Finite Group Databasebeta

← C37×#19752 #22641005

Subgroups — C37×#19752 #22641005

Order 9472.

706 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3185C211yesmaximal, characteristic, complemented
2C37×#3182C211yesmaximal, characteristic
3C37×#3182C211yesmaximal, characteristic
4C37×#3165C211yesmaximal, characteristic, complemented
5C37×#3141C211yesmaximal, characteristic
6C37×#3139C211yesmaximal, characteristic, complemented
7C37×#1723C211yesmaximal, characteristic, complemented
8C37×#1720C211yesmaximal, characteristic, complemented
9C37×#1719C211yesmaximal, characteristic, complemented
10C37×#1718C211yesmaximal, characteristic, complemented
11C37×#1718C211yesmaximal, characteristic, complemented
12C37×#1714C211yesmaximal, characteristic, complemented
13C37×#1710C211yesmaximal, characteristic, complemented
14C37×#1708C211yesmaximal, characteristic, complemented
15C37×#1455C211yesmaximal, characteristic, complemented
16C37×#533C2211yescharacteristic
17C37×#533C2211yescharacteristic
18C37×#532C2211yescharacteristic
19C2×C4⋊Q8×C37C2211yescharacteristic
20C37×#501—22no—
21C37×#500C2211yescharacteristic
22C37×#500C2211yescharacteristic
23C37×#500C2211yescharacteristic
24C37×#500C2211yescharacteristic
25C37×#498C2211yescharacteristic
26C37×#498C2211yescharacteristic
27C37×#498C2211yescharacteristic
28C37×#494C2211yescharacteristic
29C37×#492C2211yescharacteristic
30C37×#492C2211yescharacteristic
31C37×#491—22no—
32C37×#489—22no—
33C37×#487C2211yescharacteristic
34C37×#487C2211yescharacteristic
35C37×#487C2211yescharacteristic
36C37×#487C2211yescharacteristic
37C37×#487C2211yescharacteristic
38C37×#487C2211yescharacteristic
39C37×#487C2211yescharacteristic
40C37×#487C2211yescharacteristic
41C37×#487C2211yescharacteristic
42C37×#487C2211yescharacteristic
43C37×#486C2211yescharacteristic
44C37×#486C2211yescharacteristic
45C37×#486C2211yescharacteristic
46C37×#486C2211yescharacteristic
47C37×#470—22no—
48C37×#468—22no—
49C37×#468—22no—
50C37×#441—22no—
51C37×#440—22no—
52C37×#440—22no—
53C37×#428—22no—
54C37×#419—22no—
55C37×#417—22no—
56C4×M16×C37C2211yescharacteristic
57C4×M16×C37C2211yescharacteristic
58C4×M16×C37C2211yescharacteristic
59C37×#322C2211yescharacteristic
60C37×#322C2211yescharacteristic
61C37×#322C2211yescharacteristic
62C82×C37C2211yescharacteristic
63C2×#41×C37—21no—
64C22×Q8×C37—21no—
65C2×Q16×C37—22no—
66C2×SD16×C37—22no—
67C2×SD16×C37—22no—
68C2×M16×C37D412yes—
69C2×M16×C37D412yes—
70C2×M16×C37D412yes—
71C4⋊Q8×C37—21no—
72C4⋊Q8×C37—21no—
73C4⋊Q8×C37—21no—
74C4⋊Q8×C37C2311yescharacteristic
75C4⋊Q8×C37C2311yescharacteristic
76C4⋊Q8×C37C2311yescharacteristic
77C4⋊Q8×C37C2311yescharacteristic
78C4⋊Q8×C37C2311yescharacteristic
79C4⋊Q8×C37C2311yescharacteristic
80C4⋊Q8×C37C2311yescharacteristic
81#127×C37C2311yescharacteristic
82#125×C37—21no—
83#125×C37—21no—
84#124×C37—21no—
85C22⋊Q8×C37—21no—
86C22⋊Q8×C37—21no—
87C22⋊Q8×C37—21no—
88C22⋊Q8×C37—21no—
89#121×C37—21no—
90#121×C37—21no—
91C4×Q8×C37—21no—
92C4×Q8×C37—21no—
93C4×Q8×C37—21no—
94C4×Q8×C37—21no—
95C4×D4×C37—21no—
96C4×D4×C37—21no—
97#117×C37—21no—
98#117×C37—21no—
99C2×C4⋊C4×C37—21no—
100C2×C4⋊C4×C37—21no—
101C2×C42×C37C2311yescharacteristic
102#107×C37—22no—
103#107×C37—22no—
104#107×C37—22no—
105#107×C37—22no—
106#106×C37—22no—
107#106×C37—22no—
108#106×C37—22no—
109#103×C37—22no—
110#103×C37—22no—
111#103×C37—22no—
112#103×C37—22no—
113#103×C37—22no—
114#103×C37—22no—
115#103×C37—22no—
116#103×C37—22no—
117#103×C37—22no—
118#103×C37—22no—
119#102×C37—22no—
120#102×C37—22no—
121#102×C37—22no—
122#102×C37—22no—
123#97×C37D412yes—
124#97×C37D412yes—
125#97×C37D412yes—
126C4×C8×C37C2311yescharacteristic
127C4×C8×C37C2311yescharacteristic
128C4×C8×C37C2311yescharacteristic
129C4×C8×C37C2311yescharacteristic
130C4×C8×C37C2311yescharacteristic
131C4×C8×C37C2311yescharacteristic
132#41×C37—44no—
133C2×Q8×C37—21no—
134C2×Q8×C37—21no—
135C2×Q8×C37—21no—
136C2×Q8×C37—21no—
137C2×Q8×C37—21no—
138C2×Q8×C37—21no—
139C2×Q8×C37—21no—
140C2×Q8×C37—44no—
141C2×Q8×C37—41no—
142C2×D4×C37—21no—
143C2×D4×C37—21no—
144C2×D4×C37—21no—
145C2×D4×C37—41no—
146C22×C4×C37—41no—
147C22×C4×C37—41no—
148C22×C4×C37C2×D411yescharacteristic
149C22×C4×C37C2×D411yescharacteristic
150C22×C4×C37C2×D411yescharacteristic
151Q16×C37—44no—
152SD16×C37—44no—
153SD16×C37—44no—
154M16×C37—24no—
155M16×C37—42no—
156M16×C37—42no—
157C2×C8×C37C2×D412yes—
158C2×C8×C37C2×D412yes—
159C2×C8×C37C2×D412yes—
160C2×C8×C37C2×D412yes—
161C2×C8×C37C2×D412yes—
162C2×C8×C37C2×D412yes—
163C4⋊C4×C37—21no—
164C4⋊C4×C37—21no—
165C4⋊C4×C37—21no—
166C4⋊C4×C37—21no—
167C4⋊C4×C37—21no—
168C4⋊C4×C37—21no—
169C4⋊C4×C37—21no—
170C4⋊C4×C37—21no—
171C4⋊C4×C37—21no—
172C4⋊C4×C37—21no—
173C4⋊C4×C37—21no—
174C4⋊C4×C37—21no—
175C4⋊C4×C37—21no—
176C4⋊C4×C37—21no—
177C4⋊C4×C37—41no—
178C4⋊C4×C37—41no—
179C4⋊C4×C37—41no—
180C4⋊C4×C37—41no—
181C4⋊C4×C37—41no—
182C4⋊C4×C37—41no—
183C22⋊C4×C37—41no—
184C22⋊C4×C37—41no—
185C22⋊C4×C37—41no—
186C22⋊C4×C37—41no—
187C42×C37—41no—
188C42×C37—41no—
189C42×C37C2×D411yescharacteristic
190C42×C37C2×D411yescharacteristic
191C42×C37C2×D411yescharacteristic
192C42×C37C2411yescharacteristic
193C23×C37—41no—
194C23×C37#12711yescharacteristic
195Q8×C37—42no—
196Q8×C37—42no—
197Q8×C37—42no—
198Q8×C37—42no—
199Q8×C37—42no—
200Q8×C37—42no—
201Q8×C37—42no—
202Q8×C37—82no—
203D4×C37—42no—
204D4×C37—42no—
205D4×C37—42no—
206D4×C37—82no—
207C2×C4×C37—22no—
208C2×C4×C37—22no—
209C2×C4×C37—22no—
210C2×C4×C37—41no—
211C2×C4×C37—41no—
212C2×C4×C37—41no—
213C2×C4×C37—41no—
214C2×C4×C37—41no—
215C2×C4×C37—41no—
216C2×C4×C37—41no—
217C2×C4×C37—82no—
218C2×C4×C37—82no—
219C2×C4×C37#12711yescharacteristic
220C2×C4×C37#12711yescharacteristic
221C2×C4×C37#12711yescharacteristic
222C2×C4×C37C22×D411yescharacteristic
223C2×C4×C37C22×D411yescharacteristic
224C2×C4×C37C22×D411yescharacteristic
225C8×C37—22no—
226C8×C37—22no—
227C8×C37—22no—
228C8×C37—22no—
229C8×C37—22no—
230C8×C37#13714yes—
231#19752C3711yesmaximal, characteristic, direct product factor, Sylow
232C22×C37—21no—
233C22×C37—21no—
234C22×C37—21no—
235C22×C37—81no—
236C22×C37—81no—
237C22×C37—81no—
238C22×C37C2×#12711yescharacteristic
239C4×C37—21no—
240C4×C37—21no—
241C4×C37—21no—
242C4×C37—81no—
243C4×C37—81no—
244C4×C37—81no—
245C4×C37—81no—
246C4×C37—81no—
247C4×C37—81no—
248C4×C37—81no—
249C4×C37C2×#13712yes—
250C4×C37#57512yes—
251C4×C37#57512yes—
252#3185C2×C3711yescharacteristic, complemented
253#3182C2×C3711yescharacteristic
254#3182C2×C3711yescharacteristic
255#3165C2×C3711yescharacteristic, complemented
256#3141C2×C3711yescharacteristic
257#3139C2×C3711yescharacteristic, complemented
258#1723C2×C3711yescharacteristic, complemented
259#1720C2×C3711yescharacteristic, complemented
260#1719C2×C3711yescharacteristic, complemented
261#1718C2×C3711yescharacteristic, complemented
262#1718C2×C3711yescharacteristic, complemented
263#1714C2×C3711yescharacteristic, complemented
264#1710C2×C3711yescharacteristic, complemented
265#1708C2×C3711yescharacteristic, complemented
266#1455C2×C3711yescharacteristic, complemented
267C2×C37—41no—
268C2×C37—161no—
269C2×C37#315211yescharacteristic
270C2×C37#315311yescharacteristic
271C2×C37#315311yescharacteristic
272#533C22×C3711yescharacteristic
273#533C22×C3711yescharacteristic
274#532C22×C3711yescharacteristic
275C2×C4⋊Q8C22×C3711yescharacteristic
276#501—22no—
277#500C22×C3711yescharacteristic
278#500C22×C3711yescharacteristic
279#500C22×C3711yescharacteristic
280#500C22×C3711yescharacteristic
281#498C22×C3711yescharacteristic
282#498C22×C3711yescharacteristic
283#498C22×C3711yescharacteristic
284#494C22×C3711yescharacteristic
285#492C22×C3711yescharacteristic
286#492C22×C3711yescharacteristic
287#491—22no—
288#489—22no—
289#487C22×C3711yescharacteristic
290#487C22×C3711yescharacteristic
291#487C22×C3711yescharacteristic
292#487C22×C3711yescharacteristic
293#487C22×C3711yescharacteristic
294#487C22×C3711yescharacteristic
295#487C22×C3711yescharacteristic
296#487C22×C3711yescharacteristic
297#487C22×C3711yescharacteristic
298#487C22×C3711yescharacteristic
299#486C22×C3711yescharacteristic
300#486C22×C3711yescharacteristic
301#486C22×C3711yescharacteristic
302#486C22×C3711yescharacteristic
303#470—22no—
304#468—22no—
305#468—22no—
306#441—22no—
307#440—22no—
308#440—22no—
309#428—22no—
310#419—22no—
311#417—22no—
312C4×M16C22×C3711yescharacteristic
313C4×M16C22×C3711yescharacteristic
314C4×M16C22×C3711yescharacteristic
315#322C22×C3711yescharacteristic
316#322C22×C3711yescharacteristic
317#322C22×C3711yescharacteristic
318C82C22×C3711yescharacteristic
319C37#1975211yescharacteristic, direct product factor, Sylow
320C2×#41—21no—
321C22×Q8—21no—
322C2×Q16—22no—
323C2×SD16—22no—
324C2×SD16—22no—
325C2×M16D4×C3712yes—
326C2×M16D4×C3712yes—
327C2×M16D4×C3712yes—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8C23×C3711yescharacteristic
332C4⋊Q8C23×C3711yescharacteristic
333C4⋊Q8C23×C3711yescharacteristic
334C4⋊Q8C23×C3711yescharacteristic
335C4⋊Q8C23×C3711yescharacteristic
336C4⋊Q8C23×C3711yescharacteristic
337C4⋊Q8C23×C3711yescharacteristic
338#127C23×C3711yescharacteristic
339#125—21no—
340#125—21no—
341#124—21no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346#121—21no—
347#121—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×D4—21no—
353C4×D4—21no—
354#117—21no—
355#117—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C42C23×C3711yescharacteristic
359#107—22no—
360#107—22no—
361#107—22no—
362#107—22no—
363#106—22no—
364#106—22no—
365#106—22no—
366#103—22no—
367#103—22no—
368#103—22no—
369#103—22no—
370#103—22no—
371#103—22no—
372#103—22no—
373#103—22no—
374#103—22no—
375#103—22no—
376#102—22no—
377#102—22no—
378#102—22no—
379#102—22no—
380#97D4×C3712yes—
381#97D4×C3712yes—
382#97D4×C3712yes—
383C4×C8C23×C3711yescharacteristic
384C4×C8C23×C3711yescharacteristic
385C4×C8C23×C3711yescharacteristic
386C4×C8C23×C3711yescharacteristic
387C4×C8C23×C3711yescharacteristic
388C4×C8C23×C3711yescharacteristic
389#41—44no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—44no—
398C2×Q8—41no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4C2×D4×C3711yescharacteristic
406C22×C4C2×D4×C3711yescharacteristic
407C22×C4C2×D4×C3711yescharacteristic
408Q16—44no—
409SD16—44no—
410SD16—44no—
411M16—24no—
412M16—42no—
413M16—42no—
414C2×C8C2×D4×C3712yes—
415C2×C8C2×D4×C3712yes—
416C2×C8C2×D4×C3712yes—
417C2×C8C2×D4×C3712yes—
418C2×C8C2×D4×C3712yes—
419C2×C8C2×D4×C3712yes—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C42—41no—
445C42—41no—
446C42C2×D4×C3711yescharacteristic
447C42C2×D4×C3711yescharacteristic
448C42C2×D4×C3711yescharacteristic
449C42C24×C3711yescharacteristic
450C23—41no—
451C23#127×C3711yescharacteristic
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458Q8—42no—
459Q8—82no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—82no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4#127×C3711yescharacteristic
477C2×C4#127×C3711yescharacteristic
478C2×C4#127×C3711yescharacteristic
479C2×C4C22×D4×C3711yescharacteristic
480C2×C4C22×D4×C3711yescharacteristic
481C2×C4C22×D4×C3711yescharacteristic
482C8—22no—
483C8—22no—
484C8—22no—
485C8—22no—
486C8—22no—
487C8#137×C3714yes—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22C2×#127×C3711yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—81no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—81no—
504C4—81no—
505C4C2×#137×C3712yes—
506C4C37×#57512yes—
507C4C37×#57512yes—
508C2—41no—
509C2—161no—
510C2C37×#315211yescharacteristic
511C2C37×#315311yescharacteristic
512C2C37×#315311yescharacteristic
subgroupG/H
center, socleC22×C37C2×#127
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
1. C37×#3185C2semidirect
4. C37×#3165C2semidirect
6. C37×#3139C2semidirect
7. C37×#1723C2semidirect
8. C37×#1720C2semidirect
9. C37×#1719C2semidirect
10. C37×#1718C2semidirect
11. C37×#1718C2semidirect
12. C37×#1714C2semidirect
13. C37×#1710C2semidirect
14. C37×#1708C2semidirect
15. C37×#1455C2semidirect
231. #19752C37direct (N × H)
252. #3185C2×C37semidirect
255. #3165C2×C37semidirect
257. #3139C2×C37semidirect
258. #1723C2×C37semidirect
259. #1720C2×C37semidirect
260. #1719C2×C37semidirect
261. #1718C2×C37semidirect
262. #1718C2×C37semidirect
263. #1714C2×C37semidirect
264. #1710C2×C37semidirect
265. #1708C2×C37semidirect
266. #1455C2×C37semidirect
319. C37#19752direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#31852
C37×#31822
C37×#31652
C37×#31412
C37×#31392
C37×#17232
C37×#17202
C37×#17192
C37×#17182
C37×#17142
C37×#17102
C37×#17082
C37×#14552
#1975237