Finite Group Databasebeta

← C37×#61292 #22682545

Subgroups — C37×#61292 #22682545

Order 9472.

1746 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3507C212yesmaximal
2C37×#3349C218yesmaximal, complemented
3C37×#3344C218yesmaximal, complemented
4C37×#3162C211yesmaximal, characteristic, complemented
5C37×#3097C214yesmaximal, complemented
6C37×#3078C212yesmaximal, complemented
7C37×#3059C212yesmaximal, complemented
8C2×C37×#441C211yesmaximal, characteristic, complemented
9C37×#2932C211yesmaximal, characteristic
10C37×#2912C212yesmaximal, complemented
11C22×Q16×C37C2211yescharacteristic
12C2×#131×C37C2212yes—
13C37×#559—22no—
14C37×#557—22no—
15C37×#556—24no—
16C37×#556C2214yes—
17C37×#554C2214yes—
18C37×#552C2218yes—
19C37×#539—24no—
20C37×#536C2214yes—
21C37×#533C2212yes—
22C37×#532C2211yescharacteristic
23C37×#529—24no—
24C37×#520C2214yes—
25C2×C4×Q8×C37C2212yes—
26C37×#501C2214yes—
27C37×#501C2214yes—
28C37×#485C2218yes—
29C37×#485C2218yes—
30C37×#484C2218yes—
31C37×#483C2218yes—
32C37×#479C2218yes—
33C37×#477C2214yes—
34C37×#475C2214yes—
35C37×#470C2214yes—
36C37×#470C2214yes—
37C37×#467C2218yes—
38C37×#441C2218yes—
39C37×#435C2218yes—
40C37×#428C2214yes—
41C37×#428C2218yes—
42C37×#427C2212yes—
43C37×#427C2212yes—
44C37×#427C2214yes—
45C2×#106×C37C2211yescharacteristic
46C2×#106×C37C2214yes—
47C37×#423C2211yescharacteristic
48C37×#419C2214yes—
49C2×#103×C37C2212yes—
50C37×#408C2212yes—
51C2×#97×C37C2211yescharacteristic
52C2×#41×C37C2312yes—
53C22×Q8×C37C2312yes—
54C2×Q16×C37—24no—
55C2×Q16×C37C2314yes—
56#131×C37—28no—
57C2×M16×C37C2312yes—
58C2×M16×C37C2314yes—
59C22×C8×C37C2314yes—
60C22×C8×C37C2311yescharacteristic
61C22×C8×C37C2311yescharacteristic
62C4⋊Q8×C37—24no—
63C4⋊Q8×C37D411yescharacteristic
64C4⋊Q8×C37C2312yes—
65C4⋊Q8×C37C2312yes—
66#127×C37D411yescharacteristic
67#126×C37—28no—
68#126×C37—28no—
69#125×C37—24no—
70#125×C37—28no—
71#125×C37C2314yes—
72#124×C37—24no—
73#124×C37—24no—
74#124×C37D412yes—
75#123×C37—28no—
76#123×C37—28no—
77C22⋊Q8×C37—22no—
78C22⋊Q8×C37—22no—
79C22⋊Q8×C37—28no—
80C22⋊Q8×C37C2318yes—
81C22⋊Q8×C37C2318yes—
82#121×C37D414yes—
83C4×Q8×C37—24no—
84C4×Q8×C37—24no—
85C4×Q8×C37—22no—
86C4×Q8×C37—22no—
87C4×Q8×C37—22no—
88C4×Q8×C37—22no—
89C4×Q8×C37C2314yes—
90C4×Q8×C37C2314yes—
91C4×D4×C37—28no—
92C4×D4×C37—24no—
93C4×D4×C37—24no—
94C4×D4×C37C2314yes—
95#117×C37—28no—
96#117×C37C2314yes—
97#117×C37C2318yes—
98C2×C4⋊C4×C37—22no—
99C2×C4⋊C4×C37C2312yes—
100C2×C4⋊C4×C37C2318yes—
101C2×C42×C37—22no—
102C2×C42×C37C2311yescharacteristic
103#107×C37C2314yes—
104#107×C37C2318yes—
105#107×C37C2314yes—
106#106×C37C2314yes—
107#106×C37C2312yes—
108#106×C37C2318yes—
109#106×C37C2312yes—
110#106×C37C2312yes—
111#106×C37C2312yes—
112C4⋊C8×C37C2314yes—
113#103×C37C2318yes—
114#103×C37C2318yes—
115#103×C37C2318yes—
116C22⋊C8×C37C2318yes—
117#97×C37C2314yes—
118#41×C37—24no—
119#41×C37—24no—
120C2×Q8×C37—22no—
121C2×Q8×C37—22no—
122C2×Q8×C37—22no—
123C2×Q8×C37—24no—
124C2×Q8×C37—24no—
125C2×Q8×C37C2×D412yes—
126C2×Q8×C37C2414yes—
127C2×D4×C37C2×D414yes—
128C2×D4×C37C2×D412yes—
129C2×D4×C37C2×D414yes—
130C22×C4×C37—22no—
131C22×C4×C37—22no—
132C22×C4×C37—28no—
133C22×C4×C37C2×D412yes—
134C22×C4×C37C2414yes—
135C22×C4×C37C2411yescharacteristic
136Q16×C37—28no—
137M16×C37—24no—
138M16×C37—28no—
139C2×C8×C37—22no—
140C2×C8×C37—28no—
141C2×C8×C37#4114yes—
142C2×C8×C37C2412yes—
143C2×C8×C37C2414yes—
144C2×C8×C37C2412yes—
145C4⋊C4×C37—24no—
146C4⋊C4×C37—24no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—28no—
149C4⋊C4×C37—24no—
150C4⋊C4×C37—28no—
151C4⋊C4×C37—22no—
152C4⋊C4×C37—24no—
153C4⋊C4×C37—22no—
154C4⋊C4×C37—28no—
155C4⋊C4×C37C2×D414yes—
156C4⋊C4×C37C2414yes—
157C4⋊C4×C37C2414yes—
158C4⋊C4×C37C2414yes—
159C22⋊C4×C37—28no—
160C22⋊C4×C37—24no—
161C22⋊C4×C37—28no—
162C22⋊C4×C37—28no—
163C22⋊C4×C37C2×D418yes—
164C42×C37—24no—
165C42×C37—24no—
166C42×C37—28no—
167C42×C37—24no—
168C42×C37C2×D411yescharacteristic
169C42×C37C2×D411yescharacteristic
170C42×C37C2412yes—
171C23×C37C22×D414yes—
172C23×C37C22×D411yescharacteristic
173Q8×C37—24no—
174Q8×C37—24no—
175Q8×C37—24no—
176Q8×C37—44no—
177Q8×C37—44no—
178Q8×C37—82no—
179D4×C37—28no—
180D4×C37—24no—
181D4×C37—44no—
182C2×C4×C37—24no—
183C2×C4×C37—24no—
184C2×C4×C37—24no—
185C2×C4×C37—24no—
186C2×C4×C37—24no—
187C2×C4×C37—24no—
188C2×C4×C37—42no—
189C2×C4×C37—44no—
190C2×C4×C37—82no—
191C2×C4×C37—88no—
192C2×C4×C37C22×D412yes—
193C2×C4×C37C22×D412yes—
194C2×C4×C37C22×D414yes—
195C2×C4×C37C22×D411yescharacteristic
196C2×C4×C37C2×#4112yes—
197C2×C4×C372−1+412yes—
198C2×C4×C37C2511yescharacteristic
199C8×C37—24no—
200C8×C37—22no—
201C8×C37C2×#4114yes—
202#61292C3711yesmaximal, characteristic, direct product factor, Sylow
203C22×C37—22no—
204C22×C37—28no—
205C22×C37—24no—
206C22×C37#54712yes—
207C22×C37C23×D411yescharacteristic
208C4×C37—22no—
209C4×C37—22no—
210C4×C37—24no—
211C4×C37—44no—
212C4×C37—44no—
213C4×C37—44no—
214C4×C37—44no—
215C4×C37#54712yes—
216C4×C37C22×#4111yescharacteristic
217C4×C37C2×2−1+411yescharacteristic
218#3507C2×C3712yes—
219#3349C2×C3718yescomplemented
220#3344C2×C3718yescomplemented
221#3162C2×C3711yescharacteristic, complemented
222#3097C2×C3714yescomplemented
223#3078C2×C3712yescomplemented
224#3059C2×C3712yescomplemented
225C2×#441C2×C3711yescharacteristic, complemented
226#2932C2×C3711yescharacteristic
227#2912C2×C3712yescomplemented
228C2×C37—22no—
229C2×C37—44no—
230C2×C37C2×#54711yescharacteristic
231C2×C37#358612yes—
232C22×Q16C22×C3711yescharacteristic
233C2×#131C22×C3712yes—
234#559—22no—
235#557—22no—
236#556—24no—
237#556C22×C3714yes—
238#554C22×C3714yes—
239#552C22×C3718yes—
240#539—24no—
241#536C22×C3714yes—
242#533C22×C3712yes—
243#532C22×C3711yescharacteristic
244#529—24no—
245#520C22×C3714yes—
246C2×C4×Q8C22×C3712yes—
247#501C22×C3714yes—
248#501C22×C3714yes—
249#485C22×C3718yes—
250#485C22×C3718yes—
251#484C22×C3718yes—
252#483C22×C3718yes—
253#479C22×C3718yes—
254#477C22×C3714yes—
255#475C22×C3714yes—
256#470C22×C3714yes—
257#470C22×C3714yes—
258#467C22×C3718yes—
259#441C22×C3718yes—
260#435C22×C3718yes—
261#428C22×C3714yes—
262#428C22×C3718yes—
263#427C22×C3714yes—
264#427C22×C3712yes—
265#427C22×C3712yes—
266C2×#106C22×C3714yes—
267C2×#106C22×C3711yescharacteristic
268#423C22×C3711yescharacteristic
269#419C22×C3714yes—
270C2×#103C22×C3712yes—
271#408C22×C3712yes—
272C2×#97C22×C3711yescharacteristic
273C37#6129211yescharacteristic, direct product factor, Sylow
274C2×#41C23×C3712yes—
275C22×Q8C23×C3712yes—
276C2×Q16—24no—
277C2×Q16C23×C3714yes—
278#131—28no—
279C2×M16C23×C3712yes—
280C2×M16C23×C3714yes—
281C22×C8C23×C3714yes—
282C22×C8C23×C3711yescharacteristic
283C22×C8C23×C3711yescharacteristic
284C4⋊Q8—24no—
285C4⋊Q8D4×C3711yescharacteristic
286C4⋊Q8C23×C3712yes—
287C4⋊Q8C23×C3712yes—
288#127D4×C3711yescharacteristic
289#126—28no—
290#126—28no—
291#125—24no—
292#125—28no—
293#125C23×C3714yes—
294#124—24no—
295#124—24no—
296#124D4×C3712yes—
297#123—28no—
298#123—28no—
299C22⋊Q8—22no—
300C22⋊Q8—22no—
301C22⋊Q8—28no—
302C22⋊Q8C23×C3718yes—
303C22⋊Q8C23×C3718yes—
304#121D4×C3714yes—
305C4×Q8—24no—
306C4×Q8—24no—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8C23×C3714yes—
312C4×Q8C23×C3714yes—
313C4×D4—28no—
314C4×D4—24no—
315C4×D4—24no—
316C4×D4C23×C3714yes—
317#117—28no—
318#117C23×C3714yes—
319#117C23×C3718yes—
320C2×C4⋊C4—22no—
321C2×C4⋊C4C23×C3712yes—
322C2×C4⋊C4C23×C3718yes—
323C2×C42—22no—
324C2×C42C23×C3711yescharacteristic
325#107C23×C3714yes—
326#107C23×C3718yes—
327#107C23×C3714yes—
328#106C23×C3714yes—
329#106C23×C3712yes—
330#106C23×C3718yes—
331#106C23×C3712yes—
332#106C23×C3712yes—
333#106C23×C3712yes—
334C4⋊C8C23×C3714yes—
335#103C23×C3718yes—
336#103C23×C3718yes—
337#103C23×C3718yes—
338C22⋊C8C23×C3718yes—
339#97C23×C3714yes—
340#41—24no—
341#41—24no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—24no—
346C2×Q8—24no—
347C2×Q8C2×D4×C3712yes—
348C2×Q8C24×C3714yes—
349C2×D4C2×D4×C3714yes—
350C2×D4C2×D4×C3712yes—
351C2×D4C2×D4×C3714yes—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—28no—
355C22×C4C2×D4×C3712yes—
356C22×C4C24×C3714yes—
357C22×C4C24×C3711yescharacteristic
358Q16—28no—
359M16—24no—
360M16—28no—
361C2×C8—22no—
362C2×C8—28no—
363C2×C8#41×C3714yes—
364C2×C8C24×C3712yes—
365C2×C8C24×C3714yes—
366C2×C8C24×C3712yes—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—28no—
371C4⋊C4—24no—
372C4⋊C4—28no—
373C4⋊C4—22no—
374C4⋊C4—24no—
375C4⋊C4—22no—
376C4⋊C4—28no—
377C4⋊C4C2×D4×C3714yes—
378C4⋊C4C24×C3714yes—
379C4⋊C4C24×C3714yes—
380C4⋊C4C24×C3714yes—
381C22⋊C4—28no—
382C22⋊C4—24no—
383C22⋊C4—28no—
384C22⋊C4—28no—
385C22⋊C4C2×D4×C3718yes—
386C42—24no—
387C42—24no—
388C42—28no—
389C42—24no—
390C42C2×D4×C3711yescharacteristic
391C42C2×D4×C3711yescharacteristic
392C42C24×C3712yes—
393C23C22×D4×C3714yes—
394C23C22×D4×C3711yescharacteristic
395Q8—24no—
396Q8—24no—
397Q8—24no—
398Q8—44no—
399Q8—44no—
400Q8—82no—
401D4—28no—
402D4—24no—
403D4—44no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—82no—
413C2×C4—88no—
414C2×C4C22×D4×C3712yes—
415C2×C4C22×D4×C3712yes—
416C2×C4C22×D4×C3714yes—
417C2×C4C22×D4×C3711yescharacteristic
418C2×C4C2×#41×C3712yes—
419C2×C42−1+4×C3712yes—
420C2×C4C25×C3711yescharacteristic
421C8—24no—
422C8—22no—
423C8C2×#41×C3714yes—
424C22—22no—
425C22—24no—
426C22—28no—
427C22C37×#54712yes—
428C22C23×D4×C3711yescharacteristic
429C4—24no—
430C4—22no—
431C4—22no—
432C4—44no—
433C4—44no—
434C4—44no—
435C4—44no—
436C4C37×#54712yes—
437C4C22×#41×C3711yescharacteristic
438C4C2×2−1+4×C3711yescharacteristic
439C2—22no—
440C2—44no—
441C2C2×C37×#54711yescharacteristic
442C2C37×#358612yes—
subgroupG/H
center, socleC22×C37C23×D4
commutator, Frattini, cosocleC2×C4C25×C37
prime radicalC37×#532C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C37×#532 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3349C2semidirect
3. C37×#3344C2semidirect
4. C37×#3162C2semidirect
5. C37×#3097C2semidirect
6. C37×#3078C2semidirect
7. C37×#3059C2semidirect
8. C2×C37×#441C2semidirect
10. C37×#2912C2semidirect
202. #61292C37direct (N × H)
219. #3349C2×C37semidirect
220. #3344C2×C37semidirect
221. #3162C2×C37semidirect
222. #3097C2×C37semidirect
223. #3078C2×C37semidirect
224. #3059C2×C37semidirect
225. C2×#441C2×C37semidirect
227. #2912C2×C37semidirect
273. C37#61292direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35072
C37×#33492
C37×#33442
C37×#31622
C37×#30972
C37×#30782
C37×#30592
C2×C37×#4412
C37×#29322
C37×#29122
#6129237