Finite Group Databasebeta

← C37×#60330 #22681583

Subgroups — C37×#60330 #22681583

Order 9472.

1710 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3461C211yesmaximal, characteristic
2C37×#2993C214yesmaximal, complemented
3C37×#2992C214yesmaximal, complemented
4C37×#2989C212yesmaximal, complemented
5C37×#2985C214yesmaximal, complemented
6C37×#2983C211yesmaximal, characteristic, complemented
7C37×#2966C214yesmaximal, complemented
8C37×#2966C214yesmaximal, complemented
9C8×#41×C37C212yesmaximal, complemented
10C37×#2960C214yesmaximal, complemented
11C2×C8×Q8×C37C211yesmaximal, characteristic, complemented
12C37×#544C411yescharacteristic
13C37×#542C414yes—
14C37×#541C414yes—
15C37×#539C414yes—
16C37×#537C411yescharacteristic
17C37×#536C412yes—
18C37×#533C2214yes—
19C37×#529C2214yes—
20C37×#529C2214yes—
21C4×#41×C37C2212yes—
22C2×C4×Q8×C37C2211yescharacteristic
23C37×#446C2214yes—
24C37×#446C2214yes—
25C37×#446C2218yes—
26C37×#446C2214yes—
27C37×#446C2214yes—
28C8×Q8×C37C2214yes—
29C8×Q8×C37C2214yes—
30C8×Q8×C37C2212yes—
31C8×Q8×C37C2214yes—
32C8×Q8×C37C2212yes—
33C37×#436C2214yes—
34C37×#436C2214yes—
35C37×#435C2218yes—
36C37×#435C2218yes—
37C8×D4×C37C2212yes—
38C8×D4×C37C2214yes—
39C8×D4×C37C2214yes—
40C8×D4×C37C2212yes—
41C8×D4×C37C2214yes—
42C37×#433C2218yes—
43C37×#433C2218yes—
44C37×#432C2214yes—
45C37×#432C2214yes—
46C37×#431C2212yes—
47C37×#431C2214yes—
48C37×#424C2218yes—
49C37×#423C2214yes—
50C2×C4⋊C8×C37C2211yescharacteristic
51C2×C4⋊C8×C37C2212yes—
52C37×#405C2218yes—
53C2×C4×C8×C37C2211yescharacteristic
54C2×C4×C8×C37C2212yes—
55C2×C4×C8×C37C2214yes—
56C2×#41×C37C2×C412yes—
57C22×Q8×C37C2×C411yescharacteristic
58C2×M16×C37C2318yes—
59C22×C8×C37C2311yescharacteristic
60C22×C8×C37C2314yes—
61C22×C8×C37C2311yescharacteristic
62C22×C8×C37C2312yes—
63C22×C8×C37C2314yes—
64C4⋊Q8×C37C2×C414yes—
65C4⋊Q8×C37C2×C414yes—
66#126×C37C2×C418yes—
67#126×C37C2×C418yes—
68#125×C37C2×C414yes—
69#125×C37C2×C414yes—
70#125×C37C2×C418yes—
71#124×C37C2×C414yes—
72#124×C37C2×C414yes—
73#123×C37C2×C418yes—
74#123×C37C2×C418yes—
75C22⋊Q8×C37C2×C414yes—
76C22⋊Q8×C37C2×C414yes—
77C22⋊Q8×C37C2×C414yes—
78C22⋊Q8×C37C2×C414yes—
79C22⋊Q8×C37C2×C418yes—
80#121×C37C2×C414yes—
81#121×C37C2×C414yes—
82C4×Q8×C37C2×C412yes—
83C4×Q8×C37C2×C414yes—
84C4×Q8×C37C2314yes—
85C4×Q8×C37C2314yes—
86C4×Q8×C37C2312yes—
87C4×D4×C37C2×C414yes—
88C4×D4×C37C2×C412yes—
89C4×D4×C37C2314yes—
90C4×D4×C37C2314yes—
91C4×D4×C37C2312yes—
92#117×C37C2×C412yes—
93#117×C37C2×C414yes—
94#117×C37C2318yes—
95C2×C4⋊C4×C37C2×C411yescharacteristic
96C2×C4⋊C4×C37C2×C412yes—
97C2×C42×C37C2312yes—
98C2×C42×C37C2314yes—
99C2×C42×C37C2311yescharacteristic
100C4⋊C8×C37C2314yes—
101C4⋊C8×C37C2318yes—
102C4⋊C8×C37C2312yes—
103C4⋊C8×C37C2318yes—
104C4⋊C8×C37C2314yes—
105C4⋊C8×C37C2314yes—
106C4⋊C8×C37C2312yes—
107C4⋊C8×C37C2314yes—
108C4⋊C8×C37C2314yes—
109C22⋊C8×C37C2314yes—
110C22⋊C8×C37C2314yes—
111C22⋊C8×C37C2314yes—
112C22⋊C8×C37C2318yes—
113#97×C37C2318yes—
114#97×C37C2318yes—
115C4×C8×C37C2312yes—
116C4×C8×C37C2314yes—
117C4×C8×C37C2314yes—
118C4×C8×C37C2314yes—
119C4×C8×C37C2312yes—
120C4×C8×C37C2314yes—
121C4×C8×C37C2314yes—
122#41×C37—28no—
123C2×Q8×C37—24no—
124C2×Q8×C37C22×C414yes—
125C2×Q8×C37C22×C412yes—
126C2×Q8×C37C22×C414yes—
127C2×D4×C37C22×C414yes—
128C2×D4×C37C22×C412yes—
129C2×D4×C37C22×C414yes—
130C22×C4×C37C22×C412yes—
131C22×C4×C37C22×C414yes—
132C22×C4×C37C22×C411yescharacteristic
133C22×C4×C37C22×C412yes—
134C22×C4×C37C22×C414yes—
135C22×C4×C37C22×C411yescharacteristic
136C22×C4×C37C2411yescharacteristic
137C22×C4×C37C2414yes—
138M16×C37—48no—
139C2×C8×C37—22no—
140C2×C8×C37—28no—
141C2×C8×C37—41no—
142C2×C8×C37—44no—
143C2×C8×C37—42no—
144C2×C8×C37C2411yescharacteristic
145C2×C8×C37C2412yes—
146C2×C8×C37C2414yes—
147C2×C8×C37C2414yes—
148C2×C8×C37C2414yes—
149C2×C8×C37C2411yescharacteristic
150C4⋊C4×C37C22×C414yes—
151C4⋊C4×C37C22×C418yes—
152C4⋊C4×C37C22×C414yes—
153C4⋊C4×C37C22×C412yes—
154C4⋊C4×C37C22×C412yes—
155C4⋊C4×C37C22×C414yes—
156C4⋊C4×C37C22×C418yes—
157C4⋊C4×C37C22×C418yes—
158C4⋊C4×C37C22×C414yes—
159C4⋊C4×C37C22×C414yes—
160C4⋊C4×C37C22×C418yes—
161C22⋊C4×C37C22×C414yes—
162C22⋊C4×C37C22×C414yes—
163C22⋊C4×C37C22×C414yes—
164C22⋊C4×C37C22×C418yes—
165C22⋊C4×C37C22×C418yes—
166C22⋊C4×C37C22×C418yes—
167C42×C37C22×C412yes—
168C42×C37C22×C414yes—
169C42×C37C22×C414yes—
170C42×C37C22×C414yes—
171C42×C37C2412yes—
172C42×C37C2414yes—
173C42×C37C2414yes—
174C23×C37C23×C414yes—
175C23×C37C23×C411yescharacteristic
176Q8×C37—28no—
177Q8×C37—24no—
178Q8×C37—44no—
179D4×C37—28no—
180D4×C37—24no—
181D4×C37—44no—
182C2×C4×C37—24no—
183C2×C4×C37—28no—
184C2×C4×C37—21no—
185C2×C4×C37—24no—
186C2×C4×C37—21no—
187C2×C4×C37—24no—
188C2×C4×C37—41no—
189C2×C4×C37—44no—
190C2×C4×C37—42no—
191C2×C4×C37#13114yes—
192C2×C4×C37C23×C411yescharacteristic
193C2×C4×C37C23×C412yes—
194C2×C4×C37C23×C414yes—
195C2×C4×C37C23×C414yes—
196C2×C4×C37C23×C414yes—
197C2×C4×C37C23×C414yes—
198C2×C4×C37C23×C414yes—
199C2×C4×C37C23×C412yes—
200C2×C4×C37C2511yescharacteristic
201C8×C37—21no—
202C8×C37—24no—
203C8×C37—22no—
204C8×C37—24no—
205C8×C37—24no—
206C8×C372−1+412yes—
207#60330C3711yesmaximal, characteristic, direct product factor, Sylow
208C22×C37—21no—
209C22×C37—21no—
210C22×C37—24no—
211C22×C37—24no—
212C22×C37—24no—
213C22×C37C2×#13112yes—
214C22×C37C24×C411yescharacteristic
215C4×C37—21no—
216C4×C37—24no—
217C4×C37—24no—
218C4×C37—24no—
219C4×C37—22no—
220C4×C37—24no—
221C4×C37—24no—
222C4×C37C2×#13114yes—
223C4×C37C2×2−1+411yescharacteristic
224C4×C37#58511yescharacteristic
225#3461C2×C3711yescharacteristic
226#2993C2×C3714yescomplemented
227#2992C2×C3714yescomplemented
228#2989C2×C3712yescomplemented
229#2985C2×C3714yescomplemented
230#2983C2×C3711yescharacteristic, complemented
231#2966C2×C3714yescomplemented
232#2966C2×C3714yescomplemented
233C8×#41C2×C3712yescomplemented
234#2960C2×C3714yescomplemented
235C2×C8×Q8C2×C3711yescharacteristic, complemented
236C2×C37—22no—
237C2×C37—44no—
238C2×C37C4×2−1+411yescharacteristic
239C2×C37C22×#13111yescharacteristic
240C2×C37#357311yescharacteristic
241#544C4×C3711yescharacteristic
242#542C4×C3714yes—
243#541C4×C3714yes—
244#539C4×C3714yes—
245#537C4×C3711yescharacteristic
246#536C4×C3712yes—
247#533C22×C3714yes—
248#529C22×C3714yes—
249#529C22×C3714yes—
250C4×#41C22×C3712yes—
251C2×C4×Q8C22×C3711yescharacteristic
252#446C22×C3714yes—
253#446C22×C3714yes—
254#446C22×C3718yes—
255#446C22×C3714yes—
256#446C22×C3714yes—
257C8×Q8C22×C3714yes—
258C8×Q8C22×C3714yes—
259C8×Q8C22×C3712yes—
260C8×Q8C22×C3714yes—
261C8×Q8C22×C3712yes—
262#436C22×C3714yes—
263#436C22×C3714yes—
264#435C22×C3718yes—
265#435C22×C3718yes—
266C8×D4C22×C3712yes—
267C8×D4C22×C3714yes—
268C8×D4C22×C3714yes—
269C8×D4C22×C3712yes—
270C8×D4C22×C3714yes—
271#433C22×C3718yes—
272#433C22×C3718yes—
273#432C22×C3714yes—
274#432C22×C3714yes—
275#431C22×C3712yes—
276#431C22×C3714yes—
277#424C22×C3718yes—
278#423C22×C3714yes—
279C2×C4⋊C8C22×C3711yescharacteristic
280C2×C4⋊C8C22×C3712yes—
281#405C22×C3718yes—
282C2×C4×C8C22×C3711yescharacteristic
283C2×C4×C8C22×C3712yes—
284C2×C4×C8C22×C3714yes—
285C37#6033011yescharacteristic, direct product factor, Sylow
286C2×#41C2×C4×C3712yes—
287C22×Q8C2×C4×C3711yescharacteristic
288C2×M16C23×C3718yes—
289C22×C8C23×C3711yescharacteristic
290C22×C8C23×C3714yes—
291C22×C8C23×C3711yescharacteristic
292C22×C8C23×C3712yes—
293C22×C8C23×C3714yes—
294C4⋊Q8C2×C4×C3714yes—
295C4⋊Q8C2×C4×C3714yes—
296#126C2×C4×C3718yes—
297#126C2×C4×C3718yes—
298#125C2×C4×C3714yes—
299#125C2×C4×C3714yes—
300#125C2×C4×C3718yes—
301#124C2×C4×C3714yes—
302#124C2×C4×C3714yes—
303#123C2×C4×C3718yes—
304#123C2×C4×C3718yes—
305C22⋊Q8C2×C4×C3714yes—
306C22⋊Q8C2×C4×C3714yes—
307C22⋊Q8C2×C4×C3714yes—
308C22⋊Q8C2×C4×C3714yes—
309C22⋊Q8C2×C4×C3718yes—
310#121C2×C4×C3714yes—
311#121C2×C4×C3714yes—
312C4×Q8C2×C4×C3714yes—
313C4×Q8C2×C4×C3712yes—
314C4×Q8C23×C3714yes—
315C4×Q8C23×C3712yes—
316C4×Q8C23×C3714yes—
317C4×D4C2×C4×C3714yes—
318C4×D4C2×C4×C3712yes—
319C4×D4C23×C3714yes—
320C4×D4C23×C3712yes—
321C4×D4C23×C3714yes—
322#117C2×C4×C3712yes—
323#117C2×C4×C3714yes—
324#117C23×C3718yes—
325C2×C4⋊C4C2×C4×C3711yescharacteristic
326C2×C4⋊C4C2×C4×C3712yes—
327C2×C42C23×C3711yescharacteristic
328C2×C42C23×C3712yes—
329C2×C42C23×C3714yes—
330C4⋊C8C23×C3714yes—
331C4⋊C8C23×C3718yes—
332C4⋊C8C23×C3712yes—
333C4⋊C8C23×C3718yes—
334C4⋊C8C23×C3714yes—
335C4⋊C8C23×C3714yes—
336C4⋊C8C23×C3712yes—
337C4⋊C8C23×C3714yes—
338C4⋊C8C23×C3714yes—
339C22⋊C8C23×C3714yes—
340C22⋊C8C23×C3714yes—
341C22⋊C8C23×C3714yes—
342C22⋊C8C23×C3718yes—
343#97C23×C3718yes—
344#97C23×C3718yes—
345C4×C8C23×C3712yes—
346C4×C8C23×C3714yes—
347C4×C8C23×C3714yes—
348C4×C8C23×C3712yes—
349C4×C8C23×C3714yes—
350C4×C8C23×C3714yes—
351C4×C8C23×C3714yes—
352#41—28no—
353C2×Q8—24no—
354C2×Q8C22×C4×C3714yes—
355C2×Q8C22×C4×C3712yes—
356C2×Q8C22×C4×C3714yes—
357C2×D4C22×C4×C3714yes—
358C2×D4C22×C4×C3712yes—
359C2×D4C22×C4×C3714yes—
360C22×C4C22×C4×C3712yes—
361C22×C4C22×C4×C3714yes—
362C22×C4C22×C4×C3711yescharacteristic
363C22×C4C22×C4×C3712yes—
364C22×C4C22×C4×C3714yes—
365C22×C4C22×C4×C3711yescharacteristic
366C22×C4C24×C3711yescharacteristic
367C22×C4C24×C3714yes—
368M16—48no—
369C2×C8—22no—
370C2×C8—28no—
371C2×C8—41no—
372C2×C8—44no—
373C2×C8—42no—
374C2×C8C24×C3711yescharacteristic
375C2×C8C24×C3712yes—
376C2×C8C24×C3714yes—
377C2×C8C24×C3714yes—
378C2×C8C24×C3714yes—
379C2×C8C24×C3711yescharacteristic
380C4⋊C4C22×C4×C3714yes—
381C4⋊C4C22×C4×C3718yes—
382C4⋊C4C22×C4×C3714yes—
383C4⋊C4C22×C4×C3712yes—
384C4⋊C4C22×C4×C3712yes—
385C4⋊C4C22×C4×C3714yes—
386C4⋊C4C22×C4×C3718yes—
387C4⋊C4C22×C4×C3718yes—
388C4⋊C4C22×C4×C3714yes—
389C4⋊C4C22×C4×C3714yes—
390C4⋊C4C22×C4×C3718yes—
391C22⋊C4C22×C4×C3714yes—
392C22⋊C4C22×C4×C3714yes—
393C22⋊C4C22×C4×C3714yes—
394C22⋊C4C22×C4×C3718yes—
395C22⋊C4C22×C4×C3718yes—
396C22⋊C4C22×C4×C3718yes—
397C42C22×C4×C3712yes—
398C42C22×C4×C3714yes—
399C42C22×C4×C3714yes—
400C42C22×C4×C3714yes—
401C42C24×C3712yes—
402C42C24×C3714yes—
403C42C24×C3714yes—
404C23C23×C4×C3714yes—
405C23C23×C4×C3711yescharacteristic
406Q8—28no—
407Q8—24no—
408Q8—44no—
409D4—28no—
410D4—24no—
411D4—44no—
412C2×C4—24no—
413C2×C4—28no—
414C2×C4—21no—
415C2×C4—24no—
416C2×C4—21no—
417C2×C4—24no—
418C2×C4—41no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4#131×C3714yes—
422C2×C4C23×C4×C3711yescharacteristic
423C2×C4C23×C4×C3712yes—
424C2×C4C23×C4×C3714yes—
425C2×C4C23×C4×C3714yes—
426C2×C4C23×C4×C3714yes—
427C2×C4C23×C4×C3714yes—
428C2×C4C23×C4×C3714yes—
429C2×C4C23×C4×C3712yes—
430C2×C4C25×C3711yescharacteristic
431C8—21no—
432C8—24no—
433C8—22no—
434C8—24no—
435C8—24no—
436C82−1+4×C3712yes—
437C22—21no—
438C22—21no—
439C22—24no—
440C22—24no—
441C22—24no—
442C22C2×#131×C3712yes—
443C22C24×C4×C3711yescharacteristic
444C4—21no—
445C4—24no—
446C4—24no—
447C4—24no—
448C4—22no—
449C4—24no—
450C4—24no—
451C4C2×#131×C3714yes—
452C4C2×2−1+4×C3711yescharacteristic
453C4C37×#58511yescharacteristic
454C2—22no—
455C2—44no—
456C2C4×2−1+4×C3711yescharacteristic
457C2C22×#131×C3711yescharacteristic
458C2C37×#357311yescharacteristic
subgroupG/H
centerC2×C8×C37C24
commutatorC22C24×C4×C37
Frattini, cosocleC2×C4C25×C37
socleC22×C37C24×C4
prime radicalC37×#537C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2993C2semidirect
3. C37×#2992C2semidirect
4. C37×#2989C2semidirect
5. C37×#2985C2semidirect
6. C37×#2983C2semidirect
7. C37×#2966C2semidirect
8. C37×#2966C2semidirect
9. C8×#41×C37C2semidirect
10. C37×#2960C2semidirect
11. C2×C8×Q8×C37C2semidirect
207. #60330C37direct (N × H)
226. #2993C2×C37semidirect
227. #2992C2×C37semidirect
228. #2989C2×C37semidirect
229. #2985C2×C37semidirect
230. #2983C2×C37semidirect
231. #2966C2×C37semidirect
232. #2966C2×C37semidirect
233. C8×#41C2×C37semidirect
234. #2960C2×C37semidirect
235. C2×C8×Q8C2×C37semidirect
285. C37#60330direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34612
C37×#29932
C37×#29922
C37×#29892
C37×#29852
C37×#29832
C37×#29662
C8×#41×C372
C37×#29602
C2×C8×Q8×C372
#6033037