Finite Group Databasebeta

← C37×#13422 #22634675

Subgroups — C37×#13422 #22634675

Order 9472.

734 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2669C211yesmaximal, characteristic
2C2×C37×#353C211yesmaximal, characteristic, complemented
3C2×C37×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
4C37×#1889C211yesmaximal, characteristic, complemented
5C37×#1887C211yesmaximal, characteristic, complemented
6C37×#1867C211yesmaximal, characteristic, complemented
7C37×#1390C211yesmaximal, characteristic, complemented
8C2×#127×C37C2211yescharacteristic
9C2×#121×C37—21no—
10C2×#120×C37—21no—
11C2×#120×C37C2211yescharacteristic
12C37×#518C2211yescharacteristic
13C37×#418—21no—
14C2×#100×C37C2211yescharacteristic
15C2×#99×C37C2211yescharacteristic
16C2×#99×C37C2211yescharacteristic
17C37×#394—21no—
18C37×#392—21no—
19C37×#392—21no—
20C37×#388—21no—
21C37×#386C2211yescharacteristic
22C37×#385—21no—
23C37×#379—21no—
24C37×#353—22no—
25C37×AΣL(1,𝔽16)—22no—
26C37×#342—21no—
27C37×#342—21no—
28C37×#339—21no—
29C25×C37D411yescharacteristic
30C22×D4×C37—21no—
31C22×D4×C37—21no—
32C22×D4×C37—21no—
33C22×D4×C37—21no—
34C22×D4×C37—21no—
35C22×D4×C37D411yescharacteristic
36C22×D4×C37C2311yescharacteristic
37C23×C4×C37D411yescharacteristic
38C2×M16×C37—21no—
39#127×C37—21no—
40#127×C37—21no—
41#127×C37—21no—
42#127×C37—21no—
43#121×C37—44no—
44#120×C37—21no—
45#120×C37—21no—
46#120×C37—21no—
47#120×C37—21no—
48#120×C37—44no—
49C4×D4×C37—41no—
50C4×D4×C37—41no—
51#117×C37—21no—
52C2×C4⋊C4×C37—21no—
53C2×C4⋊C4×C37—41no—
54C2×C22⋊C4×C37—21no—
55C2×C22⋊C4×C37—21no—
56C2×C22⋊C4×C37—21no—
57C2×C22⋊C4×C37—21no—
58C2×C22⋊C4×C37—21no—
59C2×C22⋊C4×C37—21no—
60C2×C22⋊C4×C37—21no—
61C2×C22⋊C4×C37—21no—
62C2×C22⋊C4×C37—21no—
63C2×C22⋊C4×C37—21no—
64C2×C22⋊C4×C37—41no—
65C2×C22⋊C4×C37—41no—
66C2×C22⋊C4×C37D411yescharacteristic
67C2×C22⋊C4×C37D411yescharacteristic
68C2×C42×C37D411yescharacteristic
69#102×C37—41no—
70#102×C37—41no—
71#100×C37—21no—
72#100×C37—21no—
73#99×C37—21no—
74#99×C37—21no—
75#99×C37—21no—
76#99×C37D412yescomplemented
77#95×C37—21no—
78#95×C37—21no—
79#95×C37—41no—
80C24×C37—21no—
81C24×C37—21no—
82C24×C37—21no—
83C24×C37—21no—
84C24×C37—41no—
85C24×C37—42no—
86C24×C37—41no—
87C24×C37—81no—
88C24×C37C2×D411yescharacteristic
89C24×C37C2×D411yescharacteristic
90C2×D4×C37—21no—
91C2×D4×C37—21no—
92C2×D4×C37—41no—
93C2×D4×C37—41no—
94C2×D4×C37—41no—
95C2×D4×C37—41no—
96C2×D4×C37—42no—
97C2×D4×C37—42no—
98C2×D4×C37—42no—
99C2×D4×C37—42no—
100C2×D4×C37—42no—
101C2×D4×C37—42no—
102C2×D4×C37—41no—
103C2×D4×C37—41no—
104C2×D4×C37—41no—
105C2×D4×C37—41no—
106C2×D4×C37—41no—
107C2×D4×C37—41no—
108C2×D4×C37—81no—
109C2×D4×C37—81no—
110C2×D4×C37—81no—
111C2×D4×C37—81no—
112C2×D4×C37—81no—
113C2×D4×C37—81no—
114C2×D4×C37C2×D411yescharacteristic
115C2×D4×C37#4111yescharacteristic
116C2×D4×C37#4111yescharacteristic
117C2×D4×C37#4111yescharacteristic
118C22×C4×C37—21no—
119C22×C4×C37—21no—
120C22×C4×C37—21no—
121C22×C4×C37—21no—
122C22×C4×C37—21no—
123C22×C4×C37—21no—
124C22×C4×C37—21no—
125C22×C4×C37—21no—
126C22×C4×C37—42no—
127C22×C4×C37—41no—
128C22×C4×C37—41no—
129C22×C4×C37—41no—
130C22×C4×C37C2×D411yescharacteristic
131M16×C37—41no—
132M16×C37—41no—
133C2×C8×C37—41no—
134C4⋊C4×C37—21no—
135C4⋊C4×C37—21no—
136C4⋊C4×C37—42no—
137C4⋊C4×C37—82no—
138C22⋊C4×C37—24no—
139C22⋊C4×C37—22no—
140C22⋊C4×C37—21no—
141C22⋊C4×C37—21no—
142C22⋊C4×C37—42no—
143C22⋊C4×C37—42no—
144C22⋊C4×C37—42no—
145C22⋊C4×C37—41no—
146C22⋊C4×C37—41no—
147C22⋊C4×C37—41no—
148C22⋊C4×C37—41no—
149C22⋊C4×C37—41no—
150C22⋊C4×C37—41no—
151C22⋊C4×C37—41no—
152C22⋊C4×C37—41no—
153C22⋊C4×C37—41no—
154C22⋊C4×C37—81no—
155C22⋊C4×C37—82no—
156C22⋊C4×C37—82no—
157C42×C37—21no—
158C42×C37—21no—
159C42×C37—41no—
160C23×C37—21no—
161C23×C37—21no—
162C23×C37—21no—
163C23×C37—21no—
164C23×C37—22no—
165C23×C37—41no—
166C23×C37—41no—
167C23×C37—41no—
168C23×C37—41no—
169C23×C37—41no—
170C23×C37—41no—
171C23×C37—41no—
172C23×C37—42no—
173C23×C37—41no—
174C23×C37—41no—
175C23×C37—41no—
176C23×C37—41no—
177C23×C37—42no—
178C23×C37—42no—
179C23×C37—41no—
180C23×C37—41no—
181C23×C37—41no—
182C23×C37—41no—
183C23×C37—41no—
184C23×C37—41no—
185C23×C37—81no—
186C23×C37—82no—
187C23×C37—81no—
188C23×C37—82no—
189C23×C37—84no—
190C23×C37—81no—
191C23×C37#12011yescharacteristic
192C23×C37#12111yescharacteristic
193C23×C37#12111yescharacteristic
194C23×C37#12311yescharacteristic
195C23×C37#12411yescharacteristic
196D4×C37—41no—
197D4×C37—41no—
198D4×C37—41no—
199D4×C37—41no—
200D4×C37—42no—
201D4×C37—81no—
202D4×C37—82no—
203D4×C37—82no—
204D4×C37—82no—
205D4×C37—82no—
206D4×C37—84no—
207D4×C37—82no—
208D4×C37—82no—
209D4×C37—84no—
210C2×C4×C37—21no—
211C2×C4×C37—21no—
212C2×C4×C37—22no—
213C2×C4×C37—22no—
214C2×C4×C37—41no—
215C2×C4×C37—41no—
216C2×C4×C37—41no—
217C2×C4×C37—41no—
218C2×C4×C37—42no—
219C2×C4×C37—42no—
220C2×C4×C37—41no—
221C2×C4×C37—41no—
222C2×C4×C37—41no—
223C2×C4×C37—41no—
224C2×C4×C37—41no—
225C2×C4×C37—41no—
226C2×C4×C37—41no—
227C2×C4×C37—41no—
228C2×C4×C37—81no—
229C2×C4×C37—81no—
230C2×C4×C37—81no—
231C2×C4×C37—81no—
232C2×C4×C37—81no—
233C2×C4×C37—81no—
234C2×C4×C37—81no—
235C2×C4×C37—81no—
236C2×C4×C37—81no—
237C2×C4×C37—81no—
238C2×C4×C37#12111yescharacteristic
239C2×C4×C37#12311yescharacteristic
240C8×C37—81no—
241#13422C3711yesmaximal, characteristic, direct product factor, Sylow
242C22×C37—21no—
243C22×C37—21no—
244C22×C37—21no—
245C22×C37—21no—
246C22×C37—21no—
247C22×C37—21no—
248C22×C37—41no—
249C22×C37—41no—
250C22×C37—41no—
251C22×C37—41no—
252C22×C37—42no—
253C22×C37—42no—
254C22×C37—41no—
255C22×C37—41no—
256C22×C37—41no—
257C22×C37—41no—
258C22×C37—44no—
259C22×C37—42no—
260C22×C37—81no—
261C22×C37—81no—
262C22×C37—81no—
263C22×C37—81no—
264C22×C37—81no—
265C22×C37—81no—
266C22×C37—81no—
267C22×C37—81no—
268C22×C37—82no—
269C22×C37—82no—
270C22×C37—82no—
271C22×C37—81no—
272C22×C37—81no—
273C22×C37—81no—
274C22×C37—81no—
275C22×C37—81no—
276C22×C37#39411yescharacteristic
277C22×C37B(4,𝔽2)11yescharacteristic
278C22×C37#45811yescharacteristic
279C4×C37—21no—
280C4×C37—21no—
281C4×C37—42no—
282C4×C37—42no—
283C4×C37—81no—
284C4×C37—81no—
285C4×C37—82no—
286C4×C37—81no—
287C4×C37—81no—
288C4×C37—161no—
289#2669C2×C3711yescharacteristic
290C2×#353C2×C3711yescharacteristic, complemented
291C2×AΣL(1,𝔽16)C2×C3711yescharacteristic, complemented
292#1889C2×C3711yescharacteristic, complemented
293#1887C2×C3711yescharacteristic, complemented
294#1867C2×C3711yescharacteristic, complemented
295#1390C2×C3711yescharacteristic, complemented
296C2×C37—21no—
297C2×C37—21no—
298C2×C37—41no—
299C2×C37—41no—
300C2×C37—41no—
301C2×C37—41no—
302C2×C37—82no—
303C2×C37—161no—
304C2×C37#204411yescharacteristic
305C2×C37#219611yescharacteristic
306C2×C37#220011yescharacteristic
307C2×#127C22×C3711yescharacteristic
308C2×#121—21no—
309C2×#120—21no—
310C2×#120C22×C3711yescharacteristic
311#518C22×C3711yescharacteristic
312#418—21no—
313C2×#100C22×C3711yescharacteristic
314C2×#99C22×C3711yescharacteristic
315C2×#99C22×C3711yescharacteristic
316#394—21no—
317#392—21no—
318#392—21no—
319#388—21no—
320#386C22×C3711yescharacteristic
321#385—21no—
322#379—21no—
323#353—22no—
324AΣL(1,𝔽16)—22no—
325#342—21no—
326#342—21no—
327#339—21no—
328C37#1342211yescharacteristic, direct product factor, Sylow
329C25D4×C3711yescharacteristic
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4D4×C3711yescharacteristic
336C22×D4C23×C3711yescharacteristic
337C23×C4D4×C3711yescharacteristic
338C2×M16—21no—
339#127—21no—
340#127—21no—
341#127—21no—
342#127—21no—
343#121—44no—
344#120—21no—
345#120—21no—
346#120—21no—
347#120—21no—
348#120—44no—
349C4×D4—41no—
350C4×D4—41no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—41no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4D4×C3711yescharacteristic
367C2×C22⋊C4D4×C3711yescharacteristic
368C2×C42D4×C3711yescharacteristic
369#102—41no—
370#102—41no—
371#100—21no—
372#100—21no—
373#99—21no—
374#99—21no—
375#99—21no—
376#99D4×C3712yescomplemented
377#95—21no—
378#95—21no—
379#95—41no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—41no—
385C24—42no—
386C24—41no—
387C24—81no—
388C24C2×D4×C3711yescharacteristic
389C24C2×D4×C3711yescharacteristic
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—81no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4—81no—
412C2×D4—81no—
413C2×D4—81no—
414C2×D4C2×D4×C3711yescharacteristic
415C2×D4#41×C3711yescharacteristic
416C2×D4#41×C3711yescharacteristic
417C2×D4#41×C3711yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4C2×D4×C3711yescharacteristic
431M16—41no—
432M16—41no—
433C2×C8—41no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—42no—
437C4⋊C4—82no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—81no—
455C22⋊C4—82no—
456C22⋊C4—82no—
457C42—21no—
458C42—21no—
459C42—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—81no—
486C23—82no—
487C23—81no—
488C23—82no—
489C23—84no—
490C23—81no—
491C23#120×C3711yescharacteristic
492C23#121×C3711yescharacteristic
493C23#121×C3711yescharacteristic
494C23#123×C3711yescharacteristic
495C23#124×C3711yescharacteristic
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—81no—
502D4—82no—
503D4—82no—
504D4—82no—
505D4—82no—
506D4—84no—
507D4—82no—
508D4—82no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4#121×C3711yescharacteristic
539C2×C4#123×C3711yescharacteristic
540C8—81no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—44no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22C37×#39411yescharacteristic
576C22C37×B(4,𝔽2)11yescharacteristic
577C22C37×#45811yescharacteristic
578C4—21no—
579C4—21no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—82no—
585C4—81no—
586C4—81no—
587C4—161no—
588C2—21no—
589C2—21no—
590C2—41no—
591C2—41no—
592C2—41no—
593C2—41no—
594C2—82no—
595C2—161no—
596C2C37×#204411yescharacteristic
597C2C37×#219611yescharacteristic
598C2C37×#220011yescharacteristic
subgroupG/H
center, socleC22×C37B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C37
prime radicalC37×#2669C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C37 ◁ C22×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#353C2semidirect
3. C2×C37×AΣL(1,𝔽16)C2semidirect
4. C37×#1889C2semidirect
5. C37×#1887C2semidirect
6. C37×#1867C2semidirect
7. C37×#1390C2semidirect
76. #99×C37D4semidirect
241. #13422C37direct (N × H)
290. C2×#353C2×C37semidirect
291. C2×AΣL(1,𝔽16)C2×C37semidirect
292. #1889C2×C37semidirect
293. #1887C2×C37semidirect
294. #1867C2×C37semidirect
295. #1390C2×C37semidirect
328. C37#13422direct (N × H)
376. #99D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#26692
C2×C37×#3532
C2×C37×AΣL(1,𝔽16)2
C37×#18892
C37×#18872
C37×#18672
C37×#13902
#1342237