Finite Group Databasebeta

← C37×#33866 #22655119

Subgroups — C37×#33866 #22655119

Order 9472.

548 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3338C211yesmaximal, characteristic
2D4×Q16×C37C211yesmaximal, characteristic
3C37×#2241C211yesmaximal, characteristic, complemented
4C37×#2236C212yesmaximal, complemented
5C37×#2227C211yesmaximal, characteristic, complemented
6C37×#2216C212yesmaximal, complemented
7C37×#2209C211yesmaximal, characteristic, complemented
8C37×#2188C212yesmaximal, complemented
9C4×Q32×C37C211yesmaximal, characteristic, complemented
10D4×C16×C37C211yesmaximal, characteristic
11C2×C37×#358C212yesmaximal, complemented
12C22×Q16×C37C2212yes—
13C37×#554—21no—
14D4×Q8×C37—21no—
15C2×Q32×C37C2211yescharacteristic
16C2×Q32×C37C2212yes—
17C22×C16×C37C2212yes—
18C37×#500C2211yescharacteristic
19C37×#494C2211yescharacteristic
20C37×#484—22no—
21C37×#477—21no—
22C37×#467C2212yes—
23C37×#467C2212yes—
24C37×#462—21no—
25C37×#451—22no—
26C4×Q16×C37C2211yescharacteristic
27C4×Q16×C37C2211yescharacteristic
28C8×D4×C37C2211yescharacteristic
29C2×#107×C37C2212yes—
30C37×#366C2211yescharacteristic
31C37×#366C2212yes—
32C37×C4⋊C16C2211yescharacteristic
33C37×#358C2211yescharacteristic
34C37×#358C2212yes—
35C37×#358C2212yes—
36C37×#358C2212yes—
37C37×#358C2211yescharacteristic
38C37×#358C2212yes—
39C37×C22⋊C16C2212yes—
40C4×C16×C37C2211yescharacteristic
41C22×Q8×C37—22no—
42C2×Q16×C37—24no—
43C2×Q16×C37—22no—
44C2×Q16×C37—21no—
45C2×Q16×C37—42no—
46C2×Q16×C37C2312yes—
47C2×Q16×C37C2311yescharacteristic
48C2×Q16×C37C2311yescharacteristic
49C22×C8×C37C2312yes—
50C4⋊Q8×C37—21no—
51C4⋊Q8×C37—21no—
52C4⋊Q8×C37—41no—
53#125×C37—41no—
54C22⋊Q8×C37—22no—
55C22⋊Q8×C37—22no—
56C22⋊Q8×C37—42no—
57C22⋊Q8×C37—42no—
58C4×Q8×C37—21no—
59C4×Q8×C37—21no—
60C4×D4×C37—41no—
61C4×D4×C37—41no—
62C4×D4×C37D411yescharacteristic
63C2×C4⋊C4×C37—22no—
64Q32×C37—22no—
65Q32×C37—42no—
66C2×C16×C37—42no—
67C2×C16×C37C2311yescharacteristic
68C2×C16×C37C2311yescharacteristic
69C2×C16×C37C2312yes—
70#107×C37—22no—
71#107×C37—21no—
72#107×C37C2311yescharacteristic
73#107×C37C2312yes—
74#107×C37C2311yescharacteristic
75C4⋊C8×C37D411yescharacteristic
76#103×C37—21no—
77#103×C37—21no—
78#103×C37—22no—
79#103×C37—22no—
80C22⋊C8×C37D412yes—
81C4×C8×C37C2311yescharacteristic
82C2×Q8×C37—21no—
83C2×Q8×C37—21no—
84C2×Q8×C37—22no—
85C2×Q8×C37—44no—
86C2×Q8×C37—42no—
87C2×Q8×C37—41no—
88C2×Q8×C37—82no—
89C2×D4×C37D811yescharacteristic
90C22×C4×C37—42no—
91C22×C4×C37—42no—
92C22×C4×C37C2×D412yes—
93Q16×C37—21no—
94Q16×C37—22no—
95Q16×C37—21no—
96Q16×C37—21no—
97Q16×C37—22no—
98Q16×C37—44no—
99Q16×C37—81no—
100Q16×C37#4112yes—
101C2×C8×C37—22no—
102C2×C8×C37—22no—
103C2×C8×C37C2×D411yescharacteristic
104C2×C8×C37C2×D412yes—
105C2×C8×C37C2411yescharacteristic
106C4⋊C4×C37—21no—
107C4⋊C4×C37—21no—
108C4⋊C4×C37—22no—
109C4⋊C4×C37—42no—
110C4⋊C4×C37—41no—
111C4⋊C4×C37—41no—
112C4⋊C4×C37—41no—
113C4⋊C4×C37—41no—
114C4⋊C4×C37—42no—
115C4⋊C4×C37—42no—
116C4⋊C4×C37—41no—
117C4⋊C4×C37D811yescharacteristic
118C22⋊C4×C37—42no—
119C22⋊C4×C37—42no—
120C22⋊C4×C37D812yes—
121C42×C37—41no—
122C42×C37—41no—
123C42×C37C2×D411yescharacteristic
124C16×C37—21no—
125C16×C37—21no—
126C16×C37—22no—
127C23×C37C2×D812yes—
128Q8×C37—22no—
129Q8×C37—41no—
130Q8×C37—42no—
131Q8×C37—41no—
132Q8×C37—42no—
133Q8×C37—41no—
134Q8×C37—84no—
135Q8×C37—161no—
136D4×C37Q3214yescomplemented
137C2×C4×C37—22no—
138C2×C4×C37—22no—
139C2×C4×C37—41no—
140C2×C4×C37—41no—
141C2×C4×C37—41no—
142C2×C4×C37—41no—
143C2×C4×C37—42no—
144C2×C4×C37—42no—
145C2×C4×C37—84no—
146C2×C4×C37—162no—
147C2×C4×C37C2×D811yescharacteristic
148C2×C4×C37C2×D812yes—
149C2×C4×C37C2×D811yescharacteristic
150C2×C4×C37C22×D411yescharacteristic
151C8×C37—22no—
152C8×C37—21no—
153C8×C37C2×#4111yescharacteristic
154C8×C37H(5,𝔽2)11yescharacteristic
155#33866C3711yesmaximal, characteristic, direct product factor, Sylow
156C22×C37—22no—
157C22×C37—22no—
158C22×C37C2×Q3214yes—
159C22×C37C22×D811yescharacteristic
160C4×C37—21no—
161C4×C37—22no—
162C4×C37—42no—
163C4×C37—81no—
164C4×C37—81no—
165C4×C37—82no—
166C4×C37—82no—
167C4×C37—81no—
168C4×C37C2×Q3212yes—
169C4×C37#54611yescharacteristic
170C4×C37#57711yescharacteristic
171#3338C2×C3711yescharacteristic
172D4×Q16C2×C3711yescharacteristic
173#2241C2×C3711yescharacteristic, complemented
174#2236C2×C3712yescomplemented
175#2227C2×C3711yescharacteristic, complemented
176#2216C2×C3712yescomplemented
177#2209C2×C3711yescharacteristic, complemented
178#2188C2×C3712yescomplemented
179C4×Q32C2×C3711yescharacteristic, complemented
180D4×C16C2×C3711yescharacteristic
181C2×#358C2×C3712yescomplemented
182C2×C37—24no—
183C2×C37#329411yescharacteristic
184C2×C37C22×Q3211yescharacteristic
185C2×C37#341611yescharacteristic
186C22×Q16C22×C3712yes—
187#554—21no—
188D4×Q8—21no—
189C2×Q32C22×C3711yescharacteristic
190C2×Q32C22×C3712yes—
191C22×C16C22×C3712yes—
192#500C22×C3711yescharacteristic
193#494C22×C3711yescharacteristic
194#484—22no—
195#477—21no—
196#467C22×C3712yes—
197#467C22×C3712yes—
198#462—21no—
199#451—22no—
200C4×Q16C22×C3711yescharacteristic
201C4×Q16C22×C3711yescharacteristic
202C8×D4C22×C3711yescharacteristic
203C2×#107C22×C3712yes—
204#366C22×C3711yescharacteristic
205#366C22×C3712yes—
206C4⋊C16C22×C3711yescharacteristic
207#358C22×C3711yescharacteristic
208#358C22×C3712yes—
209#358C22×C3712yes—
210#358C22×C3712yes—
211#358C22×C3711yescharacteristic
212#358C22×C3712yes—
213C22⋊C16C22×C3712yes—
214C4×C16C22×C3711yescharacteristic
215C37#3386611yescharacteristic, direct product factor, Sylow
216C22×Q8—22no—
217C2×Q16—24no—
218C2×Q16—22no—
219C2×Q16—21no—
220C2×Q16—42no—
221C2×Q16C23×C3712yes—
222C2×Q16C23×C3711yescharacteristic
223C2×Q16C23×C3711yescharacteristic
224C22×C8C23×C3712yes—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—41no—
228#125—41no—
229C22⋊Q8—22no—
230C22⋊Q8—22no—
231C22⋊Q8—42no—
232C22⋊Q8—42no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—41no—
236C4×D4—41no—
237C4×D4D4×C3711yescharacteristic
238C2×C4⋊C4—22no—
239Q32—22no—
240Q32—42no—
241C2×C16—42no—
242C2×C16C23×C3711yescharacteristic
243C2×C16C23×C3711yescharacteristic
244C2×C16C23×C3712yes—
245#107—22no—
246#107—21no—
247#107C23×C3711yescharacteristic
248#107C23×C3712yes—
249#107C23×C3711yescharacteristic
250C4⋊C8D4×C3711yescharacteristic
251#103—21no—
252#103—21no—
253#103—22no—
254#103—22no—
255C22⋊C8D4×C3712yes—
256C4×C8C23×C3711yescharacteristic
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—22no—
260C2×Q8—44no—
261C2×Q8—42no—
262C2×Q8—41no—
263C2×Q8—82no—
264C2×D4D8×C3711yescharacteristic
265C22×C4—42no—
266C22×C4—42no—
267C22×C4C2×D4×C3712yes—
268Q16—21no—
269Q16—22no—
270Q16—21no—
271Q16—21no—
272Q16—22no—
273Q16—44no—
274Q16—81no—
275Q16#41×C3712yes—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8C2×D4×C3711yescharacteristic
279C2×C8C2×D4×C3712yes—
280C2×C8C24×C3711yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—41no—
292C4⋊C4D8×C3711yescharacteristic
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4D8×C3712yes—
296C42—41no—
297C42—41no—
298C42C2×D4×C3711yescharacteristic
299C16—21no—
300C16—21no—
301C16—22no—
302C23C2×D8×C3712yes—
303Q8—22no—
304Q8—41no—
305Q8—42no—
306Q8—41no—
307Q8—42no—
308Q8—41no—
309Q8—84no—
310Q8—161no—
311D4Q32×C3714yescomplemented
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—84no—
321C2×C4—162no—
322C2×C4C2×D8×C3711yescharacteristic
323C2×C4C2×D8×C3712yes—
324C2×C4C2×D8×C3711yescharacteristic
325C2×C4C22×D4×C3711yescharacteristic
326C8—22no—
327C8—21no—
328C8C2×#41×C3711yescharacteristic
329C8H(5,𝔽2)×C3711yescharacteristic
330C22—22no—
331C22—22no—
332C22C2×Q32×C3714yes—
333C22C22×D8×C3711yescharacteristic
334C4—21no—
335C4—22no—
336C4—42no—
337C4—81no—
338C4—82no—
339C4—81no—
340C4—82no—
341C4—81no—
342C4C2×Q32×C3712yes—
343C4C37×#54611yescharacteristic
344C4C37×#57711yescharacteristic
345C2—24no—
346C2C37×#329411yescharacteristic
347C2C22×Q32×C3711yescharacteristic
348C2C37×#341611yescharacteristic
subgroupG/H
center, socleC22×C37C22×D8
commutator, Frattini, cosocleC2×C8C24×C37
prime radicalC2×D4×C37D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C4×D4×C37 ◁ C8×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#2241C2semidirect
4. C37×#2236C2semidirect
5. C37×#2227C2semidirect
6. C37×#2216C2semidirect
7. C37×#2209C2semidirect
8. C37×#2188C2semidirect
9. C4×Q32×C37C2semidirect
11. C2×C37×#358C2semidirect
136. D4×C37Q32semidirect
155. #33866C37direct (N × H)
173. #2241C2×C37semidirect
174. #2236C2×C37semidirect
175. #2227C2×C37semidirect
176. #2216C2×C37semidirect
177. #2209C2×C37semidirect
178. #2188C2×C37semidirect
179. C4×Q32C2×C37semidirect
181. C2×#358C2×C37semidirect
215. C37#33866direct (N × H)
311. D4Q32×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#33382
D4×Q16×C372
C37×#22412
C37×#22362
C37×#22272
C37×#22162
C37×#22092
C37×#21882
C4×Q32×C372
D4×C16×C372
C2×C37×#3582
#3386637