Finite Group Databasebeta

← C37×#7694 #22628947

Subgroups — C37×#7694 #22628947

Order 9472.

556 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2854C211yesmaximal, characteristic
2C37×#1817C211yesmaximal, characteristic, complemented
3C37×#1728C211yesmaximal, characteristic, complemented
4C37×#1271C212yesmaximal, complemented
5C37×#1270C212yesmaximal, complemented
6C22×M16×C37—21no—
7C2×#123×C37—21no—
8C2×#121×C37C411yescharacteristic
9C22×C42×C37C2211yescharacteristic
10C2×C22⋊C8×C37—21no—
11C37×#390C411yescharacteristic
12C37×#390C2211yescharacteristic
13C37×#389C411yescharacteristic
14C37×#389C2211yescharacteristic
15C37×#388—21no—
16C37×#388—21no—
17C37×#386—21no—
18C37×#380C411yescharacteristic
19C37×#336—21no—
20C37×#336—21no—
21C37×#336C2212yes—
22C37×#336C2212yes—
23C22×D4×C37—21no—
24C22×D4×C37C2×C411yescharacteristic
25C23×C4×C37C2×C411yescharacteristic
26C23×C4×C37D411yescharacteristic
27C23×C4×C37D411yescharacteristic
28C2×M16×C37—24no—
29C2×M16×C37—42no—
30C2×M16×C37—42no—
31C22×C8×C37—22no—
32C22×C8×C37—22no—
33#123×C37—44no—
34#121×C37—42no—
35C2×C4⋊C4×C37—21no—
36C2×C4⋊C4×C37—21no—
37C2×C4⋊C4×C37C2×C411yescharacteristic
38C2×C4⋊C4×C37C2×C411yescharacteristic
39C2×C4⋊C4×C37C2×C411yescharacteristic
40C2×C22⋊C4×C37—21no—
41C2×C22⋊C4×C37—21no—
42C2×C22⋊C4×C37—21no—
43C2×C22⋊C4×C37—21no—
44C2×C22⋊C4×C37—21no—
45C2×C22⋊C4×C37—21no—
46C2×C42×C37—42no—
47C2×C42×C37C2×C411yescharacteristic
48C2×C42×C37D411yescharacteristic
49C2×C42×C37D411yescharacteristic
50C2×C42×C37C2311yescharacteristic
51C22⋊C8×C37—42no—
52#95×C37—21no—
53#95×C37—21no—
54#95×C37—21no—
55C24×C37—21no—
56C24×C37C22⋊C411yescharacteristic
57C2×D4×C37—22no—
58C2×D4×C37—41no—
59C2×D4×C37—41no—
60C2×D4×C37—42no—
61C2×D4×C37—42no—
62C2×D4×C37—42no—
63C22×C4×C37—22no—
64C22×C4×C37—22no—
65C22×C4×C37—21no—
66C22×C4×C37—21no—
67C22×C4×C37—22no—
68C22×C4×C37—22no—
69C22×C4×C37—22no—
70C22×C4×C37—22no—
71C22×C4×C37—21no—
72C22×C4×C37—21no—
73C22×C4×C37—21no—
74C22×C4×C37—41no—
75C22×C4×C37—41no—
76C22×C4×C37C22⋊C411yescharacteristic
77C22×C4×C37C22⋊C411yescharacteristic
78C22×C4×C37C22⋊C411yescharacteristic
79C22×C4×C37C22×C411yescharacteristic
80C22×C4×C37C2×D411yescharacteristic
81C22×C4×C37C2×D411yescharacteristic
82M16×C37—48no—
83C2×C8×C37—24no—
84C2×C8×C37—42no—
85C2×C8×C37—42no—
86C2×C8×C37—42no—
87C2×C8×C37—42no—
88C2×C8×C37—42no—
89C4⋊C4×C37—22no—
90C4⋊C4×C37—41no—
91C4⋊C4×C37—41no—
92C4⋊C4×C37—42no—
93C4⋊C4×C37—42no—
94C22⋊C4×C37—42no—
95C22⋊C4×C37—42no—
96C22⋊C4×C37—42no—
97C22⋊C4×C37—42no—
98C22⋊C4×C37—41no—
99C22⋊C4×C37—42no—
100C22⋊C4×C37—41no—
101C42×C37—41no—
102C42×C37—41no—
103C42×C37—41no—
104C42×C37—41no—
105C23×C37—21no—
106C23×C37—21no—
107C23×C37—21no—
108C23×C37—21no—
109C23×C37—21no—
110C23×C37—21no—
111C23×C37—41no—
112C23×C37—41no—
113C23×C37—41no—
114C23×C37—41no—
115C23×C37—41no—
116C23×C37—41no—
117C23×C37—41no—
118C23×C37#9912yes—
119C23×C37C2×C22⋊C411yescharacteristic
120D4×C37—82no—
121D4×C37—84no—
122C2×C4×C37—24no—
123C2×C4×C37—24no—
124C2×C4×C37—21no—
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—44no—
139C2×C4×C37—44no—
140C2×C4×C37—41no—
141C2×C4×C37—41no—
142C2×C4×C37—41no—
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#10412yes—
150C2×C4×C37#13112yes—
151C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C37AGL(1,ℤ/8)12yes—
153C2×C4×C37#13711yescharacteristic
154C8×C37—44no—
155C8×C37—82no—
156#7694C3711yesmaximal, characteristic, direct product factor, Sylow
157C22×C37—22no—
158C22×C37—22no—
159C22×C37—22no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37—81no—
165C22×C37—81no—
166C22×C37—81no—
167C22×C37—81no—
168C22×C37—81no—
169C22×C37—81no—
170C22×C37—81no—
171C22×C37#40811yescharacteristic
172C22×C37C2×#9911yescharacteristic
173C22×C37#41311yescharacteristic
174C22×C37#41711yescharacteristic
175C22×C37#41811yescharacteristic
176C22×C37C2×#10411yescharacteristic
177C22×C37#42111yescharacteristic
178C4×C37—22no—
179C4×C37—21no—
180C4×C37—22no—
181C4×C37—21no—
182C4×C37—22no—
183C4×C37—41no—
184C4×C37—41no—
185C4×C37—81no—
186C4×C37—81no—
187C4×C37—81no—
188#2854C2×C3711yescharacteristic
189#1817C2×C3711yescharacteristic, complemented
190#1728C2×C3711yescharacteristic, complemented
191#1271C2×C3712yescomplemented
192#1270C2×C3712yescomplemented
193C2×C37—42no—
194C2×C37—161no—
195C2×C37#146811yescharacteristic
196C2×C37#148411yescharacteristic
197C2×C37#149511yescharacteristic
198C2×C37#150411yescharacteristic
199C2×C37#151011yescharacteristic
200C2×C37#152911yescharacteristic
201C2×C37#155711yescharacteristic
202C22×M16—21no—
203C2×#123—21no—
204C2×#121C4×C3711yescharacteristic
205C22×C42C22×C3711yescharacteristic
206C2×C22⋊C8—21no—
207#390C4×C3711yescharacteristic
208#390C22×C3711yescharacteristic
209#389C4×C3711yescharacteristic
210#389C22×C3711yescharacteristic
211#388—21no—
212#388—21no—
213#386—21no—
214#380C4×C3711yescharacteristic
215#336—21no—
216#336—21no—
217#336C22×C3712yes—
218#336C22×C3712yes—
219C37#769411yescharacteristic, direct product factor, Sylow
220C22×D4—21no—
221C22×D4C2×C4×C3711yescharacteristic
222C23×C4C2×C4×C3711yescharacteristic
223C23×C4D4×C3711yescharacteristic
224C23×C4D4×C3711yescharacteristic
225C2×M16—24no—
226C2×M16—42no—
227C2×M16—42no—
228C22×C8—22no—
229C22×C8—22no—
230#123—44no—
231#121—42no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C2×C4×C3711yescharacteristic
235C2×C4⋊C4C2×C4×C3711yescharacteristic
236C2×C4⋊C4C2×C4×C3711yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C42—42no—
244C2×C42C2×C4×C3711yescharacteristic
245C2×C42D4×C3711yescharacteristic
246C2×C42D4×C3711yescharacteristic
247C2×C42C23×C3711yescharacteristic
248C22⋊C8—42no—
249#95—21no—
250#95—21no—
251#95—21no—
252C24—21no—
253C24C22⋊C4×C3711yescharacteristic
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—42no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C22⋊C4×C3711yescharacteristic
274C22×C4C22⋊C4×C3711yescharacteristic
275C22×C4C22⋊C4×C3711yescharacteristic
276C22×C4C22×C4×C3711yescharacteristic
277C22×C4C2×D4×C3711yescharacteristic
278C22×C4C2×D4×C3711yescharacteristic
279M16—48no—
280C2×C8—24no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—41no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C42—41no—
299C42—41no—
300C42—41no—
301C42—41no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23#99×C3712yes—
316C23C2×C22⋊C4×C3711yescharacteristic
317D4—82no—
318D4—84no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4#104×C3712yes—
347C2×C4#131×C3712yes—
348C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
349C2×C4AGL(1,ℤ/8)×C3712yes—
350C2×C4#137×C3711yescharacteristic
351C8—44no—
352C8—82no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22C37×#40811yescharacteristic
368C22C2×#99×C3711yescharacteristic
369C22C37×#41311yescharacteristic
370C22C37×#41711yescharacteristic
371C22C37×#41811yescharacteristic
372C22C2×#104×C3711yescharacteristic
373C22C37×#42111yescharacteristic
374C4—22no—
375C4—21no—
376C4—22no—
377C4—21no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—81no—
384C2—42no—
385C2—161no—
386C2C37×#146811yescharacteristic
387C2C37×#148411yescharacteristic
388C2C37×#149511yescharacteristic
389C2C37×#150411yescharacteristic
390C2C37×#151011yescharacteristic
391C2C37×#152911yescharacteristic
392C2C37×#155711yescharacteristic
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×#1817C2semidirect
3. C37×#1728C2semidirect
4. C37×#1271C2semidirect
5. C37×#1270C2semidirect
156. #7694C37direct (N × H)
189. #1817C2×C37semidirect
190. #1728C2×C37semidirect
191. #1271C2×C37semidirect
192. #1270C2×C37semidirect
219. C37#7694direct (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×#18172
C37×#17282
C37×#12712
C37×#12702
#769437