Finite Group Databasebeta

← C37×#28735 #22649988

Subgroups — C37×#28735 #22649988

Order 9472.

674 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#501C211yesmaximal, characteristic, complemented
2C37×#3142C211yesmaximal, characteristic
3C37×#3141C211yesmaximal, characteristic
4C37×#2932C211yesmaximal, characteristic
5C37×#2079C212yesmaximal, complemented
6C37×#2078C212yesmaximal, complemented
7C37×#1998C211yesmaximal, characteristic, complemented
8C37×#1997C211yesmaximal, characteristic, complemented
9C37×#1816C212yesmaximal, complemented
10C37×#1815C212yesmaximal, complemented
11C37×#1778C211yesmaximal, characteristic, complemented
12C2×#131×C37C2212yes—
13C37×#532C2211yescharacteristic
14C2×C4⋊Q8×C37C2211yescharacteristic
15C2×#125×C37C2211yescharacteristic
16C37×#501—22no—
17C37×#501—22no—
18C37×#491—21no—
19C37×#490—21no—
20C37×#489—22no—
21C37×#488—22no—
22C37×#487—21no—
23C37×#486—21no—
24C37×#435—22no—
25C37×#435—22no—
26C2×#108×C37C2212yes—
27C2×#107×C37C2211yescharacteristic
28C2×#107×C37C2211yescharacteristic
29C2×#106×C37C2211yescharacteristic
30C2×#106×C37C2211yescharacteristic
31C37×#423C2211yescharacteristic
32C37×#417C2212yes—
33C37×#417C2212yes—
34C37×#417C2212yes—
35C37×#417C2212yes—
36C37×#408C2212yes—
37C4×M16×C37C2211yescharacteristic
38C4×M16×C37C2211yescharacteristic
39C2×#97×C37C2211yescharacteristic
40C37×#343C2212yes—
41C37×#343C2212yes—
42C37×#343C2212yes—
43C37×#343C2212yes—
44C37×#341C2212yes—
45C2×#41×C37C2312yes—
46C22×Q8×C37—21no—
47#131×C37—28no—
48C2×M16×C37—22no—
49C2×M16×C37C2312yes—
50C2×M16×C37C2312yes—
51C2×M16×C37C2312yes—
52C22×C8×C37—22no—
53C22×C8×C37C2311yescharacteristic
54C22×C8×C37C2311yescharacteristic
55C4⋊Q8×C37—21no—
56C4⋊Q8×C37—21no—
57C4⋊Q8×C37—21no—
58C4⋊Q8×C37—21no—
59C4⋊Q8×C37D411yescharacteristic
60#127×C37D411yescharacteristic
61#125×C37—21no—
62#125×C37—21no—
63#125×C37—21no—
64#125×C37—21no—
65#124×C37D412yes—
66#121×C37—21no—
67#121×C37—21no—
68C4×D4×C37—21no—
69C4×D4×C37—21no—
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×C37C2311yescharacteristic
76C2×C4⋊C4×C37C2311yescharacteristic
77C2×C42×C37C2311yescharacteristic
78#108×C37—24no—
79#107×C37—22no—
80#107×C37—22no—
81#106×C37—22no—
82#106×C37—22no—
83C4⋊C8×C37—21no—
84C4⋊C8×C37—21no—
85#103×C37—22no—
86#103×C37—22no—
87#103×C37—22no—
88#103×C37—22no—
89#102×C37—22no—
90#102×C37—22no—
91#102×C37—22no—
92#102×C37—22no—
93C22⋊C8×C37—24no—
94#97×C37—21no—
95#97×C37—21no—
96#97×C37D412yes—
97#97×C37D412yes—
98C4×C8×C37—21no—
99C4×C8×C37—21no—
100#41×C37—24no—
101#41×C37—24no—
102C2×Q8×C37—41no—
103C2×Q8×C37—41no—
104C2×Q8×C37—82no—
105C2×Q8×C37C2×D412yes—
106C2×D4×C37—22no—
107C2×D4×C37—21no—
108C2×D4×C37—21no—
109C2×D4×C37C2×D412yes—
110C22×C4×C37—22no—
111C22×C4×C37—21no—
112C22×C4×C37—21no—
113C22×C4×C37—21no—
114C22×C4×C37—21no—
115C22×C4×C37#4111yescharacteristic
116C22×C4×C37#4111yescharacteristic
117C22×C4×C37C2411yescharacteristic
118M16×C37—22no—
119M16×C37—22no—
120M16×C37—24no—
121M16×C37—22no—
122M16×C37—22no—
123M16×C37—44no—
124C2×C8×C37—22no—
125C2×C8×C37—22no—
126C2×C8×C37—22no—
127C2×C8×C37—22no—
128C2×C8×C37—44no—
129C2×C8×C37C2×D412yes—
130C2×C8×C37C2×D412yes—
131C2×C8×C37#4114yes—
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—21no—
139C4⋊C4×C37—21no—
140C4⋊C4×C37—21no—
141C4⋊C4×C37—21no—
142C4⋊C4×C37—41no—
143C4⋊C4×C37—41no—
144C4⋊C4×C37—41no—
145C4⋊C4×C37—41no—
146C4⋊C4×C37—41no—
147C4⋊C4×C37—41no—
148C22⋊C4×C37—22no—
149C22⋊C4×C37—22no—
150C42×C37C2×D411yescharacteristic
151C42×C37C2×D411yescharacteristic
152C42×C37C2×D411yescharacteristic
153C42×C37C2×D411yescharacteristic
154C23×C37—22no—
155C23×C37C2×#4111yescharacteristic
156Q8×C37—24no—
157Q8×C37—82no—
158Q8×C37—82no—
159D4×C37—24no—
160D4×C37—44no—
161D4×C37—81no—
162D4×C37—81no—
163C2×C4×C37—22no—
164C2×C4×C37—41no—
165C2×C4×C37—41no—
166C2×C4×C37—42no—
167C2×C4×C37—42no—
168C2×C4×C37—41no—
169C2×C4×C37—41no—
170C2×C4×C37—41no—
171C2×C4×C37—41no—
172C2×C4×C37—81no—
173C2×C4×C37—81no—
174C2×C4×C37—81no—
175C2×C4×C37—81no—
176C2×C4×C37#12111yescharacteristic
177C2×C4×C37#12111yescharacteristic
178C2×C4×C37#12111yescharacteristic
179C2×C4×C37#12111yescharacteristic
180C2×C4×C37C22×D411yescharacteristic
181C2×C4×C37C22×D411yescharacteristic
182C2×C4×C37C2×#4112yes—
183C2×C4×C372−1+412yes—
184C8×C37—22no—
185C8×C37—42no—
186C8×C37—42no—
187C8×C37—42no—
188C8×C37#12414yes—
189#28735C3711yesmaximal, characteristic, direct product factor, Sylow
190C22×C37—21no—
191C22×C37—21no—
192C22×C37—42no—
193C22×C37—42no—
194C22×C37—42no—
195C22×C37C2×#12111yescharacteristic
196C22×C37#55612yes—
197C4×C37—21no—
198C4×C37—21no—
199C4×C37—21no—
200C4×C37—21no—
201C4×C37—42no—
202C4×C37—81no—
203C4×C37—81no—
204C4×C37—81no—
205C4×C37—81no—
206C4×C37C2×#12411yescharacteristic
207C4×C37#53611yescharacteristic
208C4×C37#54712yes—
209C2×#501C2×C3711yescharacteristic, complemented
210#3142C2×C3711yescharacteristic
211#3141C2×C3711yescharacteristic
212#2932C2×C3711yescharacteristic
213#2079C2×C3712yescomplemented
214#2078C2×C3712yescomplemented
215#1998C2×C3711yescharacteristic, complemented
216#1997C2×C3711yescharacteristic, complemented
217#1816C2×C3712yescomplemented
218#1815C2×C3712yescomplemented
219#1778C2×C3711yescharacteristic, complemented
220C2×C37—22no—
221C2×C37—82no—
222C2×C37#254711yescharacteristic
223C2×C37#306811yescharacteristic
224C2×C37#306911yescharacteristic
225C2×#131C22×C3712yes—
226#532C22×C3711yescharacteristic
227C2×C4⋊Q8C22×C3711yescharacteristic
228C2×#125C22×C3711yescharacteristic
229#501—22no—
230#501—22no—
231#491—21no—
232#490—21no—
233#489—22no—
234#488—22no—
235#487—21no—
236#486—21no—
237#435—22no—
238#435—22no—
239C2×#108C22×C3712yes—
240C2×#107C22×C3711yescharacteristic
241C2×#107C22×C3711yescharacteristic
242C2×#106C22×C3711yescharacteristic
243C2×#106C22×C3711yescharacteristic
244#423C22×C3711yescharacteristic
245#417C22×C3712yes—
246#417C22×C3712yes—
247#417C22×C3712yes—
248#417C22×C3712yes—
249#408C22×C3712yes—
250C4×M16C22×C3711yescharacteristic
251C4×M16C22×C3711yescharacteristic
252C2×#97C22×C3711yescharacteristic
253#343C22×C3712yes—
254#343C22×C3712yes—
255#343C22×C3712yes—
256#343C22×C3712yes—
257#341C22×C3712yes—
258C37#2873511yescharacteristic, direct product factor, Sylow
259C2×#41C23×C3712yes—
260C22×Q8—21no—
261#131—28no—
262C2×M16—22no—
263C2×M16C23×C3712yes—
264C2×M16C23×C3712yes—
265C2×M16C23×C3712yes—
266C22×C8—22no—
267C22×C8C23×C3711yescharacteristic
268C22×C8C23×C3711yescharacteristic
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8—21no—
273C4⋊Q8D4×C3711yescharacteristic
274#127D4×C3711yescharacteristic
275#125—21no—
276#125—21no—
277#125—21no—
278#125—21no—
279#124D4×C3712yes—
280#121—21no—
281#121—21no—
282C4×D4—21no—
283C4×D4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4C23×C3711yescharacteristic
288C2×C4⋊C4C23×C3711yescharacteristic
289C2×C4⋊C4C23×C3711yescharacteristic
290C2×C4⋊C4C23×C3711yescharacteristic
291C2×C42C23×C3711yescharacteristic
292#108—24no—
293#107—22no—
294#107—22no—
295#106—22no—
296#106—22no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299#103—22no—
300#103—22no—
301#103—22no—
302#103—22no—
303#102—22no—
304#102—22no—
305#102—22no—
306#102—22no—
307C22⋊C8—24no—
308#97—21no—
309#97—21no—
310#97D4×C3712yes—
311#97D4×C3712yes—
312C4×C8—21no—
313C4×C8—21no—
314#41—24no—
315#41—24no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—82no—
319C2×Q8C2×D4×C3712yes—
320C2×D4—22no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4C2×D4×C3712yes—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4#41×C3711yescharacteristic
330C22×C4#41×C3711yescharacteristic
331C22×C4C24×C3711yescharacteristic
332M16—22no—
333M16—22no—
334M16—24no—
335M16—22no—
336M16—22no—
337M16—44no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—44no—
343C2×C8C2×D4×C3712yes—
344C2×C8C2×D4×C3712yes—
345C2×C8#41×C3714yes—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C42C2×D4×C3711yescharacteristic
365C42C2×D4×C3711yescharacteristic
366C42C2×D4×C3711yescharacteristic
367C42C2×D4×C3711yescharacteristic
368C23—22no—
369C23C2×#41×C3711yescharacteristic
370Q8—24no—
371Q8—82no—
372Q8—82no—
373D4—24no—
374D4—44no—
375D4—81no—
376D4—81no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4#121×C3711yescharacteristic
391C2×C4#121×C3711yescharacteristic
392C2×C4#121×C3711yescharacteristic
393C2×C4#121×C3711yescharacteristic
394C2×C4C22×D4×C3711yescharacteristic
395C2×C4C22×D4×C3711yescharacteristic
396C2×C4C2×#41×C3712yes—
397C2×C42−1+4×C3712yes—
398C8—22no—
399C8—42no—
400C8—42no—
401C8—42no—
402C8#124×C3714yes—
403C22—21no—
404C22—21no—
405C22—42no—
406C22—42no—
407C22—42no—
408C22C2×#121×C3711yescharacteristic
409C22C37×#55612yes—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—42no—
415C4—81no—
416C4—81no—
417C4—81no—
418C4—81no—
419C4C2×#124×C3711yescharacteristic
420C4C37×#53611yescharacteristic
421C4C37×#54712yes—
422C2—22no—
423C2—82no—
424C2C37×#254711yescharacteristic
425C2C37×#306811yescharacteristic
426C2C37×#306911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#532C22
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×#2079C2semidirect
6. C37×#2078C2semidirect
7. C37×#1998C2semidirect
8. C37×#1997C2semidirect
9. C37×#1816C2semidirect
10. C37×#1815C2semidirect
11. C37×#1778C2semidirect
189. #28735C37direct (N × H)
209. C2×#501C2×C37semidirect
213. #2079C2×C37semidirect
214. #2078C2×C37semidirect
215. #1998C2×C37semidirect
216. #1997C2×C37semidirect
217. #1816C2×C37semidirect
218. #1815C2×C37semidirect
219. #1778C2×C37semidirect
258. C37#28735direct (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×#31422
C37×#31412
C37×#29322
C37×#20792
C37×#20782
C37×#19982
C37×#19972
C37×#18162
C37×#18152
C37×#17782
#2873537