Finite Group Databasebeta

← C37×#18855 #22640108

Subgroups — C37×#18855 #22640108

Order 9472.

868 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3502C211yesmaximal, characteristic, complemented
2C37×#3254C211yesmaximal, characteristic
3C37×#3210C211yesmaximal, characteristic
4C37×#3112C211yesmaximal, characteristic
5C37×#1636C212yesmaximal, complemented
6C37×#1633C212yesmaximal, complemented
7C37×#1626C212yesmaximal, complemented
8C37×#1623C212yesmaximal, complemented
9C37×#1559C211yesmaximal, characteristic, complemented
10C37×#1497C211yesmaximal, characteristic, complemented
11C37×#1487C211yesmaximal, characteristic, complemented
12Q82×C37—21no—
13Q82×C37C2212yes—
14C37×#557—21no—
15C37×#557—22no—
16C37×#557—22no—
17C37×#557C2212yes—
18C37×#544—22no—
19C37×#544—21no—
20C37×#533—22no—
21C37×#533C2211yescharacteristic
22C37×#533C2211yescharacteristic
23C37×#532C2211yescharacteristic
24C37×#519—21no—
25C2×C4×Q8×C37C2211yescharacteristic
26C37×#494C2211yescharacteristic
27C37×#492C2211yescharacteristic
28C37×#487C2211yescharacteristic
29C37×#486C2211yescharacteristic
30C37×#480—21no—
31C37×#477C2212yes—
32C37×#477C2212yes—
33C37×#474—21no—
34C37×#468—22no—
35C37×#464—22no—
36C37×#461—21no—
37C37×#460C2212yes—
38C37×#460C2212yes—
39C37×#452—22no—
40C37×#448—21no—
41C37×#440—22no—
42C37×#432C2211yescharacteristic
43C37×#431C2211yescharacteristic
44C37×#423C2211yescharacteristic
45C37×#333C2212yes—
46C37×#332C2212yes—
47C37×Q8⋊C8C2212yes—
48C37×Q8⋊C8C2212yes—
49C37×Q8⋊C8C2212yes—
50C37×Q8⋊C8C2212yes—
51C2×#41×C37—21no—
52C22×Q8×C37D411yescharacteristic
53C2×Q16×C37—22no—
54C2×SD16×C37—22no—
55C2×SD16×C37—22no—
56C2×SD16×C37—22no—
57C2×M16×C37—21no—
58C4⋊Q8×C37—24no—
59C4⋊Q8×C37—22no—
60C4⋊Q8×C37—22no—
61C4⋊Q8×C37—24no—
62C4⋊Q8×C37—22no—
63C4⋊Q8×C37—22no—
64C4⋊Q8×C37D411yescharacteristic
65C4⋊Q8×C37D411yescharacteristic
66C4⋊Q8×C37C2311yescharacteristic
67C4⋊Q8×C37C2311yescharacteristic
68C4⋊Q8×C37C2311yescharacteristic
69#127×C37C2311yescharacteristic
70#125×C37—24no—
71#125×C37—24no—
72#125×C37—22no—
73#125×C37—24no—
74#125×C37—22no—
75#125×C37—21no—
76#125×C37—21no—
77#124×C37—21no—
78C22⋊Q8×C37—24no—
79C22⋊Q8×C37—21no—
80C22⋊Q8×C37—21no—
81C22⋊Q8×C37D412yes—
82C22⋊Q8×C37D412yes—
83#121×C37—21no—
84#121×C37—21no—
85C4×Q8×C37—22no—
86C4×Q8×C37—22no—
87C4×Q8×C37—24no—
88C4×Q8×C37—22no—
89C4×Q8×C37—22no—
90C4×Q8×C37—22no—
91C4×Q8×C37—22no—
92C4×Q8×C37—21no—
93C4×Q8×C37—21no—
94C4×Q8×C37—21no—
95C4×Q8×C37—21no—
96C4×Q8×C37D412yes—
97C4×Q8×C37D412yes—
98C4×Q8×C37C2312yes—
99C4×Q8×C37C2312yes—
100C4×D4×C37—21no—
101C4×D4×C37—21no—
102#117×C37—24no—
103#117×C37—21no—
104#117×C37—21no—
105C2×C4⋊C4×C37—21no—
106C2×C4⋊C4×C37D411yescharacteristic
107C2×C42×C37—21no—
108C2×C42×C37C2311yescharacteristic
109#107×C37—22no—
110#107×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#102×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—82no—
127C2×Q8×C37—24no—
128C2×Q8×C37—24no—
129C2×Q8×C37—21no—
130C2×Q8×C37—21no—
131C2×Q8×C37—21no—
132C2×Q8×C37—21no—
133C2×Q8×C37C2×D412yes—
134C2×Q8×C37C2×D412yes—
135C2×Q8×C37C2×D412yes—
136C2×D4×C37—21no—
137C2×D4×C37—21no—
138C2×D4×C37—21no—
139C2×D4×C37—41no—
140C22×C4×C37—21no—
141C22×C4×C37—21no—
142C22×C4×C37—41no—
143C22×C4×C37C2×D411yescharacteristic
144C22×C4×C37C2×D411yescharacteristic
145C22×C4×C37C2×D411yescharacteristic
146Q16×C37—82no—
147SD16×C37—44no—
148SD16×C37—82no—
149SD16×C37—82no—
150M16×C37—81no—
151C2×C8×C37—21no—
152C2×C8×C37—21no—
153C2×C8×C37—22no—
154C2×C8×C37—22no—
155C4⋊C4×C37—24no—
156C4⋊C4×C37—24no—
157C4⋊C4×C37—24no—
158C4⋊C4×C37—24no—
159C4⋊C4×C37—24no—
160C4⋊C4×C37—22no—
161C4⋊C4×C37—21no—
162C4⋊C4×C37—21no—
163C4⋊C4×C37—21no—
164C4⋊C4×C37—22no—
165C4⋊C4×C37—22no—
166C4⋊C4×C37—21no—
167C4⋊C4×C37—22no—
168C4⋊C4×C37—22no—
169C4⋊C4×C37—21no—
170C4⋊C4×C37—21no—
171C4⋊C4×C37—21no—
172C4⋊C4×C37—22no—
173C4⋊C4×C37—21no—
174C4⋊C4×C37—21no—
175C4⋊C4×C37C2×D412yes—
176C4⋊C4×C37C2×D412yes—
177C4⋊C4×C37C2×D412yes—
178C22⋊C4×C37—22no—
179C22⋊C4×C37—22no—
180C22⋊C4×C37—41no—
181C22⋊C4×C37—41no—
182C42×C37—24no—
183C42×C37—24no—
184C42×C37—22no—
185C42×C37—22no—
186C42×C37—22no—
187C42×C37—22no—
188C42×C37C2×D411yescharacteristic
189C42×C37C2×D411yescharacteristic
190C42×C37C2×D411yescharacteristic
191C42×C37C2411yescharacteristic
192C23×C37—41no—
193C23×C37#12011yescharacteristic
194Q8×C37—24no—
195Q8×C37—22no—
196Q8×C37—22no—
197Q8×C37—22no—
198Q8×C37—42no—
199Q8×C37—42no—
200Q8×C37—41no—
201Q8×C37—41no—
202Q8×C37—81no—
203Q8×C37—84no—
204Q8×C37#13714yes—
205D4×C37—42no—
206D4×C37—42no—
207D4×C37—41no—
208D4×C37—41no—
209D4×C37—82no—
210C2×C4×C37—24no—
211C2×C4×C37—22no—
212C2×C4×C37—22no—
213C2×C4×C37—21no—
214C2×C4×C37—21no—
215C2×C4×C37—22no—
216C2×C4×C37—22no—
217C2×C4×C37—22no—
218C2×C4×C37—22no—
219C2×C4×C37—22no—
220C2×C4×C37—41no—
221C2×C4×C37—41no—
222C2×C4×C37—82no—
223C2×C4×C37—81no—
224C2×C4×C37#12011yescharacteristic
225C2×C4×C37#12011yescharacteristic
226C2×C4×C37#12011yescharacteristic
227C2×C4×C37C22×D411yescharacteristic
228C2×C4×C37C22×D411yescharacteristic
229C2×C4×C37C22×D411yescharacteristic
230C8×C37—41no—
231C8×C37—41no—
232C8×C37—42no—
233C8×C37—42no—
234#18855C3711yesmaximal, characteristic, direct product factor, Sylow
235C22×C37—21no—
236C22×C37—21no—
237C22×C37—21no—
238C22×C37—81no—
239C22×C37—81no—
240C22×C37—81no—
241C22×C37C2×#12011yescharacteristic
242C4×C37—24no—
243C4×C37—21no—
244C4×C37—21no—
245C4×C37—21no—
246C4×C37—21no—
247C4×C37—42no—
248C4×C37—42no—
249C4×C37—42no—
250C4×C37—42no—
251C4×C37—42no—
252C4×C37—81no—
253C4×C37C2×#13712yes—
254C4×C37#57711yescharacteristic
255C4×C37#57811yescharacteristic
256#3502C2×C3711yescharacteristic, complemented
257#3254C2×C3711yescharacteristic
258#3210C2×C3711yescharacteristic
259#3112C2×C3711yescharacteristic
260#1636C2×C3712yescomplemented
261#1633C2×C3712yescomplemented
262#1626C2×C3712yescomplemented
263#1623C2×C3712yescomplemented
264#1559C2×C3711yescharacteristic, complemented
265#1497C2×C3711yescharacteristic, complemented
266#1487C2×C3711yescharacteristic, complemented
267C2×C37—41no—
268C2×C37—161no—
269C2×C37#300411yescharacteristic
270C2×C37#301311yescharacteristic
271C2×C37#302111yescharacteristic
272Q82—21no—
273Q82C22×C3712yes—
274#557—21no—
275#557—22no—
276#557—22no—
277#557C22×C3712yes—
278#544—22no—
279#544—21no—
280#533—22no—
281#533C22×C3711yescharacteristic
282#533C22×C3711yescharacteristic
283#532C22×C3711yescharacteristic
284#519—21no—
285C2×C4×Q8C22×C3711yescharacteristic
286#494C22×C3711yescharacteristic
287#492C22×C3711yescharacteristic
288#487C22×C3711yescharacteristic
289#486C22×C3711yescharacteristic
290#480—21no—
291#477C22×C3712yes—
292#477C22×C3712yes—
293#474—21no—
294#468—22no—
295#464—22no—
296#461—21no—
297#460C22×C3712yes—
298#460C22×C3712yes—
299#452—22no—
300#448—21no—
301#440—22no—
302#432C22×C3711yescharacteristic
303#431C22×C3711yescharacteristic
304#423C22×C3711yescharacteristic
305#333C22×C3712yes—
306#332C22×C3712yes—
307Q8⋊C8C22×C3712yes—
308Q8⋊C8C22×C3712yes—
309Q8⋊C8C22×C3712yes—
310Q8⋊C8C22×C3712yes—
311C37#1885511yescharacteristic, direct product factor, Sylow
312C2×#41—21no—
313C22×Q8D4×C3711yescharacteristic
314C2×Q16—22no—
315C2×SD16—22no—
316C2×SD16—22no—
317C2×SD16—22no—
318C2×M16—21no—
319C4⋊Q8—24no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—24no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8D4×C3711yescharacteristic
326C4⋊Q8D4×C3711yescharacteristic
327C4⋊Q8C23×C3711yescharacteristic
328C4⋊Q8C23×C3711yescharacteristic
329C4⋊Q8C23×C3711yescharacteristic
330#127C23×C3711yescharacteristic
331#125—24no—
332#125—24no—
333#125—22no—
334#125—24no—
335#125—22no—
336#125—21no—
337#125—21no—
338#124—21no—
339C22⋊Q8—24no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8D4×C3712yes—
343C22⋊Q8D4×C3712yes—
344#121—21no—
345#121—21no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—24no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8D4×C3712yes—
358C4×Q8D4×C3712yes—
359C4×Q8C23×C3712yes—
360C4×Q8C23×C3712yes—
361C4×D4—21no—
362C4×D4—21no—
363#117—24no—
364#117—21no—
365#117—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C3711yescharacteristic
368C2×C42—21no—
369C2×C42C23×C3711yescharacteristic
370#107—22no—
371#107—22no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8C23×C3712yes—
375C4⋊C8C23×C3712yes—
376#103—22no—
377#103—22no—
378#103—22no—
379#102—22no—
380#102—22no—
381#102—22no—
382C22⋊C8—21no—
383C22⋊C8—21no—
384#97—21no—
385C4×C8C23×C3711yescharacteristic
386C4×C8C23×C3711yescharacteristic
387#41—82no—
388C2×Q8—24no—
389C2×Q8—24no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8C2×D4×C3712yes—
395C2×Q8C2×D4×C3712yes—
396C2×Q8C2×D4×C3712yes—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—41no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—41no—
404C22×C4C2×D4×C3711yescharacteristic
405C22×C4C2×D4×C3711yescharacteristic
406C22×C4C2×D4×C3711yescharacteristic
407Q16—82no—
408SD16—44no—
409SD16—82no—
410SD16—82no—
411M16—81no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—22no—
415C2×C8—22no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4C2×D4×C3712yes—
437C4⋊C4C2×D4×C3712yes—
438C4⋊C4C2×D4×C3712yes—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C42—24no—
444C42—24no—
445C42—22no—
446C42—22no—
447C42—22no—
448C42—22no—
449C42C2×D4×C3711yescharacteristic
450C42C2×D4×C3711yescharacteristic
451C42C2×D4×C3711yescharacteristic
452C42C24×C3711yescharacteristic
453C23—41no—
454C23#120×C3711yescharacteristic
455Q8—24no—
456Q8—22no—
457Q8—22no—
458Q8—22no—
459Q8—42no—
460Q8—42no—
461Q8—41no—
462Q8—41no—
463Q8—81no—
464Q8—84no—
465Q8#137×C3714yes—
466D4—42no—
467D4—42no—
468D4—41no—
469D4—41no—
470D4—82no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—82no—
484C2×C4—81no—
485C2×C4#120×C3711yescharacteristic
486C2×C4#120×C3711yescharacteristic
487C2×C4#120×C3711yescharacteristic
488C2×C4C22×D4×C3711yescharacteristic
489C2×C4C22×D4×C3711yescharacteristic
490C2×C4C22×D4×C3711yescharacteristic
491C8—41no—
492C8—41no—
493C8—42no—
494C8—42no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22C2×#120×C3711yescharacteristic
502C4—24no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—42no—
511C4—42no—
512C4—81no—
513C4C2×#137×C3712yes—
514C4C37×#57711yescharacteristic
515C4C37×#57811yescharacteristic
516C2—41no—
517C2—161no—
518C2C37×#300411yescharacteristic
519C2C37×#301311yescharacteristic
520C2C37×#302111yescharacteristic
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
1. C37×#3502C2semidirect
5. C37×#1636C2semidirect
6. C37×#1633C2semidirect
7. C37×#1626C2semidirect
8. C37×#1623C2semidirect
9. C37×#1559C2semidirect
10. C37×#1497C2semidirect
11. C37×#1487C2semidirect
234. #18855C37direct (N × H)
256. #3502C2×C37semidirect
260. #1636C2×C37semidirect
261. #1633C2×C37semidirect
262. #1626C2×C37semidirect
263. #1623C2×C37semidirect
264. #1559C2×C37semidirect
265. #1497C2×C37semidirect
266. #1487C2×C37semidirect
311. C37#18855direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35022
C37×#32542
C37×#32102
C37×#31122
C37×#16362
C37×#16332
C37×#16262
C37×#16232
C37×#15592
C37×#14972
C37×#14872
#1885537