Finite Group Databasebeta

← #28339287

Subgroups — #28339287

Order 13696.

928 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133817C211yesmaximal, characteristic
2C2×C4×C22⋊D107C211yesmaximal, characteristic, complemented
3C2×(C22⋊D107)⋊C4C211yesmaximal, characteristic, complemented
4#20292531C211yesmaximal, characteristic, complemented
5#20292531C211yesmaximal, characteristic, complemented
6#20292507C211yesmaximal, characteristic, complemented
7#20292503C211yesmaximal, characteristic, complemented
8#20292503C211yesmaximal, characteristic, complemented
9#20292489C211yesmaximal, characteristic, complemented
10#20292488C211yesmaximal, characteristic, complemented
11#20292485C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic107C211yesmaximal, characteristic, complemented
13C2×C107⋊#95C211yesmaximal, characteristic, complemented
14#95×D107C211yesmaximal, characteristic, complemented
15#386×C107C211yesmaximal, characteristic, complemented
16C2×#13133817—24no—
17C2×#13133817—24no—
18C2×#13133817C418yescomplemented
19C22×Dic214C2211yescharacteristic
20C22×C22⋊D107C2211yescharacteristic
21C22×C22⋊D107C2211yescharacteristic
22C23×Dic107C2211yescharacteristic
23C23×Dic107C2211yescharacteristic
24C23×Dic107C2211yescharacteristic
25C22×C4×D107C2211yescharacteristic
26C22×C4×D107C2211yescharacteristic
27C22×C4×D107C2211yescharacteristic
28C4×C22⋊D107—24no—
29(C22⋊D107)⋊C4—24no—
30C2×Dic107⋊C4C2211yescharacteristic
31C2×Dic107⋊C4C2211yescharacteristic
32C2×C22⋊Dic107C2211yescharacteristic
33C2×C22⋊Dic107C2211yescharacteristic
34C2×C22⋊Dic107C2211yescharacteristic
35C2×(C2×D107)⋊C4C2211yescharacteristic
36C2×(C2×D107)⋊C4C2211yescharacteristic
37C2×C4×Dic107C2211yescharacteristic
38C2×C4×Dic107C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C107⋊#95C2211yescharacteristic
47C107⋊#95C2211yescharacteristic
48C107⋊#95C2211yescharacteristic
49C22×D4×C107C2211yescharacteristic
50C23×C4×C107C2211yescharacteristic
51C2×C22⋊C4×C107C2211yescharacteristic
52C2×C22⋊C4×C107C2211yescharacteristic
53C2×C22⋊C4×C107C2211yescharacteristic
54#95×C107C2211yescharacteristic
55#95×C107C2211yescharacteristic
56C23×D107C2311yescharacteristic
57#13133817—232no—
58C2×Dic214—22no—
59C2×Dic214—22no—
60C2×Dic214C2×C414yescomplemented
61C2×C22⋊D107—22no—
62C2×C22⋊D107—22no—
63C2×C22⋊D107C2×C414yes—
64C2×C22⋊D107C2×C414yescomplemented
65C2×C22⋊D107D414yes—
66C2×C22⋊D107D414yes—
67C22×Dic107—22no—
68C22×Dic107—22no—
69C22×Dic107—22no—
70C22×Dic107—22no—
71C22×Dic107—22no—
72C22×Dic107—22no—
73C22×Dic107—41no—
74C22×Dic107C2×C414yescomplemented
75C22×Dic107C2×C414yescomplemented
76C22×Dic107C2311yescharacteristic
77C22×Dic107C2311yescharacteristic
78C22×Dic107C2311yescharacteristic
79C22×Dic107C2311yescharacteristic
80C22×Dic107C2311yescharacteristic
81C22×Dic107C2311yescharacteristic
82C22×Dic107C2311yescharacteristic
83C2×C4×D107—22no—
84C2×C4×D107—22no—
85C2×C4×D107—22no—
86C2×C4×D107—22no—
87C2×C4×D107—22no—
88C2×C4×D107—22no—
89C2×C4×D107—41no—
90C2×C4×D107—41no—
91C2×C4×D107C2×C414yescomplemented
92Dic107⋊C4—22no—
93Dic107⋊C4—22no—
94C22⋊Dic107—22no—
95C22⋊Dic107—22no—
96C22⋊Dic107—41no—
97(C2×D107)⋊C4—22no—
98(C2×D107)⋊C4—22no—
99C4×Dic107—22no—
100C4×Dic107—22no—
101C24×C107C2311yescharacteristic
102C24×C107C2311yescharacteristic
103C2×D4×C107—22no—
104C2×D4×C107—22no—
105C2×D4×C107C2×C414yescomplemented
106C22×C4×C107—22no—
107C22×C4×C107—22no—
108C22×C4×C107—41no—
109C22×C4×C107C2311yescharacteristic
110C22×C4×C107C2311yescharacteristic
111C22×C4×C107C2311yescharacteristic
112C22×C4×C107C2311yescharacteristic
113C22×C4×C107C2311yescharacteristic
114C22⋊C4×C107—22no—
115C22⋊C4×C107—22no—
116C22⋊C4×C107—41no—
117C23×C107—21no—
118C23×C107—21no—
119C23×C107—21no—
120C23×C107—21no—
121C23×C107—21no—
122C23×C107—21no—
123C23×C107—21no—
124C23×C107—21no—
125C23×C107—21no—
126C23×C107—21no—
127C23×C107C22×C412yes—
128C23×C107C22×C412yes—
129C23×C107C2×D412yes—
130C23×C107C2×D412yes—
131C23×C107C2411yescharacteristic
132C22×D107—21no—
133C22×D107—21no—
134C22×D107—21no—
135C22×D107—21no—
136C22×D107C22×C412yes—
137C22×D107C2×D412yes—
138C22×D107C2×D412yes—
139D4×C107—28no—
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×C107—21no—
147C2×C4×C107—21no—
148C2×C4×C107—21no—
149C2×C4×C107—21no—
150C2×C4×C107—21no—
151C2×C4×C107—21no—
152C2×C4×C107—21no—
153C2×C4×C107—44no—
154C2×C4×C107C22×C412yes—
155C2×C4×C107#4112yescomplemented
156C22⋊D107—28no—
157C22⋊D107C22⋊C4116yescomplemented
158C2×Dic107—28no—
159C2×Dic107—21no—
160C2×Dic107—21no—
161C2×Dic107—21no—
162C2×Dic107—21no—
163C2×Dic107—21no—
164C2×Dic107—21no—
165C2×Dic107—28no—
166C2×Dic107—21no—
167C2×Dic107—21no—
168C2×Dic107—21no—
169C2×Dic107—21no—
170C2×Dic107—21no—
171C2×Dic107—21no—
172C2×Dic107—21no—
173C2×Dic107—21no—
174C2×Dic107—21no—
175C2×Dic107—44no—
176C2×Dic107C22×C412yes—
177C2×Dic107C22×C412yes—
178C2×Dic107C22×C412yes—
179C2×Dic107C2×D412yes—
180C2×Dic107C2×D412yes—
181C2×Dic107#4112yescomplemented
182C4×D107—28no—
183C4×D107—44no—
184C4×D107—44no—
185Dic214—28no—
186C22×C107—22no—
187C22×C107—22no—
188C22×C107—22no—
189C22×C107—22no—
190C22×C107—22no—
191C22×C107—22no—
192C22×C107—22no—
193C22×C107—22no—
194C22×C107—22no—
195C22×C107—41no—
196C22×C107—41no—
197C22×C107—41no—
198C22×C107—41no—
199C22×C107C2×C22⋊C414yes—
200C22×C107C23×C411yescharacteristic
201C22×C107C22×D411yescharacteristic
202C22×C107C22×D411yescharacteristic
203C22×C107C2×#4111yescharacteristic
204C22×C107C2×#4111yescharacteristic
205C22×C107H(5,𝔽2)11yescharacteristic
206C22×C1072−1+411yescharacteristic
207C2×D107—22no—
208C2×D107—22no—
209C2×D107—22no—
210C2×D107—22no—
211C2×D107—22no—
212C2×D107—22no—
213C2×D107C2×C22⋊C414yes—
214C4×C107—22no—
215C4×C107—22no—
216C4×C107—41no—
217C4×C107—41no—
218C4×C107—41no—
219Dic107—22no—
220Dic107—22no—
221Dic107—22no—
222Dic107—41no—
223Dic107—41no—
224Dic107—41no—
225Dic107C2×C22⋊C414yes—
226C2×C107—24no—
227C2×C107—42no—
228C2×C107C22×C22⋊C411yescharacteristic
229C2×C107C4×#4111yescharacteristic
230C2×C107#52011yescharacteristic
231C2×C107#54611yescharacteristic
232C2×C107#54611yescharacteristic
233C2×C107#54711yescharacteristic
234C2×C107#54711yescharacteristic
235D107—24no—
236#2339—1071nomaximal, Sylow
237C107#233911yescharacteristic, complemented, Sylow
238C22×#41—1071no—
239C2×C4×D4—1071no—
240C2×C4×D4—1071no—
241#391—1071no—
242#391—1071no—
243#386—1071no—
244#386—1071no—
245#386—1071no—
246#386D10711yescharacteristic, complemented
247#381—1071no—
248#381—1071no—
249#380—1071no—
250C4×C22⋊C4—1071no—
251C2×#95—1071no—
252C2×#95—1071no—
253C2×#41—1078no—
254C2×#41—2144no—
255C2×#41—2144no—
256C22×Q8—1071no—
257C22×D4—1071no—
258C22×D4—1071no—
259C22×D4C2×D10711yescharacteristic
260C23×C4—1071no—
261C23×C4—1071no—
262C23×C4—1071no—
263C23×C4—1071no—
264C23×C4—1071no—
265C23×C4—1071no—
266C23×C4C2×D10711yescharacteristic
267C4×D4—2144no—
268C4×D4—2144no—
269C2×C4⋊C4—1071no—
270C2×C4⋊C4—1071no—
271C2×C22⋊C4—1071no—
272C2×C22⋊C4—1071no—
273C2×C22⋊C4—1071no—
274C2×C22⋊C4—1071no—
275C2×C22⋊C4—1071no—
276C2×C22⋊C4C2×D10711yescharacteristic
277C2×C22⋊C4C2×D10711yescharacteristic
278C2×C22⋊C4C2×D10711yescharacteristic
279C2×C42—1071no—
280C2×C42—1071no—
281#95—1071no—
282#95—1071no—
283#95—1071no—
284#95—1071no—
285#95—1071no—
286#95—1071no—
287#95—1071no—
288#95—1071no—
289#95—1071no—
290#95—1071no—
291#95C2×D10711yescharacteristic
292#95C2×D10711yescharacteristic
293C24—1071no—
294C24C22×D10711yescharacteristic
295C24C22×D10711yescharacteristic
296#41—21432no—
297C2×Q8—1074no—
298C2×Q8—2142no—
299C2×Q8—2142no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—1074no—
303C2×D4—1074no—
304C2×D4—1074no—
305C2×D4—1074no—
306C2×D4—2142no—
307C2×D4—2142no—
308C2×D4C4×D10714yescomplemented
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—1071no—
313C22×C4—1074no—
314C22×C4—1074no—
315C22×C4—1071no—
316C22×C4—1071no—
317C22×C4—1071no—
318C22×C4—1074no—
319C22×C4—1071no—
320C22×C4—1071no—
321C22×C4—1071no—
322C22×C4—4281no—
323C22×C4—4281no—
324C22×C4—4281no—
325C22×C4—2142no—
326C22×C4—2142no—
327C22×C4—2142no—
328C22×C4—2142no—
329C22×C4—2142no—
330C22×C4—2142no—
331C22×C4—2142no—
332C22×C4—2142no—
333C22×C4—2142no—
334C22×C4—2142no—
335C22×C4—2142no—
336C22×C4—2142no—
337C22×C4C22×D10711yescharacteristic
338C22×C4C22×D10711yescharacteristic
339C22×C4C22×D10711yescharacteristic
340C22×C4C22×D10711yescharacteristic
341C22×C4C22×D10711yescharacteristic
342C4⋊C4—2142no—
343C4⋊C4—2142no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C22⋊C4—4281no—
348C22⋊C4—2142no—
349C22⋊C4—2142no—
350C22⋊C4—2142no—
351C22⋊C4—2142no—
352C42—2142no—
353C42—2142no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—1072no—
365C23—1072no—
366C23—1072no—
367C23—2141no—
368C23—2141no—
369C23—2141no—
370C23—2141no—
371C23C2×C4×D10712yes—
372C23C2×C4×D10712yes—
373C23D4×D10712yes—
374C23D4×D10712yes—
375C23C23×D10711yescharacteristic
376Q8—2148no—
377D4—28no—
378D4—10716no—
379D4—2148no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—44no—
394C2×C4—1072no—
395C2×C4—1072no—
396C2×C4—1072no—
397C2×C4—1072no—
398C2×C4—1072no—
399C2×C4—1072no—
400C2×C4—4284no—
401C2×C4—4284no—
402C2×C4—4284no—
403C2×C4—2148no—
404C2×C4—2148no—
405C2×C4—2141no—
406C2×C4—2141no—
407C2×C4—2141no—
408C2×C4—2141no—
409C2×C4—2141no—
410C2×C4—2141no—
411C2×C4—2141no—
412C2×C4—2141no—
413C2×C4—2141no—
414C2×C4—2148no—
415C2×C4—2141no—
416C2×C4—2141no—
417C2×C4—2141no—
418C2×C4—2141no—
419C2×C4—2141no—
420C2×C4—2141no—
421C2×C4C2×C4×D10712yes—
422C2×C4#1313381712yescomplemented
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—1074no—
437C22—2142no—
438C22—2142no—
439C22—2142no—
440C22—2142no—
441C22—2142no—
442C22—2142no—
443C22C22⋊C4×D10714yes—
444C22C22×C4×D10711yescharacteristic
445C22C2×D4×D10711yescharacteristic
446C22C2×D4×D10711yescharacteristic
447C22#41×D10711yescharacteristic
448C22C2×#1313381711yescharacteristic
449C22#1681215411yescharacteristic
450C22#1681215611yescharacteristic
451C4—22no—
452C4—22no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—1074no—
457C4—4281no—
458C4—4281no—
459C4—4281no—
460C4—2142no—
461C4—2142no—
462C4—2142no—
463C2—24no—
464C2—42no—
465C2—2144no—
466C2C2×C22⋊C4×D10711yescharacteristic
467C2C4×#1313381711yescharacteristic
468C2#2029310611yescharacteristic
469C2#2029326411yescharacteristic
470C2#2029326611yescharacteristic
471C2#2029327511yescharacteristic
472C2#2029327711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#386×C107C2
socle, cosocleC23×C107C24
prime radicalC22×#13133817C2
hypercenter#386D107
hypocenterC107#2339
LCSG ▷ C22×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. C2×(C22⋊D107)⋊C4C2semidirect
4. #20292531C2semidirect
5. #20292531C2semidirect
6. #20292507C2semidirect
7. #20292503C2semidirect
8. #20292503C2semidirect
9. #20292489C2semidirect
10. #20292488C2semidirect
11. #20292485C2semidirect
12. C22⋊C4×Dic107C2semidirect
13. C2×C107⋊#95C2semidirect
14. #95×D107C2semidirect
15. #386×C107C2semidirect
18. C2×#13133817C4semidirect
60. C2×Dic214C2×C4semidirect
64. C2×C22⋊D107C2×C4semidirect
74. C22×Dic107C2×C4semidirect
75. C22×Dic107C2×C4semidirect
91. C2×C4×D107C2×C4semidirect
105. C2×D4×C107C2×C4semidirect
155. C2×C4×C107#41semidirect
157. C22⋊D107C22⋊C4semidirect
181. C2×Dic107#41semidirect
237. C107#2339semidirect
246. #386D107semidirect
308. C2×D4C4×D107semidirect
422. C2×C4#13133817semidirect

Maximal subgroups

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

subgroupindex
C22×#131338172
C2×C4×C22⋊D1072
C2×(C22⋊D107)⋊C42
#202925312
#202925072
#202925032
#202924892
#202924882
#202924852
C22⋊C4×Dic1072
C2×C107⋊#952
#95×D1072
#386×C1072
#2339107