Finite Group Databasebeta

← #23769944

Subgroups — #23769944

Order 10112.

562 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579146C211yesmaximal, characteristic, complemented
2#19098501C211yesmaximal, characteristic, complemented
3#19098489C211yesmaximal, characteristic, complemented
4#19098479C211yesmaximal, characteristic, complemented
5#19098474C211yesmaximal, characteristic, complemented
6#19098474C211yesmaximal, characteristic, complemented
7#19098472C211yesmaximal, characteristic
8#19098464C211yesmaximal, characteristic, complemented
9#19098457C211yesmaximal, characteristic, complemented
10#19098449C211yesmaximal, characteristic, complemented
11#19098442C211yesmaximal, characteristic, complemented
12#19098442C211yesmaximal, characteristic, complemented
13#19098439C211yesmaximal, characteristic, complemented
14#19098420C211yesmaximal, characteristic, complemented
15C2×C22⋊Q8×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C22×C22⋊D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20#14579146—24no—
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×C22⋊Dic79C2211yescharacteristic
24C2×C22⋊Dic79C2211yescharacteristic
25C2×(C2×D79)⋊C4C2211yescharacteristic
26C2×(C2×D79)⋊C4C2211yescharacteristic
27C2×(C2×D79)⋊C4C2211yescharacteristic
28C2×(C2×D79)⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C22×Q8×C79C2211yescharacteristic
46C23×C4×C79C2211yescharacteristic
47C22⋊Q8×C79—24no—
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C4⋊C4×C79C2211yescharacteristic
50C2×C4⋊C4×C79C2211yescharacteristic
51C2×C22⋊C4×C79C2211yescharacteristic
52C2×C22⋊C4×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C23×D79C2311yescharacteristic
55C2×D316—22no—
56C2×D316—22no—
57C2×D316—41no—
58C2×C22⋊D79—22no—
59C2×C22⋊D79—22no—
60C2×C22⋊D79—22no—
61C2×C22⋊D79—41no—
62C2×C22⋊D79—41no—
63C2×C22⋊D79—41no—
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C22×Dic79C2311yescharacteristic
70C2×C4×D79—22no—
71C2×C4×D79—22no—
72C2×C4×D79—41no—
73C4⋊Dic79—41no—
74Dic79⋊C4—22no—
75C22⋊Dic79—22no—
76C22⋊Dic79—41no—
77(C2×D79)⋊C4—22no—
78(C2×D79)⋊C4—22no—
79(C2×D79)⋊C4—22no—
80(C2×D79)⋊C4—41no—
81(C2×D79)⋊C4—41no—
82(C2×D79)⋊C4—41no—
83(C2×D79)⋊C4—41no—
84(C2×D79)⋊C4—41no—
85(C2×D79)⋊C4—41no—
86C4×Dic79—41no—
87C24×C79C2311yescharacteristic
88C2×Q8×C79—22no—
89C2×Q8×C79—41no—
90C2×Q8×C79—41no—
91C22×C4×C79—22no—
92C22×C4×C79—41no—
93C22×C4×C79—41no—
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C22×C4×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C4⋊C4×C79—22no—
101C4⋊C4×C79—22no—
102C4⋊C4×C79D414yescomplemented
103C22⋊C4×C79—22no—
104C22⋊C4×C79—22no—
105C23×C79—21no—
106C23×C79—21no—
107C23×C79—21no—
108C23×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79#4112yes—
112C23×C79C2411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—21no—
118C22×D79—21no—
119C22×D79—21no—
120C22×D79—21no—
121C22×D79—21no—
122C22×D79—21no—
123C22×D79—21no—
124C22×D79—21no—
125C22×D79—21no—
126C22×D79#4112yes—
127Q8×C79—44no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
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—44no—
144C2×C4×C79C2×D412yes—
145C2×C4×C79C2×D412yes—
146C2×C4×C79C2×D412yes—
147C22⋊D79—44no—
148C22⋊D79—44no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—21no—
156C2×Dic79—21no—
157C2×Dic79—21no—
158C2×Dic79—21no—
159C2×Dic79—21no—
160C2×Dic79—21no—
161C2×Dic79—21no—
162C2×Dic79—21no—
163C2×Dic79—21no—
164C2×Dic79—21no—
165C2×Dic79—21no—
166C2×Dic79—21no—
167D316—44no—
168C4×D79—44no—
169C22×C79—22no—
170C22×C79—22no—
171C22×C79—22no—
172C22×C79—41no—
173C22×C79—41no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79C22×D411yescharacteristic
177C22×C79C2×#4111yescharacteristic
178C22×C79C2×#4111yescharacteristic
179C22×C79H(5,𝔽2)11yescharacteristic
180C22×C79H(5,𝔽2)11yescharacteristic
181C22×C79H(5,𝔽2)11yescharacteristic
182C22×C792−1+411yescharacteristic
183C2×D79—22no—
184C2×D79—22no—
185C2×D79—22no—
186C2×D79—41no—
187C2×D79—41no—
188C2×D79—41no—
189C2×D79—41no—
190C2×D79—41no—
191C2×D79—41no—
192C2×D79—41no—
193C2×D79—41no—
194C2×D79—41no—
195C2×D79—41no—
196C2×D79—41no—
197C4×C79—22no—
198C4×C79—22no—
199C4×C79—22no—
200C4×C79—41no—
201C4×C79—41no—
202C4×C79—41no—
203Dic79—41no—
204Dic79—41no—
205Dic79—41no—
206Dic79—41no—
207Dic79—41no—
208Dic79—41no—
209C2×C79—42no—
210C2×C79#53511yescharacteristic
211C2×C79#53811yescharacteristic
212C2×C79#53911yescharacteristic
213C2×C79#54611yescharacteristic
214C2×C79#54811yescharacteristic
215C2×C79#55111yescharacteristic
216C2×C79#56211yescharacteristic
217D79—42no—
218D79—81no—
219#2696—791nomaximal, Sylow
220C79#269611yescharacteristic, complemented, Sylow
221C2×#123—791no—
222C2×C22⋊Q8D7911yescharacteristic, complemented
223#400—791no—
224#397—791no—
225#394—791no—
226#393—791no—
227#393—791no—
228#392—791no—
229#390—791no—
230#388—791no—
231#387—791no—
232#386—791no—
233#386—791no—
234#386—791no—
235#380—791no—
236C22×Q8C2×D7911yescharacteristic
237C22×D4—791no—
238C22×D4—791no—
239C22×D4—791no—
240C23×C4—791no—
241C23×C4C2×D7911yescharacteristic
242#123—1584no—
243C22⋊Q8—24no—
244C2×C4⋊C4—791no—
245C2×C4⋊C4—791no—
246C2×C4⋊C4C2×D7911yescharacteristic
247C2×C4⋊C4C2×D7911yescharacteristic
248C2×C4⋊C4C2×D7911yescharacteristic
249C2×C22⋊C4—791no—
250C2×C22⋊C4—791no—
251C2×C22⋊C4—791no—
252C2×C22⋊C4—791no—
253C2×C22⋊C4—791no—
254C2×C22⋊C4—791no—
255C2×C22⋊C4—791no—
256C2×C22⋊C4—791no—
257C2×C22⋊C4—791no—
258C2×C22⋊C4—791no—
259C2×C22⋊C4—791no—
260C2×C22⋊C4C2×D7911yescharacteristic
261C2×C22⋊C4C2×D7911yescharacteristic
262C2×C42—791no—
263#95—791no—
264#95—791no—
265#95—791no—
266#95—791no—
267#95—791no—
268#95—791no—
269#95—791no—
270#95—791no—
271#95—791no—
272#95—791no—
273C24—791no—
274C24—791no—
275C24C22×D7911yescharacteristic
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×D4—3161no—
280C2×D4—3161no—
281C2×D4—3161no—
282C2×D4—3161no—
283C2×D4—1582no—
284C2×D4—1582no—
285C2×D4—1582no—
286C2×D4—1582no—
287C2×D4—1582no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—3161no—
292C22×C4—791no—
293C22×C4—791no—
294C22×C4—791no—
295C22×C4—791no—
296C22×C4—791no—
297C22×C4—791no—
298C22×C4—1582no—
299C22×C4—1582no—
300C22×C4C22×D7911yescharacteristic
301C22×C4C22×D7911yescharacteristic
302C22×C4C22×D7911yescharacteristic
303C22×C4C22×D7911yescharacteristic
304C22×C4C22×D7911yescharacteristic
305C22×C4C22×D7911yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—3161no—
309C4⋊C4—1582no—
310C4⋊C4C22⋊D7914yescomplemented
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—3161no—
314C22⋊C4—3161no—
315C22⋊C4—3161no—
316C22⋊C4—3161no—
317C22⋊C4—3161no—
318C22⋊C4—3161no—
319C22⋊C4—3161no—
320C22⋊C4—1582no—
321C22⋊C4—1582no—
322C22⋊C4—1582no—
323C22⋊C4—1582no—
324C42—3161no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—792no—
332C23—1581no—
333C23—1581no—
334C23—1581no—
335C23—1581no—
336C23—1581no—
337C23—1581no—
338C23—1581no—
339C23—1581no—
340C23—1581no—
341C23—1581no—
342C23—1581no—
343C23—1581no—
344C23—1581no—
345C23#1192962512yes—
346C23C23×D7911yescharacteristic
347Q8—44no—
348D4—3164no—
349D4—3164no—
350D4—3164no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—44no—
367C2×C4—3164no—
368C2×C4—1581no—
369C2×C4—1581no—
370C2×C4—1581no—
371C2×C4—1581no—
372C2×C4—1581no—
373C2×C4—1581no—
374C2×C4—1581no—
375C2×C4—1581no—
376C2×C4—1581no—
377C2×C4—1581no—
378C2×C4—1581no—
379C2×C4—1581no—
380C2×C4—1581no—
381C2×C4—1581no—
382C2×C4—1581no—
383C2×C4—1581no—
384C2×C4—1581no—
385C2×C4—1581no—
386C2×C4C2×C22⋊D7912yes—
387C2×C4C2×C22⋊D7912yes—
388C2×C4C2×C22⋊D7912yes—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—3161no—
397C22—3161no—
398C22—3161no—
399C22—3161no—
400C22—3161no—
401C22—3161no—
402C22—3161no—
403C22—3161no—
404C22—3161no—
405C22—3161no—
406C22—3161no—
407C22—1582no—
408C22—1582no—
409C22—1582no—
410C22C22×C22⋊D7911yescharacteristic
411C22#41×D7911yescharacteristic
412C22C2×#1192962511yescharacteristic
413C22#1457920611yescharacteristic
414C22#1457920611yescharacteristic
415C22#1457920711yescharacteristic
416C22#1457920911yescharacteristic
417C4—22no—
418C4—22no—
419C4—22no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—3161no—
424C4—3161no—
425C4—3161no—
426C4—3161no—
427C4—3161no—
428C4—3161no—
429C2—42no—
430C2—3162no—
431C2—6321no—
432C2#1909913011yescharacteristic
433C2#1909915311yescharacteristic
434C2#1909915911yescharacteristic
435C2#1909920111yescharacteristic
436C2#1909922411yescharacteristic
437C2#1909924011yescharacteristic
438C2#1909930911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×C22⋊Q8×C79C2
prime radical#19098472C2
hypercenterC2×C22⋊Q8D79
hypocenterC79#2696
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14579146C2semidirect
2. #19098501C2semidirect
3. #19098489C2semidirect
4. #19098479C2semidirect
5. #19098474C2semidirect
6. #19098474C2semidirect
8. #19098464C2semidirect
9. #19098457C2semidirect
10. #19098449C2semidirect
11. #19098442C2semidirect
12. #19098442C2semidirect
13. #19098439C2semidirect
14. #19098420C2semidirect
15. C2×C22⋊Q8×C79C2semidirect
102. C4⋊C4×C79D4semidirect
220. C79#2696semidirect
222. C2×C22⋊Q8D79semidirect
310. C4⋊C4C22⋊D79semidirect