Finite Group Databasebeta

← C37×#9687 #22630940

Subgroups — C37×#9687 #22630940

Order 9472.

526 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×#2861C211yesmaximal, characteristic
2C37×#1767C211yesmaximal, characteristic, complemented
3C4×#97×C37C211yesmaximal, characteristic, complemented
4C2×C37×#330C212yesmaximal, complemented
5C2×C37×#329C212yesmaximal
6C2×#125×C37C2211yescharacteristic
7C2×#124×C37C2211yescharacteristic
8C2×C4⋊C8×C37—21no—
9C2×#97×C37—21no—
10C2×#97×C37C2212yes—
11C2×#97×C37C2212yes—
12C2×C4×C8×C37—21no—
13C37×#391C411yescharacteristic
14C37×#391C411yescharacteristic
15C37×#390C411yescharacteristic
16C37×#390C411yescharacteristic
17C37×#388—21no—
18C37×#388—21no—
19C37×#388—21no—
20C37×#388—21no—
21C43×C37C2211yescharacteristic
22C37×#336—21no—
23C37×#330—24no—
24C37×#329—24no—
25C22×Q8×C37C2×C411yescharacteristic
26C22×D4×C37C2×C411yescharacteristic
27C22×C8×C37—22no—
28C22×C8×C37—22no—
29#125×C37—22no—
30#125×C37—22no—
31#124×C37—22no—
32#124×C37—22no—
33C2×C4⋊C4×C37—21no—
34C2×C4⋊C4×C37—21no—
35C2×C4⋊C4×C37C2×C411yescharacteristic
36C2×C4⋊C4×C37C2×C411yescharacteristic
37C2×C22⋊C4×C37—21no—
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×C42×C37C2×C411yescharacteristic
44C2×C42×C37C2×C411yescharacteristic
45C2×C42×C37D411yescharacteristic
46C2×C42×C37D411yescharacteristic
47C2×C42×C37D411yescharacteristic
48C2×C42×C37D411yescharacteristic
49C2×C42×C37C2311yescharacteristic
50C4⋊C8×C37—24no—
51#97×C37—24no—
52#97×C37—22no—
53#97×C37—22no—
54#97×C37—22no—
55#97×C37D414yes—
56C4×C8×C37—24no—
57#95×C37—21no—
58#95×C37—21no—
59#95×C37—21no—
60#95×C37—21no—
61C24×C37—21no—
62C2×Q8×C37—22no—
63C2×Q8×C37—41no—
64C2×Q8×C37—41no—
65C2×D4×C37—22no—
66C2×D4×C37—41no—
67C2×D4×C37—41no—
68C22×C4×C37—21no—
69C22×C4×C37—21no—
70C22×C4×C37—21no—
71C22×C4×C37C22⋊C411yescharacteristic
72C22×C4×C37C22⋊C411yescharacteristic
73C22×C4×C37C22⋊C411yescharacteristic
74C22×C4×C37C22⋊C411yescharacteristic
75C22×C4×C37C22×C411yescharacteristic
76C22×C4×C37C2×D411yescharacteristic
77C22×C4×C37C2×D411yescharacteristic
78C2×C8×C37—24no—
79C2×C8×C37—24no—
80C2×C8×C37—24no—
81C2×C8×C37—24no—
82C2×C8×C37—42no—
83C2×C8×C37—42no—
84C4⋊C4×C37—22no—
85C4⋊C4×C37—22no—
86C4⋊C4×C37—42no—
87C4⋊C4×C37—41no—
88C4⋊C4×C37—41no—
89C22⋊C4×C37—42no—
90C22⋊C4×C37—42no—
91C22⋊C4×C37—42no—
92C22⋊C4×C37—42no—
93C22⋊C4×C37—42no—
94C22⋊C4×C37—41no—
95C22⋊C4×C37—41no—
96C42×C37—22no—
97C42×C37—22no—
98C42×C37—22no—
99C42×C37—41no—
100C42×C37—41no—
101C42×C37—41no—
102C42×C37C2×D412yes—
103C42×C37#4112yes—
104C23×C37—41no—
105C23×C37—41no—
106C23×C37—41no—
107C23×C37—41no—
108C23×C37—41no—
109C23×C37—41no—
110C23×C37—41no—
111C23×C37C2×C22⋊C411yescharacteristic
112Q8×C37—82no—
113D4×C37—82no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—41no—
130C2×C4×C37—41no—
131C2×C4×C37—41no—
132C2×C4×C37—41no—
133C2×C4×C37—41no—
134C2×C4×C37—41no—
135C2×C4×C37—41no—
136C2×C4×C37—41no—
137C2×C4×C37—41no—
138C2×C4×C37#10412yes—
139C2×C4×C37#10412yes—
140C2×C4×C37#10412yes—
141C2×C4×C37C4×D412yes—
142C2×C4×C37#12112yes—
143C2×C4×C37#12411yescharacteristic
144C2×C4×C37#12711yescharacteristic
145C8×C37—28no—
146C8×C37—44no—
147#9687C3711yesmaximal, characteristic, direct product factor, Sylow
148C22×C37—81no—
149C22×C37—81no—
150C22×C37—81no—
151C22×C37—81no—
152C22×C37—81no—
153C22×C37—81no—
154C22×C37—81no—
155C22×C37#39011yescharacteristic
156C22×C37#41311yescharacteristic
157C22×C37#41311yescharacteristic
158C22×C37C2×#10411yescharacteristic
159C22×C37C2×#10411yescharacteristic
160C22×C37C2×#10411yescharacteristic
161C22×C37#42111yescharacteristic
162C4×C37—22no—
163C4×C37—22no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—22no—
167C4×C37—22no—
168C4×C37—22no—
169C4×C37—41no—
170C4×C37—81no—
171C4×C37—81no—
172C4×C37—81no—
173#2861C2×C3711yescharacteristic
174#1767C2×C3711yescharacteristic, complemented
175C4×#97C2×C3711yescharacteristic, complemented
176C2×#330C2×C3712yescomplemented
177C2×#329C2×C3712yes—
178C2×C37—161no—
179C2×C37#152411yescharacteristic
180C2×C37#152411yescharacteristic
181C2×C37#152911yescharacteristic
182C2×C37#153211yescharacteristic
183C2×C37#196211yescharacteristic
184C2×C37#196711yescharacteristic
185C2×C37#198011yescharacteristic
186C2×#125C22×C3711yescharacteristic
187C2×#124C22×C3711yescharacteristic
188C2×C4⋊C8—21no—
189C2×#97—21no—
190C2×#97C22×C3712yes—
191C2×#97C22×C3712yes—
192C2×C4×C8—21no—
193#391C4×C3711yescharacteristic
194#391C4×C3711yescharacteristic
195#390C4×C3711yescharacteristic
196#390C4×C3711yescharacteristic
197#388—21no—
198#388—21no—
199#388—21no—
200#388—21no—
201C43C22×C3711yescharacteristic
202#336—21no—
203#330—24no—
204#329—24no—
205C37#968711yescharacteristic, direct product factor, Sylow
206C22×Q8C2×C4×C3711yescharacteristic
207C22×D4C2×C4×C3711yescharacteristic
208C22×C8—22no—
209C22×C8—22no—
210#125—22no—
211#125—22no—
212#124—22no—
213#124—22no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C2×C4×C3711yescharacteristic
217C2×C4⋊C4C2×C4×C3711yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C42C2×C4×C3711yescharacteristic
225C2×C42C2×C4×C3711yescharacteristic
226C2×C42D4×C3711yescharacteristic
227C2×C42D4×C3711yescharacteristic
228C2×C42D4×C3711yescharacteristic
229C2×C42D4×C3711yescharacteristic
230C2×C42C23×C3711yescharacteristic
231C4⋊C8—24no—
232#97—24no—
233#97—22no—
234#97—22no—
235#97—22no—
236#97D4×C3714yes—
237C4×C8—24no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242C24—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×D4—22no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4C22⋊C4×C3711yescharacteristic
253C22×C4C22⋊C4×C3711yescharacteristic
254C22×C4C22⋊C4×C3711yescharacteristic
255C22×C4C22⋊C4×C3711yescharacteristic
256C22×C4C22×C4×C3711yescharacteristic
257C22×C4C2×D4×C3711yescharacteristic
258C22×C4C2×D4×C3711yescharacteristic
259C2×C8—24no—
260C2×C8—24no—
261C2×C8—24no—
262C2×C8—24no—
263C2×C8—42no—
264C2×C8—42no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—41no—
281C42—41no—
282C42—41no—
283C42C2×D4×C3712yes—
284C42#41×C3712yes—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23C2×C22⋊C4×C3711yescharacteristic
293Q8—82no—
294D4—82no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4#104×C3712yes—
320C2×C4#104×C3712yes—
321C2×C4#104×C3712yes—
322C2×C4C4×D4×C3712yes—
323C2×C4#121×C3712yes—
324C2×C4#124×C3711yescharacteristic
325C2×C4#127×C3711yescharacteristic
326C8—28no—
327C8—44no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C37×#39011yescharacteristic
336C22C37×#41311yescharacteristic
337C22C37×#41311yescharacteristic
338C22C2×#104×C3711yescharacteristic
339C22C2×#104×C3711yescharacteristic
340C22C2×#104×C3711yescharacteristic
341C22C37×#42111yescharacteristic
342C4—22no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—22no—
348C4—22no—
349C4—41no—
350C4—81no—
351C4—81no—
352C4—81no—
353C2—161no—
354C2C37×#152411yescharacteristic
355C2C37×#152411yescharacteristic
356C2C37×#152911yescharacteristic
357C2C37×#153211yescharacteristic
358C2C37×#196211yescharacteristic
359C2C37×#196711yescharacteristic
360C2C37×#198011yescharacteristic
subgroupG/H
center, socleC23×C37C2×C22⋊C4
commutatorC22×C4C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC22×D4×C37C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ C43×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#1767C2semidirect
3. C4×#97×C37C2semidirect
4. C2×C37×#330C2semidirect
147. #9687C37direct (N × H)
174. #1767C2×C37semidirect
175. C4×#97C2×C37semidirect
176. C2×#330C2×C37semidirect
205. C37#9687direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#28612
C37×#17672
C4×#97×C372
C2×C37×#3302
C2×C37×#3292
#968737