Finite Group Databasebeta

← C37×#24077 #22645330

Subgroups — C37×#24077 #22645330

Order 9472.

1086 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3492C211yesmaximal, characteristic
2C37×#3092C212yesmaximal, complemented
3C2×C37×#382C211yesmaximal, characteristic, complemented
4C37×#2061C212yesmaximal, complemented
5C37×#2040C212yesmaximal, complemented
6C37×#1896C212yesmaximal, complemented
7C37×#1860C214yesmaximal, complemented
8C37×#1821C211yesmaximal, characteristic, complemented
9C37×#554—22no—
10C37×#553—22no—
11C37×#552—22no—
12C37×#547—22no—
13C37×#544C2211yescharacteristic
14C37×#539—22no—
15C37×#537C2211yescharacteristic
16C37×#525—22no—
17C37×#525C2212yes—
18C37×#520C2212yes—
19C22×C4⋊C4×C37C2211yescharacteristic
20C22×C4⋊C4×C37C2211yescharacteristic
21C22×C42×C37C2211yescharacteristic
22C37×#484—22no—
23C37×#483—22no—
24C37×#481—22no—
25C37×#480—22no—
26C37×#428C2214yes—
27C2×#104×C37C2214yes—
28C37×#417C2214yes—
29C37×#407C2212yes—
30C37×#382—22no—
31C37×#382C2212yes—
32C37×#382C2212yes—
33C2×#95×C37—22no—
34C37×#343C2212yes—
35C37×#343C2212yes—
36C37×#339C2214yes—
37C2×#41×C37—22no—
38C2×#41×C37C2312yes—
39C23×C4×C37—21no—
40C23×C4×C37—21no—
41C23×C4×C37D412yes—
42C23×C4×C37C2311yescharacteristic
43C2×M16×C37C2314yes—
44C4⋊Q8×C37—22no—
45#126×C37—24no—
46#125×C37—24no—
47#125×C37—22no—
48#123×C37—24no—
49#123×C37—24no—
50#123×C37—22no—
51C22⋊Q8×C37—22no—
52C22⋊Q8×C37—24no—
53C22⋊Q8×C37—22no—
54C22⋊Q8×C37—22no—
55C22⋊Q8×C37D412yes—
56C22⋊Q8×C37D412yes—
57#121×C37—22no—
58#121×C37—22no—
59#121×C37—22no—
60#121×C37D412yes—
61#121×C37D412yes—
62#120×C37—22no—
63C4×Q8×C37—22no—
64C4×D4×C37—24no—
65C4×D4×C37—22no—
66C4×D4×C37—24no—
67C4×D4×C37—22no—
68C4×D4×C37—22no—
69#117×C37—22no—
70#117×C37—22no—
71#117×C37C2312yes—
72C2×C4⋊C4×C37—22no—
73C2×C4⋊C4×C37—22no—
74C2×C4⋊C4×C37—22no—
75C2×C4⋊C4×C37—22no—
76C2×C4⋊C4×C37—22no—
77C2×C4⋊C4×C37—21no—
78C2×C4⋊C4×C37D412yes—
79C2×C4⋊C4×C37C2312yes—
80C2×C4⋊C4×C37C2311yescharacteristic
81C2×C4⋊C4×C37C2311yescharacteristic
82C2×C42×C37—21no—
83C2×C42×C37—24no—
84C2×C42×C37C2312yes—
85#107×C37—24no—
86#106×C37—24no—
87#104×C37—28no—
88#103×C37—24no—
89#102×C37—24no—
90C22⋊C8×C37—22no—
91C22⋊C8×C37—22no—
92#95×C37—24no—
93#95×C37—24no—
94C24×C37C2×D411yescharacteristic
95#41×C37—24no—
96#41×C37—24no—
97#41×C37—84no—
98C2×Q8×C37—22no—
99C2×Q8×C37C2×D412yes—
100C2×D4×C37—22no—
101C2×D4×C37—22no—
102C2×D4×C37—22no—
103C2×D4×C37—22no—
104C2×D4×C37C2×D412yes—
105C22×C4×C37—22no—
106C22×C4×C37—22no—
107C22×C4×C37—24no—
108C22×C4×C37—22no—
109C22×C4×C37—22no—
110C22×C4×C37—24no—
111C22×C4×C37—22no—
112C22×C4×C37—22no—
113C22×C4×C37—22no—
114C22×C4×C37—42no—
115C22×C4×C37—42no—
116C22×C4×C37—44no—
117C22×C4×C37—44no—
118C22×C4×C37—41no—
119C22×C4×C37—41no—
120C22×C4×C37C2×D411yescharacteristic
121C22×C4×C37C2×D412yes—
122C22×C4×C37C2×D412yes—
123C22×C4×C37C2×D412yes—
124C22×C4×C37C2×D412yes—
125C22×C4×C37C2411yescharacteristic
126M16×C37—24no—
127M16×C37—24no—
128C2×C8×C37—24no—
129C4⋊C4×C37—24no—
130C4⋊C4×C37—22no—
131C4⋊C4×C37—22no—
132C4⋊C4×C37—24no—
133C4⋊C4×C37—24no—
134C4⋊C4×C37—22no—
135C4⋊C4×C37—22no—
136C4⋊C4×C37—22no—
137C4⋊C4×C37—22no—
138C4⋊C4×C37—24no—
139C4⋊C4×C37—42no—
140C4⋊C4×C37C2×D412yes—
141C4⋊C4×C37C2×D412yes—
142C22⋊C4×C37—24no—
143C22⋊C4×C37—24no—
144C22⋊C4×C37—22no—
145C22⋊C4×C37—22no—
146C22⋊C4×C37—22no—
147C22⋊C4×C37—22no—
148C22⋊C4×C37—22no—
149C42×C37—24no—
150C42×C37—24no—
151C42×C37—22no—
152C42×C37—22no—
153C42×C37#4114yescomplemented
154C23×C37—21no—
155C23×C37—21no—
156C23×C37—22no—
157C23×C37—22no—
158C23×C37—22no—
159C23×C37#12011yescharacteristic
160C23×C37#12011yescharacteristic
161C23×C37C22×D411yescharacteristic
162Q8×C37—24no—
163Q8×C37—82no—
164D4×C37—24no—
165D4×C37—42no—
166D4×C37—42no—
167D4×C37—44no—
168D4×C37—44no—
169D4×C37—82no—
170C2×C4×C37—21no—
171C2×C4×C37—21no—
172C2×C4×C37—24no—
173C2×C4×C37—24no—
174C2×C4×C37—22no—
175C2×C4×C37—22no—
176C2×C4×C37—22no—
177C2×C4×C37—22no—
178C2×C4×C37—22no—
179C2×C4×C37—24no—
180C2×C4×C37—48no—
181C2×C4×C37—42no—
182C2×C4×C37—42no—
183C2×C4×C37—44no—
184C2×C4×C37—44no—
185C2×C4×C37—42no—
186C2×C4×C37—42no—
187C2×C4×C37—44no—
188C2×C4×C37—42no—
189C2×C4×C37—82no—
190C2×C4×C37—84no—
191C2×C4×C37—82no—
192C2×C4×C37—82no—
193C2×C4×C37#12012yes—
194C2×C4×C37C22×D412yes—
195C2×C4×C37C2×#4112yes—
196C2×C4×C372−1+412yes—
197C8×C37—44no—
198#24077C3711yesmaximal, characteristic, direct product factor, Sylow
199C22×C37—24no—
200C22×C37—24no—
201C22×C37—21no—
202C22×C37—21no—
203C22×C37—21no—
204C22×C37—21no—
205C22×C37—21no—
206C22×C37—21no—
207C22×C37—42no—
208C22×C37—42no—
209C22×C37—42no—
210C22×C37#45412yes—
211C22×C37#45512yes—
212C22×C37C2×#12011yescharacteristic
213C22×C37#52511yescharacteristic
214C22×C37#53611yescharacteristic
215C4×C37—22no—
216C4×C37—44no—
217C4×C37—42no—
218C4×C37—42no—
219C4×C37—42no—
220C4×C37—42no—
221C4×C37—42no—
222C4×C37—82no—
223C4×C37#54714yes—
224#3492C2×C3711yescharacteristic
225#3092C2×C3712yescomplemented
226C2×#382C2×C3711yescharacteristic, complemented
227#2061C2×C3712yescomplemented
228#2040C2×C3712yescomplemented
229#1896C2×C3712yescomplemented
230#1860C2×C3714yescomplemented
231#1821C2×C3711yescharacteristic, complemented
232C2×C37—21no—
233C2×C37—21no—
234C2×C37—22no—
235C2×C37—22no—
236C2×C37—82no—
237C2×C37#240611yescharacteristic
238C2×C37C2×#45511yescharacteristic
239C2×C37C2×#45411yescharacteristic
240#554—22no—
241#553—22no—
242#552—22no—
243#547—22no—
244#544C22×C3711yescharacteristic
245#539—22no—
246#537C22×C3711yescharacteristic
247#525—22no—
248#525C22×C3712yes—
249#520C22×C3712yes—
250C22×C4⋊C4C22×C3711yescharacteristic
251C22×C4⋊C4C22×C3711yescharacteristic
252C22×C42C22×C3711yescharacteristic
253#484—22no—
254#483—22no—
255#481—22no—
256#480—22no—
257#428C22×C3714yes—
258C2×#104C22×C3714yes—
259#417C22×C3714yes—
260#407C22×C3712yes—
261#382—22no—
262#382C22×C3712yes—
263#382C22×C3712yes—
264C2×#95—22no—
265#343C22×C3712yes—
266#343C22×C3712yes—
267#339C22×C3714yes—
268C37#2407711yescharacteristic, direct product factor, Sylow
269C2×#41—22no—
270C2×#41C23×C3712yes—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4D4×C3712yes—
274C23×C4C23×C3711yescharacteristic
275C2×M16C23×C3714yes—
276C4⋊Q8—22no—
277#126—24no—
278#125—24no—
279#125—22no—
280#123—24no—
281#123—24no—
282#123—22no—
283C22⋊Q8—22no—
284C22⋊Q8—24no—
285C22⋊Q8—22no—
286C22⋊Q8—22no—
287C22⋊Q8D4×C3712yes—
288C22⋊Q8D4×C3712yes—
289#121—22no—
290#121—22no—
291#121—22no—
292#121D4×C3712yes—
293#121D4×C3712yes—
294#120—22no—
295C4×Q8—22no—
296C4×D4—24no—
297C4×D4—22no—
298C4×D4—24no—
299C4×D4—22no—
300C4×D4—22no—
301#117—22no—
302#117—22no—
303#117C23×C3712yes—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4D4×C3712yes—
311C2×C4⋊C4C23×C3712yes—
312C2×C4⋊C4C23×C3711yescharacteristic
313C2×C4⋊C4C23×C3711yescharacteristic
314C2×C42—21no—
315C2×C42—24no—
316C2×C42C23×C3712yes—
317#107—24no—
318#106—24no—
319#104—28no—
320#103—24no—
321#102—24no—
322C22⋊C8—22no—
323C22⋊C8—22no—
324#95—24no—
325#95—24no—
326C24C2×D4×C3711yescharacteristic
327#41—24no—
328#41—24no—
329#41—84no—
330C2×Q8—22no—
331C2×Q8C2×D4×C3712yes—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4C2×D4×C3712yes—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4C2×D4×C3711yescharacteristic
353C22×C4C2×D4×C3712yes—
354C22×C4C2×D4×C3712yes—
355C22×C4C2×D4×C3712yes—
356C22×C4C2×D4×C3712yes—
357C22×C4C24×C3711yescharacteristic
358M16—24no—
359M16—24no—
360C2×C8—24no—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—42no—
372C4⋊C4C2×D4×C3712yes—
373C4⋊C4C2×D4×C3712yes—
374C22⋊C4—24no—
375C22⋊C4—24no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C42—24no—
382C42—24no—
383C42—22no—
384C42—22no—
385C42#41×C3714yescomplemented
386C23—21no—
387C23—21no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23#120×C3711yescharacteristic
392C23#120×C3711yescharacteristic
393C23C22×D4×C3711yescharacteristic
394Q8—24no—
395Q8—82no—
396D4—24no—
397D4—42no—
398D4—42no—
399D4—44no—
400D4—44no—
401D4—82no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—48no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—82no—
422C2×C4—84no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4#120×C3712yes—
426C2×C4C22×D4×C3712yes—
427C2×C4C2×#41×C3712yes—
428C2×C42−1+4×C3712yes—
429C8—44no—
430C22—24no—
431C22—24no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22C37×#45412yes—
442C22C37×#45512yes—
443C22C2×#120×C3711yescharacteristic
444C22C37×#52511yescharacteristic
445C22C37×#53611yescharacteristic
446C4—22no—
447C4—44no—
448C4—42no—
449C4—42no—
450C4—42no—
451C4—42no—
452C4—42no—
453C4—82no—
454C4C37×#54714yes—
455C2—21no—
456C2—21no—
457C2—22no—
458C2—22no—
459C2—82no—
460C2C37×#240611yescharacteristic
461C2C2×C37×#45511yescharacteristic
462C2C2×C37×#45411yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3492C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3092C2semidirect
3. C2×C37×#382C2semidirect
4. C37×#2061C2semidirect
5. C37×#2040C2semidirect
6. C37×#1896C2semidirect
7. C37×#1860C2semidirect
8. C37×#1821C2semidirect
153. C42×C37#41semidirect
198. #24077C37direct (N × H)
225. #3092C2×C37semidirect
226. C2×#382C2×C37semidirect
227. #2061C2×C37semidirect
228. #2040C2×C37semidirect
229. #1896C2×C37semidirect
230. #1860C2×C37semidirect
231. #1821C2×C37semidirect
268. C37#24077direct (N × H)
385. C42#41×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34922
C37×#30922
C2×C37×#3822
C37×#20612
C37×#20402
C37×#18962
C37×#18602
C37×#18212
#2407737