Finite Group Databasebeta

← C37×#19511 #22640764

Subgroups — C37×#19511 #22640764

Order 9472.

614 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3254C211yesmaximal, characteristic, complemented
2C37×#3245C211yesmaximal, characteristic
3C37×#3210C211yesmaximal, characteristic, complemented
4C37×#2981C211yesmaximal, characteristic, complemented
5C37×#1699C212yesmaximal, complemented
6C37×#1685C212yesmaximal, complemented
7C37×#1681C212yesmaximal, complemented
8C37×#1669C212yesmaximal, complemented
9C37×#1571C211yesmaximal, characteristic, complemented
10C37×#1557C211yesmaximal, characteristic, complemented
11C37×#1552C211yesmaximal, characteristic, complemented
12C37×#533C2211yescharacteristic
13C37×#532C2211yescharacteristic
14C37×#532C2211yescharacteristic
15C37×#494C2211yescharacteristic
16C37×#492C2211yescharacteristic
17C37×#487C2211yescharacteristic
18C37×#486C2211yescharacteristic
19C37×#477—21no—
20C37×#474—21no—
21C37×#474C2212yes—
22C37×#474C2212yes—
23C37×#468—22no—
24C37×#466—22no—
25C37×#464—22no—
26C37×#461C2212yes—
27C37×#460—21no—
28C37×#459—21no—
29C37×#459C2212yes—
30C37×#452—22no—
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×#332C2212yes—
42C37×#332C2212yes—
43C37×#332C2212yes—
44C37×#331C2212yes—
45C2×#41×C37—21no—
46C2×#41×C37—21no—
47C2×Q16×C37—22no—
48C2×SD16×C37—22no—
49C2×SD16×C37—22no—
50C2×D8×C37—22no—
51C2×M16×C37—21no—
52C2×M16×C37—22no—
53C22×C8×C37—21no—
54C22×C8×C37—22no—
55C4⋊Q8×C37D411yescharacteristic
56C4⋊Q8×C37C2311yescharacteristic
57C4⋊Q8×C37C2311yescharacteristic
58C4⋊Q8×C37C2311yescharacteristic
59#127×C37D411yescharacteristic
60#127×C37C2311yescharacteristic
61#125×C37—21no—
62#124×C37—21no—
63#124×C37—21no—
64C22⋊Q8×C37—21no—
65C22⋊Q8×C37—21no—
66#121×C37—21no—
67#121×C37—21no—
68#121×C37—21no—
69#121×C37D412yes—
70C4×Q8×C37—21no—
71C4×Q8×C37—21no—
72C4×D4×C37—21no—
73C4×D4×C37—21no—
74C4×D4×C37—21no—
75C4×D4×C37C2312yes—
76#117×C37—21no—
77C2×C42×C37C2311yescharacteristic
78#107×C37—22no—
79#107×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#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
118Q16×C37—82no—
119SD16×C37—82no—
120SD16×C37—82no—
121D8×C37—82no—
122M16×C37—82no—
123M16×C37—81no—
124C2×C8×C37—22no—
125C2×C8×C37—22no—
126C2×C8×C37—22no—
127C2×C8×C37—82no—
128C2×C8×C37—81no—
129C2×C8×C37C2×D412yes—
130C2×C8×C37C2×D412yes—
131C4⋊C4×C37—21no—
132C4⋊C4×C37—21no—
133C4⋊C4×C37—21no—
134C4⋊C4×C37—21no—
135C4⋊C4×C37—21no—
136C4⋊C4×C37—21no—
137C4⋊C4×C37—21no—
138C4⋊C4×C37—41no—
139C4⋊C4×C37—41no—
140C4⋊C4×C37C2×D412yes—
141C22⋊C4×C37—22no—
142C22⋊C4×C37—22no—
143C22⋊C4×C37—41no—
144C22⋊C4×C37—41no—
145C22⋊C4×C37—41no—
146C42×C37—41no—
147C42×C37C2×D411yescharacteristic
148C42×C37C2×D411yescharacteristic
149C42×C37#4111yescharacteristic
150C42×C37C2411yescharacteristic
151C23×C37—22no—
152C23×C37—41no—
153C23×C37#12111yescharacteristic
154Q8×C37—41no—
155Q8×C37—42no—
156Q8×C37—42no—
157Q8×C37—41no—
158Q8×C37—81no—
159D4×C37—22no—
160D4×C37—22no—
161D4×C37—41no—
162D4×C37—42no—
163D4×C37—41no—
164D4×C37—81no—
165D4×C37—81no—
166D4×C37—81no—
167D4×C37—82no—
168D4×C37—82no—
169C2×C4×C37—21no—
170C2×C4×C37—22no—
171C2×C4×C37—21no—
172C2×C4×C37—22no—
173C2×C4×C37—41no—
174C2×C4×C37—42no—
175C2×C4×C37—42no—
176C2×C4×C37—41no—
177C2×C4×C37—41no—
178C2×C4×C37—41no—
179C2×C4×C37—82no—
180C2×C4×C37#12111yescharacteristic
181C2×C4×C37#12111yescharacteristic
182C2×C4×C37#12111yescharacteristic
183C2×C4×C37C22×D411yescharacteristic
184C2×C4×C37C22×D411yescharacteristic
185C2×C4×C37C2×#4111yescharacteristic
186C8×C37—22no—
187C8×C37—22no—
188C8×C37—42no—
189C8×C37—42no—
190C8×C37—42no—
191#19511C3711yesmaximal, characteristic, direct product factor, Sylow
192C22×C37—21no—
193C22×C37—21no—
194C22×C37—21no—
195C22×C37—42no—
196C22×C37—42no—
197C22×C37—42no—
198C22×C37—81no—
199C22×C37—81no—
200C22×C37—81no—
201C22×C37C2×#12111yescharacteristic
202C4×C37—21no—
203C4×C37—21no—
204C4×C37—21no—
205C4×C37—21no—
206C4×C37—42no—
207C4×C37—81no—
208C4×C37—81no—
209C4×C37—81no—
210C4×C37#57612yes—
211C4×C37#57611yescharacteristic
212C4×C37#57811yescharacteristic
213#3254C2×C3711yescharacteristic, complemented
214#3245C2×C3711yescharacteristic
215#3210C2×C3711yescharacteristic, complemented
216#2981C2×C3711yescharacteristic, complemented
217#1699C2×C3712yescomplemented
218#1685C2×C3712yescomplemented
219#1681C2×C3712yescomplemented
220#1669C2×C3712yescomplemented
221#1571C2×C3711yescharacteristic, complemented
222#1557C2×C3711yescharacteristic, complemented
223#1552C2×C3711yescharacteristic, complemented
224C2×C37—41no—
225C2×C37—82no—
226C2×C37—161no—
227C2×C37#304111yescharacteristic
228C2×C37#306111yescharacteristic
229C2×C37#306911yescharacteristic
230#533C22×C3711yescharacteristic
231#532C22×C3711yescharacteristic
232#532C22×C3711yescharacteristic
233#494C22×C3711yescharacteristic
234#492C22×C3711yescharacteristic
235#487C22×C3711yescharacteristic
236#486C22×C3711yescharacteristic
237#477—21no—
238#474—21no—
239#474C22×C3712yes—
240#474C22×C3712yes—
241#468—22no—
242#466—22no—
243#464—22no—
244#461C22×C3712yes—
245#460—21no—
246#459—21no—
247#459C22×C3712yes—
248#452—22no—
249#436C22×C3712yes—
250#435—22no—
251C8×D4C22×C3712yes—
252#432C22×C3711yescharacteristic
253#431C22×C3711yescharacteristic
254#423C22×C3711yescharacteristic
255C2×C4⋊C8C22×C3711yescharacteristic
256#408—22no—
257#335C22×C3712yes—
258#335C22×C3712yes—
259#332C22×C3712yes—
260#332C22×C3712yes—
261#332C22×C3712yes—
262#331C22×C3712yes—
263C37#1951111yescharacteristic, direct product factor, Sylow
264C2×#41—21no—
265C2×#41—21no—
266C2×Q16—22no—
267C2×SD16—22no—
268C2×SD16—22no—
269C2×D8—22no—
270C2×M16—21no—
271C2×M16—22no—
272C22×C8—21no—
273C22×C8—22no—
274C4⋊Q8D4×C3711yescharacteristic
275C4⋊Q8C23×C3711yescharacteristic
276C4⋊Q8C23×C3711yescharacteristic
277C4⋊Q8C23×C3711yescharacteristic
278#127D4×C3711yescharacteristic
279#127C23×C3711yescharacteristic
280#125—21no—
281#124—21no—
282#124—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285#121—21no—
286#121—21no—
287#121—21no—
288#121D4×C3712yes—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4C23×C3712yes—
295#117—21no—
296C2×C42C23×C3711yescharacteristic
297#107—22no—
298#107—22no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8D4×C3712yes—
302C4⋊C8C23×C3712yes—
303C4⋊C8C23×C3712yes—
304C4⋊C8C23×C3712yes—
305#103—22no—
306#103—22no—
307#102—22no—
308#102—22no—
309#102—22no—
310#102—22no—
311C22⋊C8—21no—
312C22⋊C8—22no—
313C22⋊C8—22no—
314C22⋊C8D4×C3712yes—
315#97—21no—
316C4×C8C23×C3711yescharacteristic
317C4×C8C23×C3711yescharacteristic
318#41—82no—
319#41—82no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×D4—22no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—41no—
331C2×D4C2×D4×C3712yes—
332C22×C4—22no—
333C22×C4—41no—
334C22×C4C2×D4×C3711yescharacteristic
335C22×C4C2×D4×C3711yescharacteristic
336C22×C4#41×C3711yescharacteristic
337Q16—82no—
338SD16—82no—
339SD16—82no—
340D8—82no—
341M16—82no—
342M16—81no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—82no—
347C2×C8—81no—
348C2×C8C2×D4×C3712yes—
349C2×C8C2×D4×C3712yes—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4C2×D4×C3712yes—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C42—41no—
366C42C2×D4×C3711yescharacteristic
367C42C2×D4×C3711yescharacteristic
368C42#41×C3711yescharacteristic
369C42C24×C3711yescharacteristic
370C23—22no—
371C23—41no—
372C23#121×C3711yescharacteristic
373Q8—41no—
374Q8—42no—
375Q8—42no—
376Q8—41no—
377Q8—81no—
378D4—22no—
379D4—22no—
380D4—41no—
381D4—42no—
382D4—41no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—82no—
387D4—82no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—82no—
399C2×C4#121×C3711yescharacteristic
400C2×C4#121×C3711yescharacteristic
401C2×C4#121×C3711yescharacteristic
402C2×C4C22×D4×C3711yescharacteristic
403C2×C4C22×D4×C3711yescharacteristic
404C2×C4C2×#41×C3711yescharacteristic
405C8—22no—
406C8—22no—
407C8—42no—
408C8—42no—
409C8—42no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—42no—
414C22—42no—
415C22—42no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22C2×#121×C3711yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—81no—
427C4—81no—
428C4C37×#57612yes—
429C4C37×#57611yescharacteristic
430C4C37×#57811yescharacteristic
431C2—41no—
432C2—82no—
433C2—161no—
434C2C37×#304111yescharacteristic
435C2C37×#306111yescharacteristic
436C2C37×#306911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3245C2
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
1. C37×#3254C2semidirect
3. C37×#3210C2semidirect
4. C37×#2981C2semidirect
5. C37×#1699C2semidirect
6. C37×#1685C2semidirect
7. C37×#1681C2semidirect
8. C37×#1669C2semidirect
9. C37×#1571C2semidirect
10. C37×#1557C2semidirect
11. C37×#1552C2semidirect
191. #19511C37direct (N × H)
213. #3254C2×C37semidirect
215. #3210C2×C37semidirect
216. #2981C2×C37semidirect
217. #1699C2×C37semidirect
218. #1685C2×C37semidirect
219. #1681C2×C37semidirect
220. #1669C2×C37semidirect
221. #1571C2×C37semidirect
222. #1557C2×C37semidirect
223. #1552C2×C37semidirect
263. C37#19511direct (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×#32452
C37×#32102
C37×#29812
C37×#16992
C37×#16852
C37×#16812
C37×#16692
C37×#15712
C37×#15572
C37×#15522
#1951137