Finite Group Databasebeta

← C37×#9242 #22630495

Subgroups — C37×#9242 #22630495

Order 9472.

478 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#482C211yesmaximal, characteristic
2C37×#2924C211yesmaximal, characteristic, complemented
3C37×#1826C211yesmaximal, characteristic, complemented
4C37×#1507C211yesmaximal, characteristic
5C37×#1471C211yesmaximal, characteristic
6C37×#1293C211yesmaximal, characteristic, complemented
7C37×#1282C211yesmaximal, characteristic, complemented
8C2×#121×C37C2211yescharacteristic
9C2×#117×C37C2211yescharacteristic
10C37×#482—21no—
11C37×#482—21no—
12C37×#482—21no—
13C37×#482—21no—
14C37×#433—22no—
15C37×#432—21no—
16C37×#431—21no—
17C2×#107×C37C411yescharacteristic, complemented
18C2×#106×C37C411yescharacteristic, complemented
19C37×#424—21no—
20C2×#102×C37C411yescharacteristic, complemented
21C2×#102×C37C411yescharacteristic, complemented
22C37×#407C2211yescharacteristic
23C37×#407C2211yescharacteristic
24C2×C22⋊C8×C37C2211yescharacteristic
25C2×C22⋊C8×C37C2211yescharacteristic
26C37×#405—21no—
27C4×C22⋊C4×C37C2211yescharacteristic
28C37×#339—21no—
29C37×#339—21no—
30C37×#327—22no—
31C37×#323—21no—
32C37×#323—21no—
33C22×D4×C37—21no—
34C22×D4×C37C2×C411yescharacteristic
35C23×C4×C37C2311yescharacteristic
36C2×M16×C37—21no—
37C2×M16×C37—21no—
38C22×C8×C37—21no—
39C22×C8×C37C2×C411yescharacteristic
40C22×C8×C37C2×C411yescharacteristic
41#121×C37—21no—
42#121×C37—21no—
43#121×C37—21no—
44#121×C37—21no—
45#117×C37—21no—
46#117×C37—21no—
47#117×C37D411yescharacteristic
48#117×C37D411yescharacteristic
49#117×C37D411yescharacteristic
50#117×C37D411yescharacteristic
51C2×C4⋊C4×C37C2×C411yescharacteristic
52C2×C4⋊C4×C37C2×C411yescharacteristic
53C2×C4⋊C4×C37C2×C411yescharacteristic
54C2×C22⋊C4×C37—21no—
55C2×C22⋊C4×C37—21no—
56C2×C22⋊C4×C37—21no—
57C2×C42×C37—21no—
58C2×C42×C37—21no—
59#107×C37—21no—
60#107×C37—21no—
61#106×C37—21no—
62#106×C37—21no—
63C4⋊C8×C37—22no—
64C4⋊C8×C37—22no—
65#102×C37—21no—
66#102×C37—21no—
67#102×C37—21no—
68#102×C37—21no—
69C22⋊C8×C37—21no—
70C22⋊C8×C37—21no—
71C22⋊C8×C37—21no—
72C22⋊C8×C37—21no—
73C22⋊C8×C37—21no—
74C22⋊C8×C37—21no—
75C22⋊C8×C37D411yescharacteristic
76C22⋊C8×C37D411yescharacteristic
77C22⋊C8×C37D412yes—
78#97×C37—22no—
79C4×C8×C37—22no—
80#95×C37—21no—
81C24×C37—21no—
82C24×C37#4111yescharacteristic
83C2×D4×C37—21no—
84C2×D4×C37—21no—
85C2×D4×C37—41no—
86C2×D4×C37—41no—
87C2×D4×C37—41no—
88C2×D4×C37—41no—
89C2×D4×C37—82no—
90C22×C4×C37—21no—
91C22×C4×C37—21no—
92C22×C4×C37—21no—
93C22×C4×C37—41no—
94C22×C4×C37—41no—
95C22×C4×C37—41no—
96C22×C4×C37C22×C411yescharacteristic
97C22×C4×C37C2×D411yescharacteristic
98C22×C4×C37C2×D411yescharacteristic
99C22×C4×C37C2×D411yescharacteristic
100C22×C4×C37C2×D411yescharacteristic
101C22×C4×C37#4111yescharacteristic
102M16×C37—41no—
103M16×C37—41no—
104M16×C37—41no—
105M16×C37—41no—
106C2×C8×C37—21no—
107C2×C8×C37—21no—
108C2×C8×C37—21no—
109C2×C8×C37—22no—
110C2×C8×C37—21no—
111C2×C8×C37—41no—
112C2×C8×C37—41no—
113C2×C8×C37—41no—
114C2×C8×C37—41no—
115C2×C8×C37—41no—
116C4⋊C4×C37—21no—
117C4⋊C4×C37—21no—
118C4⋊C4×C37—21no—
119C4⋊C4×C37—21no—
120C4⋊C4×C37C22⋊C411yescharacteristic
121C4⋊C4×C37C22⋊C411yescharacteristic
122C4⋊C4×C37C22⋊C411yescharacteristic
123C4⋊C4×C37C22⋊C411yescharacteristic
124C22⋊C4×C37—21no—
125C22⋊C4×C37—21no—
126C22⋊C4×C37—21no—
127C22⋊C4×C37—21no—
128C22⋊C4×C37—22no—
129C22⋊C4×C37—41no—
130C22⋊C4×C37—41no—
131C22⋊C4×C37—41no—
132C42×C37—21no—
133C42×C37—21no—
134C42×C37—21no—
135C42×C37—21no—
136C42×C37—41no—
137C42×C37—41no—
138C23×C37—21no—
139C23×C37—21no—
140C23×C37—41no—
141C23×C37—41no—
142C23×C37—41no—
143C23×C37—41no—
144C23×C37—41no—
145C23×C37—81no—
146C23×C37—81no—
147C23×C37C4×D411yescharacteristic
148C23×C37#12111yescharacteristic
149C23×C37#12311yescharacteristic
150D4×C37—41no—
151D4×C37—41no—
152D4×C37—81no—
153D4×C37—82no—
154D4×C37—82no—
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—21no—
164C2×C4×C37—21no—
165C2×C4×C37—41no—
166C2×C4×C37—41no—
167C2×C4×C37—41no—
168C2×C4×C37—41no—
169C2×C4×C37—41no—
170C2×C4×C37—42no—
171C2×C4×C37—41no—
172C2×C4×C37—81no—
173C2×C4×C37—81no—
174C2×C4×C37—81no—
175C2×C4×C37—81no—
176C2×C4×C37C2×C22⋊C411yescharacteristic
177C2×C4×C37C4×D411yescharacteristic
178C2×C4×C37#12011yescharacteristic
179C2×C4×C37#12111yescharacteristic
180C8×C37—41no—
181C8×C37—41no—
182C8×C37—42no—
183C8×C37—41no—
184C8×C37—41no—
185C8×C37—81no—
186#9242C3711yesmaximal, characteristic, direct product factor, Sylow
187C22×C37—21no—
188C22×C37—21no—
189C22×C37—21no—
190C22×C37—21no—
191C22×C37—21no—
192C22×C37—21no—
193C22×C37—21no—
194C22×C37—21no—
195C22×C37—81no—
196C22×C37—81no—
197C22×C37—81no—
198C22×C37—81no—
199C22×C37—81no—
200C22×C37—161no—
201C22×C37—161no—
202C22×C37#38611yescharacteristic
203C22×C37#44311yescharacteristic
204C22×C37#44411yescharacteristic
205C4×C37—21no—
206C4×C37—21no—
207C4×C37—21no—
208C4×C37—41no—
209C4×C37—41no—
210C4×C37—41no—
211C4×C37—41no—
212C4×C37—82no—
213C4×C37—81no—
214C4×C37#41011yescharacteristic
215C4×C37#41011yescharacteristic
216C2×#482C2×C3711yescharacteristic
217#2924C2×C3711yescharacteristic, complemented
218#1826C2×C3711yescharacteristic, complemented
219#1507C2×C3711yescharacteristic
220#1471C2×C3711yescharacteristic
221#1293C2×C3711yescharacteristic, complemented
222#1282C2×C3711yescharacteristic, complemented
223C2×C37—21no—
224C2×C37—21no—
225C2×C37—41no—
226C2×C37—41no—
227C2×C37—161no—
228C2×C37#187611yescharacteristic
229C2×C37#189911yescharacteristic
230C2×C37#190311yescharacteristic
231C2×#121C22×C3711yescharacteristic
232C2×#117C22×C3711yescharacteristic
233#482—21no—
234#482—21no—
235#482—21no—
236#482—21no—
237#433—22no—
238#432—21no—
239#431—21no—
240C2×#107C4×C3711yescharacteristic, complemented
241C2×#106C4×C3711yescharacteristic, complemented
242#424—21no—
243C2×#102C4×C3711yescharacteristic, complemented
244C2×#102C4×C3711yescharacteristic, complemented
245#407C22×C3711yescharacteristic
246#407C22×C3711yescharacteristic
247C2×C22⋊C8C22×C3711yescharacteristic
248C2×C22⋊C8C22×C3711yescharacteristic
249#405—21no—
250C4×C22⋊C4C22×C3711yescharacteristic
251#339—21no—
252#339—21no—
253#327—22no—
254#323—21no—
255#323—21no—
256C37#924211yescharacteristic, direct product factor, Sylow
257C22×D4—21no—
258C22×D4C2×C4×C3711yescharacteristic
259C23×C4C23×C3711yescharacteristic
260C2×M16—21no—
261C2×M16—21no—
262C22×C8—21no—
263C22×C8C2×C4×C3711yescharacteristic
264C22×C8C2×C4×C3711yescharacteristic
265#121—21no—
266#121—21no—
267#121—21no—
268#121—21no—
269#117—21no—
270#117—21no—
271#117D4×C3711yescharacteristic
272#117D4×C3711yescharacteristic
273#117D4×C3711yescharacteristic
274#117D4×C3711yescharacteristic
275C2×C4⋊C4C2×C4×C3711yescharacteristic
276C2×C4⋊C4C2×C4×C3711yescharacteristic
277C2×C4⋊C4C2×C4×C3711yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C42—21no—
282C2×C42—21no—
283#107—21no—
284#107—21no—
285#106—21no—
286#106—21no—
287C4⋊C8—22no—
288C4⋊C8—22no—
289#102—21no—
290#102—21no—
291#102—21no—
292#102—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8D4×C3711yescharacteristic
300C22⋊C8D4×C3711yescharacteristic
301C22⋊C8D4×C3712yes—
302#97—22no—
303C4×C8—22no—
304#95—21no—
305C24—21no—
306C24#41×C3711yescharacteristic
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—82no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C22×C4×C3711yescharacteristic
321C22×C4C2×D4×C3711yescharacteristic
322C22×C4C2×D4×C3711yescharacteristic
323C22×C4C2×D4×C3711yescharacteristic
324C22×C4C2×D4×C3711yescharacteristic
325C22×C4#41×C3711yescharacteristic
326M16—41no—
327M16—41no—
328M16—41no—
329M16—41no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4C22⋊C4×C3711yescharacteristic
345C4⋊C4C22⋊C4×C3711yescharacteristic
346C4⋊C4C22⋊C4×C3711yescharacteristic
347C4⋊C4C22⋊C4×C3711yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—41no—
361C42—41no—
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—81no—
370C23—81no—
371C23C4×D4×C3711yescharacteristic
372C23#121×C3711yescharacteristic
373C23#123×C3711yescharacteristic
374D4—41no—
375D4—41no—
376D4—81no—
377D4—82no—
378D4—82no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4C2×C22⋊C4×C3711yescharacteristic
401C2×C4C4×D4×C3711yescharacteristic
402C2×C4#120×C3711yescharacteristic
403C2×C4#121×C3711yescharacteristic
404C8—41no—
405C8—41no—
406C8—42no—
407C8—41no—
408C8—41no—
409C8—81no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—161no—
424C22—161no—
425C22C37×#38611yescharacteristic
426C22C37×#44311yescharacteristic
427C22C37×#44411yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—82no—
436C4—81no—
437C4C37×#41011yescharacteristic
438C4C37×#41011yescharacteristic
439C2—21no—
440C2—21no—
441C2—41no—
442C2—41no—
443C2—161no—
444C2C37×#187611yescharacteristic
445C2C37×#189911yescharacteristic
446C2C37×#190311yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC22×C4C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2924C2semidirect
3. C37×#1826C2semidirect
6. C37×#1293C2semidirect
7. C37×#1282C2semidirect
17. C2×#107×C37C4semidirect
18. C2×#106×C37C4semidirect
20. C2×#102×C37C4semidirect
21. C2×#102×C37C4semidirect
186. #9242C37direct (N × H)
217. #2924C2×C37semidirect
218. #1826C2×C37semidirect
221. #1293C2×C37semidirect
222. #1282C2×C37semidirect
240. C2×#107C4×C37semidirect
241. C2×#106C4×C37semidirect
243. C2×#102C4×C37semidirect
244. C2×#102C4×C37semidirect
256. C37#9242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4822
C37×#29242
C37×#18262
C37×#15072
C37×#14712
C37×#12932
C37×#12822
#924237