Finite Group Databasebeta

← C37×#10986 #22632239

Subgroups — C37×#10986 #22632239

Order 9472.

1334 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#537C211yesmaximal, characteristic
2C2×C37×#421C212yesmaximal, complemented
3C2×C37×#413C211yesmaximal, characteristic, complemented
4C2×C37×#410C211yesmaximal, characteristic, complemented
5C37×#1736C212yesmaximal, complemented
6C22×#41×C37C2211yescharacteristic
7C22×#41×C37C2211yescharacteristic
8C22×M16×C37C2212yes—
9C37×#537—24no—
10C37×#537—24no—
11C2×C22⋊Q8×C37—21no—
12C2×C22⋊Q8×C37C412yescomplemented
13C2×#121×C37—21no—
14C2×#121×C37—22no—
15C2×#121×C37C412yescomplemented
16C2×#117×C37C2212yes—
17C22×C4⋊C4×C37C2211yescharacteristic
18C37×#421—24no—
19C37×#421—24no—
20C2×#104×C37—24no—
21C37×#413—24no—
22C2×#101×C37—21no—
23C2×#100×C37—21no—
24C37×#410—24no—
25C2×#99×C37—22no—
26C37×#340—24no—
27C2×#41×C37—22no—
28C2×#41×C37—22no—
29C2×#41×C37—22no—
30C2×#41×C37—22no—
31C2×#41×C37—22no—
32C2×#41×C37—22no—
33C2×#41×C37—22no—
34C2×#41×C37—22no—
35C2×#41×C37—22no—
36C2×#41×C37—22no—
37C2×#41×C37—22no—
38C2×#41×C37D414yes—
39C22×Q8×C37C2×C411yescharacteristic
40C22×Q8×C37D411yescharacteristic
41C22×D4×C37—21no—
42C22×D4×C37—22no—
43C22×D4×C37C2×C411yescharacteristic
44C22×D4×C37D412yes—
45C22×D4×C37D411yescharacteristic
46C23×C4×C37—21no—
47C23×C4×C37—21no—
48C23×C4×C37C2×C412yes—
49C23×C4×C37C2311yescharacteristic
50C2×M16×C37—22no—
51C2×M16×C37—22no—
52C2×M16×C37—22no—
53C2×M16×C37—22no—
54C2×M16×C37—22no—
55C2×M16×C37D414yescomplemented
56C22×C8×C37—22no—
57C22⋊Q8×C37—28no—
58C22⋊Q8×C37—24no—
59C22⋊Q8×C37—24no—
60#121×C37—216no—
61#121×C37—28no—
62#121×C37—24no—
63#121×C37—24no—
64#117×C37—22no—
65#117×C37—22no—
66#117×C37—22no—
67#117×C37D414yescomplemented
68C2×C4⋊C4×C37—22no—
69C2×C4⋊C4×C37—21no—
70C2×C4⋊C4×C37—22no—
71C2×C4⋊C4×C37—22no—
72C2×C4⋊C4×C37C2×C412yes—
73C2×C4⋊C4×C37D414yes—
74C2×C22⋊C4×C37—22no—
75C2×C22⋊C4×C37—22no—
76C2×C22⋊C4×C37—22no—
77C2×C42×C37—22no—
78#104×C37—216no—
79#101×C37—24no—
80#100×C37—24no—
81#99×C37—28no—
82C24×C37—21no—
83C24×C37C22⋊C412yes—
84C24×C37C2×D411yescharacteristic
85#41×C37—24no—
86#41×C37—24no—
87#41×C37—24no—
88#41×C37—24no—
89#41×C37—42no—
90#41×C37—42no—
91#41×C37—42no—
92#41×C37—42no—
93#41×C37—42no—
94#41×C37—42no—
95#41×C37—42no—
96#41×C37—42no—
97#41×C37—42no—
98#41×C37—42no—
99#41×C37—42no—
100#41×C37—42no—
101C2×Q8×C37—21no—
102C2×Q8×C37—21no—
103C2×Q8×C37—22no—
104C2×Q8×C37—22no—
105C2×Q8×C37—21no—
106C2×Q8×C37—22no—
107C2×Q8×C37—22no—
108C2×Q8×C37C22⋊C412yes—
109C2×D4×C37—22no—
110C2×D4×C37—24no—
111C2×D4×C37—24no—
112C2×D4×C37—24no—
113C2×D4×C37—22no—
114C2×D4×C37—28no—
115C2×D4×C37—21no—
116C2×D4×C37—22no—
117C2×D4×C37—22no—
118C2×D4×C37—21no—
119C2×D4×C37—22no—
120C2×D4×C37—22no—
121C2×D4×C37—21no—
122C2×D4×C37—41no—
123C2×D4×C37—42no—
124C2×D4×C37—41no—
125C2×D4×C37—84no—
126C2×D4×C37C22⋊C412yes—
127C22×C4×C37—22no—
128C22×C4×C37—21no—
129C22×C4×C37—24no—
130C22×C4×C37—22no—
131C22×C4×C37—22no—
132C22×C4×C37—24no—
133C22×C4×C37—24no—
134C22×C4×C37—24no—
135C22×C4×C37—41no—
136C22×C4×C37—42no—
137C22×C4×C37—41no—
138C22×C4×C37—42no—
139C22×C4×C37—82no—
140C22×C4×C37C22⋊C412yes—
141C22×C4×C37C22×C411yescharacteristic
142C22×C4×C37C2×D412yes—
143C22×C4×C37C2×D412yes—
144C22×C4×C37C2×D412yes—
145C22×C4×C37C2×D412yes—
146C22×C4×C37C2×D411yescharacteristic
147C22×C4×C37#4112yes—
148C22×C4×C37#4112yes—
149M16×C37—24no—
150M16×C37—24no—
151M16×C37—42no—
152M16×C37—42no—
153C2×C8×C37—24no—
154C2×C8×C37—42no—
155C2×C8×C37—42no—
156C4⋊C4×C37—28no—
157C4⋊C4×C37—22no—
158C4⋊C4×C37—24no—
159C4⋊C4×C37—24no—
160C4⋊C4×C37—42no—
161C4⋊C4×C37C22⋊C414yes—
162C22⋊C4×C37—28no—
163C22⋊C4×C37—28no—
164C22⋊C4×C37—24no—
165C22⋊C4×C37—42no—
166C42×C37—24no—
167C42×C37—42no—
168C23×C37—22no—
169C23×C37—22no—
170C23×C37—22no—
171C23×C37—22no—
172C23×C37—41no—
173C23×C37—41no—
174C23×C37—42no—
175C23×C37—42no—
176C23×C37—42no—
177C23×C37—42no—
178C23×C37—41no—
179C23×C37—41no—
180C23×C37C2×C22⋊C411yescharacteristic
181C23×C37#12012yes—
182C23×C37#12011yescharacteristic
183C23×C37#12112yes—
184C23×C37#12311yescharacteristic
185Q8×C37—24no—
186Q8×C37—42no—
187Q8×C37—42no—
188Q8×C37—42no—
189D4×C37—24no—
190D4×C37—44no—
191D4×C37—44no—
192D4×C37—44no—
193D4×C37—44no—
194D4×C37—42no—
195D4×C37—42no—
196D4×C37—42no—
197D4×C37—88no—
198C2×C4×C37—24no—
199C2×C4×C37—22no—
200C2×C4×C37—22no—
201C2×C4×C37—22no—
202C2×C4×C37—22no—
203C2×C4×C37—44no—
204C2×C4×C37—41no—
205C2×C4×C37—41no—
206C2×C4×C37—44no—
207C2×C4×C37—44no—
208C2×C4×C37—44no—
209C2×C4×C37—44no—
210C2×C4×C37—44no—
211C2×C4×C37—84no—
212C2×C4×C37—82no—
213C2×C4×C37—82no—
214C2×C4×C37C2×C22⋊C411yescharacteristic
215C2×C4×C37C2×C22⋊C411yescharacteristic
216C2×C4×C37C4×D412yes—
217C2×C4×C37C4×D412yes—
218C2×C4×C37#12012yes—
219C2×C4×C37#12011yescharacteristic
220C2×C4×C37#12012yes—
221C2×C4×C37#12112yes—
222C2×C4×C37#12112yes—
223C2×C4×C37#12112yes—
224C2×C4×C37#12112yes—
225C2×C4×C37#12112yes—
226C2×C4×C37#12312yes—
227C2×C4×C37#12311yescharacteristic
228C2×C4×C37#12412yes—
229C2×C4×C37#12712yes—
230C8×C37—44no—
231#10986C3711yesmaximal, characteristic, direct product factor, Sylow
232C22×C37—21no—
233C22×C37—22no—
234C22×C37—22no—
235C22×C37—21no—
236C22×C37—41no—
237C22×C37—42no—
238C22×C37—41no—
239C22×C37—42no—
240C22×C37—42no—
241C22×C37—42no—
242C22×C37—42no—
243C22×C37—42no—
244C22×C37—42no—
245C22×C37—82no—
246C22×C37—82no—
247C22×C37—82no—
248C22×C37—82no—
249C22×C37#37911yescharacteristic
250C22×C37#38611yescharacteristic
251C22×C37#38611yescharacteristic
252C22×C37#39212yes—
253C22×C37#39412yes—
254C4×C37—44no—
255C4×C37—42no—
256C4×C37—42no—
257C4×C37—84no—
258C4×C37#38612yes—
259C4×C37#39012yes—
260C4×C37#39212yes—
261C4×C37#39412yes—
262C2×#537C2×C3711yescharacteristic
263C2×#421C2×C3712yescomplemented
264C2×#413C2×C3711yescharacteristic, complemented
265C2×#410C2×C3711yescharacteristic, complemented
266#1736C2×C3712yescomplemented
267C2×C37—22no—
268C2×C37—21no—
269C2×C37—21no—
270C2×C37—22no—
271C2×C37—82no—
272C2×C37—82no—
273C2×C37#143811yescharacteristic
274C2×C37#179511yescharacteristic
275C2×C37#179611yescharacteristic
276C22×#41C22×C3711yescharacteristic
277C22×#41C22×C3711yescharacteristic
278C22×M16C22×C3712yes—
279#537—24no—
280#537—24no—
281C2×C22⋊Q8—21no—
282C2×C22⋊Q8C4×C3712yescomplemented
283C2×#121—21no—
284C2×#121—22no—
285C2×#121C4×C3712yescomplemented
286C2×#117C22×C3712yes—
287C22×C4⋊C4C22×C3711yescharacteristic
288#421—24no—
289#421—24no—
290C2×#104—24no—
291#413—24no—
292C2×#101—21no—
293C2×#100—21no—
294#410—24no—
295C2×#99—22no—
296#340—24no—
297C37#1098611yescharacteristic, direct product factor, Sylow
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41D4×C3714yes—
310C22×Q8C2×C4×C3711yescharacteristic
311C22×Q8D4×C3711yescharacteristic
312C22×D4—21no—
313C22×D4—22no—
314C22×D4C2×C4×C3711yescharacteristic
315C22×D4D4×C3712yes—
316C22×D4D4×C3711yescharacteristic
317C23×C4—21no—
318C23×C4—21no—
319C23×C4C2×C4×C3712yes—
320C23×C4C23×C3711yescharacteristic
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16D4×C3714yescomplemented
327C22×C8—22no—
328C22⋊Q8—28no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331#121—216no—
332#121—28no—
333#121—24no—
334#121—24no—
335#117—22no—
336#117—22no—
337#117—22no—
338#117D4×C3714yescomplemented
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4C2×C4×C3712yes—
344C2×C4⋊C4D4×C3714yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C42—22no—
349#104—216no—
350#101—24no—
351#100—24no—
352#99—28no—
353C24—21no—
354C24C22⋊C4×C3712yes—
355C24C2×D4×C3711yescharacteristic
356#41—24no—
357#41—24no—
358#41—24no—
359#41—24no—
360#41—42no—
361#41—42no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366#41—42no—
367#41—42no—
368#41—42no—
369#41—42no—
370#41—42no—
371#41—42no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8C22⋊C4×C3712yes—
380C2×D4—22no—
381C2×D4—24no—
382C2×D4—24no—
383C2×D4—24no—
384C2×D4—22no—
385C2×D4—28no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—41no—
394C2×D4—42no—
395C2×D4—41no—
396C2×D4—84no—
397C2×D4C22⋊C4×C3712yes—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—41no—
407C22×C4—42no—
408C22×C4—41no—
409C22×C4—42no—
410C22×C4—82no—
411C22×C4C22⋊C4×C3712yes—
412C22×C4C22×C4×C3711yescharacteristic
413C22×C4C2×D4×C3712yes—
414C22×C4C2×D4×C3712yes—
415C22×C4C2×D4×C3712yes—
416C22×C4C2×D4×C3712yes—
417C22×C4C2×D4×C3711yescharacteristic
418C22×C4#41×C3712yes—
419C22×C4#41×C3712yes—
420M16—24no—
421M16—24no—
422M16—42no—
423M16—42no—
424C2×C8—24no—
425C2×C8—42no—
426C2×C8—42no—
427C4⋊C4—28no—
428C4⋊C4—22no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—42no—
432C4⋊C4C22⋊C4×C3714yes—
433C22⋊C4—28no—
434C22⋊C4—28no—
435C22⋊C4—24no—
436C22⋊C4—42no—
437C42—24no—
438C42—42no—
439C23—22no—
440C23—22no—
441C23—22no—
442C23—22no—
443C23—41no—
444C23—41no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—41no—
450C23—41no—
451C23C2×C22⋊C4×C3711yescharacteristic
452C23#120×C3712yes—
453C23#120×C3711yescharacteristic
454C23#121×C3712yes—
455C23#123×C3711yescharacteristic
456Q8—24no—
457Q8—42no—
458Q8—42no—
459Q8—42no—
460D4—24no—
461D4—44no—
462D4—44no—
463D4—44no—
464D4—44no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4—88no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—84no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4C2×C22⋊C4×C3711yescharacteristic
486C2×C4C2×C22⋊C4×C3711yescharacteristic
487C2×C4C4×D4×C3712yes—
488C2×C4C4×D4×C3712yes—
489C2×C4#120×C3712yes—
490C2×C4#120×C3711yescharacteristic
491C2×C4#120×C3712yes—
492C2×C4#121×C3712yes—
493C2×C4#121×C3712yes—
494C2×C4#121×C3712yes—
495C2×C4#121×C3712yes—
496C2×C4#121×C3712yes—
497C2×C4#123×C3712yes—
498C2×C4#123×C3711yescharacteristic
499C2×C4#124×C3712yes—
500C2×C4#127×C3712yes—
501C8—44no—
502C22—21no—
503C22—22no—
504C22—22no—
505C22—21no—
506C22—41no—
507C22—42no—
508C22—41no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22—82no—
519C22C37×#37911yescharacteristic
520C22C37×#38611yescharacteristic
521C22C37×#38611yescharacteristic
522C22C37×#39212yes—
523C22C37×#39412yes—
524C4—42no—
525C4—42no—
526C4—44no—
527C4—84no—
528C4C37×#38612yes—
529C4C37×#39012yes—
530C4C37×#39212yes—
531C4C37×#39412yes—
532C2—22no—
533C2—21no—
534C2—21no—
535C2—22no—
536C2—82no—
537C2—82no—
538C2C37×#143811yescharacteristic
539C2C37×#179511yescharacteristic
540C2C37×#179611yescharacteristic
subgroupG/H
center, socleC22×C37#379
commutatorC22×C4C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC2×C37×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#421C2semidirect
3. C2×C37×#413C2semidirect
4. C2×C37×#410C2semidirect
5. C37×#1736C2semidirect
12. C2×C22⋊Q8×C37C4semidirect
15. C2×#121×C37C4semidirect
55. C2×M16×C37D4semidirect
67. #117×C37D4semidirect
231. #10986C37direct (N × H)
263. C2×#421C2×C37semidirect
264. C2×#413C2×C37semidirect
265. C2×#410C2×C37semidirect
266. #1736C2×C37semidirect
282. C2×C22⋊Q8C4×C37semidirect
285. C2×#121C4×C37semidirect
297. C37#10986direct (N × H)
326. C2×M16D4×C37semidirect
338. #117D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5372
C2×C37×#4212
C2×C37×#4132
C2×C37×#4102
C37×#17362
#1098637