Finite Group Databasebeta

← #23775053

Subgroups — #23775053

Order 10112.

476 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579192C211yesmaximal, characteristic, complemented
2C2×#14579191C211yesmaximal, characteristic, complemented
3#19099222C211yesmaximal, characteristic, complemented
4#19098945C211yesmaximal, characteristic, complemented
5#19098811C211yesmaximal, characteristic, complemented
6#19098807C211yesmaximal, characteristic, complemented
7#19098785C211yesmaximal, characteristic, complemented
8#19098782C211yesmaximal, characteristic, complemented
9#19098719C211yesmaximal, characteristic, complemented
10#19098718C211yesmaximal, characteristic, complemented
11#19098708C211yesmaximal, characteristic, complemented
12#19098706C211yesmaximal, characteristic, complemented
13C4×#11929614C211yesmaximal, characteristic, complemented
14#19098641C211yesmaximal, characteristic, complemented
15#548×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18#14579192—24no—
19#14579191—24no—
20C2×#11929614C2211yescharacteristic
21C2×#11929614C2211yescharacteristic
22C2×#11929614C2211yescharacteristic
23C2×#11929614C2211yescharacteristic
24C2×#11929612C2211yescharacteristic
25C2×#11929612C2211yescharacteristic
26C2×#11929611C2211yescharacteristic
27C2×#11929611C2211yescharacteristic
28C2×#11929609C2211yescharacteristic
29C2×#11929608C2211yescharacteristic
30C2×#11929608C2211yescharacteristic
31#14579149C2211yescharacteristic
32#14579147—21no—
33#14579140C2211yescharacteristic
34#14579139—21no—
35#14579135C2211yescharacteristic
36#14579133—21no—
37C4×Dic158C2211yescharacteristic
38(C22⋊D79)⋊C4—21no—
39#14579094C2211yescharacteristic
40C4⋊(C79⋊C8)C2211yescharacteristic
41#14579085C2211yescharacteristic
42#14579085C2211yescharacteristic
43#14579084C2211yescharacteristic
44#14579084C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579081C2211yescharacteristic
47C22⋊(C79⋊C8)C2211yescharacteristic
48C22⋊(C79⋊C8)C2211yescharacteristic
49C4×C79⋊C8C2211yescharacteristic
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—41no—
63C2×Dic158—22no—
64C2×Dic158—21no—
65C2×Dic158—41no—
66C2×Dic158C2311yescharacteristic
67C2×Dic158C2311yescharacteristic
68C2×D316C2311yescharacteristic
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C22×Dic79—21no—
72C2×C4×D79—21no—
73#11929614—22no—
74#11929614—22no—
75#11929614—41no—
76#11929614D414yescomplemented
77#11929612—22no—
78#11929612—22no—
79#11929611—22no—
80#11929611—22no—
81#11929609—41no—
82#11929608—22no—
83#11929608—22no—
84C2×C79⋊C8C2311yescharacteristic
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87C2×C79⋊C8C2311yescharacteristic
88C4⋊Dic79C2311yescharacteristic
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊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—
127Q8×C79—21no—
128Q8×C79—21no—
129Q8×C79—21no—
130Q8×C79—42no—
131Q8×C79C2×D412yes—
132D4×C79—21no—
133D4×C79—21no—
134D4×C79—41no—
135D4×C79—42no—
136D4×C79—42no—
137C2×C4×C79—21no—
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—42no—
145C2×C4×C79—42no—
146C2×C4×C79C2×D411yescharacteristic
147C2×C4×C79C2×D411yescharacteristic
148C2×C4×C79C2×D411yescharacteristic
149C2×C4×C79C2×D411yescharacteristic
150C2×C4×C79C2411yescharacteristic
151C22⋊D79—42no—
152C22⋊D79—42no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—21no—
156C2×Dic79—42no—
157D316—21no—
158D316—21no—
159C4×D79—42no—
160Dic158—21no—
161Dic158—21no—
162Dic158—21no—
163Dic158—42no—
164Dic158C2×D412yes—
165C79⋊C8—21no—
166C79⋊C8—21no—
167C79⋊C8—21no—
168C79⋊C8C2×D412yes—
169C22×C79—21no—
170C22×C79—21no—
171C22×C79—21no—
172C22×C79—21no—
173C22×C79—21no—
174C22×C79—21no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79—41no—
178C22×C79C22×D411yescharacteristic
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—41no—
182C4×C79—21no—
183C4×C79—21no—
184C4×C79—22no—
185C4×C79—21no—
186C4×C79—21no—
187C4×C79—41no—
188C4×C79—41no—
189C4×C79C22×D411yescharacteristic
190C4×C79H(5,𝔽2)11yescharacteristic
191Dic79—22no—
192Dic79—41no—
193Dic79—41no—
194C2×C79—41no—
195C2×C79—41no—
196C2×C79—81no—
197C2×C79D4211yescharacteristic
198C2×C79#57511yescharacteristic
199C2×C79#57811yescharacteristic
200D79—81no—
201#3277—791nomaximal, Sylow
202C79#327711yescharacteristic, complemented, Sylow
203C2×#137—791no—
204C2×#137—791no—
205#548—791no—
206#548D7911yescharacteristic, complemented
207#495—791no—
208#468—791no—
209#468—791no—
210#464—791no—
211#464—791no—
212#451—791no—
213#451—791no—
214#449—791no—
215#449—791no—
216C4×Q16—791no—
217#436—791no—
218C2×#41—791no—
219C2×#41C2×D7911yescharacteristic
220C22×Q8—791no—
221C22×Q8C2×D7911yescharacteristic
222#137—1584no—
223#137—1584no—
224C2×Q16—791no—
225C2×Q16—791no—
226C2×Q16—791no—
227C2×Q16—791no—
228C2×SD16—791no—
229C2×SD16—791no—
230C2×SD16—791no—
231C2×SD16—791no—
232C2×D8—791no—
233C2×M16—791no—
234C2×M16—791no—
235#124—21no—
236#124—791no—
237#124—1581no—
238#124C2×D7911yescharacteristic
239C22⋊Q8—21no—
240C22⋊Q8—791no—
241C22⋊Q8—1581no—
242C22⋊Q8C2×D7911yescharacteristic
243#121—21no—
244#121—791no—
245#121—1581no—
246#121C2×D7911yescharacteristic
247C4×Q8—791no—
248C4×Q8C2×D7911yescharacteristic
249C4×D4—21no—
250C4×D4—1581no—
251C4×D4C2×D7911yescharacteristic
252#107—791no—
253C4⋊C8—791no—
254#103—791no—
255#103—791no—
256#103—791no—
257#103—791no—
258#102—791no—
259#102—791no—
260C22⋊C8—791no—
261C22⋊C8—791no—
262C4×C8—791no—
263#41—22no—
264#41—41no—
265#41—3161no—
266#41—1582no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—3161no—
271C2×Q8—791no—
272C2×Q8—791no—
273C2×Q8—1582no—
274C2×Q8—1581no—
275C2×Q8C22×D7911yescharacteristic
276C2×Q8C22×D7911yescharacteristic
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—791no—
280C2×D4—1581no—
281C2×D4—1581no—
282C2×D4C22⋊D7911yescharacteristic
283C2×D4C22×D7911yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—1581no—
287C22×C4—1581no—
288C22×C4C22×D7911yescharacteristic
289C22×C4C22×D7911yescharacteristic
290Q16—3161no—
291Q16—794no—
292Q16—1582no—
293Q16—1582no—
294SD16—1582no—
295SD16—1582no—
296SD16—1582no—
297SD16—1582no—
298D8—3161no—
299M16—1582no—
300M16—1582no—
301C2×C8—791no—
302C2×C8—791no—
303C2×C8—791no—
304C2×C8—791no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—791no—
308C4⋊C4—1581no—
309C4⋊C4—1581no—
310C4⋊C4C22⋊D7911yescharacteristic
311C4⋊C4C22×D7911yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—1581no—
317C22⋊C4—1581no—
318C22⋊C4—1581no—
319C22⋊C4—1581no—
320C22⋊C4C22⋊D7911yescharacteristic
321C22⋊C4C22⋊D7911yescharacteristic
322C42—21no—
323C42—1581no—
324C42C22×D7911yescharacteristic
325C23—21no—
326C23—1581no—
327C23C2×C22⋊D7911yescharacteristic
328C23C2×C22⋊D7911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—3162no—
334Q8—792no—
335Q8—1581no—
336Q8—1581no—
337Q8—1581no—
338Q8D4×D7912yes—
339D4—21no—
340D4—21no—
341D4—41no—
342D4—42no—
343D4—42no—
344D4—3162no—
345D4—3162no—
346D4—1581no—
347D4—1581no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—3162no—
358C2×C4—3162no—
359C2×C4—1581no—
360C2×C4—1581no—
361C2×C4—1581no—
362C2×C4C2×C22⋊D7911yescharacteristic
363C2×C4C2×C22⋊D7911yescharacteristic
364C2×C4C2×C22⋊D7911yescharacteristic
365C2×C4C2×C22⋊D7911yescharacteristic
366C2×C4C23×D7911yescharacteristic
367C8—792no—
368C8—1581no—
369C8—1581no—
370C8—1581no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—3161no—
381C22—3161no—
382C22—3161no—
383C22C22×C22⋊D7911yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—21no—
388C4—21no—
389C4—41no—
390C4—41no—
391C4—3161no—
392C4—3161no—
393C4—1582no—
394C4C2×D4×D7911yescharacteristic
395C4#1457920611yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—6321no—
400C2D4×C22⋊D7911yescharacteristic
401C2#1909936111yescharacteristic
402C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#548×C79C2
socleC22×C79C22×D4
hypercenter#548D79
hypocenterC79#3277
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×#14579191C2semidirect
3. #19099222C2semidirect
4. #19098945C2semidirect
5. #19098811C2semidirect
6. #19098807C2semidirect
7. #19098785C2semidirect
8. #19098782C2semidirect
9. #19098719C2semidirect
10. #19098718C2semidirect
11. #19098708C2semidirect
12. #19098706C2semidirect
13. C4×#11929614C2semidirect
14. #19098641C2semidirect
15. #548×C79C2semidirect
76. #11929614D4semidirect
202. C79#3277semidirect
206. #548D79semidirect