Finite Group Databasebeta

← C37×#19519 #22640772

Subgroups — C37×#19519 #22640772

Order 9472.

602 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3253C211yesmaximal, characteristic
2C37×#3246C211yesmaximal, characteristic, complemented
3C37×#3228C211yesmaximal, characteristic, complemented
4C37×#2981C211yesmaximal, characteristic, complemented
5C37×#1697C212yesmaximal, complemented
6C37×#1691C212yesmaximal, complemented
7C37×#1681C212yesmaximal, complemented
8C37×#1675C212yesmaximal, complemented
9C37×#1571C211yesmaximal, characteristic, complemented
10C37×#1559C211yesmaximal, characteristic, complemented
11C37×#1551C211yesmaximal, characteristic, complemented
12C37×#533C2211yescharacteristic
13C37×#532C2211yescharacteristic
14C37×#532C2211yescharacteristic
15C37×#500C2211yescharacteristic
16C37×#498C2211yescharacteristic
17C37×#486C2211yescharacteristic
18C37×#486C2211yescharacteristic
19C37×#482—22no—
20C37×#478—22no—
21C37×#476—21no—
22C37×#476C2212yes—
23C37×#476C2212yes—
24C37×#475—21no—
25C37×#469—22no—
26C37×#465—22no—
27C37×#461C2212yes—
28C37×#460—21no—
29C37×#459—21no—
30C37×#459C2212yes—
31C37×#436C2212yes—
32C37×#435—22no—
33C8×D4×C37C2212yes—
34C37×#432C2211yescharacteristic
35C37×#431C2211yescharacteristic
36C37×#423C2211yescharacteristic
37C2×C4⋊C8×C37C2211yescharacteristic
38C37×#408—22no—
39C37×#335C2212yes—
40C37×#335C2212yes—
41C37×#333C2212yes—
42C37×#333C2212yes—
43C37×#332C2212yes—
44C37×#331C2212yes—
45C2×#41×C37—21no—
46C2×#41×C37—21no—
47C2×SD16×C37—22no—
48C2×D8×C37—22no—
49C2×M16×C37—21no—
50C2×M16×C37—22no—
51C22×C8×C37—21no—
52C22×C8×C37—22no—
53C4⋊Q8×C37D411yescharacteristic
54C4⋊Q8×C37C2311yescharacteristic
55C4⋊Q8×C37C2311yescharacteristic
56C4⋊Q8×C37C2311yescharacteristic
57#127×C37D411yescharacteristic
58#127×C37C2311yescharacteristic
59#125×C37—21no—
60#124×C37—21no—
61#124×C37—21no—
62C22⋊Q8×C37—21no—
63C22⋊Q8×C37—21no—
64#121×C37—21no—
65#121×C37—21no—
66#121×C37—21no—
67#121×C37D412yes—
68C4×Q8×C37—21no—
69C4×Q8×C37—21no—
70C4×D4×C37—21no—
71C4×D4×C37—21no—
72C4×D4×C37—21no—
73C4×D4×C37C2312yes—
74#117×C37—21no—
75C2×C42×C37C2311yescharacteristic
76#107×C37—22no—
77#106×C37—22no—
78#106×C37—22no—
79#106×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#102×C37—22no—
88#102×C37—22no—
89#102×C37—22no—
90#102×C37—22no—
91#102×C37—22no—
92C22⋊C8×C37—21no—
93C22⋊C8×C37—22no—
94C22⋊C8×C37—22no—
95C22⋊C8×C37D412yes—
96#97×C37—21no—
97C4×C8×C37C2311yescharacteristic
98C4×C8×C37C2311yescharacteristic
99#41×C37—82no—
100#41×C37—82no—
101C2×Q8×C37—21no—
102C2×Q8×C37—21no—
103C2×Q8×C37—21no—
104C2×Q8×C37—21no—
105C2×D4×C37—22no—
106C2×D4×C37—21no—
107C2×D4×C37—21no—
108C2×D4×C37—21no—
109C2×D4×C37—21no—
110C2×D4×C37—21no—
111C2×D4×C37—41no—
112C2×D4×C37C2×D412yes—
113C22×C4×C37—22no—
114C22×C4×C37—41no—
115C22×C4×C37C2×D411yescharacteristic
116C22×C4×C37C2×D411yescharacteristic
117C22×C4×C37#4111yescharacteristic
118SD16×C37—82no—
119D8×C37—82no—
120M16×C37—82no—
121M16×C37—81no—
122C2×C8×C37—22no—
123C2×C8×C37—22no—
124C2×C8×C37—22no—
125C2×C8×C37—82no—
126C2×C8×C37—81no—
127C2×C8×C37C2×D412yes—
128C2×C8×C37C2×D412yes—
129C4⋊C4×C37—21no—
130C4⋊C4×C37—21no—
131C4⋊C4×C37—21no—
132C4⋊C4×C37—21no—
133C4⋊C4×C37—21no—
134C4⋊C4×C37—21no—
135C4⋊C4×C37—21no—
136C4⋊C4×C37—41no—
137C4⋊C4×C37—41no—
138C4⋊C4×C37C2×D412yes—
139C22⋊C4×C37—22no—
140C22⋊C4×C37—22no—
141C22⋊C4×C37—41no—
142C22⋊C4×C37—41no—
143C22⋊C4×C37—41no—
144C42×C37—41no—
145C42×C37C2×D411yescharacteristic
146C42×C37C2×D411yescharacteristic
147C42×C37#4111yescharacteristic
148C42×C37C2411yescharacteristic
149C23×C37—22no—
150C23×C37—41no—
151C23×C37#12111yescharacteristic
152Q8×C37—41no—
153Q8×C37—41no—
154Q8×C37—81no—
155Q8×C37—81no—
156Q8×C37—81no—
157D4×C37—22no—
158D4×C37—22no—
159D4×C37—41no—
160D4×C37—42no—
161D4×C37—41no—
162D4×C37—81no—
163D4×C37—81no—
164D4×C37—81no—
165D4×C37—82no—
166D4×C37—82no—
167C2×C4×C37—21no—
168C2×C4×C37—22no—
169C2×C4×C37—21no—
170C2×C4×C37—22no—
171C2×C4×C37—41no—
172C2×C4×C37—42no—
173C2×C4×C37—42no—
174C2×C4×C37—41no—
175C2×C4×C37—41no—
176C2×C4×C37—41no—
177C2×C4×C37—82no—
178C2×C4×C37#12111yescharacteristic
179C2×C4×C37#12111yescharacteristic
180C2×C4×C37#12111yescharacteristic
181C2×C4×C37C22×D411yescharacteristic
182C2×C4×C37C22×D411yescharacteristic
183C2×C4×C37C2×#4111yescharacteristic
184C8×C37—22no—
185C8×C37—22no—
186C8×C37—42no—
187C8×C37—42no—
188C8×C37—42no—
189#19519C3711yesmaximal, characteristic, direct product factor, Sylow
190C22×C37—21no—
191C22×C37—21no—
192C22×C37—21no—
193C22×C37—42no—
194C22×C37—42no—
195C22×C37—42no—
196C22×C37—81no—
197C22×C37—81no—
198C22×C37—81no—
199C22×C37C2×#12111yescharacteristic
200C4×C37—21no—
201C4×C37—21no—
202C4×C37—21no—
203C4×C37—21no—
204C4×C37—42no—
205C4×C37—81no—
206C4×C37—81no—
207C4×C37—81no—
208C4×C37#57611yescharacteristic
209C4×C37#57712yes—
210C4×C37#57811yescharacteristic
211#3253C2×C3711yescharacteristic
212#3246C2×C3711yescharacteristic, complemented
213#3228C2×C3711yescharacteristic, complemented
214#2981C2×C3711yescharacteristic, complemented
215#1697C2×C3712yescomplemented
216#1691C2×C3712yescomplemented
217#1681C2×C3712yescomplemented
218#1675C2×C3712yescomplemented
219#1571C2×C3711yescharacteristic, complemented
220#1559C2×C3711yescharacteristic, complemented
221#1551C2×C3711yescharacteristic, complemented
222C2×C37—41no—
223C2×C37—82no—
224C2×C37—161no—
225C2×C37#304211yescharacteristic
226C2×C37#306111yescharacteristic
227C2×C37#306811yescharacteristic
228#533C22×C3711yescharacteristic
229#532C22×C3711yescharacteristic
230#532C22×C3711yescharacteristic
231#500C22×C3711yescharacteristic
232#498C22×C3711yescharacteristic
233#486C22×C3711yescharacteristic
234#486C22×C3711yescharacteristic
235#482—22no—
236#478—22no—
237#476—21no—
238#476C22×C3712yes—
239#476C22×C3712yes—
240#475—21no—
241#469—22no—
242#465—22no—
243#461C22×C3712yes—
244#460—21no—
245#459—21no—
246#459C22×C3712yes—
247#436C22×C3712yes—
248#435—22no—
249C8×D4C22×C3712yes—
250#432C22×C3711yescharacteristic
251#431C22×C3711yescharacteristic
252#423C22×C3711yescharacteristic
253C2×C4⋊C8C22×C3711yescharacteristic
254#408—22no—
255#335C22×C3712yes—
256#335C22×C3712yes—
257#333C22×C3712yes—
258#333C22×C3712yes—
259#332C22×C3712yes—
260#331C22×C3712yes—
261C37#1951911yescharacteristic, direct product factor, Sylow
262C2×#41—21no—
263C2×#41—21no—
264C2×SD16—22no—
265C2×D8—22no—
266C2×M16—21no—
267C2×M16—22no—
268C22×C8—21no—
269C22×C8—22no—
270C4⋊Q8D4×C3711yescharacteristic
271C4⋊Q8C23×C3711yescharacteristic
272C4⋊Q8C23×C3711yescharacteristic
273C4⋊Q8C23×C3711yescharacteristic
274#127D4×C3711yescharacteristic
275#127C23×C3711yescharacteristic
276#125—21no—
277#124—21no—
278#124—21no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281#121—21no—
282#121—21no—
283#121—21no—
284#121D4×C3712yes—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4C23×C3712yes—
291#117—21no—
292C2×C42C23×C3711yescharacteristic
293#107—22no—
294#106—22no—
295#106—22no—
296#106—22no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8D4×C3712yes—
300C4⋊C8C23×C3712yes—
301C4⋊C8C23×C3712yes—
302C4⋊C8C23×C3712yes—
303#103—22no—
304#102—22no—
305#102—22no—
306#102—22no—
307#102—22no—
308#102—22no—
309C22⋊C8—21no—
310C22⋊C8—22no—
311C22⋊C8—22no—
312C22⋊C8D4×C3712yes—
313#97—21no—
314C4×C8C23×C3711yescharacteristic
315C4×C8C23×C3711yescharacteristic
316#41—82no—
317#41—82no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×D4—22no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—41no—
329C2×D4C2×D4×C3712yes—
330C22×C4—22no—
331C22×C4—41no—
332C22×C4C2×D4×C3711yescharacteristic
333C22×C4C2×D4×C3711yescharacteristic
334C22×C4#41×C3711yescharacteristic
335SD16—82no—
336D8—82no—
337M16—82no—
338M16—81no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—82no—
343C2×C8—81no—
344C2×C8C2×D4×C3712yes—
345C2×C8C2×D4×C3712yes—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4C2×D4×C3712yes—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C42—41no—
362C42C2×D4×C3711yescharacteristic
363C42C2×D4×C3711yescharacteristic
364C42#41×C3711yescharacteristic
365C42C24×C3711yescharacteristic
366C23—22no—
367C23—41no—
368C23#121×C3711yescharacteristic
369Q8—41no—
370Q8—41no—
371Q8—81no—
372Q8—81no—
373Q8—81no—
374D4—22no—
375D4—22no—
376D4—41no—
377D4—42no—
378D4—41no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—82no—
383D4—82no—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—82no—
395C2×C4#121×C3711yescharacteristic
396C2×C4#121×C3711yescharacteristic
397C2×C4#121×C3711yescharacteristic
398C2×C4C22×D4×C3711yescharacteristic
399C2×C4C22×D4×C3711yescharacteristic
400C2×C4C2×#41×C3711yescharacteristic
401C8—22no—
402C8—22no—
403C8—42no—
404C8—42no—
405C8—42no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22C2×#121×C3711yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—42no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4C37×#57611yescharacteristic
425C4C37×#57712yes—
426C4C37×#57811yescharacteristic
427C2—41no—
428C2—82no—
429C2—161no—
430C2C37×#304211yescharacteristic
431C2C37×#306111yescharacteristic
432C2C37×#306811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3253C2
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×#3246C2semidirect
3. C37×#3228C2semidirect
4. C37×#2981C2semidirect
5. C37×#1697C2semidirect
6. C37×#1691C2semidirect
7. C37×#1681C2semidirect
8. C37×#1675C2semidirect
9. C37×#1571C2semidirect
10. C37×#1559C2semidirect
11. C37×#1551C2semidirect
189. #19519C37direct (N × H)
212. #3246C2×C37semidirect
213. #3228C2×C37semidirect
214. #2981C2×C37semidirect
215. #1697C2×C37semidirect
216. #1691C2×C37semidirect
217. #1681C2×C37semidirect
218. #1675C2×C37semidirect
219. #1571C2×C37semidirect
220. #1559C2×C37semidirect
221. #1551C2×C37semidirect
261. C37#19519direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32532
C37×#32462
C37×#32282
C37×#29812
C37×#16972
C37×#16912
C37×#16812
C37×#16752
C37×#15712
C37×#15592
C37×#15512
#1951937