Finite Group Databasebeta

← #34192093

Subgroups — #34192093

Order 20224.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098765C211yesmaximal, characteristic
2#23764194C211yesmaximal, characteristic
3#23763397C211yesmaximal, characteristic
4C2×#19098314C211yesmaximal, characteristic, complemented
5C2×#19098309C211yesmaximal, characteristic, complemented
6#23761283C211yesmaximal, characteristic, complemented
7C79×#1990C211yesmaximal, characteristic, complemented
8C22×#11929611—21no—
9C2×C4×D316C2211yescharacteristic
10#19098765—22no—
11#19098765—22no—
12C2×C4⋊(C79⋊C8)C2211yescharacteristic
13C2×C4⋊(C79⋊C8)C2211yescharacteristic
14C2×C4⋊(C79⋊C8)C2211yescharacteristic
15C2×#14579085—21no—
16C2×#14579081—21no—
17C2×(C2×D79)⋊C8—21no—
18C2×(C2×D79)⋊C8—21no—
19#19098325—21no—
20#19098314—22no—
21#19098309—22no—
22C2×C4⋊Q8×C79C2211yescharacteristic
23C2×C4×C8×C79C2211yescharacteristic
24#384×C79C2211yescharacteristic
25#340×C79—21no—
26#340×C79—21no—
27C22×D316D411yescharacteristic
28C22×C4×D79—21no—
29C2×#11929611—24no—
30C2×#11929611—42no—
31C2×#11929611—42no—
32C22×C79⋊C8—21no—
33C22×C79⋊C8—21no—
34C22×C79⋊C8—21no—
35C4×D316—21no—
36C4×D316—21no—
37C4×D316—21no—
38C4×D316—21no—
39C2×C4⋊Dic79D411yescharacteristic
40C2×(C2×D79)⋊C4—21no—
41C4⋊(C79⋊C8)—21no—
42C4⋊(C79⋊C8)—21no—
43C4⋊(C79⋊C8)—21no—
44C4⋊(C79⋊C8)—21no—
45C4⋊(C79⋊C8)—21no—
46C4⋊(C79⋊C8)D412yes—
47#14579085—24no—
48#14579081—42no—
49(C2×D79)⋊C8—42no—
50(C2×D79)⋊C8—42no—
51C22×Q8×C79—21no—
52C22×C8×C79D411yescharacteristic
53C22×C8×C79D411yescharacteristic
54C4⋊Q8×C79—21no—
55C4⋊Q8×C79—21no—
56C4⋊Q8×C79—21no—
57C4⋊Q8×C79D412yes—
58C2×C4⋊C4×C79—21no—
59C2×C4⋊C4×C79—21no—
60C2×C4⋊C4×C79—21no—
61C2×C4⋊C4×C79—21no—
62C2×C4⋊C4×C79—21no—
63C2×C42×C79C2311yescharacteristic
64C4×C8×C79—21no—
65C4×C8×C79—21no—
66C23×D79—21no—
67C2×D316—21no—
68C2×D316—21no—
69C2×D316—21no—
70C2×D316—21no—
71C2×D316—21no—
72C2×D316SD1612yes—
73C22×Dic79—21no—
74C2×C4×D79—41no—
75C2×C4×D79—41no—
76C2×C4×D79—41no—
77C2×C4×D79—41no—
78C2×C4×D79—41no—
79C2×C4×D79—41no—
80#11929611—48no—
81C2×C79⋊C8—22no—
82C2×C79⋊C8—41no—
83C2×C79⋊C8—41no—
84C2×C79⋊C8—41no—
85C2×C79⋊C8—41no—
86C2×C79⋊C8—41no—
87C2×C79⋊C8—41no—
88C2×C79⋊C8—41no—
89C2×C79⋊C8—41no—
90C4⋊Dic79—21no—
91C4⋊Dic79—21no—
92(C2×D79)⋊C4—41no—
93(C2×D79)⋊C4—41no—
94C2×Q8×C79—22no—
95C2×Q8×C79—41no—
96C2×Q8×C79—41no—
97C2×Q8×C79—41no—
98C2×Q8×C79—41no—
99C2×Q8×C79—41no—
100C22×C4×C79—41no—
101C22×C4×C79—41no—
102C22×C4×C79C2×D411yescharacteristic
103C22×C4×C79C2×D411yescharacteristic
104C22×C4×C79#4111yescharacteristic
105C2×C8×C79—21no—
106C2×C8×C79—21no—
107C2×C8×C79—21no—
108C2×C8×C79—21no—
109C2×C8×C79—21no—
110C2×C8×C79SD1612yescomplemented
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—
120C42×C79C2×D411yescharacteristic
121C42×C79C2×D411yescharacteristic
122C42×C79#4111yescharacteristic
123C42×C79#4111yescharacteristic
124C23×C79#12111yescharacteristic
125C22×D79—22no—
126C22×D79—41no—
127C22×D79—41no—
128C22×D79—41no—
129C22×D79—41no—
130C22×D79—41no—
131C22×D79—41no—
132Q8×C79—42no—
133Q8×C79—42no—
134Q8×C79—81no—
135Q8×C79—81no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—42no—
139C2×C4×C79—81no—
140C2×C4×C79—81no—
141C2×C4×C79—81no—
142C2×C4×C79—81no—
143C2×C4×C79—81no—
144C2×C4×C79#12011yescharacteristic
145C2×C4×C79#12111yescharacteristic
146C2×C4×C79#12111yescharacteristic
147C2×C4×C79#12311yescharacteristic
148C2×C4×C79#12311yescharacteristic
149C2×C4×C79#12411yescharacteristic
150C2×C4×C79C2×SD1611yescharacteristic
151C2×C4×C79C2×SD1611yescharacteristic
152C2×C4×C79#13511yescharacteristic
153C2×C4×C79#13511yescharacteristic
154C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C79#13711yescharacteristic
158C2×Dic79—41no—
159C2×Dic79—41no—
160C2×Dic79—41no—
161D316—22no—
162D316—22no—
163D316—41no—
164D316—41no—
165C4×D79—81no—
166C4×D79—81no—
167C4×D79—81no—
168C4×D79—81no—
169C8×C79—22no—
170C8×C79—41no—
171C79⋊C8—42no—
172C79⋊C8—81no—
173C79⋊C8—81no—
174C22×C79#39411yescharacteristic
175C22×C79#46111yescharacteristic
176C22×C79#46311yescharacteristic
177C22×C79#46511yescharacteristic
178C22×C79#46911yescharacteristic
179C22×C79#47111yescharacteristic
180C22×C79#47311yescharacteristic
181C2×D79—42no—
182C2×D79—42no—
183C2×D79—42no—
184C2×D79—81no—
185C2×D79—81no—
186C2×D79—81no—
187C2×D79—81no—
188C4×C79—21no—
189C4×C79—21no—
190C4×C79—82no—
191C4×C79—161no—
192C4×C79#44911yescharacteristic
193C4×C79#45011yescharacteristic
194C4×C79#46011yescharacteristic
195C4×C79#46411yescharacteristic
196C4×C79#46511yescharacteristic
197C4×C79#46811yescharacteristic
198C4×C79#48111yescharacteristic
199C4×C79#48211yescharacteristic
200Dic79—81no—
201#10477—791nomaximal, Sylow
202C2×C79#167111yescharacteristic
203C2×C79#167911yescharacteristic
204C2×C79#169311yescharacteristic
205C2×C79#170111yescharacteristic
206C2×C79#203411yescharacteristic
207C2×C79#205211yescharacteristic
208C2×C79#205511yescharacteristic
209D79—82no—
210C2×#461—791no—
211#1990D7911yescharacteristic, complemented
212#1954—791no—
213#1802—791no—
214C2×#334—791no—
215C2×#332—791no—
216#1296—791no—
217C79#1047711yescharacteristic, complemented, Sylow
218C22×SD16—1581no—
219C2×C4⋊Q8C2×D7911yescharacteristic
220C2×C4×D4—791no—
221#461—1582no—
222#461—1582no—
223C2×C4⋊C8—791no—
224C2×C4⋊C8—791no—
225C2×C4⋊C8—791no—
226C2×#103—1581no—
227C2×#102—1581no—
228C2×C22⋊C8—1581no—
229C2×C22⋊C8—1581no—
230C2×C4×C8C2×D7911yescharacteristic
231#384C2×D7911yescharacteristic
232#340—21no—
233#340—21no—
234#340—1581no—
235#334—1582no—
236#332—1582no—
237C22×Q8—21no—
238C22×D4—791no—
239C23×C4—1581no—
240C2×SD16—3162no—
241C2×SD16—3162no—
242C2×SD16—1584no—
243C22×C8—1581no—
244C22×C8—1581no—
245C22×C8—1581no—
246C22×C8C22⋊D7911yescharacteristic
247C22×C8C22⋊D7911yescharacteristic
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8D31612yes—
252C4×D4—1581no—
253C4×D4—1581no—
254C4×D4—1581no—
255C4×D4—1581no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—791no—
262C2×C22⋊C4—1581no—
263C2×C42C22×D7911yescharacteristic
264C4⋊C8—792no—
265C4⋊C8—1581no—
266C4⋊C8—1581no—
267C4⋊C8—1581no—
268C4⋊C8—1581no—
269C4⋊C8—1581no—
270#103—1584no—
271#102—3162no—
272C22⋊C8—3162no—
273C22⋊C8—3162no—
274C4×C8—21no—
275C4×C8—21no—
276C24—1581no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—792no—
284C2×D4—1581no—
285C2×D4—1581no—
286C2×D4—1581no—
287C2×D4—1581no—
288C2×D4—1581no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—3161no—
292C22×C4—3161no—
293C22×C4—3161no—
294C22×C4—3161no—
295C22×C4—3161no—
296C22×C4—3161no—
297C22×C4—1581no—
298C22×C4D4×D7911yescharacteristic
299C22×C4C2×C22⋊D7911yescharacteristic
300C22×C4#1192962311yescharacteristic
301SD16—3168no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—3161no—
308C2×C8—3161no—
309C2×C8—3161no—
310C2×C8—3161no—
311C2×C8—3161no—
312C2×C8—3161no—
313C2×C8—3161no—
314C2×C8—3161no—
315C2×C8—1582no—
316C2×C8#1192961112yescomplemented
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—81no—
326C4⋊C4—1581no—
327C4⋊C4—1581no—
328C22⋊C4—3161no—
329C22⋊C4—3161no—
330C42D4×D7911yescharacteristic
331C42C2×D31611yescharacteristic
332C42#1192962311yescharacteristic
333C42#1192962411yescharacteristic
334C23—3161no—
335C23—3161no—
336C23—3161no—
337C23—3161no—
338C23—3161no—
339C23—3161no—
340C23—1582no—
341C23#1457913211yescharacteristic
342Q8—42no—
343Q8—42no—
344Q8—81no—
345Q8—81no—
346D4—3161no—
347D4—3161no—
348D4—1582no—
349D4—1582no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—3161no—
359C2×C4—3161no—
360C2×C4—3161no—
361C2×C4—6321no—
362C2×C4—6321no—
363C2×C4—6321no—
364C2×C4—6321no—
365C2×C4#1457913111yescharacteristic
366C2×C4#1457913311yescharacteristic
367C2×C4#1457913511yescharacteristic
368C2×C4#1457914311yescharacteristic
369C2×C4#1457914511yescharacteristic
370C2×C4#1457914711yescharacteristic
371C2×C4SD16×D7911yescharacteristic
372C2×C4C2×#1192961111yescharacteristic
373C2×C4#1457918111yescharacteristic
374C2×C4#1457918211yescharacteristic
375C2×C4#1457918511yescharacteristic
376C2×C4#1457918511yescharacteristic
377C2×C4#1457918611yescharacteristic
378C2×C4#1457919211yescharacteristic
379C8—22no—
380C8—41no—
381C8—3162no—
382C8—6321no—
383C8—6321no—
384C22—3162no—
385C22—3162no—
386C22—3162no—
387C22—6321no—
388C22—6321no—
389C22—6321no—
390C22—6321no—
391C22#1909847911yescharacteristic
392C22#1909876511yescharacteristic
393C22#1909877511yescharacteristic
394C22#1909878911yescharacteristic
395C22#1909881311yescharacteristic
396C22#1909882311yescharacteristic
397C22#1909883511yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—161no—
402C4—6321no—
403C4#1909870911yescharacteristic
404C4#1909871511yescharacteristic
405C4#1909876311yescharacteristic
406C4#1909878511yescharacteristic
407C4#1909879411yescharacteristic
408C4#1909881111yescharacteristic
409C4#1909888011yescharacteristic
410C4#1909888611yescharacteristic
411C2—6322no—
412C2#2376277211yescharacteristic
413C2#2376282011yescharacteristic
414C2#2376291011yescharacteristic
415C2#2376295811yescharacteristic
416C2#2376458811yescharacteristic
417C2#2376470011yescharacteristic
418C2#2376471511yescharacteristic
subgroupG/H
centerC23#14579132
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC79×#1990C2
socleC23×C79#121
prime radicalC22×D316D4
hypercenter#1990D79
hypocenterC79#10477
LCSG ▷ C2×C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. C2×#19098314C2semidirect
5. C2×#19098309C2semidirect
6. #23761283C2semidirect
7. C79×#1990C2semidirect
110. C2×C8×C79SD16semidirect
211. #1990D79semidirect
217. C79#10477semidirect
316. C2×C8#11929611semidirect

Maximal subgroups

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

subgroupindex
C2×#190987652
#237641942
#237633972
C2×#190983142
C2×#190983092
#237612832
C79×#19902
#1047779