Finite Group Databasebeta

← C79×#9227 #34120916

Subgroups — C79×#9227 #34120916

Order 20224.

562 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C79C211yesmaximal, characteristic
2C2×#436×C79C211yesmaximal, characteristic
3C79×#1956C211yesmaximal, characteristic, complemented
4C79×#1802C211yesmaximal, characteristic
5C2×#332×C79C211yesmaximal, characteristic, complemented
6C79×#1296C211yesmaximal, characteristic, complemented
7C79×#1277C211yesmaximal, characteristic, complemented
8C22×M16×C79—21no—
9C2×C4⋊Q8×C79C2211yescharacteristic
10C2×C4×D4×C79C2211yescharacteristic
11#474×C79—22no—
12#474×C79C414yescomplemented
13#436×C79—22no—
14#436×C79—22no—
15C2×#107×C79—21no—
16C2×C4⋊C8×C79C2211yescharacteristic
17C2×C4⋊C8×C79C2211yescharacteristic
18C2×C4⋊C8×C79C2211yescharacteristic
19C2×#103×C79—21no—
20C2×#103×C79—21no—
21C2×#102×C79—21no—
22C2×#102×C79—21no—
23C2×C22⋊C8×C79—21no—
24C2×C4×C8×C79C2211yescharacteristic
25#384×C79C2211yescharacteristic
26#340×C79—21no—
27#332×C79—22no—
28C22×Q8×C79—21no—
29C22×D4×C79D411yescharacteristic
30C23×C4×C79—21no—
31C2×M16×C79—24no—
32C2×M16×C79—42no—
33C2×M16×C79—42no—
34C22×C8×C79—21no—
35C22×C8×C79—21no—
36C22×C8×C79—21no—
37C22×C8×C79D411yescharacteristic
38C22×C8×C79D411yescharacteristic
39C4⋊Q8×C79—21no—
40C4⋊Q8×C79—21no—
41C4⋊Q8×C79—21no—
42C4⋊Q8×C79C2×C412yes—
43C4×D4×C79—21no—
44C4×D4×C79—21no—
45C4×D4×C79C2×C412yes—
46C4×D4×C79D412yes—
47C2×C4⋊C4×C79—21no—
48C2×C4⋊C4×C79—21no—
49C2×C4⋊C4×C79—21no—
50C2×C4⋊C4×C79—21no—
51C2×C4⋊C4×C79—21no—
52C2×C4⋊C4×C79D411yescharacteristic
53C2×C22⋊C4×C79—21no—
54C2×C42×C79C2311yescharacteristic
55#107×C79—24no—
56C4⋊C8×C79—21no—
57C4⋊C8×C79—21no—
58C4⋊C8×C79—21no—
59C4⋊C8×C79—21no—
60C4⋊C8×C79C2×C412yes—
61C4⋊C8×C79D412yes—
62#103×C79—42no—
63#103×C79—42no—
64#102×C79—24no—
65#102×C79—42no—
66C22⋊C8×C79—24no—
67C4×C8×C79—21no—
68C4×C8×C79—21no—
69C24×C79—21no—
70C2×Q8×C79—22no—
71C2×Q8×C79—41no—
72C2×Q8×C79—41no—
73C2×Q8×C79—41no—
74C2×Q8×C79—41no—
75C2×Q8×C79—41no—
76C2×D4×C79—21no—
77C2×D4×C79—21no—
78C2×D4×C79—21no—
79C2×D4×C79—21no—
80C2×D4×C79—21no—
81C2×D4×C79C22⋊C412yes—
82C22×C4×C79—21no—
83C22×C4×C79—22no—
84C22×C4×C79—22no—
85C22×C4×C79—41no—
86C22×C4×C79—41no—
87C22×C4×C79—41no—
88C22×C4×C79—41no—
89C22×C4×C79—41no—
90C22×C4×C79—41no—
91C22×C4×C79C2×D411yescharacteristic
92C22×C4×C79C2×D411yescharacteristic
93C22×C4×C79#4111yescharacteristic
94M16×C79—48no—
95C2×C8×C79—22no—
96C2×C8×C79—21no—
97C2×C8×C79—21no—
98C2×C8×C79—22no—
99C2×C8×C79—21no—
100C2×C8×C79—21no—
101C2×C8×C79—21no—
102C2×C8×C79—41no—
103C2×C8×C79—41no—
104C2×C8×C79—41no—
105C2×C8×C79—41no—
106C2×C8×C79—41no—
107C2×C8×C79—41no—
108C2×C8×C79—41no—
109C2×C8×C79D812yes—
110C4⋊C4×C79—21no—
111C4⋊C4×C79—22no—
112C4⋊C4×C79—22no—
113C4⋊C4×C79—41no—
114C4⋊C4×C79—41no—
115C4⋊C4×C79—41no—
116C4⋊C4×C79—41no—
117C4⋊C4×C79—41no—
118C4⋊C4×C79—41no—
119C4⋊C4×C79—81no—
120C4⋊C4×C79C22⋊C412yes—
121C22⋊C4×C79—22no—
122C22⋊C4×C79—22no—
123C42×C79C22×C411yescharacteristic
124C42×C79C2×D411yescharacteristic
125C42×C79C2×D411yescharacteristic
126C42×C79#4111yescharacteristic
127C23×C79—22no—
128C23×C79—41no—
129C23×C79—41no—
130C23×C79—41no—
131C23×C79—41no—
132C23×C79—41no—
133C23×C79—41no—
134C23×C79#12111yescharacteristic
135Q8×C79—42no—
136Q8×C79—42no—
137Q8×C79—81no—
138Q8×C79—81no—
139D4×C79—22no—
140D4×C79—22no—
141D4×C79—41no—
142D4×C79—41no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—22no—
146C2×C4×C79—41no—
147C2×C4×C79—41no—
148C2×C4×C79—42no—
149C2×C4×C79—42no—
150C2×C4×C79—42no—
151C2×C4×C79—42no—
152C2×C4×C79—42no—
153C2×C4×C79—81no—
154C2×C4×C79—81no—
155C2×C4×C79—81no—
156C2×C4×C79—81no—
157C2×C4×C79—81no—
158C2×C4×C79C2×C22⋊C411yescharacteristic
159C2×C4×C79C4×D411yescharacteristic
160C2×C4×C79C4×D411yescharacteristic
161C2×C4×C79#12011yescharacteristic
162C2×C4×C79#12111yescharacteristic
163C2×C4×C79#12311yescharacteristic
164C2×C4×C79C2×D811yescharacteristic
165C2×C4×C79#13511yescharacteristic
166C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C79#13711yescharacteristic
170C2×C4×C79#13711yescharacteristic
171C2×C4×C79#13711yescharacteristic
172C8×C79—22no—
173C8×C79—42no—
174C8×C79—42no—
175C8×C79—41no—
176C8×C79—81no—
177C22×C79—42no—
178C22×C79—42no—
179C22×C79—42no—
180C22×C79—81no—
181C22×C79—81no—
182C22×C79—81no—
183C22×C79—81no—
184C22×C79#38611yescharacteristic
185C22×C79#45911yescharacteristic
186C22×C79#46311yescharacteristic
187C22×C79#46811yescharacteristic
188C22×C79#47011yescharacteristic
189C22×C79#47111yescharacteristic
190C22×C79#47311yescharacteristic
191C4×C79—21no—
192C4×C79—21no—
193C4×C79—42no—
194C4×C79—82no—
195C4×C79—161no—
196C4×C79#41711yescharacteristic
197C4×C79#41911yescharacteristic
198C4×C79C4×D811yescharacteristic
199C4×C79#44211yescharacteristic
200C4×C79#44711yescharacteristic
201C4×C79#44911yescharacteristic
202C4×C79#46811yescharacteristic
203C4×C79#47011yescharacteristic
204#9227C7911yesmaximal, characteristic, direct product factor, Sylow
205C2×C79—82no—
206C2×C79#168511yescharacteristic
207C2×C79#168911yescharacteristic
208C2×C79#169911yescharacteristic
209C2×C79#170311yescharacteristic
210C2×C79#187911yescharacteristic
211C2×C79#189411yescharacteristic
212C2×C79#190811yescharacteristic
213C2×#474C2×C7911yescharacteristic
214C2×#436C2×C7911yescharacteristic
215#1956C2×C7911yescharacteristic, complemented
216#1802C2×C7911yescharacteristic
217C2×#332C2×C7911yescharacteristic, complemented
218#1296C2×C7911yescharacteristic, complemented
219#1277C2×C7911yescharacteristic, complemented
220C79#922711yescharacteristic, direct product factor, Sylow
221C22×M16—21no—
222C2×C4⋊Q8C22×C7911yescharacteristic
223C2×C4×D4C22×C7911yescharacteristic
224#474—22no—
225#474C4×C7914yescomplemented
226#436—22no—
227#436—22no—
228C2×#107—21no—
229C2×C4⋊C8C22×C7911yescharacteristic
230C2×C4⋊C8C22×C7911yescharacteristic
231C2×C4⋊C8C22×C7911yescharacteristic
232C2×#103—21no—
233C2×#103—21no—
234C2×#102—21no—
235C2×#102—21no—
236C2×C22⋊C8—21no—
237C2×C4×C8C22×C7911yescharacteristic
238#384C22×C7911yescharacteristic
239#340—21no—
240#332—22no—
241C22×Q8—21no—
242C22×D4D4×C7911yescharacteristic
243C23×C4—21no—
244C2×M16—24no—
245C2×M16—42no—
246C2×M16—42no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8D4×C7911yescharacteristic
251C22×C8D4×C7911yescharacteristic
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8C2×C4×C7912yes—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C2×C4×C7912yes—
259C4×D4D4×C7912yes—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C7911yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42C23×C7911yescharacteristic
268#107—24no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8C2×C4×C7912yes—
274C4⋊C8D4×C7912yes—
275#103—42no—
276#103—42no—
277#102—24no—
278#102—42no—
279C22⋊C8—24no—
280C4×C8—21no—
281C4×C8—21no—
282C24—21no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4C22⋊C4×C7912yes—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4C2×D4×C7911yescharacteristic
305C22×C4C2×D4×C7911yescharacteristic
306C22×C4#41×C7911yescharacteristic
307M16—48no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8D8×C7912yes—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—81no—
333C4⋊C4C22⋊C4×C7912yes—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C42C22×C4×C7911yescharacteristic
337C42C2×D4×C7911yescharacteristic
338C42C2×D4×C7911yescharacteristic
339C42#41×C7911yescharacteristic
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#121×C7911yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352D4—22no—
353D4—22no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4C2×C22⋊C4×C7911yescharacteristic
372C2×C4C4×D4×C7911yescharacteristic
373C2×C4C4×D4×C7911yescharacteristic
374C2×C4#120×C7911yescharacteristic
375C2×C4#121×C7911yescharacteristic
376C2×C4#123×C7911yescharacteristic
377C2×C4C2×D8×C7911yescharacteristic
378C2×C4#135×C7911yescharacteristic
379C2×C4AGL(1,ℤ/8)×C7911yescharacteristic
380C2×C4AGL(1,ℤ/8)×C7911yescharacteristic
381C2×C4AGL(1,ℤ/8)×C7911yescharacteristic
382C2×C4#137×C7911yescharacteristic
383C2×C4#137×C7911yescharacteristic
384C2×C4#137×C7911yescharacteristic
385C8—22no—
386C8—42no—
387C8—42no—
388C8—41no—
389C8—81no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22#386×C7911yescharacteristic
398C22#459×C7911yescharacteristic
399C22#463×C7911yescharacteristic
400C22#468×C7911yescharacteristic
401C22#470×C7911yescharacteristic
402C22#471×C7911yescharacteristic
403C22#473×C7911yescharacteristic
404C4—21no—
405C4—21no—
406C4—42no—
407C4—82no—
408C4—161no—
409C4#417×C7911yescharacteristic
410C4#419×C7911yescharacteristic
411C4C4×D8×C7911yescharacteristic
412C4#442×C7911yescharacteristic
413C4#447×C7911yescharacteristic
414C4#449×C7911yescharacteristic
415C4#468×C7911yescharacteristic
416C4#470×C7911yescharacteristic
417C2—82no—
418C2C79×#168511yescharacteristic
419C2C79×#168911yescharacteristic
420C2C79×#169911yescharacteristic
421C2C79×#170311yescharacteristic
422C2C79×#187911yescharacteristic
423C2C79×#189411yescharacteristic
424C2C79×#190811yescharacteristic
subgroupG/H
center, socleC23×C79#121
commutatorC42C22×C4×C79
Frattini, cosocleC2×C42C23×C79
prime radicalC22×D4×C79D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C79 ◁ C2×C42×C79 ◁ G

Complements

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

NH ≅ G/Ntype
3. C79×#1956C2semidirect
5. C2×#332×C79C2semidirect
6. C79×#1296C2semidirect
7. C79×#1277C2semidirect
12. #474×C79C4semidirect
204. #9227C79direct (N × H)
215. #1956C2×C79semidirect
217. C2×#332C2×C79semidirect
218. #1296C2×C79semidirect
219. #1277C2×C79semidirect
220. C79#9227direct (N × H)
225. #474C4×C79semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C792
C2×#436×C792
C79×#19562
C79×#18022
C2×#332×C792
C79×#12962
C79×#12772
#922779