Finite Group Databasebeta

← #34307968

Subgroups — #34307968

Order 20224.

722 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14579183C211yesmaximal, characteristic
2#23772068C212yesmaximal, complemented
3#23764286C212yesmaximal
4#23764047C214yesmaximal, complemented
5#23763417C212yesmaximal, complemented
6#23763282C212yesmaximal, complemented
7C8×C4⋊Dic79C211yesmaximal, characteristic, complemented
8C79×#1848C211yesmaximal, characteristic, complemented
9C2×#14579183C2211yescharacteristic
10C4×#11929624C2212yes—
11C4×Dic316C411yescharacteristic, complemented
12C4×Dic316C411yescharacteristic, complemented
13C4×#11929613C412yescomplemented
14C4×#11929613C412yescomplemented
15C4×D632C411yescharacteristic, complemented
16C4×D632C411yescharacteristic, complemented
17#19098623—24no—
18#19098619—22no—
19#19098615—22no—
20#19098601C2211yescharacteristic
21C2×C4⋊(C79⋊C8)C2211yescharacteristic
22C2×#14579087C2214yes—
23#19098560C2212yes—
24#19098531C2214yes—
25#19098521C2214yes—
26C2×C8×Dic79C2212yes—
27C4×C4⋊Dic79C2211yescharacteristic
28#19098324C2214yes—
29#19098317C2212yes—
30C2×#108×C79C2212yes—
31C2×#108×C79C2212yes—
32#423×C79C2212yes—
33C2×C4×C8×C79C2211yescharacteristic
34C2×#11929624C2312yes—
35#14579183—22no—
36#14579183—22no—
37C2×Dic316C2×C411yescharacteristic
38C2×#11929613C2×C412yes—
39C2×D632C2×C411yescharacteristic
40C22×C79⋊C8C2312yes—
41C4×Dic158C2×C412yes—
42C4×Dic158C2×C412yes—
43C4×D316C2×C412yes—
44C4×D316C2×C412yes—
45C4×C22⋊D79—22no—
46C4×C22⋊D79—22no—
47#14579120C2312yes—
48#14579118—22no—
49C2×C4⋊Dic79—21no—
50C2×C4×Dic79C2312yes—
51C42×D79—22no—
52#14579095C2×C411yescharacteristic
53#14579095C2×C411yescharacteristic
54#14579093C2×C412yes—
55C4⋊(C79⋊C8)D411yescharacteristic
56C4⋊(C79⋊C8)D411yescharacteristic
57C4⋊(C79⋊C8)D412yes—
58#14579087—44no—
59#14579086C2×C412yes—
60#14579086C2×C412yes—
61#14579083C2×C412yes—
62#14579083C2×C412yes—
63(C2×D79)⋊C8—24no—
64(C2×D79)⋊C8—24no—
65#14579071—24no—
66C8×Dic79—24no—
67C8×Dic79—24no—
68C79⋊#95—21no—
69C2×M16×C79C2314yes—
70C22×C8×C79C2311yescharacteristic
71C22×C8×C79C2311yescharacteristic
72C2×C42×C79C2311yescharacteristic
73#108×C79—24no—
74#108×C79—42no—
75C4⋊C8×C79—22no—
76C4⋊C8×C79—22no—
77C4×C8×C79C2×C411yescharacteristic
78C4×C8×C79C2×C411yescharacteristic
79C4×C8×C79C2×C411yescharacteristic
80C4×C8×C79C2×C411yescharacteristic
81#11929624—22no—
82#11929624—22no—
83#11929624—22no—
84#11929624—22no—
85C2×Dic158C22×C412yes—
86C2×D316C22×C412yes—
87C2×C22⋊D79—22no—
88C22×Dic79—22no—
89C2×C4×D79—22no—
90C2×C4×D79—22no—
91C2×C4×D79—22no—
92Dic316—22no—
93#11929613—24no—
94D632—22no—
95C2×C79⋊C8—22no—
96C2×C79⋊C8—22no—
97C2×C79⋊C8C2×D412yes—
98C2×C79⋊C8C2×D412yes—
99C4⋊Dic79—24no—
100C4⋊Dic79C22×C412yes—
101C4⋊Dic79C22×C412yes—
102Dic79⋊C4—22no—
103Dic79⋊C4—22no—
104C22⋊Dic79—22no—
105(C2×D79)⋊C4—22no—
106(C2×D79)⋊C4—22no—
107C4×Dic79—22no—
108C4×Dic79—22no—
109C4×Dic79—22no—
110C4×Dic79—22no—
111C4×Dic79—22no—
112C22×C4×C79#4111yescharacteristic
113C22×C4×C79#4111yescharacteristic
114C22×C4×C79C2411yescharacteristic
115M16×C79—24no—
116M16×C79—24no—
117C2×C8×C79—24no—
118C2×C8×C79—21no—
119C2×C8×C79—21no—
120C2×C8×C79C22×C411yescharacteristic
121C2×C8×C79C22×C411yescharacteristic
122C2×C8×C79C22×C411yescharacteristic
123C2×C8×C79C22×C411yescharacteristic
124C2×C8×C79#4112yes—
125C2×C8×C79#4112yes—
126C42×C79C22×C411yescharacteristic
127C42×C79C22×C411yescharacteristic
128C42×C79C2×D411yescharacteristic
129C42×C79C2×D411yescharacteristic
130C23×C79C2×#4111yescharacteristic
131C22×D79—22no—
132C2×C4×C79—22no—
133C2×C4×C79—41no—
134C2×C4×C79C4×D411yescharacteristic
135C2×C4×C79C4×D411yescharacteristic
136C2×C4×C79C4×D411yescharacteristic
137C2×C4×C79C4×D411yescharacteristic
138C2×C4×C79C23×C411yescharacteristic
139C2×C4×C79C22×D411yescharacteristic
140C2×C4×C79C2×#4111yescharacteristic
141C2×C4×C79C2×#4111yescharacteristic
142C2×C4×C79H(5,𝔽2)11yescharacteristic
143C2×C4×C792−1+411yescharacteristic
144C22⋊D79—42no—
145C22⋊D79—42no—
146C2×Dic79—24no—
147C2×Dic79—22no—
148C2×Dic79—22no—
149C2×Dic79—22no—
150C2×Dic79—42no—
151C2×Dic79—42no—
152D316—22no—
153D316—22no—
154C4×D79—42no—
155C4×D79—42no—
156C4×D79—44no—
157C4×D79—82no—
158Dic158—22no—
159Dic158—22no—
160C8×C79—21no—
161C8×C79—21no—
162C8×C79—44no—
163C8×C79#11712yes—
164C8×C79#11712yes—
165C79⋊C8—22no—
166C79⋊C8—22no—
167C22×C79—21no—
168C22×C79—21no—
169C22×C79C2×C4×D411yescharacteristic
170C22×C79#55511yescharacteristic
171C22×C79#55611yescharacteristic
172C2×D79—42no—
173C2×D79—42no—
174C2×D79—42no—
175C4×C79—21no—
176C4×C79—21no—
177C4×C79—21no—
178C4×C79#44312yes—
179C4×C79C2×#11711yescharacteristic
180C4×C79#52011yescharacteristic
181C4×C79#54711yescharacteristic
182C4×C79#55011yescharacteristic
183Dic79—44no—
184Dic79—42no—
185Dic79—42no—
186Dic79—42no—
187#22802—791nomaximal, Sylow
188C2×C79—21no—
189C2×C79—21no—
190C2×C79#235411yescharacteristic
191C2×C79C2×#44311yescharacteristic
192C2×C79#295711yescharacteristic
193D79—82no—
194C4×#135—791no—
195#2925—792no—
196#1974—792no—
197#1929—794no—
198#1848D7911yescharacteristic, complemented
199#1806—792no—
200#1772—792no—
201C8×C4⋊C4—791no—
202C79#2280211yescharacteristic, complemented, Sylow
203C2×#135—791no—
204C4×#41—792no—
205C4×Q16—791no—
206C4×Q16—791no—
207C4×SD16—792no—
208C4×SD16—792no—
209C4×D8—791no—
210C4×D8—791no—
211#433—1584no—
212#432—1582no—
213#431—1582no—
214C2×#108C2×D7912yes—
215C2×#108C2×D7912yes—
216#427—791no—
217#423C2×D7912yes—
218C2×C4⋊C8—791no—
219C2×#104—794no—
220#416—792no—
221#408—794no—
222#405—794no—
223C2×C4×C8—792no—
224C2×C4×C8C2×D7911yescharacteristic
225C4×C4⋊C4—791no—
226#339—794no—
227#336—792no—
228C2×#41—792no—
229#135—1582no—
230#135—1582no—
231C2×Q16—791no—
232C2×SD16—792no—
233C2×D8—791no—
234C2×M16C22×D7914yes—
235C22×C8—792no—
236C22×C8C22×D7911yescharacteristic
237C22×C8C22×D7911yescharacteristic
238C4×Q8—792no—
239C4×Q8—792no—
240C4×D4—792no—
241C4×D4—792no—
242C4×D4—1582no—
243C4×D4—1582no—
244#117—792no—
245#117—1582no—
246C2×C4⋊C4—1581no—
247C2×C42—792no—
248C2×C42—1582no—
249C2×C42C22×D7911yescharacteristic
250#108—24no—
251#108—42no—
252#107—791no—
253#107—791no—
254#106—792no—
255C4⋊C8—22no—
256C4⋊C8—22no—
257C4⋊C8—791no—
258C4⋊C8—791no—
259C4⋊C8—792no—
260#104—3164no—
261#103—792no—
262#103—792no—
263#102—792no—
264#102—792no—
265C22⋊C8—1584no—
266C22⋊C8—1584no—
267#97—1584no—
268C4×C8—1584no—
269C4×C8—1584no—
270C4×C8C4×D7911yescharacteristic
271C4×C8C4×D7911yescharacteristic
272C4×C8C4×D7911yescharacteristic
273C4×C8C4×D7911yescharacteristic
274#95—1581no—
275#41—1582no—
276#41—1582no—
277#41—1582no—
278#41—1582no—
279C2×Q8—792no—
280C2×D4—792no—
281C2×D4—1582no—
282C22×C4—1582no—
283C22×C4—1582no—
284C22×C4—1582no—
285C22×C4—1582no—
286C22×C4#1192962511yescharacteristic
287C22×C4#1192962511yescharacteristic
288C22×C4C23×D7911yescharacteristic
289Q16—1582no—
290SD16—1584no—
291D8—1582no—
292M16—24no—
293M16—24no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—24no—
297C2×C8—792no—
298C2×C8—792no—
299C2×C8—1582no—
300C2×C8—1582no—
301C2×C8C2×C4×D7911yescharacteristic
302C2×C8C2×C4×D7911yescharacteristic
303C2×C8C2×C4×D7911yescharacteristic
304C2×C8C2×C4×D7911yescharacteristic
305C2×C8#1192962312yes—
306C2×C8#1192962512yes—
307C4⋊C4—792no—
308C4⋊C4—792no—
309C4⋊C4—1584no—
310C4⋊C4—1582no—
311C4⋊C4—1582no—
312C22⋊C4—1582no—
313C22⋊C4—1582no—
314C22⋊C4—1582no—
315C42—1582no—
316C42—1582no—
317C42—1582no—
318C42—1582no—
319C42—1582no—
320C42C2×C4×D7911yescharacteristic
321C42C2×C4×D7911yescharacteristic
322C42D4×D7911yescharacteristic
323C42D4×D7911yescharacteristic
324C23—1582no—
325C23C2×#1192962511yescharacteristic
326Q8—1582no—
327Q8—1582no—
328D4—3162no—
329D4—3162no—
330D4—1582no—
331D4—1582no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—3162no—
335C2×C4—3162no—
336C2×C4—3164no—
337C2×C4—3162no—
338C2×C4—3162no—
339C2×C4—6322no—
340C2×C4—1584no—
341C2×C4—1582no—
342C2×C4—1582no—
343C2×C4—1582no—
344C2×C4#1457912311yescharacteristic
345C2×C4#1457912311yescharacteristic
346C2×C4#1457912311yescharacteristic
347C2×C4#1457912311yescharacteristic
348C2×C4C22×C4×D7911yescharacteristic
349C2×C4C2×D4×D7911yescharacteristic
350C2×C4C2×#1192962311yescharacteristic
351C2×C4C2×#1192962511yescharacteristic
352C2×C4#1457920611yescharacteristic
353C2×C4#1457920911yescharacteristic
354C8—21no—
355C8—21no—
356C8—44no—
357C8—1582no—
358C8—1582no—
359C8#1457911912yes—
360C8#1457911912yes—
361C22—21no—
362C22—21no—
363C22—3162no—
364C22—3162no—
365C22—3162no—
366C22C2×#1457912311yescharacteristic
367C22#1909927911yescharacteristic
368C22#1909928711yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—3164no—
373C4—3162no—
374C4—3162no—
375C4—3162no—
376C4#1909867912yes—
377C4C2×#1457911911yescharacteristic
378C4#1909904411yescharacteristic
379C4#1909921611yescharacteristic
380C4#1909923311yescharacteristic
381C2—21no—
382C2—21no—
383C2—6322no—
384C2#2376635111yescharacteristic
385C2C2×#1909867911yescharacteristic
386C2#2377231611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1848C2
socleC22×C79C2×C4×D4
prime radicalC2×#14579183C22
cosocleC22×C4×C79C24
hypercenter#1848D79
hypocenterC79#22802
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1848

Complements

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

NH ≅ G/Ntype
2. #23772068C2semidirect
4. #23764047C2semidirect
5. #23763417C2semidirect
6. #23763282C2semidirect
7. C8×C4⋊Dic79C2semidirect
8. C79×#1848C2semidirect
11. C4×Dic316C4semidirect
12. C4×Dic316C4semidirect
13. C4×#11929613C4semidirect
14. C4×#11929613C4semidirect
15. C4×D632C4semidirect
16. C4×D632C4semidirect
198. #1848D79semidirect
202. C79#22802semidirect

Maximal subgroups

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

subgroupindex
C4×#145791832
#237720682
#237642862
#237640472
#237634172
#237632822
C8×C4⋊Dic792
C79×#18482
#2280279