Finite Group Databasebeta

← C37×#19017 #22640270

Subgroups — C37×#19017 #22640270

Order 9472.

944 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3559C211yesmaximal, characteristic
2C37×#3238C211yesmaximal, characteristic, complemented
3C2×C37×#501C211yesmaximal, characteristic, complemented
4C37×#3152C211yesmaximal, characteristic, complemented
5C37×#1661C214yesmaximal, complemented
6C37×#1660C214yesmaximal, complemented
7C37×#1530C211yesmaximal, characteristic, complemented
8C37×#1528C211yesmaximal, characteristic, complemented
9C37×#1524C211yesmaximal, characteristic, complemented
10C2×#137×C37—22no—
11C37×#563C2212yes—
12C37×#562C2212yes—
13C37×#554—21no—
14C37×#553—21no—
15C37×#553—21no—
16C37×#547—22no—
17C37×#547—21no—
18C37×#544—21no—
19C37×#540—21no—
20C37×#539—22no—
21C37×#539—21no—
22C37×#537—21no—
23C37×#532C2211yescharacteristic
24C2×C4⋊Q8×C37C2211yescharacteristic
25C37×#529C2211yescharacteristic
26C2×#125×C37C2211yescharacteristic
27C37×#501—22no—
28C37×#501C2214yes—
29C37×#501C2212yes—
30C37×#497C2214yes—
31C37×#494—21no—
32C37×#492—21no—
33C37×#489C2212yes—
34C37×#483—21no—
35C37×#480—21no—
36C37×#477—21no—
37C37×#476—21no—
38C37×#432C2211yescharacteristic
39C2×#107×C37—21no—
40C2×#106×C37—21no—
41C4×M16×C37C2211yescharacteristic
42C2×#97×C37C2211yescharacteristic
43C37×#330C2212yes—
44C37×#330C2214yes—
45C37×#329C2214yes—
46C37×#329C2212yes—
47C2×#41×C37—22no—
48C2×#41×C37D412yes—
49C22×Q8×C37—21no—
50#137×C37—48no—
51C2×Q16×C37—24no—
52C2×SD16×C37—24no—
53C2×M16×C37—21no—
54C22×C8×C37—21no—
55C4⋊Q8×C37—21no—
56C4⋊Q8×C37—22no—
57C4⋊Q8×C37—21no—
58C4⋊Q8×C37—21no—
59C4⋊Q8×C37—21no—
60C4⋊Q8×C37D411yescharacteristic
61C4⋊Q8×C37C2312yes—
62#127×C37D411yescharacteristic
63#126×C37—22no—
64#126×C37—22no—
65#126×C37—21no—
66#125×C37—22no—
67#125×C37—21no—
68#125×C37—21no—
69#125×C37—21no—
70#125×C37D412yes—
71#125×C37C2312yes—
72#125×C37C2311yescharacteristic
73#124×C37C2311yescharacteristic
74#124×C37C2312yes—
75#123×C37—22no—
76#123×C37—22no—
77#123×C37—22no—
78#123×C37—22no—
79#123×C37—21no—
80#123×C37—22no—
81#123×C37—22no—
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37—22no—
85C22⋊Q8×C37—22no—
86C22⋊Q8×C37—22no—
87C22⋊Q8×C37—22no—
88C22⋊Q8×C37D411yescharacteristic
89#121×C37—22no—
90#121×C37—22no—
91#121×C37—21no—
92#121×C37—21no—
93#121×C37—22no—
94#121×C37—22no—
95#121×C37—21no—
96#121×C37—21no—
97#121×C37D411yescharacteristic
98C4×Q8×C37D411yescharacteristic
99C4×D4×C37—22no—
100C4×D4×C37—22no—
101C4×D4×C37—21no—
102C4×D4×C37—21no—
103C4×D4×C37—21no—
104C4×D4×C37—21no—
105C4×D4×C37—21no—
106C4×D4×C37D411yescharacteristic
107#117×C37—21no—
108#117×C37—21no—
109C2×C4⋊C4×C37—22no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—21no—
112C2×C4⋊C4×C37—21no—
113C2×C4⋊C4×C37—21no—
114C2×C4⋊C4×C37—21no—
115C2×C4⋊C4×C37D411yescharacteristic
116C2×C4⋊C4×C37D411yescharacteristic
117C2×C42×C37C2311yescharacteristic
118#107×C37—24no—
119#107×C37—22no—
120#106×C37—24no—
121#106×C37—22no—
122C4⋊C8×C37—21no—
123#103×C37—22no—
124#102×C37—22no—
125C22⋊C8×C37—21no—
126#97×C37—21no—
127#97×C37C2312yes—
128#97×C37C2312yes—
129#97×C37C2312yes—
130C4×C8×C37—21no—
131#41×C37—44no—
132#41×C37—84no—
133C2×Q8×C37—22no—
134C2×Q8×C37—22no—
135C2×Q8×C37—44no—
136C2×Q8×C37—41no—
137C2×Q8×C37C2×D411yescharacteristic
138C2×Q8×C37C2×D412yes—
139C2×D4×C37—22no—
140C2×D4×C37—21no—
141C2×D4×C37—22no—
142C2×D4×C37—22no—
143C2×D4×C37—21no—
144C2×D4×C37—21no—
145C2×D4×C37C2×D411yescharacteristic
146C2×D4×C37C2×D412yes—
147C22×C4×C37—21no—
148C22×C4×C37—22no—
149C22×C4×C37—22no—
150C22×C4×C37—22no—
151C22×C4×C37—21no—
152C22×C4×C37—21no—
153C22×C4×C37—22no—
154C22×C4×C37—41no—
155C22×C4×C37C2×D411yescharacteristic
156C22×C4×C37C2×D411yescharacteristic
157C22×C4×C37C2×D411yescharacteristic
158Q16×C37—48no—
159SD16×C37—48no—
160M16×C37—24no—
161C2×C8×C37—24no—
162C2×C8×C37—22no—
163C2×C8×C37—22no—
164C2×C8×C37—22no—
165C4⋊C4×C37—22no—
166C4⋊C4×C37—22no—
167C4⋊C4×C37—22no—
168C4⋊C4×C37—22no—
169C4⋊C4×C37—22no—
170C4⋊C4×C37—21no—
171C4⋊C4×C37—21no—
172C4⋊C4×C37—21no—
173C4⋊C4×C37—22no—
174C4⋊C4×C37—21no—
175C4⋊C4×C37—21no—
176C4⋊C4×C37—21no—
177C4⋊C4×C37—22no—
178C4⋊C4×C37—22no—
179C4⋊C4×C37—21no—
180C4⋊C4×C37—21no—
181C4⋊C4×C37—22no—
182C4⋊C4×C37—22no—
183C4⋊C4×C37—41no—
184C4⋊C4×C37—41no—
185C4⋊C4×C37C2×D412yes—
186C4⋊C4×C37C2×D411yescharacteristic
187C4⋊C4×C37C2×D412yes—
188C4⋊C4×C37C2×D411yescharacteristic
189C22⋊C4×C37—22no—
190C22⋊C4×C37—22no—
191C22⋊C4×C37—22no—
192C22⋊C4×C37—22no—
193C22⋊C4×C37—22no—
194C22⋊C4×C37—21no—
195C22⋊C4×C37—21no—
196C22⋊C4×C37—21no—
197C22⋊C4×C37—21no—
198C22⋊C4×C37—22no—
199C22⋊C4×C37—22no—
200C22⋊C4×C37—21no—
201C42×C37—22no—
202C42×C37—21no—
203C42×C37C2×D411yescharacteristic
204C42×C37C2×D411yescharacteristic
205C42×C37C2×D411yescharacteristic
206C42×C37C2411yescharacteristic
207C23×C37—22no—
208C23×C37—21no—
209C23×C37#12011yescharacteristic
210Q8×C37—42no—
211Q8×C37—41no—
212Q8×C37—44no—
213Q8×C37—82no—
214Q8×C37—82no—
215D4×C37—42no—
216D4×C37—41no—
217D4×C37—44no—
218D4×C37—42no—
219D4×C37—42no—
220D4×C37—81no—
221D4×C37—82no—
222D4×C37—82no—
223C2×C4×C37—22no—
224C2×C4×C37—22no—
225C2×C4×C37—21no—
226C2×C4×C37—21no—
227C2×C4×C37—22no—
228C2×C4×C37—22no—
229C2×C4×C37—21no—
230C2×C4×C37—22no—
231C2×C4×C37—41no—
232C2×C4×C37—42no—
233C2×C4×C37—42no—
234C2×C4×C37—42no—
235C2×C4×C37—82no—
236C2×C4×C37—81no—
237C2×C4×C37—82no—
238C2×C4×C37—82no—
239C2×C4×C37—82no—
240C2×C4×C37—82no—
241C2×C4×C37#12011yescharacteristic
242C2×C4×C37#12011yescharacteristic
243C2×C4×C37#12011yescharacteristic
244C2×C4×C37C22×D411yescharacteristic
245C2×C4×C37C22×D411yescharacteristic
246C2×C4×C37C22×D411yescharacteristic
247C8×C37—24no—
248C8×C37—24no—
249C8×C37—42no—
250#19017C3711yesmaximal, characteristic, direct product factor, Sylow
251C22×C37—21no—
252C22×C37—21no—
253C22×C37—42no—
254C22×C37—41no—
255C22×C37—41no—
256C22×C37—42no—
257C22×C37—42no—
258C22×C37—41no—
259C22×C37#45312yes—
260C22×C37C2×#12011yescharacteristic
261C4×C37—21no—
262C4×C37—21no—
263C4×C37—21no—
264C4×C37—21no—
265C4×C37—21no—
266C4×C37—42no—
267C4×C37—42no—
268C4×C37—41no—
269C4×C37—41no—
270C4×C37—42no—
271C4×C37—41no—
272C4×C37—82no—
273C4×C37#45612yes—
274#3559C2×C3711yescharacteristic
275#3238C2×C3711yescharacteristic, complemented
276C2×#501C2×C3711yescharacteristic, complemented
277#3152C2×C3711yescharacteristic, complemented
278#1661C2×C3714yescomplemented
279#1660C2×C3714yescomplemented
280#1530C2×C3711yescharacteristic, complemented
281#1528C2×C3711yescharacteristic, complemented
282#1524C2×C3711yescharacteristic, complemented
283C2×C37—22no—
284C2×C37—82no—
285C2×C37—81no—
286C2×C37C2×#45311yescharacteristic
287C2×C37C2×#45611yescharacteristic
288C2×C37#302211yescharacteristic
289C2×#137—22no—
290#563C22×C3712yes—
291#562C22×C3712yes—
292#554—21no—
293#553—21no—
294#553—21no—
295#547—22no—
296#547—21no—
297#544—21no—
298#540—21no—
299#539—22no—
300#539—21no—
301#537—21no—
302#532C22×C3711yescharacteristic
303C2×C4⋊Q8C22×C3711yescharacteristic
304#529C22×C3711yescharacteristic
305C2×#125C22×C3711yescharacteristic
306#501—22no—
307#501C22×C3714yes—
308#501C22×C3712yes—
309#497C22×C3714yes—
310#494—21no—
311#492—21no—
312#489C22×C3712yes—
313#483—21no—
314#480—21no—
315#477—21no—
316#476—21no—
317#432C22×C3711yescharacteristic
318C2×#107—21no—
319C2×#106—21no—
320C4×M16C22×C3711yescharacteristic
321C2×#97C22×C3711yescharacteristic
322#330C22×C3712yes—
323#330C22×C3714yes—
324#329C22×C3714yes—
325#329C22×C3712yes—
326C37#1901711yescharacteristic, direct product factor, Sylow
327C2×#41—22no—
328C2×#41D4×C3712yes—
329C22×Q8—21no—
330#137—48no—
331C2×Q16—24no—
332C2×SD16—24no—
333C2×M16—21no—
334C22×C8—21no—
335C4⋊Q8—21no—
336C4⋊Q8—22no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8D4×C3711yescharacteristic
341C4⋊Q8C23×C3712yes—
342#127D4×C3711yescharacteristic
343#126—22no—
344#126—22no—
345#126—21no—
346#125—22no—
347#125—21no—
348#125—21no—
349#125—21no—
350#125D4×C3712yes—
351#125C23×C3712yes—
352#125C23×C3711yescharacteristic
353#124C23×C3711yescharacteristic
354#124C23×C3712yes—
355#123—22no—
356#123—22no—
357#123—22no—
358#123—22no—
359#123—21no—
360#123—22no—
361#123—22no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8D4×C3711yescharacteristic
369#121—22no—
370#121—22no—
371#121—21no—
372#121—21no—
373#121—22no—
374#121—22no—
375#121—21no—
376#121—21no—
377#121D4×C3711yescharacteristic
378C4×Q8D4×C3711yescharacteristic
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4D4×C3711yescharacteristic
387#117—21no—
388#117—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4D4×C3711yescharacteristic
396C2×C4⋊C4D4×C3711yescharacteristic
397C2×C42C23×C3711yescharacteristic
398#107—24no—
399#107—22no—
400#106—24no—
401#106—22no—
402C4⋊C8—21no—
403#103—22no—
404#102—22no—
405C22⋊C8—21no—
406#97—21no—
407#97C23×C3712yes—
408#97C23×C3712yes—
409#97C23×C3712yes—
410C4×C8—21no—
411#41—44no—
412#41—84no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—44no—
416C2×Q8—41no—
417C2×Q8C2×D4×C3711yescharacteristic
418C2×Q8C2×D4×C3712yes—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4C2×D4×C3711yescharacteristic
426C2×D4C2×D4×C3712yes—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—41no—
435C22×C4C2×D4×C3711yescharacteristic
436C22×C4C2×D4×C3711yescharacteristic
437C22×C4C2×D4×C3711yescharacteristic
438Q16—48no—
439SD16—48no—
440M16—24no—
441C2×C8—24no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4C2×D4×C3712yes—
466C4⋊C4C2×D4×C3711yescharacteristic
467C4⋊C4C2×D4×C3712yes—
468C4⋊C4C2×D4×C3711yescharacteristic
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—21no—
481C42—22no—
482C42—21no—
483C42C2×D4×C3711yescharacteristic
484C42C2×D4×C3711yescharacteristic
485C42C2×D4×C3711yescharacteristic
486C42C24×C3711yescharacteristic
487C23—22no—
488C23—21no—
489C23#120×C3711yescharacteristic
490Q8—42no—
491Q8—41no—
492Q8—44no—
493Q8—82no—
494Q8—82no—
495D4—42no—
496D4—41no—
497D4—44no—
498D4—42no—
499D4—42no—
500D4—81no—
501D4—82no—
502D4—82no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—81no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4#120×C3711yescharacteristic
522C2×C4#120×C3711yescharacteristic
523C2×C4#120×C3711yescharacteristic
524C2×C4C22×D4×C3711yescharacteristic
525C2×C4C22×D4×C3711yescharacteristic
526C2×C4C22×D4×C3711yescharacteristic
527C8—24no—
528C8—24no—
529C8—42no—
530C22—21no—
531C22—21no—
532C22—42no—
533C22—41no—
534C22—41no—
535C22—42no—
536C22—42no—
537C22—41no—
538C22C37×#45312yes—
539C22C2×#120×C3711yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—42no—
546C4—42no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—82no—
552C4C37×#45612yes—
553C2—22no—
554C2—82no—
555C2—81no—
556C2C2×C37×#45311yescharacteristic
557C2C2×C37×#45611yescharacteristic
558C2C37×#302211yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3559C2
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×#3238C2semidirect
3. C2×C37×#501C2semidirect
4. C37×#3152C2semidirect
5. C37×#1661C2semidirect
6. C37×#1660C2semidirect
7. C37×#1530C2semidirect
8. C37×#1528C2semidirect
9. C37×#1524C2semidirect
250. #19017C37direct (N × H)
275. #3238C2×C37semidirect
276. C2×#501C2×C37semidirect
277. #3152C2×C37semidirect
278. #1661C2×C37semidirect
279. #1660C2×C37semidirect
280. #1530C2×C37semidirect
281. #1528C2×C37semidirect
282. #1524C2×C37semidirect
326. C37#19017direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35592
C37×#32382
C2×C37×#5012
C37×#31522
C37×#16612
C37×#16602
C37×#15302
C37×#15282
C37×#15242
#1901737