplemented
65#19098706C2214yescomplemented
66#19098702C2212yescomplemented
67#19098701C2212yescomplemented
68#19098697C2212yescomplemented
69#19098696C2212yescomplemented
70#19098599C2214yescomplemented
71#19098559C2214yescomplemented
72#19098557C2214yescomplemented
73#19098527C2211yescharacteristic
74#19098527C2211yescharacteristic
75#19098527C2212yescomplemented
76#19098527C2212yescomplemented
77#19098527C2212yescomplemented
78C2×C22⋊(C79⋊C8)C2212yescomplemented
79C2×C22⋊(C79⋊C8)C2212yescomplemented
80C22×#41×C79C2211yescharacteristic, complemented
81C24×C4×C79C2211yescharacteristic
82#525×C79—21no—
83#525×C79—21no—
84#525×C79—21no—
85#525×C79—21no—
86#525×C79C2212yes—
87#525×C79C2212yes—
88#525×C79C2212yescomplemented
89#525×C79C2212yescomplemented
90C2×#123×C79—21no—
91C2×C22⋊Q8×C79C2211yescharacteristic
92C2×C22⋊Q8×C79C2211yescharacteristic, complemented
93C2×#121×C79C2211yescharacteristic
94C2×#121×C79C2211yescharacteristic, complemented
95C2×#120×C79—21no—
96C2×C4×D4×C79—21no—
97C2×C4×D4×C79—21no—
98C2×#117×C79C2211yescharacteristic, complemented
99C2×#11929624—21no—
100C2×#11929624—21no—
101C2×#11929624—44no—
102C2×#11929624C2312yes—
103C2×#11929624C2312yes—
104C22×Dic158C2311yescharacteristic
105C22×D316C2311yescharacteristic
106C22×C22⋊D79—21no—
107C22×C22⋊D79—21no—
108C22×C22⋊D79—21no—
109C22×C4×D79—21no—
110#14579181—48no—
111C2×#11929614C2314yescomplemented
112C2×#11929612C2314yescomplemented
113C2×#11929611C2314yescomplemented
114C2×#11929609C2314yescomplemented
115C2×#11929608—44no—
116C2×#11929608C2312yes—
117C2×#11929608C2312yes—
118C2×#11929608C2314yes—
119C22×C79⋊C8C2314yes—
120#14579144—22no—
121#14579144—22no—
122#14579144—22no—
123#14579144—22no—
124#14579140—21no—
125#14579140—21no—
126#14579140—21no—
127#14579140—21no—
128#14579140C2312yes—
129#14579140C2312yes—
130#14579140C2312yes—
131#14579140C2312yes—
132#14579135—21no—
133#14579135—21no—
134#14579135—21no—
135#14579135—21no—
136#14579135C2312yes—
137#14579135C2312yes—
138#14579135C2312yes—
139#14579135C2312yes—
140#14579130—22no—
141#14579130—22no—
142#14579130—22no—
143#14579130—22no—
144C4×C22⋊D79—22no—
145C4×C22⋊D79—22no—
146C4×C22⋊D79—22no—
147C4×C22⋊D79—22no—
148C4×C22⋊D79—22no—
149C4×C22⋊D79—22no—
150C4×C22⋊D79—22no—
151C4×C22⋊D79—22no—
152#14579120—21no—
153#14579120—21no—
154#14579120C2312yes—
155#14579120C2312yes—
156C2×C4⋊Dic79C2311yescharacteristic
157C2×C4⋊Dic79C2311yescharacteristic
158C2×Dic79⋊C4—21no—
159C2×Dic79⋊C4—21no—
160C2×C22⋊Dic79—21no—
161C2×C22⋊Dic79—21no—
162C2×C22⋊Dic79—21no—
163C2×(C2×D79)⋊C4—21no—
164C2×(C2×D79)⋊C4—21no—
165C2×C4×Dic79—21no—
166#14579094C2314yescomplemented
167#14579094C2314yescomplemented
168#14579092C2314yescomplemented
169#14579092C2314yescomplemented
170#14579085C2314yescomplemented
171#14579085C2314yescomplemented
172#14579084C2314yescomplemented
173#14579084C2314yescomplemented
174#14579082C2314yescomplemented
175#14579082C2314yescomplemented
176#14579081C2314yescomplemented
177#14579081C2314yescomplemented
178C22⋊(C79⋊C8)C2312yes—
179C22⋊(C79⋊C8)C2314yes—
180C22⋊(C79⋊C8)C2314yes—
181C22⋊(C79⋊C8)C2312yes—
182C22⋊(C79⋊C8)C2312yes—
183C22⋊(C79⋊C8)C2312yes—
184C25×C79D411yescharacteristic
185C2×#41×C79—21no—
186C2×#41×C79—21no—
187C2×#41×C79—44no—
188C2×#41×C79C2312yes—
189C2×#41×C79C2312yes—
190C22×Q8×C79C2311yescharacteristic
191C22×D4×C79—21no—
192C22×D4×C79—21no—
193C22×D4×C79—21no—
194C22×D4×C79C2311yescharacteristic
195C23×C4×C79—21no—
196C23×C4×C79—44no—
197C23×C4×C79D411yescharacteristic
198C23×C4×C79D411yescharacteristic
199C23×C4×C79D411yescharacteristic
200C23×C4×C79D411yescharacteristic
201C23×C4×C79D411yescharacteristic
202C23×C4×C79D411yescharacteristic
203C23×C4×C79D411yescharacteristic
204C23×C4×C79C2311yescharacteristic
205C23×C4×C79C2311yescharacteristic
206C23×C4×C79C2311yescharacteristic
207C23×C4×C79C2311yescharacteristic
208C23×C4×C79C2311yescharacteristic
209C23×C4×C79C2311yescharacteristic
210C23×C4×C79C2311yescharacteristic
211#123×C79—22no—
212#123×C79—22no—
213#123×C79—22no—
214#123×C79—22no—
215C22⋊Q8×C79—21no—
216C22⋊Q8×C79—21no—
217C22⋊Q8×C79—21no—
218C22⋊Q8×C79—21no—
219C22⋊Q8×C79C2312yes—
220C22⋊Q8×C79C2312yes—
221C22⋊Q8×C79C2312yes—
222C22⋊Q8×C79C2312yes—
223#121×C79—21no—
224#121×C79—21no—
225#121×C79—21no—
226#121×C79—21no—
227#121×C79C2312yes—
228#121×C79C2312yes—
229#121×C79C2312yes—
230#121×C79C2312yes—
231#120×C79—22no—
232#120×C79—22no—
233#120×C79—22no—
234#120×C79—22no—
235C4×D4×C79—22no—
236C4×D4×C79—22no—
237C4×D4×C79—22no—
238C4×D4×C79—22no—
239C4×D4×C79—22no—
240C4×D4×C79—22no—
241C4×D4×C79—22no—
242C4×D4×C79—22no—
243#117×C79—21no—
244#117×C79—21no—
245#117×C79C2312yes—
246#117×C79C2312yes—
247C2×C4⋊C4×C79—21no—
248C2×C4⋊C4×C79—21no—
249C2×C4⋊C4×C79C2311yescharacteristic
250C2×C4⋊C4×C79C2311yescharacteristic
251C2×C22⋊C4×C79—21no—
252C2×C22⋊C4×C79—21no—
253C2×C22⋊C4×C79—21no—
254C2×C22⋊C4×C79—21no—
255C2×C22⋊C4×C79—21no—
256C2×C42×C79—21no—
257C23×D79—21no—
258#11929624—28no—
259#11929624—44no—
260#11929624—44no—
261#11929624—44no—
262C2×Dic158—21no—
263C2×Dic158—42no—
264C2×Dic158C2412yes—
265C2×D316—21no—
266C2×D316—42no—
267C2×D316C2412yes—
268C2×C22⋊D79—22no—
269C2×C22⋊D79—22no—
270C2×C22⋊D79—22no—
271C2×C22⋊D79—22no—
272C2×C22⋊D79—22no—
273C2×C22⋊D79—22no—
274C2×C22⋊D79—44no—
275C2×C22⋊D79—44no—
276C2×C22⋊D79—44no—
277C22×Dic79—21no—
278C22×Dic79—21no—
279C22×Dic79—21no—
280C2×C4×D79—22no—
281C2×C4×D79—22no—
282C2×C4×D79—44no—
283#11929614—44no—
284#11929612—44no—
285#11929611—44no—
286#11929609—44no—
287#11929608—42no—
288#11929608—44no—
289#11929608—42no—
290C2×C79⋊C8—28no—
291C2×C79⋊C8C2414yes—
292C2×C79⋊C8C2414yes—
293C4⋊Dic79—21no—
294C4⋊Dic79—21no—
295C4⋊Dic79C2412yes—
296C4⋊Dic79C2412yes—
297Dic79⋊C4—22no—
298Dic79⋊C4—22no—
299Dic79⋊C4—22no—
300Dic79⋊C4—22no—
301C22⋊Dic79—22no—
302C22⋊Dic79—22no—
303C22⋊Dic79—22no—
304C22⋊Dic79—22no—
305C22⋊Dic79—22no—
306C22⋊Dic79—22no—
307(C2×D79)⋊C4—22no—
308(C2×D79)⋊C4—22no—
309(C2×D79)⋊C4—22no—
310(C2×D79)⋊C4—22no—
311C4×Dic79—22no—
312C4×Dic79—22no—
313C24×C79—21no—
314C24×C79—42no—
315C24×C79—42no—
316C24×C79—42no—
317C24×C79C2×D411yescharacteristic
318C24×C79C2×D411yescharacteristic
319C24×C79C2×D411yescharacteristic
320C24×C79C2×D411yescharacteristic
321C24×C79C2×D411yescharacteristic
322C24×C79C2×D411yescharacteristic
323C24×C79C2×D411yescharacteristic
324#41×C79—28no—
325#41×C79—44no—
326#41×C79—44no—
327#41×C79—44no—
328C2×Q8×C79—21no—
329C2×Q8×C79—42no—
330C2×Q8×C79C2412yes—
331C2×D4×C79—22no—
332C2×D4×C79—22no—
333C2×D4×C79—22no—
334C2×D4×C79—22no—
335C2×D4×C79—22no—
336C2×D4×C79—22no—
337C2×D4×C79—21no—
338C2×D4×C79—42no—
339C2×D4×C79—44no—
340C2×D4×C79—44no—
341C2×D4×C79—44no—
342C2×D4×C79C2412yes—
343C22×C4×C79—24no—
344C22×C4×C79—24no—
345C22×C4×C79—24no—
346C22×C4×C79—21no—
347C22×C4×C79—21no—
348C22×C4×C79—21no—
349C22×C4×C79—22no—
350C22×C4×C79—22no—
351C22×C4×C79—42no—
352C22×C4×C79—42no—
353C22×C4×C79—42no—
354C22×C4×C79—42no—
355C22×C4×C79—42no—
356C22×C4×C79—42no—
357C22×C4×C79—42no—
358C22×C4×C79—42no—
359C22×C4×C79—42no—
360C22×C4×C79—42no—
361C22×C4×C79—42no—
362C22×C4×C79—44no—
363C22×C4×C79C2×D411yescharacteristic
364C22×C4×C79C2×D411yescharacteristic
365C22×C4×C79C2×D411yescharacteristic
366C22×C4×C79C2×D411yescharacteristic
367C22×C4×C79C2×D411yescharacteristic
368C22×C4×C79C2×D411yescharacteristic
369C22×C4×C79C2×D411yescharacteristic
370C22×C4×C79C2×D411yescharacteristic
371C22×C4×C79C2×D411yescharacteristic
372C22×C4×C79C2×D411yescharacteristic
373C22×C4×C79C2×D411yescharacteristic
374C22×C4×C79C2×D411yescharacteristic
375C22×C4×C79C2×D411yescharacteristic
376C22×C4×C79C2×D411yescharacteristic
377C22×C4×C79C2×D411yescharacteristic
378C22×C4×C79C2×D411yescharacteristic
379C22×C4×C79C2×D411yescharacteristic
380C22×C4×C79C2×D411yescharacteristic
381C22×C4×C79C2×D411yescharacteristic
382C22×C4×C79C2×D411yescharacteristic
383C22×C4×C79C2×D411yescharacteristic
384C22×C4×C79C2411yescharacteristic
385C22×C4×C79C2411yescharacteristic
386C22×C4×C79C2411yescharacteristic
387C22×C4×C79C2411yescharacteristic
388C22×C4×C79C2411yescharacteristic
389C22×C4×C79C2411yescharacteristic
390C22×C4×C79C2411yescharacteristic
391C4⋊C4×C79—22no—
392C4⋊C4×C79—22no—
393C4⋊C4×C79—22no—
394C4⋊C4×C79—22no—
395C4⋊C4×C79—21no—
396C4⋊C4×C79—21no—
397C4⋊C4×C79C2412yes—
398C4⋊C4×C79C2412yes—
399C22⋊C4×C79—22no—
400C22⋊C4×C79—22no—
401C22⋊C4×C79—22no—
402C22⋊C4×C79—22no—
403C22⋊C4×C79—22no—
404C22⋊C4×C79—22no—
405C22⋊C4×C79—22no—
406C22⋊C4×C79—22no—
407C22⋊C4×C79—22no—
408C22⋊C4×C79—22no—
409C42×C79—22no—
410C42×C79—22no—
411C23×C79—22no—
412C23×C79—22no—
413C23×C79—22no—
414C23×C79—22no—
415C23×C79—22no—
416C23×C79—22no—
417C23×C79—22no—
418C23×C79—22no—
419C23×C79—22no—
420C23×C79—22no—
421C23×C79—41no—
422C23×C79—41no—
423C23×C79—41no—
424C23×C79—41no—
425C23×C79—41no—
426C23×C79—41no—
427C23×C79—41no—
428C23×C79—41no—
429C23×C79—41no—
430C23×C79—41no—
431C23×C79—41no—
432C23×C79—41no—
433C23×C79—42no—
434C23×C79—42no—
435C23×C79—416no—
436C23×C79—42no—
437C23×C79C22×D411yescharacteristic
438C23×C79C22×D411yescharacteristic
439C23×C79C22×D411yescharacteristic
440C23×C79C22×D411yescharacteristic
441C23×C79C22×D411yescharacteristic
442C23×C79C22×D411yescharacteristic
443C23×C79C22×D411yescharacteristic
444C22×D79—22no—
445C22×D79—42no—
446C22×D79—42no—
447C22×D79—42no—
448Q8×C79—24no—
449Q8×C79—42no—
450D4×C79—24no—
451D4×C79—42no—
452D4×C79—44no—
453D4×C79—44no—
454D4×C79—44no—
455D4×C79—44no—
456D4×C79—44no—
457D4×C79—44no—
458C2×C4×C79—22no—
459C2×C4×C79—22no—
460C2×C4×C79—22no—
461C2×C4×C79—22no—
462C2×C4×C79—22no—
463C2×C4×C79—22no—
464C2×C4×C79—22no—
465C2×C4×C79—22no—
466C2×C4×C79—22no—
467C2×C4×C79—22no—
468C2×C4×C79—22no—
469C2×C4×C79—22no—
470C2×C4×C79—22no—
471C2×C4×C79—22no—
472C2×C4×C79—22no—
473C2×C4×C79—22no—
474C2×C4×C79—22no—
475C2×C4×C79—22no—
476C2×C4×C79—41no—
477C2×C4×C79—41no—
478C2×C4×C79—41no—
479C2×C4×C79—41no—
480C2×C4×C79—41no—
481C2×C4×C79—41no—
482C2×C4×C79—41no—
483C2×C4×C79—41no—
484C2×C4×C79—41no—
485C2×C4×C79—41no—
486C2×C4×C79—41no—
487C2×C4×C79—41no—
488C2×C4×C79—44no—
489C2×C4×C79—42no—
490C2×C4×C79—42no—
491C2×C4×C79—42no—
492C2×C4×C79—44no—
493C2×C4×C79C22×D411yescharacteristic
494C2×C4×C79C22×D411yescharacteristic
495C2×C4×C79C22×D411yescharacteristic
496C2×C4×C79C22×D411yescharacteristic
497C2×C4×C79C22×D411yescharacteristic
498C2×C4×C79C22×D411yescharacteristic
499C2×C4×C79C22×D411yescharacteristic
500C2×C4×C79H(5,𝔽2)14yes—
501C2×C4×C79C2511yescharacteristic
502C22⋊D79—44no—
503C22⋊D79—44no—
504C22⋊D79—44no—
505C22⋊D79—44no—
506C22⋊D79—44no—
507C22⋊D79—44no—
508C2×Dic79—22no—
509C2×Dic79—22no—
510C2×Dic79—22no—
511C2×Dic79—42no—
512C2×Dic79—42no—
513C2×Dic79—42no—
514D316—24no—
515D316—42no—
516C4×D79—44no—
517C4×D79—44no—
518Dic158—24no—
519Dic158—42no—
520C79⋊C8—24no—
521C79⋊C8—24no—
522C22×C79—21no—
523C22×C79—21no—
524C22×C79—21no—
525C22×C79—21no—
526C22×C79—21no—
527C22×C79—21no—
528C22×C79—21no—
529C22×C79—21no—
530C22×C79—21no—
531C22×C79—21no—
532C22×C79—21no—
533C22×C79—21no—
534C22×C79—21no—
535C22×C79—21no—
536C22×C79—21no—
537C22×C79—21no—
538C22×C79—21no—
539C22×C79—21no—
540C22×C79—44no—
541C22×C79—44no—
542C22×C79—44no—
543C22×C79—44no—
544C22×C79—44no—
545C22×C79—44no—
546C22×C79—44no—
547C22×C79—42no—
548C22×C79—42no—
549C22×C79—42no—
550C22×C79—84no—
551C22×C79#53412yes—
552C22×C79#57512yes—
553C22×C79#57512yes—
554C22×C79C23×D411yescharacteristic
555C2×D79—42no—
556C2×D79—42no—
557C2×D79—42no—
558C2×D79—84no—
559C4×C79—21no—
560C4×C79—21no—
561C4×C79—21no—
562C4×C79—21no—
563C4×C79—21no—
564C4×C79—21no—
565C4×C79—42no—
566C4×C79—42no—
567C4×C79—42no—
568C4×C79#53412yes—
569C4×C79C2×H(5,𝔽2)12yes—
570Dic79—42no—
571Dic79—42no—
572Dic79—42no—
573#60741—791nomaximal, Sylow
574C2×C79—22no—
575C2×C79—22no—
576C2×C79—22no—
577C2×C79—41no—
578C2×C79—41no—
579C2×C79—41no—
580C2×C79—41no—
581C2×C79—82no—
582C2×C79C2×#53411yescharacteristic
583C2×C79C2×#57511yescharacteristic
584C2×C79C2×#57511yescharacteristic
585D79—82no—
586C2×#525—791no—
587C2×#525D7911yescharacteristic, complemented
588#3197—794no—
589#3196—792no—
590#3196—792no—
591#3195—791no—
592#3194—792no—
593#3194—792no—
594#3193—791no—
595#3193—791no—
596#3192—791no—
597#3091—792no—
598#3091—792no—
599#3054—794no—
600#3002—792no—
601#3002—792no—
602C2×#407—791no—
603C79#6074111yescharacteristic, complemented, Sylow
604C22×#41—791no—
605C22×#41C2×D7911yescharacteristic, complemented
606C24×C4C2×D7911yescharacteristic
607C2×#135—794no—
608C22×M16—792no—
609#525—21no—
610#525—21no—
611#525—21no—
612#525—21no—
613#525—792no—
614#525—792no—
615#525—792no—
616#525—792no—
617#525—1581no—
618#525—1581no—
619#525—1581no—
620#525—1581no—
621#525C2×D7912yes—
622#525C2×D7912yes—
623#525C2×D7912yescomplemented
624#525C2×D7912yescomplemented
625C2×#123—21no—
626C2×#123—1581no—
627C2×C22⋊Q8—791no—
628C2×C22⋊Q8—791no—
629C2×C22⋊Q8C2×D7911yescharacteristic
630C2×C22⋊Q8C2×D7911yescharacteristic, complemented
631C2×#121—791no—
632C2×#121—791no—
633C2×#121C2×D7911yescharacteristic
634C2×#121C2×D7911yescharacteristic, complemented
635C2×#120—21no—
636C2×#120—1581no—
637C2×C4×D4—21no—
638C2×C4×D4—21no—
639C2×C4×D4—1581no—
640C2×C4×D4—1581no—
641C2×#117—791no—
642C2×#117C2×D7911yescharacteristic, complemented
643#485—794no—
644#485—794no—
645#484—792no—
646#484—792no—
647#483—792no—
648#483—792no—
649#482—794no—
650#482—794no—
651#481—792no—
652#481—792no—
653#480—792no—
654#480—792no—
655#470—794no—
656#470—794no—
657#469—794no—
658#469—794no—
659#468—794no—
660#468—794no—
661#468—794no—
662#468—794no—
663#452—794no—
664#452—794no—
665#451—792no—
666#451—792no—
667#450—792no—
668#450—792no—
669#449—794no—
670#449—794no—
671#448—792no—
672#448—792no—
673#447—792no—
674#447—792no—
675#427—794no—
676#416—794no—
677#416—794no—
678#407—791no—
679#407—791no—
680#407—792no—
681#407—792no—
682#407—792no—
683C2×C22⋊C8—792no—
684C2×C22⋊C8—792no—
685C25C22⋊D7911yescharacteristic
686C2×#41—21no—
687C2×#41—21no—
688C2×#41—44no—
689C2×#41—3164no—
690C2×#41—792no—
691C2×#41—792no—
692C2×#41—1581no—
693C2×#41—1581no—
694C2×#41C22×D7912yes—
695C2×#41C22×D7912yes—
696C22×Q8—791no—
697C22×Q8C22×D7911yescharacteristic
698C22×D4—21no—
699C22×D4—21no—
700C22×D4—21no—
701C22×D4—791no—
702C22×D4—1581no—
703C22×D4—1581no—
704C22×D4—1581no—
705C22×D4C22×D7911yescharacteristic
706C23×C4—21no—
707C23×C4—44no—
708C23×C4—1581no—
709C23×C4C22⋊D7911yescharacteristic
710C23×C4C22⋊D7911yescharacteristic
711C23×C4C22⋊D7911yescharacteristic
712C23×C4C22⋊D7911yescharacteristic
713C23×C4C22⋊D7911yescharacteristic
714C23×C4C22⋊D7911yescharacteristic
715C23×C4C22⋊D7911yescharacteristic
716C23×C4C22×D7911yescharacteristic
717C23×C4C22×D7911yescharacteristic
718C23×C4C22×D7911yescharacteristic
719C23×C4C22×D7911yescharacteristic
720C23×C4C22×D7911yescharacteristic
721C23×C4C22×D7911yescharacteristic
722C23×C4C22×D7911yescharacteristic
723#135—3168no—
724C2×Q16—794no—
725C2×SD16—794no—
726C2×SD16—794no—
727C2×D8—794no—
728C2×M16—3164no—
729C2×M16—792no—
730C2×M16—794no—
731C2×M16—792no—
732C22×C8—794no—
733#123—22no—
734#123—22no—
735#123—22no—
736#123—22no—
737#123—1582no—
738#123—1582no—
739#123—1582no—
740#123—1582no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744C22⋊Q8—21no—
745C22⋊Q8—792no—
746C22⋊Q8—792no—
747C22⋊Q8—792no—
748C22⋊Q8—792no—
749C22⋊Q8—1581no—
750C22⋊Q8—1581no—
751C22⋊Q8—1581no—
752C22⋊Q8—1581no—
753C22⋊Q8C22×D7912yes—
754C22⋊Q8C22×D7912yes—
755C22⋊Q8C22×D7912yes—
756C22⋊Q8C22×D7912yes—
757#121—21no—
758#121—21no—
759#121—21no—
760#121—21no—
761#121—792no—
762#121—792no—
763#121—792no—
764#121—792no—
765#121—1581no—
766#121—1581no—
767#121—1581no—
768#121—1581no—
769#121C22×D7912yes—
770#121C22×D7912yes—
771#121C22×D7912yes—
772#121C22×D7912yes—
773#120—22no—
774#120—22no—
775#120—22no—
776#120—22no—
777#120—1582no—
778#120—1582no—
779#120—1582no—
780#120—1582no—
781C4×D4—22no—
782C4×D4—22no—
783C4×D4—22no—
784C4×D4—22no—
785C4×D4—22no—
786C4×D4—22no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—1582no—
790C4×D4—1582no—
791C4×D4—1582no—
792C4×D4—1582no—
793C4×D4—1582no—
794C4×D4—1582no—
795C4×D4—1582no—
796C4×D4—1582no—
797#117—21no—
798#117—21no—
799#117—792no—
800#117—792no—
801#117—1581no—
802#117—1581no—
803#117C22×D7912yes—
804#117C22×D7912yes—
805C2×C4⋊C4—21no—
806C2×C4⋊C4—21no—
807C2×C4⋊C4—791no—
808C2×C4⋊C4—791no—
809C2×C4⋊C4—1581no—
810C2×C4⋊C4—1581no—
811C2×C4⋊C4C22×D7911yescharacteristic
812C2×C4⋊C4C22×D7911yescharacteristic
813C2×C22⋊C4—21no—
814C2×C22⋊C4—21no—
815C2×C22⋊C4—21no—
816C2×C22⋊C4—21no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—1581no—
819C2×C22⋊C4—1581no—
820C2×C22⋊C4—1581no—
821C2×C22⋊C4—1581no—
822C2×C22⋊C4—1581no—
823C2×C42—21no—
824C2×C42—1581no—
825#107—794no—
826#107—794no—
827#106—794no—
828#106—794no—
829#103—794no—
830#103—794no—
831#103—794no—
832#103—794no—
833#102—794no—
834#102—794no—
835#102—794no—
836#102—794no—
837C22⋊C8—792no—
838C22⋊C8—792no—
839C22⋊C8—792no—
840C22⋊C8—792no—
841C22⋊C8—794no—
842C22⋊C8—794no—
843C24—21no—
844C24—42no—
845C24—42no—
846C24—42no—
847C24—1581no—
848C24C2×C22⋊D7911yescharacteristic
849C24C2×C22⋊D7911yescharacteristic
850C24C2×C22⋊D7911yescharacteristic
851C24C2×C22⋊D7911yescharacteristic
852C24C2×C22⋊D7911yescharacteristic
853C24C2×C22⋊D7911yescharacteristic
854C24C2×C22⋊D7911yescharacteristic
855#41—28no—
856#41—44no—
857#41—44no—
858#41—44no—
859#41—3164no—
860#41—3164no—
861#41—3164no—
862#41—1588no—
863C2×Q8—21no—
864C2×Q8—42no—
865C2×Q8—3162no—
866C2×Q8—792no—
867C2×Q8—1581no—
868C2×Q8C23×D7912yes—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—21no—
876C2×D4—42no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—3162no—
881C2×D4—3164no—
882C2×D4—3164no—
883C2×D4—3164no—
884C2×D4—792no—
885C2×D4—1582no—
886C2×D4—1582no—
887C2×D4—1582no—
888C2×D4—1582no—
889C2×D4—1582no—
890C2×D4—1582no—
891C2×D4—1581no—
892C2×D4C23×D7912yes—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—3164no—
914C22×C4—1581no—
915C22×C4—1581no—
916C22×C4—1581no—
917C22×C4—1582no—
918C22×C4—1582no—
919C22×C4C2×C22⋊D7911yescharacteristic
920C22×C4C2×C22⋊D7911yescharacteristic
921C22×C4C2×C22⋊D7911yescharacteristic
922C22×C4C2×C22⋊D7911yescharacteristic
923C22×C4C2×C22⋊D7911yescharacteristic
924C22×C4C2×C22⋊D7911yescharacteristic
925C22×C4C2×C22⋊D7911yescharacteristic
926C22×C4C2×C22⋊D7911yescharacteristic
927C22×C4C2×C22⋊D7911yescharacteristic
928C22×C4C2×C22⋊D7911yescharacteristic
929C22×C4C2×C22⋊D7911yescharacteristic
930C22×C4C2×C22⋊D7911yescharacteristic
931C22×C4C2×C22⋊D7911yescharacteristic
932C22×C4C2×C22⋊D7911yescharacteristic
933C22×C4C2×C22⋊D7911yescharacteristic
934C22×C4C2×C22⋊D7911yescharacteristic
935C22×C4C2×C22⋊D7911yescharacteristic
936C22×C4C2×C22⋊D7911yescharacteristic
937C22×C4C2×C22⋊D7911yescharacteristic
938C22×C4C2×C22⋊D7911yescharacteristic
939C22×C4C2×C22⋊D7911yescharacteristic
940C22×C4C23×D7911yescharacteristic
941C22×C4C23×D7911yescharacteristic
942C22×C4C23×D7911yescharacteristic
943C22×C4C23×D7911yescharacteristic
944C22×C4C23×D7911yescharacteristic
945C22×C4C23×D7911yescharacteristic
946C22×C4C23×D7911yescharacteristic
947Q16—3164no—
948SD16—3164no—
949SD16—3164no—
950D8—3164no—
951M16—3162no—
952M16—3164no—
953M16—3162no—
954C2×C8—794no—
955C2×C8—794no—
956C2×C8—1588no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—792no—
964C4⋊C4—792no—
965C4⋊C4—1582no—
966C4⋊C4—1582no—
967C4⋊C4—1582no—
968C4⋊C4—1582no—
969C4⋊C4—1581no—
970C4⋊C4—1581no—
971C4⋊C4C23×D7912yes—
972C4⋊C4C23×D7912yes—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—1582no—
984C22⋊C4—1582no—
985C22⋊C4—1582no—
986C22⋊C4—1582no—
987C22⋊C4—1582no—
988C22⋊C4—1582no—
989C22⋊C4—1582no—
990C22⋊C4—1582no—
991C22⋊C4—1582no—
992C22⋊C4—1582no—
993C42—22no—
994C42—22no—
995C42—1582no—
996C42—1582no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—42no—
1020C23—42no—
1021C23—416no—
1022C23—42no—
1023C23—3162no—
1024C23—3162no—
1025C23—3162no—
1026C23—1582no—
1027C23C22×C22⋊D7911yescharacteristic
1028C23C22×C22⋊D7911yescharacteristic
1029C23C22×C22⋊D7911yescharacteristic
1030C23C22×C22⋊D7911yescharacteristic
1031C23C22×C22⋊D7911yescharacteristic
1032C23C22×C22⋊D7911yescharacteristic
1033C23C22×C22⋊D7911yescharacteristic
1034Q8—24no—
1035Q8—42no—
1036Q8—3162no—
1037Q8—1584no—
1038D4—24no—
1039D4—42no—
1040D4—44no—
1041D4—44no—
1042D4—44no—
1043D4—44no—
1044D4—44no—
1045D4—44no—
1046D4—3162no—
1047D4—3164no—
1048D4—3164no—
1049D4—3164no—
1050D4—3164no—
1051D4—3164no—
1052D4—3164no—
1053D4—1584no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—44no—
1085C2×C4—42no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—44no—
1089C2×C4—3164no—
1090C2×C4—3162no—
1091C2×C4—3162no—
1092C2×C4—3162no—
1093C2×C4—3164no—
1094C2×C4—1582no—
1095C2×C4—1582no—
1096C2×C4—1582no—
1097C2×C4C22×C22⋊D7911yescharacteristic
1098C2×C4C22×C22⋊D7911yescharacteristic
1099C2×C4C22×C22⋊D7911yescharacteristic
1100C2×C4C22×C22⋊D7911yescharacteristic
1101C2×C4C22×C22⋊D7911yescharacteristic
1102C2×C4C22×C22⋊D7911yescharacteristic
1103C2×C4C22×C22⋊D7911yescharacteristic
1104C2×C4#1457920614yes—
1105C2×C4C24×D7911yescharacteristic
1106C8—1584no—
1107C8—1584no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—84no—
1137C22—3162no—
1138C22—3162no—
1139C22—3162no—
1140C22—6324no—
1141C22#1909912212yes—
1142C22#1909936112yes—
1143C22#1909936112yes—
1144C22C23×C22⋊D7911yescharacteristic
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—3162no—
1155C4—3162no—
1156C4—3162no—
1157C4#1909912212yes—
1158C4C2×#1457920612yes—
1159C2—22no—
1160C2—22no—
1161C2—22no—
1162C2—41no—
1163C2—41no—
1164C2—41no—
1165C2—41no—
1166C2—82no—
1167C2—6322no—
1168C2C2×#1909912211yescharacteristic
1169C2C2×#1909936111yescharacteristic
1170C2C2×#1909936111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#525×C79C2
socleC22×C79C23×D4
hypercenterC2×#525D79
hypocenterC79#60741
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#19099074C2semidirect
2. #23774237C2semidirect
3. #23774230C2semidirect
4. #23774226C2semidirect
5. #23774221C2semidirect
6. #23774214C2semidirect
7. #23774210C2semidirect
8. #23774206C2semidirect
9. #23774202C2semidirect
10. #23774197C2semidirect
11. #23773313C2semidirect
12. #23773309C2semidirect
13. #23773006C2semidirect
14. #23772618C2semidirect
15. #23772616C2semidirect
16. C2×#19098527C2semidirect
17. C2×#525×C79C2semidirect
18. C22×#11929624C22semidirect
19. C2×#14579181C22semidirect
20. C22×#11929608C22semidirect
27. #19099074C22semidirect
28. #19099074C22semidirect
31. C2×#14579140C22semidirect
33. C2×#14579135C22semidirect
37. C2×#14579120C22semidirect
38. #19098904C22semidirect
39. #19098901C22semidirect
40. #19098898C22semidirect
41. #19098896C22semidirect
42. #19098893C22semidirect
43. #19098891C22semidirect
44. #19098887C22semidirect
45. #19098884C22semidirect
46. #19098881C22semidirect
47. #19098879C22semidirect
48. #19098876C22semidirect
49. #19098874C22semidirect
50. #19098819C22semidirect
51. #19098819C22semidirect
52. #19098814C22semidirect
53. #19098814C22semidirect
54. #19098811C22semidirect
55. #19098811C22semidirect
56. #19098807C22semidirect
57. #19098807C22semidirect
58. #19098725C22semidirect
59. #19098723C22semidirect
60. #19098719C22semidirect
61. #19098718C22semidirect
62. #19098714C22semidirect
63. #19098713C22semidirect
64. #19098708C22semidirect
65. #19098706C22semidirect
66. #19098702C22semidirect
67. #19098701C22semidirect
68. #19098697C22semidirect
69. #19098696C22semidirect
70. #19098599C22semidirect
71. #19098559C22semidirect
72. #19098557C22semidirect
75. #19098527C22semidirect
76. #19098527C22semidirect
77. #19098527C22semidirect
78. C2×C22⋊(C79⋊C8)C22semidirect
79. C2×C22⋊(C79⋊C8)C22semidirect
80. C22×#41×C79C22semidirect
88. #525×C79C22semidirect
89. #525×C79C22semidirect
92. C2×C22⋊Q8×C79C22semidirect
94. C2×#121×C79C22semidirect
98. C2×#117×C79C22semidirect
111. C2×#11929614C23semidirect
112. C2×#11929612C23semidirect
113. C2×#11929611C23semidirect
114. C2×#11929609C23semidirect
166. #14579094C23semidirect
167. #14579094C23semidirect
168. #14579092C23semidirect
169. #14579092C23semidirect
170. #14579085C23semidirect
171. #14579085C23semidirect
172. #14579084C23semidirect
173. #14579084C23semidirect
174. #14579082C23semidirect
175. #14579082C23semidirect
176. #14579081C23semidirect
177. #14579081C23semidirect
587. C2×#525D79semidirect
603. C79#60741semidirect
605. C22×#41C2×D79semidirect
623. #525C2×D79semidirect
624. #525C2×D79semidirect
630. C2×C22⋊Q8C2×D79semidirect
634. C2×#121C2×D79semidirect
642. C2×#117C2×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190990742
#237742372
#237742302
#237742262
#237742212
#237742142
#237742102
#237742062
#237742022
#237741972
#237733132
#237733092
#237730062
#237726182
#237726162
C2×#190985272
C2×#525×C792
#6074179