Finite Group Databasebeta

← C37×#8534 #22629787

Subgroups — C37×#8534 #22629787

Order 9472.

1408 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 158 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×#3484C211yesmaximal, characteristic
2C37×#1898C214yesmaximal, complemented
3C37×#1781C211yesmaximal, characteristic, complemented
4C37×#1438C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C37C411yescharacteristic, complemented
6C23×D4×C37C2211yescharacteristic
7C37×#546—24no—
8D42×C37—24no—
9C37×#535—21no—
10C37×#534—21no—
11C37×#534C412yescomplemented
12C37×#525—21no—
13C2×#120×C37—21no—
14C2×#120×C37C2212yes—
15C37×#518C411yescharacteristic, complemented
16C22×C22⋊C4×C37—21no—
17C22×C22⋊C4×C37C2212yescomplemented
18C2×#99×C37—24no—
19C2×#99×C37—21no—
20C2×#99×C37—21no—
21C37×#379C2212yescomplemented
22C2×#95×C37—21no—
23C37×#342—24no—
24C25×C37D411yescharacteristic
25C25×C37C2311yescharacteristic
26H(5,𝔽2)×C37—42no—
27H(5,𝔽2)×C37—42no—
28C2×#41×C37—21no—
29C2×#41×C37—22no—
30C22×D4×C37—21no—
31C22×D4×C37—22no—
32C22×D4×C37—24no—
33C22×D4×C37—22no—
34C22×D4×C37—42no—
35C22×D4×C37—42no—
36C22×D4×C37C2×C411yescharacteristic
37C22×D4×C37C2×C411yescharacteristic
38C22×D4×C37C2×C412yes—
39C22×D4×C37D411yescharacteristic
40C22×D4×C37D411yescharacteristic
41C22×D4×C37D414yes—
42C23×C4×C37—22no—
43C23×C4×C37D411yescharacteristic
44#127×C37—22no—
45#124×C37—22no—
46#123×C37—22no—
47#123×C37—22no—
48#123×C37—22no—
49C22⋊Q8×C37—22no—
50#121×C37—22no—
51#121×C37—24no—
52#121×C37—24no—
53#121×C37—24no—
54#120×C37—24no—
55#120×C37—22no—
56#120×C37—22no—
57#120×C37—22no—
58#120×C37—22no—
59#120×C37—22no—
60#120×C37—24no—
61C4×D4×C37—24no—
62C4×D4×C37—24no—
63#117×C37—21no—
64C2×C22⋊C4×C37—22no—
65C2×C22⋊C4×C37—21no—
66C2×C22⋊C4×C37—24no—
67C2×C22⋊C4×C37—24no—
68C2×C22⋊C4×C37—22no—
69C2×C22⋊C4×C37—44no—
70C2×C22⋊C4×C37—44no—
71C2×C22⋊C4×C37—42no—
72C2×C22⋊C4×C37C2×C412yes—
73C2×C22⋊C4×C37D414yes—
74#99×C37—48no—
75#99×C37—42no—
76#99×C37—42no—
77#95×C37—42no—
78C24×C37—21no—
79C24×C37—22no—
80C24×C37—22no—
81C24×C37—42no—
82C24×C37—41no—
83C24×C37—41no—
84C24×C37—41no—
85C24×C37—42no—
86C24×C37—42no—
87C24×C37—42no—
88C24×C37C22⋊C411yescharacteristic
89C24×C37C22⋊C411yescharacteristic
90C24×C37C22⋊C412yescomplemented
91C24×C37C22×C411yescharacteristic
92C24×C37C2×D411yescharacteristic
93C24×C37C2×D414yes—
94C24×C37C2×D411yescharacteristic
95#41×C37—42no—
96#41×C37—48no—
97#41×C37—42no—
98C2×Q8×C37—21no—
99C2×D4×C37—22no—
100C2×D4×C37—22no—
101C2×D4×C37—22no—
102C2×D4×C37—21no—
103C2×D4×C37—22no—
104C2×D4×C37—22no—
105C2×D4×C37—22no—
106C2×D4×C37—22no—
107C2×D4×C37—24no—
108C2×D4×C37—22no—
109C2×D4×C37—22no—
110C2×D4×C37—24no—
111C2×D4×C37—24no—
112C2×D4×C37—22no—
113C2×D4×C37—22no—
114C2×D4×C37—41no—
115C2×D4×C37—41no—
116C2×D4×C37—41no—
117C2×D4×C37—41no—
118C2×D4×C37—416no—
119C2×D4×C37—48no—
120C2×D4×C37—42no—
121C2×D4×C37—42no—
122C2×D4×C37—42no—
123C2×D4×C37—42no—
124C2×D4×C37—44no—
125C2×D4×C37—44no—
126C2×D4×C37—82no—
127C2×D4×C37—82no—
128C22×C4×C37—21no—
129C22×C4×C37—22no—
130C22×C4×C37—22no—
131C22×C4×C37—22no—
132C22×C4×C37—22no—
133C22×C4×C37—24no—
134C22×C4×C37—41no—
135C22×C4×C37—42no—
136C22×C4×C37—42no—
137C22×C4×C37—42no—
138C22×C4×C37—42no—
139C22×C4×C37—42no—
140C22×C4×C37—42no—
141C22×C4×C37—42no—
142C22×C4×C37C22⋊C411yescharacteristic
143C22×C4×C37C22⋊C411yescharacteristic
144C22×C4×C37C22⋊C414yescomplemented
145C22×C4×C37C22⋊C412yescomplemented
146C4⋊C4×C37—22no—
147C4⋊C4×C37—24no—
148C22⋊C4×C37—22no—
149C22⋊C4×C37—24no—
150C22⋊C4×C37—24no—
151C22⋊C4×C37—22no—
152C22⋊C4×C37—22no—
153C22⋊C4×C37—24no—
154C22⋊C4×C37—24no—
155C22⋊C4×C37—28no—
156C22⋊C4×C37—44no—
157C22⋊C4×C37—48no—
158C22⋊C4×C37—42no—
159C22⋊C4×C37—42no—
160C22⋊C4×C37—44no—
161C22⋊C4×C37—44no—
162C42×C37—22no—
163C23×C37—21no—
164C23×C37—21no—
165C23×C37—22no—
166C23×C37—22no—
167C23×C37—21no—
168C23×C37—21no—
169C23×C37—21no—
170C23×C37—21no—
171C23×C37—21no—
172C23×C37—21no—
173C23×C37—24no—
174C23×C37—24no—
175C23×C37—21no—
176C23×C37—22no—
177C23×C37—21no—
178C23×C37—21no—
179C23×C37—44no—
180C23×C37—42no—
181C23×C37—44no—
182C23×C37—42no—
183C23×C37—44no—
184C23×C37—42no—
185C23×C37—42no—
186C23×C37—42no—
187C23×C37—44no—
188C23×C37—42no—
189C23×C37—42no—
190C23×C37—42no—
191C23×C37—44no—
192C23×C37—42no—
193C23×C37—42no—
194C23×C37—82no—
195C23×C37—81no—
196C23×C37—82no—
197C23×C37—82no—
198C23×C37—81no—
199C23×C37—81no—
200C23×C37—82no—
201C23×C37—81no—
202C23×C37—81no—
203C23×C37—81no—
204C23×C37—82no—
205C23×C37#9912yescomplemented
206C23×C37C2×C22⋊C412yes—
207C23×C37C2×C22⋊C411yescharacteristic
208C23×C37#12012yes—
209C23×C37#12012yes—
210Q8×C37—42no—
211D4×C37—28no—
212D4×C37—44no—
213D4×C37—42no—
214D4×C37—44no—
215D4×C37—44no—
216D4×C37—44no—
217D4×C37—44no—
218D4×C37—42no—
219D4×C37—42no—
220D4×C37—44no—
221D4×C37—44no—
222D4×C37—84no—
223D4×C37—84no—
224C2×C4×C37—21no—
225C2×C4×C37—21no—
226C2×C4×C37—24no—
227C2×C4×C37—22no—
228C2×C4×C37—21no—
229C2×C4×C37—21no—
230C2×C4×C37—21no—
231C2×C4×C37—44no—
232C2×C4×C37—44no—
233C2×C4×C37—42no—
234C2×C4×C37—44no—
235C2×C4×C37—42no—
236C2×C4×C37—44no—
237C2×C4×C37—44no—
238C2×C4×C37—44no—
239C2×C4×C37—82no—
240C2×C4×C37—82no—
241C2×C4×C37—82no—
242C2×C4×C37—82no—
243C2×C4×C37—82no—
244C2×C4×C37—82no—
245C2×C4×C37—84no—
246C2×C4×C37#9912yescomplemented
247#8534C3711yesmaximal, characteristic, direct product factor, Sylow
248C22×C37—21no—
249C22×C37—22no—
250C22×C37—21no—
251C22×C37—22no—
252C22×C37—21no—
253C22×C37—21no—
254C22×C37—22no—
255C22×C37—22no—
256C22×C37—22no—
257C22×C37—22no—
258C22×C37—22no—
259C22×C37—22no—
260C22×C37—24no—
261C22×C37—24no—
262C22×C37—42no—
263C22×C37—42no—
264C22×C37—42no—
265C22×C37—42no—
266C22×C37—41no—
267C22×C37—44no—
268C22×C37—42no—
269C22×C37—84no—
270C22×C37—81no—
271C22×C37—81no—
272C22×C37—81no—
273C22×C37—81no—
274C22×C37—81no—
275C22×C37—84no—
276C22×C37—84no—
277C22×C37—84no—
278C22×C37—81no—
279C22×C37—162no—
280C22×C37—162no—
281C22×C37#37911yescharacteristic
282C22×C37C2×#9911yescharacteristic
283C22×C37C2×#9911yescharacteristic
284C22×C37B(4,𝔽2)12yes—
285C22×C37#45812yes—
286C4×C37—22no—
287C4×C37—41no—
288C4×C37—42no—
289C4×C37—44no—
290C4×C37—84no—
291C4×C37—162no—
292#3484C2×C3711yescharacteristic
293#1898C2×C3714yescomplemented
294#1781C2×C3711yescharacteristic, complemented
295#1438C2×C3711yescharacteristic, complemented
296C2×C37—22no—
297C2×C37—21no—
298C2×C37—21no—
299C2×C37—22no—
300C2×C37—42no—
301C2×C37—42no—
302C2×C37—42no—
303C2×C37—81no—
304C2×C37—82no—
305C2×C37#178111yescharacteristic
306C2×C37#179012yes—
307C2×H(5,𝔽2)C4×C3711yescharacteristic, complemented
308C23×D4C22×C3711yescharacteristic
309#546—24no—
310D42—24no—
311#535—21no—
312#534—21no—
313#534C4×C3712yescomplemented
314#525—21no—
315C2×#120—21no—
316C2×#120C22×C3712yes—
317#518C4×C3711yescharacteristic, complemented
318C22×C22⋊C4—21no—
319C22×C22⋊C4C22×C3712yescomplemented
320C2×#99—24no—
321C2×#99—21no—
322C2×#99—21no—
323#379C22×C3712yescomplemented
324C2×#95—21no—
325#342—24no—
326C37#853411yescharacteristic, direct product factor, Sylow
327C25D4×C3711yescharacteristic
328C25C23×C3711yescharacteristic
329H(5,𝔽2)—42no—
330H(5,𝔽2)—42no—
331C2×#41—21no—
332C2×#41—22no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4C2×C4×C3711yescharacteristic
340C22×D4C2×C4×C3711yescharacteristic
341C22×D4C2×C4×C3712yes—
342C22×D4D4×C3711yescharacteristic
343C22×D4D4×C3711yescharacteristic
344C22×D4D4×C3714yes—
345C23×C4—22no—
346C23×C4D4×C3711yescharacteristic
347#127—22no—
348#124—22no—
349#123—22no—
350#123—22no—
351#123—22no—
352C22⋊Q8—22no—
353#121—22no—
354#121—24no—
355#121—24no—
356#121—24no—
357#120—24no—
358#120—22no—
359#120—22no—
360#120—22no—
361#120—22no—
362#120—22no—
363#120—24no—
364C4×D4—24no—
365C4×D4—24no—
366#117—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4C2×C4×C3712yes—
376C2×C22⋊C4D4×C3714yes—
377#99—48no—
378#99—42no—
379#99—42no—
380#95—42no—
381C24—21no—
382C24—22no—
383C24—22no—
384C24—42no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24C22⋊C4×C3711yescharacteristic
392C24C22⋊C4×C3711yescharacteristic
393C24C22⋊C4×C3712yescomplemented
394C24C22×C4×C3711yescharacteristic
395C24C2×D4×C3711yescharacteristic
396C24C2×D4×C3714yes—
397C24C2×D4×C3711yescharacteristic
398#41—42no—
399#41—48no—
400#41—42no—
401C2×Q8—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—416no—
422C2×D4—48no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—82no—
430C2×D4—82no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—41no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4C22⋊C4×C3711yescharacteristic
446C22×C4C22⋊C4×C3711yescharacteristic
447C22×C4C22⋊C4×C3714yescomplemented
448C22×C4C22⋊C4×C3712yescomplemented
449C4⋊C4—22no—
450C4⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—28no—
459C22⋊C4—44no—
460C22⋊C4—48no—
461C22⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C42—22no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—22no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—24no—
477C23—24no—
478C23—21no—
479C23—22no—
480C23—21no—
481C23—21no—
482C23—44no—
483C23—42no—
484C23—44no—
485C23—42no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—44no—
495C23—42no—
496C23—42no—
497C23—82no—
498C23—81no—
499C23—82no—
500C23—82no—
501C23—81no—
502C23—81no—
503C23—82no—
504C23—81no—
505C23—81no—
506C23—81no—
507C23—82no—
508C23#99×C3712yescomplemented
509C23C2×C22⋊C4×C3712yes—
510C23C2×C22⋊C4×C3711yescharacteristic
511C23#120×C3712yes—
512C23#120×C3712yes—
513Q8—42no—
514D4—28no—
515D4—44no—
516D4—42no—
517D4—44no—
518D4—44no—
519D4—44no—
520D4—44no—
521D4—42no—
522D4—42no—
523D4—44no—
524D4—44no—
525D4—84no—
526D4—84no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—84no—
549C2×C4#99×C3712yescomplemented
550C22—21no—
551C22—22no—
552C22—21no—
553C22—22no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—24no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—41no—
569C22—44no—
570C22—42no—
571C22—84no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—84no—
578C22—84no—
579C22—84no—
580C22—81no—
581C22—162no—
582C22—162no—
583C22C37×#37911yescharacteristic
584C22C2×#99×C3711yescharacteristic
585C22C2×#99×C3711yescharacteristic
586C22C37×B(4,𝔽2)12yes—
587C22C37×#45812yes—
588C4—22no—
589C4—41no—
590C4—42no—
591C4—44no—
592C4—84no—
593C4—162no—
594C2—22no—
595C2—21no—
596C2—21no—
597C2—22no—
598C2—42no—
599C2—42no—
600C2—42no—
601C2—81no—
602C2—82no—
603C2C37×#178111yescharacteristic
604C2C37×#179012yes—
subgroupG/H
center, socleC22×C37#379
commutatorC24C22×C4×C37
Frattini, cosocleC25C23×C37
prime radicalC37×#3484C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#1898C2semidirect
3. C37×#1781C2semidirect
4. C37×#1438C2semidirect
5. C2×H(5,𝔽2)×C37C4semidirect
11. C37×#534C4semidirect
15. C37×#518C4semidirect
17. C22×C22⋊C4×C37C22semidirect
21. C37×#379C22semidirect
90. C24×C37C22⋊C4semidirect
144. C22×C4×C37C22⋊C4semidirect
145. C22×C4×C37C22⋊C4semidirect
205. C23×C37#99semidirect
246. C2×C4×C37#99semidirect
247. #8534C37direct (N × H)
293. #1898C2×C37semidirect
294. #1781C2×C37semidirect
295. #1438C2×C37semidirect
307. C2×H(5,𝔽2)C4×C37semidirect
313. #534C4×C37semidirect
317. #518C4×C37semidirect
319. C22×C22⋊C4C22×C37semidirect
323. #379C22×C37semidirect
326. C37#8534direct (N × H)
393. C24C22⋊C4×C37semidirect
447. C22×C4C22⋊C4×C37semidirect
448. C22×C4C22⋊C4×C37semidirect
508. C23#99×C37semidirect
549. C2×C4#99×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34842
C37×#18982
C37×#17812
C37×#14382
#853437