Finite Group Databasebeta

← C37×#12995 #22634248

Subgroups — C37×#12995 #22634248

Order 9472.

476 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3067C211yesmaximal, characteristic
2C37×#2916C211yesmaximal, characteristic, complemented
3C37×#2143C211yesmaximal, characteristic, complemented
4C2×C37×#359C211yesmaximal, characteristic, complemented
5C2×C37×#350C211yesmaximal, characteristic, complemented
6C37×#1388C211yesmaximal, characteristic, complemented
7C37×#1381C211yesmaximal, characteristic, complemented
8C37×#575—21no—
9C2×#135×C37C2211yescharacteristic
10C37×#568—21no—
11C2×#131×C37C2211yescharacteristic
12C2×M32×C37C2211yescharacteristic
13C22×C16×C37C2211yescharacteristic
14C37×#473C412yes—
15C37×#472C412yes—
16C37×#471—22no—
17C37×#430—21no—
18C37×#430—22no—
19C2×#108×C37—22no—
20C2×#108×C37C2211yescharacteristic
21C2×#108×C37C2211yescharacteristic
22C2×#108×C37C2211yescharacteristic
23C37×#413—21no—
24C37×#359—22no—
25C37×#359—22no—
26C37×#350—22no—
27C2×#41×C37—21no—
28C2×#41×C37D411yescharacteristic
29#137×C37—22no—
30#137×C37—41no—
31AGL(1,ℤ/8)×C37—22no—
32AGL(1,ℤ/8)×C37—41no—
33#135×C37—21no—
34#135×C37—21no—
35#135×C37—21no—
36#135×C37—21no—
37#135×C37—42no—
38C2×Q16×C37C2×C411yescharacteristic
39C2×SD16×C37—21no—
40C2×D8×C37C2×C411yescharacteristic
41#131×C37—21no—
42#131×C37—21no—
43#131×C37—42no—
44#131×C37—42no—
45#131×C37C2×C412yes—
46#131×C37D412yes—
47C2×M16×C37—21no—
48C2×M16×C37—24no—
49C2×M16×C37—21no—
50C2×M16×C37—21no—
51C2×M16×C37—21no—
52C2×M16×C37D411yescharacteristic
53C22×C8×C37—21no—
54C22×C8×C37C2311yescharacteristic
55M32×C37—21no—
56M32×C37—21no—
57C2×C16×C37—21no—
58C2×C16×C37—21no—
59C2×C16×C37—21no—
60C2×C16×C37—21no—
61#108×C37—24no—
62#108×C37—21no—
63#108×C37—21no—
64#108×C37—21no—
65#108×C37C2×C412yes—
66#108×C37D412yes—
67#108×C37D412yes—
68#101×C37—22no—
69#100×C37—22no—
70#41×C37—21no—
71#41×C37—21no—
72#41×C37—41no—
73#41×C37—41no—
74#41×C37—41no—
75#41×C37—41no—
76#41×C37C22⋊C412yes—
77#41×C37D812yes—
78C2×Q8×C37—21no—
79C2×Q8×C37SD1611yescharacteristic
80C2×D4×C37—21no—
81C2×D4×C37—21no—
82C2×D4×C37—41no—
83C2×D4×C37SD1611yescharacteristic
84C22×C4×C37—21no—
85C22×C4×C37—41no—
86C22×C4×C37C2×D411yescharacteristic
87Q16×C37—21no—
88Q16×C37—21no—
89Q16×C37—42no—
90SD16×C37—42no—
91SD16×C37—42no—
92SD16×C37—41no—
93SD16×C37—41no—
94D8×C37—21no—
95D8×C37—21no—
96D8×C37—42no—
97M16×C37—21no—
98M16×C37—22no—
99M16×C37—22no—
100M16×C37—22no—
101M16×C37—22no—
102M16×C37—22no—
103M16×C37—44no—
104M16×C37—41no—
105M16×C37—41no—
106M16×C37—41no—
107M16×C37C22⋊C412yes—
108C2×C8×C37—21no—
109C2×C8×C37—22no—
110C2×C8×C37—22no—
111C2×C8×C37—44no—
112C2×C8×C37—41no—
113C2×C8×C37—41no—
114C2×C8×C37—41no—
115C2×C8×C37C22×C411yescharacteristic
116C2×C8×C37C2×D411yescharacteristic
117C2×C8×C37C2×D411yescharacteristic
118C2×C8×C37C2×D411yescharacteristic
119C2×C8×C37#4111yescharacteristic
120C2×C8×C37#4111yescharacteristic
121C16×C37—41no—
122C16×C37—41no—
123C23×C37—21no—
124C23×C37—41no—
125C23×C37#13711yescharacteristic
126Q8×C37—21no—
127Q8×C37—41no—
128Q8×C37—41no—
129Q8×C37#10212yes—
130D4×C37—22no—
131D4×C37—22no—
132D4×C37—21no—
133D4×C37—41no—
134D4×C37—41no—
135D4×C37—81no—
136D4×C37—81no—
137D4×C37#10212yes—
138C2×C4×C37—21no—
139C2×C4×C37—22no—
140C2×C4×C37—22no—
141C2×C4×C37—41no—
142C2×C4×C37—81no—
143C2×C4×C37—81no—
144C2×C4×C37C2×C22⋊C411yescharacteristic
145C2×C4×C37#12011yescharacteristic
146C2×C4×C37#12311yescharacteristic
147C2×C4×C37C2×D811yescharacteristic
148C2×C4×C37C2×SD1611yescharacteristic
149C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
150C8×C37—22no—
151C8×C37—42no—
152C8×C37—42no—
153C8×C37—42no—
154C8×C37C4×D411yescharacteristic
155C8×C37C4×D411yescharacteristic
156C8×C37#12111yescharacteristic
157C8×C37#12111yescharacteristic
158#12995C3711yesmaximal, characteristic, direct product factor, Sylow
159C22×C37—22no—
160C22×C37—41no—
161C22×C37—81no—
162C22×C37—81no—
163C22×C37—161no—
164C22×C37#41711yescharacteristic
165C22×C37#44811yescharacteristic
166C22×C37#48011yescharacteristic
167C4×C37—22no—
168C4×C37—81no—
169C4×C37#38611yescharacteristic
170C4×C37C2×#10211yescharacteristic
171C4×C37#44711yescharacteristic
172C4×C37#48111yescharacteristic
173#3067C2×C3711yescharacteristic
174#2916C2×C3711yescharacteristic, complemented
175#2143C2×C3711yescharacteristic, complemented
176C2×#359C2×C3711yescharacteristic, complemented
177C2×#350C2×C3711yescharacteristic, complemented
178#1388C2×C3711yescharacteristic, complemented
179#1381C2×C3711yescharacteristic, complemented
180C2×C37—21no—
181C2×C37—21no—
182C2×C37—21no—
183C2×C37—42no—
184C2×C37—161no—
185C2×C37#187411yescharacteristic
186#575—21no—
187C2×#135C22×C3711yescharacteristic
188#568—21no—
189C2×#131C22×C3711yescharacteristic
190C2×M32C22×C3711yescharacteristic
191C22×C16C22×C3711yescharacteristic
192#473C4×C3712yes—
193#472C4×C3712yes—
194#471—22no—
195#430—21no—
196#430—22no—
197C2×#108—22no—
198C2×#108C22×C3711yescharacteristic
199C2×#108C22×C3711yescharacteristic
200C2×#108C22×C3711yescharacteristic
201#413—21no—
202#359—22no—
203#359—22no—
204#350—22no—
205C37#1299511yescharacteristic, direct product factor, Sylow
206C2×#41—21no—
207C2×#41D4×C3711yescharacteristic
208#137—22no—
209#137—41no—
210AGL(1,ℤ/8)—22no—
211AGL(1,ℤ/8)—41no—
212#135—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216#135—42no—
217C2×Q16C2×C4×C3711yescharacteristic
218C2×SD16—21no—
219C2×D8C2×C4×C3711yescharacteristic
220#131—21no—
221#131—21no—
222#131—42no—
223#131—42no—
224#131C2×C4×C3712yes—
225#131D4×C3712yes—
226C2×M16—21no—
227C2×M16—24no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16D4×C3711yescharacteristic
232C22×C8—21no—
233C22×C8C23×C3711yescharacteristic
234M32—21no—
235M32—21no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240#108—24no—
241#108—21no—
242#108—21no—
243#108—21no—
244#108C2×C4×C3712yes—
245#108D4×C3712yes—
246#108D4×C3712yes—
247#101—22no—
248#100—22no—
249#41—21no—
250#41—21no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255#41C22⋊C4×C3712yes—
256#41D8×C3712yes—
257C2×Q8—21no—
258C2×Q8SD16×C3711yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4SD16×C3711yescharacteristic
263C22×C4—21no—
264C22×C4—41no—
265C22×C4C2×D4×C3711yescharacteristic
266Q16—21no—
267Q16—21no—
268Q16—42no—
269SD16—42no—
270SD16—42no—
271SD16—41no—
272SD16—41no—
273D8—21no—
274D8—21no—
275D8—42no—
276M16—21no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—22no—
282M16—44no—
283M16—41no—
284M16—41no—
285M16—41no—
286M16C22⋊C4×C3712yes—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—44no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8C22×C4×C3711yescharacteristic
295C2×C8C2×D4×C3711yescharacteristic
296C2×C8C2×D4×C3711yescharacteristic
297C2×C8C2×D4×C3711yescharacteristic
298C2×C8#41×C3711yescharacteristic
299C2×C8#41×C3711yescharacteristic
300C16—41no—
301C16—41no—
302C23—21no—
303C23—41no—
304C23#137×C3711yescharacteristic
305Q8—21no—
306Q8—41no—
307Q8—41no—
308Q8#102×C3712yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—81no—
315D4—81no—
316D4#102×C3712yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×C22⋊C4×C3711yescharacteristic
324C2×C4#120×C3711yescharacteristic
325C2×C4#123×C3711yescharacteristic
326C2×C4C2×D8×C3711yescharacteristic
327C2×C4C2×SD16×C3711yescharacteristic
328C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
329C8—22no—
330C8—42no—
331C8—42no—
332C8—42no—
333C8C4×D4×C3711yescharacteristic
334C8C4×D4×C3711yescharacteristic
335C8#121×C3711yescharacteristic
336C8#121×C3711yescharacteristic
337C22—22no—
338C22—41no—
339C22—81no—
340C22—81no—
341C22—161no—
342C22C37×#41711yescharacteristic
343C22C37×#44811yescharacteristic
344C22C37×#48011yescharacteristic
345C4—22no—
346C4—81no—
347C4C37×#38611yescharacteristic
348C4C2×#102×C3711yescharacteristic
349C4C37×#44711yescharacteristic
350C4C37×#48111yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—161no—
356C2C37×#187411yescharacteristic
subgroupG/H
centerC4×C37#447
commutatorC2×C8C22×C4×C37
Frattini, cosocleC22×C8C23×C37
socleC2×C37#1874
prime radicalC37×#3067C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C37 ◁ C22×C4×C37 ◁ C2×#131×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2916C2semidirect
3. C37×#2143C2semidirect
4. C2×C37×#359C2semidirect
5. C2×C37×#350C2semidirect
6. C37×#1388C2semidirect
7. C37×#1381C2semidirect
158. #12995C37direct (N × H)
174. #2916C2×C37semidirect
175. #2143C2×C37semidirect
176. C2×#359C2×C37semidirect
177. C2×#350C2×C37semidirect
178. #1388C2×C37semidirect
179. #1381C2×C37semidirect
205. C37#12995direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#30672
C37×#29162
C37×#21432
C2×C37×#3592
C2×C37×#3502
C37×#13882
C37×#13812
#1299537