Finite Group Databasebeta

← C2×#23766406 #34447787

Subgroups — C2×#23766406 #34447787

Order 20224.

3614 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579138C211yesmaximal, characteristic
2C22×C4×Dic158C211yesmaximal, characteristic, complemented
3C23×Dic79⋊C4C211yesmaximal, characteristic
4#23766406C2116yesmaximal, direct product factor
5C2×#19098467C211yesmaximal, characteristic, complemented
6C2×#19098461C211yesmaximal, characteristic, complemented
7C2×#19098460C211yesmaximal, characteristic, complemented
8C2×#19098460C211yesmaximal, characteristic, complemented
9C2×#19098447C211yesmaximal, characteristic, complemented
10C2×#19098446C211yesmaximal, characteristic, complemented
11C2×#19098438C211yesmaximal, characteristic
12C2×#19098436C211yesmaximal, characteristic
13C2×C4×Dic79⋊C4C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic79C211yesmaximal, characteristic
15C2×C22⋊C4×Dic79C211yesmaximal, characteristic
16C2×C4×C22⋊C4×C79C211yesmaximal, characteristic
17C23×Dic158C2211yescharacteristic
18C24×Dic79C2211yescharacteristic
19C24×Dic79C2211yescharacteristic
20C2×#14579138C4116yescomplemented
21C2×#14579138C2218yes—
22C2×C4×Dic158—28no—
23C2×C4×Dic158C2218yescomplemented
24C22×C4⋊Dic79C2211yescharacteristic
25C22×C4⋊Dic79C2211yescharacteristic
26C22×C4⋊Dic79C2211yescharacteristic
27C22×Dic79⋊C4—28no—
28C22×Dic79⋊C4C2211yescharacteristic
29C22×Dic79⋊C4C2211yescharacteristic
30C22×Dic79⋊C4C2211yescharacteristic
31C22×Dic79⋊C4C2218yes—
32C22×Dic79⋊C4C2211yescharacteristic
33C22×Dic79⋊C4C2211yescharacteristic
34C22×Dic79⋊C4C2211yescharacteristic
35C22×Dic79⋊C4C2211yescharacteristic
36C22×Dic79⋊C4C2211yescharacteristic
37C22×C22⋊Dic79C2211yescharacteristic
38C22×C22⋊Dic79C2211yescharacteristic
39C22×C4×Dic79C2211yescharacteristic
40C22×C4×Dic79C2211yescharacteristic
41C22×C4×Dic79C2211yescharacteristic
42C22×C4×Dic79C2211yescharacteristic
43#19098467C2218yescomplemented
44#19098461C2218yescomplemented
45#19098460C2218yescomplemented
46#19098460C2218yescomplemented
47#19098447C2218yescomplemented
48#19098446C2218yescomplemented
49#19098438C2218yes—
50#19098436C2218yes—
51C4×Dic79⋊C4C2218yescomplemented
52C22⋊C4×Dic79C2218yes—
53C22⋊C4×Dic79C2218yes—
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C2×C79⋊#95C2211yescharacteristic
61C2×C79⋊#95C2211yescharacteristic
62C24×C4×C79C2211yescharacteristic
63C22×C22⋊C4×C79C2211yescharacteristic
64C22×C22⋊C4×C79C2211yescharacteristic
65C22×C42×C79C2211yescharacteristic
66C22×C42×C79C2211yescharacteristic
67C4×C22⋊C4×C79C2218yes—
68C2×#95×C79C2211yescharacteristic
69C2×#95×C79C2211yescharacteristic
70C22×Dic158—24no—
71C22×Dic158—24no—
72C22×Dic158C2×C418yescomplemented
73C22×Dic158C2314yes—
74C23×Dic79—24no—
75C23×Dic79—24no—
76C23×Dic79—24no—
77C23×Dic79—24no—
78C23×Dic79—42no—
79C23×Dic79C2×C418yes—
80C23×Dic79C2311yescharacteristic
81C23×Dic79C2311yescharacteristic
82C23×Dic79C2311yescharacteristic
83C23×Dic79C2314yes—
84C23×Dic79C2311yescharacteristic
85C23×Dic79C2311yescharacteristic
86C23×Dic79C2311yescharacteristic
87C23×Dic79C2314yes—
88C23×Dic79C2311yescharacteristic
89C23×Dic79C2311yescharacteristic
90#14579138C2×C4164yescomplemented
91C4×Dic158—232no—
92C2×C4⋊Dic79—24no—
93C2×C4⋊Dic79—42no—
94C2×C4⋊Dic79C2×C418yescomplemented
95C2×C4⋊Dic79C2314yes—
96C2×C4⋊Dic79C2314yes—
97C2×C4⋊Dic79C2314yes—
98C2×Dic79⋊C4—24no—
99C2×Dic79⋊C4—24no—
100C2×Dic79⋊C4—24no—
101C2×Dic79⋊C4—24no—
102C2×Dic79⋊C4—232no—
103C2×Dic79⋊C4—42no—
104C2×Dic79⋊C4C2×C418yescomplemented
105C2×Dic79⋊C4C2×C418yescomplemented
106C2×Dic79⋊C4D418yes—
107C2×Dic79⋊C4C2314yes—
108C2×Dic79⋊C4C2314yes—
109C2×Dic79⋊C4C2314yes—
110C2×Dic79⋊C4C2314yes—
111C2×Dic79⋊C4C2314yes—
112C2×Dic79⋊C4C2314yes—
113C2×Dic79⋊C4C2314yes—
114C2×Dic79⋊C4C2314yes—
115C2×C22⋊Dic79—24no—
116C2×C22⋊Dic79C2×C418yes—
117C2×C22⋊Dic79C2314yes—
118C2×C22⋊Dic79C2314yes—
119C2×C4×Dic79—24no—
120C2×C4×Dic79—24no—
121C2×C4×Dic79—24no—
122C2×C4×Dic79—42no—
123C2×C4×Dic79C2314yes—
124C2×C4×Dic79C2314yes—
125C2×C4×Dic79C2314yes—
126C2×C4×Dic79C2314yes—
127C79⋊#95C2314yes—
128C79⋊#95C2314yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C79⋊#95C2314yes—
134C79⋊#95C2314yes—
135C25×C79C2311yescharacteristic
136C23×C4×C79—24no—
137C23×C4×C79—24no—
138C23×C4×C79—42no—
139C23×C4×C79C2311yescharacteristic
140C23×C4×C79C2314yes—
141C23×C4×C79C2311yescharacteristic
142C23×C4×C79C2311yescharacteristic
143C23×C4×C79C2311yescharacteristic
144C23×C4×C79C2311yescharacteristic
145C23×C4×C79C2311yescharacteristic
146C2×C22⋊C4×C79C2×C418yes—
147C2×C22⋊C4×C79Q818yescomplemented
148C2×C22⋊C4×C79C2314yes—
149C2×C22⋊C4×C79C2314yes—
150C2×C42×C79—24no—
151C2×C42×C79—42no—
152C2×C42×C79C2314yes—
153C2×C42×C79C2314yes—
154#95×C79C2314yes—
155#95×C79C2314yes—
156C2×Dic158—232no—
157C2×Dic158—28no—
158C2×Dic158—28no—
159C2×Dic158C22×C4116yescomplemented
160C22×Dic79—232no—
161C22×Dic79—28no—
162C22×Dic79—28no—
163C22×Dic79—28no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79—22no—
171C22×Dic79—22no—
172C22×Dic79—22no—
173C22×Dic79—22no—
174C22×Dic79—28no—
175C22×Dic79—22no—
176C22×Dic79—22no—
177C22×Dic79—22no—
178C22×Dic79—22no—
179C22×Dic79—22no—
180C22×Dic79—22no—
181C22×Dic79—22no—
182C22×Dic79—44no—
183C22×Dic79—416no—
184C22×Dic79C22×C414yes—
185C22×Dic79C22×C414yes—
186C22×Dic79C22×C414yes—
187C22×Dic79C22×C4116yes—
188C22×Dic79C22×C414yes—
189C22×Dic79C2×D414yes—
190C22×Dic79C2×D414yes—
191C22×Dic79#4114yes—
192C22×Dic79C2412yes—
193C22×Dic79C2412yes—
194C22×Dic79C2412yes—
195C22×Dic79C2412yes—
196C22×Dic79C2412yes—
197C22×Dic79C2412yes—
198C22×Dic79C2412yes—
199C22×Dic79C2412yes—
200C4⋊Dic79—28no—
201C4⋊Dic79—44no—
202C4⋊Dic79C22×C4116yescomplemented
203Dic79⋊C4—28no—
204Dic79⋊C4—28no—
205Dic79⋊C4—28no—
206Dic79⋊C4—28no—
207Dic79⋊C4—44no—
208Dic79⋊C4C22×C4116yescomplemented
209Dic79⋊C4C22×C4116yescomplemented
210Dic79⋊C4C2×D4116yes—
211C22⋊Dic79—28no—
212C22⋊Dic79C22×C4116yes—
213C4×Dic79—28no—
214C4×Dic79—28no—
215C4×Dic79—28no—
216C4×Dic79—44no—
217C24×C79—22no—
218C24×C79—22no—
219C24×C79—22no—
220C24×C79—22no—
221C24×C79C22×C414yes—
222C24×C79C2×Q814yes—
223C24×C79#4114yes—
224C24×C79C2412yes—
225C24×C79C2411yescharacteristic
226C22×C4×C79—22no—
227C22×C4×C79—22no—
228C22×C4×C79—22no—
229C22×C4×C79—22no—
230C22×C4×C79—22no—
231C22×C4×C79—22no—
232C22×C4×C79—22no—
233C22×C4×C79—22no—
234C22×C4×C79—22no—
235C22×C4×C79—22no—
236C22×C4×C79—22no—
237C22×C4×C79—28no—
238C22×C4×C79—22no—
239C22×C4×C79—22no—
240C22×C4×C79—28no—
241C22×C4×C79—44no—
242C22×C4×C79—416no—
243C22×C4×C79C22×C414yes—
244C22×C4×C79C22×C414yes—
245C22×C4×C79C2×D414yes—
246C22×C4×C79C2×Q814yes—
247C22×C4×C79C2×Q814yes—
248C22×C4×C79C2412yes—
249C22×C4×C79C2412yes—
250C22×C4×C79C2412yes—
251C22×C4×C79C2412yes—
252C22×C4×C79C2412yes—
253C22×C4×C79C2412yes—
254C22⋊C4×C79C22×C4116yes—
255C22⋊C4×C79C2×Q8116yescomplemented
256C42×C79—28no—
257C42×C79—44no—
258C23×C79—28no—
259C23×C79—28no—
260C23×C79—28no—
261C23×C79—28no—
262C23×C79—28no—
263C23×C79—28no—
264C23×C79—22no—
265C23×C79—22no—
266C23×C79—22no—
267C23×C79—22no—
268C23×C79C4×Q8116yescomplemented
269C23×C79C23×C414yes—
270C23×C79C23×C412yes—
271C23×C79C22×D412yes—
272C23×C79C22×Q814yes—
273C23×C79C22×Q812yes—
274C23×C79C2×#4112yes—
275C23×C79C2×#4114yes—
276C23×C79C2×#4112yes—
277C23×C79H(5,𝔽2)12yes—
278C23×C792−1+412yes—
279C23×C79C2511yescharacteristic
280C2×C4×C79—28no—
281C2×C4×C79—28no—
282C2×C4×C79—28no—
283C2×C4×C79—28no—
284C2×C4×C79—28no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—416no—
299C2×C4×C79—44no—
300C2×C4×C79C23×C414yes—
301C2×C4×C79C23×C414yes—
302C2×C4×C79C22×D414yes—
303C2×C4×C79C22×Q814yes—
304C2×C4×C79C22×Q814yes—
305C2×Dic79—28no—
306C2×Dic79—28no—
307C2×Dic79—28no—
308C2×Dic79—28no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—232no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—416no—
328C2×Dic79—44no—
329C2×Dic79—44no—
330C2×Dic79—44no—
331C2×Dic79C4×D4116yes—
332C2×Dic79C23×C414yes—
333C2×Dic79C23×C414yes—
334C2×Dic79C23×C414yes—
335C2×Dic79C23×C414yes—
336C2×Dic79C22×D414yes—
337C2×Dic79C22×D414yes—
338C2×Dic79C2×#4114yes—
339Dic158—232no—
340C22×C79—232no—
341C22×C79—24no—
342C22×C79—24no—
343C22×C79—24no—
344C22×C79—24no—
345C22×C79—24no—
346C22×C79—24no—
347C22×C79C2×C4×D414yes—
348C22×C79C2×C4×Q814yes—
349C22×C79C2×C4×Q818yescomplemented
350C22×C79#52014yes—
351C22×C79#54614yes—
352C22×C79D4×Q814yes—
353C22×C79#55214yes—
354C22×C79#55414yes—
355C22×C79C24×C411yescharacteristic
356C22×C79C23×D411yescharacteristic
357C22×C79C23×Q811yescharacteristic
358C22×C79C22×#4111yescharacteristic
359C22×C79C22×#4111yescharacteristic
360C22×C79C2×H(5,𝔽2)11yescharacteristic
361C22×C79C2×2−1+411yescharacteristic
362C4×C79—24no—
363C4×C79—24no—
364C4×C79—24no—
365C4×C79—24no—
366C4×C79—24no—
367C4×C79—42no—
368Dic79—24no—
369Dic79—24no—
370Dic79—24no—
371Dic79—24no—
372Dic79—42no—
373Dic79—42no—
374Dic79—42no—
375Dic79C2×C4×D418yes—
376C2×#2360—791nomaximal, Sylow
377C2×C79—28no—
378C2×C79#236018yescomplemented
379C2×C79C22×C4×D411yescharacteristic
380C2×C79C22×C4×Q811yescharacteristic
381C2×C79C2×#52011yescharacteristic
382C2×C79C2×#54611yescharacteristic
383C2×C79C2×D4×Q811yescharacteristic
384C2×C79C2×#55211yescharacteristic
385C2×C79C2×#55411yescharacteristic
386C22×C22⋊Q8—791no—
387C22×C4×Q8—791no—
388C23×C4⋊C4—791no—
389#2360—7916no—
390C2×#391—791no—
391C2×#389—791no—
392C2×#389—791no—
393C2×#389—791no—
394C2×#387—791no—
395C2×#387—791no—
396C2×#385—791no—
397C2×#385—791no—
398C2×C4×C4⋊C4—791no—
399C2×C4×C22⋊C4—791no—
400C2×C4×C22⋊C4—791no—
401C2×C4×C22⋊C4D7911yescharacteristic
402C79C2×#236011yescharacteristic, complemented, Sylow
403C23×Q8—791no—
404C24×C4—791no—
405C24×C4—791no—
406C24×C4C2×D7911yescharacteristic
407C2×C22⋊Q8—798no—
408C2×C22⋊Q8—7916no—
409C2×C4×Q8—798no—
410C2×C4×Q8—1588no—
411C22×C4⋊C4—791no—
412C22×C4⋊C4—791no—
413C22×C4⋊C4—791no—
414C22×C4⋊C4—791no—
415C22×C4⋊C4—791no—
416C22×C4⋊C4—791no—
417C22×C4⋊C4—798no—
418C22×C4⋊C4—791no—
419C22×C4⋊C4—791no—
420C22×C4⋊C4—791no—
421C22×C4⋊C4—791no—
422C22×C4⋊C4—791no—
423C22×C4⋊C4—1588no—
424C22×C22⋊C4—791no—
425C22×C22⋊C4—791no—
426C22×C22⋊C4C2×D7911yescharacteristic
427C22×C22⋊C4C2×D7911yescharacteristic
428C22×C42—791no—
429C22×C42—791no—
430C22×C42—791no—
431C22×C42—791no—
432C22×C42C2×D7911yescharacteristic
433C22×C42C2×D7911yescharacteristic
434#391—798no—
435#389—798no—
436#389—798no—
437#389—798no—
438#387—798no—
439#387—798no—
440#385—798no—
441#385—798no—
442C4×C4⋊C4—798no—
443C4×C22⋊C4—798no—
444C4×C22⋊C4—798no—
445C4×C22⋊C4C2×D7918yes—
446C2×#95—791no—
447C2×#95—791no—
448C2×#95—791no—
449C2×#95—791no—
450C2×#95—791no—
451C2×#95—791no—
452C2×#95—791no—
453C2×#95—791no—
454C2×#95C2×D7911yescharacteristic
455C2×#95C2×D7911yescharacteristic
456C25C22×D7911yescharacteristic
457C22×Q8—798no—
458C22×Q8—794no—
459C22×Q8—1584no—
460C22×Q8—1584no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—42no—
464C23×C4—3162no—
465C23×C4—794no—
466C23×C4—791no—
467C23×C4—798no—
468C23×C4—794no—
469C23×C4—791no—
470C23×C4—791no—
471C23×C4—791no—
472C23×C4—791no—
473C23×C4—791no—
474C23×C4—791no—
475C23×C4—791no—
476C23×C4—1584no—
477C23×C4—1584no—
478C23×C4—1584no—
479C23×C4—1584no—
480C23×C4C22×D7911yescharacteristic
481C23×C4C22×D7914yes—
482C23×C4C22×D7911yescharacteristic
483C23×C4C22×D7911yescharacteristic
484C23×C4C22×D7911yescharacteristic
485C23×C4C22×D7911yescharacteristic
486C23×C4C22×D7911yescharacteristic
487C22⋊Q8—7964no—
488C4×Q8—15832no—
489C2×C4⋊C4—3162no—
490C2×C4⋊C4—3162no—
491C2×C4⋊C4—794no—
492C2×C4⋊C4—794no—
493C2×C4⋊C4—798no—
494C2×C4⋊C4—798no—
495C2×C4⋊C4—798no—
496C2×C4⋊C4—798no—
497C2×C4⋊C4—794no—
498C2×C4⋊C4—794no—
499C2×C4⋊C4—794no—
500C2×C4⋊C4—794no—
501C2×C4⋊C4—794no—
502C2×C4⋊C4—794no—
503C2×C4⋊C4—794no—
504C2×C4⋊C4—794no—
505C2×C4⋊C4—794no—
506C2×C4⋊C4—15832no—
507C2×C4⋊C4—1584no—
508C2×C4⋊C4—1584no—
509C2×C4⋊C4—1584no—
510C2×C4⋊C4—1584no—
511C2×C4⋊C4—1584no—
512C2×C22⋊C4—798no—
513C2×C22⋊C4—794no—
514C2×C22⋊C4—794no—
515C2×C22⋊C4—1584no—
516C2×C22⋊C4Dic15818yescomplemented
517C2×C22⋊C4C4×D7918yes—
518C2×C22⋊C4C22×D7914yes—
519C2×C22⋊C4C22×D7914yes—
520C2×C42—24no—
521C2×C42—42no—
522C2×C42—3162no—
523C2×C42—794no—
524C2×C42—794no—
525C2×C42—794no—
526C2×C42—794no—
527C2×C42—1584no—
528C2×C42—1584no—
529C2×C42—1584no—
530C2×C42C22×D7914yes—
531C2×C42C22×D7914yes—
532#95—794no—
533#95—794no—
534#95—794no—
535#95—794no—
536#95—794no—
537#95—794no—
538#95—794no—
539#95—794no—
540#95C22×D7914yes—
541#95C22×D7914yes—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×C4×D7914yes—
547C24C2×Dic15814yes—
548C24#1192962414yes—
549C24C23×D7912yes—
550C24C23×D7911yescharacteristic
551C2×Q8—7916no—
552C2×Q8—1588no—
553C2×Q8—15832no—
554C2×Q8—1588no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—28no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—28no—
570C22×C4—44no—
571C22×C4—416no—
572C22×C4—31616no—
573C22×C4—3164no—
574C22×C4—794no—
575C22×C4—792no—
576C22×C4—794no—
577C22×C4—794no—
578C22×C4—792no—
579C22×C4—792no—
580C22×C4—792no—
581C22×C4—792no—
582C22×C4—794no—
583C22×C4—794no—
584C22×C4—794no—
585C22×C4—7916no—
586C22×C4—794no—
587C22×C4—792no—
588C22×C4—792no—
589C22×C4—792no—
590C22×C4—1588no—
591C22×C4—1582no—
592C22×C4—1582no—
593C22×C4—1582no—
594C22×C4—1582no—
595C22×C4—1588no—
596C22×C4—1582no—
597C22×C4—1582no—
598C22×C4—1582no—
599C22×C4—1582no—
600C22×C4—1582no—
601C22×C4—1588no—
602C22×C4—15832no—
603C22×C4—1588no—
604C22×C4—1582no—
605C22×C4—1582no—
606C22×C4—1582no—
607C22×C4—1582no—
608C22×C4—1582no—
609C22×C4—1582no—
610C22×C4—1582no—
611C22×C4—1582no—
612C22×C4C2×C4×D7914yes—
613C22×C4C2×C4×D7914yes—
614C22×C4D4×D7914yes—
615C22×C4C2×Dic15814yes—
616C22×C4C2×Dic15814yes—
617C22×C4C23×D7912yes—
618C22×C4C23×D7912yes—
619C22×C4C23×D7912yes—
620C22×C4C23×D7912yes—
621C22×C4C23×D7912yes—
622C22×C4C23×D7912yes—
623C4⋊C4—3164no—
624C4⋊C4—3164no—
625C4⋊C4—7916no—
626C4⋊C4—7916no—
627C4⋊C4—7916no—
628C4⋊C4—7916no—
629C4⋊C4—1588no—
630C4⋊C4—1588no—
631C4⋊C4—1588no—
632C4⋊C4—1588no—
633C4⋊C4—1588no—
634C22⋊C4—7916no—
635C22⋊C4—1588no—
636C22⋊C4C2×C4×D79116yes—
637C22⋊C4C2×Dic158116yescomplemented
638C42—28no—
639C42—44no—
640C42—3164no—
641C42—1588no—
642C42—1588no—
643C42—1588no—
644C23—22no—
645C23—22no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—28no—
651C23—28no—
652C23—22no—
653C23—22no—
654C23C4×Dic158116yescomplemented
655C23C22×C4×D7914yes—
656C23C22×C4×D7912yes—
657C23C2×D4×D7912yes—
658C23C22×Dic15814yes—
659C23C22×Dic15812yes—
660C23#41×D7912yes—
661C23C2×#1192962414yes—
662C23C2×#1192962412yes—
663C23#1457920612yes—
664C23#1457920812yes—
665C23C24×D7911yescharacteristic
666Q8—15832no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—3164no—
688C2×C4—3164no—
689C2×C4—3164no—
690C2×C4—31616no—
691C2×C4—7916no—
692C2×C4—794no—
693C2×C4—794no—
694C2×C4—794no—
695C2×C4—794no—
696C2×C4—794no—
697C2×C4—794no—
698C2×C4—794no—
699C2×C4—1582no—
700C2×C4—1582no—
701C2×C4—1582no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1582no—
708C2×C4—15832no—
709C2×C4—1582no—
710C2×C4—1582no—
711C2×C4—1582no—
712C2×C4—1588no—
713C2×C4—1588no—
714C2×C4—1588no—
715C2×C4—1588no—
716C2×C4—1582no—
717C2×C4—1582no—
718C2×C4—1582no—
719C2×C4—1582no—
720C2×C4—1582no—
721C2×C4C22×C4×D7914yes—
722C2×C4C22×C4×D7914yes—
723C2×C4C2×D4×D7914yes—
724C2×C4C22×Dic15814yes—
725C2×C4C22×Dic15814yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—232no—
731C22—24no—
732C22—24no—
733C22C4×D4×D7914yes—
734C22C2×C4×Dic15814yes—
735C22C2×C4×Dic15818yescomplemented
736C22#1909904214yes—
737C22#1909920314yes—
738C22D4×Dic15814yes—
739C22#1909924614yes—
740C22#1909927214yes—
741C22C23×C4×D7911yescharacteristic
742C22C22×D4×D7911yescharacteristic
743C22C23×Dic15811yescharacteristic
744C22C2×#41×D7911yescharacteristic
745C22C22×#1192962411yescharacteristic
746C22C2×#1457920611yescharacteristic
747C22C2×#1457920811yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—3162no—
755C4—3162no—
756C4—3162no—
757C4—798no—
758C4—1584no—
759C4—1584no—
760C4—1584no—
761C4—1584no—
762C2—28no—
763C2#2376640618yesdirect product factor
764C2C2×C4×D4×D7911yescharacteristic
765C2C22×C4×Dic15811yescharacteristic
766C2C2×#1909904211yescharacteristic
767C2C2×#1909920311yescharacteristic
768C2C2×D4×Dic15811yescharacteristic
769C2C2×#1909924611yescharacteristic
770C2C2×#1909927211yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×C4×C22⋊C4×C79C2
socleC24×C79C24
prime radicalC25×C79C23
cosocleC23×C79C25
hypercenterC2×C4×C22⋊C4D79
hypocenterC79C2×#2360
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic158C2semidirect
4. #23766406C2direct (N × H)
5. C2×#19098467C2semidirect
6. C2×#19098461C2semidirect
7. C2×#19098460C2semidirect
8. C2×#19098460C2semidirect
9. C2×#19098447C2semidirect
10. C2×#19098446C2semidirect
13. C2×C4×Dic79⋊C4C2semidirect
20. C2×#14579138C4semidirect
23. C2×C4×Dic158C22semidirect
43. #19098467C22semidirect
44. #19098461C22semidirect
45. #19098460C22semidirect
46. #19098460C22semidirect
47. #19098447C22semidirect
48. #19098446C22semidirect
51. C4×Dic79⋊C4C22semidirect
72. C22×Dic158C2×C4semidirect
90. #14579138C2×C4semidirect
94. C2×C4⋊Dic79C2×C4semidirect
104. C2×Dic79⋊C4C2×C4semidirect
105. C2×Dic79⋊C4C2×C4semidirect
147. C2×C22⋊C4×C79Q8semidirect
159. C2×Dic158C22×C4semidirect
202. C4⋊Dic79C22×C4semidirect
208. Dic79⋊C4C22×C4semidirect
209. Dic79⋊C4C22×C4semidirect
255. C22⋊C4×C79C2×Q8semidirect
268. C23×C79C4×Q8semidirect
349. C22×C79C2×C4×Q8semidirect
378. C2×C79#2360semidirect
402. C79C2×#2360semidirect
516. C2×C22⋊C4Dic158semidirect
637. C22⋊C4C2×Dic158semidirect
654. C23C4×Dic158semidirect
735. C22C2×C4×Dic158semidirect
763. C2#23766406direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791382
C22×C4×Dic1582
C23×Dic79⋊C42
#237664062
C2×#190984672
C2×#190984612
C2×#190984602
C2×#190984472
C2×#190984462
C2×#190984382
C2×#190984362
C2×C4×Dic79⋊C42
C2×C22⋊C4×Dic792
C2×C4×C22⋊C4×C792
C2×#236079