Finite Group Databasebeta

← C37×#19515 #22640768

Subgroups — C37×#19515 #22640768

Order 9472.

576 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3235C211yesmaximal, characteristic
2C37×#3230C211yesmaximal, characteristic, complemented
3C37×#3227C211yesmaximal, characteristic
4C37×#2981C211yesmaximal, characteristic
5C37×#1703C212yesmaximal, complemented
6C37×#1695C212yesmaximal, complemented
7C37×#1683C212yesmaximal, complemented
8C37×#1675C212yesmaximal, complemented
9C37×#1572C211yesmaximal, characteristic, complemented
10C37×#1558C211yesmaximal, characteristic, complemented
11C37×#1554C211yesmaximal, characteristic, complemented
12C37×#533C2211yescharacteristic
13C37×#532C2211yescharacteristic
14C2×C4⋊Q8×C37C2211yescharacteristic
15C37×#501—21no—
16C37×#500C2211yescharacteristic
17C37×#500C2211yescharacteristic
18C37×#498—21no—
19C37×#490—21no—
20C37×#487C2211yescharacteristic
21C37×#487C2211yescharacteristic
22C37×#486—21no—
23C37×#484—22no—
24C37×#482—22no—
25C37×#481—22no—
26C37×#477—22no—
27C37×#476C2212yes—
28C37×#476C2212yes—
29C37×#476C2212yes—
30C37×#474C2212yes—
31C37×#436C2212yes—
32C37×#435—22no—
33C8×D4×C37C2212yes—
34C37×#432C2211yescharacteristic
35C37×#432C2211yescharacteristic
36C37×#431C2211yescharacteristic
37C37×#431C2211yescharacteristic
38C37×#408—22no—
39C37×#335C2212yes—
40C37×#334C2212yes—
41C37×#333C2212yes—
42C37×#333C2212yes—
43C37×#333C2212yes—
44C37×#332C2212yes—
45C2×#41×C37—21no—
46C22×Q8×C37—21no—
47C2×M16×C37—22no—
48C22×C8×C37—22no—
49C4⋊Q8×C37—21no—
50C4⋊Q8×C37—21no—
51C4⋊Q8×C37—21no—
52C4⋊Q8×C37D411yescharacteristic
53C4⋊Q8×C37C2311yescharacteristic
54C4⋊Q8×C37C2311yescharacteristic
55C4⋊Q8×C37C2311yescharacteristic
56C4⋊Q8×C37C2311yescharacteristic
57#127×C37D411yescharacteristic
58#125×C37—21no—
59#124×C37—21no—
60C22⋊Q8×C37—21no—
61C22⋊Q8×C37—21no—
62#121×C37—21no—
63#121×C37D412yes—
64C4×Q8×C37—21no—
65C4×Q8×C37—21no—
66C4×D4×C37—21no—
67C4×D4×C37C2312yes—
68#117×C37—21no—
69C2×C4⋊C4×C37—21no—
70C2×C4⋊C4×C37—21no—
71C2×C42×C37C2311yescharacteristic
72#107×C37—22no—
73#107×C37—22no—
74#107×C37—22no—
75#106×C37—22no—
76#106×C37—22no—
77#106×C37—22no—
78C4⋊C8×C37D412yes—
79C4⋊C8×C37C2312yes—
80C4⋊C8×C37C2312yes—
81C4⋊C8×C37C2312yes—
82#103×C37—22no—
83#103×C37—22no—
84#102×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×C37—22no—
92C22⋊C8×C37—22no—
93C22⋊C8×C37D412yes—
94#97×C37—21no—
95#97×C37—21no—
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—21no—
105C2×Q8×C37—41no—
106C2×Q8×C37—82no—
107C2×D4×C37—22no—
108C2×D4×C37—21no—
109C2×D4×C37—21no—
110C2×D4×C37C2×D412yes—
111C22×C4×C37—22no—
112C22×C4×C37—41no—
113C22×C4×C37C2×D411yescharacteristic
114C22×C4×C37C2×D411yescharacteristic
115C22×C4×C37#4111yescharacteristic
116M16×C37—82no—
117C2×C8×C37—22no—
118C2×C8×C37—22no—
119C2×C8×C37—22no—
120C2×C8×C37—82no—
121C2×C8×C37C2×D412yes—
122C2×C8×C37C2×D412yes—
123C4⋊C4×C37—21no—
124C4⋊C4×C37—21no—
125C4⋊C4×C37—21no—
126C4⋊C4×C37—21no—
127C4⋊C4×C37—21no—
128C4⋊C4×C37—21no—
129C4⋊C4×C37—21no—
130C4⋊C4×C37—21no—
131C4⋊C4×C37—21no—
132C4⋊C4×C37—41no—
133C4⋊C4×C37—41no—
134C4⋊C4×C37—41no—
135C4⋊C4×C37—41no—
136C4⋊C4×C37C2×D412yes—
137C22⋊C4×C37—22no—
138C22⋊C4×C37—22no—
139C22⋊C4×C37—41no—
140C42×C37—41no—
141C42×C37C2×D411yescharacteristic
142C42×C37C2×D411yescharacteristic
143C42×C37#4111yescharacteristic
144C42×C37C2411yescharacteristic
145C23×C37—22no—
146C23×C37#12111yescharacteristic
147Q8×C37—42no—
148Q8×C37—81no—
149Q8×C37—81no—
150Q8×C37—81no—
151Q8×C37—81no—
152Q8×C37—82no—
153D4×C37—24no—
154D4×C37—81no—
155D4×C37—81no—
156D4×C37—82no—
157C2×C4×C37—22no—
158C2×C4×C37—22no—
159C2×C4×C37—22no—
160C2×C4×C37—41no—
161C2×C4×C37—42no—
162C2×C4×C37—42no—
163C2×C4×C37—41no—
164C2×C4×C37—41no—
165C2×C4×C37—41no—
166C2×C4×C37—41no—
167C2×C4×C37—82no—
168C2×C4×C37#12111yescharacteristic
169C2×C4×C37#12111yescharacteristic
170C2×C4×C37#12111yescharacteristic
171C2×C4×C37C22×D411yescharacteristic
172C2×C4×C37C22×D411yescharacteristic
173C2×C4×C37C2×#4111yescharacteristic
174C8×C37—22no—
175C8×C37—22no—
176C8×C37—42no—
177C8×C37—42no—
178C8×C37—42no—
179#19515C3711yesmaximal, characteristic, direct product factor, Sylow
180C22×C37—21no—
181C22×C37—21no—
182C22×C37—21no—
183C22×C37—42no—
184C22×C37—42no—
185C22×C37—42no—
186C22×C37C2×#12111yescharacteristic
187C4×C37—21no—
188C4×C37—21no—
189C4×C37—21no—
190C4×C37—21no—
191C4×C37—42no—
192C4×C37—81no—
193C4×C37—81no—
194C4×C37—81no—
195C4×C37—81no—
196C4×C37#57712yes—
197C4×C37#57812yes—
198#3235C2×C3711yescharacteristic
199#3230C2×C3711yescharacteristic, complemented
200#3227C2×C3711yescharacteristic
201#2981C2×C3711yescharacteristic
202#1703C2×C3712yescomplemented
203#1695C2×C3712yescomplemented
204#1683C2×C3712yescomplemented
205#1675C2×C3712yescomplemented
206#1572C2×C3711yescharacteristic, complemented
207#1558C2×C3711yescharacteristic, complemented
208#1554C2×C3711yescharacteristic, complemented
209C2×C37—41no—
210C2×C37—82no—
211C2×C37#304211yescharacteristic
212C2×C37#305911yescharacteristic
213C2×C37#306811yescharacteristic
214#533C22×C3711yescharacteristic
215#532C22×C3711yescharacteristic
216C2×C4⋊Q8C22×C3711yescharacteristic
217#501—21no—
218#500C22×C3711yescharacteristic
219#500C22×C3711yescharacteristic
220#498—21no—
221#490—21no—
222#487C22×C3711yescharacteristic
223#487C22×C3711yescharacteristic
224#486—21no—
225#484—22no—
226#482—22no—
227#481—22no—
228#477—22no—
229#476C22×C3712yes—
230#476C22×C3712yes—
231#476C22×C3712yes—
232#474C22×C3712yes—
233#436C22×C3712yes—
234#435—22no—
235C8×D4C22×C3712yes—
236#432C22×C3711yescharacteristic
237#432C22×C3711yescharacteristic
238#431C22×C3711yescharacteristic
239#431C22×C3711yescharacteristic
240#408—22no—
241#335C22×C3712yes—
242#334C22×C3712yes—
243#333C22×C3712yes—
244#333C22×C3712yes—
245#333C22×C3712yes—
246#332C22×C3712yes—
247C37#1951511yescharacteristic, direct product factor, Sylow
248C2×#41—21no—
249C22×Q8—21no—
250C2×M16—22no—
251C22×C8—22no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8D4×C3711yescharacteristic
256C4⋊Q8C23×C3711yescharacteristic
257C4⋊Q8C23×C3711yescharacteristic
258C4⋊Q8C23×C3711yescharacteristic
259C4⋊Q8C23×C3711yescharacteristic
260#127D4×C3711yescharacteristic
261#125—21no—
262#124—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265#121—21no—
266#121D4×C3712yes—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×D4—21no—
270C4×D4C23×C3712yes—
271#117—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C42C23×C3711yescharacteristic
275#107—22no—
276#107—22no—
277#107—22no—
278#106—22no—
279#106—22no—
280#106—22no—
281C4⋊C8D4×C3712yes—
282C4⋊C8C23×C3712yes—
283C4⋊C8C23×C3712yes—
284C4⋊C8C23×C3712yes—
285#103—22no—
286#103—22no—
287#102—22no—
288#102—22no—
289#102—22no—
290#102—22no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—22no—
295C22⋊C8—22no—
296C22⋊C8D4×C3712yes—
297#97—21no—
298#97—21no—
299C4×C8—21no—
300C4×C8C23×C3711yescharacteristic
301C4×C8C23×C3711yescharacteristic
302#41—82no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—41no—
309C2×Q8—82no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4C2×D4×C3712yes—
314C22×C4—22no—
315C22×C4—41no—
316C22×C4C2×D4×C3711yescharacteristic
317C22×C4C2×D4×C3711yescharacteristic
318C22×C4#41×C3711yescharacteristic
319M16—82no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—82no—
324C2×C8C2×D4×C3712yes—
325C2×C8C2×D4×C3712yes—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4C2×D4×C3712yes—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—41no—
343C42—41no—
344C42C2×D4×C3711yescharacteristic
345C42C2×D4×C3711yescharacteristic
346C42#41×C3711yescharacteristic
347C42C24×C3711yescharacteristic
348C23—22no—
349C23#121×C3711yescharacteristic
350Q8—42no—
351Q8—81no—
352Q8—81no—
353Q8—81no—
354Q8—81no—
355Q8—82no—
356D4—24no—
357D4—81no—
358D4—81no—
359D4—82no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—82no—
371C2×C4#121×C3711yescharacteristic
372C2×C4#121×C3711yescharacteristic
373C2×C4#121×C3711yescharacteristic
374C2×C4C22×D4×C3711yescharacteristic
375C2×C4C22×D4×C3711yescharacteristic
376C2×C4C2×#41×C3711yescharacteristic
377C8—22no—
378C8—22no—
379C8—42no—
380C8—42no—
381C8—42no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22C2×#121×C3711yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4C37×#57712yes—
399C4C37×#57812yes—
400C2—41no—
401C2—82no—
402C2C37×#304211yescharacteristic
403C2C37×#305911yescharacteristic
404C2C37×#306811yescharacteristic
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
2. C37×#3230C2semidirect
5. C37×#1703C2semidirect
6. C37×#1695C2semidirect
7. C37×#1683C2semidirect
8. C37×#1675C2semidirect
9. C37×#1572C2semidirect
10. C37×#1558C2semidirect
11. C37×#1554C2semidirect
179. #19515C37direct (N × H)
199. #3230C2×C37semidirect
202. #1703C2×C37semidirect
203. #1695C2×C37semidirect
204. #1683C2×C37semidirect
205. #1675C2×C37semidirect
206. #1572C2×C37semidirect
207. #1558C2×C37semidirect
208. #1554C2×C37semidirect
247. C37#19515direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32352
C37×#32302
C37×#32272
C37×#29812
C37×#17032
C37×#16952
C37×#16832
C37×#16752
C37×#15722
C37×#15582
C37×#15542
#1951537