Finite Group Databasebeta

← C37×#19469 #22640722

Subgroups — C37×#19469 #22640722

Order 9472.

610 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3206C211yesmaximal, characteristic
2C37×#3112C211yesmaximal, characteristic
3C2×C37×#475C211yesmaximal, characteristic, complemented
4C37×#2984C211yesmaximal, characteristic, complemented
5C37×#1704C212yesmaximal, complemented
6C37×#1686C212yesmaximal, complemented
7C37×#1684C212yesmaximal, complemented
8C37×#1666C212yesmaximal, complemented
9C37×#1573C211yesmaximal, characteristic, complemented
10C37×#1556C211yesmaximal, characteristic, complemented
11C37×#1551C211yesmaximal, characteristic
12C37×#532C2211yescharacteristic
13C2×C4⋊Q8×C37C2211yescharacteristic
14C2×C4×Q8×C37C2211yescharacteristic
15C37×#492C2212yes—
16C37×#487C2212yes—
17C37×#480—21no—
18C37×#477C2211yescharacteristic
19C37×#477C2211yescharacteristic
20C37×#475—21no—
21C37×#475—21no—
22C37×#475C2212yes—
23C37×#475C2212yes—
24C37×#461—22no—
25C37×#460C2211yescharacteristic
26C37×#460C2211yescharacteristic
27C37×#448—21no—
28C37×#448—21no—
29C37×#448—21no—
30C37×#446—22no—
31C37×#446C2212yes—
32C8×Q8×C37C2212yes—
33C37×#440—21no—
34C37×#440—21no—
35C37×#432—21no—
36C37×#432C2211yescharacteristic
37C37×#432C2211yescharacteristic
38C37×#431—21no—
39C37×#431C2211yescharacteristic
40C2×#106×C37—21no—
41C2×C4⋊C8×C37C2211yescharacteristic
42C2×#103×C37—21no—
43C37×#335C2212yes—
44C37×#334C2212yes—
45C37×#333C2212yes—
46C37×#332C2212yes—
47C37×#332C2212yes—
48C37×#331C2212yes—
49C2×#41×C37—21no—
50C22×Q8×C37—21no—
51C22×Q8×C37D411yescharacteristic
52C2×SD16×C37—21no—
53C2×SD16×C37—21no—
54C2×SD16×C37—22no—
55C2×SD16×C37—22no—
56C22×C8×C37—21no—
57C4⋊Q8×C37—21no—
58C4⋊Q8×C37—21no—
59C4⋊Q8×C37—21no—
60C4⋊Q8×C37C2312yes—
61C4⋊Q8×C37C2311yescharacteristic
62#127×C37C2311yescharacteristic
63#124×C37—21no—
64#121×C37—21no—
65#121×C37—21no—
66C4×Q8×C37—21no—
67C4×Q8×C37—21no—
68C4×Q8×C37D411yescharacteristic
69C4×Q8×C37D411yescharacteristic
70C4×Q8×C37C2311yescharacteristic
71C4×Q8×C37C2311yescharacteristic
72C4×D4×C37—21no—
73C4×D4×C37—21no—
74C2×C4⋊C4×C37—21no—
75C2×C4⋊C4×C37—21no—
76C2×C4⋊C4×C37—21no—
77C2×C4⋊C4×C37D411yescharacteristic
78C2×C42×C37—21no—
79C2×C42×C37C2311yescharacteristic
80#107×C37—21no—
81#107×C37—21no—
82#106×C37—22no—
83#106×C37—22no—
84C4⋊C8×C37—22no—
85C4⋊C8×C37—22no—
86C4⋊C8×C37—21no—
87C4⋊C8×C37D412yes—
88C4⋊C8×C37C2312yes—
89C4⋊C8×C37C2312yes—
90C4⋊C8×C37C2311yescharacteristic
91C4⋊C8×C37C2311yescharacteristic
92#103×C37—22no—
93#103×C37—22no—
94#103×C37—21no—
95#103×C37—21no—
96#103×C37—22no—
97#103×C37—22no—
98#102×C37—21no—
99#102×C37—21no—
100C22⋊C8×C37—21no—
101C22⋊C8×C37—21no—
102C22⋊C8×C37D411yescharacteristic
103C22⋊C8×C37D411yescharacteristic
104#97×C37—22no—
105#97×C37—21no—
106#97×C37—21no—
107C4×C8×C37—22no—
108C4×C8×C37C2312yes—
109#41×C37—82no—
110C2×Q8×C37—21no—
111C2×Q8×C37—22no—
112C2×Q8×C37—22no—
113C2×Q8×C37—21no—
114C2×Q8×C37—41no—
115C2×Q8×C37—41no—
116C2×Q8×C37—82no—
117C2×Q8×C37C2×D411yescharacteristic
118C2×Q8×C37C2×D411yescharacteristic
119C2×D4×C37—21no—
120C2×D4×C37—21no—
121C2×D4×C37—21no—
122C2×D4×C37—41no—
123C22×C4×C37—21no—
124C22×C4×C37—21no—
125C22×C4×C37—41no—
126C22×C4×C37—41no—
127C22×C4×C37C2×D411yescharacteristic
128C22×C4×C37C2×D411yescharacteristic
129C22×C4×C37#4111yescharacteristic
130SD16×C37—42no—
131SD16×C37—42no—
132SD16×C37—82no—
133SD16×C37—82no—
134C2×C8×C37—22no—
135C2×C8×C37—21no—
136C2×C8×C37—21no—
137C2×C8×C37—22no—
138C2×C8×C37—42no—
139C2×C8×C37C2×D412yes—
140C2×C8×C37C2×D412yes—
141C4⋊C4×C37—21no—
142C4⋊C4×C37—21no—
143C4⋊C4×C37—21no—
144C4⋊C4×C37—21no—
145C4⋊C4×C37—21no—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—22no—
150C4⋊C4×C37—41no—
151C4⋊C4×C37—41no—
152C4⋊C4×C37C2×D411yescharacteristic
153C4⋊C4×C37C2×D411yescharacteristic
154C22⋊C4×C37—41no—
155C22⋊C4×C37—41no—
156C42×C37—21no—
157C42×C37—21no—
158C42×C37—21no—
159C42×C37—21no—
160C42×C37C2×D411yescharacteristic
161C42×C37C2×D411yescharacteristic
162C42×C37#4111yescharacteristic
163C42×C37C2411yescharacteristic
164C23×C37—41no—
165C23×C37#12111yescharacteristic
166Q8×C37—21no—
167Q8×C37—21no—
168Q8×C37—21no—
169Q8×C37—42no—
170Q8×C37—42no—
171Q8×C37—42no—
172Q8×C37—81no—
173Q8×C37—82no—
174Q8×C37#13712yes—
175D4×C37—41no—
176D4×C37—41no—
177D4×C37—42no—
178D4×C37—81no—
179D4×C37—82no—
180C2×C4×C37—21no—
181C2×C4×C37—22no—
182C2×C4×C37—21no—
183C2×C4×C37—21no—
184C2×C4×C37—22no—
185C2×C4×C37—21no—
186C2×C4×C37—21no—
187C2×C4×C37—21no—
188C2×C4×C37—42no—
189C2×C4×C37—42no—
190C2×C4×C37—41no—
191C2×C4×C37—42no—
192C2×C4×C37—82no—
193C2×C4×C37—82no—
194C2×C4×C37#12111yescharacteristic
195C2×C4×C37#12111yescharacteristic
196C2×C4×C37#12111yescharacteristic
197C2×C4×C37C22×D411yescharacteristic
198C2×C4×C37C22×D411yescharacteristic
199C2×C4×C37C2×#4111yescharacteristic
200C8×C37—22no—
201C8×C37—22no—
202C8×C37—41no—
203C8×C37—42no—
204C8×C37—41no—
205C8×C37—42no—
206#19469C3711yesmaximal, characteristic, direct product factor, Sylow
207C22×C37—21no—
208C22×C37—21no—
209C22×C37—81no—
210C22×C37—81no—
211C22×C37—81no—
212C22×C37#47112yes—
213C22×C37C2×#12111yescharacteristic
214C4×C37—21no—
215C4×C37—21no—
216C4×C37—22no—
217C4×C37—21no—
218C4×C37—21no—
219C4×C37—41no—
220C4×C37—41no—
221C4×C37—41no—
222C4×C37—82no—
223C4×C37—81no—
224C4×C37C2×#13711yescharacteristic
225C4×C37#57511yescharacteristic
226C4×C37#57712yes—
227#3206C2×C3711yescharacteristic
228#3112C2×C3711yescharacteristic
229C2×#475C2×C3711yescharacteristic, complemented
230#2984C2×C3711yescharacteristic, complemented
231#1704C2×C3712yescomplemented
232#1686C2×C3712yescomplemented
233#1684C2×C3712yescomplemented
234#1666C2×C3712yescomplemented
235#1573C2×C3711yescharacteristic, complemented
236#1556C2×C3711yescharacteristic, complemented
237#1551C2×C3711yescharacteristic
238C2×C37—22no—
239C2×C37—161no—
240C2×C37#304311yescharacteristic
241C2×C37#305611yescharacteristic
242C2×C37C2×#47111yescharacteristic
243#532C22×C3711yescharacteristic
244C2×C4⋊Q8C22×C3711yescharacteristic
245C2×C4×Q8C22×C3711yescharacteristic
246#492C22×C3712yes—
247#487C22×C3712yes—
248#480—21no—
249#477C22×C3711yescharacteristic
250#477C22×C3711yescharacteristic
251#475—21no—
252#475—21no—
253#475C22×C3712yes—
254#475C22×C3712yes—
255#461—22no—
256#460C22×C3711yescharacteristic
257#460C22×C3711yescharacteristic
258#448—21no—
259#448—21no—
260#448—21no—
261#446—22no—
262#446C22×C3712yes—
263C8×Q8C22×C3712yes—
264#440—21no—
265#440—21no—
266#432—21no—
267#432C22×C3711yescharacteristic
268#432C22×C3711yescharacteristic
269#431—21no—
270#431C22×C3711yescharacteristic
271C2×#106—21no—
272C2×C4⋊C8C22×C3711yescharacteristic
273C2×#103—21no—
274#335C22×C3712yes—
275#334C22×C3712yes—
276#333C22×C3712yes—
277#332C22×C3712yes—
278#332C22×C3712yes—
279#331C22×C3712yes—
280C37#1946911yescharacteristic, direct product factor, Sylow
281C2×#41—21no—
282C22×Q8—21no—
283C22×Q8D4×C3711yescharacteristic
284C2×SD16—21no—
285C2×SD16—21no—
286C2×SD16—22no—
287C2×SD16—22no—
288C22×C8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8C23×C3712yes—
293C4⋊Q8C23×C3711yescharacteristic
294#127C23×C3711yescharacteristic
295#124—21no—
296#121—21no—
297#121—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8D4×C3711yescharacteristic
301C4×Q8D4×C3711yescharacteristic
302C4×Q8C23×C3711yescharacteristic
303C4×Q8C23×C3711yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4D4×C3711yescharacteristic
310C2×C42—21no—
311C2×C42C23×C3711yescharacteristic
312#107—21no—
313#107—21no—
314#106—22no—
315#106—22no—
316C4⋊C8—22no—
317C4⋊C8—22no—
318C4⋊C8—21no—
319C4⋊C8D4×C3712yes—
320C4⋊C8C23×C3712yes—
321C4⋊C8C23×C3712yes—
322C4⋊C8C23×C3711yescharacteristic
323C4⋊C8C23×C3711yescharacteristic
324#103—22no—
325#103—22no—
326#103—21no—
327#103—21no—
328#103—22no—
329#103—22no—
330#102—21no—
331#102—21no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8D4×C3711yescharacteristic
335C22⋊C8D4×C3711yescharacteristic
336#97—22no—
337#97—21no—
338#97—21no—
339C4×C8—22no—
340C4×C8C23×C3712yes—
341#41—82no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—82no—
349C2×Q8C2×D4×C3711yescharacteristic
350C2×Q8C2×D4×C3711yescharacteristic
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—41no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4C2×D4×C3711yescharacteristic
360C22×C4C2×D4×C3711yescharacteristic
361C22×C4#41×C3711yescharacteristic
362SD16—42no—
363SD16—42no—
364SD16—82no—
365SD16—82no—
366C2×C8—22no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—42no—
371C2×C8C2×D4×C3712yes—
372C2×C8C2×D4×C3712yes—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4C2×D4×C3711yescharacteristic
385C4⋊C4C2×D4×C3711yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C42—21no—
389C42—21no—
390C42—21no—
391C42—21no—
392C42C2×D4×C3711yescharacteristic
393C42C2×D4×C3711yescharacteristic
394C42#41×C3711yescharacteristic
395C42C24×C3711yescharacteristic
396C23—41no—
397C23#121×C3711yescharacteristic
398Q8—21no—
399Q8—21no—
400Q8—21no—
401Q8—42no—
402Q8—42no—
403Q8—42no—
404Q8—81no—
405Q8—82no—
406Q8#137×C3712yes—
407D4—41no—
408D4—41no—
409D4—42no—
410D4—81no—
411D4—82no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4#121×C3711yescharacteristic
427C2×C4#121×C3711yescharacteristic
428C2×C4#121×C3711yescharacteristic
429C2×C4C22×D4×C3711yescharacteristic
430C2×C4C22×D4×C3711yescharacteristic
431C2×C4C2×#41×C3711yescharacteristic
432C8—22no—
433C8—22no—
434C8—41no—
435C8—42no—
436C8—41no—
437C8—42no—
438C22—21no—
439C22—21no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C37×#47112yes—
444C22C2×#121×C3711yescharacteristic
445C4—21no—
446C4—21no—
447C4—22no—
448C4—21no—
449C4—21no—
450C4—41no—
451C4—41no—
452C4—41no—
453C4—82no—
454C4—81no—
455C4C2×#137×C3711yescharacteristic
456C4C37×#57511yescharacteristic
457C4C37×#57712yes—
458C2—22no—
459C2—161no—
460C2C37×#304311yescharacteristic
461C2C37×#305611yescharacteristic
462C2C2×C37×#47111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#532C22
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
3. C2×C37×#475C2semidirect
4. C37×#2984C2semidirect
5. C37×#1704C2semidirect
6. C37×#1686C2semidirect
7. C37×#1684C2semidirect
8. C37×#1666C2semidirect
9. C37×#1573C2semidirect
10. C37×#1556C2semidirect
206. #19469C37direct (N × H)
229. C2×#475C2×C37semidirect
230. #2984C2×C37semidirect
231. #1704C2×C37semidirect
232. #1686C2×C37semidirect
233. #1684C2×C37semidirect
234. #1666C2×C37semidirect
235. #1573C2×C37semidirect
236. #1556C2×C37semidirect
280. C37#19469direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32062
C37×#31122
C2×C37×#4752
C37×#29842
C37×#17042
C37×#16862
C37×#16842
C37×#16662
C37×#15732
C37×#15562
C37×#15512
#1946937