Finite Group Databasebeta

← C37×#29699 #22650952

Subgroups — C37×#29699 #22650952

Order 9472.

948 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#541C211yesmaximal, characteristic
2C2×C37×#477C211yesmaximal, characteristic, complemented
3C2×C37×#475C211yesmaximal, characteristic, complemented
4C37×#2628C211yesmaximal, characteristic
5C37×#2059C212yesmaximal, complemented
6C37×#2043C212yesmaximal, complemented
7C37×#2036C212yesmaximal
8C37×#2035C212yesmaximal
9C37×#1805C211yesmaximal, characteristic, complemented
10C37×#1805C211yesmaximal, characteristic, complemented
11C37×#1798C211yesmaximal, characteristic
12C37×#541—24no—
13C37×#541—24no—
14C2×C4⋊Q8×C37C2211yescharacteristic
15C2×C4⋊Q8×C37C2211yescharacteristic
16C2×#126×C37—21no—
17C2×#126×C37—21no—
18C2×#125×C37—21no—
19C2×#125×C37—21no—
20C2×#125×C37C2211yescharacteristic
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×C22⋊Q8×C37C2211yescharacteristic
23C2×C4×Q8×C37C2211yescharacteristic
24C2×C4×Q8×C37C2211yescharacteristic
25C2×#117×C37C2211yescharacteristic
26C37×#477—24no—
27C37×#475—24no—
28C2×#107×C37C2212yes—
29C2×#106×C37C2212yes—
30C2×C4⋊C8×C37C2211yescharacteristic
31C2×C4⋊C8×C37C2211yescharacteristic
32C2×#103×C37C2212yes—
33C2×#103×C37C2212yes—
34C2×#103×C37C2212yes—
35C2×#103×C37C2212yes—
36C2×C22⋊C8×C37C2212yes—
37C37×#400—21no—
38C37×#399—21no—
39C37×#395—21no—
40C37×#393—21no—
41C37×#389C2212yes—
42C37×#382C2211yescharacteristic
43C37×#380C2212yes—
44C37×#340C2212yes—
45C37×#340C2212yes—
46C37×#336C2212yes—
47C22×Q8×C37—21no—
48C22×Q8×C37C2311yescharacteristic
49C22×Q8×C37C2311yescharacteristic
50C23×C4×C37C2311yescharacteristic
51C22×C8×C37C2312yes—
52C22×C8×C37C2312yes—
53C4⋊Q8×C37—22no—
54C4⋊Q8×C37—22no—
55C4⋊Q8×C37—22no—
56C4⋊Q8×C37—22no—
57#126×C37—28no—
58#126×C37—28no—
59#125×C37—28no—
60#125×C37—28no—
61#125×C37—22no—
62#125×C37—22no—
63C22⋊Q8×C37—22no—
64C22⋊Q8×C37—22no—
65C22⋊Q8×C37—22no—
66C22⋊Q8×C37—22no—
67C4×Q8×C37—22no—
68C4×Q8×C37—22no—
69C4×Q8×C37D414yes—
70C4×Q8×C37D414yes—
71#117×C37—22no—
72#117×C37—22no—
73C2×C4⋊C4×C37—21no—
74C2×C4⋊C4×C37—21no—
75C2×C4⋊C4×C37—21no—
76C2×C4⋊C4×C37—21no—
77C2×C4⋊C4×C37—21no—
78C2×C4⋊C4×C37—21no—
79C2×C4⋊C4×C37—21no—
80C2×C4⋊C4×C37—21no—
81C2×C4⋊C4×C37—21no—
82C2×C4⋊C4×C37—22no—
83C2×C4⋊C4×C37D411yescharacteristic
84C2×C4⋊C4×C37D411yescharacteristic
85C2×C4⋊C4×C37C2312yes—
86C2×C4⋊C4×C37C2312yes—
87C2×C4⋊C4×C37C2311yescharacteristic
88C2×C4⋊C4×C37C2311yescharacteristic
89C2×C22⋊C4×C37—21no—
90C2×C22⋊C4×C37—21no—
91C2×C22⋊C4×C37—22no—
92C2×C22⋊C4×C37D411yescharacteristic
93C2×C22⋊C4×C37D411yescharacteristic
94C2×C42×C37—21no—
95C2×C42×C37—21no—
96C2×C42×C37C2311yescharacteristic
97C2×C42×C37C2311yescharacteristic
98#107×C37—24no—
99#106×C37—24no—
100C4⋊C8×C37—22no—
101C4⋊C8×C37—22no—
102#103×C37—24no—
103#103×C37—24no—
104#103×C37—42no—
105#103×C37—42no—
106C22⋊C8×C37—42no—
107#95×C37—22no—
108#95×C37—21no—
109#95×C37—21no—
110#95×C37—22no—
111C24×C37C2×D411yescharacteristic
112C2×Q8×C37—21no—
113C2×Q8×C37—21no—
114C2×Q8×C37—21no—
115C2×Q8×C37—21no—
116C2×Q8×C37—21no—
117C2×Q8×C37—21no—
118C2×Q8×C37—21no—
119C2×Q8×C37—21no—
120C2×Q8×C37—21no—
121C2×Q8×C37—21no—
122C2×Q8×C37—42no—
123C2×Q8×C37—82no—
124C2×Q8×C37C2×D412yes—
125C2×Q8×C37C2×D412yes—
126C22×C4×C37—21no—
127C22×C4×C37—21no—
128C22×C4×C37—21no—
129C22×C4×C37—21no—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
132C22×C4×C37—21no—
133C22×C4×C37—21no—
134C22×C4×C37—21no—
135C22×C4×C37—21no—
136C22×C4×C37—22no—
137C22×C4×C37—22no—
138C22×C4×C37C2×D411yescharacteristic
139C22×C4×C37C2×D411yescharacteristic
140C22×C4×C37C2×D411yescharacteristic
141C22×C4×C37C2×D411yescharacteristic
142C22×C4×C37C2×D411yescharacteristic
143C22×C4×C37C2411yescharacteristic
144C2×C8×C37—22no—
145C2×C8×C37—22no—
146C2×C8×C37—22no—
147C2×C8×C37—22no—
148C2×C8×C37—22no—
149C2×C8×C37—22no—
150C4⋊C4×C37—24no—
151C4⋊C4×C37—24no—
152C4⋊C4×C37—24no—
153C4⋊C4×C37—24no—
154C4⋊C4×C37—24no—
155C4⋊C4×C37—24no—
156C4⋊C4×C37—24no—
157C4⋊C4×C37—24no—
158C4⋊C4×C37—22no—
159C4⋊C4×C37—22no—
160C4⋊C4×C37—21no—
161C4⋊C4×C37—21no—
162C4⋊C4×C37—22no—
163C4⋊C4×C37—22no—
164C4⋊C4×C37—22no—
165C4⋊C4×C37—22no—
166C4⋊C4×C37—42no—
167C4⋊C4×C37—82no—
168C4⋊C4×C37C2×D412yes—
169C4⋊C4×C37C2×D412yes—
170C22⋊C4×C37—24no—
171C22⋊C4×C37—24no—
172C22⋊C4×C37—22no—
173C22⋊C4×C37—22no—
174C22⋊C4×C37—82no—
175C42×C37—24no—
176C42×C37—24no—
177C42×C37—21no—
178C42×C37—21no—
179C42×C37C2×D412yes—
180C42×C37C2×D412yes—
181C23×C37—21no—
182C23×C37—21no—
183C23×C37—21no—
184C23×C37—22no—
185C23×C37—22no—
186C23×C37C22×D411yescharacteristic
187Q8×C37—22no—
188Q8×C37—22no—
189Q8×C37—22no—
190Q8×C37—22no—
191Q8×C37—41no—
192Q8×C37—41no—
193Q8×C37—41no—
194Q8×C37—41no—
195Q8×C37—84no—
196C2×C4×C37—22no—
197C2×C4×C37—22no—
198C2×C4×C37—21no—
199C2×C4×C37—21no—
200C2×C4×C37—22no—
201C2×C4×C37—22no—
202C2×C4×C37—22no—
203C2×C4×C37—22no—
204C2×C4×C37—21no—
205C2×C4×C37—21no—
206C2×C4×C37—21no—
207C2×C4×C37—22no—
208C2×C4×C37—22no—
209C2×C4×C37—41no—
210C2×C4×C37—41no—
211C2×C4×C37—41no—
212C2×C4×C37—41no—
213C2×C4×C37—42no—
214C2×C4×C37—42no—
215C2×C4×C37—41no—
216C2×C4×C37—41no—
217C2×C4×C37—41no—
218C2×C4×C37—41no—
219C2×C4×C37—42no—
220C2×C4×C37—42no—
221C2×C4×C37—42no—
222C2×C4×C37—42no—
223C2×C4×C37—42no—
224C2×C4×C37—42no—
225C2×C4×C37#12012yes—
226C2×C4×C37#12012yes—
227C2×C4×C37C22×D411yescharacteristic
228C2×C4×C37C22×D411yescharacteristic
229C2×C4×C37H(5,𝔽2)11yescharacteristic
230C2×C4×C372−1+411yescharacteristic
231C2×C4×C372−1+411yescharacteristic
232C2×C4×C372−1+411yescharacteristic
233C8×C37—42no—
234C8×C37—42no—
235#29699C3711yesmaximal, characteristic, direct product factor, Sylow
236C22×C37—41no—
237C22×C37—42no—
238C22×C37—42no—
239C22×C37—41no—
240C22×C37—41no—
241C22×C37C2×#12011yescharacteristic
242C22×C37#53611yescharacteristic
243C22×C37#53711yescharacteristic
244C22×C37#57712yes—
245C22×C37#57812yes—
246C4×C37—22no—
247C4×C37—22no—
248C4×C37—41no—
249C4×C37—42no—
250C4×C37—42no—
251C4×C37—41no—
252C4×C37—42no—
253C4×C37—41no—
254C4×C37—42no—
255C4×C37—82no—
256C4×C37—82no—
257C4×C37#53611yescharacteristic
258C4×C37#53611yescharacteristic
259C4×C37#53711yescharacteristic
260C4×C37#53711yescharacteristic
261C2×#541C2×C3711yescharacteristic
262C2×#477C2×C3711yescharacteristic, complemented
263C2×#475C2×C3711yescharacteristic, complemented
264#2628C2×C3711yescharacteristic
265#2059C2×C3712yescomplemented
266#2043C2×C3712yescomplemented
267#2036C2×C3712yes—
268#2035C2×C3712yes—
269#1805C2×C3711yescharacteristic, complemented
270#1805C2×C3711yescharacteristic, complemented
271#1798C2×C3711yescharacteristic
272C2×C37—81no—
273C2×C37#261611yescharacteristic
274C2×C37#301011yescharacteristic
275C2×C37#301111yescharacteristic
276C2×C37#324212yes—
277C2×C37#325812yes—
278#541—24no—
279#541—24no—
280C2×C4⋊Q8C22×C3711yescharacteristic
281C2×C4⋊Q8C22×C3711yescharacteristic
282C2×#126—21no—
283C2×#126—21no—
284C2×#125—21no—
285C2×#125—21no—
286C2×#125C22×C3711yescharacteristic
287C2×C22⋊Q8C22×C3711yescharacteristic
288C2×C22⋊Q8C22×C3711yescharacteristic
289C2×C4×Q8C22×C3711yescharacteristic
290C2×C4×Q8C22×C3711yescharacteristic
291C2×#117C22×C3711yescharacteristic
292#477—24no—
293#475—24no—
294C2×#107C22×C3712yes—
295C2×#106C22×C3712yes—
296C2×C4⋊C8C22×C3711yescharacteristic
297C2×C4⋊C8C22×C3711yescharacteristic
298C2×#103C22×C3712yes—
299C2×#103C22×C3712yes—
300C2×#103C22×C3712yes—
301C2×#103C22×C3712yes—
302C2×C22⋊C8C22×C3712yes—
303#400—21no—
304#399—21no—
305#395—21no—
306#393—21no—
307#389C22×C3712yes—
308#382C22×C3711yescharacteristic
309#380C22×C3712yes—
310#340C22×C3712yes—
311#340C22×C3712yes—
312#336C22×C3712yes—
313C37#2969911yescharacteristic, direct product factor, Sylow
314C22×Q8—21no—
315C22×Q8C23×C3711yescharacteristic
316C22×Q8C23×C3711yescharacteristic
317C23×C4C23×C3711yescharacteristic
318C22×C8C23×C3712yes—
319C22×C8C23×C3712yes—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324#126—28no—
325#126—28no—
326#125—28no—
327#125—28no—
328#125—22no—
329#125—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8D4×C3714yes—
337C4×Q8D4×C3714yes—
338#117—22no—
339#117—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4D4×C3711yescharacteristic
351C2×C4⋊C4D4×C3711yescharacteristic
352C2×C4⋊C4C23×C3712yes—
353C2×C4⋊C4C23×C3712yes—
354C2×C4⋊C4C23×C3711yescharacteristic
355C2×C4⋊C4C23×C3711yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4D4×C3711yescharacteristic
360C2×C22⋊C4D4×C3711yescharacteristic
361C2×C42—21no—
362C2×C42—21no—
363C2×C42C23×C3711yescharacteristic
364C2×C42C23×C3711yescharacteristic
365#107—24no—
366#106—24no—
367C4⋊C8—22no—
368C4⋊C8—22no—
369#103—24no—
370#103—24no—
371#103—42no—
372#103—42no—
373C22⋊C8—42no—
374#95—22no—
375#95—21no—
376#95—21no—
377#95—22no—
378C24C2×D4×C3711yescharacteristic
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—42no—
390C2×Q8—82no—
391C2×Q8C2×D4×C3712yes—
392C2×Q8C2×D4×C3712yes—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4C2×D4×C3711yescharacteristic
406C22×C4C2×D4×C3711yescharacteristic
407C22×C4C2×D4×C3711yescharacteristic
408C22×C4C2×D4×C3711yescharacteristic
409C22×C4C2×D4×C3711yescharacteristic
410C22×C4C24×C3711yescharacteristic
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—42no—
434C4⋊C4—82no—
435C4⋊C4C2×D4×C3712yes—
436C4⋊C4C2×D4×C3712yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—82no—
442C42—24no—
443C42—24no—
444C42—21no—
445C42—21no—
446C42C2×D4×C3712yes—
447C42C2×D4×C3712yes—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—22no—
452C23—22no—
453C23C22×D4×C3711yescharacteristic
454Q8—22no—
455Q8—22no—
456Q8—22no—
457Q8—22no—
458Q8—41no—
459Q8—41no—
460Q8—41no—
461Q8—41no—
462Q8—84no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4#120×C3712yes—
493C2×C4#120×C3712yes—
494C2×C4C22×D4×C3711yescharacteristic
495C2×C4C22×D4×C3711yescharacteristic
496C2×C4H(5,𝔽2)×C3711yescharacteristic
497C2×C42−1+4×C3711yescharacteristic
498C2×C42−1+4×C3711yescharacteristic
499C2×C42−1+4×C3711yescharacteristic
500C8—42no—
501C8—42no—
502C22—41no—
503C22—42no—
504C22—42no—
505C22—41no—
506C22—41no—
507C22C2×#120×C3711yescharacteristic
508C22C37×#53611yescharacteristic
509C22C37×#53711yescharacteristic
510C22C37×#57712yes—
511C22C37×#57812yes—
512C4—22no—
513C4—22no—
514C4—41no—
515C4—42no—
516C4—42no—
517C4—41no—
518C4—42no—
519C4—41no—
520C4—42no—
521C4—82no—
522C4—82no—
523C4C37×#53611yescharacteristic
524C4C37×#53611yescharacteristic
525C4C37×#53711yescharacteristic
526C4C37×#53711yescharacteristic
527C2—81no—
528C2C37×#261611yescharacteristic
529C2C37×#301011yescharacteristic
530C2C37×#301111yescharacteristic
531C2C37×#324212yes—
532C2C37×#325812yes—
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC24×C37C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×#117×C37 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C37×#477C2semidirect
3. C2×C37×#475C2semidirect
5. C37×#2059C2semidirect
6. C37×#2043C2semidirect
9. C37×#1805C2semidirect
10. C37×#1805C2semidirect
235. #29699C37direct (N × H)
262. C2×#477C2×C37semidirect
263. C2×#475C2×C37semidirect
265. #2059C2×C37semidirect
266. #2043C2×C37semidirect
269. #1805C2×C37semidirect
270. #1805C2×C37semidirect
313. C37#29699direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5412
C2×C37×#4772
C2×C37×#4752
C37×#26282
C37×#20592
C37×#20432
C37×#20362
C37×#20352
C37×#18052
C37×#17982
#2969937