Finite Group Databasebeta

← C2×C37×#2022 #22644695

Subgroups — C2×C37×#2022 #22644695

Order 9472.

2394 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#534C211yesmaximal, characteristic
2C22×#123×C37C212yesmaximal, complemented
3C22×#99×C37C212yesmaximal, complemented
4C2×C37×#381C211yesmaximal, characteristic, complemented
5C37×#2022C218yesmaximal, direct product factor
6C2×C37×#342C211yesmaximal, characteristic, complemented
7C23×D4×C37C2212yes—
8C24×C4×C37C2211yescharacteristic
9C37×#534—24no—
10C37×#534—22no—
11C37×#534C2214yes—
12C2×#123×C37—24no—
13C2×#123×C37—22no—
14C2×#123×C37—28no—
15C2×#123×C37—28no—
16C2×#123×C37C2218yescomplemented
17C2×#121×C37—22no—
18C2×#120×C37—22no—
19C22×C4⋊C4×C37—22no—
20C22×C22⋊C4×C37—22no—
21C22×C22⋊C4×C37C2211yescharacteristic
22C22×C22⋊C4×C37C2211yescharacteristic
23C22×C22⋊C4×C37C2212yes—
24C2×#99×C37—28no—
25C2×#99×C37C2218yescomplemented
26C37×#381—22no—
27C37×#381C2214yescomplemented
28C2×#95×C37—22no—
29C37×#342C2214yescomplemented
30C25×C37D412yes—
31C25×C37C2311yescharacteristic
32C22×D4×C37—22no—
33C22×D4×C37—22no—
34C22×D4×C37—24no—
35C22×D4×C37—24no—
36C22×D4×C37—22no—
37C22×D4×C37—22no—
38C22×D4×C37—24no—
39C22×D4×C37—24no—
40C22×D4×C37—22no—
41C22×D4×C37D414yes—
42C22×D4×C37C2314yes—
43C23×C4×C37—24no—
44C23×C4×C37—22no—
45C23×C4×C37—21no—
46C23×C4×C37—21no—
47C23×C4×C37—22no—
48C23×C4×C37—22no—
49C23×C4×C37—22no—
50C23×C4×C37—21no—
51C23×C4×C37D412yes—
52C23×C4×C37D412yes—
53C23×C4×C37D414yescomplemented
54C23×C4×C37C2312yes—
55#123×C37—232no—
56#123×C37—28no—
57#123×C37—28no—
58#123×C37—216no—
59#123×C37—216no—
60#121×C37—28no—
61#121×C37—28no—
62#120×C37—28no—
63#120×C37—28no—
64C2×C4⋊C4×C37—22no—
65C2×C4⋊C4×C37—216no—
66C2×C4⋊C4×C37—28no—
67C2×C22⋊C4×C37—24no—
68C2×C22⋊C4×C37—216no—
69C2×C22⋊C4×C37—22no—
70C2×C22⋊C4×C37—22no—
71C2×C22⋊C4×C37—24no—
72C2×C22⋊C4×C37—28no—
73C2×C22⋊C4×C37—22no—
74C2×C22⋊C4×C37—24no—
75C2×C22⋊C4×C37—21no—
76C2×C22⋊C4×C37D412yes—
77C2×C22⋊C4×C37D418yescomplemented
78C2×C22⋊C4×C37C2312yes—
79C2×C22⋊C4×C37C2312yes—
80C2×C22⋊C4×C37C2314yes—
81#99×C37—216no—
82#95×C37—28no—
83C24×C37—24no—
84C24×C37—22no—
85C24×C37—22no—
86C24×C37—24no—
87C24×C37—44no—
88C24×C37—48no—
89C24×C37C2×D412yes—
90C24×C37C2×D411yescharacteristic
91C24×C37C2×D414yes—
92C24×C37C2×D412yes—
93C24×C37C2×D412yes—
94C24×C37C2×D411yescharacteristic
95C24×C37C2×D414yes—
96C24×C37#4112yes—
97C24×C37C2411yescharacteristic
98C2×D4×C37—24no—
99C2×D4×C37—24no—
100C2×D4×C37—28no—
101C2×D4×C37—28no—
102C2×D4×C37—24no—
103C2×D4×C37—24no—
104C2×D4×C37—24no—
105C2×D4×C37—24no—
106C2×D4×C37—24no—
107C2×D4×C37—24no—
108C2×D4×C37—28no—
109C2×D4×C37—44no—
110C2×D4×C37—44no—
111C2×D4×C37—44no—
112C2×D4×C37—44no—
113C2×D4×C37—44no—
114C2×D4×C37—44no—
115C2×D4×C37—44no—
116C2×D4×C37—44no—
117C2×D4×C37—84no—
118C22×C4×C37—28no—
119C22×C4×C37—28no—
120C22×C4×C37—24no—
121C22×C4×C37—28no—
122C22×C4×C37—22no—
123C22×C4×C37—22no—
124C22×C4×C37—22no—
125C22×C4×C37—24no—
126C22×C4×C37—24no—
127C22×C4×C37—24no—
128C22×C4×C37—22no—
129C22×C4×C37—24no—
130C22×C4×C37—24no—
131C22×C4×C37—24no—
132C22×C4×C37—22no—
133C22×C4×C37—22no—
134C22×C4×C37—22no—
135C22×C4×C37—48no—
136C22×C4×C37—42no—
137C22×C4×C37—41no—
138C22×C4×C37—41no—
139C22×C4×C37—44no—
140C22×C4×C37—44no—
141C22×C4×C37—42no—
142C22×C4×C37—42no—
143C22×C4×C37—44no—
144C22×C4×C37—44no—
145C22×C4×C37—42no—
146C22×C4×C37C2×D414yes—
147C22×C4×C37C2×D414yes—
148C22×C4×C37C2×D414yescomplemented
149C4⋊C4×C37—232no—
150C4⋊C4×C37—28no—
151C22⋊C4×C37—232no—
152C22⋊C4×C37—216no—
153C22⋊C4×C37—24no—
154C22⋊C4×C37—28no—
155C22⋊C4×C37—24no—
156C22⋊C4×C37—24no—
157C22⋊C4×C37—24no—
158C22⋊C4×C37—42no—
159C22⋊C4×C37C2×D418yescomplemented
160C23×C37—24no—
161C23×C37—28no—
162C23×C37—24no—
163C23×C37—24no—
164C23×C37—24no—
165C23×C37—42no—
166C23×C37—44no—
167C23×C37—44no—
168C23×C37—48no—
169C23×C37—44no—
170C23×C37—42no—
171C23×C37—48no—
172C23×C37—416no—
173C23×C37—44no—
174C23×C37—44no—
175C23×C37—48no—
176C23×C37—84no—
177C23×C37—88no—
178C23×C37#12012yes—
179C23×C37#12014yes—
180C23×C37#12011yescharacteristic
181C23×C37#12014yes—
182C23×C37#12011yescharacteristic
183C23×C37#12112yes—
184C23×C37#12114yes—
185C23×C37#12112yes—
186C23×C37#12114yes—
187C23×C37#12712yes—
188C23×C37#12712yes—
189C23×C37C22×D412yes—
190C23×C37C22×D411yescharacteristic
191C23×C37C22×D411yescharacteristic
192C23×C37C22×D412yes—
193C23×C37C2×#4111yescharacteristic
194D4×C37—44no—
195D4×C37—44no—
196D4×C37—44no—
197D4×C37—44no—
198D4×C37—48no—
199D4×C37—48no—
200D4×C37—88no—
201C2×C4×C37—24no—
202C2×C4×C37—28no—
203C2×C4×C37—28no—
204C2×C4×C37—24no—
205C2×C4×C37—24no—
206C2×C4×C37—24no—
207C2×C4×C37—24no—
208C2×C4×C37—48no—
209C2×C4×C37—416no—
210C2×C4×C37—42no—
211C2×C4×C37—44no—
212C2×C4×C37—42no—
213C2×C4×C37—48no—
214C2×C4×C37—44no—
215C2×C4×C37—44no—
216C2×C4×C37—44no—
217C2×C4×C37—44no—
218C2×C4×C37—44no—
219C2×C4×C37—44no—
220C2×C4×C37—44no—
221C2×C4×C37—42no—
222C2×C4×C37—82no—
223C2×C4×C37—84no—
224C2×#2022C3711yesmaximal, characteristic, direct product factor, Sylow
225C22×C37—22no—
226C22×C37—24no—
227C22×C37—22no—
228C22×C37—24no—
229C22×C37—28no—
230C22×C37—24no—
231C22×C37—28no—
232C22×C37—24no—
233C22×C37—44no—
234C22×C37—44no—
235C22×C37—42no—
236C22×C37—42no—
237C22×C37—41no—
238C22×C37—42no—
239C22×C37—41no—
240C22×C37—48no—
241C22×C37—44no—
242C22×C37—48no—
243C22×C37—84no—
244C22×C37—88no—
245C22×C37—88no—
246C22×C37#39214yes—
247C22×C37#39212yes—
248C22×C37#39212yes—
249C22×C37#45814yes—
250C22×C37C2×#12012yes—
251C22×C37C2×#12011yescharacteristic
252C22×C37C2×#12111yescharacteristic
253C22×C37C2×#12112yes—
254C22×C37C2×#12711yescharacteristic
255C4×C37—48no—
256C4×C37—44no—
257C4×C37—44no—
258C4×C37—44no—
259C4×C37—82no—
260C2×#534C2×C3711yescharacteristic
261C22×#123C2×C3712yescomplemented
262C22×#99C2×C3712yescomplemented
263C2×#381C2×C3711yescharacteristic, complemented
264#2022C2×C3718yesdirect product factor
265C2×#342C2×C3711yescharacteristic, complemented
266C2×C37—22no—
267C2×C37—21no—
268C2×C37—22no—
269C2×C37—24no—
270C2×C37—21no—
271C2×C37—22no—
272C2×C37—84no—
273C2×C37#202214yesdirect product factor
274C2×C37C2×#39211yescharacteristic
275C2×C37C2×#45812yes—
276C23×D4C22×C3712yes—
277C24×C4C22×C3711yescharacteristic
278#534—24no—
279#534—22no—
280#534C22×C3714yes—
281C2×#123—24no—
282C2×#123—22no—
283C2×#123—28no—
284C2×#123—28no—
285C2×#123C22×C3718yescomplemented
286C2×#121—22no—
287C2×#120—22no—
288C22×C4⋊C4—22no—
289C22×C22⋊C4—22no—
290C22×C22⋊C4C22×C3711yescharacteristic
291C22×C22⋊C4C22×C3711yescharacteristic
292C22×C22⋊C4C22×C3712yes—
293C2×#99—28no—
294C2×#99C22×C3718yescomplemented
295#381—22no—
296#381C22×C3714yescomplemented
297C2×#95—22no—
298#342C22×C3714yescomplemented
299C37C2×#202211yescharacteristic, direct product factor, Sylow
300C25D4×C3712yes—
301C25C23×C3711yescharacteristic
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—24no—
305C22×D4—24no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—22no—
311C22×D4D4×C3714yes—
312C22×D4C23×C3714yes—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—24no—
316C23×C4—22no—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—22no—
320C23×C4—21no—
321C23×C4D4×C3712yes—
322C23×C4D4×C3712yes—
323C23×C4D4×C3714yescomplemented
324C23×C4C23×C3712yes—
325#123—232no—
326#123—28no—
327#123—28no—
328#123—216no—
329#123—216no—
330#121—28no—
331#121—28no—
332#120—28no—
333#120—28no—
334C2×C4⋊C4—216no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—28no—
337C2×C22⋊C4—216no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4D4×C3712yes—
347C2×C22⋊C4D4×C3718yescomplemented
348C2×C22⋊C4C23×C3712yes—
349C2×C22⋊C4C23×C3712yes—
350C2×C22⋊C4C23×C3714yes—
351#99—216no—
352#95—28no—
353C24—24no—
354C24—22no—
355C24—22no—
356C24—24no—
357C24—44no—
358C24—48no—
359C24C2×D4×C3712yes—
360C24C2×D4×C3711yescharacteristic
361C24C2×D4×C3714yes—
362C24C2×D4×C3712yes—
363C24C2×D4×C3712yes—
364C24C2×D4×C3711yescharacteristic
365C24C2×D4×C3714yes—
366C24#41×C3712yes—
367C24C24×C3711yescharacteristic
368C2×D4—24no—
369C2×D4—24no—
370C2×D4—28no—
371C2×D4—28no—
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—24no—
378C2×D4—28no—
379C2×D4—44no—
380C2×D4—44no—
381C2×D4—44no—
382C2×D4—44no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4—84no—
388C22×C4—22no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—28no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—48no—
406C22×C4—42no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—44no—
410C22×C4—44no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—42no—
416C22×C4C2×D4×C3714yes—
417C22×C4C2×D4×C3714yes—
418C22×C4C2×D4×C3714yescomplemented
419C4⋊C4—232no—
420C4⋊C4—28no—
421C22⋊C4—232no—
422C22⋊C4—216no—
423C22⋊C4—24no—
424C22⋊C4—28no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—42no—
429C22⋊C4C2×D4×C3718yescomplemented
430C23—24no—
431C23—28no—
432C23—24no—
433C23—24no—
434C23—24no—
435C23—42no—
436C23—44no—
437C23—44no—
438C23—48no—
439C23—44no—
440C23—42no—
441C23—48no—
442C23—416no—
443C23—44no—
444C23—44no—
445C23—48no—
446C23—84no—
447C23—88no—
448C23#120×C3712yes—
449C23#120×C3714yes—
450C23#120×C3711yescharacteristic
451C23#120×C3714yes—
452C23#120×C3711yescharacteristic
453C23#121×C3712yes—
454C23#121×C3714yes—
455C23#121×C3712yes—
456C23#121×C3714yes—
457C23#127×C3712yes—
458C23#127×C3712yes—
459C23C22×D4×C3712yes—
460C23C22×D4×C3711yescharacteristic
461C23C22×D4×C3711yescharacteristic
462C23C22×D4×C3712yes—
463C23C2×#41×C3711yescharacteristic
464D4—44no—
465D4—44no—
466D4—44no—
467D4—44no—
468D4—48no—
469D4—48no—
470D4—88no—
471C2×C4—24no—
472C2×C4—28no—
473C2×C4—28no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—48no—
479C2×C4—416no—
480C2×C4—42no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—48no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—42no—
492C2×C4—82no—
493C2×C4—84no—
494C22—22no—
495C22—24no—
496C22—22no—
497C22—24no—
498C22—28no—
499C22—24no—
500C22—28no—
501C22—24no—
502C22—44no—
503C22—44no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22—42no—
508C22—41no—
509C22—48no—
510C22—44no—
511C22—48no—
512C22—84no—
513C22—88no—
514C22—88no—
515C22C37×#39214yes—
516C22C37×#39212yes—
517C22C37×#39212yes—
518C22C37×#45814yes—
519C22C2×#120×C3712yes—
520C22C2×#120×C3711yescharacteristic
521C22C2×#121×C3711yescharacteristic
522C22C2×#121×C3712yes—
523C22C2×#127×C3711yescharacteristic
524C4—48no—
525C4—44no—
526C4—44no—
527C4—44no—
528C4—82no—
529C2—22no—
530C2—21no—
531C2—22no—
532C2—24no—
533C2—21no—
534C2—22no—
535C2—84no—
536C2C37×#202214yesdirect product factor
537C2C2×C37×#39211yescharacteristic
538C2C2×C37×#45812yes—
subgroupG/H
center, socleC23×C37#120
commutator, Frattini, cosocleC24C24×C37
prime radicalC2×C37×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#123×C37C2semidirect
3. C22×#99×C37C2semidirect
4. C2×C37×#381C2semidirect
5. C37×#2022C2direct (N × H)
6. C2×C37×#342C2semidirect
16. C2×#123×C37C22semidirect
25. C2×#99×C37C22semidirect
27. C37×#381C22semidirect
29. C37×#342C22semidirect
53. C23×C4×C37D4semidirect
77. C2×C22⋊C4×C37D4semidirect
148. C22×C4×C37C2×D4semidirect
159. C22⋊C4×C37C2×D4semidirect
224. C2×#2022C37direct (N × H)
261. C22×#123C2×C37semidirect
262. C22×#99C2×C37semidirect
263. C2×#381C2×C37semidirect
264. #2022C2×C37direct (N × H)
265. C2×#342C2×C37semidirect
273. C2×C37#2022direct (N × H)
285. C2×#123C22×C37semidirect
294. C2×#99C22×C37semidirect
296. #381C22×C37semidirect
298. #342C22×C37semidirect
299. C37C2×#2022direct (N × H)
323. C23×C4D4×C37semidirect
347. C2×C22⋊C4D4×C37semidirect
418. C22×C4C2×D4×C37semidirect
429. C22⋊C4C2×D4×C37semidirect
536. C2C37×#2022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5342
C22×#123×C372
C22×#99×C372
C2×C37×#3812
C37×#20222
C2×C37×#3422
C2×#202237