Finite Group Databasebeta

← C37×#29889 #22651142

Subgroups — C37×#29889 #22651142

Order 9472.

596 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
1C2×C37×#501C211yesmaximal, characteristic, complemented
2C37×#3080C211yesmaximal, characteristic
3C37×#3079C211yesmaximal, characteristic
4C37×#2923C211yesmaximal, characteristic
5C37×#2090C212yesmaximal, complemented
6C37×#2089C212yesmaximal, complemented
7C37×#2079C212yesmaximal
8C37×#2078C212yesmaximal
9C37×#1998C211yesmaximal, characteristic, complemented
10C37×#1997C211yesmaximal, characteristic, complemented
11C37×#1838C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C37C2211yescharacteristic
13C2×#125×C37C2211yescharacteristic
14C4×#41×C37C2211yescharacteristic
15C37×#501—22no—
16C37×#501—22no—
17C37×#479—21no—
18C37×#479—21no—
19C37×#478—21no—
20C37×#478—21no—
21C37×#477—21no—
22C37×#476—21no—
23C37×#475—21no—
24C37×#474—21no—
25C37×#433—22no—
26C37×#432—22no—
27C37×#428C2212yes—
28C37×#428C2211yescharacteristic
29C37×#428C2211yescharacteristic
30C2×#107×C37C2212yes—
31C2×#106×C37C2212yes—
32C37×#424C2212yes—
33C37×#423C2211yescharacteristic
34C37×#423C2211yescharacteristic
35C37×#417C2212yes—
36C37×#417C2211yescharacteristic
37C37×#417C2211yescharacteristic
38C37×#408C2212yes—
39C4×M16×C37C2211yescharacteristic
40C2×#97×C37C2211yescharacteristic
41C37×#343C2212yes—
42C37×#343C2212yes—
43C37×#343C2212yes—
44C37×#343C2212yes—
45C37×#341C2212yes—
46C37×#341C2212yes—
47C2×#41×C37C2311yescharacteristic
48C22×Q8×C37—21no—
49C2×M16×C37C2311yescharacteristic
50C2×M16×C37C2312yes—
51C2×M16×C37C2311yescharacteristic
52C2×M16×C37C2312yes—
53C22×C8×C37C2312yes—
54C4⋊Q8×C37—21no—
55C4⋊Q8×C37—21no—
56C4⋊Q8×C37—21no—
57C4⋊Q8×C37—21no—
58#125×C37—21no—
59#125×C37—21no—
60#125×C37—21no—
61#125×C37—21no—
62C4×Q8×C37D411yescharacteristic
63C4×Q8×C37D411yescharacteristic
64C4×D4×C37—21no—
65C4×D4×C37—21no—
66C4×D4×C37D411yescharacteristic
67C4×D4×C37D411yescharacteristic
68#117×C37—21no—
69#117×C37C2311yescharacteristic
70C2×C4⋊C4×C37—21no—
71C2×C4⋊C4×C37—21no—
72C2×C4⋊C4×C37—21no—
73C2×C4⋊C4×C37C2311yescharacteristic
74C2×C4⋊C4×C37C2311yescharacteristic
75C2×C4⋊C4×C37C2312yes—
76C2×C42×C37—21no—
77C2×C42×C37C2311yescharacteristic
78#107×C37—24no—
79#107×C37—22no—
80#107×C37—21no—
81#107×C37—21no—
82#106×C37—24no—
83#106×C37—22no—
84#106×C37—21no—
85#106×C37—21no—
86C4⋊C8×C37—24no—
87C4⋊C8×C37—21no—
88C4⋊C8×C37—21no—
89C4⋊C8×C37—21no—
90C4⋊C8×C37—21no—
91#103×C37—22no—
92#103×C37—21no—
93#103×C37—21no—
94#102×C37—22no—
95#102×C37—21no—
96#102×C37—21no—
97C22⋊C8×C37—24no—
98#97×C37—21no—
99#97×C37D412yes—
100#97×C37D412yes—
101C4×C8×C37—21no—
102#41×C37—22no—
103#41×C37—22no—
104C2×Q8×C37—41no—
105C2×Q8×C37—41no—
106C2×Q8×C37—82no—
107C2×Q8×C37C2×D411yescharacteristic
108C2×D4×C37—21no—
109C2×D4×C37C2×D411yescharacteristic
110C22×C4×C37—21no—
111C22×C4×C37—21no—
112C22×C4×C37—21no—
113C22×C4×C37—21no—
114C22×C4×C37—21no—
115C22×C4×C37—22no—
116C22×C4×C37#4111yescharacteristic
117C22×C4×C37#4111yescharacteristic
118C22×C4×C37C2411yescharacteristic
119M16×C37—22no—
120M16×C37—24no—
121M16×C37—22no—
122M16×C37—22no—
123M16×C37—22no—
124C2×C8×C37—22no—
125C2×C8×C37—22no—
126C2×C8×C37—22no—
127C2×C8×C37—22no—
128C2×C8×C37—21no—
129C2×C8×C37—21no—
130C2×C8×C37C2×D414yes—
131C4⋊C4×C37—21no—
132C4⋊C4×C37—21no—
133C4⋊C4×C37—21no—
134C4⋊C4×C37—21no—
135C4⋊C4×C37—22no—
136C4⋊C4×C37—21no—
137C4⋊C4×C37—22no—
138C4⋊C4×C37—21no—
139C4⋊C4×C37—41no—
140C4⋊C4×C37—41no—
141C4⋊C4×C37—41no—
142C4⋊C4×C37—41no—
143C4⋊C4×C37—41no—
144C4⋊C4×C37—41no—
145C4⋊C4×C37C2×D411yescharacteristic
146C4⋊C4×C37C2×D411yescharacteristic
147C22⋊C4×C37—21no—
148C22⋊C4×C37—21no—
149C22⋊C4×C37—21no—
150C42×C37—21no—
151C42×C37—21no—
152C42×C37—21no—
153C42×C37C2×D411yescharacteristic
154C42×C37C2×D411yescharacteristic
155C42×C37C2×D411yescharacteristic
156C42×C37C2×D411yescharacteristic
157C23×C37—21no—
158C23×C37C2×#4111yescharacteristic
159Q8×C37—21no—
160Q8×C37—21no—
161Q8×C37—82no—
162Q8×C37—82no—
163D4×C37—21no—
164D4×C37—21no—
165D4×C37—42no—
166C2×C4×C37—21no—
167C2×C4×C37—21no—
168C2×C4×C37—21no—
169C2×C4×C37—41no—
170C2×C4×C37—41no—
171C2×C4×C37—42no—
172C2×C4×C37—41no—
173C2×C4×C37—41no—
174C2×C4×C37—42no—
175C2×C4×C37—81no—
176C2×C4×C37—81no—
177C2×C4×C37—81no—
178C2×C4×C37—81no—
179C2×C4×C37—82no—
180C2×C4×C37#12111yescharacteristic
181C2×C4×C37#12111yescharacteristic
182C2×C4×C37#12111yescharacteristic
183C2×C4×C37#12111yescharacteristic
184C2×C4×C37C22×D411yescharacteristic
185C2×C4×C37C22×D411yescharacteristic
186C2×C4×C372−1+412yes—
187C2×C4×C372−1+412yes—
188C8×C37—24no—
189C8×C37—42no—
190C8×C37—42no—
191C8×C37—41no—
192C8×C37—41no—
193#29889C3711yesmaximal, characteristic, direct product factor, Sylow
194C22×C37—21no—
195C22×C37—21no—
196C22×C37—41no—
197C22×C37—41no—
198C22×C37—41no—
199C22×C37C2×#12111yescharacteristic
200C22×C37#54112yes—
201C4×C37—21no—
202C4×C37—21no—
203C4×C37—21no—
204C4×C37—21no—
205C4×C37—41no—
206C4×C37—41no—
207C4×C37—41no—
208C4×C37—81no—
209C4×C37—82no—
210C4×C37—81no—
211C4×C37#53612yes—
212C4×C37#53611yescharacteristic
213C4×C37#53611yescharacteristic
214C2×#501C2×C3711yescharacteristic, complemented
215#3080C2×C3711yescharacteristic
216#3079C2×C3711yescharacteristic
217#2923C2×C3711yescharacteristic
218#2090C2×C3712yescomplemented
219#2089C2×C3712yescomplemented
220#2079C2×C3712yes—
221#2078C2×C3712yes—
222#1998C2×C3711yescharacteristic, complemented
223#1997C2×C3711yescharacteristic, complemented
224#1838C2×C3711yescharacteristic, complemented
225C2×C37—22no—
226C2×C37—81no—
227C2×C37#262111yescharacteristic
228C2×C37#306811yescharacteristic
229C2×C37#306911yescharacteristic
230C2×C4⋊Q8C22×C3711yescharacteristic
231C2×#125C22×C3711yescharacteristic
232C4×#41C22×C3711yescharacteristic
233#501—22no—
234#501—22no—
235#479—21no—
236#479—21no—
237#478—21no—
238#478—21no—
239#477—21no—
240#476—21no—
241#475—21no—
242#474—21no—
243#433—22no—
244#432—22no—
245#428C22×C3712yes—
246#428C22×C3711yescharacteristic
247#428C22×C3711yescharacteristic
248C2×#107C22×C3712yes—
249C2×#106C22×C3712yes—
250#424C22×C3712yes—
251#423C22×C3711yescharacteristic
252#423C22×C3711yescharacteristic
253#417C22×C3712yes—
254#417C22×C3711yescharacteristic
255#417C22×C3711yescharacteristic
256#408C22×C3712yes—
257C4×M16C22×C3711yescharacteristic
258C2×#97C22×C3711yescharacteristic
259#343C22×C3712yes—
260#343C22×C3712yes—
261#343C22×C3712yes—
262#343C22×C3712yes—
263#341C22×C3712yes—
264#341C22×C3712yes—
265C37#2988911yescharacteristic, direct product factor, Sylow
266C2×#41C23×C3711yescharacteristic
267C22×Q8—21no—
268C2×M16C23×C3711yescharacteristic
269C2×M16C23×C3712yes—
270C2×M16C23×C3711yescharacteristic
271C2×M16C23×C3712yes—
272C22×C8C23×C3712yes—
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277#125—21no—
278#125—21no—
279#125—21no—
280#125—21no—
281C4×Q8D4×C3711yescharacteristic
282C4×Q8D4×C3711yescharacteristic
283C4×D4—21no—
284C4×D4—21no—
285C4×D4D4×C3711yescharacteristic
286C4×D4D4×C3711yescharacteristic
287#117—21no—
288#117C23×C3711yescharacteristic
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4C23×C3711yescharacteristic
293C2×C4⋊C4C23×C3711yescharacteristic
294C2×C4⋊C4C23×C3712yes—
295C2×C42—21no—
296C2×C42C23×C3711yescharacteristic
297#107—24no—
298#107—22no—
299#107—21no—
300#107—21no—
301#106—24no—
302#106—22no—
303#106—21no—
304#106—21no—
305C4⋊C8—24no—
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—21no—
310#103—22no—
311#103—21no—
312#103—21no—
313#102—22no—
314#102—21no—
315#102—21no—
316C22⋊C8—24no—
317#97—21no—
318#97D4×C3712yes—
319#97D4×C3712yes—
320C4×C8—21no—
321#41—22no—
322#41—22no—
323C2×Q8—41no—
324C2×Q8—41no—
325C2×Q8—82no—
326C2×Q8C2×D4×C3711yescharacteristic
327C2×D4—21no—
328C2×D4C2×D4×C3711yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4#41×C3711yescharacteristic
336C22×C4#41×C3711yescharacteristic
337C22×C4C24×C3711yescharacteristic
338M16—22no—
339M16—24no—
340M16—22no—
341M16—22no—
342M16—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8C2×D4×C3714yes—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4C2×D4×C3711yescharacteristic
365C4⋊C4C2×D4×C3711yescharacteristic
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C42—21no—
370C42—21no—
371C42—21no—
372C42C2×D4×C3711yescharacteristic
373C42C2×D4×C3711yescharacteristic
374C42C2×D4×C3711yescharacteristic
375C42C2×D4×C3711yescharacteristic
376C23—21no—
377C23C2×#41×C3711yescharacteristic
378Q8—21no—
379Q8—21no—
380Q8—82no—
381Q8—82no—
382D4—21no—
383D4—21no—
384D4—42no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—82no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4#121×C3711yescharacteristic
400C2×C4#121×C3711yescharacteristic
401C2×C4#121×C3711yescharacteristic
402C2×C4#121×C3711yescharacteristic
403C2×C4C22×D4×C3711yescharacteristic
404C2×C4C22×D4×C3711yescharacteristic
405C2×C42−1+4×C3712yes—
406C2×C42−1+4×C3712yes—
407C8—24no—
408C8—42no—
409C8—42no—
410C8—41no—
411C8—41no—
412C22—21no—
413C22—21no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22C2×#121×C3711yescharacteristic
418C22C37×#54112yes—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—41no—
424C4—41no—
425C4—41no—
426C4—82no—
427C4—81no—
428C4—81no—
429C4C37×#53612yes—
430C4C37×#53611yescharacteristic
431C4C37×#53611yescharacteristic
432C2—22no—
433C2—81no—
434C2C37×#262111yescharacteristic
435C2C37×#306811yescharacteristic
436C2C37×#306911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#41×C37C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#501C2semidirect
5. C37×#2090C2semidirect
6. C37×#2089C2semidirect
9. C37×#1998C2semidirect
10. C37×#1997C2semidirect
11. C37×#1838C2semidirect
193. #29889C37direct (N × H)
214. C2×#501C2×C37semidirect
218. #2090C2×C37semidirect
219. #2089C2×C37semidirect
222. #1998C2×C37semidirect
223. #1997C2×C37semidirect
224. #1838C2×C37semidirect
265. C37#29889direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5012
C37×#30802
C37×#30792
C37×#29232
C37×#20902
C37×#20892
C37×#20792
C37×#20782
C37×#19982
C37×#19972
C37×#18382
#2988937