Finite Group Databasebeta

← C37×#9299 #22630552

Subgroups — C37×#9299 #22630552

Order 9472.

632 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3205C211yesmaximal, characteristic
2C37×#2328C211yesmaximal, characteristic, complemented
3C37×#1963C211yesmaximal, characteristic, complemented
4C37×#1545C211yesmaximal, characteristic, complemented
5C37×#1517C211yesmaximal, characteristic, complemented
6C37×#1286C211yesmaximal, characteristic, complemented
7C37×#1274C211yesmaximal, characteristic, complemented
8C37×#532C2211yescharacteristic
9C2×#127×C37C2211yescharacteristic
10C2×C4×D4×C37—21no—
11C37×#493C412yescomplemented
12C37×#486C412yescomplemented
13C37×#459—22no—
14C37×#447—22no—
15C37×#431C2211yescharacteristic
16C37×#431C2211yescharacteristic
17C37×#423C2211yescharacteristic
18C2×#104×C37—21no—
19C2×#104×C37—21no—
20C37×#390—21no—
21C37×#386—22no—
22C37×#386—22no—
23C37×#382C2211yescharacteristic
24C37×#376C2211yescharacteristic
25C37×#331—22no—
26C37×#327—22no—
27C2×#41×C37—21no—
28C22×D4×C37—21no—
29C22×D4×C37—21no—
30C22×D4×C37D412yes—
31C23×C4×C37—22no—
32C2×D8×C37—24no—
33C2×M16×C37—21no—
34C4⋊Q8×C37C2×C411yescharacteristic, complemented
35#127×C37—21no—
36#127×C37—21no—
37#127×C37C2×C412yes—
38#127×C37C2×C411yescharacteristic, complemented
39#127×C37D412yes—
40#124×C37—21no—
41#121×C37—21no—
42#121×C37—21no—
43C4×D4×C37—21no—
44C4×D4×C37—21no—
45C4×D4×C37—42no—
46C4×D4×C37—42no—
47C2×C4⋊C4×C37—21no—
48C2×C22⋊C4×C37—22no—
49C2×C22⋊C4×C37—22no—
50C2×C22⋊C4×C37—22no—
51C2×C42×C37D411yescharacteristic
52C2×C42×C37D411yescharacteristic
53C2×C42×C37C2311yescharacteristic
54C4⋊C8×C37—21no—
55C4⋊C8×C37—21no—
56C4⋊C8×C37—21no—
57C4⋊C8×C37—21no—
58#104×C37—42no—
59#104×C37—42no—
60#102×C37—24no—
61C22⋊C8×C37—21no—
62C22⋊C8×C37—21no—
63C4×C8×C37—21no—
64C4×C8×C37C2×C412yescomplemented
65#95×C37—21no—
66#95×C37—21no—
67#95×C37—21no—
68#95×C37D412yes—
69C24×C37—22no—
70#41×C37—41no—
71#41×C37—41no—
72#41×C37—41no—
73#41×C37—41no—
74C2×Q8×C37—21no—
75C2×D4×C37—21no—
76C2×D4×C37—22no—
77C2×D4×C37—21no—
78C2×D4×C37—22no—
79C2×D4×C37—21no—
80C2×D4×C37—22no—
81C2×D4×C37—22no—
82C2×D4×C37—22no—
83C2×D4×C37—41no—
84C2×D4×C37—41no—
85C2×D4×C37—41no—
86C2×D4×C37—41no—
87C2×D4×C37—41no—
88C2×D4×C37—82no—
89C2×D4×C37—82no—
90C2×D4×C37C22⋊C414yes—
91C22×C4×C37—21no—
92C22×C4×C37—21no—
93C22×C4×C37—22no—
94C22×C4×C37—44no—
95C22×C4×C37—41no—
96C22×C4×C37—82no—
97C22×C4×C37—82no—
98C22×C4×C37C2×D411yescharacteristic
99C22×C4×C37C2×D411yescharacteristic
100C22×C4×C37C2×D411yescharacteristic
101D8×C37—84no—
102M16×C37—41no—
103M16×C37—41no—
104C2×C8×C37—22no—
105C2×C8×C37—41no—
106C2×C8×C37—41no—
107C4⋊C4×C37—21no—
108C4⋊C4×C37—21no—
109C4⋊C4×C37—41no—
110C4⋊C4×C37—41no—
111C22⋊C4×C37—44no—
112C22⋊C4×C37—41no—
113C22⋊C4×C37—41no—
114C22⋊C4×C37—82no—
115C22⋊C4×C37—82no—
116C42×C37—21no—
117C42×C37—21no—
118C42×C37—21no—
119C42×C37D812yescomplemented
120C42×C37C22×C411yescharacteristic
121C42×C37C2×D411yescharacteristic
122C42×C37#4111yescharacteristic
123C42×C37#4111yescharacteristic
124C23×C37—24no—
125C23×C37—42no—
126C23×C37—42no—
127C23×C37—42no—
128C23×C37—42no—
129C23×C37—42no—
130C23×C37—42no—
131C23×C37—41no—
132C23×C37#12011yescharacteristic
133Q8×C37—41no—
134Q8×C37—41no—
135D4×C37—44no—
136D4×C37—42no—
137D4×C37—42no—
138D4×C37—41no—
139D4×C37—42no—
140D4×C37—41no—
141D4×C37—42no—
142D4×C37—42no—
143D4×C37—82no—
144D4×C37—82no—
145D4×C37—82no—
146D4×C37—81no—
147D4×C37—81no—
148D4×C37—81no—
149C2×C4×C37—22no—
150C2×C4×C37—41no—
151C2×C4×C37—41no—
152C2×C4×C37—41no—
153C2×C4×C37—41no—
154C2×C4×C37—41no—
155C2×C4×C37—41no—
156C2×C4×C37—42no—
157C2×C4×C37—42no—
158C2×C4×C37—41no—
159C2×C4×C37—42no—
160C2×C4×C37—41no—
161C2×C4×C37—88no—
162C2×C4×C37—81no—
163C2×C4×C37—81no—
164C2×C4×C37C2×C22⋊C411yescharacteristic
165C2×C4×C37C4×D411yescharacteristic
166C2×C4×C37C4×D411yescharacteristic
167C2×C4×C37#12111yescharacteristic
168C2×C4×C37#12111yescharacteristic
169C2×C4×C37#12311yescharacteristic
170C2×C4×C37C2×D811yescharacteristic
171C2×C4×C37#13511yescharacteristic
172C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
174C8×C37—42no—
175C8×C37—81no—
176C8×C37—81no—
177#9299C3711yesmaximal, characteristic, direct product factor, Sylow
178C22×C37—21no—
179C22×C37—21no—
180C22×C37—44no—
181C22×C37—44no—
182C22×C37—44no—
183C22×C37—82no—
184C22×C37—82no—
185C22×C37—82no—
186C22×C37—82no—
187C22×C37—81no—
188C22×C37—81no—
189C22×C37—81no—
190C22×C37#38611yescharacteristic
191C22×C37#44711yescharacteristic
192C22×C37#44911yescharacteristic
193C4×C37—21no—
194C4×C37—21no—
195C4×C37—21no—
196C4×C37—21no—
197C4×C37—42no—
198C4×C37—81no—
199C4×C37—82no—
200C4×C37—81no—
201C4×C37C4×D811yescharacteristic
202C4×C37#44211yescharacteristic
203C4×C37#45911yescharacteristic
204C4×C37#46311yescharacteristic
205#3205C2×C3711yescharacteristic
206#2328C2×C3711yescharacteristic, complemented
207#1963C2×C3711yescharacteristic, complemented
208#1545C2×C3711yescharacteristic, complemented
209#1517C2×C3711yescharacteristic, complemented
210#1286C2×C3711yescharacteristic, complemented
211#1274C2×C3711yescharacteristic, complemented
212C2×C37—21no—
213C2×C37—21no—
214C2×C37—84no—
215C2×C37—161no—
216C2×C37#187911yescharacteristic
217C2×C37#190411yescharacteristic
218C2×C37#191111yescharacteristic
219#532C22×C3711yescharacteristic
220C2×#127C22×C3711yescharacteristic
221C2×C4×D4—21no—
222#493C4×C3712yescomplemented
223#486C4×C3712yescomplemented
224#459—22no—
225#447—22no—
226#431C22×C3711yescharacteristic
227#431C22×C3711yescharacteristic
228#423C22×C3711yescharacteristic
229C2×#104—21no—
230C2×#104—21no—
231#390—21no—
232#386—22no—
233#386—22no—
234#382C22×C3711yescharacteristic
235#376C22×C3711yescharacteristic
236#331—22no—
237#327—22no—
238C37#929911yescharacteristic, direct product factor, Sylow
239C2×#41—21no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4D4×C3712yes—
243C23×C4—22no—
244C2×D8—24no—
245C2×M16—21no—
246C4⋊Q8C2×C4×C3711yescharacteristic, complemented
247#127—21no—
248#127—21no—
249#127C2×C4×C3712yes—
250#127C2×C4×C3711yescharacteristic, complemented
251#127D4×C3712yes—
252#124—21no—
253#121—21no—
254#121—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—42no—
258C4×D4—42no—
259C2×C4⋊C4—21no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C42D4×C3711yescharacteristic
264C2×C42D4×C3711yescharacteristic
265C2×C42C23×C3711yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270#104—42no—
271#104—42no—
272#102—24no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C4×C8—21no—
276C4×C8C2×C4×C3712yescomplemented
277#95—21no—
278#95—21no—
279#95—21no—
280#95D4×C3712yes—
281C24—22no—
282#41—41no—
283#41—41no—
284#41—41no—
285#41—41no—
286C2×Q8—21no—
287C2×D4—21no—
288C2×D4—22no—
289C2×D4—21no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—82no—
301C2×D4—82no—
302C2×D4C22⋊C4×C3714yes—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—44no—
307C22×C4—41no—
308C22×C4—82no—
309C22×C4—82no—
310C22×C4C2×D4×C3711yescharacteristic
311C22×C4C2×D4×C3711yescharacteristic
312C22×C4C2×D4×C3711yescharacteristic
313D8—84no—
314M16—41no—
315M16—41no—
316C2×C8—22no—
317C2×C8—41no—
318C2×C8—41no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C22⋊C4—44no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—82no—
327C22⋊C4—82no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42D8×C3712yescomplemented
332C42C22×C4×C3711yescharacteristic
333C42C2×D4×C3711yescharacteristic
334C42#41×C3711yescharacteristic
335C42#41×C3711yescharacteristic
336C23—24no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—41no—
344C23#120×C3711yescharacteristic
345Q8—41no—
346Q8—41no—
347D4—44no—
348D4—42no—
349D4—42no—
350D4—41no—
351D4—42no—
352D4—41no—
353D4—42no—
354D4—42no—
355D4—82no—
356D4—82no—
357D4—82no—
358D4—81no—
359D4—81no—
360D4—81no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—88no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4C2×C22⋊C4×C3711yescharacteristic
377C2×C4C4×D4×C3711yescharacteristic
378C2×C4C4×D4×C3711yescharacteristic
379C2×C4#121×C3711yescharacteristic
380C2×C4#121×C3711yescharacteristic
381C2×C4#123×C3711yescharacteristic
382C2×C4C2×D8×C3711yescharacteristic
383C2×C4#135×C3711yescharacteristic
384C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
385C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
386C8—42no—
387C8—81no—
388C8—81no—
389C22—21no—
390C22—21no—
391C22—44no—
392C22—44no—
393C22—44no—
394C22—82no—
395C22—82no—
396C22—82no—
397C22—82no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22C37×#38611yescharacteristic
402C22C37×#44711yescharacteristic
403C22C37×#44911yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—82no—
410C4—81no—
411C4—81no—
412C4C4×D8×C3711yescharacteristic
413C4C37×#44211yescharacteristic
414C4C37×#45911yescharacteristic
415C4C37×#46311yescharacteristic
416C2—21no—
417C2—21no—
418C2—84no—
419C2—161no—
420C2C37×#187911yescharacteristic
421C2C37×#190411yescharacteristic
422C2C37×#191111yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC42C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC37×#3205C2
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×#2328C2semidirect
3. C37×#1963C2semidirect
4. C37×#1545C2semidirect
5. C37×#1517C2semidirect
6. C37×#1286C2semidirect
7. C37×#1274C2semidirect
11. C37×#493C4semidirect
12. C37×#486C4semidirect
34. C4⋊Q8×C37C2×C4semidirect
38. #127×C37C2×C4semidirect
64. C4×C8×C37C2×C4semidirect
119. C42×C37D8semidirect
177. #9299C37direct (N × H)
206. #2328C2×C37semidirect
207. #1963C2×C37semidirect
208. #1545C2×C37semidirect
209. #1517C2×C37semidirect
210. #1286C2×C37semidirect
211. #1274C2×C37semidirect
222. #493C4×C37semidirect
223. #486C4×C37semidirect
238. C37#9299direct (N × H)
246. C4⋊Q8C2×C4×C37semidirect
250. #127C2×C4×C37semidirect
276. C4×C8C2×C4×C37semidirect
331. C42D8×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#32052
C37×#23282
C37×#19632
C37×#15452
C37×#15172
C37×#12862
C37×#12742
#929937