Finite Group Databasebeta

← C4×C79⋊#564 #34450990

Subgroups — C4×C79⋊#564 #34450990

Order 20224.

1800 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C79⋊#564C211yesmaximal, characteristic
2#23766586C211yesmaximal, characteristic
3#23766585C212yesmaximal
4#23766584C214yesmaximal
5#23766583C214yesmaximal
6#23766582C214yesmaximal
7C4×#14579153C212yesmaximal
8C4×#14579152C214yesmaximal
9C4×#14579151C214yesmaximal
10C4×#14579151C214yesmaximal
11C4×#125×C79C211yesmaximal, characteristic
12C79⋊#564C4116yesdirect product factor
13C2×#14579153C2212yes—
14C2×#14579152C2214yes—
15C2×#14579151C2214yes—
16C2×#14579151C2214yes—
17#19098462C2214yes—
18#19098461C2212yes—
19#19098461C2212yes—
20#19098460C2214yes—
21#19098460C2214yes—
22#19098459C2214yes—
23#19098458C2214yes—
24#19098458C2214yes—
25#19098450C2214yes—
26#19098450C2214yes—
27#19098449C2214yes—
28#19098449C2214yes—
29#19098448C2214yes—
30#19098448C2214yes—
31#19098447C2214yes—
32#19098447C2214yes—
33#19098446C2214yes—
34#19098446C2214yes—
35#19098445C2214yes—
36#19098445C2214yes—
37#19098444C2214yes—
38#19098444C2214yes—
39#19098429C2212yes—
40#19098428C2214yes—
41#19098427C2214yes—
42#19098427C2214yes—
43C4×Dic79⋊C4C2214yes—
44C4×Dic79⋊C4C2214yes—
45C4×Dic79⋊C4C2214yes—
46C4×Dic79⋊C4C2214yes—
47C4×C4⋊Dic79C2212yes—
48C4×C4⋊Dic79C2214yes—
49C4×C4⋊Dic79C2212yes—
50C42×Dic79C2214yes—
51C2×#125×C79C2211yescharacteristic
52#389×C79C2212yes—
53#387×C79C2214yes—
54#382×C79C2211yescharacteristic
55C4×C4⋊C4×C79C2212yes—
56C4×C4⋊C4×C79C2214yes—
57C43×C79C2211yescharacteristic
58#14579153C2×C4116yes—
59#14579152C2×C4132yes—
60#14579151C2×C4132yes—
61#14579151C2×C4132yes—
62C2×C4⋊Dic79C2314yes—
63C2×C4⋊Dic79C2312yes—
64C2×C4⋊Dic79C2312yes—
65C2×C4⋊Dic79C2312yes—
66C2×C4⋊Dic79C2314yes—
67C2×C4⋊Dic79C2312yes—
68C2×Dic79⋊C4C2314yes—
69C2×Dic79⋊C4C2314yes—
70C2×Dic79⋊C4C2314yes—
71C2×Dic79⋊C4C2314yes—
72C2×Dic79⋊C4C2314yes—
73C2×Dic79⋊C4C2314yes—
74C2×Dic79⋊C4C2314yes—
75C2×Dic79⋊C4C2314yes—
76C2×C4×Dic79C2314yes—
77C2×C4×Dic79C2314yes—
78C2×C4×Dic79C2314yes—
79C2×C4×Dic79C2314yes—
80C2×C4×Dic79C2314yes—
81C2×C4×Dic79C2314yes—
82C79⋊#95C2314yes—
83C79⋊#95C2314yes—
84C79⋊#95C2314yes—
85C79⋊#95C2314yes—
86C79⋊#95C2314yes—
87C79⋊#95C2314yes—
88C79⋊#95C2314yes—
89C79⋊#95C2314yes—
90C79⋊#95C2314yes—
91C79⋊#95C2314yes—
92C79⋊#95C2314yes—
93C79⋊#95C2314yes—
94#125×C79C2×C418yes—
95C2×C4⋊C4×C79C2314yes—
96C2×C4⋊C4×C79C2312yes—
97C2×C4⋊C4×C79C2312yes—
98C2×C4⋊C4×C79C2314yes—
99C2×C42×C79C2314yes—
100C2×C42×C79C2312yes—
101C2×C42×C79C2311yescharacteristic
102C2×C42×C79C2311yescharacteristic
103C2×C42×C79C2312yes—
104C2×C42×C79C2311yescharacteristic
105#95×C79C2314yes—
106#95×C79C2314yes—
107#95×C79C2314yes—
108C22×Dic79C2414yes—
109C22×Dic79C2414yes—
110C22×Dic79C2414yes—
111C22×Dic79C2414yes—
112C4⋊Dic79—44no—
113C4⋊Dic79—42no—
114C4⋊Dic79—42no—
115C4⋊Dic79C22×C418yes—
116C4⋊Dic79C22×C4116yes—
117C4⋊Dic79C22×C418yes—
118Dic79⋊C4—44no—
119Dic79⋊C4—44no—
120Dic79⋊C4—44no—
121Dic79⋊C4—44no—
122Dic79⋊C4C22×C4116yes—
123Dic79⋊C4C22×C4116yes—
124Dic79⋊C4C22×C4116yes—
125Dic79⋊C4C22×C4116yes—
126C4×Dic79—28no—
127C4×Dic79—28no—
128C4×Dic79—44no—
129C4×Dic79—44no—
130C4×Dic79—44no—
131C4×Dic79C22×C4116yes—
132C22×C4×C79C2411yescharacteristic
133C22×C4×C79C2414yes—
134C22×C4×C79C2412yes—
135C22×C4×C79C2412yes—
136C22×C4×C79C2414yes—
137C22×C4×C79C2411yescharacteristic
138C22×C4×C79C2411yescharacteristic
139C4⋊C4×C79—44no—
140C4⋊C4×C79—42no—
141C4⋊C4×C79C22×C418yes—
142C4⋊C4×C79C22×C4116yes—
143C42×C79—28no—
144C42×C79—24no—
145C42×C79—22no—
146C42×C79—42no—
147C42×C79—41no—
148C42×C79C22×C414yes—
149C23×C79C2511yescharacteristic
150C2×C4×C79—22no—
151C2×C4×C79—24no—
152C2×C4×C79—21no—
153C2×C4×C79—24no—
154C2×C4×C79—22no—
155C2×C4×C79—21no—
156C2×C4×C79—24no—
157C2×C4×C79—22no—
158C2×C4×C79—21no—
159C2×C4×C79—24no—
160C2×C4×C79—24no—
161C2×C4×C79—22no—
162C2×C4×C79—22no—
163C2×C4×C79—22no—
164C2×C4×C79C23×C418yes—
165C2×C4×C79C23×C412yes—
166C2×C4×C79C23×C414yes—
167C2×C4×C792−1+414yes—
168C2×C4×C792−1+412yes—
169C2×Dic79—24no—
170C2×Dic79—24no—
171C2×Dic79—24no—
172C2×Dic79—24no—
173C2×Dic79—24no—
174C2×Dic79—24no—
175C2×Dic79—24no—
176C2×Dic79—24no—
177C2×Dic79—24no—
178C2×Dic79—24no—
179C2×Dic79C23×C418yes—
180C2×Dic79C23×C418yes—
181C22×C79C24×C411yescharacteristic
182C22×C79C2×2−1+412yes—
183C22×C79C2×2−1+411yescharacteristic
184C22×C79#58511yescharacteristic
185C22×C79#58512yes—
186C4×C79—28no—
187C4×C79—24no—
188C4×C79—22no—
189C4×C79—44no—
190C4×C79—42no—
191C4×C79—41no—
192C4×C79#56414yescomplemented
193Dic79—28no—
194Dic79—28no—
195Dic79—44no—
196Dic79—44no—
197C4×#564—791nomaximal, Sylow
198C2×C79C4×2−1+412yes—
199C2×C79C4×2−1+411yescharacteristic
200C2×C79C2×#56411yescharacteristic
201C2×C79#353112yes—
202C2×C79#353111yescharacteristic
203C2×#564—791no—
204#2382—794no—
205#2382—794no—
206#2382—794no—
207#2382—792no—
208#2382—791no—
209C4×#125—794no—
210C4×#125—794no—
211C4×#125—794no—
212C4×#125—792no—
213C4×#125D7911yescharacteristic
214C79C4×#56411yescharacteristic, complemented, Sylow
215#564—7916no—
216C2×#125—794no—
217C2×#125—794no—
218C2×#125—794no—
219C2×#125—792no—
220C2×#125C2×D7911yescharacteristic
221#389—794no—
222#389—794no—
223#389—794no—
224#389—794no—
225#389—792no—
226#389—792no—
227#389—794no—
228#389—794no—
229#389C2×D7912yes—
230#387—794no—
231#387—794no—
232#387—794no—
233#387—794no—
234#387—794no—
235#387—794no—
236#387—794no—
237#387—794no—
238#387—794no—
239#387—794no—
240#387—794no—
241#387—794no—
242#387—794no—
243#387—794no—
244#387C2×D7914yes—
245#382—794no—
246#382—792no—
247#382—794no—
248#382—794no—
249#382C2×D7911yescharacteristic
250C4×C4⋊C4—794no—
251C4×C4⋊C4—792no—
252C4×C4⋊C4—792no—
253C4×C4⋊C4—794no—
254C4×C4⋊C4—794no—
255C4×C4⋊C4—794no—
256C4×C4⋊C4—794no—
257C4×C4⋊C4C2×D7914yes—
258C4×C4⋊C4C2×D7912yes—
259C43—794no—
260C43C2×D7911yescharacteristic
261#125—7932no—
262#125—7932no—
263#125—7932no—
264#125—7916no—
265#125C4×D7918yes—
266C2×C4⋊C4—794no—
267C2×C4⋊C4—794no—
268C2×C4⋊C4—794no—
269C2×C4⋊C4—794no—
270C2×C4⋊C4—794no—
271C2×C4⋊C4—792no—
272C2×C4⋊C4—792no—
273C2×C4⋊C4—794no—
274C2×C4⋊C4—794no—
275C2×C4⋊C4—794no—
276C2×C4⋊C4—794no—
277C2×C4⋊C4—794no—
278C2×C4⋊C4—792no—
279C2×C4⋊C4—792no—
280C2×C4⋊C4C22×D7914yes—
281C2×C4⋊C4C22×D7912yes—
282C2×C4⋊C4C22×D7912yes—
283C2×C4⋊C4C22×D7914yes—
284C2×C42—794no—
285C2×C42—794no—
286C2×C42—794no—
287C2×C42—794no—
288C2×C42—794no—
289C2×C42—794no—
290C2×C42C22×D7914yes—
291C2×C42C22×D7912yes—
292C2×C42C22×D7911yescharacteristic
293C2×C42C22×D7911yescharacteristic
294C2×C42C22×D7912yes—
295C2×C42C22×D7911yescharacteristic
296#95—794no—
297#95—794no—
298#95—794no—
299#95—794no—
300#95—794no—
301#95—794no—
302#95—794no—
303#95—794no—
304#95—794no—
305#95—794no—
306#95—794no—
307#95—794no—
308#95C22×D7914yes—
309#95C22×D7914yes—
310#95C22×D7914yes—
311C22×C4—794no—
312C22×C4—794no—
313C22×C4—794no—
314C22×C4—794no—
315C22×C4C23×D7912yes—
316C22×C4C23×D7914yes—
317C22×C4C23×D7911yescharacteristic
318C22×C4C23×D7911yescharacteristic
319C22×C4C23×D7914yes—
320C22×C4C23×D7912yes—
321C22×C4C23×D7911yescharacteristic
322C4⋊C4—42no—
323C4⋊C4—44no—
324C4⋊C4—3164no—
325C4⋊C4—3164no—
326C4⋊C4—3164no—
327C4⋊C4—3164no—
328C4⋊C4—3162no—
329C4⋊C4—3162no—
330C4⋊C4—3164no—
331C4⋊C4—7916no—
332C4⋊C4—7916no—
333C4⋊C4—7916no—
334C4⋊C4—7916no—
335C4⋊C4—7916no—
336C4⋊C4—798no—
337C4⋊C4—798no—
338C4⋊C4C2×C4×D7918yes—
339C4⋊C4C2×C4×D79116yes—
340C42—28no—
341C42—24no—
342C42—22no—
343C42—41no—
344C42—42no—
345C42—3164no—
346C42—3164no—
347C42—3164no—
348C42—7916no—
349C42—1588no—
350C42—1588no—
351C42C2×C4×D7914yes—
352C23C24×D7911yescharacteristic
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—798no—
368C2×C4—798no—
369C2×C4—1584no—
370C2×C4—1584no—
371C2×C4—1584no—
372C2×C4—1584no—
373C2×C4—1584no—
374C2×C4—1584no—
375C2×C4—1584no—
376C2×C4—1584no—
377C2×C4—1584no—
378C2×C4—1584no—
379C2×C4C22×C4×D7918yes—
380C2×C4C22×C4×D7914yes—
381C2×C4C22×C4×D7912yes—
382C2×C4#1457920814yes—
383C2×C4#1457920912yes—
384C22C23×C4×D7911yescharacteristic
385C22C2×#1457920812yes—
386C22C2×#1457920911yescharacteristic
387C22#1909939911yescharacteristic
388C22#1909939912yes—
389C4—24no—
390C4—28no—
391C4—22no—
392C4—42no—
393C4—44no—
394C4—41no—
395C4—3164no—
396C4—3164no—
397C4—1588no—
398C4—1588no—
399C4C79⋊#56414yesdirect product factor
400C2C4×#1457920812yes—
401C2C4×#1457920911yescharacteristic
402C2C2×C79⋊#56411yescharacteristic
403C2#2377754512yes—
404C2#2377754711yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC4×#125×C79C2
socle, prime radical, cosocleC23×C79C25
hypercenterC4×#125D79
hypocenterC79C4×#564
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
12. C79⋊#564C4direct (N × H)
192. C4×C79#564semidirect
214. C79C4×#564semidirect
399. C4C79⋊#564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C79⋊#5642
#237665862
#237665852
#237665842
#237665832
#237665822
C4×#145791532
C4×#145791522
C4×#145791512
C4×#125×C792
C4×#56479