Finite Group Databasebeta

← C2×#23766296 #34447550

Subgroups — C2×#23766296 #34447550

Order 20224.

4718 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D79C211yesmaximal, characteristic
2C22×(C22⋊D79)⋊C4C212yesmaximal
3C23×C4⋊Dic79C211yesmaximal, characteristic, complemented
4C22×C4⋊C4×D79C211yesmaximal, characteristic, complemented
5#23766296C2116yesmaximal, direct product factor
6C2×#19098460C212yesmaximal, complemented
7C2×#19098437C212yesmaximal, complemented
8C2×#19098435C212yesmaximal, complemented
9C2×#19098432C211yesmaximal, characteristic, complemented
10C2×#19098420C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
12C2×#380×C79C211yesmaximal, characteristic, complemented
13C23×C22⋊D79C2211yescharacteristic
14C24×Dic79C2212yes—
15C23×C4×D79C2212yes—
16C23×C4×D79C2211yescharacteristic
17C2×C4×C22⋊D79C4116yescomplemented
18C2×C4×C22⋊D79C2218yes—
19C2×(C22⋊D79)⋊C4—216no—
20C2×(C22⋊D79)⋊C4C22116yes—
21C22×C4⋊Dic79—28no—
22C22×C4⋊Dic79C2211yescharacteristic
23C22×C4⋊Dic79C2212yes—
24C22×C4⋊Dic79C2211yescharacteristic
25C22×C4⋊Dic79C2218yescomplemented
26C22×Dic79⋊C4C2212yes—
27C22×Dic79⋊C4C2212yes—
28C22×Dic79⋊C4C2212yes—
29C22×Dic79⋊C4C2211yescharacteristic
30C2×C4⋊C4×D79—28no—
31C2×C4⋊C4×D79C2218yescomplemented
32C22×C22⋊Dic79C2211yescharacteristic
33C22×(C2×D79)⋊C4C2212yes—
34C22×(C2×D79)⋊C4C2211yescharacteristic
35C22×C4×Dic79C2212yes—
36C22×C4×Dic79C2211yescharacteristic
37#19098460C22116yescomplemented
38#19098437C22116yescomplemented
39#19098435C22116yescomplemented
40#19098432C2218yescomplemented
41#19098420C2218yescomplemented
42C4⋊C4×Dic79C2218yescomplemented
43C2×C79⋊#95C2212yes—
44C2×C79⋊#95C2212yes—
45C24×C4×C79C2211yescharacteristic
46C22×C4⋊C4×C79C2211yescharacteristic
47C22×C4⋊C4×C79C2211yescharacteristic
48C22×C22⋊C4×C79C2212yes—
49#380×C79C2218yescomplemented
50C2×#95×C79C2212yes—
51C24×D79C2311yescharacteristic
52C22×C22⋊D79C2×C418yes—
53C22×C22⋊D79D418yes—
54C22×C22⋊D79Q818yes—
55C22×C22⋊D79C2314yes—
56C23×Dic79—28no—
57C23×Dic79—28no—
58C23×Dic79—44no—
59C23×Dic79C2312yes—
60C23×Dic79C2318yes—
61C23×Dic79C2311yescharacteristic
62C23×Dic79C2311yescharacteristic
63C23×Dic79C2312yes—
64C23×Dic79C2311yescharacteristic
65C22×C4×D79—24no—
66C22×C4×D79—24no—
67C22×C4×D79—28no—
68C22×C4×D79—28no—
69C22×C4×D79—44no—
70C22×C4×D79C2×C418yescomplemented
71C22×C4×D79C2318yes—
72C22×C4×D79C2314yes—
73C4×C22⋊D79C2×C4164yescomplemented
74(C22⋊D79)⋊C4—264no—
75C2×C4⋊Dic79—24no—
76C2×C4⋊Dic79—28no—
77C2×C4⋊Dic79—232no—
78C2×C4⋊Dic79D418yescomplemented
79C2×C4⋊Dic79C2314yes—
80C2×C4⋊Dic79C2318yes—
81C2×C4⋊Dic79C2314yes—
82C2×Dic79⋊C4—28no—
83C2×Dic79⋊C4—28no—
84C2×Dic79⋊C4—44no—
85C2×Dic79⋊C4C2×C418yescomplemented
86C2×Dic79⋊C4C2318yes—
87C2×Dic79⋊C4C2318yes—
88C2×Dic79⋊C4C2318yes—
89C2×Dic79⋊C4C2314yes—
90C4⋊C4×D79—232no—
91C2×C22⋊Dic79C2×C418yescomplemented
92C2×C22⋊Dic79C2314yes—
93C2×(C2×D79)⋊C4—28no—
94C2×(C2×D79)⋊C4C2×C418yescomplemented
95C2×(C2×D79)⋊C4C2318yes—
96C2×(C2×D79)⋊C4C2314yes—
97C2×C4×Dic79—28no—
98C2×C4×Dic79C2×C418yescomplemented
99C2×C4×Dic79C2318yes—
100C2×C4×Dic79C2314yes—
101C79⋊#95C2318yes—
102C79⋊#95C2318yes—
103C25×C79C2311yescharacteristic
104C23×C4×C79—24no—
105C23×C4×C79—24no—
106C23×C4×C79C2×C418yescomplemented
107C23×C4×C79C2312yes—
108C23×C4×C79C2312yes—
109C23×C4×C79C2311yescharacteristic
110C23×C4×C79C2314yes—
111C23×C4×C79C2311yescharacteristic
112C2×C4⋊C4×C79—24no—
113C2×C4⋊C4×C79—24no—
114C2×C4⋊C4×C79C2314yes—
115C2×C4⋊C4×C79C2314yes—
116C2×C22⋊C4×C79—28no—
117C2×C22⋊C4×C79C2318yes—
118#95×C79C2318yes—
119C23×D79—22no—
120C23×D79—22no—
121C23×D79—22no—
122C23×D79—22no—
123C23×D79C22×C414yes—
124C23×D79C2×D414yes—
125C23×D79C2×Q814yes—
126C23×D79C2412yes—
127C2×C22⋊D79C4⋊C4164yescomplemented
128C2×C22⋊D79C22×C4116yes—
129C2×C22⋊D79C2×D4116yes—
130C2×C22⋊D79C2×Q8116yes—
131C22×Dic79—216no—
132C22×Dic79—24no—
133C22×Dic79—22no—
134C22×Dic79—24no—
135C22×Dic79—24no—
136C22×Dic79—216no—
137C22×Dic79—22no—
138C22×Dic79—22no—
139C22×Dic79—24no—
140C22×Dic79—24no—
141C22×Dic79—22no—
142C22×Dic79—48no—
143C22×Dic79—432no—
144C22×Dic79C22×C414yes—
145C22×Dic79C22×C414yes—
146C22×Dic79C22×C414yes—
147C22×Dic79C2×D418yes—
148C22×Dic79C2×D414yes—
149C22×Dic79C2×Q814yes—
150C22×Dic79C2414yes—
151C22×Dic79C2412yes—
152C22×Dic79C2412yes—
153C22×Dic79C2414yes—
154C22×Dic79C2412yes—
155C2×C4×D79—216no—
156C2×C4×D79—216no—
157C2×C4×D79—232no—
158C2×C4×D79—28no—
159C2×C4×D79—28no—
160C2×C4×D79—48no—
161C2×C4×D79—432no—
162C2×C4×D79C22×C4116yescomplemented
163C4⋊Dic79—216no—
164C4⋊Dic79—28no—
165C4⋊Dic79C2×D4116yescomplemented
166Dic79⋊C4—216no—
167Dic79⋊C4—216no—
168Dic79⋊C4—48no—
169Dic79⋊C4C22×C4116yescomplemented
170C22⋊Dic79C22×C4116yescomplemented
171(C2×D79)⋊C4—216no—
172(C2×D79)⋊C4C22×C4116yescomplemented
173C4×Dic79—216no—
174C4×Dic79C22×C4116yescomplemented
175C24×C79—22no—
176C24×C79—22no—
177C24×C79—22no—
178C24×C79—22no—
179C24×C79C22×C414yes—
180C24×C79C2×D414yes—
181C24×C79C2×Q814yes—
182C24×C79C2412yes—
183C24×C79C2411yescharacteristic
184C22×C4×C79—22no—
185C22×C4×C79—22no—
186C22×C4×C79—232no—
187C22×C4×C79—28no—
188C22×C4×C79—28no—
189C22×C4×C79—24no—
190C22×C4×C79—24no—
191C22×C4×C79—24no—
192C22×C4×C79—24no—
193C22×C4×C79—24no—
194C22×C4×C79—24no—
195C22×C4×C79C22×C414yes—
196C22×C4×C79C22×C414yes—
197C22×C4×C79C22×C4116yescomplemented
198C22×C4×C79C2×D414yes—
199C22×C4×C79#4114yes—
200C22×C4×C79C2414yes—
201C22×C4×C79C2414yes—
202C22×C4×C79C2412yes—
203C22×C4×C79C2412yes—
204C4⋊C4×C79—28no—
205C4⋊C4×C79—28no—
206C22⋊C4×C79—216no—
207C23×C79—28no—
208C23×C79—28no—
209C23×C79—28no—
210C23×C79—28no—
211C23×C79—28no—
212C23×C79—28no—
213C23×C79—22no—
214C23×C79—22no—
215C23×C79—22no—
216C23×C79—22no—
217C23×C79C2×C4⋊C4116yescomplemented
218C23×C79C23×C414yes—
219C23×C79C23×C412yes—
220C23×C79C22×D414yes—
221C23×C79C22×D412yes—
222C23×C79C22×D412yes—
223C23×C79C22×Q814yes—
224C23×C79C22×Q812yes—
225C23×C79C2×#4112yes—
226C23×C79H(5,𝔽2)12yes—
227C23×C792−1+412yes—
228C23×C79C2511yescharacteristic
229C22×D79—28no—
230C22×D79—28no—
231C22×D79—28no—
232C22×D79—28no—
233C22×D79—28no—
234C22×D79—28no—
235C22×D79—22no—
236C22×D79—22no—
237C22×D79—22no—
238C22×D79—22no—
239C22×D79C2×C4⋊C4116yescomplemented
240C22×D79C23×C414yes—
241C22×D79C22×D414yes—
242C22×D79C22×Q814yes—
243C2×C4×C79—28no—
244C2×C4×C79—22no—
245C2×C4×C79—22no—
246C2×C4×C79—232no—
247C2×C4×C79—24no—
248C2×C4×C79—24no—
249C2×C4×C79—24no—
250C2×C4×C79—24no—
251C2×C4×C79—24no—
252C2×C4×C79—24no—
253C2×C4×C79—48no—
254C2×C4×C79—48no—
255C2×C4×C79C4×D4116yescomplemented
256C2×C4×C79C23×C414yes—
257C2×C4×C79C23×C414yes—
258C2×C4×C79C22×D414yes—
259C2×C4×C79C2×#4114yes—
260C22⋊D79C2×C4⋊C4164yescomplemented
261C2×Dic79—28no—
262C2×Dic79—28no—
263C2×Dic79—216no—
264C2×Dic79—24no—
265C2×Dic79—22no—
266C2×Dic79—22no—
267C2×Dic79—22no—
268C2×Dic79—24no—
269C2×Dic79—22no—
270C2×Dic79—24no—
271C2×Dic79—24no—
272C2×Dic79—24no—
273C2×Dic79—432no—
274C2×Dic79—48no—
275C2×Dic79C2×C4⋊C4116yescomplemented
276C2×Dic79C23×C414yes—
277C2×Dic79C23×C414yes—
278C2×Dic79C23×C414yes—
279C2×Dic79C22×D418yes—
280C2×Dic79C22×D414yes—
281C2×Dic79C22×Q814yes—
282C4×D79—232no—
283C4×D79—432no—
284C22×C79—232no—
285C22×C79—24no—
286C22×C79—24no—
287C22×C79—24no—
288C22×C79—24no—
289C22×C79—24no—
290C22×C79—24no—
291C22×C79C22×C4⋊C414yes—
292C22×C79C22×C4⋊C418yescomplemented
293C22×C79C2×C4×D414yes—
294C22×C79#52014yes—
295C22×C79D4214yes—
296C22×C79#54714yes—
297C22×C79D4×Q814yes—
298C22×C79#55414yes—
299C22×C79C24×C411yescharacteristic
300C22×C79C23×D411yescharacteristic
301C22×C79C23×D411yescharacteristic
302C22×C79C23×Q811yescharacteristic
303C22×C79C22×#4111yescharacteristic
304C22×C79C2×H(5,𝔽2)11yescharacteristic
305C22×C79C2×2−1+411yescharacteristic
306C2×D79—232no—
307C2×D79—24no—
308C2×D79—24no—
309C2×D79—24no—
310C2×D79—24no—
311C2×D79—24no—
312C2×D79—24no—
313C2×D79C22×C4⋊C418yescomplemented
314C4×C79—24no—
315C4×C79—44no—
316C4×C79—44no—
317C4×C79C2×C4×D418yescomplemented
318Dic79—24no—
319Dic79—24no—
320Dic79—28no—
321Dic79—44no—
322Dic79C22×C4⋊C418yescomplemented
323C2×D4×C4⋊C4—791nomaximal, Sylow
324C2×C79—28no—
325C2×C79D4×C4⋊C418yescomplemented
326C2×C79C23×C4⋊C411yescharacteristic
327C2×C79C22×C4×D411yescharacteristic
328C2×C79C2×#52011yescharacteristic
329C2×C79C2×D4211yescharacteristic
330C2×C79C2×#54711yescharacteristic
331C2×C79C2×D4×Q811yescharacteristic
332C2×C79C2×#55411yescharacteristic
333D79—28no—
334C22×C4×D4—791no—
335C22×C4×D4—792no—
336C23×C4⋊C4—791no—
337C23×C4⋊C4—791no—
338D4×C4⋊C4—7916no—
339C2×#389—792no—
340C2×#385—792no—
341C2×#385—792no—
342C2×#384—791no—
343C2×#380—791no—
344C2×#380D7911yescharacteristic, complemented
345C2×C4×C4⋊C4—791no—
346C79C2×D4×C4⋊C411yescharacteristic, complemented, Sylow
347C23×D4—791no—
348C24×C4—792no—
349C24×C4—792no—
350C24×C4—791no—
351C24×C4C2×D7911yescharacteristic
352C2×C4×D4—798no—
353C2×C4×D4—7916no—
354C2×C4×D4—7916no—
355C2×C4×D4—15816no—
356C22×C4⋊C4—792no—
357C22×C4⋊C4—791no—
358C22×C4⋊C4—791no—
359C22×C4⋊C4—798no—
360C22×C4⋊C4—792no—
361C22×C4⋊C4—791no—
362C22×C4⋊C4—792no—
363C22×C4⋊C4—792no—
364C22×C4⋊C4—798no—
365C22×C4⋊C4—1588no—
366C22×C4⋊C4—1588no—
367C22×C4⋊C4C2×D7911yescharacteristic
368C22×C4⋊C4C2×D7911yescharacteristic
369C22×C22⋊C4—791no—
370C22×C22⋊C4—791no—
371C22×C22⋊C4—792no—
372C22×C22⋊C4C2×D7912yes—
373C22×C42—791no—
374C22×C42—792no—
375#389—7916no—
376#385—7916no—
377#385—7916no—
378#384—798no—
379#380—798no—
380#380C2×D7918yescomplemented
381C4×C4⋊C4—798no—
382C2×#95—792no—
383C2×#95—792no—
384C2×#95C2×D7912yes—
385C25—791no—
386C25C22×D7911yescharacteristic
387C22×D4—798no—
388C22×D4—798no—
389C22×D4—798no—
390C22×D4—794no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—3164no—
394C23×C4—3164no—
395C23×C4—798no—
396C23×C4—798no—
397C23×C4—791no—
398C23×C4—791no—
399C23×C4—791no—
400C23×C4—792no—
401C23×C4—798no—
402C23×C4—794no—
403C23×C4—792no—
404C23×C4—1588no—
405C23×C4—1588no—
406C23×C4—1588no—
407C23×C4—1588no—
408C23×C4—1584no—
409C23×C4—1584no—
410C23×C4C4×D7918yescomplemented
411C23×C4C22×D7912yes—
412C23×C4C22×D7912yes—
413C23×C4C22×D7911yescharacteristic
414C23×C4C22×D7914yes—
415C23×C4C22×D7911yescharacteristic
416C4×D4—7964no—
417C4×D4—15864no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—3164no—
421C2×C4⋊C4—798no—
422C2×C4⋊C4—798no—
423C2×C4⋊C4—798no—
424C2×C4⋊C4—794no—
425C2×C4⋊C4—794no—
426C2×C4⋊C4—794no—
427C2×C4⋊C4—798no—
428C2×C4⋊C4—798no—
429C2×C4⋊C4—798no—
430C2×C4⋊C4—15832no—
431C2×C4⋊C4—15832no—
432C2×C4⋊C4—1588no—
433C2×C4⋊C4—1588no—
434C2×C4⋊C4—1588no—
435C2×C4⋊C4—1584no—
436C2×C4⋊C4C22×D7914yes—
437C2×C4⋊C4C22×D7914yes—
438C2×C22⋊C4—28no—
439C2×C22⋊C4—798no—
440C2×C22⋊C4—794no—
441C2×C22⋊C4—798no—
442C2×C22⋊C4—794no—
443C2×C22⋊C4—798no—
444C2×C22⋊C4—1588no—
445C2×C22⋊C4C22×D7918yes—
446C2×C42—798no—
447C2×C42—794no—
448C2×C42—798no—
449C2×C42—1588no—
450#95—798no—
451#95—798no—
452#95C22×D7918yes—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—794no—
458C24—792no—
459C24—794no—
460C24—794no—
461C24—1582no—
462C24—1582no—
463C24—1582no—
464C24—1582no—
465C24C2×C4×D7914yes—
466C24D4×D7914yes—
467C24Q8×D7914yes—
468C24C23×D7912yes—
469C24C23×D7911yescharacteristic
470C2×D4—7916no—
471C2×D4—7964no—
472C2×D4—7916no—
473C2×D4—7916no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—28no—
477C22×C4—232no—
478C22×C4—28no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—3168no—
486C22×C4—31632no—
487C22×C4—31632no—
488C22×C4—3168no—
489C22×C4—794no—
490C22×C4—792no—
491C22×C4—794no—
492C22×C4—794no—
493C22×C4—792no—
494C22×C4—792no—
495C22×C4—794no—
496C22×C4—794no—
497C22×C4—794no—
498C22×C4—798no—
499C22×C4—7916no—
500C22×C4—794no—
501C22×C4—15816no—
502C22×C4—15816no—
503C22×C4—15816no—
504C22×C4—1584no—
505C22×C4—1584no—
506C22×C4—1584no—
507C22×C4—15816no—
508C22×C4—1582no—
509C22×C4—1582no—
510C22×C4—1584no—
511C22×C4—1582no—
512C22×C4—1584no—
513C22×C4—1582no—
514C22×C4—1588no—
515C22×C4—15832no—
516C22×C4—1588no—
517C22×C4C2×C4×D7914yes—
518C22×C4C2×C4×D7914yes—
519C22×C4C2×C4×D79116yescomplemented
520C22×C4D4×D7914yes—
521C22×C4#1192962314yes—
522C22×C4C23×D7914yes—
523C22×C4C23×D7914yes—
524C22×C4C23×D7912yes—
525C22×C4C23×D7912yes—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—3168no—
529C4⋊C4—7916no—
530C4⋊C4—7916no—
531C4⋊C4—15816no—
532C4⋊C4—15816no—
533C4⋊C4—15816no—
534C4⋊C4—1588no—
535C22⋊C4—216no—
536C22⋊C4—7916no—
537C22⋊C4—7916no—
538C22⋊C4—15816no—
539C42—7916no—
540C42—15816no—
541C23—22no—
542C23—22no—
543C23—28no—
544C23—28no—
545C23—28no—
546C23—28no—
547C23—28no—
548C23—28no—
549C23—22no—
550C23—22no—
551C23—7916no—
552C23—794no—
553C23—794no—
554C23—794no—
555C23—1582no—
556C23—1582no—
557C23—1588no—
558C23—1588no—
559C23—1588no—
560C23—1588no—
561C23—1588no—
562C23—1588no—
563C23—1582no—
564C23—1582no—
565C23C4⋊C4×D79116yescomplemented
566C23C22×C4×D7914yes—
567C23C22×C4×D7912yes—
568C23C2×D4×D7914yes—
569C23C2×D4×D7912yes—
570C23C2×D4×D7912yes—
571C23C2×Q8×D7914yes—
572C23C2×Q8×D7912yes—
573C23C2×#1192962312yes—
574C23#1457920712yes—
575C23#1457920812yes—
576C23C24×D7911yescharacteristic
577D4—7964no—
578C2×C4—28no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—232no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—48no—
589C2×C4—48no—
590C2×C4—31632no—
591C2×C4—3168no—
592C2×C4—31632no—
593C2×C4—7916no—
594C2×C4—794no—
595C2×C4—794no—
596C2×C4—794no—
597C2×C4—794no—
598C2×C4—794no—
599C2×C4—798no—
600C2×C4—1584no—
601C2×C4—1584no—
602C2×C4—1584no—
603C2×C4—1582no—
604C2×C4—1584no—
605C2×C4—1582no—
606C2×C4—15816no—
607C2×C4—1588no—
608C2×C4—1588no—
609C2×C4—1584no—
610C2×C4—1582no—
611C2×C4—1582no—
612C2×C4—15832no—
613C2×C4(C22⋊D79)⋊C4116yescomplemented
614C2×C4C22×C4×D7914yes—
615C2×C4C22×C4×D7914yes—
616C2×C4C2×D4×D7914yes—
617C2×C4C2×#1192962314yes—
618C22—232no—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—24no—
625C22—798no—
626C22—15832no—
627C22—1584no—
628C22—1584no—
629C22—1584no—
630C22—1584no—
631C22—1584no—
632C22—1584no—
633C22C2×C4⋊C4×D7914yes—
634C22C2×C4⋊C4×D7918yescomplemented
635C22C2×(C22⋊D79)⋊C414yes—
636C22#1909904314yes—
637C22#1909919714yes—
638C22#1909921314yes—
639C22#1909922614yes—
640C22#1909927114yes—
641C22C23×C4×D7911yescharacteristic
642C22C22×D4×D7911yescharacteristic
643C22C22×D4×D7911yescharacteristic
644C22C22×Q8×D7911yescharacteristic
645C22C22×#1192962311yescharacteristic
646C22C2×#1457920711yescharacteristic
647C22C2×#1457920811yescharacteristic
648C4—24no—
649C4—44no—
650C4—44no—
651C4—3164no—
652C4—798no—
653C4—1584no—
654C4—1588no—
655C4—1584no—
656C4C2×(C22⋊D79)⋊C418yescomplemented
657C2—28no—
658C2—1588no—
659C2#2376629618yesdirect product factor
660C2C22×C4⋊C4×D7911yescharacteristic
661C2C22×(C22⋊D79)⋊C411yescharacteristic
662C2C2×#1909904311yescharacteristic
663C2C2×#1909919711yescharacteristic
664C2C2×#1909921311yescharacteristic
665C2C2×#1909922611yescharacteristic
666C2C2×#1909927111yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#380×C79C2
socleC24×C79C24
prime radicalC23×C22⋊D79C22
cosocleC23×C79C25
hypercenterC2×#380D79
hypocenterC79C2×D4×C4⋊C4
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C23×C4⋊Dic79C2semidirect
4. C22×C4⋊C4×D79C2semidirect
5. #23766296C2direct (N × H)
6. C2×#19098460C2semidirect
7. C2×#19098437C2semidirect
8. C2×#19098435C2semidirect
9. C2×#19098432C2semidirect
10. C2×#19098420C2semidirect
11. C2×C4⋊C4×Dic79C2semidirect
12. C2×#380×C79C2semidirect
17. C2×C4×C22⋊D79C4semidirect
25. C22×C4⋊Dic79C22semidirect
31. C2×C4⋊C4×D79C22semidirect
37. #19098460C22semidirect
38. #19098437C22semidirect
39. #19098435C22semidirect
40. #19098432C22semidirect
41. #19098420C22semidirect
42. C4⋊C4×Dic79C22semidirect
49. #380×C79C22semidirect
70. C22×C4×D79C2×C4semidirect
73. C4×C22⋊D79C2×C4semidirect
78. C2×C4⋊Dic79D4semidirect
85. C2×Dic79⋊C4C2×C4semidirect
91. C2×C22⋊Dic79C2×C4semidirect
94. C2×(C2×D79)⋊C4C2×C4semidirect
98. C2×C4×Dic79C2×C4semidirect
106. C23×C4×C79C2×C4semidirect
127. C2×C22⋊D79C4⋊C4semidirect
162. C2×C4×D79C22×C4semidirect
165. C4⋊Dic79C2×D4semidirect
169. Dic79⋊C4C22×C4semidirect
170. C22⋊Dic79C22×C4semidirect
172. (C2×D79)⋊C4C22×C4semidirect
174. C4×Dic79C22×C4semidirect
197. C22×C4×C79C22×C4semidirect
217. C23×C79C2×C4⋊C4semidirect
239. C22×D79C2×C4⋊C4semidirect
255. C2×C4×C79C4×D4semidirect
260. C22⋊D79C2×C4⋊C4semidirect
275. C2×Dic79C2×C4⋊C4semidirect
292. C22×C79C22×C4⋊C4semidirect
313. C2×D79C22×C4⋊C4semidirect
317. C4×C79C2×C4×D4semidirect
322. Dic79C22×C4⋊C4semidirect
325. C2×C79D4×C4⋊C4semidirect
344. C2×#380D79semidirect
346. C79C2×D4×C4⋊C4semidirect
380. #380C2×D79semidirect
410. C23×C4C4×D79semidirect
519. C22×C4C2×C4×D79semidirect
565. C23C4⋊C4×D79semidirect
613. C2×C4(C22⋊D79)⋊C4semidirect
634. C22C2×C4⋊C4×D79semidirect
656. C4C2×(C22⋊D79)⋊C4semidirect
659. C2#23766296direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D792
C22×(C22⋊D79)⋊C42
C23×C4⋊Dic792
C22×C4⋊C4×D792
#237662962
C2×#190984602
C2×#190984372
C2×#190984352
C2×#190984322
C2×#190984202
C2×C4⋊C4×Dic792
C2×#380×C792
C2×D4×C4⋊C479