Finite Group Databasebeta

← C37×#8970 #22630223

Subgroups — C37×#8970 #22630223

Order 9472.

514 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3106C211yesmaximal, characteristic
2C37×#2991C211yesmaximal, characteristic, complemented
3C37×#1962C211yesmaximal, characteristic, complemented
4C4×#104×C37C211yesmaximal, characteristic, complemented
5C37×#1484C211yesmaximal, characteristic, complemented
6C37×#1299C211yesmaximal, characteristic, complemented
7C37×#1276C211yesmaximal, characteristic, complemented
8C37×#532C2211yescharacteristic
9C4×#41×C37C2211yescharacteristic
10C37×#482—21no—
11C37×#477C411yescharacteristic, complemented
12C37×#476C411yescharacteristic, complemented
13C37×#460C411yescharacteristic, complemented
14C37×#459C411yescharacteristic, complemented
15C37×#449—21no—
16C8×Q8×C37—21no—
17C4×SD16×C37—21no—
18C4×D8×C37—21no—
19C37×#436—22no—
20C37×#436—21no—
21C37×#431—21no—
22C37×#431C2211yescharacteristic
23C37×#431C2211yescharacteristic
24C37×#423—21no—
25C37×#423C2211yescharacteristic
26C2×#104×C37—21no—
27C2×#104×C37—22no—
28C4×M16×C37C2211yescharacteristic
29C43×C37C2211yescharacteristic
30C37×#339—21no—
31C37×D4⋊C8—21no—
32C37×D4⋊C8—21no—
33C2×#41×C37—21no—
34C2×#41×C37D411yescharacteristic
35C2×SD16×C37—21no—
36C2×D8×C37—21no—
37C2×M16×C37—22no—
38C2×M16×C37—21no—
39C2×M16×C37D412yes—
40C4⋊Q8×C37C2×C411yescharacteristic
41#127×C37C2×C411yescharacteristic
42#124×C37—21no—
43#121×C37—21no—
44#121×C37—21no—
45C4×Q8×C37C2×C411yescharacteristic
46C4×Q8×C37D411yescharacteristic
47C4×D4×C37—21no—
48C4×D4×C37—21no—
49C4×D4×C37—21no—
50C4×D4×C37—21no—
51C4×D4×C37C2×C411yescharacteristic
52C4×D4×C37D411yescharacteristic
53#117×C37—21no—
54#117×C37D411yescharacteristic
55C2×C42×C37—21no—
56C2×C42×C37—21no—
57C2×C42×C37—21no—
58C2×C42×C37—21no—
59C2×C42×C37C2311yescharacteristic
60#107×C37—21no—
61#106×C37—21no—
62C4⋊C8×C37—22no—
63C4⋊C8×C37—21no—
64C4⋊C8×C37—21no—
65C4⋊C8×C37C2×C411yescharacteristic
66C4⋊C8×C37C2×C411yescharacteristic
67C4⋊C8×C37D411yescharacteristic
68C4⋊C8×C37D411yescharacteristic
69#104×C37—24no—
70#104×C37—44no—
71#103×C37—21no—
72#102×C37—21no—
73#102×C37—21no—
74#102×C37—21no—
75C22⋊C8×C37—22no—
76C22⋊C8×C37—21no—
77C22⋊C8×C37—21no—
78#97×C37—21no—
79C4×C8×C37—22no—
80C4×C8×C37—21no—
81C4×C8×C37—21no—
82C4×C8×C37—21no—
83#41×C37—22no—
84#41×C37—41no—
85#41×C37—42no—
86#41×C37—42no—
87C2×Q8×C37—21no—
88C2×Q8×C37C22⋊C411yescharacteristic
89C2×D4×C37—21no—
90C2×D4×C37—21no—
91C2×D4×C37—21no—
92C2×D4×C37—21no—
93C2×D4×C37—41no—
94C2×D4×C37C22⋊C411yescharacteristic
95C22×C4×C37—21no—
96C22×C4×C37—21no—
97C22×C4×C37—21no—
98C22×C4×C37—41no—
99C22×C4×C37—41no—
100C22×C4×C37C2×D411yescharacteristic
101C22×C4×C37C2×D411yescharacteristic
102C22×C4×C37#4111yescharacteristic
103SD16×C37—42no—
104D8×C37—42no—
105M16×C37—22no—
106M16×C37—41no—
107M16×C37—42no—
108M16×C37—82no—
109C2×C8×C37—21no—
110C2×C8×C37—21no—
111C2×C8×C37—21no—
112C2×C8×C37—22no—
113C2×C8×C37—21no—
114C2×C8×C37—41no—
115C4⋊C4×C37—21no—
116C4⋊C4×C37—21no—
117C4⋊C4×C37—21no—
118C4⋊C4×C37—21no—
119C4⋊C4×C37C22⋊C411yescharacteristic
120C4⋊C4×C37C22⋊C411yescharacteristic
121C22⋊C4×C37—21no—
122C22⋊C4×C37—21no—
123C22⋊C4×C37—21no—
124C22⋊C4×C37—41no—
125C22⋊C4×C37—41no—
126C42×C37—21no—
127C42×C37—21no—
128C42×C37—21no—
129C42×C37—22no—
130C42×C37—22no—
131C42×C37—22no—
132C42×C37—41no—
133C42×C37—41no—
134C42×C37—41no—
135C42×C37C22×C411yescharacteristic
136C42×C37C2×D411yescharacteristic
137C42×C37C2×D411yescharacteristic
138C42×C37#4111yescharacteristic
139C23×C37—21no—
140C23×C37—41no—
141C23×C37#12111yescharacteristic
142Q8×C37—21no—
143Q8×C37—42no—
144Q8×C37#10412yescomplemented
145D4×C37—21no—
146D4×C37—21no—
147D4×C37—42no—
148D4×C37—42no—
149D4×C37—41no—
150D4×C37—41no—
151D4×C37—41no—
152D4×C37—41no—
153D4×C37—82no—
154C2×C4×C37—21no—
155C2×C4×C37—21no—
156C2×C4×C37—21no—
157C2×C4×C37—21no—
158C2×C4×C37—21no—
159C2×C4×C37—21no—
160C2×C4×C37—21no—
161C2×C4×C37—21no—
162C2×C4×C37—21no—
163C2×C4×C37—42no—
164C2×C4×C37—42no—
165C2×C4×C37—42no—
166C2×C4×C37—42no—
167C2×C4×C37—41no—
168C2×C4×C37—41no—
169C2×C4×C37—41no—
170C2×C4×C37—41no—
171C2×C4×C37—41no—
172C2×C4×C37—81no—
173C2×C4×C37—81no—
174C2×C4×C37C2×C22⋊C411yescharacteristic
175C2×C4×C37C4×D411yescharacteristic
176C2×C4×C37C4×D411yescharacteristic
177C2×C4×C37#12011yescharacteristic
178C2×C4×C37#12111yescharacteristic
179C2×C4×C37#12311yescharacteristic
180C8×C37—42no—
181C8×C37—41no—
182C8×C37—41no—
183C8×C37—42no—
184C8×C37—41no—
185C8×C37—41no—
186#8970C3711yesmaximal, characteristic, direct product factor, Sylow
187C22×C37—21no—
188C22×C37—21no—
189C22×C37—21no—
190C22×C37—41no—
191C22×C37—41no—
192C22×C37—41no—
193C22×C37—81no—
194C22×C37—81no—
195C22×C37—81no—
196C22×C37#38611yescharacteristic
197C4×C37—21no—
198C4×C37—22no—
199C4×C37—21no—
200C4×C37—21no—
201C4×C37—44no—
202C4×C37—41no—
203C4×C37—41no—
204C4×C37—81no—
205C4×C37C2×#10411yescharacteristic
206C4×C37#42111yescharacteristic
207C4×C37#44311yescharacteristic
208C4×C37#44411yescharacteristic
209C4×C37#45311yescharacteristic
210C4×C37#45411yescharacteristic
211#3106C2×C3711yescharacteristic
212#2991C2×C3711yescharacteristic, complemented
213#1962C2×C3711yescharacteristic, complemented
214C4×#104C2×C3711yescharacteristic, complemented
215#1484C2×C3711yescharacteristic, complemented
216#1299C2×C3711yescharacteristic, complemented
217#1276C2×C3711yescharacteristic, complemented
218C2×C37—41no—
219C2×C37—81no—
220C2×C37—161no—
221C2×C37#187111yescharacteristic
222C2×C37#187611yescharacteristic
223C2×C37#188311yescharacteristic
224#532C22×C3711yescharacteristic
225C4×#41C22×C3711yescharacteristic
226#482—21no—
227#477C4×C3711yescharacteristic, complemented
228#476C4×C3711yescharacteristic, complemented
229#460C4×C3711yescharacteristic, complemented
230#459C4×C3711yescharacteristic, complemented
231#449—21no—
232C8×Q8—21no—
233C4×SD16—21no—
234C4×D8—21no—
235#436—22no—
236#436—21no—
237#431—21no—
238#431C22×C3711yescharacteristic
239#431C22×C3711yescharacteristic
240#423—21no—
241#423C22×C3711yescharacteristic
242C2×#104—21no—
243C2×#104—22no—
244C4×M16C22×C3711yescharacteristic
245C43C22×C3711yescharacteristic
246#339—21no—
247D4⋊C8—21no—
248D4⋊C8—21no—
249C37#897011yescharacteristic, direct product factor, Sylow
250C2×#41—21no—
251C2×#41D4×C3711yescharacteristic
252C2×SD16—21no—
253C2×D8—21no—
254C2×M16—22no—
255C2×M16—21no—
256C2×M16D4×C3712yes—
257C4⋊Q8C2×C4×C3711yescharacteristic
258#127C2×C4×C3711yescharacteristic
259#124—21no—
260#121—21no—
261#121—21no—
262C4×Q8C2×C4×C3711yescharacteristic
263C4×Q8D4×C3711yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4C2×C4×C3711yescharacteristic
269C4×D4D4×C3711yescharacteristic
270#117—21no—
271#117D4×C3711yescharacteristic
272C2×C42—21no—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42C23×C3711yescharacteristic
277#107—21no—
278#106—21no—
279C4⋊C8—22no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8C2×C4×C3711yescharacteristic
283C4⋊C8C2×C4×C3711yescharacteristic
284C4⋊C8D4×C3711yescharacteristic
285C4⋊C8D4×C3711yescharacteristic
286#104—24no—
287#104—44no—
288#103—21no—
289#102—21no—
290#102—21no—
291#102—21no—
292C22⋊C8—22no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295#97—21no—
296C4×C8—22no—
297C4×C8—21no—
298C4×C8—21no—
299C4×C8—21no—
300#41—22no—
301#41—41no—
302#41—42no—
303#41—42no—
304C2×Q8—21no—
305C2×Q8C22⋊C4×C3711yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C2×D4C22⋊C4×C3711yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4C2×D4×C3711yescharacteristic
318C22×C4C2×D4×C3711yescharacteristic
319C22×C4#41×C3711yescharacteristic
320SD16—42no—
321D8—42no—
322M16—22no—
323M16—41no—
324M16—42no—
325M16—82no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—22no—
330C2×C8—21no—
331C2×C8—41no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C22⋊C4×C3711yescharacteristic
337C4⋊C4C22⋊C4×C3711yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—22no—
347C42—22no—
348C42—22no—
349C42—41no—
350C42—41no—
351C42—41no—
352C42C22×C4×C3711yescharacteristic
353C42C2×D4×C3711yescharacteristic
354C42C2×D4×C3711yescharacteristic
355C42#41×C3711yescharacteristic
356C23—21no—
357C23—41no—
358C23#121×C3711yescharacteristic
359Q8—21no—
360Q8—42no—
361Q8#104×C3712yescomplemented
362D4—21no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4C2×C22⋊C4×C3711yescharacteristic
392C2×C4C4×D4×C3711yescharacteristic
393C2×C4C4×D4×C3711yescharacteristic
394C2×C4#120×C3711yescharacteristic
395C2×C4#121×C3711yescharacteristic
396C2×C4#123×C3711yescharacteristic
397C8—42no—
398C8—41no—
399C8—41no—
400C8—42no—
401C8—41no—
402C8—41no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22C37×#38611yescharacteristic
413C4—21no—
414C4—22no—
415C4—21no—
416C4—21no—
417C4—44no—
418C4—41no—
419C4—41no—
420C4—81no—
421C4C2×#104×C3711yescharacteristic
422C4C37×#42111yescharacteristic
423C4C37×#44311yescharacteristic
424C4C37×#44411yescharacteristic
425C4C37×#45311yescharacteristic
426C4C37×#45411yescharacteristic
427C2—41no—
428C2—81no—
429C2—161no—
430C2C37×#187111yescharacteristic
431C2C37×#187611yescharacteristic
432C2C37×#188311yescharacteristic
subgroupG/H
centerC2×C4×C37#120
commutatorC42C22×C4×C37
Frattini, cosocleC2×C42C23×C37
socleC22×C37#386
prime radicalC37×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2991C2semidirect
3. C37×#1962C2semidirect
4. C4×#104×C37C2semidirect
5. C37×#1484C2semidirect
6. C37×#1299C2semidirect
7. C37×#1276C2semidirect
11. C37×#477C4semidirect
12. C37×#476C4semidirect
13. C37×#460C4semidirect
14. C37×#459C4semidirect
144. Q8×C37#104semidirect
186. #8970C37direct (N × H)
212. #2991C2×C37semidirect
213. #1962C2×C37semidirect
214. C4×#104C2×C37semidirect
215. #1484C2×C37semidirect
216. #1299C2×C37semidirect
217. #1276C2×C37semidirect
227. #477C4×C37semidirect
228. #476C4×C37semidirect
229. #460C4×C37semidirect
230. #459C4×C37semidirect
249. C37#8970direct (N × H)
361. Q8#104×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#31062
C37×#29912
C37×#19622
C4×#104×C372
C37×#14842
C37×#12992
C37×#12762
#897037