Finite Group Databasebeta

← #28340212

Subgroups — #28340212

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×#16812084C211yesmaximal, characteristic
2C2×#16812071C211yesmaximal, characteristic, complemented
3#20292554C211yesmaximal, characteristic, complemented
4#20292553C211yesmaximal, characteristic, complemented
5#20292545C211yesmaximal, characteristic, complemented
6#20292519C211yesmaximal, characteristic, complemented
7#20292508C211yesmaximal, characteristic, complemented
8#20292505C211yesmaximal, characteristic, complemented
9#20292505C211yesmaximal, characteristic, complemented
10#20292505C211yesmaximal, characteristic, complemented
11#20292505C211yesmaximal, characteristic, complemented
12#20292501C211yesmaximal, characteristic, complemented
13#20292489C211yesmaximal, characteristic, complemented
14#95×D107C211yesmaximal, characteristic, complemented
15#400×C107C211yesmaximal, characteristic, complemented
16C22×D428C2211yescharacteristic
17C22×D428C2211yescharacteristic
18C22×D428C2211yescharacteristic
19C22×C4×D107C2211yescharacteristic
20C22×C4×D107C2211yescharacteristic
21C22×C4×D107C2211yescharacteristic
22C22×C4×D107C2211yescharacteristic
23#16812084—24no—
24#16812071—24no—
25C2×C4⋊Dic107C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×(C2×D107)⋊C4C2211yescharacteristic
28C2×(C2×D107)⋊C4C2211yescharacteristic
29C2×(C2×D107)⋊C4C2211yescharacteristic
30C2×(C2×D107)⋊C4C2211yescharacteristic
31C2×(C2×D107)⋊C4C2211yescharacteristic
32C2×(C2×D107)⋊C4C2211yescharacteristic
33C2×(C2×D107)⋊C4C2211yescharacteristic
34C2×(C2×D107)⋊C4C2211yescharacteristic
35C2×(C2×D107)⋊C4C2211yescharacteristic
36C2×(C2×D107)⋊C4C2211yescharacteristic
37C2×(C2×D107)⋊C4C2211yescharacteristic
38C2×C4×Dic107C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C4⋊C4×C107C2211yescharacteristic
48#95×C107C2211yescharacteristic
49#95×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53C23×D107C2311yescharacteristic
54C23×D107C2311yescharacteristic
55C23×D107C2311yescharacteristic
56C2×D428—22no—
57C2×D428—22no—
58C2×D428—22no—
59C2×D428—22no—
60C2×D428—22no—
61C2×D428—22no—
62C2×D428—22no—
63C2×D428—41no—
64C2×D428D414yes—
65C22×Dic107C2311yescharacteristic
66C22×Dic107C2311yescharacteristic
67C22×Dic107C2311yescharacteristic
68C22×Dic107C2311yescharacteristic
69C22×Dic107C2311yescharacteristic
70C2×C4×D107—22no—
71C2×C4×D107—22no—
72C2×C4×D107—22no—
73C2×C4×D107—22no—
74C2×C4×D107—22no—
75C2×C4×D107—22no—
76C2×C4×D107—22no—
77C2×C4×D107—41no—
78C2×C4×D107—41no—
79C2×C4×D107—41no—
80C2×C4×D107—41no—
81C2×C4×D107—41no—
82C4⋊Dic107—41no—
83Dic107⋊C4—22no—
84(C2×D107)⋊C4—22no—
85(C2×D107)⋊C4—22no—
86(C2×D107)⋊C4—22no—
87(C2×D107)⋊C4—22no—
88(C2×D107)⋊C4—22no—
89(C2×D107)⋊C4—22no—
90(C2×D107)⋊C4—41no—
91(C2×D107)⋊C4—41no—
92(C2×D107)⋊C4—41no—
93(C2×D107)⋊C4—41no—
94(C2×D107)⋊C4—41no—
95C4×Dic107—22no—
96C22×C4×C107C2311yescharacteristic
97C22×C4×C107C2311yescharacteristic
98C22×C4×C107C2311yescharacteristic
99C22×C4×C107C2311yescharacteristic
100C22×C4×C107C2311yescharacteristic
101C22×C4×C107C2311yescharacteristic
102C22×C4×C107C2311yescharacteristic
103C4⋊C4×C107—22no—
104C4⋊C4×C107—22no—
105C23×C107C2411yescharacteristic
106C22×D107—21no—
107C22×D107—21no—
108C22×D107—21no—
109C22×D107—21no—
110C22×D107—21no—
111C22×D107—21no—
112C22×D107—21no—
113C22×D107—21no—
114C22×D107—21no—
115C22×D107—21no—
116C22×D107—21no—
117C22×D107—21no—
118C22×D107—21no—
119C22×D107—21no—
120C22×D107—21no—
121C22×D107—21no—
122C22×D107—21no—
123C22×D107C2×D412yes—
124C22×D107C2×D412yes—
125C22×D107#4112yes—
126C22×D107#4112yes—
127C2×C4×C107—21no—
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—21no—
142C2×C4×C107—21no—
143C2×C4×C107—21no—
144C2×C4×C107—21no—
145C2×C4×C107—21no—
146C2×C4×C107C2×D412yes—
147C2×C4×C107#4112yes—
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#4112yes—
163D428—28no—
164D428—44no—
165D428—44no—
166C4×D107—44no—
167C4×D107—44no—
168C4×D107—44no—
169C4×D107—44no—
170C22×C107C22×D411yescharacteristic
171C22×C107C2×#4111yescharacteristic
172C22×C107C2×#4111yescharacteristic
173C22×C107C2×#4111yescharacteristic
174C22×C107C2×#4111yescharacteristic
175C22×C107H(5,𝔽2)11yescharacteristic
176C22×C107H(5,𝔽2)11yescharacteristic
177C2×D107—22no—
178C2×D107—22no—
179C2×D107—22no—
180C2×D107—22no—
181C2×D107—22no—
182C2×D107—22no—
183C2×D107—22no—
184C2×D107—22no—
185C2×D107—22no—
186C2×D107—41no—
187C2×D107—41no—
188C2×D107—41no—
189C2×D107—41no—
190C2×D107—41no—
191C2×D107—41no—
192C2×D107—41no—
193C2×D107—41no—
194C2×D107—41no—
195C2×D107—41no—
196C2×D107—41no—
197C2×D107#12314yes—
198C4×C107—22no—
199C4×C107—22no—
200C4×C107—41no—
201C4×C107—41no—
202C4×C107—41no—
203C4×C107—41no—
204C4×C107—41no—
205Dic107—22no—
206Dic107—41no—
207Dic107—41no—
208Dic107—41no—
209Dic107—41no—
210C2×C107C2×#12311yescharacteristic
211C2×C107#52911yescharacteristic
212C2×C107#53811yescharacteristic
213C2×C107#54611yescharacteristic
214C2×C107#54611yescharacteristic
215C2×C107#55311yescharacteristic
216C2×C107#55311yescharacteristic
217D107—24no—
218D107—42no—
219D107—81no—
220#2444—1071nomaximal, Sylow
221C107#244411yescharacteristic, complemented, Sylow
222C2×#121—1071no—
223C2×C4×D4—1071no—
224#400D10711yescharacteristic, complemented
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#386—1071no—
234#385—1071no—
235#381—1071no—
236C2×#95—1071no—
237C22×D4—1071no—
238C22×D4—1071no—
239C22×D4—1071no—
240C23×C4—1071no—
241C23×C4—1071no—
242C23×C4—1071no—
243C23×C4—1071no—
244#121—2144no—
245C4×D4—2144no—
246C2×C4⋊C4—1071no—
247C2×C4⋊C4—1071no—
248C2×C4⋊C4C2×D10711yescharacteristic
249C2×C4⋊C4C2×D10711yescharacteristic
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⋊C4—1071no—
259C2×C22⋊C4—1071no—
260C2×C22⋊C4—1071no—
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#95C2×D10711yescharacteristic
270#95C2×D10711yescharacteristic
271#95C2×D10711yescharacteristic
272#95C2×D10711yescharacteristic
273#95C2×D10711yescharacteristic
274C24—1071no—
275C24—1071no—
276C24—1071no—
277C2×D4—1074no—
278C2×D4—4281no—
279C2×D4—2142no—
280C2×D4—2142no—
281C2×D4—2142no—
282C2×D4—2142no—
283C2×D4—2142no—
284C2×D4—2142no—
285C2×D4—2142no—
286C22×C4—1071no—
287C22×C4—1071no—
288C22×C4—1071no—
289C22×C4—1071no—
290C22×C4—1071no—
291C22×C4—4281no—
292C22×C4—4281no—
293C22×C4—4281no—
294C22×C4—4281no—
295C22×C4—4281no—
296C22×C4—2142no—
297C22×C4—2142no—
298C22×C4—2142no—
299C22×C4—2142no—
300C22×C4—2142no—
301C22×C4—2142no—
302C22×C4—2142no—
303C22×C4C22×D10711yescharacteristic
304C22×C4C22×D10711yescharacteristic
305C22×C4C22×D10711yescharacteristic
306C22×C4C22×D10711yescharacteristic
307C22×C4C22×D10711yescharacteristic
308C22×C4C22×D10711yescharacteristic
309C22×C4C22×D10711yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—4281no—
313C4⋊C4—2142no—
314C22⋊C4—4281no—
315C22⋊C4—4281no—
316C22⋊C4—4281no—
317C22⋊C4—4281no—
318C22⋊C4—4281no—
319C22⋊C4—2142no—
320C22⋊C4—2142no—
321C22⋊C4—2142no—
322C22⋊C4—2142no—
323C22⋊C4—2142no—
324C22⋊C4—2142no—
325C42—2142no—
326C23—1072no—
327C23—1072no—
328C23—1072no—
329C23—1072no—
330C23—2141no—
331C23—2141no—
332C23—2141no—
333C23—2141no—
334C23—2141no—
335C23—2141no—
336C23—2141no—
337C23—2141no—
338C23—2141no—
339C23—2141no—
340C23—2141no—
341C23—2141no—
342C23—2141no—
343C23—2141no—
344C23—2141no—
345C23—2141no—
346C23—2141no—
347C23C23×D10711yescharacteristic
348D4—4284no—
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—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—1072no—
371C2×C4—4284no—
372C2×C4—4284no—
373C2×C4—4284no—
374C2×C4—4284no—
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×C4D4×D10712yes—
390C2×C4#1313381912yes—
391C22—1074no—
392C22—4281no—
393C22—4281no—
394C22—4281no—
395C22—4281no—
396C22—4281no—
397C22—4281no—
398C22—4281no—
399C22—4281no—
400C22—4281no—
401C22—4281no—
402C22—4281no—
403C22—2142no—
404C22—2142no—
405C22—2142no—
406C22—2142no—
407C22—2142no—
408C22—2142no—
409C22—2142no—
410C22—2142no—
411C22—2142no—
412C22C2×D4×D10711yescharacteristic
413C22#41×D10711yescharacteristic
414C22#41×D10711yescharacteristic
415C22#41×D10711yescharacteristic
416C22C2×#1313381911yescharacteristic
417C22#1681215511yescharacteristic
418C22#1681215511yescharacteristic
419C4—22no—
420C4—22no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—41no—
426C4—4281no—
427C4—4281no—
428C4—4281no—
429C4—4281no—
430C4—2142no—
431C2—8561no—
432C2—4282no—
433C2—2144no—
434C2#123×D10711yescharacteristic
435C2#2029316211yescharacteristic
436C2#2029321611yescharacteristic
437C2#2029326811yescharacteristic
438C2#2029327011yescharacteristic
439C2#2029332811yescharacteristic
440C2#2029333011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#400×C107C2
prime radicalC2×#16812084C2
hypercenter#400D107
hypocenterC107#2444
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#16812071C2semidirect
3. #20292554C2semidirect
4. #20292553C2semidirect
5. #20292545C2semidirect
6. #20292519C2semidirect
7. #20292508C2semidirect
8. #20292505C2semidirect
9. #20292505C2semidirect
10. #20292505C2semidirect
11. #20292505C2semidirect
12. #20292501C2semidirect
13. #20292489C2semidirect
14. #95×D107C2semidirect
15. #400×C107C2semidirect
221. C107#2444semidirect
224. #400D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120842
C2×#168120712
#202925542
#202925532
#202925452
#202925192
#202925082
#202925052
#202925012
#202924892
#95×D1072
#400×C1072
#2444107