Finite Group Databasebeta

← C37×#18908 #22640161

Subgroups — C37×#18908 #22640161

Order 9472.

902 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3507C211yesmaximal, characteristic
2C37×#3229C211yesmaximal, characteristic, complemented
3C37×#3226C211yesmaximal, characteristic
4C2×C37×#462C211yesmaximal, characteristic, complemented
5C37×#1652C214yesmaximal, complemented
6C37×#1644C214yesmaximal, complemented
7C37×#1542C211yesmaximal, characteristic, complemented
8C37×#1480C211yesmaximal, characteristic
9C37×#1479C211yesmaximal, characteristic, complemented
10C22×Q16×C37—21no—
11C37×#559—21no—
12C37×#557—21no—
13C37×#556—22no—
14C37×#556C2212yes—
15C37×#554C2212yes—
16C37×#552—22no—
17C37×#539—22no—
18C37×#536—21no—
19C37×#533C2211yescharacteristic
20C37×#532C2211yescharacteristic
21C2×C4⋊Q8×C37C2211yescharacteristic
22C37×#529—22no—
23C37×#520—21no—
24C2×C4×Q8×C37C2211yescharacteristic
25C37×#500—21no—
26C37×#498C2212yes—
27C37×#487C2212yes—
28C37×#486—21no—
29C37×#483—22no—
30C37×#480—22no—
31C37×#475—22no—
32C37×#474C2214yes—
33C37×#462—22no—
34C37×#462C2214yes—
35C37×#431C2211yescharacteristic
36C37×#431C2211yescharacteristic
37C2×C4⋊C8×C37C2211yescharacteristic
38C2×#103×C37—21no—
39C37×#333C2212yes—
40C37×#332C2212yes—
41C37×Q8⋊C8C2214yes—
42C37×D4⋊C8C2214yes—
43C2×#41×C37—21no—
44C22×Q8×C37—21no—
45C22×Q8×C37D411yescharacteristic
46C2×Q16×C37—24no—
47C2×Q16×C37—44no—
48C22×C8×C37—21no—
49C4⋊Q8×C37—22no—
50C4⋊Q8×C37—21no—
51C4⋊Q8×C37—21no—
52C4⋊Q8×C37—21no—
53C4⋊Q8×C37D411yescharacteristic
54C4⋊Q8×C37C2312yes—
55C4⋊Q8×C37C2311yescharacteristic
56C4⋊Q8×C37C2311yescharacteristic
57#127×C37D411yescharacteristic
58#126×C37—24no—
59#126×C37—24no—
60#125×C37—24no—
61#125×C37—22no—
62#125×C37—21no—
63#124×C37—22no—
64#124×C37—22no—
65#124×C37—21no—
66#123×C37—24no—
67#123×C37—24no—
68C22⋊Q8×C37—22no—
69C22⋊Q8×C37—22no—
70C22⋊Q8×C37—24no—
71C22⋊Q8×C37—21no—
72C22⋊Q8×C37D412yes—
73#121×C37—21no—
74#121×C37D412yes—
75C4×Q8×C37—22no—
76C4×Q8×C37—22no—
77C4×Q8×C37—21no—
78C4×Q8×C37—21no—
79C4×Q8×C37—21no—
80C4×Q8×C37D412yes—
81C4×Q8×C37D412yes—
82C4×Q8×C37C2312yes—
83C4×D4×C37—24no—
84C4×D4×C37—22no—
85C4×D4×C37—22no—
86C4×D4×C37—21no—
87C4×D4×C37C2312yes—
88#117×C37—24no—
89#117×C37—21no—
90#117×C37—22no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—22no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37D411yescharacteristic
96C2×C42×C37—21no—
97C2×C42×C37C2311yescharacteristic
98#107×C37—24no—
99#106×C37—24no—
100C4⋊C8×C37—21no—
101C4⋊C8×C37—21no—
102C4⋊C8×C37C2312yes—
103C4⋊C8×C37C2312yes—
104#103×C37—24no—
105#103×C37—24no—
106#102×C37—24no—
107C22⋊C8×C37—21no—
108C22⋊C8×C37—21no—
109C4×C8×C37—21no—
110C4×C8×C37C2312yes—
111#41×C37—42no—
112#41×C37—42no—
113C2×Q8×C37—21no—
114C2×Q8×C37—21no—
115C2×Q8×C37—21no—
116C2×Q8×C37—22no—
117C2×Q8×C37—22no—
118C2×Q8×C37—22no—
119C2×Q8×C37—41no—
120C2×Q8×C37—42no—
121C2×Q8×C37—42no—
122C2×Q8×C37C2×D412yes—
123C2×Q8×C37C2×D412yes—
124C2×D4×C37—22no—
125C2×D4×C37—21no—
126C2×D4×C37—21no—
127C2×D4×C37C2×D412yes—
128C22×C4×C37—21no—
129C22×C4×C37—24no—
130C22×C4×C37—21no—
131C22×C4×C37—22no—
132C22×C4×C37—41no—
133C22×C4×C37C2×D411yescharacteristic
134C22×C4×C37C2×D411yescharacteristic
135C22×C4×C37C2×D411yescharacteristic
136Q16×C37—48no—
137C2×C8×C37—22no—
138C2×C8×C37—22no—
139C2×C8×C37—22no—
140C2×C8×C37—42no—
141C4⋊C4×C37—24no—
142C4⋊C4×C37—24no—
143C4⋊C4×C37—24no—
144C4⋊C4×C37—22no—
145C4⋊C4×C37—21no—
146C4⋊C4×C37—22no—
147C4⋊C4×C37—21no—
148C4⋊C4×C37—22no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—22no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—22no—
154C4⋊C4×C37—22no—
155C4⋊C4×C37—41no—
156C4⋊C4×C37—41no—
157C4⋊C4×C37C2×D412yes—
158C4⋊C4×C37C2×D412yes—
159C4⋊C4×C37C2×D412yes—
160C22⋊C4×C37—24no—
161C22⋊C4×C37—24no—
162C22⋊C4×C37—24no—
163C22⋊C4×C37—22no—
164C22⋊C4×C37—22no—
165C22⋊C4×C37—22no—
166C42×C37—24no—
167C42×C37—22no—
168C42×C37—22no—
169C42×C37—22no—
170C42×C37C2×D411yescharacteristic
171C42×C37C2×D411yescharacteristic
172C42×C37C2×D411yescharacteristic
173C42×C37C2411yescharacteristic
174C23×C37—22no—
175C23×C37#12011yescharacteristic
176Q8×C37—22no—
177Q8×C37—22no—
178Q8×C37—42no—
179Q8×C37—42no—
180Q8×C37—42no—
181Q8×C37—42no—
182Q8×C37—42no—
183Q8×C37—42no—
184Q8×C37—82no—
185D4×C37—24no—
186D4×C37—44no—
187D4×C37—42no—
188D4×C37—81no—
189C2×C4×C37—22no—
190C2×C4×C37—22no—
191C2×C4×C37—22no—
192C2×C4×C37—22no—
193C2×C4×C37—22no—
194C2×C4×C37—22no—
195C2×C4×C37—41no—
196C2×C4×C37—42no—
197C2×C4×C37—42no—
198C2×C4×C37—42no—
199C2×C4×C37—42no—
200C2×C4×C37—81no—
201C2×C4×C37—84no—
202C2×C4×C37—82no—
203C2×C4×C37#12011yescharacteristic
204C2×C4×C37#12011yescharacteristic
205C2×C4×C37#12011yescharacteristic
206C2×C4×C37#13512yes—
207C2×C4×C37AGL(1,ℤ/8)12yes—
208C2×C4×C37C22×D411yescharacteristic
209C2×C4×C37C22×D411yescharacteristic
210C2×C4×C37C22×D411yescharacteristic
211C8×C37—42no—
212C8×C37—42no—
213C8×C37—42no—
214#18908C3711yesmaximal, characteristic, direct product factor, Sylow
215C22×C37—21no—
216C22×C37—21no—
217C22×C37—42no—
218C22×C37—42no—
219C22×C37—42no—
220C22×C37#44912yes—
221C22×C37C2×#12011yescharacteristic
222C4×C37—21no—
223C4×C37—21no—
224C4×C37—21no—
225C4×C37—42no—
226C4×C37—42no—
227C4×C37—42no—
228C4×C37—42no—
229C4×C37—42no—
230C4×C37—82no—
231C4×C37#44912yes—
232C4×C37C2×#13511yescharacteristic
233C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
234C4×C37#57812yes—
235#3507C2×C3711yescharacteristic
236#3229C2×C3711yescharacteristic, complemented
237#3226C2×C3711yescharacteristic
238C2×#462C2×C3711yescharacteristic, complemented
239#1652C2×C3714yescomplemented
240#1644C2×C3714yescomplemented
241#1542C2×C3711yescharacteristic, complemented
242#1480C2×C3711yescharacteristic
243#1479C2×C3711yescharacteristic, complemented
244C2×C37—22no—
245C2×C37—82no—
246C2×C37C2×#44911yescharacteristic
247C2×C37#301111yescharacteristic
248C2×C37#302211yescharacteristic
249C22×Q16—21no—
250#559—21no—
251#557—21no—
252#556—22no—
253#556C22×C3712yes—
254#554C22×C3712yes—
255#552—22no—
256#539—22no—
257#536—21no—
258#533C22×C3711yescharacteristic
259#532C22×C3711yescharacteristic
260C2×C4⋊Q8C22×C3711yescharacteristic
261#529—22no—
262#520—21no—
263C2×C4×Q8C22×C3711yescharacteristic
264#500—21no—
265#498C22×C3712yes—
266#487C22×C3712yes—
267#486—21no—
268#483—22no—
269#480—22no—
270#475—22no—
271#474C22×C3714yes—
272#462—22no—
273#462C22×C3714yes—
274#431C22×C3711yescharacteristic
275#431C22×C3711yescharacteristic
276C2×C4⋊C8C22×C3711yescharacteristic
277C2×#103—21no—
278#333C22×C3712yes—
279#332C22×C3712yes—
280Q8⋊C8C22×C3714yes—
281D4⋊C8C22×C3714yes—
282C37#1890811yescharacteristic, direct product factor, Sylow
283C2×#41—21no—
284C22×Q8—21no—
285C22×Q8D4×C3711yescharacteristic
286C2×Q16—24no—
287C2×Q16—44no—
288C22×C8—21no—
289C4⋊Q8—22no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8D4×C3711yescharacteristic
294C4⋊Q8C23×C3712yes—
295C4⋊Q8C23×C3711yescharacteristic
296C4⋊Q8C23×C3711yescharacteristic
297#127D4×C3711yescharacteristic
298#126—24no—
299#126—24no—
300#125—24no—
301#125—22no—
302#125—21no—
303#124—22no—
304#124—22no—
305#124—21no—
306#123—24no—
307#123—24no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—24no—
311C22⋊Q8—21no—
312C22⋊Q8D4×C3712yes—
313#121—21no—
314#121D4×C3712yes—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8D4×C3712yes—
321C4×Q8D4×C3712yes—
322C4×Q8C23×C3712yes—
323C4×D4—24no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—21no—
327C4×D4C23×C3712yes—
328#117—24no—
329#117—21no—
330#117—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4D4×C3711yescharacteristic
336C2×C42—21no—
337C2×C42C23×C3711yescharacteristic
338#107—24no—
339#106—24no—
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8C23×C3712yes—
343C4⋊C8C23×C3712yes—
344#103—24no—
345#103—24no—
346#102—24no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C4×C8—21no—
350C4×C8C23×C3712yes—
351#41—42no—
352#41—42no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—41no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8C2×D4×C3712yes—
363C2×Q8C2×D4×C3712yes—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C2×D4×C3712yes—
368C22×C4—21no—
369C22×C4—24no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4C2×D4×C3711yescharacteristic
374C22×C4C2×D4×C3711yescharacteristic
375C22×C4C2×D4×C3711yescharacteristic
376Q16—48no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—42no—
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—24no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4C2×D4×C3712yes—
398C4⋊C4C2×D4×C3712yes—
399C4⋊C4C2×D4×C3712yes—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C42—24no—
407C42—22no—
408C42—22no—
409C42—22no—
410C42C2×D4×C3711yescharacteristic
411C42C2×D4×C3711yescharacteristic
412C42C2×D4×C3711yescharacteristic
413C42C24×C3711yescharacteristic
414C23—22no—
415C23#120×C3711yescharacteristic
416Q8—22no—
417Q8—22no—
418Q8—42no—
419Q8—42no—
420Q8—42no—
421Q8—42no—
422Q8—42no—
423Q8—42no—
424Q8—82no—
425D4—24no—
426D4—44no—
427D4—42no—
428D4—81no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—84no—
442C2×C4—82no—
443C2×C4#120×C3711yescharacteristic
444C2×C4#120×C3711yescharacteristic
445C2×C4#120×C3711yescharacteristic
446C2×C4#135×C3712yes—
447C2×C4AGL(1,ℤ/8)×C3712yes—
448C2×C4C22×D4×C3711yescharacteristic
449C2×C4C22×D4×C3711yescharacteristic
450C2×C4C22×D4×C3711yescharacteristic
451C8—42no—
452C8—42no—
453C8—42no—
454C22—21no—
455C22—21no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22C37×#44912yes—
460C22C2×#120×C3711yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4C37×#44912yes—
471C4C2×#135×C3711yescharacteristic
472C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
473C4C37×#57812yes—
474C2—22no—
475C2—82no—
476C2C2×C37×#44911yescharacteristic
477C2C37×#301111yescharacteristic
478C2C37×#302211yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
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
2. C37×#3229C2semidirect
4. C2×C37×#462C2semidirect
5. C37×#1652C2semidirect
6. C37×#1644C2semidirect
7. C37×#1542C2semidirect
9. C37×#1479C2semidirect
214. #18908C37direct (N × H)
236. #3229C2×C37semidirect
238. C2×#462C2×C37semidirect
239. #1652C2×C37semidirect
240. #1644C2×C37semidirect
241. #1542C2×C37semidirect
243. #1479C2×C37semidirect
282. C37#18908direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35072
C37×#32292
C37×#32262
C2×C37×#4622
C37×#16522
C37×#16442
C37×#15422
C37×#14802
C37×#14792
#1890837