Finite Group Databasebeta

← C37×#19532 #22640785

Subgroups — C37×#19532 #22640785

Order 9472.

562 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3254C211yesmaximal, characteristic
2C37×#3249C211yesmaximal, characteristic, complemented
3C37×#3228C211yesmaximal, characteristic
4C37×#2985C211yesmaximal, characteristic, complemented
5C37×#1702C212yesmaximal, complemented
6C37×#1696C212yesmaximal, complemented
7C37×#1678C212yesmaximal, complemented
8C37×#1672C212yesmaximal, complemented
9C37×#1570C211yesmaximal, characteristic, complemented
10C37×#1559C211yesmaximal, characteristic, complemented
11C37×#1551C211yesmaximal, characteristic
12C37×#533C2211yescharacteristic
13C37×#533C2211yescharacteristic
14C37×#532C2211yescharacteristic
15C37×#500C2211yescharacteristic
16C37×#498C2211yescharacteristic
17C37×#486C2211yescharacteristic
18C37×#486C2211yescharacteristic
19C37×#482—22no—
20C37×#478—22no—
21C37×#477—21no—
22C37×#477C2212yes—
23C37×#477C2212yes—
24C37×#474—21no—
25C37×#468—22no—
26C37×#467—22no—
27C37×#462—21no—
28C37×#462C2212yes—
29C37×#461—21no—
30C37×#460C2212yes—
31C37×#446—22no—
32C37×#446C2212yes—
33C8×Q8×C37C2212yes—
34C37×#433—22no—
35C37×#432C2211yescharacteristic
36C37×#431C2211yescharacteristic
37C37×#423C2211yescharacteristic
38C2×C4⋊C8×C37C2211yescharacteristic
39C37×#334C2212yes—
40C37×#334C2212yes—
41C37×#333C2212yes—
42C37×#333C2212yes—
43C37×#332C2212yes—
44C37×#331C2212yes—
45C2×#41×C37—21no—
46C2×Q16×C37—22no—
47C2×SD16×C37—22no—
48C2×M16×C37—21no—
49C22×C8×C37—21no—
50C4⋊Q8×C37D411yescharacteristic
51C4⋊Q8×C37D411yescharacteristic
52C4⋊Q8×C37C2311yescharacteristic
53C4⋊Q8×C37C2311yescharacteristic
54C4⋊Q8×C37C2311yescharacteristic
55#127×C37C2311yescharacteristic
56#125×C37—21no—
57#125×C37—21no—
58#124×C37—21no—
59C22⋊Q8×C37—21no—
60C22⋊Q8×C37—21no—
61C22⋊Q8×C37—21no—
62C22⋊Q8×C37D412yes—
63#121×C37—21no—
64#121×C37—21no—
65C4×Q8×C37—21no—
66C4×Q8×C37—21no—
67C4×Q8×C37—21no—
68C4×Q8×C37C2312yes—
69C4×D4×C37—21no—
70C4×D4×C37—21no—
71#117×C37—21no—
72#117×C37—21no—
73C2×C42×C37C2311yescharacteristic
74#107×C37—22no—
75#107×C37—22no—
76#107×C37—22no—
77#106×C37—22no—
78C4⋊C8×C37—22no—
79C4⋊C8×C37—22no—
80C4⋊C8×C37—21no—
81C4⋊C8×C37—21no—
82C4⋊C8×C37D412yes—
83C4⋊C8×C37C2312yes—
84C4⋊C8×C37C2312yes—
85C4⋊C8×C37C2312yes—
86#103×C37—22no—
87#103×C37—22no—
88#103×C37—22no—
89#102×C37—22no—
90#102×C37—22no—
91#102×C37—22no—
92C22⋊C8×C37—21no—
93C22⋊C8×C37D412yes—
94#97×C37—22no—
95#97×C37—21no—
96C4×C8×C37—22no—
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×C37C2×D412yes—
105C2×D4×C37—21no—
106C2×D4×C37—21no—
107C2×D4×C37—21no—
108C2×D4×C37—41no—
109C22×C4×C37—41no—
110C22×C4×C37C2×D411yescharacteristic
111C22×C4×C37C2×D411yescharacteristic
112C22×C4×C37#4111yescharacteristic
113Q16×C37—82no—
114SD16×C37—82no—
115M16×C37—81no—
116C2×C8×C37—22no—
117C2×C8×C37—22no—
118C2×C8×C37—22no—
119C2×C8×C37—81no—
120C2×C8×C37C2×D412yes—
121C2×C8×C37C2×D412yes—
122C4⋊C4×C37—21no—
123C4⋊C4×C37—21no—
124C4⋊C4×C37—21no—
125C4⋊C4×C37—22no—
126C4⋊C4×C37—22no—
127C4⋊C4×C37—21no—
128C4⋊C4×C37—21no—
129C4⋊C4×C37—21no—
130C4⋊C4×C37—21no—
131C4⋊C4×C37—21no—
132C4⋊C4×C37—21no—
133C4⋊C4×C37—41no—
134C4⋊C4×C37—41no—
135C4⋊C4×C37C2×D412yes—
136C22⋊C4×C37—22no—
137C22⋊C4×C37—41no—
138C22⋊C4×C37—41no—
139C22⋊C4×C37—41no—
140C42×C37—22no—
141C42×C37—41no—
142C42×C37C2×D411yescharacteristic
143C42×C37C2×D411yescharacteristic
144C42×C37#4111yescharacteristic
145C42×C37C2411yescharacteristic
146C23×C37—41no—
147C23×C37#12111yescharacteristic
148Q8×C37—22no—
149Q8×C37—22no—
150Q8×C37—41no—
151Q8×C37—41no—
152Q8×C37—81no—
153Q8×C37—81no—
154Q8×C37—81no—
155D4×C37—41no—
156D4×C37—41no—
157D4×C37—42no—
158D4×C37—81no—
159D4×C37—82no—
160C2×C4×C37—21no—
161C2×C4×C37—21no—
162C2×C4×C37—22no—
163C2×C4×C37—22no—
164C2×C4×C37—22no—
165C2×C4×C37—41no—
166C2×C4×C37—41no—
167C2×C4×C37—41no—
168C2×C4×C37—41no—
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#19532C3711yesmaximal, 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#57711yescharacteristic
199C4×C37#57711yescharacteristic
200C4×C37#57812yes—
201#3254C2×C3711yescharacteristic
202#3249C2×C3711yescharacteristic, complemented
203#3228C2×C3711yescharacteristic
204#2985C2×C3711yescharacteristic, complemented
205#1702C2×C3712yescomplemented
206#1696C2×C3712yescomplemented
207#1678C2×C3712yescomplemented
208#1672C2×C3712yescomplemented
209#1570C2×C3711yescharacteristic, complemented
210#1559C2×C3711yescharacteristic, complemented
211#1551C2×C3711yescharacteristic
212C2×C37—41no—
213C2×C37—161no—
214C2×C37#304411yescharacteristic
215C2×C37#306011yescharacteristic
216C2×C37#306811yescharacteristic
217#533C22×C3711yescharacteristic
218#533C22×C3711yescharacteristic
219#532C22×C3711yescharacteristic
220#500C22×C3711yescharacteristic
221#498C22×C3711yescharacteristic
222#486C22×C3711yescharacteristic
223#486C22×C3711yescharacteristic
224#482—22no—
225#478—22no—
226#477—21no—
227#477C22×C3712yes—
228#477C22×C3712yes—
229#474—21no—
230#468—22no—
231#467—22no—
232#462—21no—
233#462C22×C3712yes—
234#461—21no—
235#460C22×C3712yes—
236#446—22no—
237#446C22×C3712yes—
238C8×Q8C22×C3712yes—
239#433—22no—
240#432C22×C3711yescharacteristic
241#431C22×C3711yescharacteristic
242#423C22×C3711yescharacteristic
243C2×C4⋊C8C22×C3711yescharacteristic
244#334C22×C3712yes—
245#334C22×C3712yes—
246#333C22×C3712yes—
247#333C22×C3712yes—
248#332C22×C3712yes—
249#331C22×C3712yes—
250C37#1953211yescharacteristic, direct product factor, Sylow
251C2×#41—21no—
252C2×Q16—22no—
253C2×SD16—22no—
254C2×M16—21no—
255C22×C8—21no—
256C4⋊Q8D4×C3711yescharacteristic
257C4⋊Q8D4×C3711yescharacteristic
258C4⋊Q8C23×C3711yescharacteristic
259C4⋊Q8C23×C3711yescharacteristic
260C4⋊Q8C23×C3711yescharacteristic
261#127C23×C3711yescharacteristic
262#125—21no—
263#125—21no—
264#124—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8D4×C3712yes—
269#121—21no—
270#121—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8C23×C3712yes—
275C4×D4—21no—
276C4×D4—21no—
277#117—21no—
278#117—21no—
279C2×C42C23×C3711yescharacteristic
280#107—22no—
281#107—22no—
282#107—22no—
283#106—22no—
284C4⋊C8—22no—
285C4⋊C8—22no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8D4×C3712yes—
289C4⋊C8C23×C3712yes—
290C4⋊C8C23×C3712yes—
291C4⋊C8C23×C3712yes—
292#103—22no—
293#103—22no—
294#103—22no—
295#102—22no—
296#102—22no—
297#102—22no—
298C22⋊C8—21no—
299C22⋊C8D4×C3712yes—
300#97—22no—
301#97—21no—
302C4×C8—22no—
303C4×C8C23×C3711yescharacteristic
304C4×C8C23×C3711yescharacteristic
305#41—82no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8C2×D4×C3712yes—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—41no—
315C22×C4—41no—
316C22×C4C2×D4×C3711yescharacteristic
317C22×C4C2×D4×C3711yescharacteristic
318C22×C4#41×C3711yescharacteristic
319Q16—82no—
320SD16—82no—
321M16—81no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—81no—
326C2×C8C2×D4×C3712yes—
327C2×C8C2×D4×C3712yes—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4C2×D4×C3712yes—
342C22⋊C4—22no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42—22no—
347C42—41no—
348C42C2×D4×C3711yescharacteristic
349C42C2×D4×C3711yescharacteristic
350C42#41×C3711yescharacteristic
351C42C24×C3711yescharacteristic
352C23—41no—
353C23#121×C3711yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—41no—
357Q8—41no—
358Q8—81no—
359Q8—81no—
360Q8—81no—
361D4—41no—
362D4—41no—
363D4—42no—
364D4—81no—
365D4—82no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4#121×C3711yescharacteristic
377C2×C4#121×C3711yescharacteristic
378C2×C4#121×C3711yescharacteristic
379C2×C4C22×D4×C3711yescharacteristic
380C2×C4C22×D4×C3711yescharacteristic
381C2×C4C2×#41×C3711yescharacteristic
382C8—22no—
383C8—22no—
384C8—42no—
385C8—42no—
386C8—42no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22C2×#121×C3711yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—42no—
399C4—42no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4C37×#57711yescharacteristic
404C4C37×#57711yescharacteristic
405C4C37×#57812yes—
406C2—41no—
407C2—161no—
408C2C37×#304411yescharacteristic
409C2C37×#306011yescharacteristic
410C2C37×#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×#3249C2semidirect
4. C37×#2985C2semidirect
5. C37×#1702C2semidirect
6. C37×#1696C2semidirect
7. C37×#1678C2semidirect
8. C37×#1672C2semidirect
9. C37×#1570C2semidirect
10. C37×#1559C2semidirect
181. #19532C37direct (N × H)
202. #3249C2×C37semidirect
204. #2985C2×C37semidirect
205. #1702C2×C37semidirect
206. #1696C2×C37semidirect
207. #1678C2×C37semidirect
208. #1672C2×C37semidirect
209. #1570C2×C37semidirect
210. #1559C2×C37semidirect
250. C37#19532direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32542
C37×#32492
C37×#32282
C37×#29852
C37×#17022
C37×#16962
C37×#16782
C37×#16722
C37×#15702
C37×#15592
C37×#15512
#1953237