Finite Group Databasebeta

← C37×#18953 #22640206

Subgroups — C37×#18953 #22640206

Order 9472.

846 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3550C211yesmaximal, characteristic
2C37×#3249C211yesmaximal, characteristic, complemented
3C37×#3235C211yesmaximal, characteristic
4C37×#3231C211yesmaximal, characteristic, complemented
5C37×#1652C212yesmaximal, complemented
6C37×#1649C212yesmaximal, complemented
7C37×#1638C212yesmaximal, complemented
8C37×#1637C212yesmaximal, complemented
9C37×#1552C211yesmaximal, characteristic, complemented
10C37×#1497C211yesmaximal, characteristic, complemented
11C37×#1480C211yesmaximal, characteristic
12C37×#563—22no—
13C37×#559—21no—
14Q82×C37—21no—
15C37×#556—21no—
16C37×#556C2212yes—
17D4×Q8×C37—21no—
18D4×Q8×C37C2212yes—
19C37×#542—22no—
20C37×#542—22no—
21C37×#536—22no—
22C37×#533C2211yescharacteristic
23C37×#533C2211yescharacteristic
24C37×#533C2211yescharacteristic
25C37×#532C2211yescharacteristic
26C37×#501—21no—
27C37×#500C2211yescharacteristic
28C37×#498C2211yescharacteristic
29C37×#490—21no—
30C37×#487C2211yescharacteristic
31C37×#487C2211yescharacteristic
32C37×#485—22no—
33C37×#482—22no—
34C37×#479—22no—
35C37×#477—21no—
36C37×#477C2212yes—
37C37×#476C2212yes—
38C37×#474C2212yes—
39C37×#467—22no—
40C37×#462—21no—
41C37×#462C2212yes—
42C37×#432C2211yescharacteristic
43C37×#431C2211yescharacteristic
44C2×C4⋊C8×C37C2211yescharacteristic
45C37×#332C2212yes—
46C37×#332C2212yes—
47C37×Q8⋊C8C2212yes—
48C37×Q8⋊C8C2212yes—
49C37×D4⋊C8C2212yes—
50C37×D4⋊C8C2212yes—
51C2×#41×C37—21no—
52C22×Q8×C37—22no—
53C2×Q16×C37—22no—
54C22×C8×C37—21no—
55C4⋊Q8×C37—24no—
56C4⋊Q8×C37—22no—
57C4⋊Q8×C37—22no—
58C4⋊Q8×C37D411yescharacteristic
59C4⋊Q8×C37D411yescharacteristic
60C4⋊Q8×C37D411yescharacteristic
61C4⋊Q8×C37C2311yescharacteristic
62C4⋊Q8×C37C2311yescharacteristic
63C4⋊Q8×C37C2311yescharacteristic
64C4⋊Q8×C37C2311yescharacteristic
65#127×C37D411yescharacteristic
66#126×C37—24no—
67#126×C37—24no—
68#125×C37—21no—
69#125×C37—21no—
70#125×C37D412yes—
71#124×C37—24no—
72#124×C37—22no—
73#124×C37—22no—
74#124×C37—21no—
75#123×C37—24no—
76#123×C37—24no—
77C22⋊Q8×C37—24no—
78C22⋊Q8×C37—22no—
79C22⋊Q8×C37—21no—
80C22⋊Q8×C37—21no—
81C22⋊Q8×C37—21no—
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—24no—
84C22⋊Q8×C37—21no—
85C22⋊Q8×C37—21no—
86C22⋊Q8×C37D412yes—
87#121×C37—21no—
88#121×C37D412yes—
89C4×Q8×C37—22no—
90C4×Q8×C37—22no—
91C4×Q8×C37—21no—
92C4×Q8×C37—21no—
93C4×Q8×C37—21no—
94C4×Q8×C37—21no—
95C4×Q8×C37—21no—
96C4×Q8×C37C2312yes—
97C4×D4×C37—22no—
98C4×D4×C37—22no—
99C4×D4×C37—21no—
100C4×D4×C37C2312yes—
101#117×C37—21no—
102#117×C37—22no—
103#117×C37—21no—
104#117×C37D412yes—
105C2×C42×C37C2311yescharacteristic
106#107×C37—22no—
107#107×C37—22no—
108#107×C37—22no—
109#106×C37—22no—
110#106×C37—22no—
111C4⋊C8×C37—21no—
112C4⋊C8×C37—21no—
113C4⋊C8×C37C2312yes—
114C4⋊C8×C37C2312yes—
115#103×C37—22no—
116#103×C37—22no—
117#103×C37—22no—
118#103×C37—22no—
119#102×C37—22no—
120#102×C37—22no—
121C22⋊C8×C37—21no—
122C22⋊C8×C37—21no—
123#97×C37—21no—
124C4×C8×C37C2311yescharacteristic
125C4×C8×C37C2311yescharacteristic
126#41×C37—81no—
127#41×C37—81no—
128C2×Q8×C37—24no—
129C2×Q8×C37—21no—
130C2×Q8×C37—21no—
131C2×Q8×C37—21no—
132C2×Q8×C37—21no—
133C2×Q8×C37—21no—
134C2×Q8×C37—21no—
135C2×Q8×C37—82no—
136C2×Q8×C37—82no—
137C2×Q8×C37C2×D412yes—
138C2×D4×C37—22no—
139C2×D4×C37—21no—
140C2×D4×C37—21no—
141C2×D4×C37C2×D412yes—
142C22×C4×C37—24no—
143C22×C4×C37—22no—
144C22×C4×C37C2×D411yescharacteristic
145C22×C4×C37C2×D411yescharacteristic
146C22×C4×C37C2×D411yescharacteristic
147Q16×C37—82no—
148C2×C8×C37—21no—
149C2×C8×C37—21no—
150C2×C8×C37—22no—
151C2×C8×C37—22no—
152C2×C8×C37—81no—
153C4⋊C4×C37—24no—
154C4⋊C4×C37—24no—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—21no—
157C4⋊C4×C37—21no—
158C4⋊C4×C37—21no—
159C4⋊C4×C37—22no—
160C4⋊C4×C37—22no—
161C4⋊C4×C37—22no—
162C4⋊C4×C37—21no—
163C4⋊C4×C37—21no—
164C4⋊C4×C37—22no—
165C4⋊C4×C37—21no—
166C4⋊C4×C37—21no—
167C4⋊C4×C37—21no—
168C4⋊C4×C37—21no—
169C4⋊C4×C37—41no—
170C4⋊C4×C37—41no—
171C4⋊C4×C37C2×D412yes—
172C4⋊C4×C37C2×D412yes—
173C4⋊C4×C37C2×D412yes—
174C4⋊C4×C37C2×D412yes—
175C22⋊C4×C37—24no—
176C22⋊C4×C37—24no—
177C22⋊C4×C37—24no—
178C22⋊C4×C37—22no—
179C22⋊C4×C37—22no—
180C22⋊C4×C37—22no—
181C22⋊C4×C37—22no—
182C22⋊C4×C37—41no—
183C42×C37—24no—
184C42×C37—22no—
185C42×C37—22no—
186C42×C37—41no—
187C42×C37C2×D411yescharacteristic
188C42×C37C2×D411yescharacteristic
189C42×C37C2×D411yescharacteristic
190C42×C37C2411yescharacteristic
191C23×C37—22no—
192C23×C37#12011yescharacteristic
193Q8×C37—22no—
194Q8×C37—22no—
195Q8×C37—42no—
196Q8×C37—42no—
197Q8×C37—41no—
198Q8×C37—41no—
199Q8×C37—42no—
200Q8×C37—41no—
201Q8×C37—41no—
202Q8×C37—81no—
203Q8×C37—84no—
204D4×C37—24no—
205D4×C37—42no—
206D4×C37—81no—
207D4×C37—82no—
208C2×C4×C37—21no—
209C2×C4×C37—21no—
210C2×C4×C37—22no—
211C2×C4×C37—22no—
212C2×C4×C37—22no—
213C2×C4×C37—22no—
214C2×C4×C37—22no—
215C2×C4×C37—22no—
216C2×C4×C37—41no—
217C2×C4×C37—42no—
218C2×C4×C37—42no—
219C2×C4×C37—41no—
220C2×C4×C37—41no—
221C2×C4×C37—84no—
222C2×C4×C37#12011yescharacteristic
223C2×C4×C37#12011yescharacteristic
224C2×C4×C37#12011yescharacteristic
225C2×C4×C37C22×D411yescharacteristic
226C2×C4×C37C22×D411yescharacteristic
227C2×C4×C37C22×D411yescharacteristic
228C8×C37—41no—
229C8×C37—41no—
230C8×C37—42no—
231C8×C37—42no—
232#18953C3711yesmaximal, characteristic, direct product factor, Sylow
233C22×C37—21no—
234C22×C37—21no—
235C22×C37—21no—
236C22×C37—42no—
237C22×C37—42no—
238C22×C37—42no—
239C22×C37C2×#12011yescharacteristic
240C4×C37—21no—
241C4×C37—21no—
242C4×C37—21no—
243C4×C37—21no—
244C4×C37—42no—
245C4×C37—42no—
246C4×C37—42no—
247C4×C37—42no—
248C4×C37—42no—
249C4×C37—81no—
250C4×C37—81no—
251C4×C37#57611yescharacteristic
252C4×C37#57711yescharacteristic
253C4×C37#57812yes—
254#3550C2×C3711yescharacteristic
255#3249C2×C3711yescharacteristic, complemented
256#3235C2×C3711yescharacteristic
257#3231C2×C3711yescharacteristic, complemented
258#1652C2×C3712yescomplemented
259#1649C2×C3712yescomplemented
260#1638C2×C3712yescomplemented
261#1637C2×C3712yescomplemented
262#1552C2×C3711yescharacteristic, complemented
263#1497C2×C3711yescharacteristic, complemented
264#1480C2×C3711yescharacteristic
265C2×C37—41no—
266C2×C37—82no—
267C2×C37#301111yescharacteristic
268C2×C37#301211yescharacteristic
269C2×C37#302011yescharacteristic
270#563—22no—
271#559—21no—
272Q82—21no—
273#556—21no—
274#556C22×C3712yes—
275D4×Q8—21no—
276D4×Q8C22×C3712yes—
277#542—22no—
278#542—22no—
279#536—22no—
280#533C22×C3711yescharacteristic
281#533C22×C3711yescharacteristic
282#533C22×C3711yescharacteristic
283#532C22×C3711yescharacteristic
284#501—21no—
285#500C22×C3711yescharacteristic
286#498C22×C3711yescharacteristic
287#490—21no—
288#487C22×C3711yescharacteristic
289#487C22×C3711yescharacteristic
290#485—22no—
291#482—22no—
292#479—22no—
293#477—21no—
294#477C22×C3712yes—
295#476C22×C3712yes—
296#474C22×C3712yes—
297#467—22no—
298#462—21no—
299#462C22×C3712yes—
300#432C22×C3711yescharacteristic
301#431C22×C3711yescharacteristic
302C2×C4⋊C8C22×C3711yescharacteristic
303#332C22×C3712yes—
304#332C22×C3712yes—
305Q8⋊C8C22×C3712yes—
306Q8⋊C8C22×C3712yes—
307D4⋊C8C22×C3712yes—
308D4⋊C8C22×C3712yes—
309C37#1895311yescharacteristic, direct product factor, Sylow
310C2×#41—21no—
311C22×Q8—22no—
312C2×Q16—22no—
313C22×C8—21no—
314C4⋊Q8—24no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8D4×C3711yescharacteristic
318C4⋊Q8D4×C3711yescharacteristic
319C4⋊Q8D4×C3711yescharacteristic
320C4⋊Q8C23×C3711yescharacteristic
321C4⋊Q8C23×C3711yescharacteristic
322C4⋊Q8C23×C3711yescharacteristic
323C4⋊Q8C23×C3711yescharacteristic
324#127D4×C3711yescharacteristic
325#126—24no—
326#126—24no—
327#125—21no—
328#125—21no—
329#125D4×C3712yes—
330#124—24no—
331#124—22no—
332#124—22no—
333#124—21no—
334#123—24no—
335#123—24no—
336C22⋊Q8—24no—
337C22⋊Q8—22no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—22no—
342C22⋊Q8—24no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8D4×C3712yes—
346#121—21no—
347#121D4×C3712yes—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C23×C3712yes—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—21no—
359C4×D4C23×C3712yes—
360#117—21no—
361#117—22no—
362#117—21no—
363#117D4×C3712yes—
364C2×C42C23×C3711yescharacteristic
365#107—22no—
366#107—22no—
367#107—22no—
368#106—22no—
369#106—22no—
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8C23×C3712yes—
373C4⋊C8C23×C3712yes—
374#103—22no—
375#103—22no—
376#103—22no—
377#103—22no—
378#102—22no—
379#102—22no—
380C22⋊C8—21no—
381C22⋊C8—21no—
382#97—21no—
383C4×C8C23×C3711yescharacteristic
384C4×C8C23×C3711yescharacteristic
385#41—81no—
386#41—81no—
387C2×Q8—24no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—82no—
395C2×Q8—82no—
396C2×Q8C2×D4×C3712yes—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4C2×D4×C3712yes—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4C2×D4×C3711yescharacteristic
404C22×C4C2×D4×C3711yescharacteristic
405C22×C4C2×D4×C3711yescharacteristic
406Q16—82no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—81no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4C2×D4×C3712yes—
431C4⋊C4C2×D4×C3712yes—
432C4⋊C4C2×D4×C3712yes—
433C4⋊C4C2×D4×C3712yes—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—41no—
442C42—24no—
443C42—22no—
444C42—22no—
445C42—41no—
446C42C2×D4×C3711yescharacteristic
447C42C2×D4×C3711yescharacteristic
448C42C2×D4×C3711yescharacteristic
449C42C24×C3711yescharacteristic
450C23—22no—
451C23#120×C3711yescharacteristic
452Q8—22no—
453Q8—22no—
454Q8—42no—
455Q8—42no—
456Q8—41no—
457Q8—41no—
458Q8—42no—
459Q8—41no—
460Q8—41no—
461Q8—81no—
462Q8—84no—
463D4—24no—
464D4—42no—
465D4—81no—
466D4—82no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—84no—
481C2×C4#120×C3711yescharacteristic
482C2×C4#120×C3711yescharacteristic
483C2×C4#120×C3711yescharacteristic
484C2×C4C22×D4×C3711yescharacteristic
485C2×C4C22×D4×C3711yescharacteristic
486C2×C4C22×D4×C3711yescharacteristic
487C8—41no—
488C8—41no—
489C8—42no—
490C8—42no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22C2×#120×C3711yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—81no—
508C4—81no—
509C4C37×#57611yescharacteristic
510C4C37×#57711yescharacteristic
511C4C37×#57812yes—
512C2—41no—
513C2—82no—
514C2C37×#301111yescharacteristic
515C2C37×#301211yescharacteristic
516C2C37×#302011yescharacteristic
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×#3249C2semidirect
4. C37×#3231C2semidirect
5. C37×#1652C2semidirect
6. C37×#1649C2semidirect
7. C37×#1638C2semidirect
8. C37×#1637C2semidirect
9. C37×#1552C2semidirect
10. C37×#1497C2semidirect
232. #18953C37direct (N × H)
255. #3249C2×C37semidirect
257. #3231C2×C37semidirect
258. #1652C2×C37semidirect
259. #1649C2×C37semidirect
260. #1638C2×C37semidirect
261. #1637C2×C37semidirect
262. #1552C2×C37semidirect
263. #1497C2×C37semidirect
309. C37#18953direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35502
C37×#32492
C37×#32352
C37×#32312
C37×#16522
C37×#16492
C37×#16382
C37×#16372
C37×#15522
C37×#14972
C37×#14802
#1895337