Finite Group Databasebeta

← #23767210

Subgroups — #23767210

Order 10112.

648 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579141C211yesmaximal, characteristic, complemented
2C2×#14579138C211yesmaximal, characteristic, complemented
3C2×(C22⋊D79)⋊C4C211yesmaximal, characteristic
4C2×C4⋊C4×D79C211yesmaximal, characteristic, complemented
5#19098499C211yesmaximal, characteristic, complemented
6#19098497C211yesmaximal, characteristic, complemented
7#19098483C211yesmaximal, characteristic, complemented
8#19098462C211yesmaximal, characteristic, complemented
9#19098444C211yesmaximal, characteristic, complemented
10#19098439C211yesmaximal, characteristic
11#19098439C211yesmaximal, characteristic
12#19098438C211yesmaximal, characteristic, complemented
13#19098437C211yesmaximal, characteristic, complemented
14#19098434C211yesmaximal, characteristic, complemented
15#396×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C23×Dic79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20C22×C4×D79C2211yescharacteristic
21C22×C4×D79C2211yescharacteristic
22#14579141—24no—
23#14579138—24no—
24(C22⋊D79)⋊C4—24no—
25C2×C4⋊Dic79C2211yescharacteristic
26C2×C4⋊Dic79C2211yescharacteristic
27C2×C4⋊Dic79C2211yescharacteristic
28C2×C4⋊Dic79C2211yescharacteristic
29C2×Dic79⋊C4C2211yescharacteristic
30C2×Dic79⋊C4C2211yescharacteristic
31C2×Dic79⋊C4C2211yescharacteristic
32C2×Dic79⋊C4C2211yescharacteristic
33C2×Dic79⋊C4C2211yescharacteristic
34C4⋊C4×D79—24no—
35C2×C22⋊Dic79C2211yescharacteristic
36C2×C22⋊Dic79C2211yescharacteristic
37C2×(C2×D79)⋊C4C2211yescharacteristic
38C2×(C2×D79)⋊C4C2211yescharacteristic
39C2×(C2×D79)⋊C4C2211yescharacteristic
40C2×C4×Dic79C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C79⋊#95C2211yescharacteristic
47C79⋊#95C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C4⋊C4×C79C2211yescharacteristic
50C2×C4⋊C4×C79C2211yescharacteristic
51C2×C22⋊C4×C79C2211yescharacteristic
52C2×C22⋊C4×C79C2211yescharacteristic
53C2×C22⋊C4×C79C2211yescharacteristic
54#95×C79C2211yescharacteristic
55C23×D79C2311yescharacteristic
56C2×Dic158—22no—
57C2×Dic158—22no—
58C2×Dic158—41no—
59C2×C22⋊D79—22no—
60C2×C22⋊D79—22no—
61C2×C22⋊D79Q814yescomplemented
62C22×Dic79—22no—
63C22×Dic79—22no—
64C22×Dic79—41no—
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C22×Dic79C2311yescharacteristic
70C22×Dic79C2311yescharacteristic
71C22×Dic79C2311yescharacteristic
72C2×C4×D79—22no—
73C2×C4×D79—22no—
74C2×C4×D79—22no—
75C2×C4×D79—22no—
76C2×C4×D79—22no—
77C2×C4×D79—22no—
78C2×C4×D79—22no—
79C2×C4×D79—41no—
80C2×C4×D79—41no—
81C4⋊Dic79—22no—
82C4⋊Dic79—22no—
83C4⋊Dic79—22no—
84C4⋊Dic79—22no—
85Dic79⋊C4—22no—
86Dic79⋊C4—22no—
87Dic79⋊C4—22no—
88Dic79⋊C4—41no—
89Dic79⋊C4D414yescomplemented
90C22⋊Dic79—22no—
91C22⋊Dic79—41no—
92(C2×D79)⋊C4—22no—
93(C2×D79)⋊C4—22no—
94(C2×D79)⋊C4D414yes—
95C4×Dic79—22no—
96C24×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102C22×C4×C79C2311yescharacteristic
103C4⋊C4×C79—22no—
104C4⋊C4×C79—22no—
105C4⋊C4×C79—22no—
106C22⋊C4×C79—22no—
107C22⋊C4×C79—22no—
108C22⋊C4×C79—22no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—21no—
115C23×C79C2×Q812yes—
116C23×C79C2411yescharacteristic
117C22×D79—21no—
118C22×D79—21no—
119C22×D79—21no—
120C22×D79—21no—
121C22×D79C2×D412yes—
122C22×D79C2×Q812yes—
123C22×D79#4112yes—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
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×C79C2×D412yes—
140C2×C4×C79C2×D412yes—
141C2×C4×C79#4112yes—
142C22⋊D79—28no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—21no—
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—44no—
161C2×Dic79C2×D412yes—
162C2×Dic79C2×D412yes—
163C2×Dic79C2×D412yes—
164C2×Dic79C2×Q812yes—
165C4×D79—28no—
166C4×D79—44no—
167C4×D79—44no—
168Dic158—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×C79C22×D411yescharacteristic
178C22×C79C22×Q811yescharacteristic
179C22×C79C2×#4111yescharacteristic
180C22×C79C2×#4111yescharacteristic
181C22×C79H(5,𝔽2)11yescharacteristic
182C22×C792−1+411yescharacteristic
183C2×D79—22no—
184C2×D79—22no—
185C2×D79—22no—
186C2×D79—22no—
187C2×D79—22no—
188C2×D79—22no—
189C2×D79C22⋊Q814yescomplemented
190C4×C79—22no—
191C4×C79—22no—
192C4×C79—22no—
193C4×C79—41no—
194C4×C79—41no—
195C4×C79—41no—
196Dic79—22no—
197Dic79—22no—
198Dic79—22no—
199Dic79—22no—
200Dic79—41no—
201Dic79—41no—
202Dic79—41no—
203C2×C79—42no—
204C2×C79C2×C22⋊Q811yescharacteristic
205C2×C79#52511yescharacteristic
206C2×C79#53911yescharacteristic
207C2×C79D4211yescharacteristic
208C2×C79#54711yescharacteristic
209C2×C79D4×Q811yescharacteristic
210C2×C79#55411yescharacteristic
211D79—24no—
212#2449—791nomaximal, Sylow
213C79#244911yescharacteristic, complemented, Sylow
214C2×C22⋊Q8—791no—
215C2×C22⋊Q8—791no—
216C2×C4×D4—791no—
217C22×C4⋊C4—791no—
218#399—791no—
219#398—791no—
220#396D7911yescharacteristic, complemented
221#395—791no—
222#389—791no—
223#387—791no—
224#386—791no—
225#386—791no—
226#385—791no—
227#385—791no—
228#385—791no—
229C22×Q8—791no—
230C22×D4—791no—
231C23×C4—791no—
232C23×C4—791no—
233C23×C4—791no—
234C23×C4—791no—
235C22⋊Q8—1584no—
236C22⋊Q8—1584no—
237C4×D4—1584no—
238C2×C4⋊C4—791no—
239C2×C4⋊C4—791no—
240C2×C4⋊C4—791no—
241C2×C4⋊C4—791no—
242C2×C4⋊C4—791no—
243C2×C4⋊C4—791no—
244C2×C4⋊C4—791no—
245C2×C4⋊C4—791no—
246C2×C4⋊C4—791no—
247C2×C4⋊C4—1584no—
248C2×C4⋊C4C2×D7911yescharacteristic
249C2×C4⋊C4C2×D7911yescharacteristic
250C2×C4⋊C4C2×D7911yescharacteristic
251C2×C22⋊C4—791no—
252C2×C22⋊C4—791no—
253C2×C22⋊C4—791no—
254C2×C22⋊C4—791no—
255C2×C22⋊C4—791no—
256C2×C22⋊C4C2×D7911yescharacteristic
257C2×C22⋊C4C2×D7911yescharacteristic
258C2×C22⋊C4C2×D7911yescharacteristic
259C2×C42—791no—
260#95—791no—
261#95—791no—
262#95—791no—
263#95—791no—
264#95—791no—
265#95—791no—
266#95—791no—
267#95C2×D7911yescharacteristic
268C24—791no—
269C24C22×D7911yescharacteristic
270C2×Q8—3161no—
271C2×Q8—1582no—
272C2×Q8—1582no—
273C2×D4—794no—
274C2×D4—1582no—
275C2×D4—1582no—
276C22×C4—3161no—
277C22×C4—3161no—
278C22×C4—3161no—
279C22×C4—791no—
280C22×C4—791no—
281C22×C4—791no—
282C22×C4—791no—
283C22×C4—791no—
284C22×C4—791no—
285C22×C4—791no—
286C22×C4—1582no—
287C22×C4—1582no—
288C22×C4—1582no—
289C22×C4—1582no—
290C22×C4—1582no—
291C22×C4—1582no—
292C22×C4—1582no—
293C22×C4—1582no—
294C22×C4—1582no—
295C22×C4C22×D7911yescharacteristic
296C22×C4C22×D7911yescharacteristic
297C22×C4C22×D7911yescharacteristic
298C22×C4C22×D7911yescharacteristic
299C22×C4C22×D7911yescharacteristic
300C22×C4C22×D7911yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—3161no—
305C4⋊C4—794no—
306C4⋊C4—1582no—
307C4⋊C4—1582no—
308C4⋊C4—1582no—
309C4⋊C4—1582no—
310C4⋊C4—1582no—
311C4⋊C4—1582no—
312C4⋊C4—1582no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—3161no—
317C22⋊C4—794no—
318C22⋊C4—1582no—
319C22⋊C4—1582no—
320C22⋊C4—1582no—
321C42—1582no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—792no—
329C23—792no—
330C23—792no—
331C23—1581no—
332C23—1581no—
333C23—1581no—
334C23—1581no—
335C23Q8×D7912yes—
336C23C23×D7911yescharacteristic
337Q8—3164no—
338D4—1588no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—3164no—
355C2×C4—3164no—
356C2×C4—3164no—
357C2×C4—792no—
358C2×C4—792no—
359C2×C4—792no—
360C2×C4—792no—
361C2×C4—1588no—
362C2×C4—1581no—
363C2×C4—1581no—
364C2×C4—1581no—
365C2×C4—1581no—
366C2×C4—1581no—
367C2×C4—1581no—
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×C4D4×D7912yes—
380C2×C4D4×D7912yes—
381C2×C4#1192962312yes—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—794no—
390C22—1582no—
391C22—1582no—
392C22—1582no—
393C22—1582no—
394C22—1582no—
395C22—1582no—
396C22C2×D4×D7911yescharacteristic
397C22C2×D4×D7911yescharacteristic
398C22C2×Q8×D7911yescharacteristic
399C22#41×D7911yescharacteristic
400C22C2×#1192962311yescharacteristic
401C22#1457920711yescharacteristic
402C22#1457920811yescharacteristic
403C4—22no—
404C4—22no—
405C4—22no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—3161no—
410C4—3161no—
411C4—3161no—
412C4—1582no—
413C4—1582no—
414C4—1582no—
415C4—1582no—
416C2—42no—
417C2—1584no—
418C2C22⋊Q8×D7911yescharacteristic
419C2#1909907311yescharacteristic
420C2#1909915411yescharacteristic
421C2#1909919711yescharacteristic
422C2#1909921311yescharacteristic
423C2#1909922611yescharacteristic
424C2#1909927111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#396×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#396D79
hypocenterC79#2449
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14579141C2semidirect
2. C2×#14579138C2semidirect
4. C2×C4⋊C4×D79C2semidirect
5. #19098499C2semidirect
6. #19098497C2semidirect
7. #19098483C2semidirect
8. #19098462C2semidirect
9. #19098444C2semidirect
12. #19098438C2semidirect
13. #19098437C2semidirect
14. #19098434C2semidirect
15. #396×C79C2semidirect
61. C2×C22⋊D79Q8semidirect
89. Dic79⋊C4D4semidirect
189. C2×D79C22⋊Q8semidirect
213. C79#2449semidirect
220. #396D79semidirect