Finite Group Databasebeta

← C37×#18375 #22639628

Subgroups — C37×#18375 #22639628

Order 9472.

942 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3506C211yesmaximal, characteristic
2C37×#3236C211yesmaximal, characteristic, complemented
3C37×#3234C211yesmaximal, characteristic, complemented
4C37×#2633C211yesmaximal, characteristic, complemented
5C37×#1618C214yesmaximal, complemented
6C37×#1612C214yesmaximal, complemented
7C37×#1515C211yesmaximal, characteristic, complemented
8C37×#1514C211yesmaximal, characteristic, complemented
9C37×#1466C211yesmaximal, characteristic, complemented
10C37×#559—22no—
11C37×#556—21no—
12C37×#555—21no—
13C37×#553—22no—
14C37×#550—21no—
15C37×#547—21no—
16C37×#538C2214yes—
17C37×#535—21no—
18C37×#533C2211yescharacteristic
19C37×#532C2211yescharacteristic
20C2×#125×C37C2211yescharacteristic
21C37×#525—22no—
22C37×#520—21no—
23C2×C4×D4×C37C2211yescharacteristic
24C37×#501—21no—
25C37×#501—21no—
26C37×#491—21no—
27C37×#490—21no—
28C37×#484C2212yes—
29C37×#483C2212yes—
30C37×#481C2212yes—
31C37×#480C2212yes—
32C37×#479—22no—
33C37×#478—22no—
34C37×#432C2211yescharacteristic
35C37×#432C2211yescharacteristic
36C37×#399C2212yes—
37C37×#398—21no—
38C37×#397C2212yes—
39C37×#394—21no—
40C37×#385—22no—
41C37×#383C2211yescharacteristic
42C37×#328C2214yes—
43C37×#327C2214yes—
44C37×#323C2214yes—
45C2×#41×C37—22no—
46C2×#41×C37—21no—
47C22×D4×C37D411yescharacteristic
48C23×C4×C37D412yes—
49C4⋊Q8×C37D411yescharacteristic
50C4⋊Q8×C37D411yescharacteristic
51C4⋊Q8×C37D411yescharacteristic
52#127×C37—22no—
53#127×C37D411yescharacteristic
54#126×C37—24no—
55#125×C37—21no—
56#125×C37—21no—
57#125×C37—21no—
58#125×C37—21no—
59#125×C37—21no—
60#124×C37—22no—
61#124×C37—24no—
62#124×C37—21no—
63#123×C37—24no—
64#123×C37—24no—
65C22⋊Q8×C37—22no—
66C22⋊Q8×C37—21no—
67C22⋊Q8×C37C2312yes—
68#121×C37—22no—
69#121×C37—22no—
70#121×C37—22no—
71#121×C37—24no—
72#121×C37—21no—
73#121×C37C2312yes—
74#120×C37—24no—
75C4×Q8×C37—22no—
76C4×Q8×C37—21no—
77C4×Q8×C37D412yes—
78C4×D4×C37—22no—
79C4×D4×C37—24no—
80C4×D4×C37—24no—
81C4×D4×C37—21no—
82C4×D4×C37—21no—
83C4×D4×C37—21no—
84C4×D4×C37—21no—
85C4×D4×C37—21no—
86C4×D4×C37D412yes—
87#117×C37—22no—
88#117×C37—22no—
89#117×C37—21no—
90C2×C4⋊C4×C37—22no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—21no—
93C2×C4⋊C4×C37—22no—
94C2×C4⋊C4×C37D411yescharacteristic
95C2×C4⋊C4×C37C2311yescharacteristic
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C22⋊C4×C37—22no—
98C2×C22⋊C4×C37—22no—
99C2×C22⋊C4×C37C2312yes—
100C2×C42×C37C2311yescharacteristic
101#107×C37—22no—
102#107×C37—22no—
103#106×C37—22no—
104#106×C37—22no—
105C4⋊C8×C37—21no—
106C4⋊C8×C37—21no—
107#103×C37—22no—
108#103×C37—22no—
109#102×C37—22no—
110#102×C37—22no—
111C22⋊C8×C37C2312yes—
112C22⋊C8×C37C2312yes—
113#97×C37—21no—
114#97×C37—21no—
115#95×C37—21no—
116#95×C37—21no—
117#95×C37—22no—
118#95×C37C2312yes—
119C24×C37C2×D412yes—
120#41×C37—44no—
121#41×C37—84no—
122C2×Q8×C37—21no—
123C2×Q8×C37—21no—
124C2×Q8×C37C2×D412yes—
125C2×D4×C37—22no—
126C2×D4×C37—24no—
127C2×D4×C37—24no—
128C2×D4×C37—21no—
129C2×D4×C37—21no—
130C2×D4×C37—21no—
131C2×D4×C37—21no—
132C2×D4×C37—42no—
133C2×D4×C37C2×D412yes—
134C22×C4×C37—24no—
135C22×C4×C37—22no—
136C22×C4×C37—22no—
137C22×C4×C37—22no—
138C22×C4×C37—22no—
139C22×C4×C37—21no—
140C22×C4×C37—21no—
141C22×C4×C37—82no—
142C22×C4×C37C2×D411yescharacteristic
143C22×C4×C37C2×D412yes—
144C22×C4×C37C2×D411yescharacteristic
145C22×C4×C37C2411yescharacteristic
146C2×C8×C37—22no—
147C2×C8×C37—22no—
148C4⋊C4×C37—24no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—21no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—22no—
156C4⋊C4×C37—22no—
157C4⋊C4×C37—21no—
158C4⋊C4×C37—21no—
159C4⋊C4×C37—21no—
160C4⋊C4×C37—21no—
161C4⋊C4×C37—41no—
162C4⋊C4×C37—41no—
163C4⋊C4×C37—41no—
164C4⋊C4×C37—41no—
165C4⋊C4×C37—82no—
166C4⋊C4×C37C2×D412yes—
167C4⋊C4×C37C2×D412yes—
168C22⋊C4×C37—24no—
169C22⋊C4×C37—24no—
170C22⋊C4×C37—24no—
171C22⋊C4×C37—22no—
172C22⋊C4×C37—22no—
173C22⋊C4×C37—22no—
174C22⋊C4×C37—22no—
175C22⋊C4×C37—22no—
176C22⋊C4×C37—44no—
177C22⋊C4×C37—82no—
178C42×C37—24no—
179C42×C37—22no—
180C42×C37C2×D411yescharacteristic
181C42×C37C2×D411yescharacteristic
182C42×C37C2×D411yescharacteristic
183C42×C37C2×D411yescharacteristic
184C23×C37—22no—
185C23×C37—22no—
186C23×C37—22no—
187C23×C37—22no—
188C23×C37—42no—
189C23×C37—42no—
190C23×C37C22×D411yescharacteristic
191Q8×C37—42no—
192Q8×C37—42no—
193Q8×C37—42no—
194D4×C37—42no—
195D4×C37—42no—
196D4×C37—42no—
197D4×C37—42no—
198D4×C37—42no—
199D4×C37—44no—
200D4×C37—84no—
201D4×C37—84no—
202C2×C4×C37—22no—
203C2×C4×C37—22no—
204C2×C4×C37—22no—
205C2×C4×C37—22no—
206C2×C4×C37—22no—
207C2×C4×C37—41no—
208C2×C4×C37—41no—
209C2×C4×C37—44no—
210C2×C4×C37—44no—
211C2×C4×C37—42no—
212C2×C4×C37—41no—
213C2×C4×C37—42no—
214C2×C4×C37—41no—
215C2×C4×C37—42no—
216C2×C4×C37—41no—
217C2×C4×C37—41no—
218C2×C4×C37—42no—
219C2×C4×C37—42no—
220C2×C4×C37—82no—
221C2×C4×C37—84no—
222C2×C4×C37#12011yescharacteristic
223C2×C4×C37#12011yescharacteristic
224C2×C4×C37#12011yescharacteristic
225C2×C4×C37#12011yescharacteristic
226C2×C4×C37C22×D411yescharacteristic
227C2×C4×C37C22×D411yescharacteristic
228C8×C37—42no—
229C8×C37—42no—
230#18375C3711yesmaximal, characteristic, direct product factor, Sylow
231C22×C37—21no—
232C22×C37—21no—
233C22×C37—44no—
234C22×C37—42no—
235C22×C37—42no—
236C22×C37—42no—
237C22×C37—42no—
238C22×C37—42no—
239C22×C37—42no—
240C22×C37—82no—
241C22×C37C2×#12011yescharacteristic
242C22×C37#57512yes—
243C4×C37—21no—
244C4×C37—21no—
245C4×C37—21no—
246C4×C37—21no—
247C4×C37—21no—
248C4×C37—21no—
249C4×C37—42no—
250C4×C37—42no—
251C4×C37—42no—
252C4×C37—42no—
253C4×C37—82no—
254C4×C37—81no—
255C4×C37—81no—
256#3506C2×C3711yescharacteristic
257#3236C2×C3711yescharacteristic, complemented
258#3234C2×C3711yescharacteristic, complemented
259#2633C2×C3711yescharacteristic, complemented
260#1618C2×C3714yescomplemented
261#1612C2×C3714yescomplemented
262#1515C2×C3711yescharacteristic, complemented
263#1514C2×C3711yescharacteristic, complemented
264#1466C2×C3711yescharacteristic, complemented
265C2×C37—22no—
266C2×C37—82no—
267C2×C37—82no—
268C2×C37#300511yescharacteristic
269C2×C37#301911yescharacteristic
270C2×C37#302811yescharacteristic
271#559—22no—
272#556—21no—
273#555—21no—
274#553—22no—
275#550—21no—
276#547—21no—
277#538C22×C3714yes—
278#535—21no—
279#533C22×C3711yescharacteristic
280#532C22×C3711yescharacteristic
281C2×#125C22×C3711yescharacteristic
282#525—22no—
283#520—21no—
284C2×C4×D4C22×C3711yescharacteristic
285#501—21no—
286#501—21no—
287#491—21no—
288#490—21no—
289#484C22×C3712yes—
290#483C22×C3712yes—
291#481C22×C3712yes—
292#480C22×C3712yes—
293#479—22no—
294#478—22no—
295#432C22×C3711yescharacteristic
296#432C22×C3711yescharacteristic
297#399C22×C3712yes—
298#398—21no—
299#397C22×C3712yes—
300#394—21no—
301#385—22no—
302#383C22×C3711yescharacteristic
303#328C22×C3714yes—
304#327C22×C3714yes—
305#323C22×C3714yes—
306C37#1837511yescharacteristic, direct product factor, Sylow
307C2×#41—22no—
308C2×#41—21no—
309C22×D4D4×C3711yescharacteristic
310C23×C4D4×C3712yes—
311C4⋊Q8D4×C3711yescharacteristic
312C4⋊Q8D4×C3711yescharacteristic
313C4⋊Q8D4×C3711yescharacteristic
314#127—22no—
315#127D4×C3711yescharacteristic
316#126—24no—
317#125—21no—
318#125—21no—
319#125—21no—
320#125—21no—
321#125—21no—
322#124—22no—
323#124—24no—
324#124—21no—
325#123—24no—
326#123—24no—
327C22⋊Q8—22no—
328C22⋊Q8—21no—
329C22⋊Q8C23×C3712yes—
330#121—22no—
331#121—22no—
332#121—22no—
333#121—24no—
334#121—21no—
335#121C23×C3712yes—
336#120—24no—
337C4×Q8—22no—
338C4×Q8—21no—
339C4×Q8D4×C3712yes—
340C4×D4—22no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4D4×C3712yes—
349#117—22no—
350#117—22no—
351#117—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C3711yescharacteristic
357C2×C4⋊C4C23×C3711yescharacteristic
358C2×C4⋊C4C23×C3711yescharacteristic
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4C23×C3712yes—
362C2×C42C23×C3711yescharacteristic
363#107—22no—
364#107—22no—
365#106—22no—
366#106—22no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369#103—22no—
370#103—22no—
371#102—22no—
372#102—22no—
373C22⋊C8C23×C3712yes—
374C22⋊C8C23×C3712yes—
375#97—21no—
376#97—21no—
377#95—21no—
378#95—21no—
379#95—22no—
380#95C23×C3712yes—
381C24C2×D4×C3712yes—
382#41—44no—
383#41—84no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8C2×D4×C3712yes—
387C2×D4—22no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—42no—
395C2×D4C2×D4×C3712yes—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—82no—
404C22×C4C2×D4×C3711yescharacteristic
405C22×C4C2×D4×C3712yes—
406C22×C4C2×D4×C3711yescharacteristic
407C22×C4C24×C3711yescharacteristic
408C2×C8—22no—
409C2×C8—22no—
410C4⋊C4—24no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—82no—
428C4⋊C4C2×D4×C3712yes—
429C4⋊C4C2×D4×C3712yes—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—44no—
439C22⋊C4—82no—
440C42—24no—
441C42—22no—
442C42C2×D4×C3711yescharacteristic
443C42C2×D4×C3711yescharacteristic
444C42C2×D4×C3711yescharacteristic
445C42C2×D4×C3711yescharacteristic
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—42no—
451C23—42no—
452C23C22×D4×C3711yescharacteristic
453Q8—42no—
454Q8—42no—
455Q8—42no—
456D4—42no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—44no—
462D4—84no—
463D4—84no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—82no—
483C2×C4—84no—
484C2×C4#120×C3711yescharacteristic
485C2×C4#120×C3711yescharacteristic
486C2×C4#120×C3711yescharacteristic
487C2×C4#120×C3711yescharacteristic
488C2×C4C22×D4×C3711yescharacteristic
489C2×C4C22×D4×C3711yescharacteristic
490C8—42no—
491C8—42no—
492C22—21no—
493C22—21no—
494C22—44no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—82no—
502C22C2×#120×C3711yescharacteristic
503C22C37×#57512yes—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—82no—
515C4—81no—
516C4—81no—
517C2—22no—
518C2—82no—
519C2—82no—
520C2C37×#300511yescharacteristic
521C2C37×#301911yescharacteristic
522C2C37×#302811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3506C2
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×#3236C2semidirect
3. C37×#3234C2semidirect
4. C37×#2633C2semidirect
5. C37×#1618C2semidirect
6. C37×#1612C2semidirect
7. C37×#1515C2semidirect
8. C37×#1514C2semidirect
9. C37×#1466C2semidirect
230. #18375C37direct (N × H)
257. #3236C2×C37semidirect
258. #3234C2×C37semidirect
259. #2633C2×C37semidirect
260. #1618C2×C37semidirect
261. #1612C2×C37semidirect
262. #1515C2×C37semidirect
263. #1514C2×C37semidirect
264. #1466C2×C37semidirect
306. C37#18375direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35062
C37×#32362
C37×#32342
C37×#26332
C37×#16182
C37×#16122
C37×#15152
C37×#15142
C37×#14662
#1837537