Finite Group Databasebeta

← C79×#8993 #34120682

Subgroups — C79×#8993 #34120682

Order 20224.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3076C211yesmaximal, characteristic
2C79×#2906C211yesmaximal, characteristic
3C79×#1493C211yesmaximal, characteristic, complemented
4C79×#1481C211yesmaximal, characteristic, complemented
5C79×#1476C211yesmaximal, characteristic
6C79×#1301C211yesmaximal, characteristic, complemented
7C79×#1277C211yesmaximal, characteristic, complemented
8C2×#131×C79—21no—
9#533×C79C2211yescharacteristic
10C4×#41×C79C2211yescharacteristic
11#479×C79—21no—
12#478×C79—21no—
13#477×C79C411yescharacteristic
14#476×C79C411yescharacteristic
15#475×C79C411yescharacteristic
16#474×C79C411yescharacteristic
17#431×C79C2211yescharacteristic
18#427×C79—21no—
19#424×C79—21no—
20#424×C79—22no—
21#423×C79—21no—
22#423×C79C2211yescharacteristic
23C2×C4⋊C8×C79—21no—
24C2×C4⋊C8×C79C2211yescharacteristic
25C2×C4⋊C8×C79C2211yescharacteristic
26#416×C79—21no—
27C2×C4×C8×C79C2211yescharacteristic
28Q8⋊C8×C79—21no—
29Q8⋊C8×C79—22no—
30Q8⋊C8×C79—21no—
31Q8⋊C8×C79—21no—
32D4⋊C8×C79—21no—
33C2×#41×C79D411yescharacteristic
34#131×C79—42no—
35#131×C79—42no—
36C2×M16×C79—22no—
37C2×M16×C79—21no—
38C22×C8×C79—22no—
39C22×C8×C79—21no—
40C22×C8×C79—21no—
41C22×C8×C79—21no—
42C4⋊Q8×C79C2×C411yescharacteristic
43C4⋊Q8×C79C2×C411yescharacteristic
44#125×C79—21no—
45C22⋊Q8×C79—21no—
46C22⋊Q8×C79—21no—
47C4×Q8×C79—21no—
48C4×Q8×C79—21no—
49C4×Q8×C79C2×C411yescharacteristic
50C4×Q8×C79D411yescharacteristic
51C4×D4×C79—21no—
52C4×D4×C79—21no—
53C4×D4×C79C2×C411yescharacteristic
54C4×D4×C79D411yescharacteristic
55#117×C79—21no—
56#117×C79—21no—
57#117×C79D411yescharacteristic
58C2×C42×C79—21no—
59C2×C42×C79C2311yescharacteristic
60#107×C79—21no—
61#107×C79—21no—
62#106×C79—21no—
63#106×C79—21no—
64C4⋊C8×C79—22no—
65C4⋊C8×C79—22no—
66C4⋊C8×C79—21no—
67C4⋊C8×C79—21no—
68C4⋊C8×C79—21no—
69C4⋊C8×C79—21no—
70C4⋊C8×C79C2×C411yescharacteristic
71C4⋊C8×C79C2×C411yescharacteristic
72C4⋊C8×C79D411yescharacteristic
73C4⋊C8×C79D411yescharacteristic
74C4⋊C8×C79D412yes—
75#103×C79—21no—
76#103×C79—21no—
77#102×C79—21no—
78#102×C79—21no—
79C22⋊C8×C79—21no—
80C4×C8×C79—21no—
81C4×C8×C79—21no—
82C4×C8×C79—21no—
83#41×C79—21no—
84#41×C79—21no—
85#41×C79SD1612yes—
86#41×C79Q1612yes—
87C2×Q8×C79—21no—
88C2×Q8×C79—21no—
89C2×Q8×C79C22⋊C411yescharacteristic
90C2×D4×C79—21no—
91C2×D4×C79C22⋊C411yescharacteristic
92C22×C4×C79—21no—
93C22×C4×C79—21no—
94C22×C4×C79—21no—
95C22×C4×C79C2×D411yescharacteristic
96C22×C4×C79#4111yescharacteristic
97C22×C4×C79#4111yescharacteristic
98M16×C79—44no—
99M16×C79—41no—
100M16×C79—41no—
101C2×C8×C79—22no—
102C2×C8×C79—21no—
103C2×C8×C79—21no—
104C2×C8×C79—21no—
105C2×C8×C79—22no—
106C2×C8×C79—21no—
107C2×C8×C79—41no—
108C2×C8×C79—44no—
109C2×C8×C79—41no—
110C2×C8×C79—41no—
111C2×C8×C79—41no—
112C2×C8×C79—41no—
113C2×C8×C79—41no—
114C2×C8×C79—41no—
115C4⋊C4×C79—21no—
116C4⋊C4×C79—21no—
117C4⋊C4×C79—21no—
118C4⋊C4×C79—21no—
119C4⋊C4×C79—21no—
120C4⋊C4×C79—21no—
121C4⋊C4×C79—41no—
122C4⋊C4×C79—41no—
123C4⋊C4×C79C22⋊C411yescharacteristic
124C4⋊C4×C79C22⋊C411yescharacteristic
125C22⋊C4×C79—21no—
126C22⋊C4×C79—21no—
127C22⋊C4×C79—21no—
128C22⋊C4×C79—41no—
129C42×C79—21no—
130C42×C79—21no—
131C42×C79—21no—
132C42×C79—41no—
133C42×C79C22×C411yescharacteristic
134C42×C79C2×D411yescharacteristic
135C42×C79C2×D411yescharacteristic
136C42×C79C2×D411yescharacteristic
137C23×C79—21no—
138C23×C79#12311yescharacteristic
139Q8×C79—21no—
140Q8×C79—42no—
141Q8×C79—41no—
142Q8×C79—41no—
143Q8×C79#10312yes—
144D4×C79—22no—
145D4×C79—22no—
146D4×C79—21no—
147D4×C79#10312yes—
148C2×C4×C79—21no—
149C2×C4×C79—21no—
150C2×C4×C79—21no—
151C2×C4×C79—22no—
152C2×C4×C79—22no—
153C2×C4×C79—21no—
154C2×C4×C79—21no—
155C2×C4×C79—41no—
156C2×C4×C79—41no—
157C2×C4×C79—41no—
158C2×C4×C79—41no—
159C2×C4×C79—41no—
160C2×C4×C79—81no—
161C2×C4×C79C2×C22⋊C411yescharacteristic
162C2×C4×C79C4×D411yescharacteristic
163C2×C4×C79C4×D411yescharacteristic
164C2×C4×C79#12011yescharacteristic
165C2×C4×C79#12111yescharacteristic
166C2×C4×C79#12111yescharacteristic
167C2×C4×C79C2×SD1611yescharacteristic
168C2×C4×C79C2×Q1611yescharacteristic
169C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C79#13711yescharacteristic
171C8×C79—42no—
172C8×C79—41no—
173C8×C79—41no—
174C8×C79—41no—
175C8×C79—42no—
176C8×C79—41no—
177C8×C79—81no—
178C22×C79—21no—
179C22×C79—21no—
180C22×C79—22no—
181C22×C79—41no—
182C22×C79—41no—
183C22×C79#38611yescharacteristic
184C22×C79#48311yescharacteristic
185C22×C79#48411yescharacteristic
186C4×C79—22no—
187C4×C79—21no—
188C4×C79—21no—
189C4×C79—21no—
190C4×C79—41no—
191C4×C79—41no—
192C4×C79—81no—
193C4×C79—81no—
194C4×C79C2×#10311yescharacteristic
195C4×C79#41711yescharacteristic
196C4×C79#44311yescharacteristic
197C4×C79#44411yescharacteristic
198C4×C79#45011yescharacteristic
199C4×C79#45111yescharacteristic
200#8993C7911yesmaximal, characteristic, direct product factor, Sylow
201C2×C79—21no—
202C2×C79—21no—
203C2×C79—42no—
204C2×C79#187211yescharacteristic
205C2×C79#187611yescharacteristic
206C2×C79#188111yescharacteristic
207#3076C2×C7911yescharacteristic
208#2906C2×C7911yescharacteristic
209#1493C2×C7911yescharacteristic, complemented
210#1481C2×C7911yescharacteristic, complemented
211#1476C2×C7911yescharacteristic
212#1301C2×C7911yescharacteristic, complemented
213#1277C2×C7911yescharacteristic, complemented
214C79#899311yescharacteristic, direct product factor, Sylow
215C2×#131—21no—
216#533C22×C7911yescharacteristic
217C4×#41C22×C7911yescharacteristic
218#479—21no—
219#478—21no—
220#477C4×C7911yescharacteristic
221#476C4×C7911yescharacteristic
222#475C4×C7911yescharacteristic
223#474C4×C7911yescharacteristic
224#431C22×C7911yescharacteristic
225#427—21no—
226#424—21no—
227#424—22no—
228#423—21no—
229#423C22×C7911yescharacteristic
230C2×C4⋊C8—21no—
231C2×C4⋊C8C22×C7911yescharacteristic
232C2×C4⋊C8C22×C7911yescharacteristic
233#416—21no—
234C2×C4×C8C22×C7911yescharacteristic
235Q8⋊C8—21no—
236Q8⋊C8—21no—
237Q8⋊C8—21no—
238Q8⋊C8—22no—
239D4⋊C8—21no—
240C2×#41D4×C7911yescharacteristic
241#131—42no—
242#131—42no—
243C2×M16—22no—
244C2×M16—21no—
245C22×C8—22no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C4⋊Q8C2×C4×C7911yescharacteristic
250C4⋊Q8C2×C4×C7911yescharacteristic
251#125—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8C2×C4×C7911yescharacteristic
257C4×Q8D4×C7911yescharacteristic
258C4×D4—21no—
259C4×D4—21no—
260C4×D4C2×C4×C7911yescharacteristic
261C4×D4D4×C7911yescharacteristic
262#117—21no—
263#117—21no—
264#117D4×C7911yescharacteristic
265C2×C42—21no—
266C2×C42C23×C7911yescharacteristic
267#107—21no—
268#107—21no—
269#106—21no—
270#106—21no—
271C4⋊C8—22no—
272C4⋊C8—22no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8C2×C4×C7911yescharacteristic
278C4⋊C8C2×C4×C7911yescharacteristic
279C4⋊C8D4×C7911yescharacteristic
280C4⋊C8D4×C7911yescharacteristic
281C4⋊C8D4×C7912yes—
282#103—21no—
283#103—21no—
284#102—21no—
285#102—21no—
286C22⋊C8—21no—
287C4×C8—21no—
288C4×C8—21no—
289C4×C8—21no—
290#41—21no—
291#41—21no—
292#41SD16×C7912yes—
293#41Q16×C7912yes—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8C22⋊C4×C7911yescharacteristic
297C2×D4—21no—
298C2×D4C22⋊C4×C7911yescharacteristic
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4C2×D4×C7911yescharacteristic
303C22×C4#41×C7911yescharacteristic
304C22×C4#41×C7911yescharacteristic
305M16—44no—
306M16—41no—
307M16—41no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—44no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4C22⋊C4×C7911yescharacteristic
331C4⋊C4C22⋊C4×C7911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—41no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42—41no—
340C42C22×C4×C7911yescharacteristic
341C42C2×D4×C7911yescharacteristic
342C42C2×D4×C7911yescharacteristic
343C42C2×D4×C7911yescharacteristic
344C23—21no—
345C23#123×C7911yescharacteristic
346Q8—21no—
347Q8—42no—
348Q8—41no—
349Q8—41no—
350Q8#103×C7912yes—
351D4—22no—
352D4—22no—
353D4—21no—
354D4#103×C7912yes—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4C2×C22⋊C4×C7911yescharacteristic
369C2×C4C4×D4×C7911yescharacteristic
370C2×C4C4×D4×C7911yescharacteristic
371C2×C4#120×C7911yescharacteristic
372C2×C4#121×C7911yescharacteristic
373C2×C4#121×C7911yescharacteristic
374C2×C4C2×SD16×C7911yescharacteristic
375C2×C4C2×Q16×C7911yescharacteristic
376C2×C4AGL(1,ℤ/8)×C7911yescharacteristic
377C2×C4#137×C7911yescharacteristic
378C8—42no—
379C8—41no—
380C8—41no—
381C8—41no—
382C8—42no—
383C8—41no—
384C8—81no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22#386×C7911yescharacteristic
391C22#483×C7911yescharacteristic
392C22#484×C7911yescharacteristic
393C4—22no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4C2×#103×C7911yescharacteristic
402C4#417×C7911yescharacteristic
403C4#443×C7911yescharacteristic
404C4#444×C7911yescharacteristic
405C4#450×C7911yescharacteristic
406C4#451×C7911yescharacteristic
407C2—21no—
408C2—21no—
409C2—42no—
410C2C79×#187211yescharacteristic
411C2C79×#187611yescharacteristic
412C2C79×#188111yescharacteristic
subgroupG/H
centerC2×C4×C79#120
commutatorC42C22×C4×C79
Frattini, cosocleC2×C42C23×C79
socleC22×C79#386
prime radicalC2×#41×C79D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C79 ◁ C2×C42×C79 ◁ G

Complements

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

NH ≅ G/Ntype
3. C79×#1493C2semidirect
4. C79×#1481C2semidirect
6. C79×#1301C2semidirect
7. C79×#1277C2semidirect
200. #8993C79direct (N × H)
209. #1493C2×C79semidirect
210. #1481C2×C79semidirect
212. #1301C2×C79semidirect
213. #1277C2×C79semidirect
214. C79#8993direct (N × H)

Maximal subgroups

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

subgroupindex
C79×#30762
C79×#29062
C79×#14932
C79×#14812
C79×#14762
C79×#13012
C79×#12772
#899379