Finite Group Databasebeta

← #23774986

Subgroups — #23774986

Order 10112.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579192C211yesmaximal, characteristic, complemented
2C2×#14579181C211yesmaximal, characteristic, complemented
3#19099234C211yesmaximal, characteristic, complemented
4#19098953C211yesmaximal, characteristic, complemented
5#19098814C211yesmaximal, characteristic, complemented
6#19098794C211yesmaximal, characteristic, complemented
7#19098782C211yesmaximal, characteristic, complemented
8#19098763C211yesmaximal, characteristic, complemented
9#19098723C211yesmaximal, characteristic, complemented
10#19098708C211yesmaximal, characteristic, complemented
11#19098706C211yesmaximal, characteristic, complemented
12#19098702C211yesmaximal, characteristic, complemented
13#19098668C211yesmaximal, characteristic, complemented
14#19098635C211yesmaximal, characteristic, complemented
15#548×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929624C2211yescharacteristic
18#14579192—24no—
19#14579181—24no—
20C2×#11929614C2211yescharacteristic
21C2×#11929614C2211yescharacteristic
22C2×#11929612C2211yescharacteristic
23C2×#11929611C2211yescharacteristic
24C2×#11929611C2211yescharacteristic
25C2×#11929611C2211yescharacteristic
26C2×#11929611C2211yescharacteristic
27C2×#11929609C2211yescharacteristic
28C2×#11929609C2211yescharacteristic
29C2×#11929608C2211yescharacteristic
30C22×C79⋊C8C2211yescharacteristic
31#14579158C2211yescharacteristic
32#14579157—21no—
33#14579135C2211yescharacteristic
34#14579135C2211yescharacteristic
35#14579134—21no—
36#14579134—21no—
37C4×Dic158C2211yescharacteristic
38#14579123—21no—
39#14579092C2211yescharacteristic
40C4⋊(C79⋊C8)C2211yescharacteristic
41#14579085C2211yescharacteristic
42#14579085C2211yescharacteristic
43#14579084C2211yescharacteristic
44#14579082C2211yescharacteristic
45#14579081C2211yescharacteristic
46#14579081C2211yescharacteristic
47C22⋊(C79⋊C8)C2211yescharacteristic
48C22⋊(C79⋊C8)C2211yescharacteristic
49#14579072C2211yescharacteristic
50C2×#41×C79C2211yescharacteristic
51C22×Q8×C79C2211yescharacteristic
52#124×C79—21no—
53#124×C79C2211yescharacteristic
54C22⋊Q8×C79—21no—
55C22⋊Q8×C79C2211yescharacteristic
56#121×C79—21no—
57#121×C79C2211yescharacteristic
58C4×Q8×C79C2211yescharacteristic
59C4×D4×C79—21no—
60C4×D4×C79C2211yescharacteristic
61#11929624—22no—
62#11929624—22no—
63#11929624—41no—
64#11929624—41no—
65C2×Dic158C2311yescharacteristic
66C2×D316—21no—
67C2×D316—21no—
68C2×D316C2311yescharacteristic
69C2×D316C2311yescharacteristic
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76#11929614—22no—
77#11929614D414yescomplemented
78#11929612—22no—
79#11929611—22no—
80#11929611—22no—
81#11929611—22no—
82#11929611—41no—
83#11929609—22no—
84#11929609—41no—
85#11929608—22no—
86C2×C79⋊C8—22no—
87C2×C79⋊C8C2311yescharacteristic
88C2×C79⋊C8C2311yescharacteristic
89C2×C79⋊C8C2311yescharacteristic
90C2×C79⋊C8C2311yescharacteristic
91C4⋊Dic79C2311yescharacteristic
92Dic79⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95C4×Dic79—21no—
96#41×C79—22no—
97#41×C79—41no—
98C2×Q8×C79—21no—
99C2×Q8×C79—22no—
100C2×Q8×C79—41no—
101C2×Q8×C79C2311yescharacteristic
102C2×Q8×C79C2311yescharacteristic
103C2×D4×C79—21no—
104C2×D4×C79—21no—
105C2×D4×C79D411yescharacteristic
106C2×D4×C79C2311yescharacteristic
107C22×C4×C79—21no—
108C22×C4×C79—21no—
109C22×C4×C79C2311yescharacteristic
110C22×C4×C79C2311yescharacteristic
111C4⋊C4×C79—21no—
112C4⋊C4×C79—21no—
113C4⋊C4×C79D411yescharacteristic
114C4⋊C4×C79C2311yescharacteristic
115C22⋊C4×C79—21no—
116C22⋊C4×C79—21no—
117C22⋊C4×C79—21no—
118C22⋊C4×C79—21no—
119C22⋊C4×C79D411yescharacteristic
120C22⋊C4×C79D411yescharacteristic
121C42×C79—21no—
122C42×C79C2311yescharacteristic
123C23×C79—21no—
124C23×C79C2×D411yescharacteristic
125C23×C79C2×D411yescharacteristic
126C22×D79—21no—
127C22×D79—21no—
128Q8×C79—21no—
129Q8×C79—21no—
130Q8×C79—21no—
131Q8×C79—42no—
132Q8×C79C2×D412yes—
133D4×C79—21no—
134D4×C79—21no—
135D4×C79—41no—
136D4×C79—42no—
137D4×C79—42no—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—42no—
146C2×C4×C79—42no—
147C2×C4×C79C2×D411yescharacteristic
148C2×C4×C79C2×D411yescharacteristic
149C2×C4×C79C2×D411yescharacteristic
150C2×C4×C79C2×D411yescharacteristic
151C2×C4×C79C2411yescharacteristic
152C22⋊D79—42no—
153C22⋊D79—42no—
154C22⋊D79—81no—
155C22⋊D79—81no—
156C2×Dic79—21no—
157C2×Dic79—21no—
158D316—21no—
159D316—21no—
160D316—21no—
161D316—21no—
162D316—42no—
163D316—81no—
164C4×D79—42no—
165C4×D79—42no—
166Dic158—21no—
167Dic158C2×D412yes—
168C79⋊C8—21no—
169C79⋊C8—21no—
170C79⋊C8—21no—
171C79⋊C8C2×D412yes—
172C22×C79—21no—
173C22×C79—21no—
174C22×C79—21no—
175C22×C79—21no—
176C22×C79—21no—
177C22×C79—21no—
178C22×C79—41no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79C22×D411yescharacteristic
182C2×D79—41no—
183C2×D79—41no—
184C2×D79—41no—
185C2×D79—41no—
186C2×D79—41no—
187C2×D79—41no—
188C4×C79—21no—
189C4×C79—21no—
190C4×C79—22no—
191C4×C79—21no—
192C4×C79—21no—
193C4×C79—41no—
194C4×C79—41no—
195C4×C79C22×D411yescharacteristic
196C4×C79H(5,𝔽2)11yescharacteristic
197Dic79—22no—
198Dic79—41no—
199C2×C79—41no—
200C2×C79—41no—
201C2×C79—81no—
202C2×C79D4211yescharacteristic
203C2×C79#57511yescharacteristic
204C2×C79#57711yescharacteristic
205D79—81no—
206D79—81no—
207#3271—791nomaximal, Sylow
208C79#327111yescharacteristic, complemented, Sylow
209C2×#137—791no—
210C2×#135—791no—
211#550—791no—
212#548D7911yescharacteristic, complemented
213#496—791no—
214#469—791no—
215#465—791no—
216#464—791no—
217#460—791no—
218#452—791no—
219#449—791no—
220#449—791no—
221#448—791no—
222#441—791no—
223#435—791no—
224C2×#41—791no—
225C2×#41—791no—
226C2×#41C2×D7911yescharacteristic
227C22×Q8C2×D7911yescharacteristic
228#137—1584no—
229#135—1584no—
230C2×Q16—791no—
231C2×Q16—791no—
232C2×SD16—791no—
233C2×SD16—791no—
234C2×SD16—791no—
235C2×SD16—791no—
236C2×SD16—791no—
237C2×D8—791no—
238C2×D8—791no—
239C2×M16—791no—
240C22×C8—791no—
241#127—791no—
242#127—1581no—
243#124—21no—
244#124C2×D7911yescharacteristic
245C22⋊Q8—21no—
246C22⋊Q8C2×D7911yescharacteristic
247#121—21no—
248#121—791no—
249#121—791no—
250#121—1581no—
251#121—1581no—
252#121C2×D7911yescharacteristic
253C4×Q8—791no—
254C4×Q8C2×D7911yescharacteristic
255C4×D4—21no—
256C4×D4—1581no—
257C4×D4C2×D7911yescharacteristic
258#106—791no—
259C4⋊C8—791no—
260#103—791no—
261#103—791no—
262#103—791no—
263#102—791no—
264#102—791no—
265#102—791no—
266C22⋊C8—791no—
267C22⋊C8—791no—
268#97—791no—
269#41—22no—
270#41—41no—
271#41—3161no—
272#41—3161no—
273#41—1582no—
274#41—1582no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—791no—
279C2×Q8C22×D7911yescharacteristic
280C2×Q8C22×D7911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—791no—
284C2×D4—791no—
285C2×D4—1581no—
286C2×D4—1581no—
287C2×D4—1581no—
288C2×D4—1581no—
289C2×D4—1581no—
290C2×D4—1581no—
291C2×D4C22⋊D7911yescharacteristic
292C2×D4C22×D7911yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—1581no—
296C22×C4—1581no—
297C22×C4C22×D7911yescharacteristic
298C22×C4C22×D7911yescharacteristic
299Q16—794no—
300Q16—1582no—
301SD16—3161no—
302SD16—1582no—
303SD16—1582no—
304SD16—1582no—
305SD16—1582no—
306D8—3161no—
307D8—1582no—
308M16—1582no—
309C2×C8—791no—
310C2×C8—791no—
311C2×C8—791no—
312C2×C8—791no—
313C2×C8—1582no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—791no—
317C4⋊C4—1581no—
318C4⋊C4C22⋊D7911yescharacteristic
319C4⋊C4C22×D7911yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—1581no—
325C22⋊C4—1581no—
326C22⋊C4C22⋊D7911yescharacteristic
327C22⋊C4C22⋊D7911yescharacteristic
328C42—21no—
329C42—1581no—
330C42C22×D7911yescharacteristic
331C23—21no—
332C23—1581no—
333C23—1581no—
334C23C2×C22⋊D7911yescharacteristic
335C23C2×C22⋊D7911yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—42no—
340Q8—792no—
341Q8—1581no—
342Q8D4×D7912yes—
343D4—21no—
344D4—21no—
345D4—41no—
346D4—42no—
347D4—42no—
348D4—3162no—
349D4—3162no—
350D4—3162no—
351D4—6321no—
352D4—6321no—
353D4—6321no—
354D4—1581no—
355D4—1581no—
356D4—1581no—
357D4—1581no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—3162no—
368C2×C4—3162no—
369C2×C4—1581no—
370C2×C4—1581no—
371C2×C4C2×C22⋊D7911yescharacteristic
372C2×C4C2×C22⋊D7911yescharacteristic
373C2×C4C2×C22⋊D7911yescharacteristic
374C2×C4C2×C22⋊D7911yescharacteristic
375C2×C4C23×D7911yescharacteristic
376C8—792no—
377C8—1581no—
378C8—1581no—
379C8—1581no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—3161no—
390C22—3161no—
391C22—3161no—
392C22—3161no—
393C22—3161no—
394C22—3161no—
395C22C22×C22⋊D7911yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—3161no—
404C4—1582no—
405C4C2×D4×D7911yescharacteristic
406C4#1457920611yescharacteristic
407C2—41no—
408C2—41no—
409C2—81no—
410C2—6321no—
411C2—6321no—
412C2D4×C22⋊D7911yescharacteristic
413C2#1909936111yescharacteristic
414C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#548×C79C2
socleC22×C79C22×D4
hypercenter#548D79
hypocenterC79#3271
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14579192C2semidirect
2. C2×#14579181C2semidirect
3. #19099234C2semidirect
4. #19098953C2semidirect
5. #19098814C2semidirect
6. #19098794C2semidirect
7. #19098782C2semidirect
8. #19098763C2semidirect
9. #19098723C2semidirect
10. #19098708C2semidirect
11. #19098706C2semidirect
12. #19098702C2semidirect
13. #19098668C2semidirect
14. #19098635C2semidirect
15. #548×C79C2semidirect
77. #11929614D4semidirect
208. C79#3271semidirect
212. #548D79semidirect