Finite Group Databasebeta

← C37×#19530 #22640783

Subgroups — C37×#19530 #22640783

Order 9472.

582 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3226C211yesmaximal, characteristic
2C37×#3216C211yesmaximal, characteristic
3C37×#3209C211yesmaximal, characteristic, complemented
4C37×#2985C211yesmaximal, characteristic, complemented
5C37×#1702C212yesmaximal, complemented
6C37×#1694C212yesmaximal, complemented
7C37×#1682C212yesmaximal, complemented
8C37×#1674C212yesmaximal, complemented
9C37×#1572C211yesmaximal, characteristic, complemented
10C37×#1556C211yesmaximal, characteristic, complemented
11C37×#1553C211yesmaximal, characteristic
12C37×#533C2211yescharacteristic
13C37×#532C2211yescharacteristic
14C2×C4⋊Q8×C37C2211yescharacteristic
15C37×#500C2211yescharacteristic
16C37×#500C2211yescharacteristic
17C37×#497—21no—
18C37×#494—21no—
19C37×#489—21no—
20C37×#487—21no—
21C37×#486C2211yescharacteristic
22C37×#486C2211yescharacteristic
23C37×#480—22no—
24C37×#474—22no—
25C37×#462C2212yes—
26C37×#462C2212yes—
27C37×#462C2212yes—
28C37×#460C2212yes—
29C37×#452—22no—
30C37×#451—22no—
31C37×#446—22no—
32C37×#446C2212yes—
33C8×Q8×C37C2212yes—
34C37×#433—22no—
35C37×#432C2211yescharacteristic
36C37×#432C2211yescharacteristic
37C37×#431C2211yescharacteristic
38C37×#431C2211yescharacteristic
39C37×#335C2212yes—
40C37×#334C2212yes—
41C37×#332C2212yes—
42C37×#332C2212yes—
43C37×#332C2212yes—
44C37×#331C2212yes—
45C2×#41×C37—21no—
46C22×Q8×C37—21no—
47C2×Q16×C37—22no—
48C2×Q16×C37—22no—
49C2×Q16×C37—22no—
50C2×SD16×C37—22no—
51C4⋊Q8×C37—21no—
52C4⋊Q8×C37—21no—
53C4⋊Q8×C37—21no—
54C4⋊Q8×C37D411yescharacteristic
55C4⋊Q8×C37D411yescharacteristic
56C4⋊Q8×C37C2311yescharacteristic
57C4⋊Q8×C37C2311yescharacteristic
58C4⋊Q8×C37C2311yescharacteristic
59#127×C37C2311yescharacteristic
60#125×C37—21no—
61#124×C37—21no—
62C22⋊Q8×C37—21no—
63C22⋊Q8×C37D412yes—
64#121×C37—21no—
65#121×C37—21no—
66C4×Q8×C37—21no—
67C4×Q8×C37C2312yes—
68C4×D4×C37—21no—
69C4×D4×C37—21no—
70#117×C37—21no—
71C2×C4⋊C4×C37—21no—
72C2×C4⋊C4×C37—21no—
73C2×C42×C37C2311yescharacteristic
74#107×C37—22no—
75#107×C37—22no—
76C4⋊C8×C37—22no—
77C4⋊C8×C37—22no—
78C4⋊C8×C37D412yes—
79C4⋊C8×C37C2312yes—
80C4⋊C8×C37C2312yes—
81C4⋊C8×C37C2312yes—
82#103×C37—22no—
83#103×C37—22no—
84#103×C37—22no—
85#102×C37—22no—
86#102×C37—22no—
87#102×C37—22no—
88C22⋊C8×C37—21no—
89C22⋊C8×C37—21no—
90C22⋊C8×C37—21no—
91C22⋊C8×C37D412yes—
92#97×C37—22no—
93#97×C37—21no—
94#97×C37—21no—
95C4×C8×C37—22no—
96C4×C8×C37—21no—
97C4×C8×C37C2311yescharacteristic
98C4×C8×C37C2311yescharacteristic
99#41×C37—82no—
100C2×Q8×C37—21no—
101C2×Q8×C37—21no—
102C2×Q8×C37—21no—
103C2×Q8×C37—21no—
104C2×Q8×C37—41no—
105C2×Q8×C37—82no—
106C2×Q8×C37C2×D412yes—
107C2×D4×C37—21no—
108C2×D4×C37—21no—
109C2×D4×C37—21no—
110C2×D4×C37—41no—
111C22×C4×C37—41no—
112C22×C4×C37—41no—
113C22×C4×C37C2×D411yescharacteristic
114C22×C4×C37C2×D411yescharacteristic
115C22×C4×C37#4111yescharacteristic
116Q16×C37—82no—
117Q16×C37—82no—
118Q16×C37—82no—
119SD16×C37—82no—
120C2×C8×C37—22no—
121C2×C8×C37—22no—
122C2×C8×C37—22no—
123C2×C8×C37C2×D412yes—
124C2×C8×C37C2×D412yes—
125C4⋊C4×C37—21no—
126C4⋊C4×C37—21no—
127C4⋊C4×C37—21no—
128C4⋊C4×C37—22no—
129C4⋊C4×C37—22no—
130C4⋊C4×C37—21no—
131C4⋊C4×C37—21no—
132C4⋊C4×C37—21no—
133C4⋊C4×C37—21no—
134C4⋊C4×C37—21no—
135C4⋊C4×C37—21no—
136C4⋊C4×C37—41no—
137C4⋊C4×C37—41no—
138C4⋊C4×C37C2×D412yes—
139C22⋊C4×C37—22no—
140C22⋊C4×C37—41no—
141C22⋊C4×C37—41no—
142C42×C37—22no—
143C42×C37C2×D411yescharacteristic
144C42×C37C2×D411yescharacteristic
145C42×C37#4111yescharacteristic
146C42×C37C2411yescharacteristic
147C23×C37—41no—
148C23×C37#12111yescharacteristic
149Q8×C37—22no—
150Q8×C37—22no—
151Q8×C37—42no—
152Q8×C37—42no—
153Q8×C37—42no—
154Q8×C37—81no—
155Q8×C37—82no—
156D4×C37—42no—
157D4×C37—42no—
158D4×C37—81no—
159D4×C37—82no—
160C2×C4×C37—22no—
161C2×C4×C37—22no—
162C2×C4×C37—22no—
163C2×C4×C37—22no—
164C2×C4×C37—41no—
165C2×C4×C37—41no—
166C2×C4×C37—41no—
167C2×C4×C37—41no—
168C2×C4×C37—82no—
169C2×C4×C37—82no—
170C2×C4×C37#12111yescharacteristic
171C2×C4×C37#12111yescharacteristic
172C2×C4×C37#12111yescharacteristic
173C2×C4×C37C22×D411yescharacteristic
174C2×C4×C37C22×D411yescharacteristic
175C2×C4×C37C2×#4111yescharacteristic
176C8×C37—22no—
177C8×C37—22no—
178C8×C37—42no—
179C8×C37—42no—
180C8×C37—42no—
181#19530C3711yesmaximal, characteristic, direct product factor, Sylow
182C22×C37—21no—
183C22×C37—21no—
184C22×C37—21no—
185C22×C37—81no—
186C22×C37—81no—
187C22×C37—81no—
188C22×C37C2×#12111yescharacteristic
189C4×C37—21no—
190C4×C37—21no—
191C4×C37—21no—
192C4×C37—21no—
193C4×C37—42no—
194C4×C37—42no—
195C4×C37—81no—
196C4×C37—81no—
197C4×C37—81no—
198C4×C37#57612yes—
199C4×C37#57812yes—
200#3226C2×C3711yescharacteristic
201#3216C2×C3711yescharacteristic
202#3209C2×C3711yescharacteristic, complemented
203#2985C2×C3711yescharacteristic, complemented
204#1702C2×C3712yescomplemented
205#1694C2×C3712yescomplemented
206#1682C2×C3712yescomplemented
207#1674C2×C3712yescomplemented
208#1572C2×C3711yescharacteristic, complemented
209#1556C2×C3711yescharacteristic, complemented
210#1553C2×C3711yescharacteristic
211C2×C37—41no—
212C2×C37—161no—
213C2×C37#304411yescharacteristic
214C2×C37#305811yescharacteristic
215C2×C37#306911yescharacteristic
216#533C22×C3711yescharacteristic
217#532C22×C3711yescharacteristic
218C2×C4⋊Q8C22×C3711yescharacteristic
219#500C22×C3711yescharacteristic
220#500C22×C3711yescharacteristic
221#497—21no—
222#494—21no—
223#489—21no—
224#487—21no—
225#486C22×C3711yescharacteristic
226#486C22×C3711yescharacteristic
227#480—22no—
228#474—22no—
229#462C22×C3712yes—
230#462C22×C3712yes—
231#462C22×C3712yes—
232#460C22×C3712yes—
233#452—22no—
234#451—22no—
235#446—22no—
236#446C22×C3712yes—
237C8×Q8C22×C3712yes—
238#433—22no—
239#432C22×C3711yescharacteristic
240#432C22×C3711yescharacteristic
241#431C22×C3711yescharacteristic
242#431C22×C3711yescharacteristic
243#335C22×C3712yes—
244#334C22×C3712yes—
245#332C22×C3712yes—
246#332C22×C3712yes—
247#332C22×C3712yes—
248#331C22×C3712yes—
249C37#1953011yescharacteristic, direct product factor, Sylow
250C2×#41—21no—
251C22×Q8—21no—
252C2×Q16—22no—
253C2×Q16—22no—
254C2×Q16—22no—
255C2×SD16—22no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8D4×C3711yescharacteristic
260C4⋊Q8D4×C3711yescharacteristic
261C4⋊Q8C23×C3711yescharacteristic
262C4⋊Q8C23×C3711yescharacteristic
263C4⋊Q8C23×C3711yescharacteristic
264#127C23×C3711yescharacteristic
265#125—21no—
266#124—21no—
267C22⋊Q8—21no—
268C22⋊Q8D4×C3712yes—
269#121—21no—
270#121—21no—
271C4×Q8—21no—
272C4×Q8C23×C3712yes—
273C4×D4—21no—
274C4×D4—21no—
275#117—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C42C23×C3711yescharacteristic
279#107—22no—
280#107—22no—
281C4⋊C8—22no—
282C4⋊C8—22no—
283C4⋊C8D4×C3712yes—
284C4⋊C8C23×C3712yes—
285C4⋊C8C23×C3712yes—
286C4⋊C8C23×C3712yes—
287#103—22no—
288#103—22no—
289#103—22no—
290#102—22no—
291#102—22no—
292#102—22no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8D4×C3712yes—
297#97—22no—
298#97—21no—
299#97—21no—
300C4×C8—22no—
301C4×C8—21no—
302C4×C8C23×C3711yescharacteristic
303C4×C8C23×C3711yescharacteristic
304#41—82no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—41no—
310C2×Q8—82no—
311C2×Q8C2×D4×C3712yes—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C2×D4×C3711yescharacteristic
319C22×C4C2×D4×C3711yescharacteristic
320C22×C4#41×C3711yescharacteristic
321Q16—82no—
322Q16—82no—
323Q16—82no—
324SD16—82no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8C2×D4×C3712yes—
329C2×C8C2×D4×C3712yes—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4C2×D4×C3712yes—
344C22⋊C4—22no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C42—22no—
348C42C2×D4×C3711yescharacteristic
349C42C2×D4×C3711yescharacteristic
350C42#41×C3711yescharacteristic
351C42C24×C3711yescharacteristic
352C23—41no—
353C23#121×C3711yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—42no—
357Q8—42no—
358Q8—42no—
359Q8—81no—
360Q8—82no—
361D4—42no—
362D4—42no—
363D4—81no—
364D4—82no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4#121×C3711yescharacteristic
376C2×C4#121×C3711yescharacteristic
377C2×C4#121×C3711yescharacteristic
378C2×C4C22×D4×C3711yescharacteristic
379C2×C4C22×D4×C3711yescharacteristic
380C2×C4C2×#41×C3711yescharacteristic
381C8—22no—
382C8—22no—
383C8—42no—
384C8—42no—
385C8—42no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C2×#121×C3711yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4—42no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4C37×#57612yes—
403C4C37×#57812yes—
404C2—41no—
405C2—161no—
406C2C37×#304411yescharacteristic
407C2C37×#305811yescharacteristic
408C2C37×#306911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#532C22
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
3. C37×#3209C2semidirect
4. C37×#2985C2semidirect
5. C37×#1702C2semidirect
6. C37×#1694C2semidirect
7. C37×#1682C2semidirect
8. C37×#1674C2semidirect
9. C37×#1572C2semidirect
10. C37×#1556C2semidirect
181. #19530C37direct (N × H)
202. #3209C2×C37semidirect
203. #2985C2×C37semidirect
204. #1702C2×C37semidirect
205. #1694C2×C37semidirect
206. #1682C2×C37semidirect
207. #1674C2×C37semidirect
208. #1572C2×C37semidirect
209. #1556C2×C37semidirect
249. C37#19530direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32262
C37×#32162
C37×#32092
C37×#29852
C37×#17022
C37×#16942
C37×#16822
C37×#16742
C37×#15722
C37×#15562
C37×#15532
#1953037