Finite Group Databasebeta

← C37×#29859 #22651112

Subgroups — C37×#29859 #22651112

Order 9472.

684 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#487C211yesmaximal, characteristic, complemented
2C37×#3079C211yesmaximal, characteristic
3C37×#3039C211yesmaximal, characteristic
4C37×#2922C211yesmaximal, characteristic
5C37×#2064C214yesmaximal, complemented
6C37×#2052C214yesmaximal
7C37×#1997C211yesmaximal, characteristic, complemented
8C37×#1966C211yesmaximal, characteristic, complemented
9C37×#1848C211yesmaximal, characteristic, complemented
10C2×#137×C37C2212yes—
11C2×C4⋊Q8×C37C2211yescharacteristic
12C2×C4⋊Q8×C37C2211yescharacteristic
13C4×#41×C37C2211yescharacteristic
14C37×#487—22no—
15C37×#487—22no—
16C37×#477—21no—
17C37×#476—21no—
18C37×#475—21no—
19C37×#474—21no—
20C37×#462—21no—
21C37×#462—21no—
22C37×#461—21no—
23C37×#461—21no—
24C37×#433—22no—
25C37×#431—22no—
26C2×#108×C37C2214yes—
27C37×#428C2212yes—
28C37×#424C2212yes—
29C37×#423C2211yescharacteristic
30C37×#423C2211yescharacteristic
31C37×#419C2212yes—
32C37×#417C2212yes—
33C2×#103×C37C2214yes—
34C2×#101×C37C2214yes—
35C37×#408C2212yes—
36C4×M16×C37C2211yescharacteristic
37C2×C4×C8×C37C2211yescharacteristic
38C37×#343C2214yes—
39C2×#41×C37C2311yescharacteristic
40C22×Q8×C37—21no—
41C22×Q8×C37C2312yes—
42#137×C37—44no—
43C2×Q16×C37—22no—
44C2×SD16×C37—22no—
45C2×M16×C37C2312yes—
46C2×M16×C37C2312yes—
47C2×M16×C37C2312yes—
48C22×C8×C37C2312yes—
49C4⋊Q8×C37—21no—
50C4⋊Q8×C37—21no—
51C4⋊Q8×C37—21no—
52C4⋊Q8×C37—21no—
53C4⋊Q8×C37—21no—
54C4⋊Q8×C37—21no—
55C4⋊Q8×C37—21no—
56C4⋊Q8×C37—21no—
57C4×Q8×C37D411yescharacteristic
58C4×Q8×C37D411yescharacteristic
59C4×D4×C37—21no—
60C4×D4×C37—21no—
61C4×D4×C37D411yescharacteristic
62C4×D4×C37D411yescharacteristic
63#117×C37—21no—
64#117×C37C2311yescharacteristic
65C2×C4⋊C4×C37—21no—
66C2×C4⋊C4×C37—21no—
67C2×C4⋊C4×C37—21no—
68C2×C4⋊C4×C37C2312yes—
69C2×C42×C37—21no—
70C2×C42×C37C2311yescharacteristic
71#108×C37—44no—
72#107×C37—22no—
73#106×C37—22no—
74C4⋊C8×C37—24no—
75C4⋊C8×C37—21no—
76C4⋊C8×C37—21no—
77C4⋊C8×C37—21no—
78C4⋊C8×C37—21no—
79#103×C37—22no—
80#103×C37—28no—
81#103×C37—22no—
82#103×C37—22no—
83#102×C37—22no—
84#101×C37—44no—
85C22⋊C8×C37—24no—
86#97×C37—21no—
87C4×C8×C37—21no—
88C4×C8×C37D412yes—
89C4×C8×C37D412yes—
90#41×C37—22no—
91#41×C37—22no—
92C2×Q8×C37—22no—
93C2×Q8×C37—22no—
94C2×Q8×C37—24no—
95C2×Q8×C37—24no—
96C2×Q8×C37—41no—
97C2×Q8×C37—41no—
98C2×Q8×C37—82no—
99C2×Q8×C37C2×D411yescharacteristic
100C2×D4×C37—21no—
101C2×D4×C37C2×D411yescharacteristic
102C22×C4×C37—21no—
103C22×C4×C37—21no—
104C22×C4×C37—21no—
105C22×C4×C37—22no—
106C22×C4×C37—22no—
107C22×C4×C37#4111yescharacteristic
108C22×C4×C37#4111yescharacteristic
109C22×C4×C37C2411yescharacteristic
110Q16×C37—44no—
111SD16×C37—44no—
112M16×C37—22no—
113M16×C37—24no—
114M16×C37—24no—
115M16×C37—22no—
116C2×C8×C37—22no—
117C2×C8×C37—22no—
118C2×C8×C37—22no—
119C2×C8×C37—22no—
120C2×C8×C37—22no—
121C2×C8×C37C2×D414yes—
122C4⋊C4×C37—21no—
123C4⋊C4×C37—21no—
124C4⋊C4×C37—22no—
125C4⋊C4×C37—22no—
126C4⋊C4×C37—41no—
127C4⋊C4×C37—41no—
128C4⋊C4×C37—41no—
129C4⋊C4×C37—41no—
130C4⋊C4×C37—41no—
131C4⋊C4×C37—41no—
132C4⋊C4×C37C2×D411yescharacteristic
133C4⋊C4×C37C2×D411yescharacteristic
134C22⋊C4×C37—21no—
135C22⋊C4×C37—21no—
136C22⋊C4×C37—21no—
137C42×C37—21no—
138C42×C37—21no—
139C42×C37—21no—
140C42×C37C2×D411yescharacteristic
141C42×C37C2×D411yescharacteristic
142C42×C37C2×D411yescharacteristic
143C42×C37C2×D411yescharacteristic
144C23×C37—21no—
145C23×C37C2×#4111yescharacteristic
146Q8×C37—21no—
147Q8×C37—21no—
148Q8×C37—42no—
149Q8×C37—42no—
150Q8×C37—44no—
151Q8×C37—82no—
152Q8×C37—82no—
153D4×C37—21no—
154D4×C37—21no—
155D4×C37—42no—
156C2×C4×C37—22no—
157C2×C4×C37—22no—
158C2×C4×C37—21no—
159C2×C4×C37—21no—
160C2×C4×C37—21no—
161C2×C4×C37—42no—
162C2×C4×C37—42no—
163C2×C4×C37—42no—
164C2×C4×C37—42no—
165C2×C4×C37—42no—
166C2×C4×C37—44no—
167C2×C4×C37—82no—
168C2×C4×C37#12111yescharacteristic
169C2×C4×C37#12111yescharacteristic
170C2×C4×C37#12111yescharacteristic
171C2×C4×C37#12111yescharacteristic
172C2×C4×C37C22×D411yescharacteristic
173C2×C4×C37C22×D411yescharacteristic
174C2×C4×C37H(5,𝔽2)12yes—
175C2×C4×C372−1+412yes—
176C8×C37—24no—
177C8×C37—42no—
178C8×C37—42no—
179C8×C37—42no—
180#29859C3711yesmaximal, characteristic, direct product factor, Sylow
181C22×C37—21no—
182C22×C37—21no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37C2×#12111yescharacteristic
187C22×C37#54212yes—
188C4×C37—21no—
189C4×C37—21no—
190C4×C37—41no—
191C4×C37—41no—
192C4×C37—41no—
193C4×C37—82no—
194C4×C37—82no—
195C4×C37#47112yes—
196C4×C37#47312yes—
197C4×C37#53511yescharacteristic
198C4×C37#53611yescharacteristic
199C4×C37#53712yes—
200C2×#487C2×C3711yescharacteristic, complemented
201#3079C2×C3711yescharacteristic
202#3039C2×C3711yescharacteristic
203#2922C2×C3711yescharacteristic
204#2064C2×C3714yescomplemented
205#2052C2×C3714yes—
206#1997C2×C3711yescharacteristic, complemented
207#1966C2×C3711yescharacteristic, complemented
208#1848C2×C3711yescharacteristic, complemented
209C2×C37—22no—
210C2×C37—81no—
211C2×C37#262011yescharacteristic
212C2×C37C2×#47111yescharacteristic
213C2×C37C2×#47311yescharacteristic
214C2×#137C22×C3712yes—
215C2×C4⋊Q8C22×C3711yescharacteristic
216C2×C4⋊Q8C22×C3711yescharacteristic
217C4×#41C22×C3711yescharacteristic
218#487—22no—
219#487—22no—
220#477—21no—
221#476—21no—
222#475—21no—
223#474—21no—
224#462—21no—
225#462—21no—
226#461—21no—
227#461—21no—
228#433—22no—
229#431—22no—
230C2×#108C22×C3714yes—
231#428C22×C3712yes—
232#424C22×C3712yes—
233#423C22×C3711yescharacteristic
234#423C22×C3711yescharacteristic
235#419C22×C3712yes—
236#417C22×C3712yes—
237C2×#103C22×C3714yes—
238C2×#101C22×C3714yes—
239#408C22×C3712yes—
240C4×M16C22×C3711yescharacteristic
241C2×C4×C8C22×C3711yescharacteristic
242#343C22×C3714yes—
243C37#2985911yescharacteristic, direct product factor, Sylow
244C2×#41C23×C3711yescharacteristic
245C22×Q8—21no—
246C22×Q8C23×C3712yes—
247#137—44no—
248C2×Q16—22no—
249C2×SD16—22no—
250C2×M16C23×C3712yes—
251C2×M16C23×C3712yes—
252C2×M16C23×C3712yes—
253C22×C8C23×C3712yes—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4×Q8D4×C3711yescharacteristic
263C4×Q8D4×C3711yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4D4×C3711yescharacteristic
267C4×D4D4×C3711yescharacteristic
268#117—21no—
269#117C23×C3711yescharacteristic
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4C23×C3712yes—
274C2×C42—21no—
275C2×C42C23×C3711yescharacteristic
276#108—44no—
277#107—22no—
278#106—22no—
279C4⋊C8—24no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284#103—22no—
285#103—28no—
286#103—22no—
287#103—22no—
288#102—22no—
289#101—44no—
290C22⋊C8—24no—
291#97—21no—
292C4×C8—21no—
293C4×C8D4×C3712yes—
294C4×C8D4×C3712yes—
295#41—22no—
296#41—22no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—24no—
300C2×Q8—24no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—82no—
304C2×Q8C2×D4×C3711yescharacteristic
305C2×D4—21no—
306C2×D4C2×D4×C3711yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4#41×C3711yescharacteristic
313C22×C4#41×C3711yescharacteristic
314C22×C4C24×C3711yescharacteristic
315Q16—44no—
316SD16—44no—
317M16—22no—
318M16—24no—
319M16—24no—
320M16—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8C2×D4×C3714yes—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4C2×D4×C3711yescharacteristic
338C4⋊C4C2×D4×C3711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C42—21no—
343C42—21no—
344C42—21no—
345C42C2×D4×C3711yescharacteristic
346C42C2×D4×C3711yescharacteristic
347C42C2×D4×C3711yescharacteristic
348C42C2×D4×C3711yescharacteristic
349C23—21no—
350C23C2×#41×C3711yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—42no—
354Q8—42no—
355Q8—44no—
356Q8—82no—
357Q8—82no—
358D4—21no—
359D4—21no—
360D4—42no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—82no—
373C2×C4#121×C3711yescharacteristic
374C2×C4#121×C3711yescharacteristic
375C2×C4#121×C3711yescharacteristic
376C2×C4#121×C3711yescharacteristic
377C2×C4C22×D4×C3711yescharacteristic
378C2×C4C22×D4×C3711yescharacteristic
379C2×C4H(5,𝔽2)×C3712yes—
380C2×C42−1+4×C3712yes—
381C8—24no—
382C8—42no—
383C8—42no—
384C8—42no—
385C22—21no—
386C22—21no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22C2×#121×C3711yescharacteristic
391C22C37×#54212yes—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—82no—
398C4—82no—
399C4C37×#47112yes—
400C4C37×#47312yes—
401C4C37×#53511yescharacteristic
402C4C37×#53611yescharacteristic
403C4C37×#53712yes—
404C2—22no—
405C2—81no—
406C2C37×#262011yescharacteristic
407C2C2×C37×#47111yescharacteristic
408C2C2×C37×#47311yescharacteristic
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×#487C2semidirect
5. C37×#2064C2semidirect
7. C37×#1997C2semidirect
8. C37×#1966C2semidirect
9. C37×#1848C2semidirect
180. #29859C37direct (N × H)
200. C2×#487C2×C37semidirect
204. #2064C2×C37semidirect
206. #1997C2×C37semidirect
207. #1966C2×C37semidirect
208. #1848C2×C37semidirect
243. C37#29859direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4872
C37×#30792
C37×#30392
C37×#29222
C37×#20642
C37×#20522
C37×#19972
C37×#19662
C37×#18482
#2985937