Finite Group Databasebeta

← #34190891

Subgroups — #34190891

Order 20224.

510 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098966C211yesmaximal, characteristic
2C2×#19098858C211yesmaximal, characteristic
3#23764337C211yesmaximal, characteristic
4C2×#19098312C211yesmaximal, characteristic
5C2×#19098311C211yesmaximal, characteristic
6#23761234C211yesmaximal, characteristic
7C2×#477×C79C211yesmaximal, characteristic
8C2×#14579161C2211yescharacteristic
9#19098966—22no—
10#19098966—22no—
11#19098858—22no—
12#19098858—22no—
13C2×#14579094—22no—
14C2×#14579094—21no—
15C2×C4⋊(C79⋊C8)C2211yescharacteristic
16C2×C4⋊(C79⋊C8)C2211yescharacteristic
17C2×#14579085—21no—
18C2×C4×C79⋊C8C2211yescharacteristic
19#19098318—22no—
20#19098312—22no—
21#19098311—22no—
22C2×C4⋊Q8×C79C2211yescharacteristic
23C2×C4×Q8×C79C2211yescharacteristic
24#477×C79—22no—
25#477×C79—22no—
26C2×#107×C79—21no—
27C2×C4⋊C8×C79C2211yescharacteristic
28C2×#103×C79—21no—
29C22×Dic158—21no—
30C22×C79⋊C8—21no—
31C22×C79⋊C8—21no—
32C22×C79⋊C8D412yes—
33#14579161—21no—
34#14579161—21no—
35#14579161—21no—
36#14579161D412yes—
37C2×C4⋊Dic79—21no—
38C2×C4⋊Dic79—21no—
39#14579094—28no—
40#14579094—24no—
41C4⋊(C79⋊C8)—21no—
42C4⋊(C79⋊C8)—21no—
43C4⋊(C79⋊C8)—21no—
44C4⋊(C79⋊C8)D412yes—
45#14579085—24no—
46C4×C79⋊C8—21no—
47C4×C79⋊C8—21no—
48C22×Q8×C79—21no—
49C22×Q8×C79D411yescharacteristic
50C22×C8×C79—21no—
51C4⋊Q8×C79—21no—
52C4⋊Q8×C79—21no—
53C4⋊Q8×C79—21no—
54C4⋊Q8×C79D412yes—
55C4×Q8×C79—21no—
56C4×Q8×C79—21no—
57C4×Q8×C79—21no—
58C4×Q8×C79—21no—
59C2×C4⋊C4×C79—21no—
60C2×C4⋊C4×C79—21no—
61C2×C4⋊C4×C79—21no—
62C2×C4⋊C4×C79D411yescharacteristic
63C2×C42×C79—21no—
64C2×C42×C79C2311yescharacteristic
65#107×C79—24no—
66C4⋊C8×C79—21no—
67C4⋊C8×C79D412yes—
68#103×C79—24no—
69C2×Dic158—22no—
70C2×Dic158—41no—
71C2×Dic158—82no—
72C22×Dic79—41no—
73C2×C79⋊C8—22no—
74C2×C79⋊C8—22no—
75C2×C79⋊C8—22no—
76C2×C79⋊C8—41no—
77C2×C79⋊C8—41no—
78C2×C79⋊C8—41no—
79C2×C79⋊C8—42no—
80C2×C79⋊C8Q1614yes—
81C4⋊Dic79—22no—
82C4⋊Dic79—22no—
83C4⋊Dic79—41no—
84C4⋊Dic79—41no—
85C2×Q8×C79—21no—
86C2×Q8×C79—21no—
87C2×Q8×C79—21no—
88C2×Q8×C79—22no—
89C2×Q8×C79—21no—
90C2×Q8×C79—21no—
91C2×Q8×C79—41no—
92C2×Q8×C79—82no—
93C2×Q8×C79Q1612yes—
94C22×C4×C79—21no—
95C22×C4×C79—21no—
96C22×C4×C79—41no—
97C22×C4×C79C2×D411yescharacteristic
98C22×C4×C79C2×D411yescharacteristic
99C22×C4×C79#4111yescharacteristic
100C2×C8×C79—22no—
101C2×C8×C79—41no—
102C2×C8×C79—41no—
103C4⋊C4×C79—22no—
104C4⋊C4×C79—21no—
105C4⋊C4×C79—22no—
106C4⋊C4×C79—21no—
107C4⋊C4×C79—41no—
108C4⋊C4×C79—41no—
109C4⋊C4×C79—41no—
110C4⋊C4×C79—41no—
111C42×C79—41no—
112C42×C79—41no—
113C42×C79C2×D411yescharacteristic
114C42×C79C2×D411yescharacteristic
115C42×C79C2×D411yescharacteristic
116C42×C79C2×D411yescharacteristic
117C23×C79#12111yescharacteristic
118Q8×C79—22no—
119Q8×C79—22no—
120Q8×C79—41no—
121Q8×C79—41no—
122Q8×C79—82no—
123Q8×C79—82no—
124C2×C4×C79—22no—
125C2×C4×C79—22no—
126C2×C4×C79—41no—
127C2×C4×C79—41no—
128C2×C4×C79—41no—
129C2×C4×C79—42no—
130C2×C4×C79—42no—
131C2×C4×C79—82no—
132C2×C4×C79#12011yescharacteristic
133C2×C4×C79#12011yescharacteristic
134C2×C4×C79#12011yescharacteristic
135C2×C4×C79#12111yescharacteristic
136C2×C4×C79#12111yescharacteristic
137C2×C4×C79#12711yescharacteristic
138C2×C4×C79C2×Q1612yes—
139C2×C4×C79C2×Q1611yescharacteristic
140C2×C4×C79#13511yescharacteristic
141C2×C4×C79#13711yescharacteristic
142C2×C4×C79#13711yescharacteristic
143C2×C4×C79#13712yes—
144C2×Dic79—42no—
145C2×Dic79—82no—
146Dic158—82no—
147Dic158—82no—
148C8×C79—42no—
149C79⋊C8—24no—
150C79⋊C8—42no—
151C79⋊C8—81no—
152C22×C79#39211yescharacteristic
153C22×C79#46212yes—
154C22×C79#46711yescharacteristic
155C22×C79#47011yescharacteristic
156C22×C79#47212yes—
157C4×C79—21no—
158C4×C79—21no—
159C4×C79—42no—
160C4×C79—81no—
161C4×C79—82no—
162C4×C79#45112yes—
163C4×C79#45111yescharacteristic
164C4×C79#45111yescharacteristic
165C4×C79#45211yescharacteristic
166C4×C79#45211yescharacteristic
167C4×C79#49411yescharacteristic
168C4×C79#49711yescharacteristic
169Dic79—82no—
170#10279—791nomaximal, Sylow
171C2×C79#167612yes—
172C2×C79#169612yes—
173C2×C79#200111yescharacteristic
174C2×C79#201611yescharacteristic
175C2×C79#201811yescharacteristic
176C2×#500—791no—
177C2×#477—791no—
178C2×#477D7911yescharacteristic
179#1984—791no—
180C2×#333—791no—
181C2×#333—791no—
182#1277—791no—
183C79#1027911yescharacteristic, complemented, Sylow
184C2×C4⋊Q8—791no—
185C2×C4⋊Q8C2×D7911yescharacteristic
186C2×C4×Q8C2×D7911yescharacteristic
187#500—1582no—
188#500—1582no—
189#477—22no—
190#477—22no—
191#477—1582no—
192#477—1582no—
193C2×#107—21no—
194C2×#107—1582no—
195C2×#107—1581no—
196C2×C4⋊C8—791no—
197C2×C4⋊C8—791no—
198C2×C4⋊C8C2×D7911yescharacteristic
199C2×#103—21no—
200C2×#103—1581no—
201C2×C4×C8—791no—
202#336—1582no—
203#333—1582no—
204#333—1582no—
205C22×Q8—21no—
206C22×Q8—1581no—
207C22×Q8C22⋊D7911yescharacteristic
208C22×C8—21no—
209C22×C8—792no—
210C22×C8—1581no—
211C22×C8—1581no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—792no—
216C4⋊Q8—1581no—
217C4⋊Q8—1581no—
218C4⋊Q8—1581no—
219C4⋊Q8C22⋊D7912yes—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—1581no—
228C2×C4⋊C4—1581no—
229C2×C4⋊C4C22⋊D7911yescharacteristic
230C2×C42—21no—
231C2×C42C22×D7911yescharacteristic
232#107—24no—
233#107—1584no—
234#107—1588no—
235C4⋊C8—21no—
236C4⋊C8—792no—
237C4⋊C8—1581no—
238C4⋊C8—1581no—
239C4⋊C8—1581no—
240C4⋊C8C22⋊D7912yes—
241#103—24no—
242#103—1584no—
243C4×C8—1581no—
244C4×C8—1581no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—22no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—41no—
252C2×Q8—82no—
253C2×Q8—3161no—
254C2×Q8—6322no—
255C2×Q8—1582no—
256C2×Q8#1192961412yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—3161no—
261C22×C4D4×D7911yescharacteristic
262C22×C4C2×C22⋊D7911yescharacteristic
263C22×C4#1192962311yescharacteristic
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—3161no—
268C2×C8—3161no—
269C2×C8—3161no—
270C2×C8—3162no—
271C2×C8—794no—
272C2×C8—1582no—
273C2×C8—1582no—
274C2×C8—1582no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—3161no—
284C4⋊C4—3161no—
285C4⋊C4—1582no—
286C4⋊C4—1582no—
287C42—41no—
288C42—41no—
289C42D4×D7911yescharacteristic
290C42D4×D7911yescharacteristic
291C42C2×C22⋊D7911yescharacteristic
292C42C2×C22⋊D7911yescharacteristic
293C23#1457913311yescharacteristic
294Q8—22no—
295Q8—22no—
296Q8—41no—
297Q8—41no—
298Q8—82no—
299Q8—82no—
300Q8—6322no—
301Q8—6322no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4—3162no—
311C2×C4—6322no—
312C2×C4#1457912911yescharacteristic
313C2×C4#1457912911yescharacteristic
314C2×C4#1457913011yescharacteristic
315C2×C4#1457913211yescharacteristic
316C2×C4#1457913311yescharacteristic
317C2×C4#1457915711yescharacteristic
318C2×C4Q16×D7912yes—
319C2×C4C2×#1192961411yescharacteristic
320C2×C4#1457918111yescharacteristic
321C2×C4#1457919111yescharacteristic
322C2×C4#1457919211yescharacteristic
323C2×C4#1457919312yes—
324C8—42no—
325C8—3162no—
326C8—6321no—
327C8—1584no—
328C22#1909847111yescharacteristic
329C22#1909877112yes—
330C22#1909880211yescharacteristic
331C22#1909881911yescharacteristic
332C22#1909883112yes—
333C4—21no—
334C4—21no—
335C4—42no—
336C4—81no—
337C4—82no—
338C4—6322no—
339C4#1909871712yes—
340C4#1909871811yescharacteristic
341C4#1909871911yescharacteristic
342C4#1909872311yescharacteristic
343C4#1909872511yescharacteristic
344C4#1909894111yescharacteristic
345C4#1909895611yescharacteristic
346C2#2376280212yes—
347C2#2376292612yes—
348C2#2376440811yescharacteristic
349C2#2376449811yescharacteristic
350C2#2376450611yescharacteristic
subgroupG/H
centerC23#14579133
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC2×#477×C79C2
socle, prime radicalC23×C79#121
hypercenterC2×#477D79
hypocenterC79#10279
LCSG ▷ C2×C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
183. C79#10279semidirect

Maximal subgroups

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

subgroupindex
C2×#190989662
C2×#190988582
#237643372
C2×#190983122
C2×#190983112
#237612342
C2×#477×C792
#1027979