Finite Group Databasebeta

← C37×#18344 #22639597

Subgroups — C37×#18344 #22639597

Order 9472.

924 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3461C211yesmaximal, characteristic
2C37×#3238C212yesmaximal, complemented
3C37×#2546C211yesmaximal, characteristic, complemented
4C37×#1611C212yesmaximal, complemented
5C37×#1610C212yesmaximal
6C37×#1609C214yesmaximal, complemented
7C37×#1509C212yesmaximal, complemented
8C37×#1467C211yesmaximal, characteristic, complemented
9C37×#544C2211yescharacteristic
10C37×#542—22no—
11C37×#541—22no—
12C37×#539—21no—
13C37×#539C2212yes—
14C37×#537C2211yescharacteristic
15C37×#536—21no—
16C37×#533—22no—
17C2×C4⋊Q8×C37—21no—
18C2×C4⋊Q8×C37C2211yescharacteristic
19C37×#529—22no—
20C37×#529—21no—
21C37×#529C2212yes—
22C4×#41×C37—21no—
23C2×C4×Q8×C37C2211yescharacteristic
24C37×#501—22no—
25C37×#489—22no—
26C37×#483C2214yes—
27C37×#480C2214yes—
28C37×#477—22no—
29C37×#476—22no—
30C37×#432C2212yes—
31C37×#398C2212yes—
32C37×#398C2212yes—
33C37×#391—21no—
34C37×#389—21no—
35C37×#389—21no—
36C4×C4⋊C4×C37C2211yescharacteristic
37C37×#328C2214yes—
38C37×#327C2214yes—
39C37×#324C2212yes—
40C37×#324C2212yes—
41C2×#41×C37—21no—
42C22×Q8×C37—21no—
43C22×Q8×C37D411yescharacteristic
44C4⋊Q8×C37—22no—
45C4⋊Q8×C37—22no—
46C4⋊Q8×C37—22no—
47C4⋊Q8×C37—22no—
48C4⋊Q8×C37—44no—
49#126×C37—22no—
50#126×C37—22no—
51#126×C37—22no—
52#126×C37—22no—
53#125×C37—21no—
54#125×C37—22no—
55#125×C37—22no—
56#125×C37—22no—
57#125×C37D412yes—
58#124×C37—22no—
59#124×C37—21no—
60#124×C37D412yes—
61#123×C37—22no—
62#123×C37—22no—
63#123×C37—22no—
64#123×C37—22no—
65C22⋊Q8×C37—22no—
66C22⋊Q8×C37—22no—
67C22⋊Q8×C37—22no—
68C22⋊Q8×C37—22no—
69C22⋊Q8×C37—21no—
70C22⋊Q8×C37—22no—
71C22⋊Q8×C37C2312yes—
72#121×C37—22no—
73#121×C37—21no—
74#121×C37C2312yes—
75C4×Q8×C37—21no—
76C4×Q8×C37—21no—
77C4×Q8×C37—21no—
78C4×Q8×C37—22no—
79C4×Q8×C37—22no—
80C4×Q8×C37D412yes—
81C4×D4×C37—21no—
82C4×D4×C37—21no—
83C4×D4×C37—21no—
84C4×D4×C37—22no—
85C4×D4×C37—22no—
86C4×D4×C37D412yes—
87#117×C37—22no—
88#117×C37—22no—
89#117×C37—21no—
90#117×C37—22no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—22no—
93C2×C4⋊C4×C37—22no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37D411yescharacteristic
96C2×C4⋊C4×C37C2312yes—
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C42×C37—22no—
100C2×C42×C37—21no—
101C2×C42×C37D411yescharacteristic
102C2×C42×C37D411yescharacteristic
103C2×C42×C37C2311yescharacteristic
104#107×C37—24no—
105#106×C37—24no—
106C4⋊C8×C37—22no—
107#103×C37—24no—
108#102×C37—24no—
109C22⋊C8×C37C2314yes—
110#97×C37—22no—
111#95×C37—22no—
112#95×C37—22no—
113#95×C37C2312yes—
114#41×C37—42no—
115#41×C37—42no—
116C2×Q8×C37—21no—
117C2×Q8×C37—21no—
118C2×Q8×C37—22no—
119C2×Q8×C37—22no—
120C2×Q8×C37—41no—
121C2×Q8×C37—42no—
122C2×Q8×C37—42no—
123C2×Q8×C37—42no—
124C2×Q8×C37C2×D412yes—
125C2×D4×C37—21no—
126C2×D4×C37—22no—
127C2×D4×C37—21no—
128C2×D4×C37C2×D412yes—
129C22×C4×C37—22no—
130C22×C4×C37—22no—
131C22×C4×C37—22no—
132C22×C4×C37—22no—
133C22×C4×C37—22no—
134C22×C4×C37C2×D411yescharacteristic
135C22×C4×C37C2×D411yescharacteristic
136C22×C4×C37C2×D411yescharacteristic
137C22×C4×C37C2×D411yescharacteristic
138C22×C4×C37C2×D411yescharacteristic
139C22×C4×C37C2×D411yescharacteristic
140C22×C4×C37C2411yescharacteristic
141C2×C8×C37—24no—
142C4⋊C4×C37—24no—
143C4⋊C4×C37—21no—
144C4⋊C4×C37—22no—
145C4⋊C4×C37—21no—
146C4⋊C4×C37—22no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—22no—
151C4⋊C4×C37—22no—
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—44no—
160C4⋊C4×C37—41no—
161C4⋊C4×C37—41no—
162C4⋊C4×C37—44no—
163C4⋊C4×C37C2×D412yes—
164C4⋊C4×C37C2×D412yes—
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—
174C42×C37—22no—
175C42×C37—22no—
176C42×C37—21no—
177C42×C37—22no—
178C42×C37—21no—
179C42×C37—21no—
180C42×C37—21no—
181C42×C37—42no—
182C42×C37C2×D412yes—
183C42×C37C2×D412yes—
184C23×C37—22no—
185C23×C37C22×D411yescharacteristic
186Q8×C37—44no—
187Q8×C37—42no—
188Q8×C37—42no—
189Q8×C37—84no—
190Q8×C37—81no—
191D4×C37—42no—
192D4×C37—42no—
193D4×C37—42no—
194D4×C37—42no—
195D4×C37—81no—
196C2×C4×C37—21no—
197C2×C4×C37—21no—
198C2×C4×C37—21no—
199C2×C4×C37—21no—
200C2×C4×C37—22no—
201C2×C4×C37—24no—
202C2×C4×C37—21no—
203C2×C4×C37—22no—
204C2×C4×C37—22no—
205C2×C4×C37—21no—
206C2×C4×C37—21no—
207C2×C4×C37—22no—
208C2×C4×C37—21no—
209C2×C4×C37—21no—
210C2×C4×C37—41no—
211C2×C4×C37—44no—
212C2×C4×C37—42no—
213C2×C4×C37—42no—
214C2×C4×C37—44no—
215C2×C4×C37—41no—
216C2×C4×C37—41no—
217C2×C4×C37—42no—
218C2×C4×C37—42no—
219C2×C4×C37—42no—
220C2×C4×C37—82no—
221C2×C4×C37#12011yescharacteristic
222C2×C4×C37#12012yes—
223C2×C4×C37#12011yescharacteristic
224C2×C4×C37AGL(1,ℤ/8)12yes—
225C2×C4×C37C22×D412yes—
226C8×C37—44no—
227#18344C3711yesmaximal, characteristic, direct product factor, Sylow
228C22×C37—21no—
229C22×C37—21no—
230C22×C37—42no—
231C22×C37—42no—
232C22×C37—42no—
233C22×C37C2×#12011yescharacteristic
234C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
235C22×C37#57511yescharacteristic
236C4×C37—22no—
237C4×C37—22no—
238C4×C37—21no—
239C4×C37—22no—
240C4×C37—44no—
241C4×C37—41no—
242C4×C37—42no—
243C4×C37—42no—
244C4×C37—41no—
245C4×C37—41no—
246C4×C37—42no—
247C4×C37—82no—
248C4×C37#45612yes—
249#3461C2×C3711yescharacteristic
250#3238C2×C3712yescomplemented
251#2546C2×C3711yescharacteristic, complemented
252#1611C2×C3712yescomplemented
253#1610C2×C3712yes—
254#1609C2×C3714yescomplemented
255#1509C2×C3712yescomplemented
256#1467C2×C3711yescharacteristic, complemented
257C2×C37—21no—
258C2×C37—21no—
259C2×C37—82no—
260C2×C37#300611yescharacteristic
261C2×C37C2×#45611yescharacteristic
262C2×C37#302811yescharacteristic
263#544C22×C3711yescharacteristic
264#542—22no—
265#541—22no—
266#539—21no—
267#539C22×C3712yes—
268#537C22×C3711yescharacteristic
269#536—21no—
270#533—22no—
271C2×C4⋊Q8—21no—
272C2×C4⋊Q8C22×C3711yescharacteristic
273#529—22no—
274#529—21no—
275#529C22×C3712yes—
276C4×#41—21no—
277C2×C4×Q8C22×C3711yescharacteristic
278#501—22no—
279#489—22no—
280#483C22×C3714yes—
281#480C22×C3714yes—
282#477—22no—
283#476—22no—
284#432C22×C3712yes—
285#398C22×C3712yes—
286#398C22×C3712yes—
287#391—21no—
288#389—21no—
289#389—21no—
290C4×C4⋊C4C22×C3711yescharacteristic
291#328C22×C3714yes—
292#327C22×C3714yes—
293#324C22×C3712yes—
294#324C22×C3712yes—
295C37#1834411yescharacteristic, direct product factor, Sylow
296C2×#41—21no—
297C22×Q8—21no—
298C22×Q8D4×C3711yescharacteristic
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303C4⋊Q8—44no—
304#126—22no—
305#126—22no—
306#126—22no—
307#126—22no—
308#125—21no—
309#125—22no—
310#125—22no—
311#125—22no—
312#125D4×C3712yes—
313#124—22no—
314#124—21no—
315#124D4×C3712yes—
316#123—22no—
317#123—22no—
318#123—22no—
319#123—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—21no—
325C22⋊Q8—22no—
326C22⋊Q8C23×C3712yes—
327#121—22no—
328#121—21no—
329#121C23×C3712yes—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8D4×C3712yes—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4D4×C3712yes—
342#117—22no—
343#117—22no—
344#117—21no—
345#117—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4D4×C3711yescharacteristic
351C2×C4⋊C4C23×C3712yes—
352C2×C4⋊C4C23×C3711yescharacteristic
353C2×C4⋊C4C23×C3711yescharacteristic
354C2×C42—22no—
355C2×C42—21no—
356C2×C42D4×C3711yescharacteristic
357C2×C42D4×C3711yescharacteristic
358C2×C42C23×C3711yescharacteristic
359#107—24no—
360#106—24no—
361C4⋊C8—22no—
362#103—24no—
363#102—24no—
364C22⋊C8C23×C3714yes—
365#97—22no—
366#95—22no—
367#95—22no—
368#95C23×C3712yes—
369#41—42no—
370#41—42no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—41no—
376C2×Q8—42no—
377C2×Q8—42no—
378C2×Q8—42no—
379C2×Q8C2×D4×C3712yes—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4C2×D4×C3712yes—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4C2×D4×C3711yescharacteristic
390C22×C4C2×D4×C3711yescharacteristic
391C22×C4C2×D4×C3711yescharacteristic
392C22×C4C2×D4×C3711yescharacteristic
393C22×C4C2×D4×C3711yescharacteristic
394C22×C4C2×D4×C3711yescharacteristic
395C22×C4C24×C3711yescharacteristic
396C2×C8—24no—
397C4⋊C4—24no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—24no—
414C4⋊C4—44no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—44no—
418C4⋊C4C2×D4×C3712yes—
419C4⋊C4C2×D4×C3712yes—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C42—22no—
430C42—22no—
431C42—21no—
432C42—22no—
433C42—21no—
434C42—21no—
435C42—21no—
436C42—42no—
437C42C2×D4×C3712yes—
438C42C2×D4×C3712yes—
439C23—22no—
440C23C22×D4×C3711yescharacteristic
441Q8—44no—
442Q8—42no—
443Q8—42no—
444Q8—84no—
445Q8—81no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—42no—
450D4—81no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—41no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4#120×C3711yescharacteristic
477C2×C4#120×C3712yes—
478C2×C4#120×C3711yescharacteristic
479C2×C4AGL(1,ℤ/8)×C3712yes—
480C2×C4C22×D4×C3712yes—
481C8—44no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22C2×#120×C3711yescharacteristic
488C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
489C22C37×#57511yescharacteristic
490C4—22no—
491C4—22no—
492C4—21no—
493C4—22no—
494C4—44no—
495C4—41no—
496C4—42no—
497C4—42no—
498C4—41no—
499C4—41no—
500C4—42no—
501C4—82no—
502C4C37×#45612yes—
503C2—21no—
504C2—21no—
505C2—82no—
506C2C37×#300611yescharacteristic
507C2C2×C37×#45611yescharacteristic
508C2C37×#302811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#537C22
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×#2546C2semidirect
4. C37×#1611C2semidirect
6. C37×#1609C2semidirect
7. C37×#1509C2semidirect
8. C37×#1467C2semidirect
227. #18344C37direct (N × H)
250. #3238C2×C37semidirect
251. #2546C2×C37semidirect
252. #1611C2×C37semidirect
254. #1609C2×C37semidirect
255. #1509C2×C37semidirect
256. #1467C2×C37semidirect
295. C37#18344direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34612
C37×#32382
C37×#25462
C37×#16112
C37×#16102
C37×#16092
C37×#15092
C37×#14672
#1834437