Finite Group Databasebeta

← C37×#19089 #22640342

Subgroups — C37×#19089 #22640342

Order 9472.

850 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3559C211yesmaximal, characteristic
2C37×#3240C211yesmaximal, characteristic, complemented
3C37×#3236C211yesmaximal, characteristic, complemented
4C37×#3216C211yesmaximal, characteristic, complemented
5C37×#1664C212yesmaximal, complemented
6C37×#1662C212yesmaximal, complemented
7C37×#1661C212yesmaximal, complemented
8C37×#1660C212yesmaximal, complemented
9C37×#1536C211yesmaximal, characteristic, complemented
10C37×#1535C211yesmaximal, characteristic, complemented
11C37×#1534C211yesmaximal, characteristic, complemented
12C37×#563C2212yes—
13C37×#562C2212yes—
14C37×#554—21no—
15C37×#553—21no—
16C37×#553—21no—
17C37×#547—22no—
18C37×#547—21no—
19C37×#544—21no—
20C37×#540—21no—
21C37×#539—22no—
22C37×#539—21no—
23C37×#537—21no—
24C37×#533C2211yescharacteristic
25C37×#532C2211yescharacteristic
26C37×#529C2211yescharacteristic
27C2×#125×C37C2211yescharacteristic
28C37×#501C2211yescharacteristic
29C37×#501C2212yes—
30C37×#501C2211yescharacteristic
31C37×#497C2212yes—
32C37×#491C2212yes—
33C37×#489C2211yescharacteristic
34C37×#489C2211yescharacteristic
35C37×#489C2212yes—
36C37×#485—21no—
37C37×#484—21no—
38C37×#483—21no—
39C37×#482—21no—
40C37×#479—22no—
41C37×#479—21no—
42C37×#478—21no—
43C37×#462—21no—
44C37×#460—21no—
45C37×#452—22no—
46C37×#432C2211yescharacteristic
47C37×#432C2211yescharacteristic
48C37×#432C2211yescharacteristic
49C37×#330C2212yes—
50C37×#330C2212yes—
51C37×#330C2212yes—
52C37×#329C2212yes—
53C37×#329C2212yes—
54C37×#329C2212yes—
55C2×#41×C37—22no—
56C2×#41×C37D412yes—
57C2×Q16×C37—22no—
58C2×SD16×C37—22no—
59C4⋊Q8×C37—21no—
60C4⋊Q8×C37—22no—
61C4⋊Q8×C37D411yescharacteristic
62C4⋊Q8×C37C2311yescharacteristic
63C4⋊Q8×C37C2311yescharacteristic
64#127×C37D411yescharacteristic
65#126×C37—22no—
66#126×C37—22no—
67#126×C37—21no—
68#125×C37—22no—
69#125×C37—21no—
70#125×C37—21no—
71#125×C37—21no—
72#125×C37—21no—
73#125×C37D412yes—
74#125×C37C2312yes—
75#125×C37C2311yescharacteristic
76#124×C37C2311yescharacteristic
77#124×C37C2312yes—
78#123×C37—22no—
79#123×C37—22no—
80#123×C37—22no—
81#123×C37—22no—
82#123×C37—21no—
83#123×C37—22no—
84#123×C37—22no—
85C22⋊Q8×C37—22no—
86C22⋊Q8×C37—22no—
87C22⋊Q8×C37—22no—
88C22⋊Q8×C37—22no—
89C22⋊Q8×C37—22no—
90C22⋊Q8×C37—22no—
91C22⋊Q8×C37—21no—
92C22⋊Q8×C37—21no—
93C22⋊Q8×C37D411yescharacteristic
94#121×C37—22no—
95#121×C37—22no—
96#121×C37—21no—
97#121×C37—21no—
98#121×C37—22no—
99#121×C37—22no—
100#121×C37—21no—
101#121×C37—21no—
102#121×C37D411yescharacteristic
103C4×Q8×C37—21no—
104C4×Q8×C37—21no—
105C4×Q8×C37D411yescharacteristic
106C4×D4×C37—22no—
107C4×D4×C37—22no—
108C4×D4×C37—21no—
109C4×D4×C37—21no—
110C4×D4×C37—21no—
111C4×D4×C37—21no—
112C4×D4×C37—21no—
113C4×D4×C37D411yescharacteristic
114#117×C37—21no—
115#117×C37—21no—
116#117×C37—21no—
117C2×C4⋊C4×C37—22no—
118C2×C4⋊C4×C37—21no—
119C2×C4⋊C4×C37—21no—
120C2×C4⋊C4×C37—21no—
121C2×C4⋊C4×C37D411yescharacteristic
122C2×C4⋊C4×C37D411yescharacteristic
123C2×C42×C37C2311yescharacteristic
124#107×C37—21no—
125#107×C37—21no—
126#107×C37—22no—
127#106×C37—21no—
128#106×C37—21no—
129#106×C37—22no—
130C4⋊C8×C37—21no—
131C4⋊C8×C37—21no—
132C4⋊C8×C37—21no—
133#103×C37—22no—
134#103×C37—21no—
135#103×C37—21no—
136#103×C37—22no—
137#103×C37—22no—
138#102×C37—22no—
139#102×C37—21no—
140#102×C37—21no—
141C22⋊C8×C37—21no—
142C22⋊C8×C37—21no—
143C22⋊C8×C37—21no—
144#97×C37C2312yes—
145#97×C37C2311yescharacteristic
146#97×C37C2311yescharacteristic
147#97×C37C2312yes—
148#41×C37—84no—
149#41×C37—82no—
150C2×Q8×C37—22no—
151C2×Q8×C37—21no—
152C2×Q8×C37—21no—
153C2×Q8×C37C2×D411yescharacteristic
154C2×Q8×C37C2×D412yes—
155C2×D4×C37—22no—
156C2×D4×C37—21no—
157C2×D4×C37—22no—
158C2×D4×C37—22no—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37C2×D411yescharacteristic
162C2×D4×C37C2×D412yes—
163C22×C4×C37—21no—
164C22×C4×C37—22no—
165C22×C4×C37—22no—
166C22×C4×C37—22no—
167C22×C4×C37—21no—
168C22×C4×C37—21no—
169C22×C4×C37—22no—
170C22×C4×C37C2×D411yescharacteristic
171C22×C4×C37C2×D411yescharacteristic
172C22×C4×C37C2×D411yescharacteristic
173Q16×C37—82no—
174SD16×C37—82no—
175C2×C8×C37—21no—
176C2×C8×C37—21no—
177C2×C8×C37—22no—
178C2×C8×C37—22no—
179C4⋊C4×C37—22no—
180C4⋊C4×C37—22no—
181C4⋊C4×C37—22no—
182C4⋊C4×C37—22no—
183C4⋊C4×C37—22no—
184C4⋊C4×C37—21no—
185C4⋊C4×C37—21no—
186C4⋊C4×C37—21no—
187C4⋊C4×C37—22no—
188C4⋊C4×C37—21no—
189C4⋊C4×C37—21no—
190C4⋊C4×C37—21no—
191C4⋊C4×C37—22no—
192C4⋊C4×C37—22no—
193C4⋊C4×C37—21no—
194C4⋊C4×C37—21no—
195C4⋊C4×C37—21no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—21no—
199C4⋊C4×C37—41no—
200C4⋊C4×C37—41no—
201C4⋊C4×C37C2×D412yes—
202C4⋊C4×C37C2×D412yes—
203C4⋊C4×C37C2×D411yescharacteristic
204C4⋊C4×C37C2×D411yescharacteristic
205C22⋊C4×C37—22no—
206C22⋊C4×C37—22no—
207C22⋊C4×C37—22no—
208C22⋊C4×C37—22no—
209C22⋊C4×C37—22no—
210C22⋊C4×C37—21no—
211C22⋊C4×C37—21no—
212C22⋊C4×C37—21no—
213C22⋊C4×C37—21no—
214C22⋊C4×C37—22no—
215C22⋊C4×C37—22no—
216C22⋊C4×C37—21no—
217C22⋊C4×C37—41no—
218C42×C37—22no—
219C42×C37—21no—
220C42×C37—41no—
221C42×C37C2×D411yescharacteristic
222C42×C37C2×D411yescharacteristic
223C42×C37C2×D411yescharacteristic
224C42×C37C2411yescharacteristic
225C23×C37—22no—
226C23×C37—21no—
227C23×C37#12011yescharacteristic
228Q8×C37—42no—
229Q8×C37—41no—
230Q8×C37—41no—
231Q8×C37—41no—
232Q8×C37—42no—
233Q8×C37—82no—
234D4×C37—42no—
235D4×C37—41no—
236D4×C37—42no—
237D4×C37—44no—
238D4×C37—42no—
239D4×C37—81no—
240D4×C37—82no—
241D4×C37—82no—
242C2×C4×C37—21no—
243C2×C4×C37—21no—
244C2×C4×C37—22no—
245C2×C4×C37—22no—
246C2×C4×C37—21no—
247C2×C4×C37—22no—
248C2×C4×C37—41no—
249C2×C4×C37—41no—
250C2×C4×C37—41no—
251C2×C4×C37—42no—
252C2×C4×C37—42no—
253C2×C4×C37—41no—
254C2×C4×C37—41no—
255C2×C4×C37—82no—
256C2×C4×C37—81no—
257C2×C4×C37—82no—
258C2×C4×C37—82no—
259C2×C4×C37—82no—
260C2×C4×C37#12011yescharacteristic
261C2×C4×C37#12011yescharacteristic
262C2×C4×C37#12011yescharacteristic
263C2×C4×C37C22×D411yescharacteristic
264C2×C4×C37C22×D411yescharacteristic
265C2×C4×C37C22×D411yescharacteristic
266C8×C37—42no—
267C8×C37—41no—
268C8×C37—41no—
269C8×C37—42no—
270#19089C3711yesmaximal, characteristic, direct product factor, Sylow
271C22×C37—21no—
272C22×C37—21no—
273C22×C37—21no—
274C22×C37—42no—
275C22×C37—41no—
276C22×C37—41no—
277C22×C37—42no—
278C22×C37—42no—
279C22×C37—41no—
280C22×C37C2×#12011yescharacteristic
281C4×C37—21no—
282C4×C37—21no—
283C4×C37—21no—
284C4×C37—21no—
285C4×C37—21no—
286C4×C37—21no—
287C4×C37—42no—
288C4×C37—42no—
289C4×C37—41no—
290C4×C37—41no—
291C4×C37—42no—
292C4×C37—41no—
293C4×C37—81no—
294C4×C37—81no—
295#3559C2×C3711yescharacteristic
296#3240C2×C3711yescharacteristic, complemented
297#3236C2×C3711yescharacteristic, complemented
298#3216C2×C3711yescharacteristic, complemented
299#1664C2×C3712yescomplemented
300#1662C2×C3712yescomplemented
301#1661C2×C3712yescomplemented
302#1660C2×C3712yescomplemented
303#1536C2×C3711yescharacteristic, complemented
304#1535C2×C3711yescharacteristic, complemented
305#1534C2×C3711yescharacteristic, complemented
306C2×C37—41no—
307C2×C37—82no—
308C2×C37—81no—
309C2×C37#301911yescharacteristic
310C2×C37#302011yescharacteristic
311C2×C37#302211yescharacteristic
312#563C22×C3712yes—
313#562C22×C3712yes—
314#554—21no—
315#553—21no—
316#553—21no—
317#547—22no—
318#547—21no—
319#544—21no—
320#540—21no—
321#539—22no—
322#539—21no—
323#537—21no—
324#533C22×C3711yescharacteristic
325#532C22×C3711yescharacteristic
326#529C22×C3711yescharacteristic
327C2×#125C22×C3711yescharacteristic
328#501C22×C3711yescharacteristic
329#501C22×C3712yes—
330#501C22×C3711yescharacteristic
331#497C22×C3712yes—
332#491C22×C3712yes—
333#489C22×C3711yescharacteristic
334#489C22×C3711yescharacteristic
335#489C22×C3712yes—
336#485—21no—
337#484—21no—
338#483—21no—
339#482—21no—
340#479—22no—
341#479—21no—
342#478—21no—
343#462—21no—
344#460—21no—
345#452—22no—
346#432C22×C3711yescharacteristic
347#432C22×C3711yescharacteristic
348#432C22×C3711yescharacteristic
349#330C22×C3712yes—
350#330C22×C3712yes—
351#330C22×C3712yes—
352#329C22×C3712yes—
353#329C22×C3712yes—
354#329C22×C3712yes—
355C37#1908911yescharacteristic, direct product factor, Sylow
356C2×#41—22no—
357C2×#41D4×C3712yes—
358C2×Q16—22no—
359C2×SD16—22no—
360C4⋊Q8—21no—
361C4⋊Q8—22no—
362C4⋊Q8D4×C3711yescharacteristic
363C4⋊Q8C23×C3711yescharacteristic
364C4⋊Q8C23×C3711yescharacteristic
365#127D4×C3711yescharacteristic
366#126—22no—
367#126—22no—
368#126—21no—
369#125—22no—
370#125—21no—
371#125—21no—
372#125—21no—
373#125—21no—
374#125D4×C3712yes—
375#125C23×C3712yes—
376#125C23×C3711yescharacteristic
377#124C23×C3711yescharacteristic
378#124C23×C3712yes—
379#123—22no—
380#123—22no—
381#123—22no—
382#123—22no—
383#123—21no—
384#123—22no—
385#123—22no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8D4×C3711yescharacteristic
395#121—22no—
396#121—22no—
397#121—21no—
398#121—21no—
399#121—22no—
400#121—22no—
401#121—21no—
402#121—21no—
403#121D4×C3711yescharacteristic
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8D4×C3711yescharacteristic
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4D4×C3711yescharacteristic
415#117—21no—
416#117—21no—
417#117—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4D4×C3711yescharacteristic
423C2×C4⋊C4D4×C3711yescharacteristic
424C2×C42C23×C3711yescharacteristic
425#107—21no—
426#107—21no—
427#107—22no—
428#106—21no—
429#106—21no—
430#106—22no—
431C4⋊C8—21no—
432C4⋊C8—21no—
433C4⋊C8—21no—
434#103—22no—
435#103—21no—
436#103—21no—
437#103—22no—
438#103—22no—
439#102—22no—
440#102—21no—
441#102—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445#97C23×C3712yes—
446#97C23×C3711yescharacteristic
447#97C23×C3711yescharacteristic
448#97C23×C3712yes—
449#41—84no—
450#41—82no—
451C2×Q8—22no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C3711yescharacteristic
455C2×Q8C2×D4×C3712yes—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4C2×D4×C3711yescharacteristic
463C2×D4C2×D4×C3712yes—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4C2×D4×C3711yescharacteristic
472C22×C4C2×D4×C3711yescharacteristic
473C22×C4C2×D4×C3711yescharacteristic
474Q16—82no—
475SD16—82no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—22no—
479C2×C8—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C3712yes—
503C4⋊C4C2×D4×C3712yes—
504C4⋊C4C2×D4×C3711yescharacteristic
505C4⋊C4C2×D4×C3711yescharacteristic
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—41no—
519C42—22no—
520C42—21no—
521C42—41no—
522C42C2×D4×C3711yescharacteristic
523C42C2×D4×C3711yescharacteristic
524C42C2×D4×C3711yescharacteristic
525C42C24×C3711yescharacteristic
526C23—22no—
527C23—21no—
528C23#120×C3711yescharacteristic
529Q8—42no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—42no—
534Q8—82no—
535D4—42no—
536D4—41no—
537D4—42no—
538D4—44no—
539D4—42no—
540D4—81no—
541D4—82no—
542D4—82no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—81no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4#120×C3711yescharacteristic
562C2×C4#120×C3711yescharacteristic
563C2×C4#120×C3711yescharacteristic
564C2×C4C22×D4×C3711yescharacteristic
565C2×C4C22×D4×C3711yescharacteristic
566C2×C4C22×D4×C3711yescharacteristic
567C8—42no—
568C8—42no—
569C8—41no—
570C8—41no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22C2×#120×C3711yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—42no—
588C4—42no—
589C4—41no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—81no—
594C4—81no—
595C2—41no—
596C2—82no—
597C2—81no—
598C2C37×#301911yescharacteristic
599C2C37×#302011yescharacteristic
600C2C37×#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×#3240C2semidirect
3. C37×#3236C2semidirect
4. C37×#3216C2semidirect
5. C37×#1664C2semidirect
6. C37×#1662C2semidirect
7. C37×#1661C2semidirect
8. C37×#1660C2semidirect
9. C37×#1536C2semidirect
10. C37×#1535C2semidirect
11. C37×#1534C2semidirect
270. #19089C37direct (N × H)
296. #3240C2×C37semidirect
297. #3236C2×C37semidirect
298. #3216C2×C37semidirect
299. #1664C2×C37semidirect
300. #1662C2×C37semidirect
301. #1661C2×C37semidirect
302. #1660C2×C37semidirect
303. #1536C2×C37semidirect
304. #1535C2×C37semidirect
305. #1534C2×C37semidirect
355. C37#19089direct (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×#32402
C37×#32362
C37×#32162
C37×#16642
C37×#16622
C37×#16612
C37×#16602
C37×#15362
C37×#15352
C37×#15342
#1908937