Finite Group Databasebeta

← C37×#19085 #22640338

Subgroups — C37×#19085 #22640338

Order 9472.

842 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3553C211yesmaximal, characteristic
2C37×#3181C212yesmaximal, complemented
3C37×#3166C211yesmaximal, characteristic, complemented
4C37×#1664C212yesmaximal, complemented
5C37×#1663C212yesmaximal, complemented
6C37×#1661C212yesmaximal, complemented
7C37×#1660C212yesmaximal, complemented
8C37×#1524C212yesmaximal, complemented
9C2×C37×#330C211yesmaximal, characteristic, complemented
10C37×#564C2211yescharacteristic
11C37×#563C2212yes—
12C37×#562C2211yescharacteristic
13C37×#554—22no—
14C37×#553—22no—
15C37×#552—22no—
16C37×#541—22no—
17C37×#539—22no—
18C37×#539—22no—
19C37×#533C2211yescharacteristic
20C37×#529C2212yes—
21C2×#125×C37C2211yescharacteristic
22C37×#501C2212yes—
23C37×#501C2212yes—
24C37×#501C2212yes—
25C37×#499—22no—
26C37×#497C2212yes—
27C37×#491C2212yes—
28C37×#489C2212yes—
29C37×#467—22no—
30C37×#465—22no—
31C37×#441—22no—
32C37×#440—22no—
33C37×#428—22no—
34C4×M16×C37C2211yescharacteristic
35C2×#97×C37C2212yes—
36C37×#330C2211yescharacteristic
37C37×#330C2212yes—
38C37×#330C2212yes—
39C37×#330C2212yes—
40C37×#330C2211yescharacteristic
41C37×#329C2212yes—
42C37×#329C2212yes—
43C2×Q16×C37—22no—
44C2×SD16×C37—22no—
45C2×M16×C37—21no—
46C22×C8×C37—22no—
47C4⋊Q8×C37—22no—
48C4⋊Q8×C37C2312yes—
49#126×C37—22no—
50#126×C37—22no—
51#126×C37—22no—
52#126×C37—22no—
53#126×C37—22no—
54#125×C37—22no—
55#125×C37—22no—
56#125×C37—22no—
57#125×C37—22no—
58#125×C37—22no—
59#125×C37—22no—
60#125×C37—21no—
61#125×C37D412yes—
62#125×C37C2311yescharacteristic
63#125×C37C2311yescharacteristic
64#125×C37C2312yes—
65#124×C37C2312yes—
66#123×C37—22no—
67#123×C37—22no—
68#123×C37—22no—
69#123×C37—22no—
70#123×C37—22no—
71C22⋊Q8×C37—22no—
72C22⋊Q8×C37—22no—
73C22⋊Q8×C37—22no—
74C22⋊Q8×C37—22no—
75C22⋊Q8×C37—22no—
76C22⋊Q8×C37—22no—
77C22⋊Q8×C37—22no—
78C22⋊Q8×C37D412yes—
79#121×C37—22no—
80#121×C37—22no—
81#121×C37D412yes—
82C4×Q8×C37—22no—
83C4×Q8×C37—22no—
84C4×Q8×C37D412yes—
85C4×D4×C37—22no—
86C4×D4×C37—22no—
87C4×D4×C37—22no—
88C4×D4×C37—22no—
89C4×D4×C37D412yes—
90#117×C37—22no—
91#117×C37—22no—
92#117×C37—21no—
93C2×C4⋊C4×C37—22no—
94C2×C4⋊C4×C37—22no—
95C2×C4⋊C4×C37D412yes—
96C2×C42×C37C2311yescharacteristic
97#107×C37—22no—
98#107×C37—22no—
99#107×C37—22no—
100#106×C37—22no—
101#106×C37—22no—
102#106×C37—22no—
103#103×C37—22no—
104#103×C37—22no—
105#103×C37—22no—
106#102×C37—22no—
107#97×C37—22no—
108#97×C37C2312yes—
109#97×C37C2312yes—
110#97×C37C2312yes—
111C4×C8×C37—21no—
112C2×Q8×C37—22no—
113C2×Q8×C37—22no—
114C2×Q8×C37C2×D412yes—
115C2×D4×C37—22no—
116C2×D4×C37—22no—
117C2×D4×C37C2×D412yes—
118C22×C4×C37—22no—
119C22×C4×C37—22no—
120C22×C4×C37—22no—
121C22×C4×C37—22no—
122C22×C4×C37C2×D411yescharacteristic
123C22×C4×C37C2×D412yes—
124Q16×C37—44no—
125SD16×C37—44no—
126M16×C37—24no—
127C2×C8×C37—22no—
128C2×C8×C37—22no—
129C2×C8×C37—22no—
130C2×C8×C37—44no—
131C4⋊C4×C37—22no—
132C4⋊C4×C37—22no—
133C4⋊C4×C37—22no—
134C4⋊C4×C37—22no—
135C4⋊C4×C37—22no—
136C4⋊C4×C37—22no—
137C4⋊C4×C37—22no—
138C4⋊C4×C37—22no—
139C4⋊C4×C37—22no—
140C4⋊C4×C37—22no—
141C4⋊C4×C37—22no—
142C4⋊C4×C37—22no—
143C4⋊C4×C37—22no—
144C4⋊C4×C37—22no—
145C4⋊C4×C37—22no—
146C4⋊C4×C37—22no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—42no—
149C4⋊C4×C37C2×D412yes—
150C4⋊C4×C37C2×D412yes—
151C4⋊C4×C37C2×D412yes—
152C4⋊C4×C37C2×D412yes—
153C22⋊C4×C37—22no—
154C22⋊C4×C37—22no—
155C22⋊C4×C37—22no—
156C22⋊C4×C37—22no—
157C22⋊C4×C37—22no—
158C22⋊C4×C37—22no—
159C22⋊C4×C37—22no—
160C22⋊C4×C37—22no—
161C22⋊C4×C37—22no—
162C22⋊C4×C37—41no—
163C42×C37—22no—
164C42×C37—22no—
165C42×C37—22no—
166C42×C37—41no—
167C42×C37C2×D411yescharacteristic
168C42×C37C2×D412yes—
169C42×C37C2411yescharacteristic
170C23×C37—22no—
171C23×C37#12011yescharacteristic
172Q8×C37—42no—
173Q8×C37—42no—
174Q8×C37—42no—
175Q8×C37—82no—
176D4×C37—42no—
177D4×C37—44no—
178D4×C37—82no—
179C2×C4×C37—22no—
180C2×C4×C37—22no—
181C2×C4×C37—22no—
182C2×C4×C37—22no—
183C2×C4×C37—22no—
184C2×C4×C37—22no—
185C2×C4×C37—42no—
186C2×C4×C37—42no—
187C2×C4×C37—82no—
188C2×C4×C37—82no—
189C2×C4×C37—82no—
190C2×C4×C37—82no—
191C2×C4×C37#12012yes—
192C2×C4×C37#12011yescharacteristic
193C2×C4×C37C22×D411yescharacteristic
194C2×C4×C37C22×D412yes—
195C8×C37—24no—
196C8×C37—24no—
197C8×C37—42no—
198#19085C3711yesmaximal, characteristic, direct product factor, Sylow
199C22×C37—22no—
200C22×C37—42no—
201C22×C37—42no—
202C22×C37—42no—
203C22×C37#45612yes—
204C22×C37C2×#12011yescharacteristic
205C4×C37—21no—
206C4×C37—21no—
207C4×C37—22no—
208C4×C37—22no—
209C4×C37—42no—
210C4×C37—42no—
211C4×C37—42no—
212C4×C37—42no—
213C4×C37—42no—
214C4×C37—82no—
215#3553C2×C3711yescharacteristic
216#3181C2×C3712yescomplemented
217#3166C2×C3711yescharacteristic, complemented
218#1664C2×C3712yescomplemented
219#1663C2×C3712yescomplemented
220#1661C2×C3712yescomplemented
221#1660C2×C3712yescomplemented
222#1524C2×C3712yescomplemented
223C2×#330C2×C3711yescharacteristic, complemented
224C2×C37—22no—
225C2×C37—82no—
226C2×C37C2×#45611yescharacteristic
227C2×C37#301812yes—
228#564C22×C3711yescharacteristic
229#563C22×C3712yes—
230#562C22×C3711yescharacteristic
231#554—22no—
232#553—22no—
233#552—22no—
234#541—22no—
235#539—22no—
236#539—22no—
237#533C22×C3711yescharacteristic
238#529C22×C3712yes—
239C2×#125C22×C3711yescharacteristic
240#501C22×C3712yes—
241#501C22×C3712yes—
242#501C22×C3712yes—
243#499—22no—
244#497C22×C3712yes—
245#491C22×C3712yes—
246#489C22×C3712yes—
247#467—22no—
248#465—22no—
249#441—22no—
250#440—22no—
251#428—22no—
252C4×M16C22×C3711yescharacteristic
253C2×#97C22×C3712yes—
254#330C22×C3711yescharacteristic
255#330C22×C3712yes—
256#330C22×C3712yes—
257#330C22×C3712yes—
258#330C22×C3711yescharacteristic
259#329C22×C3712yes—
260#329C22×C3712yes—
261C37#1908511yescharacteristic, direct product factor, Sylow
262C2×Q16—22no—
263C2×SD16—22no—
264C2×M16—21no—
265C22×C8—22no—
266C4⋊Q8—22no—
267C4⋊Q8C23×C3712yes—
268#126—22no—
269#126—22no—
270#126—22no—
271#126—22no—
272#126—22no—
273#125—22no—
274#125—22no—
275#125—22no—
276#125—22no—
277#125—22no—
278#125—22no—
279#125—21no—
280#125D4×C3712yes—
281#125C23×C3711yescharacteristic
282#125C23×C3711yescharacteristic
283#125C23×C3712yes—
284#124C23×C3712yes—
285#123—22no—
286#123—22no—
287#123—22no—
288#123—22no—
289#123—22no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8—22no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8D4×C3712yes—
298#121—22no—
299#121—22no—
300#121D4×C3712yes—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×Q8D4×C3712yes—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—22no—
307C4×D4—22no—
308C4×D4D4×C3712yes—
309#117—22no—
310#117—22no—
311#117—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4D4×C3712yes—
315C2×C42C23×C3711yescharacteristic
316#107—22no—
317#107—22no—
318#107—22no—
319#106—22no—
320#106—22no—
321#106—22no—
322#103—22no—
323#103—22no—
324#103—22no—
325#102—22no—
326#97—22no—
327#97C23×C3712yes—
328#97C23×C3712yes—
329#97C23×C3712yes—
330C4×C8—21no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8C2×D4×C3712yes—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4C2×D4×C3712yes—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4C2×D4×C3711yescharacteristic
342C22×C4C2×D4×C3712yes—
343Q16—44no—
344SD16—44no—
345M16—24no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—44no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—42no—
368C4⋊C4C2×D4×C3712yes—
369C4⋊C4C2×D4×C3712yes—
370C4⋊C4C2×D4×C3712yes—
371C4⋊C4C2×D4×C3712yes—
372C22⋊C4—22no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—41no—
382C42—22no—
383C42—22no—
384C42—22no—
385C42—41no—
386C42C2×D4×C3711yescharacteristic
387C42C2×D4×C3712yes—
388C42C24×C3711yescharacteristic
389C23—22no—
390C23#120×C3711yescharacteristic
391Q8—42no—
392Q8—42no—
393Q8—42no—
394Q8—82no—
395D4—42no—
396D4—44no—
397D4—82no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4#120×C3712yes—
411C2×C4#120×C3711yescharacteristic
412C2×C4C22×D4×C3711yescharacteristic
413C2×C4C22×D4×C3712yes—
414C8—24no—
415C8—24no—
416C8—42no—
417C22—22no—
418C22—42no—
419C22—42no—
420C22—42no—
421C22C37×#45612yes—
422C22C2×#120×C3711yescharacteristic
423C4—21no—
424C4—21no—
425C4—22no—
426C4—22no—
427C4—42no—
428C4—42no—
429C4—42no—
430C4—42no—
431C4—42no—
432C4—82no—
433C2—22no—
434C2—82no—
435C2C2×C37×#45611yescharacteristic
436C2C37×#301812yes—
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3553C2
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
2. C37×#3181C2semidirect
3. C37×#3166C2semidirect
4. C37×#1664C2semidirect
5. C37×#1663C2semidirect
6. C37×#1661C2semidirect
7. C37×#1660C2semidirect
8. C37×#1524C2semidirect
9. C2×C37×#330C2semidirect
198. #19085C37direct (N × H)
216. #3181C2×C37semidirect
217. #3166C2×C37semidirect
218. #1664C2×C37semidirect
219. #1663C2×C37semidirect
220. #1661C2×C37semidirect
221. #1660C2×C37semidirect
222. #1524C2×C37semidirect
223. C2×#330C2×C37semidirect
261. C37#19085direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35532
C37×#31812
C37×#31662
C37×#16642
C37×#16632
C37×#16612
C37×#16602
C37×#15242
C2×C37×#3302
#1908537