Finite Group Databasebeta

← #28340215

Subgroups — #28340215

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×#16812083C211yesmaximal, characteristic
2C2×(C22⋊D107)⋊C4C211yesmaximal, characteristic, complemented
3#20292569C211yesmaximal, characteristic, complemented
4#20292556C211yesmaximal, characteristic, complemented
5#20292553C211yesmaximal, characteristic, complemented
6#20292544C211yesmaximal, characteristic, complemented
7#20292517C211yesmaximal, characteristic, complemented
8#20292513C211yesmaximal, characteristic, complemented
9#20292505C211yesmaximal, characteristic, complemented
10#20292504C211yesmaximal, characteristic, complemented
11#20292504C211yesmaximal, characteristic, complemented
12#20292504C211yesmaximal, characteristic, complemented
13#20292489C211yesmaximal, characteristic, complemented
14C2×C107⋊#95C211yesmaximal, characteristic, complemented
15#385×C107C211yesmaximal, characteristic, complemented
16C22×D428C2211yescharacteristic
17C22×C22⋊D107C2211yescharacteristic
18C22×C22⋊D107C2211yescharacteristic
19C23×Dic107C2211yescharacteristic
20C23×Dic107C2211yescharacteristic
21C22×C4×D107C2211yescharacteristic
22#16812083—24no—
23(C22⋊D107)⋊C4—24no—
24C2×C4⋊Dic107C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×(C2×D107)⋊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×C4×Dic107C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C23×C4×C107C2211yescharacteristic
47C2×C4⋊C4×C107C2211yescharacteristic
48C2×C4⋊C4×C107C2211yescharacteristic
49C2×C22⋊C4×C107C2211yescharacteristic
50C2×C22⋊C4×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53C23×D107C2311yescharacteristic
54C23×D107C2311yescharacteristic
55C2×D428—22no—
56C2×D428—22no—
57C2×D428—41no—
58C2×C22⋊D107—22no—
59C2×C22⋊D107—22no—
60C2×C22⋊D107—22no—
61C2×C22⋊D107—22no—
62C2×C22⋊D107—22no—
63C2×C22⋊D107D414yes—
64C22×Dic107—22no—
65C22×Dic107—22no—
66C22×Dic107—22no—
67C22×Dic107—41no—
68C22×Dic107—41no—
69C22×Dic107—41no—
70C22×Dic107C2311yescharacteristic
71C22×Dic107C2311yescharacteristic
72C22×Dic107C2311yescharacteristic
73C22×Dic107C2311yescharacteristic
74C22×Dic107C2311yescharacteristic
75C22×Dic107C2311yescharacteristic
76C2×C4×D107—22no—
77C2×C4×D107—22no—
78C2×C4×D107—41no—
79C4⋊Dic107—22no—
80Dic107⋊C4—22no—
81(C2×D107)⋊C4—22no—
82(C2×D107)⋊C4—22no—
83(C2×D107)⋊C4—22no—
84(C2×D107)⋊C4—22no—
85(C2×D107)⋊C4—41no—
86(C2×D107)⋊C4—41no—
87(C2×D107)⋊C4—41no—
88(C2×D107)⋊C4—41no—
89(C2×D107)⋊C4—41no—
90C4×Dic107—22no—
91C24×C107C2311yescharacteristic
92C22×C4×C107—22no—
93C22×C4×C107—22no—
94C22×C4×C107—41no—
95C22×C4×C107C2311yescharacteristic
96C22×C4×C107C2311yescharacteristic
97C22×C4×C107C2311yescharacteristic
98C22×C4×C107C2311yescharacteristic
99C22×C4×C107C2311yescharacteristic
100C22×C4×C107C2311yescharacteristic
101C4⋊C4×C107—22no—
102C4⋊C4×C107—41no—
103C22⋊C4×C107—22no—
104C22⋊C4×C107—22no—
105C23×C107—21no—
106C23×C107—21no—
107C23×C107—21no—
108C23×C107—21no—
109C23×C107C2×D412yes—
110C23×C107#4112yes—
111C23×C107#4112yes—
112C23×C107C2411yescharacteristic
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×D107—21no—
124C22×D107—21no—
125C22×D107—21no—
126C22×D107C2×D412yes—
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—44no—
145C2×C4×C107#4112yes—
146C22⋊D107—28no—
147C22⋊D107—44no—
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—44no—
165C2×Dic107—44no—
166C2×Dic107C2×D412yes—
167C2×Dic107#4112yes—
168D428—44no—
169C4×D107—44no—
170C22×C107—22no—
171C22×C107—22no—
172C22×C107—22no—
173C22×C107—22no—
174C22×C107—22no—
175C22×C107—22no—
176C22×C107#12314yes—
177C22×C107C22×D411yescharacteristic
178C22×C107C2×#4111yescharacteristic
179C22×C107C2×#4111yescharacteristic
180C22×C107C2×#4111yescharacteristic
181C22×C107C2×#4111yescharacteristic
182C22×C107H(5,𝔽2)11yescharacteristic
183C22×C107H(5,𝔽2)11yescharacteristic
184C2×D107—22no—
185C2×D107—22no—
186C2×D107—22no—
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—41no—
198C4×C107—22no—
199C4×C107—41no—
200C4×C107—41no—
201C4×C107—41no—
202C4×C107—41no—
203C4×C107—41no—
204Dic107—22no—
205Dic107—22no—
206Dic107—41no—
207Dic107—41no—
208Dic107—41no—
209Dic107—41no—
210C2×C107—24no—
211C2×C107C2×#12311yescharacteristic
212C2×C107#52911yescharacteristic
213C2×C107#53811yescharacteristic
214C2×C107#54611yescharacteristic
215C2×C107#54611yescharacteristic
216C2×C107#55311yescharacteristic
217C2×C107#55311yescharacteristic
218D107—42no—
219D107—81no—
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#386—1071no—
234#385D10711yescharacteristic, complemented
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×C4C2×D10711yescharacteristic
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⋊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—
275C24—1071no—
276C24C22×D10711yescharacteristic
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—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—4281no—
296C22×C4—4281no—
297C22×C4—4281no—
298C22×C4—4281no—
299C22×C4—2142no—
300C22×C4—2142no—
301C22×C4—2142no—
302C22×C4—2142no—
303C22×C4—2142no—
304C22×C4C22×D10711yescharacteristic
305C22×C4C22×D10711yescharacteristic
306C22×C4C22×D10711yescharacteristic
307C22×C4C22×D10711yescharacteristic
308C22×C4C22×D10711yescharacteristic
309C22×C4C22×D10711yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—2142no—
313C4⋊C4—2142no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—4281no—
317C22⋊C4—4281no—
318C22⋊C4—4281no—
319C22⋊C4—4281no—
320C22⋊C4—4281no—
321C22⋊C4—2142no—
322C22⋊C4—2142no—
323C22⋊C4—2142no—
324C22⋊C4—2142no—
325C42—2142no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—1072no—
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—
344C23D4×D10712yes—
345C23#1313381812yes—
346C23#1313381912yes—
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—44no—
369C2×C4—1072no—
370C2×C4—1072no—
371C2×C4—4284no—
372C2×C4—4284no—
373C2×C4—4284no—
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—2141no—
390C2×C4#1313381712yes—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—4281no—
398C22—4281no—
399C22—4281no—
400C22—4281no—
401C22—4281no—
402C22—4281no—
403C22—4281no—
404C22—4281no—
405C22—4281no—
406C22—4281no—
407C22—4281no—
408C22—2142no—
409C22—2142no—
410C22—2142no—
411C22#1681209414yes—
412C22C2×D4×D10711yescharacteristic
413C22#41×D10711yescharacteristic
414C22C2×#1313381711yescharacteristic
415C22C2×#1313381811yescharacteristic
416C22C2×#1313381911yescharacteristic
417C22#1681215411yescharacteristic
418C22#1681215511yescharacteristic
419C4—22no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—4281no—
426C4—4281no—
427C4—4281no—
428C4—4281no—
429C4—2142no—
430C4—2142no—
431C2—24no—
432C2—8561no—
433C2—4282no—
434C2C2×#1681209411yescharacteristic
435C2#2029316311yescharacteristic
436C2#2029321711yescharacteristic
437C2#2029326411yescharacteristic
438C2#2029326911yescharacteristic
439C2#2029332311yescharacteristic
440C2#2029332611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#385×C107C2
prime radicalC2×#16812083C2
hypercenter#385D107
hypocenterC107#2444
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D107)⋊C4C2semidirect
3. #20292569C2semidirect
4. #20292556C2semidirect
5. #20292553C2semidirect
6. #20292544C2semidirect
7. #20292517C2semidirect
8. #20292513C2semidirect
9. #20292505C2semidirect
10. #20292504C2semidirect
11. #20292504C2semidirect
12. #20292504C2semidirect
13. #20292489C2semidirect
14. C2×C107⋊#95C2semidirect
15. #385×C107C2semidirect
221. C107#2444semidirect
234. #385D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120832
C2×(C22⋊D107)⋊C42
#202925692
#202925562
#202925532
#202925442
#202925172
#202925132
#202925052
#202925042
#202924892
C2×C107⋊#952
#385×C1072
#2444107