Finite Group Databasebeta

← C37×#19444 #22640697

Subgroups — C37×#19444 #22640697

Order 9472.

652 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3206C211yesmaximal, characteristic, complemented
2C37×#3079C211yesmaximal, characteristic, complemented
3C37×#3035C211yesmaximal, characteristic
4C37×#2989C211yesmaximal, characteristic, complemented
5C37×#1700C212yesmaximal, complemented
6C37×#1699C212yesmaximal, complemented
7C37×#1686C212yesmaximal, complemented
8C37×#1685C212yesmaximal, complemented
9C37×#1571C211yesmaximal, characteristic, complemented
10C37×#1547C211yesmaximal, characteristic, complemented
11C2×C37×#332C211yesmaximal, characteristic, complemented
12C2×#135×C37—21no—
13C37×#532C2211yescharacteristic
14C2×C4⋊Q8×C37C2211yescharacteristic
15C4×#41×C37C2211yescharacteristic
16C37×#492C2212yes—
17C37×#487C2212yes—
18C37×#477—21no—
19C37×#476—21no—
20C37×#475C2212yes—
21C37×#474C2212yes—
22C37×#464—21no—
23C37×#463—21no—
24C37×#462C2211yescharacteristic
25C37×#461—21no—
26C37×#461—21no—
27C37×#461C2211yescharacteristic
28C37×#460C2211yescharacteristic
29C37×#459C2211yescharacteristic
30C37×#448—22no—
31C37×#446C2212yes—
32C37×#436C2212yes—
33C37×#435—22no—
34C37×#432—21no—
35C37×#431C2211yescharacteristic
36C37×#428—21no—
37C37×#423—21no—
38C37×#423C2211yescharacteristic
39C2×C4⋊C8×C37C2211yescharacteristic
40C2×C4⋊C8×C37C2211yescharacteristic
41C37×#417—21no—
42C37×#416—21no—
43C37×#335C2212yes—
44C37×#335C2212yes—
45C37×#332C2212yes—
46C37×#332C2212yes—
47C37×#332C2212yes—
48C37×#331C2212yes—
49C2×#41×C37—21no—
50C2×#41×C37D411yescharacteristic
51C22×Q8×C37—21no—
52#135×C37—44no—
53C2×Q16×C37—21no—
54C2×SD16×C37—21no—
55C2×SD16×C37—21no—
56C2×SD16×C37—22no—
57C2×SD16×C37—22no—
58C2×D8×C37—21no—
59C2×M16×C37—21no—
60C2×M16×C37—22no—
61C22×C8×C37—21no—
62C22×C8×C37—21no—
63C4⋊Q8×C37—21no—
64C4⋊Q8×C37—21no—
65C4⋊Q8×C37—21no—
66C4⋊Q8×C37C2312yes—
67C4⋊Q8×C37C2311yescharacteristic
68#127×C37C2311yescharacteristic
69#124×C37—21no—
70#121×C37—21no—
71#121×C37—21no—
72C4×Q8×C37D411yescharacteristic
73C4×Q8×C37C2311yescharacteristic
74C4×D4×C37—21no—
75C4×D4×C37—21no—
76C4×D4×C37—21no—
77C4×D4×C37—21no—
78C4×D4×C37D411yescharacteristic
79C4×D4×C37C2311yescharacteristic
80#117×C37—21no—
81#117×C37D411yescharacteristic
82C2×C4⋊C4×C37—21no—
83C2×C4⋊C4×C37—21no—
84C2×C42×C37—21no—
85C2×C42×C37C2311yescharacteristic
86#107×C37—22no—
87#106×C37—22no—
88C4⋊C8×C37—22no—
89C4⋊C8×C37—21no—
90C4⋊C8×C37—21no—
91C4⋊C8×C37—21no—
92C4⋊C8×C37D411yescharacteristic
93C4⋊C8×C37D411yescharacteristic
94C4⋊C8×C37C2312yes—
95C4⋊C8×C37C2312yes—
96C4⋊C8×C37C2311yescharacteristic
97C4⋊C8×C37C2311yescharacteristic
98#103×C37—22no—
99#103×C37—22no—
100#103×C37—22no—
101#103×C37—21no—
102#103×C37—21no—
103#102×C37—22no—
104#102×C37—21no—
105#102×C37—21no—
106C22⋊C8×C37—22no—
107C22⋊C8×C37D412yes—
108#97×C37—22no—
109C4×C8×C37C2312yes—
110#41×C37—22no—
111#41×C37—22no—
112#41×C37—42no—
113#41×C37—42no—
114C2×Q8×C37—21no—
115C2×Q8×C37—22no—
116C2×Q8×C37—41no—
117C2×Q8×C37—81no—
118C2×Q8×C37—81no—
119C2×Q8×C37C2×D411yescharacteristic
120C2×D4×C37—21no—
121C2×D4×C37—21no—
122C2×D4×C37—21no—
123C2×D4×C37—21no—
124C2×D4×C37—41no—
125C2×D4×C37C2×D411yescharacteristic
126C22×C4×C37—21no—
127C22×C4×C37—21no—
128C22×C4×C37—21no—
129C22×C4×C37—41no—
130C22×C4×C37—41no—
131C22×C4×C37C2×D411yescharacteristic
132C22×C4×C37C2×D411yescharacteristic
133C22×C4×C37#4111yescharacteristic
134Q16×C37—42no—
135SD16×C37—42no—
136SD16×C37—42no—
137SD16×C37—82no—
138SD16×C37—82no—
139D8×C37—42no—
140M16×C37—42no—
141M16×C37—82no—
142C2×C8×C37—22no—
143C2×C8×C37—22no—
144C2×C8×C37—21no—
145C2×C8×C37—21no—
146C2×C8×C37—42no—
147C2×C8×C37—81no—
148C2×C8×C37C2×D412yes—
149C2×C8×C37C2×D412yes—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—22no—
153C4⋊C4×C37—21no—
154C4⋊C4×C37—22no—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—41no—
157C4⋊C4×C37—41no—
158C4⋊C4×C37C2×D411yescharacteristic
159C4⋊C4×C37C2×D411yescharacteristic
160C22⋊C4×C37—21no—
161C22⋊C4×C37—21no—
162C22⋊C4×C37—21no—
163C22⋊C4×C37—41no—
164C22⋊C4×C37—41no—
165C42×C37—21no—
166C42×C37—21no—
167C42×C37—21no—
168C42×C37C2×D411yescharacteristic
169C42×C37C2×D411yescharacteristic
170C42×C37#4111yescharacteristic
171C42×C37C2411yescharacteristic
172C23×C37—21no—
173C23×C37—41no—
174C23×C37#12111yescharacteristic
175Q8×C37—21no—
176Q8×C37—21no—
177Q8×C37—41no—
178Q8×C37—41no—
179Q8×C37—42no—
180Q8×C37—42no—
181Q8×C37—82no—
182D4×C37—21no—
183D4×C37—21no—
184D4×C37—42no—
185D4×C37—41no—
186D4×C37—41no—
187D4×C37—41no—
188D4×C37—41no—
189D4×C37—81no—
190D4×C37—82no—
191C2×C4×C37—21no—
192C2×C4×C37—21no—
193C2×C4×C37—21no—
194C2×C4×C37—21no—
195C2×C4×C37—21no—
196C2×C4×C37—41no—
197C2×C4×C37—41no—
198C2×C4×C37—41no—
199C2×C4×C37—42no—
200C2×C4×C37—41no—
201C2×C4×C37—42no—
202C2×C4×C37—81no—
203C2×C4×C37—82no—
204C2×C4×C37—82no—
205C2×C4×C37#12111yescharacteristic
206C2×C4×C37#12111yescharacteristic
207C2×C4×C37#12111yescharacteristic
208C2×C4×C37AGL(1,ℤ/8)12yes—
209C2×C4×C37#13712yes—
210C2×C4×C37C22×D411yescharacteristic
211C2×C4×C37C22×D411yescharacteristic
212C2×C4×C37C2×#4111yescharacteristic
213C8×C37—22no—
214C8×C37—22no—
215C8×C37—41no—
216C8×C37—41no—
217C8×C37—42no—
218C8×C37—42no—
219#19444C3711yesmaximal, characteristic, direct product factor, Sylow
220C22×C37—21no—
221C22×C37—21no—
222C22×C37—41no—
223C22×C37—41no—
224C22×C37—41no—
225C22×C37—81no—
226C22×C37—81no—
227C22×C37—81no—
228C22×C37#46812yes—
229C22×C37C2×#12111yescharacteristic
230C4×C37—21no—
231C4×C37—21no—
232C4×C37—21no—
233C4×C37—41no—
234C4×C37—41no—
235C4×C37—41no—
236C4×C37—82no—
237C4×C37—81no—
238C4×C37#46812yes—
239C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
240C4×C37C2×#13711yescharacteristic
241C4×C37#57611yescharacteristic
242C4×C37#57711yescharacteristic
243#3206C2×C3711yescharacteristic, complemented
244#3079C2×C3711yescharacteristic, complemented
245#3035C2×C3711yescharacteristic
246#2989C2×C3711yescharacteristic, complemented
247#1700C2×C3712yescomplemented
248#1699C2×C3712yescomplemented
249#1686C2×C3712yescomplemented
250#1685C2×C3712yescomplemented
251#1571C2×C3711yescharacteristic, complemented
252#1547C2×C3711yescharacteristic, complemented
253C2×#332C2×C3711yescharacteristic, complemented
254C2×C37—22no—
255C2×C37—81no—
256C2×C37—161no—
257C2×C37#304511yescharacteristic
258C2×C37C2×#46811yescharacteristic
259C2×C37#306911yescharacteristic
260C2×#135—21no—
261#532C22×C3711yescharacteristic
262C2×C4⋊Q8C22×C3711yescharacteristic
263C4×#41C22×C3711yescharacteristic
264#492C22×C3712yes—
265#487C22×C3712yes—
266#477—21no—
267#476—21no—
268#475C22×C3712yes—
269#474C22×C3712yes—
270#464—21no—
271#463—21no—
272#462C22×C3711yescharacteristic
273#461—21no—
274#461—21no—
275#461C22×C3711yescharacteristic
276#460C22×C3711yescharacteristic
277#459C22×C3711yescharacteristic
278#448—22no—
279#446C22×C3712yes—
280#436C22×C3712yes—
281#435—22no—
282#432—21no—
283#431C22×C3711yescharacteristic
284#428—21no—
285#423—21no—
286#423C22×C3711yescharacteristic
287C2×C4⋊C8C22×C3711yescharacteristic
288C2×C4⋊C8C22×C3711yescharacteristic
289#417—21no—
290#416—21no—
291#335C22×C3712yes—
292#335C22×C3712yes—
293#332C22×C3712yes—
294#332C22×C3712yes—
295#332C22×C3712yes—
296#331C22×C3712yes—
297C37#1944411yescharacteristic, direct product factor, Sylow
298C2×#41—21no—
299C2×#41D4×C3711yescharacteristic
300C22×Q8—21no—
301#135—44no—
302C2×Q16—21no—
303C2×SD16—21no—
304C2×SD16—21no—
305C2×SD16—22no—
306C2×SD16—22no—
307C2×D8—21no—
308C2×M16—21no—
309C2×M16—22no—
310C22×C8—21no—
311C22×C8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8C23×C3712yes—
316C4⋊Q8C23×C3711yescharacteristic
317#127C23×C3711yescharacteristic
318#124—21no—
319#121—21no—
320#121—21no—
321C4×Q8D4×C3711yescharacteristic
322C4×Q8C23×C3711yescharacteristic
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4D4×C3711yescharacteristic
328C4×D4C23×C3711yescharacteristic
329#117—21no—
330#117D4×C3711yescharacteristic
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C42—21no—
334C2×C42C23×C3711yescharacteristic
335#107—22no—
336#106—22no—
337C4⋊C8—22no—
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8—21no—
341C4⋊C8D4×C3711yescharacteristic
342C4⋊C8D4×C3711yescharacteristic
343C4⋊C8C23×C3712yes—
344C4⋊C8C23×C3712yes—
345C4⋊C8C23×C3711yescharacteristic
346C4⋊C8C23×C3711yescharacteristic
347#103—22no—
348#103—22no—
349#103—22no—
350#103—21no—
351#103—21no—
352#102—22no—
353#102—21no—
354#102—21no—
355C22⋊C8—22no—
356C22⋊C8D4×C3712yes—
357#97—22no—
358C4×C8C23×C3712yes—
359#41—22no—
360#41—22no—
361#41—42no—
362#41—42no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—41no—
366C2×Q8—81no—
367C2×Q8—81no—
368C2×Q8C2×D4×C3711yescharacteristic
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4C2×D4×C3711yescharacteristic
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4C2×D4×C3711yescharacteristic
381C22×C4C2×D4×C3711yescharacteristic
382C22×C4#41×C3711yescharacteristic
383Q16—42no—
384SD16—42no—
385SD16—42no—
386SD16—82no—
387SD16—82no—
388D8—42no—
389M16—42no—
390M16—82no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—42no—
396C2×C8—81no—
397C2×C8C2×D4×C3712yes—
398C2×C8C2×D4×C3712yes—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4C2×D4×C3711yescharacteristic
408C4⋊C4C2×D4×C3711yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42C2×D4×C3711yescharacteristic
418C42C2×D4×C3711yescharacteristic
419C42#41×C3711yescharacteristic
420C42C24×C3711yescharacteristic
421C23—21no—
422C23—41no—
423C23#121×C3711yescharacteristic
424Q8—21no—
425Q8—21no—
426Q8—41no—
427Q8—41no—
428Q8—42no—
429Q8—42no—
430Q8—82no—
431D4—21no—
432D4—21no—
433D4—42no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—81no—
439D4—82no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—81no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4#121×C3711yescharacteristic
455C2×C4#121×C3711yescharacteristic
456C2×C4#121×C3711yescharacteristic
457C2×C4AGL(1,ℤ/8)×C3712yes—
458C2×C4#137×C3712yes—
459C2×C4C22×D4×C3711yescharacteristic
460C2×C4C22×D4×C3711yescharacteristic
461C2×C4C2×#41×C3711yescharacteristic
462C8—22no—
463C8—22no—
464C8—41no—
465C8—41no—
466C8—42no—
467C8—42no—
468C22—21no—
469C22—21no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22C37×#46812yes—
477C22C2×#121×C3711yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—82no—
485C4—81no—
486C4C37×#46812yes—
487C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
488C4C2×#137×C3711yescharacteristic
489C4C37×#57611yescharacteristic
490C4C37×#57711yescharacteristic
491C2—22no—
492C2—81no—
493C2—161no—
494C2C37×#304511yescharacteristic
495C2C2×C37×#46811yescharacteristic
496C2C37×#306911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3035C2
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
1. C37×#3206C2semidirect
2. C37×#3079C2semidirect
4. C37×#2989C2semidirect
5. C37×#1700C2semidirect
6. C37×#1699C2semidirect
7. C37×#1686C2semidirect
8. C37×#1685C2semidirect
9. C37×#1571C2semidirect
10. C37×#1547C2semidirect
11. C2×C37×#332C2semidirect
219. #19444C37direct (N × H)
243. #3206C2×C37semidirect
244. #3079C2×C37semidirect
246. #2989C2×C37semidirect
247. #1700C2×C37semidirect
248. #1699C2×C37semidirect
249. #1686C2×C37semidirect
250. #1685C2×C37semidirect
251. #1571C2×C37semidirect
252. #1547C2×C37semidirect
253. C2×#332C2×C37semidirect
297. C37#19444direct (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×#30792
C37×#30352
C37×#29892
C37×#17002
C37×#16992
C37×#16862
C37×#16852
C37×#15712
C37×#15472
C2×C37×#3322
#1944437