Finite Group Databasebeta

← #34187151

Subgroups — #34187151

Order 20224.

534 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11929611C211yesmaximal, characteristic
2#23764337C211yesmaximal, characteristic, complemented
3#23764193C211yesmaximal, characteristic
4C2×#19098313C211yesmaximal, characteristic, complemented
5C2×#19098292C211yesmaximal, characteristic
6C2×#19098285C211yesmaximal, characteristic, complemented
7C2×Q8⋊C8×C79C211yesmaximal, characteristic, complemented
8C22×#11929611C411yescharacteristic
9C2×C4×D316C2211yescharacteristic
10C4×#11929611—22no—
11C4×#11929611—22no—
12C2×#14579092C411yescharacteristic
13C2×C4⋊(C79⋊C8)C2211yescharacteristic
14C2×#14579085C411yescharacteristic
15C2×#14579081C411yescharacteristic
16C2×(C2×D79)⋊C8—22no—
17C2×C4×C79⋊C8C2211yescharacteristic
18C2×C4×C79⋊C8C2211yescharacteristic
19#19098318—22no—
20#19098313—22no—
21#19098292—22no—
22#19098285—22no—
23C2×C4×Q8×C79C2211yescharacteristic
24C2×C4⋊C8×C79C2211yescharacteristic
25C2×C4×C8×C79C2211yescharacteristic
26Q8⋊C8×C79—22no—
27C22×D316C2×C411yescharacteristic
28C22×C4×D79—21no—
29C2×#11929611—22no—
30C2×#11929611—22no—
31C2×#11929611—22no—
32C22×C79⋊C8—21no—
33C22×C79⋊C8C2×C411yescharacteristic
34C22×C79⋊C8C2×C411yescharacteristic
35C22×C79⋊C8D412yes—
36C4×D316—21no—
37C4×D316—21no—
38C4×D316—21no—
39C4×D316—21no—
40C2×C4⋊Dic79C2×C411yescharacteristic
41C2×(C2×D79)⋊C4—21no—
42#14579092—22no—
43C4⋊(C79⋊C8)—21no—
44C4⋊(C79⋊C8)—21no—
45#14579085—22no—
46#14579081—22no—
47(C2×D79)⋊C8—44no—
48C4×C79⋊C8—21no—
49C4×C79⋊C8—21no—
50C4×C79⋊C8D412yes—
51C4×C79⋊C8D412yes—
52C22×Q8×C79C2×C411yescharacteristic
53C22×C8×C79—21no—
54C22×C8×C79—21no—
55C4×Q8×C79—21no—
56C4×Q8×C79—21no—
57C4×Q8×C79—21no—
58C4×Q8×C79—21no—
59C2×C4⋊C4×C79—21no—
60C2×C4⋊C4×C79C2×C411yescharacteristic
61C2×C42×C79—21no—
62C2×C42×C79C2311yescharacteristic
63C4⋊C8×C79—21no—
64C4⋊C8×C79—21no—
65C4×C8×C79—21no—
66C4×C8×C79D412yes—
67C23×D79—21no—
68C2×D316—21no—
69C2×D316—21no—
70C2×D316—21no—
71C2×D316—21no—
72C2×D316—21no—
73C2×D316M1612yes—
74C22×Dic79—21no—
75C2×C4×D79—41no—
76C2×C4×D79—41no—
77C2×C4×D79—42no—
78C2×C4×D79—42no—
79#11929611—28no—
80C2×C79⋊C8—22no—
81C2×C79⋊C8—21no—
82C2×C79⋊C8—21no—
83C2×C79⋊C8—21no—
84C2×C79⋊C8—21no—
85C2×C79⋊C8—22no—
86C2×C79⋊C8—41no—
87C2×C79⋊C8—42no—
88C2×C79⋊C8C22⋊C412yes—
89C2×C79⋊C8C22⋊C412yes—
90C2×C79⋊C8SD1614yescomplemented
91C4⋊Dic79—21no—
92C4⋊Dic79—21no—
93(C2×D79)⋊C4—41no—
94(C2×D79)⋊C4—41no—
95C2×Q8×C79—21no—
96C2×Q8×C79—21no—
97C2×Q8×C79—21no—
98C2×Q8×C79—21no—
99C2×Q8×C79—21no—
100C2×Q8×C79M1612yes—
101C22×C4×C79—21no—
102C22×C4×C79—21no—
103C22×C4×C79C22×C411yescharacteristic
104C22×C4×C79C2×D411yescharacteristic
105C22×C4×C79#4111yescharacteristic
106C2×C8×C79—22no—
107C2×C8×C79—42no—
108C2×C8×C79—41no—
109C2×C8×C79—42no—
110C4⋊C4×C79—21no—
111C4⋊C4×C79—21no—
112C4⋊C4×C79—41no—
113C4⋊C4×C79—41no—
114C42×C79—41no—
115C42×C79—41no—
116C42×C79C2×D411yescharacteristic
117C42×C79C2×D411yescharacteristic
118C42×C79C2×D411yescharacteristic
119C42×C79#4111yescharacteristic
120C23×C79C4×D411yescharacteristic
121C22×D79—22no—
122C22×D79—41no—
123C22×D79—41no—
124C22×D79—42no—
125C22×D79—42no—
126Q8×C79—22no—
127Q8×C79—22no—
128Q8×C79—41no—
129Q8×C79—41no—
130C2×C4×C79—22no—
131C2×C4×C79—22no—
132C2×C4×C79—41no—
133C2×C4×C79—41no—
134C2×C4×C79—41no—
135C2×C4×C79—42no—
136C2×C4×C79C2×C22⋊C411yescharacteristic
137C2×C4×C79C4×D411yescharacteristic
138C2×C4×C79#12111yescharacteristic
139C2×C4×C79#12111yescharacteristic
140C2×C4×C79#12411yescharacteristic
141C2×C4×C79#12711yescharacteristic
142C2×C4×C79C2×M1611yescharacteristic
143C2×C4×C79C2×M1611yescharacteristic
144C2×C4×C79#13111yescharacteristic
145C2×C4×C79#13111yescharacteristic
146C2×C4×C79C2×SD1612yes—
147C2×C4×C79#13512yes—
148C2×Dic79—41no—
149C2×Dic79—42no—
150D316—22no—
151D316—22no—
152D316—41no—
153D316—41no—
154C4×D79—82no—
155C4×D79—81no—
156C4×D79—81no—
157C8×C79—42no—
158C8×C79—81no—
159C79⋊C8—22no—
160C79⋊C8—22no—
161C79⋊C8—24no—
162C79⋊C8—81no—
163C22×C79#39011yescharacteristic
164C22×C79#43511yescharacteristic
165C22×C79#43511yescharacteristic
166C22×C79C4×SD1612yes—
167C22×C79#44412yes—
168C2×D79—44no—
169C2×D79—42no—
170C2×D79—82no—
171C2×D79—81no—
172C2×D79—81no—
173C4×C79—21no—
174C4×C79—21no—
175C4×C79—42no—
176C4×C79—81no—
177C4×C79#40711yescharacteristic
178C4×C79#40811yescharacteristic
179C4×C79#43511yescharacteristic
180C4×C79#43511yescharacteristic
181C4×C79#46512yes—
182C4×C79#49211yescharacteristic
183C4×C79#49511yescharacteristic
184Dic79—81no—
185#9661—791nomaximal, Sylow
186C2×C79#158212yes—
187C2×C79#158312yes—
188C2×C79#195511yescharacteristic
189C2×C79#196811yescharacteristic
190C2×C79#197511yescharacteristic
191D79—82no—
192C2×C4×SD16—791no—
193#1984—791no—
194#1954—791no—
195C2×#334—791no—
196C2×Q8⋊C8D7911yescharacteristic, complemented
197C2×D4⋊C8—791no—
198C2×#322—791no—
199C79#966111yescharacteristic, complemented, Sylow
200C22×SD16—791no—
201C2×C4×Q8C2×D7911yescharacteristic
202C2×C4×D4—791no—
203C4×SD16—1582no—
204C4×SD16—1582no—
205C2×#106—791no—
206C2×C4⋊C8—791no—
207C2×C4⋊C8C2×D7911yescharacteristic
208C2×#103—791no—
209C2×#102—791no—
210C2×C22⋊C8—1582no—
211C2×C4×C8—791no—
212C2×C4×C8—791no—
213C2×C4×C8C2×D7911yescharacteristic
214#336—1582no—
215#334—1582no—
216Q8⋊C8—22no—
217D4⋊C8—1582no—
218#322—1582no—
219C22×Q8C4×D7911yescharacteristic
220C22×D4—791no—
221C23×C4—1581no—
222C2×SD16—1582no—
223C2×SD16—1582no—
224C2×SD16—1582no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—791no—
228C22×C8—791no—
229C22×C8—792no—
230C22×C8—1581no—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—1581no—
236C4×D4—1581no—
237C4×D4—1581no—
238C4×D4—1581no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—791no—
241C2×C4⋊C4C4×D7911yescharacteristic
242C2×C22⋊C4—1581no—
243C2×C42—21no—
244C2×C42C22×D7911yescharacteristic
245#106—1582no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—1581no—
249C4⋊C8—1581no—
250#103—1582no—
251#102—1582no—
252C22⋊C8—3164no—
253C4×C8—21no—
254C4×C8—792no—
255C4×C8—792no—
256C4×C8—1581no—
257C4×C8—1581no—
258C4×C8C22⋊D7912yes—
259C24—1581no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8#1192960712yes—
266C2×D4—792no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1581no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—3161no—
275C22×C4—3161no—
276C22×C4—3162no—
277C22×C4—3162no—
278C22×C4—1581no—
279C22×C4C2×C4×D7911yescharacteristic
280C22×C4D4×D7911yescharacteristic
281C22×C4#1192962311yescharacteristic
282SD16—1588no—
283C2×C8—22no—
284C2×C8—42no—
285C2×C8—41no—
286C2×C8—42no—
287C2×C8—3161no—
288C2×C8—3162no—
289C2×C8—792no—
290C2×C8—792no—
291C2×C8—794no—
292C2×C8—1582no—
293C2×C8—1581no—
294C2×C8—1581no—
295C2×C8—1581no—
296C2×C8—1581no—
297C2×C8—1582no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—1581no—
303C4⋊C4—1581no—
304C22⋊C4—3161no—
305C22⋊C4—3161no—
306C42—41no—
307C42—41no—
308C42D4×D7911yescharacteristic
309C42D4×D7911yescharacteristic
310C42C2×C22⋊D7911yescharacteristic
311C42#1192962411yescharacteristic
312C23—3161no—
313C23—3162no—
314C23—3162no—
315C23—3161no—
316C23—1582no—
317C23(C22⋊D79)⋊C411yescharacteristic
318Q8—22no—
319Q8—22no—
320Q8—41no—
321Q8—41no—
322D4—3161no—
323D4—3161no—
324D4—1582no—
325D4—1582no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—3162no—
333C2×C4—3161no—
334C2×C4—6321no—
335C2×C4—6321no—
336C2×C4—6322no—
337C2×C4C22⋊C4×D7911yescharacteristic
338C2×C4C4×C22⋊D7911yescharacteristic
339C2×C4#1457913311yescharacteristic
340C2×C4#1457913411yescharacteristic
341C2×C4#1457914711yescharacteristic
342C2×C4#1457915711yescharacteristic
343C2×C4M16×D7911yescharacteristic
344C2×C4C2×#1192960711yescharacteristic
345C2×C4#1457916711yescharacteristic
346C2×C4#1457916911yescharacteristic
347C2×C4SD16×D7912yes—
348C2×C4#1457918412yes—
349C8—42no—
350C8—81no—
351C8—6321no—
352C8—1582no—
353C8—1582no—
354C8—1584no—
355C22—3164no—
356C22—3162no—
357C22—6321no—
358C22—6322no—
359C22—6321no—
360C22#1909846311yescharacteristic
361C22#1909863111yescharacteristic
362C22#1909863711yescharacteristic
363C22#1909864812yes—
364C22#1909868212yes—
365C4—21no—
366C4—21no—
367C4—42no—
368C4—81no—
369C4—6321no—
370C4#1909852511yescharacteristic
371C4#1909852811yescharacteristic
372C4#1909863211yescharacteristic
373C4#1909863411yescharacteristic
374C4#1909879512yes—
375C4#1909893411yescharacteristic
376C4#1909894811yescharacteristic
377C2—6322no—
378C2#2376223912yes—
379C2#2376224012yes—
380C2#2376419611yescharacteristic
381C2#2376425111yescharacteristic
382C2#2376429011yescharacteristic
subgroupG/H
centerC22×C4D4×D79
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC2×Q8⋊C8×C79C2
socleC23×C79C4×D4
prime radicalC22×D316C2×C4
cosocleC2×C42×C79C23
hypercenterC2×Q8⋊C8D79
hypocenterC79#9661
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #23764337C2semidirect
4. C2×#19098313C2semidirect
6. C2×#19098285C2semidirect
7. C2×Q8⋊C8×C79C2semidirect
90. C2×C79⋊C8SD16semidirect
196. C2×Q8⋊C8D79semidirect
199. C79#9661semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#119296112
#237643372
#237641932
C2×#190983132
C2×#190982922
C2×#190982852
C2×Q8⋊C8×C792
#966179