Finite Group Databasebeta

← C37×#18371 #22639624

Subgroups — C37×#18371 #22639624

Order 9472.

924 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3493C211yesmaximal, characteristic
2C37×#3238C212yesmaximal, complemented
3C37×#2621C211yesmaximal, characteristic, complemented
4C37×#1612C214yesmaximal, complemented
5C37×#1611C212yesmaximal, complemented
6C37×#1610C212yesmaximal, complemented
7C37×#1512C212yesmaximal, complemented
8C37×#1464C211yesmaximal, characteristic, complemented
9C37×#556—22no—
10C37×#555—22no—
11C37×#553—22no—
12C37×#552—22no—
13C37×#544C2211yescharacteristic
14C37×#538—21no—
15C37×#538C2212yes—
16C37×#537C2211yescharacteristic
17C2×C4⋊Q8×C37C2211yescharacteristic
18C37×#529—21no—
19C37×#529C2212yes—
20C37×#525—21no—
21C2×C22⋊Q8×C37—21no—
22C37×#520—21no—
23C2×#117×C37C2211yescharacteristic
24C37×#501—22no—
25C37×#489—22no—
26C37×#483C2214yes—
27C37×#480C2214yes—
28C37×#477—22no—
29C37×#476—22no—
30C37×#432C2212yes—
31C37×#398—21no—
32C37×#398C2212yes—
33C37×#397—21no—
34C37×#397C2212yes—
35C37×#391—21no—
36C37×#382C2211yescharacteristic
37C37×#328C2214yes—
38C37×#327C2214yes—
39C37×#324C2212yes—
40C37×#323C2212yes—
41C2×#41×C37—21no—
42C22×Q8×C37—21no—
43C23×C4×C37D411yescharacteristic
44C4⋊Q8×C37—22no—
45C4⋊Q8×C37—22no—
46C4⋊Q8×C37—22no—
47#126×C37—22no—
48#126×C37—22no—
49#126×C37—22no—
50#126×C37—22no—
51#125×C37—21no—
52#125×C37—22no—
53#125×C37D412yes—
54#124×C37—21no—
55#124×C37—22no—
56#124×C37—22no—
57#124×C37D412yes—
58#123×C37—22no—
59#123×C37—22no—
60#123×C37—22no—
61C22⋊Q8×C37—21no—
62C22⋊Q8×C37—21no—
63C22⋊Q8×C37—21no—
64C22⋊Q8×C37—22no—
65C22⋊Q8×C37—44no—
66C22⋊Q8×C37C2312yes—
67#121×C37—21no—
68#121×C37—21no—
69#121×C37—22no—
70#121×C37—22no—
71#121×C37—22no—
72#121×C37—21no—
73#121×C37C2312yes—
74#120×C37—22no—
75C4×Q8×C37—22no—
76C4×Q8×C37—21no—
77C4×Q8×C37D412yes—
78C4×D4×C37—22no—
79C4×D4×C37—22no—
80C4×D4×C37—22no—
81C4×D4×C37—21no—
82C4×D4×C37—22no—
83C4×D4×C37—22no—
84C4×D4×C37D412yes—
85#117×C37—22no—
86#117×C37—22no—
87#117×C37—21no—
88#117×C37—22no—
89#117×C37—22no—
90#117×C37—22no—
91C2×C4⋊C4×C37—22no—
92C2×C4⋊C4×C37—21no—
93C2×C4⋊C4×C37—22no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37D411yescharacteristic
96C2×C4⋊C4×C37C2312yes—
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C22⋊C4×C37—22no—
99C2×C22⋊C4×C37D411yescharacteristic
100C2×C22⋊C4×C37C2311yescharacteristic
101C2×C42×C37D411yescharacteristic
102C2×C42×C37C2311yescharacteristic
103#107×C37—24no—
104#106×C37—24no—
105C4⋊C8×C37—22no—
106#103×C37—24no—
107#102×C37—24no—
108C22⋊C8×C37C2314yes—
109#97×C37—22no—
110#95×C37—21no—
111#95×C37—22no—
112#95×C37—22no—
113#95×C37C2312yes—
114C24×C37C2×D411yescharacteristic
115#41×C37—42no—
116#41×C37—42no—
117C2×Q8×C37—21no—
118C2×Q8×C37—21no—
119C2×Q8×C37—42no—
120C2×Q8×C37—42no—
121C2×Q8×C37—41no—
122C2×Q8×C37—41no—
123C2×Q8×C37C2×D412yes—
124C2×D4×C37—21no—
125C2×D4×C37—22no—
126C2×D4×C37—22no—
127C2×D4×C37—22no—
128C2×D4×C37—21no—
129C2×D4×C37C2×D412yes—
130C22×C4×C37—22no—
131C22×C4×C37—22no—
132C22×C4×C37—21no—
133C22×C4×C37—21no—
134C22×C4×C37—22no—
135C22×C4×C37—22no—
136C22×C4×C37—22no—
137C22×C4×C37—22no—
138C22×C4×C37—41no—
139C22×C4×C37C2×D411yescharacteristic
140C22×C4×C37C2×D411yescharacteristic
141C22×C4×C37C2×D411yescharacteristic
142C22×C4×C37C2×D411yescharacteristic
143C22×C4×C37C2×D411yescharacteristic
144C22×C4×C37C2411yescharacteristic
145C2×C8×C37—24no—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—22no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—22no—
153C4⋊C4×C37—22no—
154C4⋊C4×C37—22no—
155C4⋊C4×C37—22no—
156C4⋊C4×C37—22no—
157C4⋊C4×C37—22no—
158C4⋊C4×C37—24no—
159C4⋊C4×C37—42no—
160C4⋊C4×C37—42no—
161C4⋊C4×C37—44no—
162C4⋊C4×C37C2×D412yes—
163C4⋊C4×C37C2×D412yes—
164C22⋊C4×C37—22no—
165C22⋊C4×C37—22no—
166C22⋊C4×C37—22no—
167C22⋊C4×C37—22no—
168C22⋊C4×C37—22no—
169C22⋊C4×C37—22no—
170C22⋊C4×C37—22no—
171C22⋊C4×C37—22no—
172C22⋊C4×C37—22no—
173C22⋊C4×C37—22no—
174C22⋊C4×C37—22no—
175C22⋊C4×C37—44no—
176C42×C37—22no—
177C42×C37—22no—
178C42×C37—21no—
179C42×C37—21no—
180C42×C37—22no—
181C42×C37C2×D412yes—
182C42×C37C2×D412yes—
183C23×C37—21no—
184C23×C37—22no—
185C23×C37—21no—
186C23×C37—21no—
187C23×C37—41no—
188C23×C37—41no—
189C23×C37C22×D411yescharacteristic
190Q8×C37—42no—
191Q8×C37—42no—
192Q8×C37—82no—
193Q8×C37—82no—
194Q8×C37—81no—
195D4×C37—42no—
196D4×C37—42no—
197D4×C37—42no—
198D4×C37—42no—
199D4×C37—82no—
200D4×C37—81no—
201D4×C37—82no—
202C2×C4×C37—21no—
203C2×C4×C37—21no—
204C2×C4×C37—21no—
205C2×C4×C37—21no—
206C2×C4×C37—21no—
207C2×C4×C37—22no—
208C2×C4×C37—21no—
209C2×C4×C37—22no—
210C2×C4×C37—22no—
211C2×C4×C37—41no—
212C2×C4×C37—41no—
213C2×C4×C37—42no—
214C2×C4×C37—42no—
215C2×C4×C37—44no—
216C2×C4×C37—41no—
217C2×C4×C37—41no—
218C2×C4×C37—42no—
219C2×C4×C37—42no—
220C2×C4×C37—42no—
221C2×C4×C37—42no—
222C2×C4×C37—42no—
223C2×C4×C37—42no—
224C2×C4×C37—82no—
225C2×C4×C37—82no—
226C2×C4×C37#12012yes—
227C2×C4×C37#12011yescharacteristic
228C2×C4×C37#12011yescharacteristic
229C2×C4×C37AGL(1,ℤ/8)12yes—
230C2×C4×C37C22×D412yes—
231C8×C37—44no—
232#18371C3711yesmaximal, characteristic, direct product factor, Sylow
233C22×C37—21no—
234C22×C37—21no—
235C22×C37—42no—
236C22×C37—41no—
237C22×C37—42no—
238C22×C37—42no—
239C22×C37—41no—
240C22×C37—42no—
241C22×C37—41no—
242C22×C37—81no—
243C22×C37C2×#12011yescharacteristic
244C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
245C22×C37#57511yescharacteristic
246C4×C37—22no—
247C4×C37—21no—
248C4×C37—21no—
249C4×C37—22no—
250C4×C37—22no—
251C4×C37—42no—
252C4×C37—41no—
253C4×C37—42no—
254C4×C37—41no—
255C4×C37—42no—
256C4×C37—82no—
257C4×C37—82no—
258#3493C2×C3711yescharacteristic
259#3238C2×C3712yescomplemented
260#2621C2×C3711yescharacteristic, complemented
261#1612C2×C3714yescomplemented
262#1611C2×C3712yescomplemented
263#1610C2×C3712yescomplemented
264#1512C2×C3712yescomplemented
265#1464C2×C3711yescharacteristic, complemented
266C2×C37—21no—
267C2×C37—21no—
268C2×C37—82no—
269C2×C37—81no—
270C2×C37#300611yescharacteristic
271C2×C37#302211yescharacteristic
272C2×C37#302811yescharacteristic
273#556—22no—
274#555—22no—
275#553—22no—
276#552—22no—
277#544C22×C3711yescharacteristic
278#538—21no—
279#538C22×C3712yes—
280#537C22×C3711yescharacteristic
281C2×C4⋊Q8C22×C3711yescharacteristic
282#529—21no—
283#529C22×C3712yes—
284#525—21no—
285C2×C22⋊Q8—21no—
286#520—21no—
287C2×#117C22×C3711yescharacteristic
288#501—22no—
289#489—22no—
290#483C22×C3714yes—
291#480C22×C3714yes—
292#477—22no—
293#476—22no—
294#432C22×C3712yes—
295#398—21no—
296#398C22×C3712yes—
297#397—21no—
298#397C22×C3712yes—
299#391—21no—
300#382C22×C3711yescharacteristic
301#328C22×C3714yes—
302#327C22×C3714yes—
303#324C22×C3712yes—
304#323C22×C3712yes—
305C37#1837111yescharacteristic, direct product factor, Sylow
306C2×#41—21no—
307C22×Q8—21no—
308C23×C4D4×C3711yescharacteristic
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312#126—22no—
313#126—22no—
314#126—22no—
315#126—22no—
316#125—21no—
317#125—22no—
318#125D4×C3712yes—
319#124—21no—
320#124—22no—
321#124—22no—
322#124D4×C3712yes—
323#123—22no—
324#123—22no—
325#123—22no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—22no—
330C22⋊Q8—44no—
331C22⋊Q8C23×C3712yes—
332#121—21no—
333#121—21no—
334#121—22no—
335#121—22no—
336#121—22no—
337#121—21no—
338#121C23×C3712yes—
339#120—22no—
340C4×Q8—22no—
341C4×Q8—21no—
342C4×Q8D4×C3712yes—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—21no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4D4×C3712yes—
350#117—22no—
351#117—22no—
352#117—21no—
353#117—22no—
354#117—22no—
355#117—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4D4×C3711yescharacteristic
361C2×C4⋊C4C23×C3712yes—
362C2×C4⋊C4C23×C3711yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4D4×C3711yescharacteristic
365C2×C22⋊C4C23×C3711yescharacteristic
366C2×C42D4×C3711yescharacteristic
367C2×C42C23×C3711yescharacteristic
368#107—24no—
369#106—24no—
370C4⋊C8—22no—
371#103—24no—
372#102—24no—
373C22⋊C8C23×C3714yes—
374#97—22no—
375#95—21no—
376#95—22no—
377#95—22no—
378#95C23×C3712yes—
379C24C2×D4×C3711yescharacteristic
380#41—42no—
381#41—42no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—42no—
385C2×Q8—42no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8C2×D4×C3712yes—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4C2×D4×C3712yes—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4C2×D4×C3711yescharacteristic
405C22×C4C2×D4×C3711yescharacteristic
406C22×C4C2×D4×C3711yescharacteristic
407C22×C4C2×D4×C3711yescharacteristic
408C22×C4C2×D4×C3711yescharacteristic
409C22×C4C24×C3711yescharacteristic
410C2×C8—24no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—24no—
424C4⋊C4—42no—
425C4⋊C4—42no—
426C4⋊C4—44no—
427C4⋊C4C2×D4×C3712yes—
428C4⋊C4C2×D4×C3712yes—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—44no—
441C42—22no—
442C42—22no—
443C42—21no—
444C42—21no—
445C42—22no—
446C42C2×D4×C3712yes—
447C42C2×D4×C3712yes—
448C23—21no—
449C23—22no—
450C23—21no—
451C23—21no—
452C23—41no—
453C23—41no—
454C23C22×D4×C3711yescharacteristic
455Q8—42no—
456Q8—42no—
457Q8—82no—
458Q8—82no—
459Q8—81no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—82no—
465D4—81no—
466D4—82no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—82no—
490C2×C4—82no—
491C2×C4#120×C3712yes—
492C2×C4#120×C3711yescharacteristic
493C2×C4#120×C3711yescharacteristic
494C2×C4AGL(1,ℤ/8)×C3712yes—
495C2×C4C22×D4×C3712yes—
496C8—44no—
497C22—21no—
498C22—21no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—42no—
503C22—41no—
504C22—42no—
505C22—41no—
506C22—81no—
507C22C2×#120×C3711yescharacteristic
508C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
509C22C37×#57511yescharacteristic
510C4—22no—
511C4—21no—
512C4—21no—
513C4—22no—
514C4—22no—
515C4—42no—
516C4—41no—
517C4—42no—
518C4—41no—
519C4—42no—
520C4—82no—
521C4—82no—
522C2—21no—
523C2—21no—
524C2—81no—
525C2—82no—
526C2C37×#300611yescharacteristic
527C2C37×#302211yescharacteristic
528C2C37×#302811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3493C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3238C2semidirect
3. C37×#2621C2semidirect
4. C37×#1612C2semidirect
5. C37×#1611C2semidirect
6. C37×#1610C2semidirect
7. C37×#1512C2semidirect
8. C37×#1464C2semidirect
232. #18371C37direct (N × H)
259. #3238C2×C37semidirect
260. #2621C2×C37semidirect
261. #1612C2×C37semidirect
262. #1611C2×C37semidirect
263. #1610C2×C37semidirect
264. #1512C2×C37semidirect
265. #1464C2×C37semidirect
305. C37#18371direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34932
C37×#32382
C37×#26212
C37×#16122
C37×#16112
C37×#16102
C37×#15122
C37×#14642
#1837137