Finite Group Databasebeta

← #34448676

Subgroups — #34448676

Order 20224.

3102 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×D79C211yesmaximal, characteristic
2C2×#19099039C211yesmaximal, characteristic, complemented
3C2×#19099035C211yesmaximal, characteristic
4#23766476C211yesmaximal, characteristic, complemented
5#23766475C211yesmaximal, characteristic, complemented
6#23766473C211yesmaximal, characteristic, complemented
7#23766471C211yesmaximal, characteristic, complemented
8#23766470C211yesmaximal, characteristic, complemented
9#23766469C211yesmaximal, characteristic, complemented
10#23766467C211yesmaximal, characteristic, complemented
11#23766248C212yesmaximal, complemented
12#23766247C212yesmaximal, complemented
13#23766244C212yesmaximal, complemented
14#23766243C212yesmaximal, complemented
15#23766109C212yesmaximal, complemented
16#23766106C212yesmaximal, complemented
17#23765983C211yesmaximal, characteristic, complemented
18#23765979C211yesmaximal, characteristic
19#23765941C212yesmaximal, complemented
20C4×#14579147C212yesmaximal, complemented
21#23765804C211yesmaximal, characteristic, complemented
22C4×#14579119C211yesmaximal, characteristic, complemented
23C79×#2367C211yesmaximal, characteristic, complemented
24C22×Q8×D79C2211yescharacteristic
25C22×D4×D79C2211yescharacteristic
26C2×#14579150C2211yescharacteristic
27C2×#14579149C2211yescharacteristic
28C2×#14579148C2211yescharacteristic
29C2×#14579147C2212yes—
30C2×#14579147C2212yes—
31#124×D79C4116yescomplemented
32#19099039—28no—
33#19099035—28no—
34C2×Q8×Dic79C2211yescharacteristic, complemented
35C2×C4×Dic158C2212yescomplemented
36C2×C4×Dic158C2211yescharacteristic, complemented
37C2×#14579126C2212yescomplemented
38C2×#14579126C2211yescharacteristic, complemented
39C2×C4×D316C2211yescharacteristic
40C2×D4×Dic79C2211yescharacteristic
41C2×#14579123C2211yescharacteristic
42C2×C4×C22⋊D79C2212yes—
43C2×(C22⋊D79)⋊C4C2212yes—
44C2×#14579119C2212yes—
45C2×#14579119C2211yescharacteristic
46C2×#14579119C2211yescharacteristic
47C2×#14579118C2211yescharacteristic
48C2×#14579118C2211yescharacteristic
49C2×#14579118C2212yes—
50C22×(C2×D79)⋊C4C2212yes—
51C2×C22⋊C4×D79C2212yes—
52C2×C22⋊C4×D79C2212yes—
53C2×C22⋊C4×D79C2212yes—
54C2×C42×D79C2211yescharacteristic
55#19098470C2211yescharacteristic, complemented
56#19098469C2211yescharacteristic, complemented
57#19098468C2211yescharacteristic, complemented
58#19098467C2212yescomplemented
59#19098467C2212yescomplemented
60#19098466C2211yescharacteristic
61#19098465C2211yescharacteristic
62#19098464C2211yescharacteristic
63#19098463C2212yes—
64#19098463C2212yes—
65#19098457C2212yescomplemented
66#19098457C2212yescomplemented
67#19098456C2212yescomplemented
68#19098456C2212yescomplemented
69#19098455C2212yescomplemented
70#19098455C2212yescomplemented
71#19098454C2212yescomplemented
72#19098454C2212yescomplemented
73#19098453C2212yescomplemented
74#19098453C2212yescomplemented
75#19098452C2212yescomplemented
76#19098452C2212yescomplemented
77#19098451C2212yescomplemented
78#19098451C2212yescomplemented
79#19098438C2212yescomplemented
80#19098437C2212yescomplemented
81#19098437C2212yescomplemented
82#19098436C2212yescomplemented
83#19098435C2212yescomplemented
84#19098434C2212yescomplemented
85#19098434C2212yescomplemented
86#19098432C2211yescharacteristic, complemented
87#19098432C2211yescharacteristic, complemented
88#19098427C2211yescharacteristic, complemented
89#19098427C2211yescharacteristic, complemented
90#19098425C2212yes—
91#19098425C2212yes—
92#19098422C2211yescharacteristic
93#19098422C2211yescharacteristic
94#19098420C2211yescharacteristic
95#19098420C2211yescharacteristic
96#19098418C2212yes—
97#19098418C2212yes—
98C4⋊C4×Dic79C2211yescharacteristic, complemented
99C4⋊C4×Dic79C2211yescharacteristic, complemented
100C4×Dic79⋊C4C2211yescharacteristic, complemented
101C4×Dic79⋊C4C2211yescharacteristic, complemented
102C4×C4⋊Dic79C2211yescharacteristic, complemented
103C4×C4⋊Dic79C2211yescharacteristic, complemented
104C22⋊C4×Dic79C2212yescomplemented
105C22⋊C4×Dic79C2212yescomplemented
106C4×(C2×D79)⋊C4C2212yes—
107C4×(C2×D79)⋊C4C2212yescomplemented
108C4×(C2×D79)⋊C4C2212yescomplemented
109C4×C22⋊Dic79C2212yescomplemented
110#19098410C2212yes—
111#19098410C2212yescomplemented
112#19098410C2212yescomplemented
113#19098408C2212yescomplemented
114C42×Dic79C2212yescomplemented
115C2×#124×C79C2211yescharacteristic
116C2×C4×Q8×C79C2211yescharacteristic, complemented
117C2×C4×D4×C79C2211yescharacteristic
118#391×C79C2211yescharacteristic, complemented
119#390×C79C2211yescharacteristic
120#388×C79C2212yescomplemented
121#388×C79C2212yescomplemented
122#385×C79C2212yescomplemented
123C4×C4⋊C4×C79C2211yescharacteristic, complemented
124C4×C4⋊C4×C79C2211yescharacteristic, complemented
125C4×C22⋊C4×C79C2212yescomplemented
126C24×D79C2312yes—
127C22×Dic158C2312yes—
128C22×Dic158C2311yescharacteristic
129C2×Q8×D79—24no—
130C2×Q8×D79—24no—
131C2×Q8×D79C2×C418yescomplemented
132C22×D316C2311yescharacteristic
133C22×C22⋊D79C2312yes—
134C2×D4×D79—24no—
135C2×D4×D79—24no—
136C2×D4×D79C2×C418yes—
137C23×Dic79C2312yes—
138C22×C4×D79C2312yes—
139C22×C4×D79C2312yes—
140C22×C4×D79C2312yes—
141C22×C4×D79C2311yescharacteristic
142C22×C4×D79C2311yescharacteristic
143C22×C4×D79C2311yescharacteristic
144#14579150C2×C418yescomplemented
145#14579149C2×C418yescomplemented
146#14579148C2×C418yescomplemented
147#14579147C2×C4116yescomplemented
148#14579147C2×C4116yescomplemented
149Q8×Dic79—24no—
150C4×Dic158—24no—
151C4×Dic158—28no—
152#14579126—24no—
153#14579126—28no—
154C4×D316—24no—
155D4×Dic79—24no—
156#14579123—24no—
157C4×C22⋊D79—28no—
158(C22⋊D79)⋊C4—28no—
159#14579119—24no—
160#14579119—28no—
161#14579119D418yes—
162#14579118—24no—
163#14579118—24no—
164#14579118—28no—
165C2×C4⋊Dic79C2311yescharacteristic
166C2×C4⋊Dic79C2312yes—
167C2×C4⋊Dic79C2311yescharacteristic
168C2×C4⋊Dic79C2311yescharacteristic
169C2×C4⋊Dic79C2311yescharacteristic
170C2×Dic79⋊C4C2311yescharacteristic
171C2×Dic79⋊C4C2311yescharacteristic
172C2×Dic79⋊C4C2311yescharacteristic
173C2×Dic79⋊C4C2311yescharacteristic
174C2×Dic79⋊C4C2312yes—
175C2×Dic79⋊C4C2312yes—
176C2×Dic79⋊C4C2311yescharacteristic
177C2×Dic79⋊C4C2311yescharacteristic
178C2×Dic79⋊C4C2311yescharacteristic
179C2×Dic79⋊C4C2311yescharacteristic
180C2×C22⋊Dic79C2312yes—
181C2×C22⋊Dic79C2312yes—
182C2×C22⋊Dic79C2312yes—
183C2×C22⋊Dic79C2312yes—
184C2×C22⋊Dic79C2312yes—
185C2×(C2×D79)⋊C4—28no—
186C2×(C2×D79)⋊C4C2312yes—
187C2×(C2×D79)⋊C4C2311yescharacteristic
188C2×(C2×D79)⋊C4C2311yescharacteristic
189C2×(C2×D79)⋊C4C2311yescharacteristic
190C2×(C2×D79)⋊C4C2311yescharacteristic
191C2×(C2×D79)⋊C4C2312yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2312yes—
194C2×(C2×D79)⋊C4C2312yes—
195C2×(C2×D79)⋊C4C2312yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×(C2×D79)⋊C4C2312yes—
200C2×(C2×D79)⋊C4C2312yes—
201C2×(C2×D79)⋊C4C2312yes—
202C22⋊C4×D79—28no—
203C22⋊C4×D79C2×C4116yescomplemented
204C22⋊C4×D79C2×C4116yescomplemented
205C2×C4×Dic79C2312yes—
206C2×C4×Dic79C2312yes—
207C2×C4×Dic79C2312yes—
208C2×C4×Dic79C2312yes—
209C2×C4×Dic79C2311yescharacteristic
210C2×C4×Dic79C2311yescharacteristic
211C2×C4×Dic79C2312yes—
212C2×C4×Dic79C2312yes—
213C2×C4×Dic79C2312yes—
214C2×C4×Dic79C2311yescharacteristic
215C2×C4×Dic79C2311yescharacteristic
216C2×C4×Dic79C2311yescharacteristic
217C2×C4×Dic79C2312yes—
218C42×D79C2×C418yescomplemented
219C79⋊#95C2312yes—
220C79⋊#95C2312yes—
221C79⋊#95C2312yes—
222C79⋊#95C2311yescharacteristic
223C79⋊#95C2312yes—
224C79⋊#95C2311yescharacteristic
225C79⋊#95C2312yes—
226C79⋊#95C2311yescharacteristic
227C79⋊#95C2311yescharacteristic
228C79⋊#95C2312yes—
229C79⋊#95C2312yes—
230C79⋊#95C2311yescharacteristic
231C79⋊#95C2311yescharacteristic
232C79⋊#95C2312yes—
233C79⋊#95C2312yes—
234C22×Q8×C79C2311yescharacteristic
235C22×D4×C79C2311yescharacteristic
236C23×C4×C79C2312yes—
237#124×C79C2×C418yescomplemented
238C4×Q8×C79—24no—
239C4×D4×C79—24no—
240C2×C4⋊C4×C79C2311yescharacteristic
241C2×C4⋊C4×C79C2312yes—
242C2×C4⋊C4×C79C2311yescharacteristic
243C2×C4⋊C4×C79C2311yescharacteristic
244C2×C4⋊C4×C79C2311yescharacteristic
245C2×C22⋊C4×C79C2312yes—
246C2×C22⋊C4×C79C2312yes—
247C2×C22⋊C4×C79C2312yes—
248C2×C22⋊C4×C79C2312yes—
249C2×C22⋊C4×C79C2312yes—
250C2×C42×C79C2312yes—
251C2×C42×C79C2311yescharacteristic
252C2×C42×C79C2311yescharacteristic
253C2×C42×C79C2312yes—
254C2×C42×C79C2311yescharacteristic
255#95×C79C2312yes—
256#95×C79C2311yescharacteristic
257#95×C79C2312yes—
258#95×C79C2311yescharacteristic
259#95×C79C2312yes—
260C23×D79—24no—
261C23×D79—24no—
262C23×D79—42no—
263C23×D79—42no—
264C23×D79—42no—
265C23×D79—42no—
266C23×D79C22×C418yes—
267C23×D79C2412yes—
268C23×D79C2411yescharacteristic
269C2×Dic158—24no—
270C2×Dic158—24no—
271C2×Dic158—22no—
272C2×Dic158—22no—
273C2×Dic158C22×C418yes—
274C2×Dic158C22×C414yes—
275Q8×D79—232no—
276C2×D316—22no—
277C2×D316—22no—
278C2×D316C22×C414yes—
279C2×C22⋊D79—24no—
280C2×C22⋊D79—24no—
281C2×C22⋊D79C22×C418yes—
282D4×D79—232no—
283C22×Dic79—24no—
284C22×Dic79—42no—
285C22×Dic79—42no—
286C22×Dic79C2412yes—
287C22×Dic79C2411yescharacteristic
288C22×Dic79C2411yescharacteristic
289C22×Dic79C2411yescharacteristic
290C22×Dic79C2411yescharacteristic
291C22×Dic79C2412yes—
292C22×Dic79C2411yescharacteristic
293C22×Dic79C2411yescharacteristic
294C22×Dic79C2412yes—
295C22×Dic79C2411yescharacteristic
296C2×C4×D79—24no—
297C2×C4×D79—24no—
298C2×C4×D79—24no—
299C2×C4×D79—24no—
300C2×C4×D79—41no—
301C2×C4×D79—41no—
302C2×C4×D79—41no—
303C2×C4×D79—41no—
304C2×C4×D79—42no—
305C2×C4×D79—42no—
306C2×C4×D79—42no—
307C2×C4×D79—42no—
308C2×C4×D79C22×C418yes—
309C2×C4×D79C22×C414yes—
310C2×C4×D79C22×C414yes—
311C2×C4×D79C22×C414yes—
312C2×C4×D79C2×D414yes—
313C2×C4×D79#4114yes—
314C4⋊Dic79—24no—
315C4⋊Dic79—22no—
316C4⋊Dic79—41no—
317C4⋊Dic79—41no—
318C4⋊Dic79C2×D414yes—
319Dic79⋊C4—22no—
320Dic79⋊C4—22no—
321Dic79⋊C4—22no—
322Dic79⋊C4—24no—
323Dic79⋊C4—22no—
324Dic79⋊C4—24no—
325Dic79⋊C4—41no—
326Dic79⋊C4—41no—
327Dic79⋊C4—41no—
328Dic79⋊C4—41no—
329C22⋊Dic79—24no—
330C22⋊Dic79—42no—
331C22⋊Dic79—42no—
332C22⋊Dic79C22×C418yes—
333C22⋊Dic79C22×C418yes—
334(C2×D79)⋊C4—24no—
335(C2×D79)⋊C4—22no—
336(C2×D79)⋊C4—22no—
337(C2×D79)⋊C4—22no—
338(C2×D79)⋊C4—22no—
339(C2×D79)⋊C4—24no—
340(C2×D79)⋊C4—24no—
341(C2×D79)⋊C4—42no—
342(C2×D79)⋊C4—42no—
343(C2×D79)⋊C4—42no—
344(C2×D79)⋊C4—42no—
345(C2×D79)⋊C4C22×C418yes—
346(C2×D79)⋊C4C22×C418yes—
347(C2×D79)⋊C4C22×C418yes—
348(C2×D79)⋊C4C22×C418yes—
349(C2×D79)⋊C4C2×D418yes—
350C4×Dic79—24no—
351C4×Dic79—24no—
352C4×Dic79—24no—
353C4×Dic79—22no—
354C4×Dic79—22no—
355C4×Dic79—24no—
356C4×Dic79—42no—
357C4×Dic79—42no—
358C4×Dic79—42no—
359C4×Dic79C22×C414yes—
360C4×Dic79C22×C414yes—
361C4×Dic79C22×C414yes—
362C4×Dic79C2×D418yes—
363C24×C79C2412yes—
364C2×Q8×C79—22no—
365C2×Q8×C79—22no—
366C2×Q8×C79C22×C414yes—
367C2×D4×C79—22no—
368C2×D4×C79—22no—
369C2×D4×C79C22×C414yes—
370C22×C4×C79—24no—
371C22×C4×C79—42no—
372C22×C4×C79—42no—
373C22×C4×C79C2412yes—
374C22×C4×C79C2411yescharacteristic
375C22×C4×C79C2411yescharacteristic
376C22×C4×C79C2411yescharacteristic
377C22×C4×C79C2411yescharacteristic
378C22×C4×C79C2412yes—
379C22×C4×C79C2411yescharacteristic
380C22×C4×C79C2411yescharacteristic
381C22×C4×C79C2412yes—
382C22×C4×C79C2411yescharacteristic
383C4⋊C4×C79—24no—
384C4⋊C4×C79—22no—
385C4⋊C4×C79—41no—
386C4⋊C4×C79—41no—
387C4⋊C4×C79C2×D414yes—
388C22⋊C4×C79—24no—
389C22⋊C4×C79—42no—
390C22⋊C4×C79—42no—
391C22⋊C4×C79C22×C418yes—
392C22⋊C4×C79C22×C418yes—
393C42×C79—22no—
394C42×C79—24no—
395C42×C79—22no—
396C42×C79—42no—
397C42×C79C22×C414yes—
398C23×C79—22no—
399C23×C79—22no—
400C23×C79—22no—
401C23×C79—22no—
402C23×C79—22no—
403C23×C79—22no—
404C23×C79C23×C414yes—
405C23×C79C2511yescharacteristic
406C22×D79—21no—
407C22×D79—21no—
408C22×D79—21no—
409C22×D79—21no—
410C22×D79—22no—
411C22×D79—22no—
412C22×D79—22no—
413C22×D79—22no—
414C22×D79—22no—
415C22×D79—22no—
416C22×D79—216no—
417C22×D79—48no—
418C22×D79—48no—
419C22×D79—84no—
420C22×D79—84no—
421C22×D79—84no—
422C22×D79—84no—
423C22×D79C23×C414yes—
424C22×D79C23×C412yes—
425C22×D79C22×D412yes—
426C22×D79C2×#4112yes—
427Q8×C79—28no—
428D4×C79—28no—
429C2×C4×C79—22no—
430C2×C4×C79—22no—
431C2×C4×C79—21no—
432C2×C4×C79—22no—
433C2×C4×C79—21no—
434C2×C4×C79—21no—
435C2×C4×C79—21no—
436C2×C4×C79—22no—
437C2×C4×C79—21no—
438C2×C4×C79—21no—
439C2×C4×C79—21no—
440C2×C4×C79—21no—
441C2×C4×C79—22no—
442C2×C4×C79—22no—
443C2×C4×C79—21no—
444C2×C4×C79—21no—
445C2×C4×C79—22no—
446C2×C4×C79—21no—
447C2×C4×C79—21no—
448C2×C4×C79—21no—
449C2×C4×C79—21no—
450C2×C4×C79—21no—
451C2×C4×C79—21no—
452C2×C4×C79—84no—
453C2×C4×C79C23×C412yes—
454C2×C4×C79C23×C412yes—
455C2×C4×C79C23×C414yes—
456C2×C4×C79C23×C412yes—
457C2×C4×C79C22×D414yes—
458C2×C4×C79C22×D412yes—
459C2×C4×C79C2×#4112yes—
460C22⋊D79—216no—
461C2×Dic79—22no—
462C2×Dic79—22no—
463C2×Dic79—21no—
464C2×Dic79—21no—
465C2×Dic79—22no—
466C2×Dic79—22no—
467C2×Dic79—21no—
468C2×Dic79—21no—
469C2×Dic79—21no—
470C2×Dic79—21no—
471C2×Dic79—21no—
472C2×Dic79—21no—
473C2×Dic79—22no—
474C2×Dic79—22no—
475C2×Dic79—22no—
476C2×Dic79—21no—
477C2×Dic79—21no—
478C2×Dic79—21no—
479C2×Dic79—21no—
480C2×Dic79—21no—
481C2×Dic79—21no—
482C2×Dic79—21no—
483C2×Dic79—21no—
484C2×Dic79—84no—
485C2×Dic79C23×C412yes—
486C2×Dic79C23×C412yes—
487C2×Dic79C23×C414yes—
488C2×Dic79C23×C412yes—
489C2×Dic79C22×D414yes—
490C2×Dic79C22×D412yes—
491C2×Dic79C2×#4112yes—
492D316—28no—
493C4×D79—216no—
494C4×D79—44no—
495C4×D79—44no—
496C4×D79—84no—
497C4×D79—84no—
498C4×D79C4×D4116yes—
499Dic158—28no—
500Dic158—216no—
501C22×C79—24no—
502C22×C79—24no—
503C22×C79—24no—
504C22×C79—42no—
505C22×C79—42no—
506C22×C79—42no—
507C22×C79—42no—
508C22×C79C24×C411yescharacteristic
509C22×C79C23×D411yescharacteristic
510C22×C79C22×#4111yescharacteristic
511C22×C79#58511yescharacteristic
512C22×C79#58511yescharacteristic
513C22×C79#58511yescharacteristic
514C22×C79#58511yescharacteristic
515C2×D79—22no—
516C2×D79—22no—
517C2×D79—22no—
518C2×D79—22no—
519C2×D79—22no—
520C2×D79—22no—
521C2×D79—24no—
522C2×D79—24no—
523C2×D79—24no—
524C2×D79—42no—
525C2×D79—42no—
526C2×D79—42no—
527C2×D79—42no—
528C2×D79—816no—
529C2×D79C2×C4×D414yes—
530C4×C79—24no—
531C4×C79—22no—
532C4×C79—22no—
533C4×C79—24no—
534C4×C79—41no—
535C4×C79—41no—
536C4×C79—41no—
537C4×C79—41no—
538C4×C79—42no—
539C4×C79C2×C4×D414yes—
540Dic79—24no—
541Dic79—22no—
542Dic79—22no—
543Dic79—24no—
544Dic79—41no—
545Dic79—41no—
546Dic79—41no—
547Dic79—41no—
548Dic79—42no—
549Dic79C2×C4×D414yes—
550#34211—791nomaximal, Sylow
551C2×C79—44no—
552C2×C79C22×C4×D411yescharacteristic
553C2×C79#342811yescharacteristic
554C2×C79#342811yescharacteristic
555C2×C79#350011yescharacteristic
556C2×C79#350011yescharacteristic
557C2×C79#351011yescharacteristic
558C2×C79#351011yescharacteristic
559D79—24no—
560D79—44no—
561C22×#124—791no—
562C2×#519—791no—
563C2×#518—791no—
564#2367—791no—
565#2367—791no—
566#2367—791no—
567#2367—791no—
568#2367—791no—
569#2367—791no—
570#2367—791no—
571#2367D7911yescharacteristic, complemented
572#2342—792no—
573#2342—792no—
574#2342—792no—
575#2342—792no—
576#2326—792no—
577#2326—792no—
578#2310—791no—
579#2309—791no—
580C4×#124—792no—
581C4×#124—792no—
582#2285—791no—
583C4×#117—791no—
584C79#3421111yescharacteristic, complemented, Sylow
585C23×Q8—791no—
586C23×D4—791no—
587C2×#124—791no—
588C2×#124—791no—
589C2×#124—7916no—
590C2×#124—792no—
591C2×#124—792no—
592C2×#124—791no—
593C2×#124C2×D7911yescharacteristic
594#519—1588no—
595#518—1588no—
596C2×C4×Q8—791no—
597C2×C4×Q8—792no—
598C2×C4×Q8—791no—
599C2×C4×Q8—792no—
600C2×C4×Q8—791no—
601C2×C4×Q8C2×D7911yescharacteristic, complemented
602C2×C4×D4—791no—
603C2×C4×D4—792no—
604C2×C4×D4—791no—
605C2×C4×D4—792no—
606C2×C4×D4—791no—
607C2×C4×D4C2×D7911yescharacteristic
608C2×#117—791no—
609C2×#117—791no—
610C2×#117—792no—
611C2×#117—791no—
612C2×#117—791no—
613C2×#117—792no—
614C22×C22⋊C4—792no—
615C22×C22⋊C4—792no—
616C22×C22⋊C4—792no—
617C22×C22⋊C4—792no—
618C22×C42—791no—
619#391—791no—
620#391—791no—
621#391—791no—
622#391—792no—
623#391—792no—
624#391C2×D7911yescharacteristic, complemented
625#390—791no—
626#390—791no—
627#390—792no—
628#390—792no—
629#390—791no—
630#390C2×D7911yescharacteristic
631#388—792no—
632#388—792no—
633#388—792no—
634#388—792no—
635#388—792no—
636#388—792no—
637#388—792no—
638#388—792no—
639#388—792no—
640#388—792no—
641#388—792no—
642#388—792no—
643#388—792no—
644#388—792no—
645#388C2×D7912yescomplemented
646#388C2×D7912yescomplemented
647#385—792no—
648#385—792no—
649#385—792no—
650#385—792no—
651#385—792no—
652#385—792no—
653#385—792no—
654#385C2×D7912yescomplemented
655#384—791no—
656#384—791no—
657#382—791no—
658#382—791no—
659#381—792no—
660#381—792no—
661#380—791no—
662#380—791no—
663#380—791no—
664#380—791no—
665#379—792no—
666#379—792no—
667C4×C4⋊C4—791no—
668C4×C4⋊C4—791no—
669C4×C4⋊C4—791no—
670C4×C4⋊C4—791no—
671C4×C4⋊C4—791no—
672C4×C4⋊C4—791no—
673C4×C4⋊C4C2×D7911yescharacteristic, complemented
674C4×C4⋊C4C2×D7911yescharacteristic, complemented
675C4×C22⋊C4—792no—
676C4×C22⋊C4—792no—
677C4×C22⋊C4—792no—
678C4×C22⋊C4—792no—
679C4×C22⋊C4—792no—
680C4×C22⋊C4—792no—
681C4×C22⋊C4—792no—
682C4×C22⋊C4—792no—
683C4×C22⋊C4—792no—
684C4×C22⋊C4C2×D7912yescomplemented
685#376—792no—
686C43—792no—
687C25—792no—
688C22×Q8—798no—
689C22×Q8—792no—
690C22×Q8—791no—
691C22×Q8—1584no—
692C22×Q8—1584no—
693C22×Q8C22×D7911yescharacteristic
694C22×D4—792no—
695C22×D4—798no—
696C22×D4—791no—
697C22×D4—1584no—
698C22×D4—1584no—
699C22×D4C22×D7911yescharacteristic
700C23×C4—791no—
701C23×C4—791no—
702C23×C4—792no—
703C23×C4—792no—
704C23×C4—792no—
705C23×C4—791no—
706C23×C4—792no—
707C23×C4C22×D7912yes—
708#124—798no—
709#124—798no—
710#124—7916no—
711#124—7916no—
712#124—798no—
713#124C4×D7918yescomplemented
714C4×Q8—24no—
715C4×Q8—1588no—
716C4×Q8—1584no—
717C4×Q8—1588no—
718C4×Q8—1584no—
719C4×Q8—1584no—
720C4×D4—24no—
721C4×D4—1584no—
722C4×D4—1588no—
723C4×D4—1588no—
724C4×D4—1584no—
725C4×D4—1584no—
726#117—798no—
727#117—1588no—
728#117—1584no—
729#117—1584no—
730#117—1588no—
731#117—1584no—
732C2×C4⋊C4—791no—
733C2×C4⋊C4—791no—
734C2×C4⋊C4—791no—
735C2×C4⋊C4—791no—
736C2×C4⋊C4—791no—
737C2×C4⋊C4—791no—
738C2×C4⋊C4—791no—
739C2×C4⋊C4—791no—
740C2×C4⋊C4—791no—
741C2×C4⋊C4—791no—
742C2×C4⋊C4—791no—
743C2×C4⋊C4—792no—
744C2×C4⋊C4—792no—
745C2×C4⋊C4—792no—
746C2×C4⋊C4—791no—
747C2×C4⋊C4C22×D7912yes—
748C2×C4⋊C4C22×D7911yescharacteristic
749C2×C4⋊C4C22×D7911yescharacteristic
750C2×C4⋊C4C22×D7911yescharacteristic
751C2×C4⋊C4C22×D7911yescharacteristic
752C2×C22⋊C4—792no—
753C2×C22⋊C4—792no—
754C2×C22⋊C4—792no—
755C2×C22⋊C4—792no—
756C2×C22⋊C4—792no—
757C2×C22⋊C4—792no—
758C2×C22⋊C4—792no—
759C2×C22⋊C4—792no—
760C2×C22⋊C4—792no—
761C2×C22⋊C4—792no—
762C2×C22⋊C4—792no—
763C2×C22⋊C4—792no—
764C2×C22⋊C4—792no—
765C2×C22⋊C4—7916no—
766C2×C22⋊C4—7916no—
767C2×C22⋊C4—792no—
768C2×C22⋊C4—791no—
769C2×C22⋊C4—791no—
770C2×C22⋊C4—792no—
771C2×C22⋊C4—792no—
772C2×C22⋊C4—791no—
773C2×C22⋊C4—791no—
774C2×C22⋊C4—792no—
775C2×C22⋊C4—1588no—
776C2×C22⋊C4—1588no—
777C2×C22⋊C4C22×D7912yes—
778C2×C22⋊C4C22×D7912yes—
779C2×C22⋊C4C22×D7912yes—
780C2×C22⋊C4C22×D7912yes—
781C2×C22⋊C4C22×D7912yes—
782C2×C42—792no—
783C2×C42—792no—
784C2×C42—792no—
785C2×C42—792no—
786C2×C42—791no—
787C2×C42—791no—
788C2×C42—791no—
789C2×C42—798no—
790C2×C42—791no—
791C2×C42—792no—
792C2×C42—792no—
793C2×C42—792no—
794C2×C42—791no—
795C2×C42—792no—
796C2×C42C22×D7911yescharacteristic
797C2×C42C22×D7912yes—
798C2×C42C22×D7911yescharacteristic
799C2×C42C22×D7912yes—
800C2×C42C22×D7911yescharacteristic
801#95—792no—
802#95—792no—
803#95—792no—
804#95—791no—
805#95—791no—
806#95—791no—
807#95—791no—
808#95—791no—
809#95—791no—
810#95—792no—
811#95—792no—
812#95—792no—
813#95—792no—
814#95—792no—
815#95—792no—
816#95C22×D7912yes—
817#95C22×D7911yescharacteristic
818#95C22×D7912yes—
819#95C22×D7911yescharacteristic
820#95C22×D7912yes—
821C24—3162no—
822C24—3162no—
823C24—3162no—
824C24—3162no—
825C24—798no—
826C24—791no—
827C24—792no—
828C24—1584no—
829C24—1584no—
830C24C23×D7912yes—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—798no—
834C2×Q8—794no—
835C2×Q8—1584no—
836C2×Q8—1584no—
837C2×Q8—15832no—
838C2×Q8—1582no—
839C2×Q8—1582no—
840C2×Q8C2×C4×D7914yes—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—798no—
844C2×D4—794no—
845C2×D4—15832no—
846C2×D4—1584no—
847C2×D4—1584no—
848C2×D4—1582no—
849C2×D4—1582no—
850C2×D4C2×C4×D7914yes—
851C22×C4—24no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—3161no—
855C22×C4—3161no—
856C22×C4—3161no—
857C22×C4—3161no—
858C22×C4—3162no—
859C22×C4—3162no—
860C22×C4—3162no—
861C22×C4—3162no—
862C22×C4—3162no—
863C22×C4—3162no—
864C22×C4—794no—
865C22×C4—794no—
866C22×C4—791no—
867C22×C4—794no—
868C22×C4—794no—
869C22×C4—794no—
870C22×C4—791no—
871C22×C4—791no—
872C22×C4—792no—
873C22×C4—792no—
874C22×C4—798no—
875C22×C4—792no—
876C22×C4—791no—
877C22×C4—791no—
878C22×C4—791no—
879C22×C4—791no—
880C22×C4—1584no—
881C22×C4—1584no—
882C22×C4—1584no—
883C22×C4—1584no—
884C22×C4—1584no—
885C22×C4C23×D7912yes—
886C22×C4C23×D7911yescharacteristic
887C22×C4C23×D7911yescharacteristic
888C22×C4C23×D7911yescharacteristic
889C22×C4C23×D7911yescharacteristic
890C22×C4C23×D7911yescharacteristic
891C22×C4C23×D7911yescharacteristic
892C22×C4C23×D7912yes—
893C22×C4C23×D7912yes—
894C22×C4C23×D7911yescharacteristic
895C4⋊C4—22no—
896C4⋊C4—24no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—3161no—
900C4⋊C4—3161no—
901C4⋊C4—3161no—
902C4⋊C4—3161no—
903C4⋊C4—3161no—
904C4⋊C4—3161no—
905C4⋊C4—794no—
906C4⋊C4—1582no—
907C4⋊C4—1582no—
908C4⋊C4—1582no—
909C4⋊C4—1584no—
910C4⋊C4—1582no—
911C4⋊C4—1584no—
912C4⋊C4—1582no—
913C4⋊C4—1584no—
914C4⋊C4D4×D7914yes—
915C22⋊C4—24no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—3162no—
919C22⋊C4—3162no—
920C22⋊C4—3162no—
921C22⋊C4—3162no—
922C22⋊C4—3162no—
923C22⋊C4—3162no—
924C22⋊C4—798no—
925C22⋊C4—798no—
926C22⋊C4—798no—
927C22⋊C4—798no—
928C22⋊C4—798no—
929C22⋊C4—798no—
930C22⋊C4—798no—
931C22⋊C4—1584no—
932C22⋊C4—1582no—
933C22⋊C4—1582no—
934C22⋊C4—1584no—
935C22⋊C4—1582no—
936C22⋊C4—1582no—
937C22⋊C4—1584no—
938C22⋊C4—1584no—
939C22⋊C4C2×C4×D7918yes—
940C22⋊C4C2×C4×D7918yes—
941C42—22no—
942C42—24no—
943C42—22no—
944C42—42no—
945C42—3162no—
946C42—3162no—
947C42—3162no—
948C42—794no—
949C42—794no—
950C42—794no—
951C42—798no—
952C42—1584no—
953C42—1584no—
954C42—1584no—
955C42—1582no—
956C42—1582no—
957C42—1584no—
958C42C2×C4×D7914yes—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—3168no—
966C23—3168no—
967C23—792no—
968C23—792no—
969C23—792no—
970C23—794no—
971C23—6324no—
972C23—6324no—
973C23—6324no—
974C23—6324no—
975C23—15816no—
976C23—1582no—
977C23—1582no—
978C23—1582no—
979C23—1582no—
980C23—1582no—
981C23—1582no—
982C23—1581no—
983C23—1581no—
984C23—1581no—
985C23—1581no—
986C23C22×C4×D7914yes—
987C23C24×D7911yescharacteristic
988Q8—28no—
989Q8—15816no—
990Q8—1588no—
991D4—28no—
992D4—15816no—
993D4—1588no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—84no—
1018C2×C4—3164no—
1019C2×C4—3164no—
1020C2×C4—792no—
1021C2×C4—792no—
1022C2×C4—792no—
1023C2×C4—7916no—
1024C2×C4—792no—
1025C2×C4—792no—
1026C2×C4—794no—
1027C2×C4—794no—
1028C2×C4—6324no—
1029C2×C4—6324no—
1030C2×C4—6324no—
1031C2×C4—15816no—
1032C2×C4—1581no—
1033C2×C4—1581no—
1034C2×C4—1582no—
1035C2×C4—1581no—
1036C2×C4—1581no—
1037C2×C4—1581no—
1038C2×C4—1581no—
1039C2×C4—1582no—
1040C2×C4—1581no—
1041C2×C4—1581no—
1042C2×C4—1581no—
1043C2×C4—1581no—
1044C2×C4—1581no—
1045C2×C4—1581no—
1046C2×C4—1582no—
1047C2×C4—1581no—
1048C2×C4—1581no—
1049C2×C4—1581no—
1050C2×C4—1582no—
1051C2×C4—1582no—
1052C2×C4—1581no—
1053C2×C4—1582no—
1054C2×C4—1582no—
1055C2×C4C22×C4×D7912yes—
1056C2×C4C22×C4×D7912yes—
1057C2×C4C22×C4×D7914yes—
1058C2×C4C22×C4×D7912yes—
1059C2×C4C2×D4×D7914yes—
1060C2×C4C2×D4×D7912yes—
1061C2×C4#41×D7912yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—3162no—
1070C22—3162no—
1071C22—3162no—
1072C22—3162no—
1073C22—794no—
1074C22—63216no—
1075C22—1584no—
1076C22—1584no—
1077C22—1584no—
1078C22—1582no—
1079C22—1582no—
1080C22—1582no—
1081C22—1582no—
1082C22—1582no—
1083C22—1582no—
1084C22C23×C4×D7911yescharacteristic
1085C22C22×D4×D7911yescharacteristic
1086C22C2×#41×D7911yescharacteristic
1087C22#1909939811yescharacteristic
1088C22#1909939911yescharacteristic
1089C22#1909939911yescharacteristic
1090C22#1909940011yescharacteristic
1091C4—24no—
1092C4—22no—
1093C4—22no—
1094C4—24no—
1095C4—42no—
1096C4—41no—
1097C4—41no—
1098C4—41no—
1099C4—41no—
1100C4—3162no—
1101C4—3161no—
1102C4—3161no—
1103C4—3161no—
1104C4—3161no—
1105C4—794no—
1106C4—1584no—
1107C4—1582no—
1108C4—1582no—
1109C4—1584no—
1110C4C4×D4×D7914yes—
1111C2—44no—
1112C2—3164no—
1113C2—1584no—
1114C2C2×C4×D4×D7911yescharacteristic
1115C2#2377659911yescharacteristic
1116C2#2377660011yescharacteristic
1117C2#2377718611yescharacteristic
1118C2#2377719111yescharacteristic
1119C2#2377729011yescharacteristic
1120C2#2377729311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2367C2
socle, cosocleC23×C79C25
prime radicalC22×D4×D79C22
hypercenter#2367D79
hypocenterC79#34211
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. C2×#19099039C2semidirect
4. #23766476C2semidirect
5. #23766475C2semidirect
6. #23766473C2semidirect
7. #23766471C2semidirect
8. #23766470C2semidirect
9. #23766469C2semidirect
10. #23766467C2semidirect
11. #23766248C2semidirect
12. #23766247C2semidirect
13. #23766244C2semidirect
14. #23766243C2semidirect
15. #23766109C2semidirect
16. #23766106C2semidirect
17. #23765983C2semidirect
19. #23765941C2semidirect
20. C4×#14579147C2semidirect
21. #23765804C2semidirect
22. C4×#14579119C2semidirect
23. C79×#2367C2semidirect
31. #124×D79C4semidirect
34. C2×Q8×Dic79C22semidirect
35. C2×C4×Dic158C22semidirect
36. C2×C4×Dic158C22semidirect
37. C2×#14579126C22semidirect
38. C2×#14579126C22semidirect
55. #19098470C22semidirect
56. #19098469C22semidirect
57. #19098468C22semidirect
58. #19098467C22semidirect
59. #19098467C22semidirect
65. #19098457C22semidirect
66. #19098457C22semidirect
67. #19098456C22semidirect
68. #19098456C22semidirect
69. #19098455C22semidirect
70. #19098455C22semidirect
71. #19098454C22semidirect
72. #19098454C22semidirect
73. #19098453C22semidirect
74. #19098453C22semidirect
75. #19098452C22semidirect
76. #19098452C22semidirect
77. #19098451C22semidirect
78. #19098451C22semidirect
79. #19098438C22semidirect
80. #19098437C22semidirect
81. #19098437C22semidirect
82. #19098436C22semidirect
83. #19098435C22semidirect
84. #19098434C22semidirect
85. #19098434C22semidirect
86. #19098432C22semidirect
87. #19098432C22semidirect
88. #19098427C22semidirect
89. #19098427C22semidirect
98. C4⋊C4×Dic79C22semidirect
99. C4⋊C4×Dic79C22semidirect
100. C4×Dic79⋊C4C22semidirect
101. C4×Dic79⋊C4C22semidirect
102. C4×C4⋊Dic79C22semidirect
103. C4×C4⋊Dic79C22semidirect
104. C22⋊C4×Dic79C22semidirect
105. C22⋊C4×Dic79C22semidirect
107. C4×(C2×D79)⋊C4C22semidirect
108. C4×(C2×D79)⋊C4C22semidirect
109. C4×C22⋊Dic79C22semidirect
111. #19098410C22semidirect
112. #19098410C22semidirect
113. #19098408C22semidirect
114. C42×Dic79C22semidirect
116. C2×C4×Q8×C79C22semidirect
118. #391×C79C22semidirect
120. #388×C79C22semidirect
121. #388×C79C22semidirect
122. #385×C79C22semidirect
123. C4×C4⋊C4×C79C22semidirect
124. C4×C4⋊C4×C79C22semidirect
125. C4×C22⋊C4×C79C22semidirect
131. C2×Q8×D79C2×C4semidirect
144. #14579150C2×C4semidirect
145. #14579149C2×C4semidirect
146. #14579148C2×C4semidirect
147. #14579147C2×C4semidirect
148. #14579147C2×C4semidirect
203. C22⋊C4×D79C2×C4semidirect
204. C22⋊C4×D79C2×C4semidirect
218. C42×D79C2×C4semidirect
237. #124×C79C2×C4semidirect
571. #2367D79semidirect
584. C79#34211semidirect
601. C2×C4×Q8C2×D79semidirect
624. #391C2×D79semidirect
645. #388C2×D79semidirect
646. #388C2×D79semidirect
654. #385C2×D79semidirect
673. C4×C4⋊C4C2×D79semidirect
674. C4×C4⋊C4C2×D79semidirect
684. C4×C22⋊C4C2×D79semidirect
713. #124C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D792
C2×#190990392
C2×#190990352
#237664762
#237664752
#237664732
#237664712
#237664702
#237664692
#237664672
#237662482
#237662472
#237662442
#237662432
#237661092
#237661062
#237659832
#237659792
#237659412
C4×#145791472
#237658042
C4×#145791192
C79×#23672
#3421179