Finite Group Databasebeta

← C37×#12149 #22633402

Subgroups — C37×#12149 #22633402

Order 9472.

498 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2693C211yesmaximal, characteristic, complemented
2C37×#2044C211yesmaximal, characteristic, complemented
3C37×#1607C211yesmaximal, characteristic, complemented
4C37×#1595C211yesmaximal, characteristic
5C37×#1344C211yesmaximal, characteristic, complemented
6C37×#1343C211yesmaximal, characteristic, complemented
7C37×#1326C211yesmaximal, characteristic, complemented
8C37×#534C2211yescharacteristic
9C2×#123×C37—21no—
10C37×#480—21no—
11C37×#447—21no—
12C2×#99×C37—21no—
13C37×#400—21no—
14C37×#397C2211yescharacteristic
15C37×#396—21no—
16C37×#392C2211yescharacteristic
17C37×#386—21no—
18C37×#386—21no—
19C37×#386—21no—
20C37×#385C2211yescharacteristic
21C37×#380—21no—
22C37×#342C2211yescharacteristic
23C37×#327—21no—
24C37×#327—21no—
25C37×#323C2211yescharacteristic
26C37×#323C2211yescharacteristic
27C22×D4×C37—21no—
28C22×D4×C37—21no—
29C22×D4×C37D411yescharacteristic
30C23×C4×C37—21no—
31C23×C4×C37D411yescharacteristic
32C2×D8×C37—41no—
33#123×C37—42no—
34#123×C37—41no—
35#123×C37—42no—
36#121×C37—21no—
37#121×C37—21no—
38#120×C37—41no—
39C2×C4⋊C4×C37—21no—
40C2×C4⋊C4×C37—21no—
41C2×C4⋊C4×C37—21no—
42C2×C4⋊C4×C37D411yescharacteristic
43C2×C22⋊C4×C37—21no—
44C2×C22⋊C4×C37—21no—
45C2×C22⋊C4×C37—21no—
46C2×C22⋊C4×C37—21no—
47C2×C22⋊C4×C37—21no—
48C2×C22⋊C4×C37—21no—
49C2×C22⋊C4×C37—41no—
50C2×C22⋊C4×C37D411yescharacteristic
51C2×C22⋊C4×C37C2311yescharacteristic
52#107×C37—41no—
53#102×C37—41no—
54#102×C37—41no—
55#99×C37—42no—
56C22⋊C8×C37—21no—
57C22⋊C8×C37—21no—
58#95×C37—21no—
59#95×C37—21no—
60#95×C37—21no—
61#95×C37—21no—
62#95×C37—41no—
63#95×C37D411yescharacteristic
64#95×C37D411yescharacteristic
65C24×C37—21no—
66C24×C37—21no—
67C24×C37C2×D411yescharacteristic
68C2×D4×C37—21no—
69C2×D4×C37—21no—
70C2×D4×C37—41no—
71C2×D4×C37—42no—
72C2×D4×C37—41no—
73C2×D4×C37—41no—
74C2×D4×C37—41no—
75C2×D4×C37—42no—
76C2×D4×C37—41no—
77C2×D4×C37—41no—
78C2×D4×C37—41no—
79C2×D4×C37—41no—
80C2×D4×C37—41no—
81C2×D4×C37—81no—
82C22×C4×C37—21no—
83C22×C4×C37—21no—
84C22×C4×C37—21no—
85C22×C4×C37—21no—
86C22×C4×C37—21no—
87C22×C4×C37—21no—
88C22×C4×C37—42no—
89C22×C4×C37—41no—
90C22×C4×C37—42no—
91C22×C4×C37—41no—
92C22×C4×C37—81no—
93C22×C4×C37—81no—
94C22×C4×C37C2×D411yescharacteristic
95C22×C4×C37C2×D411yescharacteristic
96D8×C37—82no—
97C2×C8×C37—41no—
98C2×C8×C37—41no—
99C4⋊C4×C37—21no—
100C4⋊C4×C37—21no—
101C4⋊C4×C37—41no—
102C4⋊C4×C37—42no—
103C4⋊C4×C37—42no—
104C4⋊C4×C37—81no—
105C22⋊C4×C37—21no—
106C22⋊C4×C37—41no—
107C22⋊C4×C37—42no—
108C22⋊C4×C37—41no—
109C22⋊C4×C37—41no—
110C22⋊C4×C37—41no—
111C22⋊C4×C37—41no—
112C22⋊C4×C37—41no—
113C22⋊C4×C37—41no—
114C22⋊C4×C37—81no—
115C22⋊C4×C37—81no—
116C22⋊C4×C37—81no—
117C22⋊C4×C37—82no—
118C22⋊C4×C37D812yescomplemented
119C23×C37—21no—
120C23×C37—21no—
121C23×C37—22no—
122C23×C37—41no—
123C23×C37—41no—
124C23×C37—41no—
125C23×C37—41no—
126C23×C37—41no—
127C23×C37—41no—
128C23×C37—41no—
129C23×C37—41no—
130C23×C37—41no—
131C23×C37—41no—
132C23×C37—41no—
133C23×C37—81no—
134C23×C37—81no—
135C23×C37#12011yescharacteristic
136C23×C37C2×D811yescharacteristic
137C23×C37AGL(1,ℤ/8)11yescharacteristic
138D4×C37—42no—
139D4×C37—81no—
140D4×C37—81no—
141D4×C37—81no—
142D4×C37—81no—
143D4×C37—81no—
144D4×C37—82no—
145D4×C37—82no—
146D4×C37—81no—
147D4×C37—81no—
148C2×C4×C37—22no—
149C2×C4×C37—21no—
150C2×C4×C37—21no—
151C2×C4×C37—41no—
152C2×C4×C37—41no—
153C2×C4×C37—41no—
154C2×C4×C37—41no—
155C2×C4×C37—41no—
156C2×C4×C37—41no—
157C2×C4×C37—41no—
158C2×C4×C37—41no—
159C2×C4×C37—41no—
160C2×C4×C37—41no—
161C2×C4×C37—41no—
162C2×C4×C37—41no—
163C2×C4×C37—42no—
164C2×C4×C37—41no—
165C2×C4×C37—41no—
166C2×C4×C37—41no—
167C2×C4×C37—41no—
168C2×C4×C37—41no—
169C2×C4×C37—41no—
170C2×C4×C37—41no—
171C2×C4×C37—84no—
172C2×C4×C37—81no—
173C2×C4×C37—81no—
174C2×C4×C37—81no—
175C2×C4×C37—81no—
176C8×C37—81no—
177C8×C37—81no—
178#12149C3711yesmaximal, characteristic, direct product factor, Sylow
179C22×C37—21no—
180C22×C37—21no—
181C22×C37—21no—
182C22×C37—21no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—42no—
186C22×C37—42no—
187C22×C37—41no—
188C22×C37—41no—
189C22×C37—42no—
190C22×C37—81no—
191C22×C37—81no—
192C22×C37—81no—
193C22×C37—82no—
194C22×C37—81no—
195C22×C37—81no—
196C22×C37—81no—
197C22×C37—81no—
198C22×C37—81no—
199C22×C37—161no—
200C22×C37#44711yescharacteristic
201C22×C37#45411yescharacteristic
202C22×C37B(4,𝔽2)11yescharacteristic
203C4×C37—42no—
204C4×C37—41no—
205C4×C37—41no—
206C4×C37—81no—
207C4×C37—81no—
208C4×C37—81no—
209C4×C37—81no—
210C4×C37—81no—
211C4×C37—161no—
212#2693C2×C3711yescharacteristic, complemented
213#2044C2×C3711yescharacteristic, complemented
214#1607C2×C3711yescharacteristic, complemented
215#1595C2×C3711yescharacteristic
216#1344C2×C3711yescharacteristic, complemented
217#1343C2×C3711yescharacteristic, complemented
218#1326C2×C3711yescharacteristic, complemented
219C2×C37—21no—
220C2×C37—21no—
221C2×C37—41no—
222C2×C37—41no—
223C2×C37—82no—
224C2×C37—161no—
225C2×C37#159811yescharacteristic
226C2×C37#219711yescharacteristic
227C2×C37#220011yescharacteristic
228#534C22×C3711yescharacteristic
229C2×#123—21no—
230#480—21no—
231#447—21no—
232C2×#99—21no—
233#400—21no—
234#397C22×C3711yescharacteristic
235#396—21no—
236#392C22×C3711yescharacteristic
237#386—21no—
238#386—21no—
239#386—21no—
240#385C22×C3711yescharacteristic
241#380—21no—
242#342C22×C3711yescharacteristic
243#327—21no—
244#327—21no—
245#323C22×C3711yescharacteristic
246#323C22×C3711yescharacteristic
247C37#1214911yescharacteristic, direct product factor, Sylow
248C22×D4—21no—
249C22×D4—21no—
250C22×D4D4×C3711yescharacteristic
251C23×C4—21no—
252C23×C4D4×C3711yescharacteristic
253C2×D8—41no—
254#123—42no—
255#123—41no—
256#123—42no—
257#121—21no—
258#121—21no—
259#120—41no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4D4×C3711yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—41no—
271C2×C22⋊C4D4×C3711yescharacteristic
272C2×C22⋊C4C23×C3711yescharacteristic
273#107—41no—
274#102—41no—
275#102—41no—
276#99—42no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—41no—
284#95D4×C3711yescharacteristic
285#95D4×C3711yescharacteristic
286C24—21no—
287C24—21no—
288C24C2×D4×C3711yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—81no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—42no—
312C22×C4—41no—
313C22×C4—81no—
314C22×C4—81no—
315C22×C4C2×D4×C3711yescharacteristic
316C22×C4C2×D4×C3711yescharacteristic
317D8—82no—
318C2×C8—41no—
319C2×C8—41no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—81no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C22⋊C4—42no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—81no—
336C22⋊C4—81no—
337C22⋊C4—81no—
338C22⋊C4—82no—
339C22⋊C4D8×C3712yescomplemented
340C23—21no—
341C23—21no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—81no—
355C23—81no—
356C23#120×C3711yescharacteristic
357C23C2×D8×C3711yescharacteristic
358C23AGL(1,ℤ/8)×C3711yescharacteristic
359D4—42no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—81no—
364D4—81no—
365D4—82no—
366D4—82no—
367D4—81no—
368D4—81no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—84no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C8—81no—
398C8—81no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—42no—
406C22—42no—
407C22—41no—
408C22—41no—
409C22—42no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—82no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—161no—
420C22C37×#44711yescharacteristic
421C22C37×#45411yescharacteristic
422C22C37×B(4,𝔽2)11yescharacteristic
423C4—42no—
424C4—41no—
425C4—41no—
426C4—81no—
427C4—81no—
428C4—81no—
429C4—81no—
430C4—81no—
431C4—161no—
432C2—21no—
433C2—21no—
434C2—41no—
435C2—41no—
436C2—82no—
437C2—161no—
438C2C37×#159811yescharacteristic
439C2C37×#219711yescharacteristic
440C2C37×#220011yescharacteristic
subgroupG/H
center, socleC22×C37B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C37
prime radicalC37×#1595C2
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C37 ◁ C2×C22⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#2693C2semidirect
2. C37×#2044C2semidirect
3. C37×#1607C2semidirect
5. C37×#1344C2semidirect
6. C37×#1343C2semidirect
7. C37×#1326C2semidirect
118. C22⋊C4×C37D8semidirect
178. #12149C37direct (N × H)
212. #2693C2×C37semidirect
213. #2044C2×C37semidirect
214. #1607C2×C37semidirect
216. #1344C2×C37semidirect
217. #1343C2×C37semidirect
218. #1326C2×C37semidirect
247. C37#12149direct (N × H)
339. C22⋊C4D8×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#26932
C37×#20442
C37×#16072
C37×#15952
C37×#13442
C37×#13432
C37×#13262
#1214937