Finite Group Databasebeta

← C37×#13412 #22634665

Subgroups — C37×#13412 #22634665

Order 9472.

430 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3156C211yesmaximal, characteristic
2C2×C37×#362C211yesmaximal, characteristic, complemented
3C2×C37×#359C211yesmaximal, characteristic
4C37×#2139C211yesmaximal, characteristic
5C2×C37×#358C211yesmaximal, characteristic, complemented
6C37×#1952C211yesmaximal, characteristic, complemented
7C37×#1379C211yesmaximal, characteristic, complemented
8C2×#137×C37—21no—
9C2×#135×C37C2211yescharacteristic
10C22×Q16×C37C2211yescharacteristic
11C37×#536—21no—
12C2×M32×C37C2211yescharacteristic
13C22×C16×C37C2211yescharacteristic
14C37×#497—22no—
15C37×#495—21no—
16C37×#494—21no—
17C2×#108×C37C2211yescharacteristic
18C37×#428—21no—
19C2×#107×C37C2211yescharacteristic
20C37×#405C2211yescharacteristic
21C37×#362—22no—
22C37×#359—22no—
23C37×#358—22no—
24C37×#358—21no—
25C37×#357—21no—
26C37×#343—21no—
27C2×#41×C37—21no—
28C22×Q8×C37—21no—
29#137×C37—42no—
30#137×C37—42no—
31#135×C37—21no—
32#135×C37—21no—
33#135×C37—21no—
34#135×C37—21no—
35C2×Q16×C37—22no—
36C2×Q16×C37—21no—
37C2×Q16×C37—21no—
38C2×Q16×C37—21no—
39C2×Q16×C37—21no—
40C2×Q16×C37—21no—
41C2×Q16×C37D412yes—
42C2×Q16×C37D411yescharacteristic
43C2×SD16×C37—22no—
44C2×SD16×C37—21no—
45C2×D8×C37D411yescharacteristic
46C2×M16×C37—21no—
47C2×M16×C37D411yescharacteristic
48C22×C8×C37C2311yescharacteristic
49C4⋊Q8×C37—22no—
50#124×C37—22no—
51#123×C37—42no—
52C22⋊Q8×C37—41no—
53C22⋊Q8×C37—41no—
54#117×C37D411yescharacteristic
55C2×C4⋊C4×C37—21no—
56M32×C37—21no—
57M32×C37—21no—
58C2×C16×C37—21no—
59C2×C16×C37—21no—
60C2×C16×C37—21no—
61C2×C16×C37—21no—
62#108×C37—21no—
63#108×C37D412yes—
64#107×C37—21no—
65#107×C37—21no—
66#107×C37—41no—
67#106×C37—41no—
68#97×C37—21no—
69C4×C8×C37—21no—
70#41×C37—41no—
71#41×C37—41no—
72#41×C37—41no—
73#41×C37—41no—
74C2×Q8×C37—22no—
75C2×Q8×C37—21no—
76C2×Q8×C37—41no—
77C2×Q8×C37—41no—
78C2×Q8×C37—41no—
79C2×Q8×C37—41no—
80C2×Q8×C37—41no—
81C2×D4×C37—21no—
82C2×D4×C37—41no—
83C22×C4×C37—41no—
84C22×C4×C37—41no—
85C22×C4×C37—41no—
86C22×C4×C37C2×D411yescharacteristic
87Q16×C37—22no—
88Q16×C37—21no—
89Q16×C37—22no—
90Q16×C37—21no—
91Q16×C37—44no—
92Q16×C37—41no—
93Q16×C37—41no—
94SD16×C37—44no—
95SD16×C37—41no—
96SD16×C37—41no—
97D8×C37—21no—
98D8×C37—21no—
99M16×C37—21no—
100M16×C37—22no—
101M16×C37—41no—
102M16×C37SD1612yes—
103C2×C8×C37—21no—
104C2×C8×C37—41no—
105C2×C8×C37C2×D411yescharacteristic
106C2×C8×C37C2×D411yescharacteristic
107C2×C8×C37C2×D411yescharacteristic
108C2×C8×C37#4111yescharacteristic
109C2×C8×C37#4111yescharacteristic
110C2×C8×C37#4111yescharacteristic
111C4⋊C4×C37—42no—
112C4⋊C4×C37—42no—
113C4⋊C4×C37—41no—
114C4⋊C4×C37—41no—
115C4⋊C4×C37D811yescharacteristic
116C4⋊C4×C37D811yescharacteristic
117C22⋊C4×C37—21no—
118C22⋊C4×C37—42no—
119C22⋊C4×C37—42no—
120C42×C37—21no—
121C16×C37—41no—
122C16×C37—41no—
123C23×C37—41no—
124C23×C37AGL(1,ℤ/8)11yescharacteristic
125Q8×C37—41no—
126Q8×C37—42no—
127Q8×C37—42no—
128Q8×C37—41no—
129Q8×C37—81no—
130Q8×C37—81no—
131D4×C37—41no—
132D4×C37—41no—
133D4×C37—81no—
134D4×C37—81no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—42no—
138C2×C4×C37—41no—
139C2×C4×C37—81no—
140C2×C4×C37—81no—
141C2×C4×C37—81no—
142C2×C4×C37—81no—
143C2×C4×C37—81no—
144C2×C4×C37—161no—
145C2×C4×C37#12011yescharacteristic
146C2×C4×C37#12111yescharacteristic
147C2×C4×C37#12411yescharacteristic
148C2×C4×C37C2×D811yescharacteristic
149C2×C4×C37C2×SD1611yescharacteristic
150C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
151C8×C37—22no—
152C8×C37—42no—
153C8×C37#12111yescharacteristic
154C8×C37#12111yescharacteristic
155C8×C37#12311yescharacteristic
156C8×C37#12311yescharacteristic
157#13412C3711yesmaximal, characteristic, direct product factor, Sylow
158C22×C37—21no—
159C22×C37—21no—
160C22×C37—81no—
161C22×C37—81no—
162C22×C37—81no—
163C22×C37#44711yescharacteristic
164C22×C37#46011yescharacteristic
165C22×C37#49011yescharacteristic
166C4×C37—41no—
167C4×C37—41no—
168C4×C37—81no—
169C4×C37—82no—
170C4×C37—161no—
171C4×C37#39411yescharacteristic
172C4×C37#45011yescharacteristic
173C4×C37#45911yescharacteristic
174C4×C37#48611yescharacteristic
175#3156C2×C3711yescharacteristic
176C2×#362C2×C3711yescharacteristic, complemented
177C2×#359C2×C3711yescharacteristic
178#2139C2×C3711yescharacteristic
179C2×#358C2×C3711yescharacteristic, complemented
180#1952C2×C3711yescharacteristic, complemented
181#1379C2×C3711yescharacteristic, complemented
182C2×C37—21no—
183C2×C37—21no—
184C2×C37—161no—
185C2×C37#204111yescharacteristic
186C2×C37#219311yescharacteristic
187C2×C37#219511yescharacteristic
188C2×#137—21no—
189C2×#135C22×C3711yescharacteristic
190C22×Q16C22×C3711yescharacteristic
191#536—21no—
192C2×M32C22×C3711yescharacteristic
193C22×C16C22×C3711yescharacteristic
194#497—22no—
195#495—21no—
196#494—21no—
197C2×#108C22×C3711yescharacteristic
198#428—21no—
199C2×#107C22×C3711yescharacteristic
200#405C22×C3711yescharacteristic
201#362—22no—
202#359—22no—
203#358—22no—
204#358—21no—
205#357—21no—
206#343—21no—
207C37#1341211yescharacteristic, direct product factor, Sylow
208C2×#41—21no—
209C22×Q8—21no—
210#137—42no—
211#137—42no—
212#135—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216C2×Q16—22no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16D4×C3712yes—
223C2×Q16D4×C3711yescharacteristic
224C2×SD16—22no—
225C2×SD16—21no—
226C2×D8D4×C3711yescharacteristic
227C2×M16—21no—
228C2×M16D4×C3711yescharacteristic
229C22×C8C23×C3711yescharacteristic
230C4⋊Q8—22no—
231#124—22no—
232#123—42no—
233C22⋊Q8—41no—
234C22⋊Q8—41no—
235#117D4×C3711yescharacteristic
236C2×C4⋊C4—21no—
237M32—21no—
238M32—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243#108—21no—
244#108D4×C3712yes—
245#107—21no—
246#107—21no—
247#107—41no—
248#106—41no—
249#97—21no—
250C4×C8—21no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255C2×Q8—22no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×D4—21no—
263C2×D4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4C2×D4×C3711yescharacteristic
268Q16—22no—
269Q16—21no—
270Q16—22no—
271Q16—21no—
272Q16—44no—
273Q16—41no—
274Q16—41no—
275SD16—44no—
276SD16—41no—
277SD16—41no—
278D8—21no—
279D8—21no—
280M16—21no—
281M16—22no—
282M16—41no—
283M16SD16×C3712yes—
284C2×C8—21no—
285C2×C8—41no—
286C2×C8C2×D4×C3711yescharacteristic
287C2×C8C2×D4×C3711yescharacteristic
288C2×C8C2×D4×C3711yescharacteristic
289C2×C8#41×C3711yescharacteristic
290C2×C8#41×C3711yescharacteristic
291C2×C8#41×C3711yescharacteristic
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4D8×C3711yescharacteristic
297C4⋊C4D8×C3711yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C42—21no—
302C16—41no—
303C16—41no—
304C23—41no—
305C23AGL(1,ℤ/8)×C3711yescharacteristic
306Q8—41no—
307Q8—42no—
308Q8—42no—
309Q8—41no—
310Q8—81no—
311Q8—81no—
312D4—41no—
313D4—41no—
314D4—81no—
315D4—81no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—161no—
326C2×C4#120×C3711yescharacteristic
327C2×C4#121×C3711yescharacteristic
328C2×C4#124×C3711yescharacteristic
329C2×C4C2×D8×C3711yescharacteristic
330C2×C4C2×SD16×C3711yescharacteristic
331C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
332C8—22no—
333C8—42no—
334C8#121×C3711yescharacteristic
335C8#121×C3711yescharacteristic
336C8#123×C3711yescharacteristic
337C8#123×C3711yescharacteristic
338C22—21no—
339C22—21no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C37×#44711yescharacteristic
344C22C37×#46011yescharacteristic
345C22C37×#49011yescharacteristic
346C4—41no—
347C4—41no—
348C4—81no—
349C4—82no—
350C4—161no—
351C4C37×#39411yescharacteristic
352C4C37×#45011yescharacteristic
353C4C37×#45911yescharacteristic
354C4C37×#48611yescharacteristic
355C2—21no—
356C2—21no—
357C2—161no—
358C2C37×#204111yescharacteristic
359C2C37×#219311yescharacteristic
360C2C37×#219511yescharacteristic
subgroupG/H
center, socleC22×C37#447
commutator, Frattini, cosocleC22×C8C23×C37
prime radicalC2×#135×C37C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C22×C4×C37 ◁ C37×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#362C2semidirect
5. C2×C37×#358C2semidirect
6. C37×#1952C2semidirect
7. C37×#1379C2semidirect
157. #13412C37direct (N × H)
176. C2×#362C2×C37semidirect
179. C2×#358C2×C37semidirect
180. #1952C2×C37semidirect
181. #1379C2×C37semidirect
207. C37#13412direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#31562
C2×C37×#3622
C2×C37×#3592
C37×#21392
C2×C37×#3582
C37×#19522
C37×#13792
#1341237