Finite Group Databasebeta

← C79×#61935 #34173624

Subgroups — C79×#61935 #34173624

Order 20224.

1746 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3548C211yesmaximal, characteristic, complemented
2C79×#3509C211yesmaximal, characteristic, complemented
3C79×#3397C214yesmaximal, complemented
4C79×#3392C214yesmaximal, complemented
5C79×#3372C214yesmaximal, complemented
6C79×#3360C214yesmaximal, complemented
7C79×#3221C214yesmaximal, complemented
8C79×#3206C212yesmaximal, complemented
9C79×#3126C214yesmaximal, complemented
10C79×#3106C212yesmaximal, complemented
11C79×#2986C211yesmaximal, characteristic, complemented
12#562×C79—22no—
13#557×C79C2214yes—
14#556×C79C2214yes—
15#554×C79C2214yes—
16#552×C79—24no—
17#550×C79C2214yes—
18#547×C79—22no—
19#541×C79—22no—
20#540×C79C2214yes—
21#537×C79—24no—
22#536×C79C2212yes—
23#533×C79—22no—
24#533×C79C2211yescharacteristic
25#532×C79C2212yes—
26C2×C4⋊Q8×C79C2211yescharacteristic
27#519×C79C2212yes—
28C4×#41×C79C2211yescharacteristic
29#496×C79C2214yes—
30#492×C79C2214yes—
31#492×C79C2214yes—
32#491×C79C2214yes—
33#488×C79C2214yes—
34#487×C79C2214yes—
35#482×C79C2214yes—
36#479×C79C2218yes—
37#477×C79C2212yes—
38#476×C79C2212yes—
39#463×C79C2218yes—
40#461×C79C2214yes—
41#461×C79C2218yes—
42#461×C79C2214yes—
43#460×C79C2212yes—
44#460×C79C2218yes—
45#459×C79C2212yes—
46#449×C79C2214yes—
47#448×C79C2218yes—
48#446×C79C2214yes—
49C8×Q8×C79C2214yes—
50#440×C79C2218yes—
51C4×SD16×C79C2218yes—
52C4×SD16×C79C2214yes—
53C4×D8×C79C2214yes—
54#433×C79C2214yes—
55#431×C79C2212yes—
56C2×#41×C79—24no—
57C2×#41×C79—22no—
58C2×#41×C79C2311yescharacteristic
59C22×Q8×C79C2312yes—
60C2×SD16×C79C2318yes—
61C2×SD16×C79C2314yes—
62C2×SD16×C79C2318yes—
63C2×D8×C79C2314yes—
64C4⋊Q8×C79—21no—
65C4⋊Q8×C79—21no—
66C4⋊Q8×C79D412yes—
67C4⋊Q8×C79C2314yes—
68C4⋊Q8×C79C2314yes—
69C4⋊Q8×C79C2312yes—
70#127×C79C2312yes—
71#127×C79C2314yes—
72#126×C79—28no—
73#125×C79—24no—
74#125×C79—28no—
75#125×C79D412yes—
76#125×C79C2314yes—
77#124×C79—22no—
78#124×C79C2314yes—
79#123×C79—28no—
80#123×C79—24no—
81C22⋊Q8×C79—24no—
82C22⋊Q8×C79—24no—
83C22⋊Q8×C79—24no—
84C22⋊Q8×C79—28no—
85C22⋊Q8×C79D414yes—
86#121×C79—22no—
87#121×C79—24no—
88#121×C79—28no—
89#121×C79—28no—
90#121×C79C2314yes—
91C4×Q8×C79—24no—
92C4×Q8×C79—24no—
93C4×Q8×C79C2312yes—
94C4×Q8×C79C2318yes—
95C4×Q8×C79C2314yes—
96C4×D4×C79—22no—
97C4×D4×C79—22no—
98C4×D4×C79C2312yes—
99C4×D4×C79C2314yes—
100C4×D4×C79C2318yes—
101#117×C79—24no—
102#117×C79—24no—
103#117×C79—21no—
104#117×C79C2311yescharacteristic
105#117×C79C2312yes—
106C2×C4⋊C4×C79—22no—
107C2×C4⋊C4×C79—24no—
108C2×C42×C79—21no—
109C2×C42×C79C2311yescharacteristic
110#107×C79C2314yes—
111#106×C79C2314yes—
112C4⋊C8×C79C2312yes—
113C4⋊C8×C79C2312yes—
114C4⋊C8×C79C2318yes—
115#103×C79C2318yes—
116#103×C79C2314yes—
117#103×C79C2318yes—
118#102×C79C2314yes—
119#102×C79C2314yes—
120#102×C79C2314yes—
121C22⋊C8×C79C2314yes—
122#97×C79C2314yes—
123C4×C8×C79C2314yes—
124C4×C8×C79C2314yes—
125#41×C79—42no—
126#41×C79—84no—
127#41×C79—88no—
128C2×Q8×C79—22no—
129C2×Q8×C79—22no—
130C2×Q8×C79—44no—
131C2×Q8×C79C2×D414yes—
132C2×Q8×C79C2414yes—
133C2×Q8×C79C2411yescharacteristic
134C2×D4×C79—21no—
135C2×D4×C79—24no—
136C2×D4×C79—22no—
137C2×D4×C79—28no—
138C2×D4×C79—22no—
139C2×D4×C79C2411yescharacteristic
140C2×D4×C79C2414yes—
141C22×C4×C79—22no—
142C22×C4×C79—22no—
143C22×C4×C79—21no—
144C22×C4×C79—24no—
145C22×C4×C79—28no—
146C22×C4×C79C2×D412yes—
147C22×C4×C79C2411yescharacteristic
148SD16×C79—48no—
149SD16×C79—48no—
150SD16×C79—44no—
151D8×C79—44no—
152C2×C8×C79C2414yes—
153C2×C8×C79C2414yes—
154C4⋊C4×C79—22no—
155C4⋊C4×C79—24no—
156C4⋊C4×C79—28no—
157C4⋊C4×C79—24no—
158C4⋊C4×C79—22no—
159C4⋊C4×C79—28no—
160C4⋊C4×C79—28no—
161C4⋊C4×C79C2×D414yes—
162C4⋊C4×C79C2×D414yes—
163C4⋊C4×C79C2×D418yes—
164C4⋊C4×C79C2412yes—
165C4⋊C4×C79C2414yes—
166C22⋊C4×C79—21no—
167C22⋊C4×C79—22no—
168C22⋊C4×C79—28no—
169C22⋊C4×C79—24no—
170C22⋊C4×C79—28no—
171C22⋊C4×C79—24no—
172C22⋊C4×C79C2×D414yes—
173C42×C79—21no—
174C42×C79—22no—
175C42×C79—28no—
176C42×C79C2×D411yescharacteristic
177C42×C79C2×D411yescharacteristic
178C42×C79C2412yes—
179C42×C79C2414yes—
180C23×C79—21no—
181C23×C79—24no—
182C23×C79C22×D411yescharacteristic
183Q8×C79—28no—
184Q8×C79—28no—
185Q8×C79—22no—
186Q8×C79—44no—
187Q8×C79—82no—
188D4×C79—22no—
189D4×C79—24no—
190D4×C79—24no—
191D4×C79—42no—
192D4×C79—44no—
193D4×C79—82no—
194D4×C79—88no—
195D4×C79—84no—
196C2×C4×C79—24no—
197C2×C4×C79—22no—
198C2×C4×C79—22no—
199C2×C4×C79—24no—
200C2×C4×C79—21no—
201C2×C4×C79—24no—
202C2×C4×C79—42no—
203C2×C4×C79—44no—
204C2×C4×C79—44no—
205C2×C4×C79—48no—
206C2×C4×C79—88no—
207C2×C4×C79C22×D411yescharacteristic
208C2×C4×C79C22×D418yes—
209C2×C4×C79C22×D412yes—
210C2×C4×C79C22×D412yes—
211C2×C4×C79C2511yescharacteristic
212C8×C79—24no—
213C8×C79—24no—
214C22×C79—21no—
215C22×C79—22no—
216C22×C79—41no—
217C22×C79—44no—
218C22×C79—44no—
219C22×C79—42no—
220C22×C79—44no—
221C22×C79C23×D411yescharacteristic
222C4×C79—21no—
223C4×C79—22no—
224C4×C79—28no—
225C4×C79—41no—
226C4×C79—44no—
227C4×C79—42no—
228C4×C79—44no—
229C4×C79#57714yes—
230C4×C79#58512yes—
231#61935C7911yesmaximal, characteristic, direct product factor, Sylow
232C2×C79—41no—
233C2×C79—81no—
234C2×C79—84no—
235C2×C79#348711yescharacteristic
236C2×C79C2×#57712yes—
237#3548C2×C7911yescharacteristic, complemented
238#3509C2×C7911yescharacteristic, complemented
239#3397C2×C7914yescomplemented
240#3392C2×C7914yescomplemented
241#3372C2×C7914yescomplemented
242#3360C2×C7914yescomplemented
243#3221C2×C7914yescomplemented
244#3206C2×C7912yescomplemented
245#3126C2×C7914yescomplemented
246#3106C2×C7912yescomplemented
247#2986C2×C7911yescharacteristic, complemented
248C79#6193511yescharacteristic, direct product factor, Sylow
249#562—22no—
250#557C22×C7914yes—
251#556C22×C7914yes—
252#554C22×C7914yes—
253#552—24no—
254#550C22×C7914yes—
255#547—22no—
256#541—22no—
257#540C22×C7914yes—
258#537—24no—
259#536C22×C7912yes—
260#533—22no—
261#533C22×C7911yescharacteristic
262#532C22×C7912yes—
263C2×C4⋊Q8C22×C7911yescharacteristic
264#519C22×C7912yes—
265C4×#41C22×C7911yescharacteristic
266#496C22×C7914yes—
267#492C22×C7914yes—
268#492C22×C7914yes—
269#491C22×C7914yes—
270#488C22×C7914yes—
271#487C22×C7914yes—
272#482C22×C7914yes—
273#479C22×C7918yes—
274#477C22×C7912yes—
275#476C22×C7912yes—
276#463C22×C7918yes—
277#461C22×C7914yes—
278#461C22×C7918yes—
279#461C22×C7914yes—
280#460C22×C7912yes—
281#460C22×C7918yes—
282#459C22×C7912yes—
283#449C22×C7914yes—
284#448C22×C7918yes—
285#446C22×C7914yes—
286C8×Q8C22×C7914yes—
287#440C22×C7918yes—
288C4×SD16C22×C7918yes—
289C4×SD16C22×C7914yes—
290C4×D8C22×C7914yes—
291#433C22×C7914yes—
292#431C22×C7912yes—
293C2×#41—24no—
294C2×#41—22no—
295C2×#41C23×C7911yescharacteristic
296C22×Q8C23×C7912yes—
297C2×SD16C23×C7918yes—
298C2×SD16C23×C7914yes—
299C2×SD16C23×C7918yes—
300C2×D8C23×C7914yes—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8D4×C7912yes—
304C4⋊Q8C23×C7914yes—
305C4⋊Q8C23×C7914yes—
306C4⋊Q8C23×C7912yes—
307#127C23×C7912yes—
308#127C23×C7914yes—
309#126—28no—
310#125—24no—
311#125—28no—
312#125D4×C7912yes—
313#125C23×C7914yes—
314#124—22no—
315#124C23×C7914yes—
316#123—28no—
317#123—24no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—24no—
321C22⋊Q8—28no—
322C22⋊Q8D4×C7914yes—
323#121—22no—
324#121—24no—
325#121—28no—
326#121—28no—
327#121C23×C7914yes—
328C4×Q8—24no—
329C4×Q8—24no—
330C4×Q8C23×C7912yes—
331C4×Q8C23×C7918yes—
332C4×Q8C23×C7914yes—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4C23×C7912yes—
336C4×D4C23×C7914yes—
337C4×D4C23×C7918yes—
338#117—24no—
339#117—24no—
340#117—21no—
341#117C23×C7911yescharacteristic
342#117C23×C7912yes—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C42—21no—
346C2×C42C23×C7911yescharacteristic
347#107C23×C7914yes—
348#106C23×C7914yes—
349C4⋊C8C23×C7912yes—
350C4⋊C8C23×C7912yes—
351C4⋊C8C23×C7918yes—
352#103C23×C7918yes—
353#103C23×C7914yes—
354#103C23×C7918yes—
355#102C23×C7914yes—
356#102C23×C7914yes—
357#102C23×C7914yes—
358C22⋊C8C23×C7914yes—
359#97C23×C7914yes—
360C4×C8C23×C7914yes—
361C4×C8C23×C7914yes—
362#41—42no—
363#41—84no—
364#41—88no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—44no—
368C2×Q8C2×D4×C7914yes—
369C2×Q8C24×C7914yes—
370C2×Q8C24×C7911yescharacteristic
371C2×D4—21no—
372C2×D4—24no—
373C2×D4—22no—
374C2×D4—28no—
375C2×D4—22no—
376C2×D4C24×C7911yescharacteristic
377C2×D4C24×C7914yes—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—24no—
382C22×C4—28no—
383C22×C4C2×D4×C7912yes—
384C22×C4C24×C7911yescharacteristic
385SD16—48no—
386SD16—48no—
387SD16—44no—
388D8—44no—
389C2×C8C24×C7914yes—
390C2×C8C24×C7914yes—
391C4⋊C4—22no—
392C4⋊C4—24no—
393C4⋊C4—28no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—28no—
397C4⋊C4—28no—
398C4⋊C4C2×D4×C7914yes—
399C4⋊C4C2×D4×C7914yes—
400C4⋊C4C2×D4×C7918yes—
401C4⋊C4C24×C7912yes—
402C4⋊C4C24×C7914yes—
403C22⋊C4—21no—
404C22⋊C4—22no—
405C22⋊C4—28no—
406C22⋊C4—24no—
407C22⋊C4—28no—
408C22⋊C4—24no—
409C22⋊C4C2×D4×C7914yes—
410C42—21no—
411C42—22no—
412C42—28no—
413C42C2×D4×C7911yescharacteristic
414C42C2×D4×C7911yescharacteristic
415C42C24×C7912yes—
416C42C24×C7914yes—
417C23—21no—
418C23—24no—
419C23C22×D4×C7911yescharacteristic
420Q8—28no—
421Q8—28no—
422Q8—22no—
423Q8—44no—
424Q8—82no—
425D4—22no—
426D4—24no—
427D4—24no—
428D4—42no—
429D4—44no—
430D4—82no—
431D4—88no—
432D4—84no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—21no—
438C2×C4—24no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—48no—
443C2×C4—88no—
444C2×C4C22×D4×C7911yescharacteristic
445C2×C4C22×D4×C7918yes—
446C2×C4C22×D4×C7912yes—
447C2×C4C22×D4×C7912yes—
448C2×C4C25×C7911yescharacteristic
449C8—24no—
450C8—24no—
451C22—22no—
452C22—21no—
453C22—44no—
454C22—42no—
455C22—44no—
456C22—41no—
457C22—44no—
458C22C23×D4×C7911yescharacteristic
459C4—22no—
460C4—28no—
461C4—21no—
462C4—44no—
463C4—42no—
464C4—41no—
465C4—44no—
466C4#577×C7914yes—
467C4#585×C7912yes—
468C2—41no—
469C2—84no—
470C2—81no—
471C2C79×#348711yescharacteristic
472C2C2×#577×C7912yes—
subgroupG/H
center, socleC22×C79C23×D4
commutator, Frattini, cosocleC2×C4C25×C79
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C79 ◁ #533×C79 ◁ G

Complements

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

NH ≅ G/Ntype
1. C79×#3548C2semidirect
2. C79×#3509C2semidirect
3. C79×#3397C2semidirect
4. C79×#3392C2semidirect
5. C79×#3372C2semidirect
6. C79×#3360C2semidirect
7. C79×#3221C2semidirect
8. C79×#3206C2semidirect
9. C79×#3126C2semidirect
10. C79×#3106C2semidirect
11. C79×#2986C2semidirect
231. #61935C79direct (N × H)
237. #3548C2×C79semidirect
238. #3509C2×C79semidirect
239. #3397C2×C79semidirect
240. #3392C2×C79semidirect
241. #3372C2×C79semidirect
242. #3360C2×C79semidirect
243. #3221C2×C79semidirect
244. #3206C2×C79semidirect
245. #3126C2×C79semidirect
246. #3106C2×C79semidirect
247. #2986C2×C79semidirect
248. C79#61935direct (N × H)

Maximal subgroups

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

subgroupindex
C79×#35482
C79×#35092
C79×#33972
C79×#33922
C79×#33722
C79×#33602
C79×#32212
C79×#32062
C79×#31262
C79×#31062
C79×#29862
#6193579