Finite Group Databasebeta

← C37×#60328 #22681581

Subgroups — C37×#60328 #22681581

Order 9472.

1920 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3483C211yesmaximal, characteristic
2C37×#2991C211yesmaximal, characteristic, complemented
3C37×#2990C213yesmaximal, complemented
4C37×#2988C212yesmaximal, complemented
5C37×#2981C216yesmaximal, complemented
6C37×#2979C213yesmaximal, complemented
7C37×#2971C212yesmaximal, complemented
8C37×#2965C213yesmaximal, complemented
9C8×#41×C37C211yesmaximal, characteristic, complemented
10C37×#2935C216yesmaximal, complemented
11C37×#2931C213yesmaximal, complemented
12C2×#131×C37C2216yes—
13Q82×C37C411yescharacteristic
14C37×#555C416yes—
15C37×#555C413yes—
16C37×#550C411yescharacteristic
17C37×#550C412yes—
18C37×#550C413yes—
19C37×#532C2213yes—
20C37×#532C2216yes—
21C4×#41×C37C2211yescharacteristic
22C4×#41×C37C2213yes—
23C4×#41×C37C2212yes—
24C37×#446C2211yescharacteristic
25C37×#446C2213yes—
26C8×Q8×C37C2211yescharacteristic
27C8×Q8×C37C2211yescharacteristic
28C8×Q8×C37C2212yes—
29C37×#436C2213yes—
30C37×#436C2216yes—
31C37×#436C2216yes—
32C37×#436C2213yes—
33C37×#436C2216yes—
34C37×#435C2216yes—
35C37×#435C22112yes—
36C37×#435C2216yes—
37C8×D4×C37C2216yes—
38C8×D4×C37C2216yes—
39C8×D4×C37C2213yes—
40C8×D4×C37C2216yes—
41C8×D4×C37C2213yes—
42C37×#432C2216yes—
43C37×#431C2213yes—
44C37×#431C2213yes—
45C37×#431C2216yes—
46C37×#423C2213yes—
47C2×C4⋊C8×C37C2216yes—
48C37×#408C2216yes—
49C37×#408C22112yes—
50C4×M16×C37C2216yes—
51C2×C4×C8×C37C2213yes—
52C2×#41×C37C2×C411yescharacteristic
53C2×#41×C37C2×C412yes—
54C2×#41×C37C2×C413yes—
55C2×#41×C37C2316yes—
56#131×C37—412no—
57C2×M16×C37C2316yes—
58C2×M16×C37C2316yes—
59C2×M16×C37C2316yes—
60C22×C8×C37C2313yes—
61C22×C8×C37C23112yes—
62C22×C8×C37C2313yes—
63C4⋊Q8×C37C2×C413yes—
64C4⋊Q8×C37C2×C416yes—
65#127×C37C2×C413yes—
66#127×C37C2×C416yes—
67#124×C37C2×C416yes—
68#124×C37C2×C4112yes—
69#121×C37C2×C416yes—
70#121×C37C2×C416yes—
71#121×C37C2×C416yes—
72#121×C37C2×C416yes—
73#121×C37C2×C4112yes—
74C4×Q8×C37C2×C413yes—
75C4×Q8×C37C2×C411yescharacteristic
76C4×Q8×C37C2×C412yes—
77C4×Q8×C37C2311yescharacteristic
78C4×Q8×C37C2311yescharacteristic
79C4×D4×C37C2×C413yes—
80C4×D4×C37C2×C413yes—
81C4×D4×C37C2×C416yes—
82C4×D4×C37C2×C416yes—
83C4×D4×C37C2313yes—
84C4×D4×C37C2316yes—
85C4×D4×C37C2313yes—
86C4×D4×C37C2316yes—
87#117×C37C2×C413yes—
88#117×C37C2×C413yes—
89#117×C37C2×C416yes—
90#117×C37C2×C416yes—
91C2×C42×C37C2313yes—
92C2×C42×C37C2316yes—
93C4⋊C8×C37C2313yes—
94C4⋊C8×C37C2316yes—
95C4⋊C8×C37C2316yes—
96C4⋊C8×C37C2313yes—
97C4⋊C8×C37C2312yes—
98C4⋊C8×C37C2311yescharacteristic
99C4⋊C8×C37C2313yes—
100C22⋊C8×C37C2316yes—
101C22⋊C8×C37C2316yes—
102C22⋊C8×C37C2316yes—
103C22⋊C8×C37C2316yes—
104C22⋊C8×C37C23112yes—
105#97×C37C2312yes—
106#97×C37C2316yes—
107C4×C8×C37C2311yescharacteristic
108C4×C8×C37C2313yes—
109C4×C8×C37C2313yes—
110C4×C8×C37C2313yes—
111C4×C8×C37C2316yes—
112#41×C37—24no—
113#41×C37—28no—
114#41×C37—46no—
115#41×C37—46no—
116#41×C37—46no—
117C2×Q8×C37C22×C411yescharacteristic
118C2×Q8×C37C22×C416yes—
119C2×Q8×C37C22×C411yescharacteristic
120C2×D4×C37C22×C413yes—
121C2×D4×C37C22×C416yes—
122C2×D4×C37C22×C413yes—
123C2×D4×C37C22×C416yes—
124C2×D4×C37C22×C4112yes—
125C2×D4×C37C22×C416yes—
126C22×C4×C37C22×C413yes—
127C22×C4×C37C22×C416yes—
128C22×C4×C37C22×C413yes—
129C22×C4×C37C22×C416yes—
130C22×C4×C37C2413yes—
131C22×C4×C37C2416yes—
132M16×C37—212no—
133M16×C37—46no—
134M16×C37—46no—
135C2×C8×C37—26no—
136C2×C8×C37—43no—
137C2×C8×C37—412no—
138C2×C8×C37C2411yescharacteristic
139C2×C8×C37C2412yes—
140C2×C8×C37C2413yes—
141C2×C8×C37C2413yes—
142C2×C8×C37C2416yes—
143C2×C8×C37C2411yescharacteristic
144C4⋊C4×C37C22×C412yes—
145C4⋊C4×C37C22×C413yes—
146C4⋊C4×C37C22×C411yescharacteristic
147C4⋊C4×C37C22×C416yes—
148C4⋊C4×C37C22×C413yes—
149C4⋊C4×C37C22×C416yes—
150C4⋊C4×C37C22×C413yes—
151C22⋊C4×C37C22×C416yes—
152C22⋊C4×C37C22×C416yes—
153C22⋊C4×C37C22×C4112yes—
154C22⋊C4×C37C22×C416yes—
155C22⋊C4×C37C22×C416yes—
156C42×C37C22×C413yes—
157C42×C37C22×C416yes—
158C42×C37C22×C416yes—
159C42×C37C22×C413yes—
160C42×C37C2413yes—
161C42×C37C2411yescharacteristic
162C42×C37C2412yes—
163C23×C37C23×C413yes—
164C23×C37C23×C416yes—
165Q8×C37—22no—
166Q8×C37—46no—
167Q8×C37#13114yescomplemented
168D4×C37—26no—
169D4×C37—212no—
170D4×C37—26no—
171D4×C37—46no—
172D4×C37—412no—
173D4×C37—46no—
174C2×C4×C37—26no—
175C2×C4×C37—212no—
176C2×C4×C37—26no—
177C2×C4×C37—23no—
178C2×C4×C37—26no—
179C2×C4×C37—23no—
180C2×C4×C37—26no—
181C2×C4×C37—46no—
182C2×C4×C37C23×C411yescharacteristic
183C2×C4×C37C23×C412yes—
184C2×C4×C37C23×C413yes—
185C2×C4×C37C23×C412yes—
186C2×C4×C37C23×C413yes—
187C2×C4×C37C23×C416yes—
188C2×C4×C37C23×C413yes—
189C2×C4×C37C23×C411yescharacteristic
190C2×C4×C37C2511yescharacteristic
191C8×C37—23no—
192C8×C37—26no—
193C8×C37—21no—
194C8×C37—23no—
195C8×C37—22no—
196C8×C37H(5,𝔽2)12yes—
197#60328C3711yesmaximal, characteristic, direct product factor, Sylow
198C22×C37—23no—
199C22×C37—26no—
200C22×C37—23no—
201C22×C37—26no—
202C22×C37—23no—
203C22×C37—26no—
204C22×C37C24×C411yescharacteristic
205C4×C37—23no—
206C4×C37—26no—
207C4×C37—21no—
208C4×C37—22no—
209C4×C37—23no—
210C4×C37—22no—
211C4×C37C2×#13116yes—
212C4×C37#56812yes—
213C4×C37C2×H(5,𝔽2)11yescharacteristic
214C4×C37#58511yescharacteristic
215#3483C2×C3711yescharacteristic
216#2991C2×C3711yescharacteristic, complemented
217#2990C2×C3713yescomplemented
218#2988C2×C3712yescomplemented
219#2981C2×C3716yescomplemented
220#2979C2×C3713yescomplemented
221#2971C2×C3712yescomplemented
222#2965C2×C3713yescomplemented
223C8×#41C2×C3711yescharacteristic, complemented
224#2935C2×C3716yescomplemented
225#2931C2×C3713yescomplemented
226C2×C37—43no—
227C2×C37—46no—
228C2×C37C4×H(5,𝔽2)11yescharacteristic
229C2×C37C22×#13111yescharacteristic
230C2×C37C2×#56811yescharacteristic
231C2×#131C22×C3716yes—
232Q82C4×C3711yescharacteristic
233#555C4×C3716yes—
234#555C4×C3713yes—
235#550C4×C3711yescharacteristic
236#550C4×C3712yes—
237#550C4×C3713yes—
238#532C22×C3713yes—
239#532C22×C3716yes—
240C4×#41C22×C3711yescharacteristic
241C4×#41C22×C3713yes—
242C4×#41C22×C3712yes—
243#446C22×C3711yescharacteristic
244#446C22×C3713yes—
245C8×Q8C22×C3711yescharacteristic
246C8×Q8C22×C3711yescharacteristic
247C8×Q8C22×C3712yes—
248#436C22×C3713yes—
249#436C22×C3716yes—
250#436C22×C3716yes—
251#436C22×C3713yes—
252#436C22×C3716yes—
253#435C22×C3716yes—
254#435C22×C37112yes—
255#435C22×C3716yes—
256C8×D4C22×C3716yes—
257C8×D4C22×C3716yes—
258C8×D4C22×C3713yes—
259C8×D4C22×C3716yes—
260C8×D4C22×C3713yes—
261#432C22×C3716yes—
262#431C22×C3713yes—
263#431C22×C3713yes—
264#431C22×C3716yes—
265#423C22×C3713yes—
266C2×C4⋊C8C22×C3716yes—
267#408C22×C3716yes—
268#408C22×C37112yes—
269C4×M16C22×C3716yes—
270C2×C4×C8C22×C3713yes—
271C37#6032811yescharacteristic, direct product factor, Sylow
272C2×#41C2×C4×C3711yescharacteristic
273C2×#41C2×C4×C3712yes—
274C2×#41C2×C4×C3713yes—
275C2×#41C23×C3716yes—
276#131—412no—
277C2×M16C23×C3716yes—
278C2×M16C23×C3716yes—
279C2×M16C23×C3716yes—
280C22×C8C23×C3713yes—
281C22×C8C23×C37112yes—
282C22×C8C23×C3713yes—
283C4⋊Q8C2×C4×C3713yes—
284C4⋊Q8C2×C4×C3716yes—
285#127C2×C4×C3713yes—
286#127C2×C4×C3716yes—
287#124C2×C4×C3716yes—
288#124C2×C4×C37112yes—
289#121C2×C4×C3716yes—
290#121C2×C4×C3716yes—
291#121C2×C4×C3716yes—
292#121C2×C4×C3716yes—
293#121C2×C4×C37112yes—
294C4×Q8C2×C4×C3713yes—
295C4×Q8C2×C4×C3711yescharacteristic
296C4×Q8C2×C4×C3712yes—
297C4×Q8C23×C3711yescharacteristic
298C4×Q8C23×C3711yescharacteristic
299C4×D4C2×C4×C3713yes—
300C4×D4C2×C4×C3713yes—
301C4×D4C2×C4×C3716yes—
302C4×D4C2×C4×C3716yes—
303C4×D4C23×C3713yes—
304C4×D4C23×C3713yes—
305C4×D4C23×C3716yes—
306C4×D4C23×C3716yes—
307#117C2×C4×C3713yes—
308#117C2×C4×C3713yes—
309#117C2×C4×C3716yes—
310#117C2×C4×C3716yes—
311C2×C42C23×C3713yes—
312C2×C42C23×C3716yes—
313C4⋊C8C23×C3713yes—
314C4⋊C8C23×C3716yes—
315C4⋊C8C23×C3716yes—
316C4⋊C8C23×C3713yes—
317C4⋊C8C23×C3712yes—
318C4⋊C8C23×C3711yescharacteristic
319C4⋊C8C23×C3713yes—
320C22⋊C8C23×C3716yes—
321C22⋊C8C23×C3716yes—
322C22⋊C8C23×C3716yes—
323C22⋊C8C23×C3716yes—
324C22⋊C8C23×C37112yes—
325#97C23×C3712yes—
326#97C23×C3716yes—
327C4×C8C23×C3711yescharacteristic
328C4×C8C23×C3713yes—
329C4×C8C23×C3713yes—
330C4×C8C23×C3713yes—
331C4×C8C23×C3716yes—
332#41—24no—
333#41—28no—
334#41—46no—
335#41—46no—
336#41—46no—
337C2×Q8C22×C4×C3711yescharacteristic
338C2×Q8C22×C4×C3716yes—
339C2×Q8C22×C4×C3711yescharacteristic
340C2×D4C22×C4×C3713yes—
341C2×D4C22×C4×C3716yes—
342C2×D4C22×C4×C3713yes—
343C2×D4C22×C4×C3716yes—
344C2×D4C22×C4×C37112yes—
345C2×D4C22×C4×C3716yes—
346C22×C4C22×C4×C3713yes—
347C22×C4C22×C4×C3716yes—
348C22×C4C22×C4×C3713yes—
349C22×C4C22×C4×C3716yes—
350C22×C4C24×C3713yes—
351C22×C4C24×C3716yes—
352M16—212no—
353M16—46no—
354M16—46no—
355C2×C8—26no—
356C2×C8—43no—
357C2×C8—412no—
358C2×C8C24×C3711yescharacteristic
359C2×C8C24×C3712yes—
360C2×C8C24×C3713yes—
361C2×C8C24×C3713yes—
362C2×C8C24×C3716yes—
363C2×C8C24×C3711yescharacteristic
364C4⋊C4C22×C4×C3712yes—
365C4⋊C4C22×C4×C3713yes—
366C4⋊C4C22×C4×C3711yescharacteristic
367C4⋊C4C22×C4×C3716yes—
368C4⋊C4C22×C4×C3713yes—
369C4⋊C4C22×C4×C3716yes—
370C4⋊C4C22×C4×C3713yes—
371C22⋊C4C22×C4×C3716yes—
372C22⋊C4C22×C4×C3716yes—
373C22⋊C4C22×C4×C37112yes—
374C22⋊C4C22×C4×C3716yes—
375C22⋊C4C22×C4×C3716yes—
376C42C22×C4×C3713yes—
377C42C22×C4×C3716yes—
378C42C22×C4×C3716yes—
379C42C22×C4×C3713yes—
380C42C24×C3713yes—
381C42C24×C3711yescharacteristic
382C42C24×C3712yes—
383C23C23×C4×C3713yes—
384C23C23×C4×C3716yes—
385Q8—22no—
386Q8—46no—
387Q8#131×C3714yescomplemented
388D4—26no—
389D4—212no—
390D4—26no—
391D4—46no—
392D4—412no—
393D4—46no—
394C2×C4—26no—
395C2×C4—212no—
396C2×C4—26no—
397C2×C4—23no—
398C2×C4—26no—
399C2×C4—23no—
400C2×C4—26no—
401C2×C4—46no—
402C2×C4C23×C4×C3711yescharacteristic
403C2×C4C23×C4×C3712yes—
404C2×C4C23×C4×C3713yes—
405C2×C4C23×C4×C3712yes—
406C2×C4C23×C4×C3713yes—
407C2×C4C23×C4×C3716yes—
408C2×C4C23×C4×C3713yes—
409C2×C4C23×C4×C3711yescharacteristic
410C2×C4C25×C3711yescharacteristic
411C8—23no—
412C8—26no—
413C8—21no—
414C8—23no—
415C8—22no—
416C8H(5,𝔽2)×C3712yes—
417C22—23no—
418C22—26no—
419C22—23no—
420C22—26no—
421C22—23no—
422C22—26no—
423C22C24×C4×C3711yescharacteristic
424C4—23no—
425C4—26no—
426C4—21no—
427C4—22no—
428C4—23no—
429C4—22no—
430C4C2×#131×C3716yes—
431C4C37×#56812yes—
432C4C2×H(5,𝔽2)×C3711yescharacteristic
433C4C37×#58511yescharacteristic
434C2—43no—
435C2—46no—
436C2C4×H(5,𝔽2)×C3711yescharacteristic
437C2C22×#131×C3711yescharacteristic
438C2C2×C37×#56811yescharacteristic
subgroupG/H
centerC2×C4×C37C25
commutatorC22C24×C4×C37
Frattini, cosocleC2×C4C25×C37
socleC22×C37C24×C4
prime radicalC37×#3483C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2991C2semidirect
3. C37×#2990C2semidirect
4. C37×#2988C2semidirect
5. C37×#2981C2semidirect
6. C37×#2979C2semidirect
7. C37×#2971C2semidirect
8. C37×#2965C2semidirect
9. C8×#41×C37C2semidirect
10. C37×#2935C2semidirect
11. C37×#2931C2semidirect
167. Q8×C37#131semidirect
197. #60328C37direct (N × H)
216. #2991C2×C37semidirect
217. #2990C2×C37semidirect
218. #2988C2×C37semidirect
219. #2981C2×C37semidirect
220. #2979C2×C37semidirect
221. #2971C2×C37semidirect
222. #2965C2×C37semidirect
223. C8×#41C2×C37semidirect
224. #2935C2×C37semidirect
225. #2931C2×C37semidirect
271. C37#60328direct (N × H)
387. Q8#131×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34832
C37×#29912
C37×#29902
C37×#29882
C37×#29812
C37×#29792
C37×#29712
C37×#29652
C8×#41×C372
C37×#29352
C37×#29312
#6032837