Finite Group Databasebeta

← C37×#9379 #22630632

Subgroups — C37×#9379 #22630632

Order 9472.

492 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3215C211yesmaximal, characteristic
2C37×#2337C211yesmaximal, characteristic
3C37×#1986C211yesmaximal, characteristic, complemented
4C37×#1527C211yesmaximal, characteristic
5C37×#1515C211yesmaximal, characteristic, complemented
6C37×#1288C211yesmaximal, characteristic, complemented
7C37×#1285C211yesmaximal, characteristic, complemented
8C37×#533C2211yescharacteristic
9C2×#124×C37C2211yescharacteristic
10C37×#497C412yescomplemented
11C37×#489C412yescomplemented
12C37×#464—22no—
13C37×#451—21no—
14C37×#450—21no—
15C37×#432C2211yescharacteristic
16C37×#432C2211yescharacteristic
17C4×M16×C37C2211yescharacteristic
18C37×#391—21no—
19C37×#388—21no—
20C37×#388—21no—
21C37×#386—21no—
22C37×#385—21no—
23C37×#383C2211yescharacteristic
24C4×C4⋊C4×C37C2211yescharacteristic
25C4×C22⋊C4×C37—21no—
26C37×#339—21no—
27C37×#339—21no—
28C37×#329—22no—
29C37×#328—21no—
30C37×#328—21no—
31C22×Q8×C37D411yescharacteristic
32C22×D4×C37D411yescharacteristic
33C23×C4×C37—21no—
34C2×Q16×C37—22no—
35C2×SD16×C37—22no—
36C2×M16×C37—21no—
37C4⋊Q8×C37C2×C411yescharacteristic, complemented
38C4⋊Q8×C37C2×C411yescharacteristic, complemented
39#125×C37—21no—
40#124×C37—21no—
41#124×C37—21no—
42#124×C37C2×C412yes—
43#124×C37D412yes—
44C22⋊Q8×C37—21no—
45C22⋊Q8×C37—21no—
46C4×Q8×C37—21no—
47C4×Q8×C37—21no—
48#117×C37—21no—
49C2×C4⋊C4×C37—21no—
50C2×C4⋊C4×C37—21no—
51C2×C22⋊C4×C37—21no—
52C2×C22⋊C4×C37—21no—
53C2×C22⋊C4×C37—21no—
54C2×C22⋊C4×C37—21no—
55C2×C22⋊C4×C37—21no—
56C2×C42×C37—21no—
57C2×C42×C37D411yescharacteristic
58C2×C42×C37D411yescharacteristic
59C2×C42×C37C2311yescharacteristic
60C4⋊C8×C37—21no—
61C4⋊C8×C37—21no—
62#103×C37—22no—
63#102×C37—22no—
64C22⋊C8×C37—21no—
65C22⋊C8×C37—21no—
66#97×C37—21no—
67#97×C37—21no—
68#97×C37C2×C412yescomplemented
69C4×C8×C37—21no—
70#95×C37—21no—
71#95×C37—21no—
72#95×C37—21no—
73#95×C37—21no—
74#95×C37—21no—
75#95×C37D411yescharacteristic
76#95×C37D411yescharacteristic
77C24×C37—21no—
78C2×Q8×C37—21no—
79C2×Q8×C37—21no—
80C2×Q8×C37—21no—
81C2×Q8×C37—81no—
82C2×Q8×C37C22⋊C412yes—
83C2×D4×C37—21no—
84C2×D4×C37—81no—
85C2×D4×C37C22⋊C412yes—
86C22×C4×C37—21no—
87C22×C4×C37—21no—
88C22×C4×C37—21no—
89C22×C4×C37—21no—
90C22×C4×C37—21no—
91C22×C4×C37—42no—
92C22×C4×C37—81no—
93C22×C4×C37—81no—
94C22×C4×C37C2×D411yescharacteristic
95C22×C4×C37C2×D411yescharacteristic
96C22×C4×C37C2×D411yescharacteristic
97Q16×C37—82no—
98SD16×C37—82no—
99M16×C37—22no—
100M16×C37—41no—
101C2×C8×C37—22no—
102C2×C8×C37—41no—
103C2×C8×C37—41no—
104C4⋊C4×C37—21no—
105C4⋊C4×C37—21no—
106C4⋊C4×C37—21no—
107C4⋊C4×C37—21no—
108C4⋊C4×C37—42no—
109C4⋊C4×C37—41no—
110C4⋊C4×C37—41no—
111C4⋊C4×C37—81no—
112C22⋊C4×C37—22no—
113C22⋊C4×C37—22no—
114C22⋊C4×C37—22no—
115C22⋊C4×C37—22no—
116C22⋊C4×C37—42no—
117C22⋊C4×C37—41no—
118C22⋊C4×C37—81no—
119C22⋊C4×C37—81no—
120C42×C37—41no—
121C42×C37—41no—
122C42×C37—41no—
123C42×C37—81no—
124C42×C37C22×C411yescharacteristic
125C42×C37C2×D411yescharacteristic
126C42×C37#4111yescharacteristic
127C42×C37#4111yescharacteristic
128C23×C37—22no—
129C23×C37—41no—
130C23×C37—41no—
131C23×C37—41no—
132C23×C37—41no—
133C23×C37—41no—
134C23×C37—41no—
135C23×C37#12011yescharacteristic
136Q8×C37—42no—
137Q8×C37—42no—
138Q8×C37—81no—
139Q8×C37—81no—
140D4×C37—42no—
141D4×C37—81no—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—22no—
145C2×C4×C37—22no—
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—41no—
153C2×C4×C37—41no—
154C2×C4×C37—41no—
155C2×C4×C37—41no—
156C2×C4×C37—41no—
157C2×C4×C37—41no—
158C2×C4×C37—41no—
159C2×C4×C37—41no—
160C2×C4×C37—41no—
161C2×C4×C37—41no—
162C2×C4×C37—41no—
163C2×C4×C37—84no—
164C2×C4×C37C2×C22⋊C411yescharacteristic
165C2×C4×C37C4×D411yescharacteristic
166C2×C4×C37C4×D411yescharacteristic
167C2×C4×C37#12111yescharacteristic
168C2×C4×C37#12111yescharacteristic
169C2×C4×C37#12311yescharacteristic
170C8×C37—42no—
171C8×C37—42no—
172C8×C37—81no—
173#9379C3711yesmaximal, characteristic, direct product factor, Sylow
174C22×C37—21no—
175C22×C37—21no—
176C22×C37—42no—
177C22×C37—42no—
178C22×C37—42no—
179C22×C37—81no—
180C22×C37—81no—
181C22×C37—81no—
182C22×C37—81no—
183C22×C37#38611yescharacteristic
184C22×C37#45511yescharacteristic
185C22×C37#45611yescharacteristic
186C4×C37—21no—
187C4×C37—21no—
188C4×C37—21no—
189C4×C37—21no—
190C4×C37—21no—
191C4×C37—21no—
192C4×C37—42no—
193C4×C37—42no—
194C4×C37—81no—
195C4×C37—81no—
196C4×C37—81no—
197C4×C37—81no—
198C4×C37—81no—
199#3215C2×C3711yescharacteristic
200#2337C2×C3711yescharacteristic
201#1986C2×C3711yescharacteristic, complemented
202#1527C2×C3711yescharacteristic
203#1515C2×C3711yescharacteristic, complemented
204#1288C2×C3711yescharacteristic, complemented
205#1285C2×C3711yescharacteristic, complemented
206C2×C37—21no—
207C2×C37—21no—
208C2×C37—82no—
209C2×C37#188211yescharacteristic
210C2×C37#190611yescharacteristic
211C2×C37#191111yescharacteristic
212#533C22×C3711yescharacteristic
213C2×#124C22×C3711yescharacteristic
214#497C4×C3712yescomplemented
215#489C4×C3712yescomplemented
216#464—22no—
217#451—21no—
218#450—21no—
219#432C22×C3711yescharacteristic
220#432C22×C3711yescharacteristic
221C4×M16C22×C3711yescharacteristic
222#391—21no—
223#388—21no—
224#388—21no—
225#386—21no—
226#385—21no—
227#383C22×C3711yescharacteristic
228C4×C4⋊C4C22×C3711yescharacteristic
229C4×C22⋊C4—21no—
230#339—21no—
231#339—21no—
232#329—22no—
233#328—21no—
234#328—21no—
235C37#937911yescharacteristic, direct product factor, Sylow
236C22×Q8D4×C3711yescharacteristic
237C22×D4D4×C3711yescharacteristic
238C23×C4—21no—
239C2×Q16—22no—
240C2×SD16—22no—
241C2×M16—21no—
242C4⋊Q8C2×C4×C3711yescharacteristic, complemented
243C4⋊Q8C2×C4×C3711yescharacteristic, complemented
244#125—21no—
245#124—21no—
246#124—21no—
247#124C2×C4×C3712yes—
248#124D4×C3712yes—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253#117—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C42—21no—
262C2×C42D4×C3711yescharacteristic
263C2×C42D4×C3711yescharacteristic
264C2×C42C23×C3711yescharacteristic
265C4⋊C8—21no—
266C4⋊C8—21no—
267#103—22no—
268#102—22no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271#97—21no—
272#97—21no—
273#97C2×C4×C3712yescomplemented
274C4×C8—21no—
275#95—21no—
276#95—21no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95D4×C3711yescharacteristic
281#95D4×C3711yescharacteristic
282C24—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—81no—
287C2×Q8C22⋊C4×C3712yes—
288C2×D4—21no—
289C2×D4—81no—
290C2×D4C22⋊C4×C3712yes—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4C2×D4×C3711yescharacteristic
300C22×C4C2×D4×C3711yescharacteristic
301C22×C4C2×D4×C3711yescharacteristic
302Q16—82no—
303SD16—82no—
304M16—22no—
305M16—41no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—81no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—42no—
322C22⋊C4—41no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C42—41no—
326C42—41no—
327C42—41no—
328C42—81no—
329C42C22×C4×C3711yescharacteristic
330C42C2×D4×C3711yescharacteristic
331C42#41×C3711yescharacteristic
332C42#41×C3711yescharacteristic
333C23—22no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23#120×C3711yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—81no—
344Q8—81no—
345D4—42no—
346D4—81no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—84no—
369C2×C4C2×C22⋊C4×C3711yescharacteristic
370C2×C4C4×D4×C3711yescharacteristic
371C2×C4C4×D4×C3711yescharacteristic
372C2×C4#121×C3711yescharacteristic
373C2×C4#121×C3711yescharacteristic
374C2×C4#123×C3711yescharacteristic
375C8—42no—
376C8—42no—
377C8—81no—
378C22—21no—
379C22—21no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22C37×#38611yescharacteristic
388C22C37×#45511yescharacteristic
389C22C37×#45611yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—42no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C2—21no—
404C2—21no—
405C2—82no—
406C2C37×#188211yescharacteristic
407C2C37×#190611yescharacteristic
408C2C37×#191111yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC42C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC22×D4×C37D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#1986C2semidirect
5. C37×#1515C2semidirect
6. C37×#1288C2semidirect
7. C37×#1285C2semidirect
10. C37×#497C4semidirect
11. C37×#489C4semidirect
37. C4⋊Q8×C37C2×C4semidirect
38. C4⋊Q8×C37C2×C4semidirect
68. #97×C37C2×C4semidirect
173. #9379C37direct (N × H)
201. #1986C2×C37semidirect
203. #1515C2×C37semidirect
204. #1288C2×C37semidirect
205. #1285C2×C37semidirect
214. #497C4×C37semidirect
215. #489C4×C37semidirect
235. C37#9379direct (N × H)
242. C4⋊Q8C2×C4×C37semidirect
243. C4⋊Q8C2×C4×C37semidirect
273. #97C2×C4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#32152
C37×#23372
C37×#19862
C37×#15272
C37×#15152
C37×#12882
C37×#12852
#937937