Finite Group Databasebeta

← C37×#13072 #22634325

Subgroups — C37×#13072 #22634325

Order 9472.

458 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#504C211yesmaximal, characteristic
2C2×C37×#473C211yesmaximal, characteristic
3C2×C37×#362C211yesmaximal, characteristic, complemented
4C2×C37×#358C211yesmaximal, characteristic, complemented
5C37×#1816C211yesmaximal, characteristic
6C37×#1387C211yesmaximal, characteristic, complemented
7C37×#1381C211yesmaximal, characteristic, complemented
8C2×#137×C37—21no—
9C22×Q16×C37C2211yescharacteristic
10C2×#131×C37C2211yescharacteristic
11C37×#504—22no—
12C37×#504—22no—
13C2×M32×C37—21no—
14C2×M32×C37C2211yescharacteristic
15C22×C16×C37—21no—
16C22×C16×C37C2211yescharacteristic
17C37×#473—22no—
18C37×#473C414yescomplemented
19C2×#108×C37C2211yescharacteristic
20C2×#108×C37C2211yescharacteristic
21C2×#107×C37C2211yescharacteristic
22C37×#417—21no—
23C2×#101×C37—21no—
24C37×#362—22no—
25C37×#358—21no—
26C37×#358—21no—
27C37×#343—21no—
28C2×#41×C37D411yescharacteristic
29C22×Q8×C37—21no—
30#137×C37—24no—
31#137×C37—42no—
32C2×Q16×C37—21no—
33C2×Q16×C37—21no—
34C2×Q16×C37—21no—
35C2×Q16×C37—21no—
36C2×Q16×C37—21no—
37C2×Q16×C37—41no—
38C2×Q16×C37C2×C412yes—
39C2×SD16×C37—41no—
40#131×C37—21no—
41#131×C37—21no—
42#131×C37C2×C412yes—
43#131×C37D412yes—
44C2×M16×C37—21no—
45C2×M16×C37—21no—
46C2×M16×C37—21no—
47C2×M16×C37D411yescharacteristic
48C22×C8×C37—21no—
49C22×C8×C37C2311yescharacteristic
50C2×C4⋊C4×C37—21no—
51M32×C37—24no—
52M32×C37—21no—
53M32×C37D412yes—
54C2×C16×C37—24no—
55C2×C16×C37—21no—
56C2×C16×C37—21no—
57C2×C16×C37—21no—
58C2×C16×C37D411yescharacteristic
59C2×C16×C37D411yescharacteristic
60#108×C37—21no—
61#108×C37—21no—
62#108×C37—21no—
63#108×C37C2×C412yes—
64#107×C37—21no—
65#107×C37—21no—
66#103×C37—41no—
67#102×C37—41no—
68#101×C37—24no—
69#41×C37—21no—
70#41×C37—21no—
71#41×C37C22⋊C412yes—
72#41×C37SD1612yes—
73C2×Q8×C37—22no—
74C2×Q8×C37—41no—
75C2×Q8×C37—41no—
76C2×Q8×C37—41no—
77C2×Q8×C37—41no—
78C2×Q8×C37—41no—
79C2×Q8×C37D811yescharacteristic
80C2×D4×C37—21no—
81C2×D4×C37D811yescharacteristic
82C22×C4×C37—21no—
83C22×C4×C37—41no—
84C22×C4×C37—41no—
85C22×C4×C37C2×D411yescharacteristic
86Q16×C37—22no—
87Q16×C37—22no—
88Q16×C37—44no—
89Q16×C37—41no—
90Q16×C37—41no—
91SD16×C37—44no—
92M16×C37—21no—
93M16×C37—22no—
94M16×C37—22no—
95M16×C37—22no—
96M16×C37—41no—
97M16×C37—41no—
98M16×C37—41no—
99M16×C37C22⋊C412yes—
100C2×C8×C37—21no—
101C2×C8×C37—22no—
102C2×C8×C37—22no—
103C2×C8×C37—41no—
104C2×C8×C37—41no—
105C2×C8×C37C22×C411yescharacteristic
106C2×C8×C37C2×D411yescharacteristic
107C2×C8×C37C2×D411yescharacteristic
108C2×C8×C37C2×D411yescharacteristic
109C2×C8×C37#4111yescharacteristic
110C2×C8×C37#4111yescharacteristic
111C4⋊C4×C37—41no—
112C4⋊C4×C37—41no—
113C16×C37—21no—
114C16×C37—22no—
115C16×C37—21no—
116C23×C37—21no—
117C23×C37#13511yescharacteristic
118Q8×C37—21no—
119Q8×C37—42no—
120Q8×C37—42no—
121Q8×C37—81no—
122Q8×C37—81no—
123Q8×C37#10212yes—
124D4×C37—22no—
125D4×C37—22no—
126D4×C37—21no—
127D4×C37#10212yes—
128C2×C4×C37—21no—
129C2×C4×C37—22no—
130C2×C4×C37—22no—
131C2×C4×C37—42no—
132C2×C4×C37—81no—
133C2×C4×C37—81no—
134C2×C4×C37—81no—
135C2×C4×C37—161no—
136C2×C4×C37C2×C22⋊C411yescharacteristic
137C2×C4×C37#12111yescharacteristic
138C2×C4×C37#12111yescharacteristic
139C2×C4×C37C2×D811yescharacteristic
140C2×C4×C37C2×SD1611yescharacteristic
141C2×C4×C37#13511yescharacteristic
142C8×C37—22no—
143C8×C37—42no—
144C8×C37—81no—
145C8×C37C4×D411yescharacteristic
146C8×C37C4×D411yescharacteristic
147C8×C37#12011yescharacteristic
148C8×C37#12311yescharacteristic
149#13072C3711yesmaximal, characteristic, direct product factor, Sylow
150C22×C37—21no—
151C22×C37—21no—
152C22×C37—22no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37#41611yescharacteristic
156C22×C37#46511yescharacteristic
157C22×C37#46611yescharacteristic
158C4×C37—22no—
159C4×C37—82no—
160C4×C37—161no—
161C4×C37#38611yescharacteristic
162C4×C37C2×#10211yescharacteristic
163C4×C37#46511yescharacteristic
164C4×C37#46611yescharacteristic
165C2×#504C2×C3711yescharacteristic
166C2×#473C2×C3711yescharacteristic
167C2×#362C2×C3711yescharacteristic, complemented
168C2×#358C2×C3711yescharacteristic, complemented
169#1816C2×C3711yescharacteristic
170#1387C2×C3711yescharacteristic, complemented
171#1381C2×C3711yescharacteristic, complemented
172C2×C37—21no—
173C2×C37—21no—
174C2×C37—42no—
175C2×C37#189311yescharacteristic
176C2×C37#222211yescharacteristic
177C2×C37#222311yescharacteristic
178C2×#137—21no—
179C22×Q16C22×C3711yescharacteristic
180C2×#131C22×C3711yescharacteristic
181#504—22no—
182#504—22no—
183C2×M32—21no—
184C2×M32C22×C3711yescharacteristic
185C22×C16—21no—
186C22×C16C22×C3711yescharacteristic
187#473—22no—
188#473C4×C3714yescomplemented
189C2×#108C22×C3711yescharacteristic
190C2×#108C22×C3711yescharacteristic
191C2×#107C22×C3711yescharacteristic
192#417—21no—
193C2×#101—21no—
194#362—22no—
195#358—21no—
196#358—21no—
197#343—21no—
198C37#1307211yescharacteristic, direct product factor, Sylow
199C2×#41D4×C3711yescharacteristic
200C22×Q8—21no—
201#137—24no—
202#137—42no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—41no—
209C2×Q16C2×C4×C3712yes—
210C2×SD16—41no—
211#131—21no—
212#131—21no—
213#131C2×C4×C3712yes—
214#131D4×C3712yes—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16D4×C3711yescharacteristic
219C22×C8—21no—
220C22×C8C23×C3711yescharacteristic
221C2×C4⋊C4—21no—
222M32—24no—
223M32—21no—
224M32D4×C3712yes—
225C2×C16—24no—
226C2×C16—21no—
227C2×C16—21no—
228C2×C16—21no—
229C2×C16D4×C3711yescharacteristic
230C2×C16D4×C3711yescharacteristic
231#108—21no—
232#108—21no—
233#108—21no—
234#108C2×C4×C3712yes—
235#107—21no—
236#107—21no—
237#103—41no—
238#102—41no—
239#101—24no—
240#41—21no—
241#41—21no—
242#41C22⋊C4×C3712yes—
243#41SD16×C3712yes—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8D8×C3711yescharacteristic
251C2×D4—21no—
252C2×D4D8×C3711yescharacteristic
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4C2×D4×C3711yescharacteristic
257Q16—22no—
258Q16—22no—
259Q16—44no—
260Q16—41no—
261Q16—41no—
262SD16—44no—
263M16—21no—
264M16—22no—
265M16—22no—
266M16—22no—
267M16—41no—
268M16—41no—
269M16—41no—
270M16C22⋊C4×C3712yes—
271C2×C8—21no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8C22×C4×C3711yescharacteristic
277C2×C8C2×D4×C3711yescharacteristic
278C2×C8C2×D4×C3711yescharacteristic
279C2×C8C2×D4×C3711yescharacteristic
280C2×C8#41×C3711yescharacteristic
281C2×C8#41×C3711yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C16—21no—
285C16—22no—
286C16—21no—
287C23—21no—
288C23#135×C3711yescharacteristic
289Q8—21no—
290Q8—42no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8#102×C3712yes—
295D4—22no—
296D4—22no—
297D4—21no—
298D4#102×C3712yes—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—161no—
307C2×C4C2×C22⋊C4×C3711yescharacteristic
308C2×C4#121×C3711yescharacteristic
309C2×C4#121×C3711yescharacteristic
310C2×C4C2×D8×C3711yescharacteristic
311C2×C4C2×SD16×C3711yescharacteristic
312C2×C4#135×C3711yescharacteristic
313C8—22no—
314C8—42no—
315C8—81no—
316C8C4×D4×C3711yescharacteristic
317C8C4×D4×C3711yescharacteristic
318C8#120×C3711yescharacteristic
319C8#123×C3711yescharacteristic
320C22—21no—
321C22—21no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22C37×#41611yescharacteristic
326C22C37×#46511yescharacteristic
327C22C37×#46611yescharacteristic
328C4—22no—
329C4—82no—
330C4—161no—
331C4C37×#38611yescharacteristic
332C4C2×#102×C3711yescharacteristic
333C4C37×#46511yescharacteristic
334C4C37×#46611yescharacteristic
335C2—21no—
336C2—21no—
337C2—42no—
338C2C37×#189311yescharacteristic
339C2C37×#222211yescharacteristic
340C2C37×#222311yescharacteristic
subgroupG/H
center, socleC22×C37#466
commutatorC2×C8C22×C4×C37
Frattini, cosocleC22×C8C23×C37
prime radicalC2×#41×C37D4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C22×C4×C37 ◁ C2×#131×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C37×#362C2semidirect
4. C2×C37×#358C2semidirect
6. C37×#1387C2semidirect
7. C37×#1381C2semidirect
18. C37×#473C4semidirect
149. #13072C37direct (N × H)
167. C2×#362C2×C37semidirect
168. C2×#358C2×C37semidirect
170. #1387C2×C37semidirect
171. #1381C2×C37semidirect
188. #473C4×C37semidirect
198. C37#13072direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5042
C2×C37×#4732
C2×C37×#3622
C2×C37×#3582
C37×#18162
C37×#13872
C37×#13812
#1307237