Finite Group Databasebeta

← #34450989

Subgroups — #34450989

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#23766585C212yesmaximal
3#23766584C214yesmaximal
4#23766583C214yesmaximal
5#23766582C214yesmaximal
6#125×Dic79C211yesmaximal, characteristic
7#23765959C214yesmaximal
8#23765957C214yesmaximal
9#23765957C214yesmaximal
10#23765955C212yesmaximal
11C79×#2382C211yesmaximal, characteristic
12C79⋊#564C4116yescomplemented
13C2×#14579153C2212yes—
14C2×#14579152C2214yes—
15C2×#14579151C2214yes—
16C2×#14579151C2214yes—
17#19098462C2212yes—
18#19098461C2214yes—
19#19098460C2214yes—
20#19098460C2214yes—
21#19098459C2212yes—
22#19098459C2212yes—
23#19098458C2214yes—
24#19098458C2214yes—
25#19098450C2214yes—
26#19098450C2214yes—
27#19098449C2214yes—
28#19098448C2214yes—
29#19098448C2214yes—
30#19098447C2214yes—
31#19098447C2214yes—
32#19098446C2214yes—
33#19098446C2214yes—
34#19098445C2214yes—
35#19098445C2214yes—
36#19098444C2214yes—
37#19098444C2214yes—
38#19098429C2211yescharacteristic
39#19098428C2214yes—
40#19098427C2214yes—
41#19098427C2214yes—
42C4⋊C4×Dic79C2212yes—
43C4⋊C4×Dic79C2212yes—
44C4⋊C4×Dic79C2212yes—
45C4⋊C4×Dic79C2214yes—
46C4⋊C4×Dic79C2214yes—
47#19098414C2214yes—
48#19098414C2214yes—
49#19098414C2214yes—
50#19098414C2214yes—
51C42×Dic79C2211yescharacteristic
52C42×Dic79C2214yes—
53C2×#125×C79C2211yescharacteristic
54#389×C79C2214yes—
55#387×C79C2214yes—
56#387×C79C2214yes—
57#382×C79C2212yes—
58#14579153C2×C4116yes—
59#14579152C2×C4132yes—
60#14579151C2×C4132yes—
61#14579151C2×C4132yes—
62C2×C4⋊Dic79C2314yes—
63C2×C4⋊Dic79C2312yes—
64C2×C4⋊Dic79C2312yes—
65C2×C4⋊Dic79C2314yes—
66C2×C4⋊Dic79C2312yes—
67C2×Dic79⋊C4C2314yes—
68C2×Dic79⋊C4C2314yes—
69C2×Dic79⋊C4C2314yes—
70C2×Dic79⋊C4C2314yes—
71C2×Dic79⋊C4C2314yes—
72C2×Dic79⋊C4C2314yes—
73C2×Dic79⋊C4C2314yes—
74C2×Dic79⋊C4C2314yes—
75C2×C4×Dic79C2314yes—
76C2×C4×Dic79C2311yescharacteristic
77C2×C4×Dic79C2314yes—
78C2×C4×Dic79C2312yes—
79C2×C4×Dic79C2314yes—
80C2×C4×Dic79C2314yes—
81C2×C4×Dic79C2311yescharacteristic
82C2×C4×Dic79C2312yes—
83C2×C4×Dic79C2314yes—
84C2×C4×Dic79C2314yes—
85C79⋊#95C2314yes—
86C79⋊#95C2314yes—
87C79⋊#95C2314yes—
88C79⋊#95C2314yes—
89C79⋊#95C2314yes—
90C79⋊#95C2314yes—
91C79⋊#95C2314yes—
92C79⋊#95C2314yes—
93C79⋊#95C2314yes—
94C79⋊#95C2314yes—
95C79⋊#95C2314yes—
96#125×C79C2×C418yes—
97C2×C4⋊C4×C79C2314yes—
98C2×C4⋊C4×C79C2312yes—
99C2×C4⋊C4×C79C2312yes—
100C2×C4⋊C4×C79C2314yes—
101C2×C4⋊C4×C79C2312yes—
102C2×C42×C79C2314yes—
103C2×C42×C79C2311yescharacteristic
104#95×C79C2314yes—
105#95×C79C2314yes—
106#95×C79C2314yes—
107#95×C79C2314yes—
108C22×Dic79C2411yescharacteristic
109C22×Dic79C2412yes—
110C22×Dic79C2414yes—
111C22×Dic79C2414yes—
112C22×Dic79C2414yes—
113C22×Dic79C2411yescharacteristic
114C4⋊Dic79—42no—
115C4⋊Dic79—44no—
116C4⋊Dic79C22×C418yes—
117C4⋊Dic79C22×C4116yes—
118C4⋊Dic79C22×C418yes—
119Dic79⋊C4—44no—
120Dic79⋊C4—44no—
121Dic79⋊C4—44no—
122Dic79⋊C4—44no—
123Dic79⋊C4C22×C4116yes—
124Dic79⋊C4C22×C4116yes—
125Dic79⋊C4C22×C4116yes—
126Dic79⋊C4C22×C4116yes—
127C4×Dic79—22no—
128C4×Dic79—24no—
129C4×Dic79—28no—
130C4×Dic79—28no—
131C4×Dic79—28no—
132C4×Dic79—41no—
133C4×Dic79—42no—
134C4×Dic79—44no—
135C4×Dic79—44no—
136C4×Dic79C22×C4116yes—
137C22×C4×C79C2414yes—
138C22×C4×C79C2414yes—
139C22×C4×C79C2411yescharacteristic
140C22×C4×C79C2412yes—
141C22×C4×C79C2414yes—
142C4⋊C4×C79—42no—
143C4⋊C4×C79—42no—
144C4⋊C4×C79—44no—
145C4⋊C4×C79C22×C418yes—
146C4⋊C4×C79C22×C4116yes—
147C42×C79—44no—
148C42×C79C22×C414yes—
149C23×C79C2511yescharacteristic
150C2×C4×C79—21no—
151C2×C4×C79—22no—
152C2×C4×C79—24no—
153C2×C4×C79—21no—
154C2×C4×C79—22no—
155C2×C4×C79—24no—
156C2×C4×C79—24no—
157C2×C4×C79—24no—
158C2×C4×C79—24no—
159C2×C4×C79—24no—
160C2×C4×C79—24no—
161C2×C4×C79—24no—
162C2×C4×C79C23×C418yes—
163C2×C4×C79C23×C412yes—
164C2×C4×C79C23×C414yes—
165C2×Dic79—24no—
166C2×Dic79—24no—
167C2×Dic79—24no—
168C2×Dic79—24no—
169C2×Dic79—21no—
170C2×Dic79—22no—
171C2×Dic79—24no—
172C2×Dic79—22no—
173C2×Dic79—22no—
174C2×Dic79—24no—
175C2×Dic79—24no—
176C2×Dic79—22no—
177C2×Dic79C23×C418yes—
178C2×Dic79C23×C418yes—
179C2×Dic792−1+412yes—
180C2×Dic792−1+414yes—
181C22×C79C24×C411yescharacteristic
182C22×C79C2×2−1+411yescharacteristic
183C22×C79C2×2−1+412yes—
184C22×C79#58512yes—
185C22×C79#58511yescharacteristic
186C4×C79—22no—
187C4×C79—24no—
188C4×C79—28no—
189C4×C79—44no—
190C4×C79—44no—
191Dic79—28no—
192Dic79—28no—
193Dic79—41no—
194Dic79—42no—
195Dic79—44no—
196Dic79#56414yescomplemented
197C4×#564—791nomaximal, Sylow
198C2×C79C4×2−1+411yescharacteristic
199C2×C79C4×2−1+412yes—
200C2×C79C2×#56411yescharacteristic
201C2×C79#353111yescharacteristic
202C2×C79#353112yes—
203C2×#564—791no—
204#2382—794no—
205#2382—794no—
206#2382—794no—
207#2382—792no—
208#2382D7911yescharacteristic
209C4×#125—794no—
210C4×#125—794no—
211C4×#125—794no—
212C4×#125—792no—
213C4×#125—791no—
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—792no—
224#389—792no—
225#389—792no—
226#389—794no—
227#389—794no—
228#389—794no—
229#389C2×D7914yes—
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#387C2×D7914yes—
244#387C2×D7914yes—
245#382—794no—
246#382—791no—
247#382—794no—
248#382—794no—
249#382C2×D7912yes—
250C4×C4⋊C4—794no—
251C4×C4⋊C4—792no—
252C4×C4⋊C4—794no—
253C4×C4⋊C4—792no—
254C4×C4⋊C4—792no—
255C4×C4⋊C4—794no—
256C4×C4⋊C4—794no—
257C4×C4⋊C4—794no—
258C4×C4⋊C4—794no—
259C43—791no—
260C43—794no—
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—794no—
273C2×C4⋊C4—794no—
274C2×C4⋊C4—794no—
275C2×C4⋊C4—794no—
276C2×C4⋊C4—792no—
277C2×C4⋊C4—794no—
278C2×C4⋊C4—792no—
279C2×C4⋊C4C22×D7914yes—
280C2×C4⋊C4C22×D7912yes—
281C2×C4⋊C4C22×D7912yes—
282C2×C4⋊C4C22×D7914yes—
283C2×C4⋊C4C22×D7912yes—
284C2×C42—794no—
285C2×C42—794no—
286C2×C42—792no—
287C2×C42—791no—
288C2×C42—794no—
289C2×C42—794no—
290C2×C42—794no—
291C2×C42—794no—
292C2×C42—792no—
293C2×C42—791no—
294C2×C42C22×D7914yes—
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#95C22×D7914yes—
308#95C22×D7914yes—
309#95C22×D7914yes—
310#95C22×D7914yes—
311C22×C4—791no—
312C22×C4—794no—
313C22×C4—794no—
314C22×C4—791no—
315C22×C4—794no—
316C22×C4—792no—
317C22×C4C23×D7914yes—
318C22×C4C23×D7914yes—
319C22×C4C23×D7914yes—
320C22×C4C23×D7912yes—
321C22×C4C23×D7911yescharacteristic
322C4⋊C4—44no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—3164no—
326C4⋊C4—3164no—
327C4⋊C4—3164no—
328C4⋊C4—3164no—
329C4⋊C4—3164no—
330C4⋊C4—3162no—
331C4⋊C4—7916no—
332C4⋊C4—7916no—
333C4⋊C4—7916no—
334C4⋊C4—7916no—
335C4⋊C4—7916no—
336C4⋊C4—798no—
337C4⋊C4—798no—
338C4⋊C4C2×C4×D79116yes—
339C4⋊C4C2×C4×D7918yes—
340C42—44no—
341C42—3162no—
342C42—3161no—
343C42—3164no—
344C42—3164no—
345C42—7916no—
346C42—1582no—
347C42—1588no—
348C42—1584no—
349C42—1588no—
350C42—1588no—
351C42C2×C4×D7914yes—
352C23C24×D7911yescharacteristic
353C2×C4—21no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—792no—
366C2×C4—794no—
367C2×C4—798no—
368C2×C4—798no—
369C2×C4—1581no—
370C2×C4—1584no—
371C2×C4—1582no—
372C2×C4—1582no—
373C2×C4—1584no—
374C2×C4—1582no—
375C2×C4—1582no—
376C2×C4—1584no—
377C2×C4—1584no—
378C2×C4—1584no—
379C2×C4—1584no—
380C2×C4—1584no—
381C2×C4C22×C4×D7918yes—
382C2×C4C22×C4×D7912yes—
383C2×C4C22×C4×D7914yes—
384C22C23×C4×D7911yescharacteristic
385C222−1+4×D7911yescharacteristic
386C222−1+4×D7912yes—
387C22#1909939812yes—
388C22#1909940011yescharacteristic
389C4—22no—
390C4—28no—
391C4—24no—
392C4—44no—
393C4—44no—
394C4—3161no—
395C4—3164no—
396C4—3162no—
397C4—794no—
398C4—1588no—
399C4—1588no—
400C2#2377660911yescharacteristic
401C2#2377661112yes—
402C2#564×D7911yescharacteristic
403C2#2377754411yescharacteristic
404C2#2377754612yes—
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2382C2
socle, prime radical, cosocleC23×C79C25
hypercenter#2382D79
hypocenterC79C4×#564
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
12. C79⋊#564C4semidirect
196. Dic79#564semidirect
214. C79C4×#564semidirect

Maximal subgroups

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

subgroupindex
C2×C79⋊#5642
#237665852
#237665842
#237665832
#237665822
#125×Dic792
#237659592
#237659572
#237659552
C79×#23822
C4×#56479