Finite Group Databasebeta

← #28340208

Subgroups — #28340208

Order 13696.

610 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812080C211yesmaximal, characteristic
2C2×C4×C22⋊D107C211yesmaximal, characteristic, complemented
3#20292569C211yesmaximal, characteristic, complemented
4#20292555C211yesmaximal, characteristic, complemented
5#20292552C211yesmaximal, characteristic, complemented
6#20292541C211yesmaximal, characteristic, complemented
7#20292520C211yesmaximal, characteristic, complemented
8#20292514C211yesmaximal, characteristic, complemented
9#20292503C211yesmaximal, characteristic, complemented
10#20292503C211yesmaximal, characteristic, complemented
11#20292503C211yesmaximal, characteristic, complemented
12#20292501C211yesmaximal, characteristic, complemented
13#20292490C211yesmaximal, characteristic, complemented
14#95×D107C211yesmaximal, characteristic, complemented
15#386×C107C211yesmaximal, characteristic, complemented
16C22×C22⋊D107C2211yescharacteristic
17C22×C22⋊D107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19C22×C4×D107C2211yescharacteristic
20C22×C4×D107C2211yescharacteristic
21#16812080—24no—
22C4×C22⋊D107—24no—
23C2×C4⋊Dic107C2211yescharacteristic
24C2×C4⋊Dic107C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×C22⋊Dic107C2211yescharacteristic
28C2×C22⋊Dic107C2211yescharacteristic
29C2×C22⋊Dic107C2211yescharacteristic
30C2×C22⋊Dic107C2211yescharacteristic
31C2×C22⋊Dic107C2211yescharacteristic
32C2×C22⋊Dic107C2211yescharacteristic
33C2×(C2×D107)⋊C4C2211yescharacteristic
34C2×(C2×D107)⋊C4C2211yescharacteristic
35C2×C4×Dic107C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C22×D4×C107C2211yescharacteristic
47C23×C4×C107C2211yescharacteristic
48C2×C22⋊C4×C107C2211yescharacteristic
49C2×C22⋊C4×C107C2211yescharacteristic
50C2×C22⋊C4×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53C23×D107C2311yescharacteristic
54C2×C22⋊D107—22no—
55C2×C22⋊D107—22no—
56C2×C22⋊D107—22no—
57C2×C22⋊D107—22no—
58C2×C22⋊D107—22no—
59C2×C22⋊D107D414yes—
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C22×Dic107C2311yescharacteristic
64C22×Dic107C2311yescharacteristic
65C22×Dic107C2311yescharacteristic
66C22×Dic107C2311yescharacteristic
67C2×C4×D107—22no—
68C2×C4×D107—22no—
69C2×C4×D107—22no—
70C2×C4×D107—22no—
71C2×C4×D107—22no—
72C2×C4×D107—41no—
73C2×C4×D107—41no—
74C2×C4×D107—41no—
75C2×C4×D107—41no—
76C4⋊Dic107—22no—
77C4⋊Dic107—41no—
78Dic107⋊C4—22no—
79Dic107⋊C4—22no—
80C22⋊Dic107—22no—
81C22⋊Dic107—22no—
82C22⋊Dic107—22no—
83C22⋊Dic107—41no—
84C22⋊Dic107—41no—
85C22⋊Dic107—41no—
86(C2×D107)⋊C4—22no—
87(C2×D107)⋊C4—22no—
88C4×Dic107—22no—
89C24×C107C2311yescharacteristic
90C24×C107C2311yescharacteristic
91C2×D4×C107—22no—
92C2×D4×C107—22no—
93C2×D4×C107—41no—
94C22×C4×C107—22no—
95C22×C4×C107—22no—
96C22×C4×C107—41no—
97C22×C4×C107C2311yescharacteristic
98C22×C4×C107C2311yescharacteristic
99C22×C4×C107C2311yescharacteristic
100C22×C4×C107C2311yescharacteristic
101C22×C4×C107C2311yescharacteristic
102C22⋊C4×C107—22no—
103C22⋊C4×C107—41no—
104C22⋊C4×C107—41no—
105C23×C107—21no—
106C23×C107—21no—
107C23×C107—21no—
108C23×C107—21no—
109C23×C107—21no—
110C23×C107—21no—
111C23×C107—21no—
112C23×C107—21no—
113C23×C107—21no—
114C23×C107—21no—
115C23×C107—21no—
116C23×C107—21no—
117C23×C107—21no—
118C23×C107C2×D412yes—
119C23×C107C2411yescharacteristic
120C22×D107—21no—
121C22×D107—21no—
122C22×D107—21no—
123C22×D107—21no—
124C22×D107C2×D412yes—
125C22×D107#4112yes—
126C22×D107#4112yes—
127D4×C107—44no—
128C2×C4×C107—21no—
129C2×C4×C107—21no—
130C2×C4×C107—21no—
131C2×C4×C107—21no—
132C2×C4×C107—21no—
133C2×C4×C107—21no—
134C2×C4×C107—21no—
135C2×C4×C107—21no—
136C2×C4×C107—21no—
137C2×C4×C107—21no—
138C2×C4×C107—21no—
139C2×C4×C107—21no—
140C2×C4×C107—21no—
141C2×C4×C107—44no—
142C2×C4×C107#4112yes—
143C2×C4×C107#4112yes—
144C22⋊D107—28no—
145C22⋊D107—44no—
146C2×Dic107—21no—
147C2×Dic107—21no—
148C2×Dic107—21no—
149C2×Dic107—21no—
150C2×Dic107—21no—
151C2×Dic107—21no—
152C2×Dic107—21no—
153C2×Dic107—21no—
154C2×Dic107—21no—
155C2×Dic107—21no—
156C2×Dic107—21no—
157C2×Dic107—21no—
158C2×Dic107—21no—
159C2×Dic107—21no—
160C2×Dic107—21no—
161C2×Dic107—21no—
162C2×Dic107—21no—
163C2×Dic107—21no—
164C2×Dic107—21no—
165C2×Dic107—21no—
166C2×Dic107C2×D412yes—
167C4×D107—44no—
168C4×D107—44no—
169C4×D107—44no—
170C22×C107—22no—
171C22×C107—22no—
172C22×C107—22no—
173C22×C107—41no—
174C22×C107—41no—
175C22×C107—41no—
176C22×C107—41no—
177C22×C107—41no—
178C22×C107—41no—
179C22×C107—41no—
180C22×C107—41no—
181C22×C107—41no—
182C22×C107—41no—
183C22×C107—41no—
184C22×C107C22×D411yescharacteristic
185C22×C107C2×#4111yescharacteristic
186C22×C107C2×#4111yescharacteristic
187C22×C107C2×#4111yescharacteristic
188C22×C107C2×#4111yescharacteristic
189C22×C107H(5,𝔽2)11yescharacteristic
190C22×C107H(5,𝔽2)11yescharacteristic
191C2×D107—22no—
192C2×D107—22no—
193C2×D107—22no—
194C2×D107—22no—
195C2×D107—22no—
196C2×D107—22no—
197C2×D107#12314yes—
198C4×C107—22no—
199C4×C107—22no—
200C4×C107—41no—
201C4×C107—41no—
202C4×C107—41no—
203Dic107—22no—
204Dic107—41no—
205Dic107—41no—
206Dic107—41no—
207Dic107—41no—
208Dic107—41no—
209Dic107—41no—
210C2×C107—42no—
211C2×C107—81no—
212C2×C107C2×#12311yescharacteristic
213C2×C107#52911yescharacteristic
214C2×C107#53811yescharacteristic
215C2×C107#54611yescharacteristic
216C2×C107#54611yescharacteristic
217C2×C107#55311yescharacteristic
218C2×C107#55311yescharacteristic
219D107—24no—
220#2444—1071nomaximal, Sylow
221C107#244411yescharacteristic, complemented, Sylow
222C2×#121—1071no—
223C2×C4×D4—1071no—
224#400—1071no—
225#397—1071no—
226#397—1071no—
227#394—1071no—
228#388—1071no—
229#387—1071no—
230#386—1071no—
231#386—1071no—
232#386—1071no—
233#386D10711yescharacteristic, complemented
234#385—1071no—
235#381—1071no—
236C2×#95—1071no—
237C22×D4—1071no—
238C22×D4—1071no—
239C22×D4C2×D10711yescharacteristic
240C23×C4—1071no—
241C23×C4—1071no—
242C23×C4—1071no—
243C23×C4C2×D10711yescharacteristic
244#121—2144no—
245C4×D4—2144no—
246C2×C4⋊C4—1071no—
247C2×C4⋊C4—1071no—
248C2×C4⋊C4—1071no—
249C2×C4⋊C4—1071no—
250C2×C22⋊C4—1071no—
251C2×C22⋊C4—1071no—
252C2×C22⋊C4—1071no—
253C2×C22⋊C4—1071no—
254C2×C22⋊C4—1071no—
255C2×C22⋊C4—1071no—
256C2×C22⋊C4—1071no—
257C2×C22⋊C4—1071no—
258C2×C22⋊C4C2×D10711yescharacteristic
259C2×C22⋊C4C2×D10711yescharacteristic
260C2×C22⋊C4C2×D10711yescharacteristic
261C2×C42—1071no—
262#95—1071no—
263#95—1071no—
264#95—1071no—
265#95—1071no—
266#95—1071no—
267#95—1071no—
268#95—1071no—
269#95—1071no—
270#95—1071no—
271#95—1071no—
272#95C2×D10711yescharacteristic
273#95C2×D10711yescharacteristic
274C24—1071no—
275C24C22×D10711yescharacteristic
276C24C22×D10711yescharacteristic
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—41no—
280C2×D4—1074no—
281C2×D4—2142no—
282C2×D4—2142no—
283C2×D4—2142no—
284C2×D4—2142no—
285C2×D4—2142no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—1071no—
290C22×C4—1071no—
291C22×C4—1071no—
292C22×C4—1071no—
293C22×C4—1071no—
294C22×C4—1071no—
295C22×C4—1071no—
296C22×C4—4281no—
297C22×C4—4281no—
298C22×C4—4281no—
299C22×C4—4281no—
300C22×C4—2142no—
301C22×C4—2142no—
302C22×C4—2142no—
303C22×C4—2142no—
304C22×C4—2142no—
305C22×C4C22×D10711yescharacteristic
306C22×C4C22×D10711yescharacteristic
307C22×C4C22×D10711yescharacteristic
308C22×C4C22×D10711yescharacteristic
309C22×C4C22×D10711yescharacteristic
310C4⋊C4—4281no—
311C4⋊C4—2142no—
312C4⋊C4—2142no—
313C4⋊C4—2142no—
314C22⋊C4—22no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—4281no—
318C22⋊C4—4281no—
319C22⋊C4—4281no—
320C22⋊C4—2142no—
321C22⋊C4—2142no—
322C22⋊C4—2142no—
323C22⋊C4—2142no—
324C22⋊C4—2142no—
325C42—2142no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—1072no—
340C23—1072no—
341C23—1072no—
342C23—2141no—
343C23—2141no—
344C23—2141no—
345C23—2141no—
346C23D4×D10712yes—
347C23C23×D10711yescharacteristic
348D4—44no—
349D4—4284no—
350D4—2148no—
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—44no—
365C2×C4—1072no—
366C2×C4—4284no—
367C2×C4—4284no—
368C2×C4—4284no—
369C2×C4—2141no—
370C2×C4—2141no—
371C2×C4—2141no—
372C2×C4—2141no—
373C2×C4—2141no—
374C2×C4—2141no—
375C2×C4—2141no—
376C2×C4—2141no—
377C2×C4—2141no—
378C2×C4—2141no—
379C2×C4—2141no—
380C2×C4—2141no—
381C2×C4—2141no—
382C2×C4—2141no—
383C2×C4—2141no—
384C2×C4—2141no—
385C2×C4—2141no—
386C2×C4—2141no—
387C2×C4—2141no—
388C2×C4—2141no—
389C2×C4#1313381712yes—
390C2×C4#1313381812yes—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—1074no—
406C22—2142no—
407C22—2142no—
408C22—2142no—
409C22—2142no—
410C22—2142no—
411C22—2142no—
412C22C2×D4×D10711yescharacteristic
413C22#41×D10711yescharacteristic
414C22#41×D10711yescharacteristic
415C22C2×#1313381711yescharacteristic
416C22C2×#1313381811yescharacteristic
417C22#1681215411yescharacteristic
418C22#1681215411yescharacteristic
419C4—22no—
420C4—22no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—4281no—
425C4—4281no—
426C4—4281no—
427C4—4281no—
428C4—4281no—
429C4—4281no—
430C4—2142no—
431C2—42no—
432C2—81no—
433C2—2144no—
434C2#123×D10711yescharacteristic
435C2#2029315911yescharacteristic
436C2#2029320911yescharacteristic
437C2#2029326411yescharacteristic
438C2#2029326711yescharacteristic
439C2#2029332411yescharacteristic
440C2#2029332711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#386×C107C2
prime radicalC2×#16812080C2
hypercenter#386D107
hypocenterC107#2444
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D107C2semidirect
3. #20292569C2semidirect
4. #20292555C2semidirect
5. #20292552C2semidirect
6. #20292541C2semidirect
7. #20292520C2semidirect
8. #20292514C2semidirect
9. #20292503C2semidirect
10. #20292503C2semidirect
11. #20292503C2semidirect
12. #20292501C2semidirect
13. #20292490C2semidirect
14. #95×D107C2semidirect
15. #386×C107C2semidirect
221. C107#2444semidirect
233. #386D107semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168120802
C2×C4×C22⋊D1072
#202925692
#202925552
#202925522
#202925412
#202925202
#202925142
#202925032
#202925012
#202924902
#95×D1072
#386×C1072
#2444107