Finite Group Databasebeta

← C37×#18215 #22639468

Subgroups — C37×#18215 #22639468

Order 9472.

914 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×#3507C211yesmaximal, characteristic
2C37×#3104C211yesmaximal, characteristic, complemented
3C37×#3103C211yesmaximal, characteristic
4C37×#2581C211yesmaximal, characteristic, complemented
5C37×#1615C214yesmaximal, complemented
6C37×#1603C214yesmaximal, complemented
7C37×#1518C211yesmaximal, characteristic, complemented
8C37×#1517C211yesmaximal, characteristic
9C37×#1461C211yesmaximal, characteristic, complemented
10C37×#559—21no—
11C37×#557—21no—
12C37×#556—21no—
13C37×#556—22no—
14C37×#554—21no—
15C37×#552—22no—
16C37×#539C2214yes—
17C37×#536—21no—
18C37×#533C2211yescharacteristic
19C37×#532C2211yescharacteristic
20C37×#529—22no—
21C37×#520—21no—
22C2×C4×Q8×C37C2211yescharacteristic
23C2×C4×Q8×C37C2211yescharacteristic
24C37×#484C2212yes—
25C37×#481C2212yes—
26C37×#477—21no—
27C37×#475—21no—
28C37×#462—21no—
29C37×#460—21no—
30C37×#451C2212yes—
31C37×#448C2212yes—
32C4×Q16×C37—22no—
33C4×SD16×C37—22no—
34C37×#431C2211yescharacteristic
35C37×#431C2211yescharacteristic
36C37×#400C2212yes—
37C37×#395C2212yes—
38C37×#391—21no—
39C37×#389—21no—
40C37×#387—22no—
41C37×#382C2211yescharacteristic
42C37×#328C2214yes—
43C37×#327C2214yes—
44C37×#324C2214yes—
45C2×#41×C37—21no—
46C22×Q8×C37D411yescharacteristic
47C22×Q8×C37C2311yescharacteristic
48C2×Q16×C37—22no—
49C2×SD16×C37—22no—
50C4⋊Q8×C37—22no—
51C4⋊Q8×C37D411yescharacteristic
52C4⋊Q8×C37D411yescharacteristic
53C4⋊Q8×C37D411yescharacteristic
54#127×C37D411yescharacteristic
55#126×C37—24no—
56#126×C37—24no—
57#125×C37—22no—
58#125×C37—24no—
59#125×C37—21no—
60#124×C37—22no—
61#124×C37—22no—
62#124×C37—21no—
63#123×C37—24no—
64#123×C37—24no—
65C22⋊Q8×C37—22no—
66C22⋊Q8×C37—22no—
67C22⋊Q8×C37—24no—
68C22⋊Q8×C37—21no—
69C22⋊Q8×C37C2312yes—
70#121×C37—21no—
71#121×C37C2312yes—
72C4×Q8×C37—22no—
73C4×Q8×C37—22no—
74C4×Q8×C37—21no—
75C4×Q8×C37—21no—
76C4×Q8×C37—21no—
77C4×Q8×C37—21no—
78C4×Q8×C37—21no—
79C4×Q8×C37—21no—
80C4×Q8×C37—21no—
81C4×Q8×C37—21no—
82C4×Q8×C37—21no—
83C4×Q8×C37D412yes—
84C4×D4×C37—22no—
85C4×D4×C37—22no—
86C4×D4×C37—24no—
87C4×D4×C37—21no—
88C4×D4×C37D412yes—
89#117×C37—22no—
90#117×C37—24no—
91#117×C37—21no—
92C2×C4⋊C4×C37—22no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37—22no—
96C2×C4⋊C4×C37D411yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2312yes—
99C2×C42×C37—21no—
100C2×C42×C37D412yes—
101C2×C42×C37C2311yescharacteristic
102#107×C37—22no—
103#106×C37—22no—
104C4⋊C8×C37—21no—
105C4⋊C8×C37—21no—
106#103×C37—22no—
107#103×C37—22no—
108#103×C37—22no—
109#102×C37—22no—
110C22⋊C8×C37C2312yes—
111C22⋊C8×C37C2312yes—
112C4×C8×C37—21no—
113C4×C8×C37—21no—
114#95×C37—21no—
115#95×C37—22no—
116#95×C37—22no—
117#95×C37—22no—
118#95×C37C2312yes—
119#41×C37—42no—
120#41×C37—42no—
121C2×Q8×C37—21no—
122C2×Q8×C37—21no—
123C2×Q8×C37—21no—
124C2×Q8×C37—21no—
125C2×Q8×C37—22no—
126C2×Q8×C37—22no—
127C2×Q8×C37—21no—
128C2×Q8×C37—21no—
129C2×Q8×C37—42no—
130C2×Q8×C37C2×D412yes—
131C2×D4×C37—22no—
132C2×D4×C37—21no—
133C2×D4×C37—21no—
134C2×D4×C37C2×D412yes—
135C22×C4×C37—21no—
136C22×C4×C37—24no—
137C22×C4×C37—22no—
138C22×C4×C37—22no—
139C22×C4×C37—21no—
140C22×C4×C37C2×D412yes—
141C22×C4×C37C2×D412yes—
142C22×C4×C37C2×D411yescharacteristic
143C22×C4×C37C2×D411yescharacteristic
144C22×C4×C37C2411yescharacteristic
145Q16×C37—44no—
146SD16×C37—44no—
147C2×C8×C37—22no—
148C2×C8×C37—22no—
149C4⋊C4×C37—24no—
150C4⋊C4×C37—24no—
151C4⋊C4×C37—24no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—21no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—22no—
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—44no—
165C4⋊C4×C37—41no—
166C4⋊C4×C37—41no—
167C4⋊C4×C37—42no—
168C4⋊C4×C37C2×D412yes—
169C4⋊C4×C37C2×D412yes—
170C22⋊C4×C37—24no—
171C22⋊C4×C37—24no—
172C22⋊C4×C37—24no—
173C22⋊C4×C37—22no—
174C22⋊C4×C37—22no—
175C22⋊C4×C37—22no—
176C42×C37—24no—
177C42×C37—22no—
178C42×C37—22no—
179C42×C37—22no—
180C42×C37—41no—
181C42×C37—41no—
182C42×C37C2×D411yescharacteristic
183C42×C37C2×D411yescharacteristic
184C42×C37C2×D411yescharacteristic
185C42×C37C2×D411yescharacteristic
186C23×C37—22no—
187C23×C37C22×D411yescharacteristic
188Q8×C37—22no—
189Q8×C37—22no—
190Q8×C37—42no—
191Q8×C37—42no—
192Q8×C37—41no—
193Q8×C37—41no—
194Q8×C37—42no—
195Q8×C37—42no—
196Q8×C37—42no—
197D4×C37—42no—
198D4×C37—42no—
199D4×C37—42no—
200D4×C37—42no—
201D4×C37—42no—
202C2×C4×C37—22no—
203C2×C4×C37—22no—
204C2×C4×C37—22no—
205C2×C4×C37—22no—
206C2×C4×C37—22no—
207C2×C4×C37—22no—
208C2×C4×C37—22no—
209C2×C4×C37—22no—
210C2×C4×C37—41no—
211C2×C4×C37—41no—
212C2×C4×C37—41no—
213C2×C4×C37—41no—
214C2×C4×C37—44no—
215C2×C4×C37—42no—
216C2×C4×C37—42no—
217C2×C4×C37—42no—
218C2×C4×C37—42no—
219C2×C4×C37—41no—
220C2×C4×C37—42no—
221C2×C4×C37—84no—
222C2×C4×C37#12011yescharacteristic
223C2×C4×C37#12011yescharacteristic
224C2×C4×C37#12011yescharacteristic
225C2×C4×C37#12011yescharacteristic
226C2×C4×C37#13512yes—
227C2×C4×C37#13712yes—
228C2×C4×C37C22×D411yescharacteristic
229C2×C4×C37C22×D411yescharacteristic
230C8×C37—42no—
231C8×C37—42no—
232#18215C3711yesmaximal, characteristic, direct product factor, Sylow
233C22×C37—21no—
234C22×C37—21no—
235C22×C37—42no—
236C22×C37—42no—
237C22×C37—42no—
238C22×C37C2×#12011yescharacteristic
239C22×C37C2×#13511yescharacteristic
240C22×C37C2×#13711yescharacteristic
241C4×C37—21no—
242C4×C37—21no—
243C4×C37—21no—
244C4×C37—21no—
245C4×C37—42no—
246C4×C37—42no—
247C4×C37—42no—
248C4×C37—42no—
249C4×C37—42no—
250C4×C37—42no—
251C4×C37—82no—
252C4×C37—81no—
253C4×C37#45212yes—
254C4×C37#45212yes—
255#3507C2×C3711yescharacteristic
256#3104C2×C3711yescharacteristic, complemented
257#3103C2×C3711yescharacteristic
258#2581C2×C3711yescharacteristic, complemented
259#1615C2×C3714yescomplemented
260#1603C2×C3714yescomplemented
261#1518C2×C3711yescharacteristic, complemented
262#1517C2×C3711yescharacteristic
263#1461C2×C3711yescharacteristic, complemented
264C2×C37—21no—
265C2×C37—21no—
266C2×C37—82no—
267C2×C37C2×#45211yescharacteristic
268C2×C37#302011yescharacteristic
269C2×C37#302511yescharacteristic
270#559—21no—
271#557—21no—
272#556—21no—
273#556—22no—
274#554—21no—
275#552—22no—
276#539C22×C3714yes—
277#536—21no—
278#533C22×C3711yescharacteristic
279#532C22×C3711yescharacteristic
280#529—22no—
281#520—21no—
282C2×C4×Q8C22×C3711yescharacteristic
283C2×C4×Q8C22×C3711yescharacteristic
284#484C22×C3712yes—
285#481C22×C3712yes—
286#477—21no—
287#475—21no—
288#462—21no—
289#460—21no—
290#451C22×C3712yes—
291#448C22×C3712yes—
292C4×Q16—22no—
293C4×SD16—22no—
294#431C22×C3711yescharacteristic
295#431C22×C3711yescharacteristic
296#400C22×C3712yes—
297#395C22×C3712yes—
298#391—21no—
299#389—21no—
300#387—22no—
301#382C22×C3711yescharacteristic
302#328C22×C3714yes—
303#327C22×C3714yes—
304#324C22×C3714yes—
305C37#1821511yescharacteristic, direct product factor, Sylow
306C2×#41—21no—
307C22×Q8D4×C3711yescharacteristic
308C22×Q8C23×C3711yescharacteristic
309C2×Q16—22no—
310C2×SD16—22no—
311C4⋊Q8—22no—
312C4⋊Q8D4×C3711yescharacteristic
313C4⋊Q8D4×C3711yescharacteristic
314C4⋊Q8D4×C3711yescharacteristic
315#127D4×C3711yescharacteristic
316#126—24no—
317#126—24no—
318#125—22no—
319#125—24no—
320#125—21no—
321#124—22no—
322#124—22no—
323#124—21no—
324#123—24no—
325#123—24no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—24no—
329C22⋊Q8—21no—
330C22⋊Q8C23×C3712yes—
331#121—21no—
332#121C23×C3712yes—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8D4×C3712yes—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—24no—
348C4×D4—21no—
349C4×D4D4×C3712yes—
350#117—22no—
351#117—24no—
352#117—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4D4×C3711yescharacteristic
358C2×C4⋊C4C23×C3711yescharacteristic
359C2×C4⋊C4C23×C3712yes—
360C2×C42—21no—
361C2×C42D4×C3712yes—
362C2×C42C23×C3711yescharacteristic
363#107—22no—
364#106—22no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367#103—22no—
368#103—22no—
369#103—22no—
370#102—22no—
371C22⋊C8C23×C3712yes—
372C22⋊C8C23×C3712yes—
373C4×C8—21no—
374C4×C8—21no—
375#95—21no—
376#95—22no—
377#95—22no—
378#95—22no—
379#95C23×C3712yes—
380#41—42no—
381#41—42no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—42no—
391C2×Q8C2×D4×C3712yes—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4C2×D4×C3712yes—
396C22×C4—21no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4C2×D4×C3712yes—
402C22×C4C2×D4×C3712yes—
403C22×C4C2×D4×C3711yescharacteristic
404C22×C4C2×D4×C3711yescharacteristic
405C22×C4C24×C3711yescharacteristic
406Q16—44no—
407SD16—44no—
408C2×C8—22no—
409C2×C8—22no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—44no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—42no—
429C4⋊C4C2×D4×C3712yes—
430C4⋊C4C2×D4×C3712yes—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C42—24no—
438C42—22no—
439C42—22no—
440C42—22no—
441C42—41no—
442C42—41no—
443C42C2×D4×C3711yescharacteristic
444C42C2×D4×C3711yescharacteristic
445C42C2×D4×C3711yescharacteristic
446C42C2×D4×C3711yescharacteristic
447C23—22no—
448C23C22×D4×C3711yescharacteristic
449Q8—22no—
450Q8—22no—
451Q8—42no—
452Q8—41no—
453Q8—41no—
454Q8—42no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—84no—
483C2×C4#120×C3711yescharacteristic
484C2×C4#120×C3711yescharacteristic
485C2×C4#120×C3711yescharacteristic
486C2×C4#120×C3711yescharacteristic
487C2×C4#135×C3712yes—
488C2×C4#137×C3712yes—
489C2×C4C22×D4×C3711yescharacteristic
490C2×C4C22×D4×C3711yescharacteristic
491C8—42no—
492C8—42no—
493C22—21no—
494C22—21no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22C2×#120×C3711yescharacteristic
499C22C2×#135×C3711yescharacteristic
500C22C2×#137×C3711yescharacteristic
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—42no—
506C4—42no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—42no—
511C4—82no—
512C4—81no—
513C4C37×#45212yes—
514C4C37×#45212yes—
515C2—21no—
516C2—21no—
517C2—82no—
518C2C2×C37×#45211yescharacteristic
519C2C37×#302011yescharacteristic
520C2C37×#302511yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#532C22
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×#3104C2semidirect
4. C37×#2581C2semidirect
5. C37×#1615C2semidirect
6. C37×#1603C2semidirect
7. C37×#1518C2semidirect
9. C37×#1461C2semidirect
232. #18215C37direct (N × H)
256. #3104C2×C37semidirect
258. #2581C2×C37semidirect
259. #1615C2×C37semidirect
260. #1603C2×C37semidirect
261. #1518C2×C37semidirect
263. #1461C2×C37semidirect
305. C37#18215direct (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×#31042
C37×#31032
C37×#25812
C37×#16152
C37×#16032
C37×#15182
C37×#15172
C37×#14612
#1821537