Finite Group Databasebeta

← C37×#7714 #22628967

Subgroups — C37×#7714 #22628967

Order 9472.

526 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2854C211yesmaximal, characteristic
2C37×#1797C211yesmaximal, characteristic, complemented
3C37×#1797C211yesmaximal, characteristic, complemented
4C37×#1271C212yesmaximal, complemented
5C37×#1270C212yesmaximal, complemented
6C2×#123×C37—21no—
7C2×#121×C37C411yescharacteristic
8C22×C42×C37C2211yescharacteristic
9C2×C4⋊C8×C37—21no—
10C2×C4⋊C8×C37—21no—
11C2×C22⋊C8×C37—21no—
12C2×C22⋊C8×C37—21no—
13C37×#390C411yescharacteristic
14C37×#390C2211yescharacteristic
15C37×#389C411yescharacteristic
16C37×#389C2211yescharacteristic
17C37×#388—21no—
18C37×#388—21no—
19C37×#386—21no—
20C37×#380C411yescharacteristic
21C37×#336C2212yes—
22C37×#336C2212yes—
23C22×D4×C37—21no—
24C22×D4×C37C2×C411yescharacteristic
25C23×C4×C37C2×C411yescharacteristic
26C23×C4×C37D411yescharacteristic
27C23×C4×C37D411yescharacteristic
28C22×C8×C37—22no—
29C22×C8×C37—22no—
30#123×C37—42no—
31#123×C37—42no—
32#121×C37—42no—
33C2×C4⋊C4×C37—21no—
34C2×C4⋊C4×C37—21no—
35C2×C4⋊C4×C37C2×C411yescharacteristic
36C2×C4⋊C4×C37C2×C411yescharacteristic
37C2×C4⋊C4×C37C2×C411yescharacteristic
38C2×C22⋊C4×C37—21no—
39C2×C22⋊C4×C37—21no—
40C2×C22⋊C4×C37—21no—
41C2×C22⋊C4×C37—21no—
42C2×C22⋊C4×C37—21no—
43C2×C22⋊C4×C37—21no—
44C2×C42×C37—42no—
45C2×C42×C37C2×C411yescharacteristic
46C2×C42×C37D411yescharacteristic
47C2×C42×C37D411yescharacteristic
48C2×C42×C37C2311yescharacteristic
49C4⋊C8×C37—42no—
50C4⋊C8×C37—42no—
51C22⋊C8×C37—42no—
52C22⋊C8×C37—42no—
53#95×C37—21no—
54#95×C37—21no—
55#95×C37—21no—
56C24×C37—21no—
57C24×C37C22⋊C411yescharacteristic
58C2×D4×C37—22no—
59C2×D4×C37—41no—
60C2×D4×C37—41no—
61C2×D4×C37—42no—
62C2×D4×C37—42no—
63C2×D4×C37—42no—
64C22×C4×C37—22no—
65C22×C4×C37—22no—
66C22×C4×C37—21no—
67C22×C4×C37—21no—
68C22×C4×C37—21no—
69C22×C4×C37—21no—
70C22×C4×C37—21no—
71C22×C4×C37—41no—
72C22×C4×C37—41no—
73C22×C4×C37—41no—
74C22×C4×C37—41no—
75C22×C4×C37—41no—
76C22×C4×C37C22⋊C411yescharacteristic
77C22×C4×C37C22⋊C411yescharacteristic
78C22×C4×C37C22⋊C411yescharacteristic
79C22×C4×C37D812yes—
80C22×C4×C37SD1612yes—
81C22×C4×C37C22×C411yescharacteristic
82C22×C4×C37C2×D411yescharacteristic
83C22×C4×C37C2×D411yescharacteristic
84C2×C8×C37—42no—
85C2×C8×C37—42no—
86C2×C8×C37—42no—
87C2×C8×C37—42no—
88C2×C8×C37—42no—
89C2×C8×C37—42no—
90C4⋊C4×C37—22no—
91C4⋊C4×C37—41no—
92C4⋊C4×C37—41no—
93C4⋊C4×C37—42no—
94C4⋊C4×C37—41no—
95C4⋊C4×C37—41no—
96C22⋊C4×C37—42no—
97C22⋊C4×C37—42no—
98C22⋊C4×C37—42no—
99C22⋊C4×C37—42no—
100C22⋊C4×C37—41no—
101C22⋊C4×C37—41no—
102C22⋊C4×C37—41no—
103C22⋊C4×C37—41no—
104C42×C37—22no—
105C42×C37—22no—
106C42×C37—41no—
107C42×C37—41no—
108C23×C37—21no—
109C23×C37—21no—
110C23×C37—21no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37—41no—
115C23×C37—41no—
116C23×C37—41no—
117C23×C37—41no—
118C23×C37—41no—
119C23×C37—41no—
120C23×C37—41no—
121C23×C37#10212yes—
122C23×C37C2×C22⋊C411yescharacteristic
123D4×C37—82no—
124D4×C37—84no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—42no—
139C2×C4×C37—42no—
140C2×C4×C37—44no—
141C2×C4×C37—42no—
142C2×C4×C37—42no—
143C2×C4×C37—41no—
144C2×C4×C37—41no—
145C2×C4×C37—41no—
146C2×C4×C37—41no—
147C2×C4×C37—41no—
148C2×C4×C37—41no—
149C2×C4×C37—41no—
150C2×C4×C37—41no—
151C2×C4×C37—41no—
152C2×C4×C37#9912yes—
153C2×C4×C37#10212yes—
154C2×C4×C37#13112yes—
155C2×C4×C37C2×D811yescharacteristic
156C2×C4×C37C2×SD1611yescharacteristic
157C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C37#13711yescharacteristic
159C8×C37—82no—
160C8×C37—82no—
161#7714C3711yesmaximal, characteristic, direct product factor, Sylow
162C22×C37—22no—
163C22×C37—22no—
164C22×C37—22no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37—41no—
168C22×C37—41no—
169C22×C37—81no—
170C22×C37—81no—
171C22×C37—81no—
172C22×C37—81no—
173C22×C37—81no—
174C22×C37—81no—
175C22×C37—81no—
176C22×C37#40811yescharacteristic
177C22×C37C2×#9911yescharacteristic
178C22×C37#41311yescharacteristic
179C22×C37C2×#10211yescharacteristic
180C22×C37#41711yescharacteristic
181C22×C37#42111yescharacteristic
182C22×C37#42111yescharacteristic
183C4×C37—22no—
184C4×C37—22no—
185C4×C37—21no—
186C4×C37—21no—
187C4×C37—21no—
188C4×C37—22no—
189C4×C37—21no—
190C4×C37—41no—
191C4×C37—81no—
192C4×C37—81no—
193C4×C37—81no—
194#2854C2×C3711yescharacteristic
195#1797C2×C3711yescharacteristic, complemented
196#1797C2×C3711yescharacteristic, complemented
197#1271C2×C3712yescomplemented
198#1270C2×C3712yescomplemented
199C2×C37—42no—
200C2×C37—161no—
201C2×C37#146811yescharacteristic
202C2×C37#148011yescharacteristic
203C2×C37#149511yescharacteristic
204C2×C37#151311yescharacteristic
205C2×C37#151911yescharacteristic
206C2×C37#153511yescharacteristic
207C2×C37#154711yescharacteristic
208C2×#123—21no—
209C2×#121C4×C3711yescharacteristic
210C22×C42C22×C3711yescharacteristic
211C2×C4⋊C8—21no—
212C2×C4⋊C8—21no—
213C2×C22⋊C8—21no—
214C2×C22⋊C8—21no—
215#390C4×C3711yescharacteristic
216#390C22×C3711yescharacteristic
217#389C4×C3711yescharacteristic
218#389C22×C3711yescharacteristic
219#388—21no—
220#388—21no—
221#386—21no—
222#380C4×C3711yescharacteristic
223#336C22×C3712yes—
224#336C22×C3712yes—
225C37#771411yescharacteristic, direct product factor, Sylow
226C22×D4—21no—
227C22×D4C2×C4×C3711yescharacteristic
228C23×C4C2×C4×C3711yescharacteristic
229C23×C4D4×C3711yescharacteristic
230C23×C4D4×C3711yescharacteristic
231C22×C8—22no—
232C22×C8—22no—
233#123—42no—
234#123—42no—
235#121—42no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C2×C4×C3711yescharacteristic
239C2×C4⋊C4C2×C4×C3711yescharacteristic
240C2×C4⋊C4C2×C4×C3711yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C42—42no—
248C2×C42C2×C4×C3711yescharacteristic
249C2×C42D4×C3711yescharacteristic
250C2×C42D4×C3711yescharacteristic
251C2×C42C23×C3711yescharacteristic
252C4⋊C8—42no—
253C4⋊C8—42no—
254C22⋊C8—42no—
255C22⋊C8—42no—
256#95—21no—
257#95—21no—
258#95—21no—
259C24—21no—
260C24C22⋊C4×C3711yescharacteristic
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4C22⋊C4×C3711yescharacteristic
280C22×C4C22⋊C4×C3711yescharacteristic
281C22×C4C22⋊C4×C3711yescharacteristic
282C22×C4D8×C3712yes—
283C22×C4SD16×C3712yes—
284C22×C4C22×C4×C3711yescharacteristic
285C22×C4C2×D4×C3711yescharacteristic
286C22×C4C2×D4×C3711yescharacteristic
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—22no—
308C42—22no—
309C42—41no—
310C42—41no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23#102×C3712yes—
325C23C2×C22⋊C4×C3711yescharacteristic
326D4—82no—
327D4—84no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4#99×C3712yes—
356C2×C4#102×C3712yes—
357C2×C4#131×C3712yes—
358C2×C4C2×D8×C3711yescharacteristic
359C2×C4C2×SD16×C3711yescharacteristic
360C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
361C2×C4#137×C3711yescharacteristic
362C8—82no—
363C8—82no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22C37×#40811yescharacteristic
379C22C2×#99×C3711yescharacteristic
380C22C37×#41311yescharacteristic
381C22C2×#102×C3711yescharacteristic
382C22C37×#41711yescharacteristic
383C22C37×#42111yescharacteristic
384C22C37×#42111yescharacteristic
385C4—22no—
386C4—22no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—22no—
391C4—21no—
392C4—41no—
393C4—81no—
394C4—81no—
395C4—81no—
396C2—42no—
397C2—161no—
398C2C37×#146811yescharacteristic
399C2C37×#148011yescharacteristic
400C2C37×#149511yescharacteristic
401C2C37×#151311yescharacteristic
402C2C37×#151911yescharacteristic
403C2C37×#153511yescharacteristic
404C2C37×#154711yescharacteristic
subgroupG/H
center, socleC23×C37C2×C22⋊C4
commutatorC22×C4C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC2×#121×C37C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#1797C2semidirect
3. C37×#1797C2semidirect
4. C37×#1271C2semidirect
5. C37×#1270C2semidirect
161. #7714C37direct (N × H)
195. #1797C2×C37semidirect
196. #1797C2×C37semidirect
197. #1271C2×C37semidirect
198. #1270C2×C37semidirect
225. C37#7714direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#28542
C37×#17972
C37×#12712
C37×#12702
#771437