Finite Group Databasebeta

← #23774956

Subgroups — #23774956

Order 10112.

478 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×#14579181C211yesmaximal, characteristic, complemented
3#19099218C211yesmaximal, characteristic, complemented
4#19098958C211yesmaximal, characteristic, complemented
5#19098807C211yesmaximal, characteristic, complemented
6#19098802C211yesmaximal, characteristic, complemented
7#19098775C211yesmaximal, characteristic, complemented
8#19098773C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098723C211yesmaximal, characteristic, complemented
11#19098719C211yesmaximal, characteristic, complemented
12#19098706C211yesmaximal, characteristic, complemented
13#19098661C211yesmaximal, 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×#11929614C2211yescharacteristic
23C2×#11929614C2211yescharacteristic
24C2×#11929612C2211yescharacteristic
25C2×#11929612C2211yescharacteristic
26C2×#11929611C2211yescharacteristic
27C2×#11929611C2211yescharacteristic
28C2×#11929609C2211yescharacteristic
29C2×#11929608C2211yescharacteristic
30C22×C79⋊C8C2211yescharacteristic
31#14579161C2211yescharacteristic
32#14579143—21no—
33#14579143—21no—
34#14579140C2211yescharacteristic
35#14579140C2211yescharacteristic
36#14579132—21no—
37C4×D316C2211yescharacteristic
38C4⋊C4×D79—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
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×Dic158C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73#11929614—22no—
74#11929614—22no—
75#11929614—22no—
76#11929614—41no—
77#11929612—22no—
78#11929612—41no—
79#11929611—22no—
80#11929611D414yescomplemented
81#11929609—22no—
82#11929608—22no—
83C2×C79⋊C8—22no—
84C2×C79⋊C8C2311yescharacteristic
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87C2×C79⋊C8C2311yescharacteristic
88C4⋊Dic79—21no—
89C4⋊Dic79—21no—
90C4⋊Dic79C2311yescharacteristic
91Dic79⋊C4—21no—
92Dic79⋊C4—21no—
93C22⋊Dic79—21no—
94C22⋊Dic79—21no—
95(C2×D79)⋊C4—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—
156D316—21no—
157D316C2×D412yes—
158C4×D79—42no—
159C4×D79—42no—
160C4×D79—42no—
161Dic158—21no—
162Dic158—21no—
163Dic158—21no—
164Dic158—21no—
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—22no—
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—41no—
192Dic79—41no—
193Dic79—41no—
194C2×C79—41no—
195C2×C79—41no—
196C2×C79—81no—
197C2×C79D4211yescharacteristic
198C2×C79#57511yescharacteristic
199C2×C79#57811yescharacteristic
200D79—42no—
201#3269—791nomaximal, Sylow
202C79#326911yescharacteristic, complemented, Sylow
203C2×#137—791no—
204C2×#135—791no—
205#548D7911yescharacteristic, complemented
206#547—791no—
207#497—791no—
208#468—791no—
209#467—791no—
210#463—791no—
211#462—791no—
212#452—791no—
213#452—791no—
214#451—791no—
215#449—791no—
216#440—791no—
217#435—791no—
218C2×#41—791no—
219C2×#41—791no—
220C2×#41C2×D7911yescharacteristic
221C22×Q8C2×D7911yescharacteristic
222#137—1584no—
223#135—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—
234C22×C8—791no—
235C4⋊Q8—791no—
236#124—21no—
237#124C2×D7911yescharacteristic
238#123—1581no—
239#123—1581no—
240C22⋊Q8—21no—
241C22⋊Q8—791no—
242C22⋊Q8—791no—
243C22⋊Q8C2×D7911yescharacteristic
244#121—21no—
245#121—1581no—
246#121C2×D7911yescharacteristic
247C4×Q8C2×D7911yescharacteristic
248C4×D4—21no—
249C4×D4—791no—
250C4×D4C2×D7911yescharacteristic
251C2×C4⋊C4—1581no—
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—
262#97—791no—
263#41—22no—
264#41—41no—
265#41—3161no—
266#41—3161no—
267#41—1582no—
268#41—1582no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—791no—
273C2×Q8—791no—
274C2×Q8C22×D7911yescharacteristic
275C2×Q8C22×D7911yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—791no—
279C2×D4—1581no—
280C2×D4—1581no—
281C2×D4C22⋊D7911yescharacteristic
282C2×D4C22×D7911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—1581no—
286C22×C4—1581no—
287C22×C4—1581no—
288C22×C4C22×D7911yescharacteristic
289C22×C4C22×D7911yescharacteristic
290Q16—3161no—
291Q16—1582no—
292Q16—1582no—
293Q16—1582no—
294SD16—3161no—
295SD16—794no—
296SD16—1582no—
297SD16—1582no—
298D8—1582no—
299M16—1582no—
300C2×C8—791no—
301C2×C8—791no—
302C2×C8—791no—
303C2×C8—791no—
304C2×C8—1582no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—791no—
308C4⋊C4—1581no—
309C4⋊C4—1581no—
310C4⋊C4—1581no—
311C4⋊C4—1581no—
312C4⋊C4C22⋊D7911yescharacteristic
313C4⋊C4C22×D7911yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—21no—
318C22⋊C4—1581no—
319C22⋊C4—1581no—
320C22⋊C4—1581no—
321C22⋊C4C22⋊D7911yescharacteristic
322C22⋊C4C22⋊D7911yescharacteristic
323C42—21no—
324C42C22×D7911yescharacteristic
325C23—21no—
326C23—1581no—
327C23C2×C22⋊D7911yescharacteristic
328C23C2×C22⋊D7911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—1581no—
334Q8—1581no—
335Q8—1581no—
336Q8—1581no—
337Q8D4×D7912yes—
338D4—21no—
339D4—21no—
340D4—41no—
341D4—42no—
342D4—42no—
343D4—3162no—
344D4—3162no—
345D4—792no—
346D4—1581no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—3162no—
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—1582no—
383C22C22×C22⋊D7911yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—21no—
388C4—21no—
389C4—41no—
390C4—41no—
391C4—3161no—
392C4—3161no—
393C4—3161no—
394C4C2×D4×D7911yescharacteristic
395C4#1457920611yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—3162no—
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#3269
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. #19099218C2semidirect
4. #19098958C2semidirect
5. #19098807C2semidirect
6. #19098802C2semidirect
7. #19098775C2semidirect
8. #19098773C2semidirect
9. #19098725C2semidirect
10. #19098723C2semidirect
11. #19098719C2semidirect
12. #19098706C2semidirect
13. #19098661C2semidirect
14. #19098635C2semidirect
15. #548×C79C2semidirect
80. #11929611D4semidirect
202. C79#3269semidirect
205. #548D79semidirect