Finite Group Databasebeta

← C2×D37⋊#104 #18011220

Subgroups — C2×D37⋊#104 #18011220

Order 4736.

856 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D37⋊M16C211yesmaximal, characteristic, complemented
2C22×C4×#3866C211yesmaximal, characteristic, complemented
3C2×#11924601C212yesmaximal, complemented
4D37⋊#104C218yesmaximal, direct product factor
5C2×#11924600C212yesmaximal, complemented
6C2×#41×D37C211yesmaximal, characteristic
7C23×#3866—21no—
8C2×#10596953C2212yescomplemented
9D37⋊M16—22no—
10D37⋊M16C2214yescomplemented
11C2×#10596957—21no—
12C2×D37⋊C8—21no—
13C2×C4×#3866—22no—
14C2×C4×#3866—21no—
15C2×C4×#3866C2212yescomplemented
16C2×C4×#3866C2214yescomplemented
17#11924601C2218yescomplemented
18#11924600C2218yescomplemented
19C2×#10596966C2211yescharacteristic
20C2×#10596962—21no—
21C2×#10596962C411yescharacteristic, complemented
22C2×#10596964—21no—
23C2×#10596964C2211yescharacteristic
24#41×D37—22no—
25#41×D37—22no—
26#41×D37C414yescomplemented
27#41×D37C2214yes—
28C2×Q8×D37C411yescharacteristic, complemented
29C2×D4×D37—21no—
30C2×D4×D37C411yescharacteristic, complemented
31C22×C4×D37—21no—
32C22×C4×D37C2211yescharacteristic
33C2×#41×C37C411yescharacteristic, complemented
34C23×D37—21no—
35C23×D37D411yescharacteristic
36C22×#3866—28no—
37C22×#3866—22no—
38C22×#3866—24no—
39#41×C37—22no—
40#41×C37C2×C414yescomplemented
41C2×Q8×C37C2×C411yescharacteristic, complemented
42C2×D4×C37—21no—
43C2×D4×C37C2×C411yescharacteristic, complemented
44C22×C4×C37—21no—
45C22×C4×C37C2×C411yescharacteristic
46C2×C22⋊D37—21no—
47C2×C22⋊D37—21no—
48C2×C22⋊D37—21no—
49C22×Dic37—21no—
50C22×Dic37D411yescharacteristic
51#10596966—21no—
52#10596966—21no—
53#10596966C2×C412yescomplemented
54#10596966C2312yes—
55Q8×D37—22no—
56Q8×D37C2×C414yescomplemented
57#10596964—24no—
58#10596964—24no—
59#10596964—21no—
60#10596964—21no—
61#10596964C2×C412yescomplemented
62#10596964C2312yes—
63D4×D37—24no—
64D4×D37—24no—
65D4×D37—22no—
66D4×D37C2×C414yescomplemented
67#10596962—22no—
68#10596962—24no—
69#10596962—24no—
70#10596962C2×C414yescomplemented
71C2×D148—21no—
72C2×D148C2×C411yescharacteristic, complemented
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37—24no—
77C2×C4×D37—24no—
78C2×C4×D37C2×C411yescharacteristic
79C2×C4×D37C2×C412yes—
80C2×C4×D37D412yes—
81C2×C4×D37D411yescharacteristic
82C2×C4×D37D411yescharacteristic
83C2×C4×D37D412yes—
84C2×C4×D37C2312yes—
85C2×C4×D37C2311yescharacteristic
86C2×Dic74—21no—
87C2×Dic74C2×C411yescharacteristic, complemented
88#10596957—24no—
89C2×#64438—22no—
90C4×#3866—24no—
91C4×#3866—22no—
92C4×#3866C2314yescomplemented
93#10596953—22no—
94#10596953C2314yescomplemented
95D37⋊C8—24no—
96C23×C37—21no—
97C23×C37C22⋊C411yescharacteristic
98C22×D37—24no—
99C22×D37—21no—
100C22×D37—24no—
101C22×D37—44no—
102C22×D37C22⋊C412yes—
103C22×D37C22⋊C411yescharacteristic
104C22×D37C2×D411yescharacteristic
105C22×D37C2×D412yes—
106C2×#3866—28no—
107C2×#3866—216no—
108C2×#3866—24no—
109Q8×C37—21no—
110Q8×C37C22×C412yescomplemented
111D4×C37—24no—
112D4×C37—21no—
113D4×C37C22×C412yescomplemented
114C2×C4×C37—21no—
115C2×C4×C37—24no—
116C2×C4×C37C22⋊C412yes—
117C2×C4×C37C22⋊C411yescharacteristic
118C2×C4×C37C22×C411yescharacteristic
119C2×C4×C37C22×C412yes—
120C22⋊D37—24no—
121C22⋊D37—22no—
122C22⋊D37—22no—
123C22⋊D37—24no—
124C2×Dic37—21no—
125C2×Dic37—22no—
126C2×Dic37—22no—
127C2×Dic37C22⋊C411yescharacteristic
128C2×Dic37C22⋊C412yes—
129C2×Dic37C2×D411yescharacteristic
130C2×Dic37C2×D412yes—
131D148—22no—
132D148—22no—
133D148—21no—
134D148C22×C412yescomplemented
135C4×D37—24no—
136C4×D37—24no—
137C4×D37—22no—
138C4×D37—22no—
139C4×D37C22⋊C412yes—
140C4×D37C22⋊C412yes—
141C4×D37C22⋊C412yes—
142C4×D37C22×C412yes—
143C4×D37C22×C411yescharacteristic
144C4×D37C2×D412yes—
145C4×D37C2×D411yescharacteristic
146C4×D37C2×D412yes—
147C4×D37C2×D411yescharacteristic
148C4×D37C2411yescharacteristic
149Dic74—21no—
150Dic74—24no—
151Dic74C22×C412yescomplemented
152#64438—24no—
153C22×C37—22no—
154C22×C37—22no—
155C22×C37—42no—
156C22×C37C2×C22⋊C412yes—
157C22×C37C2×C22⋊C411yescharacteristic
158C2×D37—22no—
159C2×D37—24no—
160C2×D37—24no—
161C2×D37—22no—
162C2×D37—42no—
163C2×D37—48no—
164C2×D37#10414yescomplemented
165C2×D37C2×C22⋊C411yescharacteristic
166C2×D37C2×C22⋊C412yes—
167C2×D37C22×D411yescharacteristic
168#3866—28no—
169C4×C37—22no—
170C4×C37C2×C22⋊C411yescharacteristic
171C4×C37C2×C22⋊C412yes—
172C4×C37C23×C411yescharacteristic
173Dic37—22no—
174Dic37C2×C22⋊C412yes—
175Dic37C2×C22⋊C411yescharacteristic
176Dic37C22×D411yescharacteristic
177C22×#104—371nomaximal, Sylow
178C2×C37—22no—
179C2×C37—42no—
180C2×C37C2×#10412yescomplemented
181C2×C37C22×C22⋊C411yescharacteristic
182D37—21no—
183D37—21no—
184D37—42no—
185D37C2×#10414yescomplemented
186C22×#41—371no—
187C22×M16—371no—
188C22×C42—371no—
189C2×#104—372no—
190C2×#104—378no—
191C2×#104—372no—
192C37C22×#10411yescharacteristic, complemented, Sylow
193C2×#41—374no—
194C2×#41—374no—
195C2×#41—371no—
196C2×#41—371no—
197C2×#41—371no—
198C2×#41—741no—
199C2×#41—741no—
200C2×#41—742no—
201C2×#41—742no—
202C2×#41#386611yescharacteristic, complemented
203C22×Q8—371no—
204C22×D4—371no—
205C22×D4—741no—
206C23×C4—371no—
207C23×C4—741no—
208C23×C4—741no—
209C2×M16—374no—
210C2×M16—372no—
211C2×M16—741no—
212C2×M16—742no—
213C22×C8—741no—
214C2×C42—372no—
215C2×C42—374no—
216C2×C42—742no—
217C2×C42—741no—
218#104—378no—
219#104—378no—
220C24—371no—
221C24—741no—
222#41—22no—
223#41—372no—
224#41—372no—
225#41—372no—
226#41—372no—
227#41—374no—
228#41—744no—
229#41—744no—
230#41—744no—
231#41—744no—
232#41—741no—
233#41—741no—
234#41—741no—
235#41—741no—
236#41—742no—
237#41C2×#386614yescomplemented
238C2×Q8—374no—
239C2×Q8—371no—
240C2×Q8—741no—
241C2×Q8—742no—
242C2×Q8C2×#386611yescharacteristic, complemented
243C2×D4—21no—
244C2×D4—374no—
245C2×D4—371no—
246C2×D4—741no—
247C2×D4—742no—
248C2×D4—741no—
249C2×D4—744no—
250C2×D4—744no—
251C2×D4—741no—
252C2×D4—741no—
253C2×D4C2×#386611yescharacteristic, complemented
254C22×C4—21no—
255C22×C4—371no—
256C22×C4—372no—
257C22×C4—372no—
258C22×C4—371no—
259C22×C4—371no—
260C22×C4—371no—
261C22×C4—372no—
262C22×C4—371no—
263C22×C4—372no—
264C22×C4—741no—
265C22×C4—744no—
266C22×C4—744no—
267C22×C4—741no—
268C22×C4—741no—
269C22×C4—744no—
270C22×C4—742no—
271C22×C4—748no—
272C22×C4—741no—
273C22×C4C2×#386611yescharacteristic
274M16—374no—
275M16—742no—
276M16—744no—
277C2×C8—744no—
278C2×C8—742no—
279C42—374no—
280C42—742no—
281C42—744no—
282C23—21no—
283C23—371no—
284C23—372no—
285C23—371no—
286C23—372no—
287C23—744no—
288C23—744no—
289C23—741no—
290C23—1484no—
291C23C22⋊#386611yescharacteristic
292Q8—21no—
293Q8—372no—
294Q8—744no—
295Q8—741no—
296Q8C22×#386612yescomplemented
297D4—24no—
298D4—21no—
299D4—372no—
300D4—742no—
301D4—742no—
302D4—744no—
303D4—742no—
304D4—742no—
305D4—744no—
306D4—741no—
307D4C22×#386612yescomplemented
308C2×C4—21no—
309C2×C4—24no—
310C2×C4—371no—
311C2×C4—372no—
312C2×C4—371no—
313C2×C4—372no—
314C2×C4—371no—
315C2×C4—372no—
316C2×C4—372no—
317C2×C4—371no—
318C2×C4—372no—
319C2×C4—372no—
320C2×C4—372no—
321C2×C4—371no—
322C2×C4—372no—
323C2×C4—371no—
324C2×C4—742no—
325C2×C4—742no—
326C2×C4—744no—
327C2×C4—742no—
328C2×C4—742no—
329C2×C4—744no—
330C2×C4—7416no—
331C2×C4—748no—
332C2×C4—741no—
333C2×C4—744no—
334C2×C4C22⋊#386612yes—
335C2×C4C22⋊#386611yescharacteristic
336C2×C4C22×#386611yescharacteristic
337C2×C4C22×#386612yes—
338C8—744no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—374no—
343C22—372no—
344C22—371no—
345C22—371no—
346C22—744no—
347C22—744no—
348C22—742no—
349C22—742no—
350C22—1488no—
351C22—1482no—
352C22C2×C22⋊#386612yes—
353C22C2×C22⋊#386611yescharacteristic
354C4—22no—
355C4—371no—
356C4—371no—
357C4—372no—
358C4—748no—
359C4—742no—
360C4C2×C22⋊#386612yes—
361C4C2×C22⋊#386611yescharacteristic
362C4C23×#386611yescharacteristic
363C2—22no—
364C2—42no—
365C2—374no—
366C2—741no—
367C2—741no—
368C2—1482no—
369C2D37⋊#10412yesdirect product factor
370C2C22×C22⋊#386611yescharacteristic
subgroupG/H
centerC2×C4C22⋊#3866
commutatorC4×C37C23×C4
FrattiniC4C23×#3866
FittingC2×#41×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#41×D37C2
cosocleC4×D37C24
hypercenterC2×#41#3866
hypocenterC37C22×#104
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D37⋊M16C2semidirect
2. C22×C4×#3866C2semidirect
3. C2×#11924601C2semidirect
4. D37⋊#104C2direct (N × H)
5. C2×#11924600C2semidirect
8. C2×#10596953C22semidirect
10. D37⋊M16C22semidirect
15. C2×C4×#3866C22semidirect
16. C2×C4×#3866C22semidirect
17. #11924601C22semidirect
18. #11924600C22semidirect
21. C2×#10596962C4semidirect
26. #41×D37C4semidirect
28. C2×Q8×D37C4semidirect
30. C2×D4×D37C4semidirect
33. C2×#41×C37C4semidirect
40. #41×C37C2×C4semidirect
41. C2×Q8×C37C2×C4semidirect
43. C2×D4×C37C2×C4semidirect
53. #10596966C2×C4semidirect
56. Q8×D37C2×C4semidirect
61. #10596964C2×C4semidirect
66. D4×D37C2×C4semidirect
70. #10596962C2×C4semidirect
72. C2×D148C2×C4semidirect
87. C2×Dic74C2×C4semidirect
92. C4×#3866C23semidirect
94. #10596953C23semidirect
110. Q8×C37C22×C4semidirect
113. D4×C37C22×C4semidirect
134. D148C22×C4semidirect
151. Dic74C22×C4semidirect
164. C2×D37#104semidirect
180. C2×C37C2×#104semidirect
185. D37C2×#104semidirect
192. C37C22×#104semidirect
202. C2×#41#3866semidirect
237. #41C2×#3866semidirect
242. C2×Q8C2×#3866semidirect
253. C2×D4C2×#3866semidirect
296. Q8C22×#3866semidirect
307. D4C22×#3866semidirect
369. C2D37⋊#104direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D37⋊M162
C22×C4×#38662
C2×#119246012
D37⋊#1042
C2×#119246002
C2×#41×D372
C22×#10437