Finite Group Databasebeta

← C2×C37×#1603 #22639352

Subgroups — C2×C37×#1603 #22639352

Order 9472.

1232 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#539C211yesmaximal, characteristic
2C2×C37×#451C211yesmaximal, characteristic, complemented
3C2×C37×#448C211yesmaximal, characteristic
4C2×C37×#395C211yesmaximal, characteristic, complemented
5C37×#1603C218yesmaximal, direct product factor
6C2×C37×#328C211yesmaximal, characteristic, complemented
7C2×C37×#327C211yesmaximal, characteristic
8C2×C37×#324C211yesmaximal, characteristic, complemented
9C23×Q8×C37C2211yescharacteristic
10C22×Q16×C37—21no—
11C22×SD16×C37—21no—
12C37×#539—22no—
13C37×#539—22no—
14C37×#539—22no—
15C37×#539C2214yes—
16C2×#126×C37—21no—
17C2×#125×C37—21no—
18C2×#123×C37—21no—
19C2×#123×C37—21no—
20C2×C22⋊Q8×C37—21no—
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×#121×C37C2211yescharacteristic
23C2×C4×D4×C37—21no—
24C22×C4⋊C4×C37—21no—
25C22×C4⋊C4×C37C2211yescharacteristic
26C37×#451—22no—
27C37×#451C2214yescomplemented
28C37×#448—22no—
29C37×#448C2214yes—
30C2×#103×C37—21no—
31C2×#103×C37—21no—
32C2×C22⋊C8×C37C2211yescharacteristic
33C2×C22⋊C8×C37C2211yescharacteristic
34C37×#395—22no—
35C37×#395C2214yescomplemented
36C2×#95×C37—21no—
37C2×#95×C37C2211yescharacteristic
38C37×#328C2214yescomplemented
39C37×#327C2214yes—
40C37×#324C2214yescomplemented
41C22×Q8×C37—21no—
42C22×Q8×C37—21no—
43C22×Q8×C37—21no—
44C22×Q8×C37—21no—
45C22×Q8×C37—21no—
46C22×Q8×C37—44no—
47C22×Q8×C37D411yescharacteristic
48C22×Q8×C37C2312yes—
49C22×D4×C37—21no—
50C22×D4×C37D411yescharacteristic
51C23×C4×C37—21no—
52C23×C4×C37—21no—
53C23×C4×C37—21no—
54C23×C4×C37D411yescharacteristic
55C23×C4×C37D411yescharacteristic
56C23×C4×C37C2311yescharacteristic
57C2×Q16×C37—24no—
58C2×Q16×C37—44no—
59C2×SD16×C37—24no—
60C2×SD16×C37—44no—
61C22×C8×C37—21no—
62C22×C8×C37—21no—
63#126×C37—24no—
64#126×C37—24no—
65#125×C37—24no—
66#125×C37—24no—
67#123×C37—24no—
68#123×C37—24no—
69#123×C37—24no—
70#123×C37—24no—
71C22⋊Q8×C37—24no—
72C22⋊Q8×C37—24no—
73C22⋊Q8×C37—21no—
74C22⋊Q8×C37—21no—
75C22⋊Q8×C37D412yes—
76C22⋊Q8×C37C2312yes—
77#121×C37—21no—
78#121×C37—21no—
79#121×C37D412yes—
80#121×C37C2312yes—
81C4×D4×C37—24no—
82C4×D4×C37—24no—
83C2×C4⋊C4×C37—21no—
84C2×C4⋊C4×C37—21no—
85C2×C4⋊C4×C37—21no—
86C2×C4⋊C4×C37—21no—
87C2×C4⋊C4×C37—21no—
88C2×C4⋊C4×C37—21no—
89C2×C4⋊C4×C37—21no—
90C2×C4⋊C4×C37—21no—
91C2×C4⋊C4×C37—24no—
92C2×C4⋊C4×C37—44no—
93C2×C4⋊C4×C37D412yes—
94C2×C4⋊C4×C37D411yescharacteristic
95C2×C4⋊C4×C37D411yescharacteristic
96C2×C4⋊C4×C37C2312yes—
97C2×C22⋊C4×C37—21no—
98C2×C22⋊C4×C37—21no—
99C2×C22⋊C4×C37—21no—
100C2×C22⋊C4×C37—21no—
101C2×C22⋊C4×C37—21no—
102C2×C42×C37—21no—
103#103×C37—24no—
104#103×C37—24no—
105C22⋊C8×C37—21no—
106C22⋊C8×C37—21no—
107C22⋊C8×C37C2312yes—
108C22⋊C8×C37C2312yes—
109#95×C37—24no—
110#95×C37—21no—
111#95×C37C2312yes—
112C24×C37—21no—
113C24×C37C2×D411yescharacteristic
114C2×Q8×C37—21no—
115C2×Q8×C37—24no—
116C2×Q8×C37—24no—
117C2×Q8×C37—22no—
118C2×Q8×C37—22no—
119C2×Q8×C37—44no—
120C2×Q8×C37—42no—
121C2×Q8×C37—42no—
122C2×Q8×C37—44no—
123C2×Q8×C37—42no—
124C2×Q8×C37—44no—
125C2×Q8×C37—44no—
126C2×Q8×C37—41no—
127C2×Q8×C37—41no—
128C2×Q8×C37C2×D412yes—
129C2×D4×C37—22no—
130C2×D4×C37—22no—
131C2×D4×C37—21no—
132C2×D4×C37—42no—
133C2×D4×C37—42no—
134C2×D4×C37—42no—
135C2×D4×C37C2×D412yes—
136C22×C4×C37—24no—
137C22×C4×C37—24no—
138C22×C4×C37—21no—
139C22×C4×C37—21no—
140C22×C4×C37—21no—
141C22×C4×C37—21no—
142C22×C4×C37—21no—
143C22×C4×C37—21no—
144C22×C4×C37—22no—
145C22×C4×C37—22no—
146C22×C4×C37—22no—
147C22×C4×C37—22no—
148C22×C4×C37—24no—
149C22×C4×C37—21no—
150C22×C4×C37—42no—
151C22×C4×C37—42no—
152C22×C4×C37—42no—
153C22×C4×C37—41no—
154C22×C4×C37—41no—
155C22×C4×C37—42no—
156C22×C4×C37—42no—
157C22×C4×C37—82no—
158C22×C4×C37C2×D412yes—
159C22×C4×C37C2×D411yescharacteristic
160C22×C4×C37C2×D411yescharacteristic
161C22×C4×C37C2×D412yes—
162C22×C4×C37C2×D411yescharacteristic
163C22×C4×C37C2×D411yescharacteristic
164C22×C4×C37C2×D411yescharacteristic
165C22×C4×C37C2411yescharacteristic
166Q16×C37—48no—
167SD16×C37—48no—
168C2×C8×C37—22no—
169C2×C8×C37—22no—
170C2×C8×C37—42no—
171C2×C8×C37—42no—
172C4⋊C4×C37—24no—
173C4⋊C4×C37—24no—
174C4⋊C4×C37—24no—
175C4⋊C4×C37—22no—
176C4⋊C4×C37—22no—
177C4⋊C4×C37—22no—
178C4⋊C4×C37—21no—
179C4⋊C4×C37—21no—
180C4⋊C4×C37—22no—
181C4⋊C4×C37—22no—
182C4⋊C4×C37—22no—
183C4⋊C4×C37—48no—
184C4⋊C4×C37C2×D412yes—
185C4⋊C4×C37C2×D412yes—
186C22⋊C4×C37—24no—
187C22⋊C4×C37—24no—
188C22⋊C4×C37—24no—
189C22⋊C4×C37—22no—
190C22⋊C4×C37—22no—
191C22⋊C4×C37—22no—
192C22⋊C4×C37—22no—
193C42×C37—24no—
194C23×C37—22no—
195C23×C37—22no—
196C23×C37—22no—
197C23×C37—42no—
198C23×C37—42no—
199C23×C37—42no—
200C23×C37#12011yescharacteristic
201C23×C37#12011yescharacteristic
202C23×C37#13512yes—
203C23×C37#13712yes—
204C23×C37C22×D411yescharacteristic
205Q8×C37—24no—
206Q8×C37—24no—
207Q8×C37—42no—
208Q8×C37—42no—
209Q8×C37—42no—
210Q8×C37—44no—
211Q8×C37—44no—
212Q8×C37—81no—
213D4×C37—42no—
214D4×C37—42no—
215D4×C37—42no—
216D4×C37—44no—
217D4×C37—81no—
218C2×C4×C37—22no—
219C2×C4×C37—22no—
220C2×C4×C37—24no—
221C2×C4×C37—24no—
222C2×C4×C37—22no—
223C2×C4×C37—22no—
224C2×C4×C37—22no—
225C2×C4×C37—22no—
226C2×C4×C37—22no—
227C2×C4×C37—22no—
228C2×C4×C37—22no—
229C2×C4×C37—41no—
230C2×C4×C37—41no—
231C2×C4×C37—41no—
232C2×C4×C37—41no—
233C2×C4×C37—42no—
234C2×C4×C37—48no—
235C2×C4×C37—42no—
236C2×C4×C37—44no—
237C2×C4×C37—42no—
238C2×C4×C37—42no—
239C2×C4×C37—42no—
240C2×C4×C37—42no—
241C2×C4×C37—42no—
242C2×C4×C37—42no—
243C2×C4×C37—44no—
244C2×C4×C37—42no—
245C2×C4×C37—42no—
246C2×C4×C37—42no—
247C2×C4×C37—81no—
248C2×C4×C37—84no—
249C2×C4×C37#12011yescharacteristic
250C2×C4×C37#12011yescharacteristic
251C2×C4×C37C22×D411yescharacteristic
252C2×C4×C37C22×D411yescharacteristic
253C8×C37—42no—
254C8×C37—42no—
255C2×#1603C3711yesmaximal, characteristic, direct product factor, Sylow
256C22×C37—24no—
257C22×C37—24no—
258C22×C37—21no—
259C22×C37—21no—
260C22×C37—21no—
261C22×C37—21no—
262C22×C37—42no—
263C22×C37—42no—
264C22×C37—42no—
265C22×C37—84no—
266C22×C37#45212yes—
267C22×C37#45212yes—
268C22×C37#45612yes—
269C22×C37B(4,𝔽2)12yes—
270C22×C37C2×#12011yescharacteristic
271C22×C37C2×#13511yescharacteristic
272C22×C37C2×#13711yescharacteristic
273C4×C37—21no—
274C4×C37—21no—
275C4×C37—21no—
276C4×C37—21no—
277C4×C37—44no—
278C4×C37—42no—
279C4×C37—42no—
280C4×C37—42no—
281C4×C37—44no—
282C4×C37—42no—
283C4×C37—42no—
284C2×#539C2×C3711yescharacteristic
285C2×#451C2×C3711yescharacteristic, complemented
286C2×#448C2×C3711yescharacteristic
287C2×#395C2×C3711yescharacteristic, complemented
288#1603C2×C3718yesdirect product factor
289C2×#328C2×C3711yescharacteristic, complemented
290C2×#327C2×C3711yescharacteristic
291C2×#324C2×C3711yescharacteristic, complemented
292C2×C37—21no—
293C2×C37—21no—
294C2×C37—22no—
295C2×C37—82no—
296C2×C37#160314yesdirect product factor
297C2×C37C2×#45211yescharacteristic
298C2×C37C2×#45611yescharacteristic
299C2×C37C2×B(4,𝔽2)11yescharacteristic
300C23×Q8C22×C3711yescharacteristic
301C22×Q16—21no—
302C22×SD16—21no—
303#539—22no—
304#539—22no—
305#539—22no—
306#539C22×C3714yes—
307C2×#126—21no—
308C2×#125—21no—
309C2×#123—21no—
310C2×#123—21no—
311C2×C22⋊Q8—21no—
312C2×C22⋊Q8C22×C3711yescharacteristic
313C2×#121C22×C3711yescharacteristic
314C2×C4×D4—21no—
315C22×C4⋊C4—21no—
316C22×C4⋊C4C22×C3711yescharacteristic
317#451—22no—
318#451C22×C3714yescomplemented
319#448—22no—
320#448C22×C3714yes—
321C2×#103—21no—
322C2×#103—21no—
323C2×C22⋊C8C22×C3711yescharacteristic
324C2×C22⋊C8C22×C3711yescharacteristic
325#395—22no—
326#395C22×C3714yescomplemented
327C2×#95—21no—
328C2×#95C22×C3711yescharacteristic
329#328C22×C3714yescomplemented
330#327C22×C3714yes—
331#324C22×C3714yescomplemented
332C37C2×#160311yescharacteristic, direct product factor, Sylow
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8—44no—
339C22×Q8D4×C3711yescharacteristic
340C22×Q8C23×C3712yes—
341C22×D4—21no—
342C22×D4D4×C3711yescharacteristic
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4D4×C3711yescharacteristic
347C23×C4D4×C3711yescharacteristic
348C23×C4C23×C3711yescharacteristic
349C2×Q16—24no—
350C2×Q16—44no—
351C2×SD16—24no—
352C2×SD16—44no—
353C22×C8—21no—
354C22×C8—21no—
355#126—24no—
356#126—24no—
357#125—24no—
358#125—24no—
359#123—24no—
360#123—24no—
361#123—24no—
362#123—24no—
363C22⋊Q8—24no—
364C22⋊Q8—24no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8D4×C3712yes—
368C22⋊Q8C23×C3712yes—
369#121—21no—
370#121—21no—
371#121D4×C3712yes—
372#121C23×C3712yes—
373C4×D4—24no—
374C4×D4—24no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4D4×C3712yes—
386C2×C4⋊C4D4×C3711yescharacteristic
387C2×C4⋊C4D4×C3711yescharacteristic
388C2×C4⋊C4C23×C3712yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395#103—24no—
396#103—24no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8C23×C3712yes—
400C22⋊C8C23×C3712yes—
401#95—24no—
402#95—21no—
403#95C23×C3712yes—
404C24—21no—
405C24C2×D4×C3711yescharacteristic
406C2×Q8—21no—
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—44no—
412C2×Q8—42no—
413C2×Q8—42no—
414C2×Q8—44no—
415C2×Q8—42no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8C2×D4×C3712yes—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4C2×D4×C3712yes—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—21no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—82no—
450C22×C4C2×D4×C3712yes—
451C22×C4C2×D4×C3711yescharacteristic
452C22×C4C2×D4×C3711yescharacteristic
453C22×C4C2×D4×C3712yes—
454C22×C4C2×D4×C3711yescharacteristic
455C22×C4C2×D4×C3711yescharacteristic
456C22×C4C2×D4×C3711yescharacteristic
457C22×C4C24×C3711yescharacteristic
458Q16—48no—
459SD16—48no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—42no—
463C2×C8—42no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—48no—
476C4⋊C4C2×D4×C3712yes—
477C4⋊C4C2×D4×C3712yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C42—24no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23#120×C3711yescharacteristic
493C23#120×C3711yescharacteristic
494C23#135×C3712yes—
495C23#137×C3712yes—
496C23C22×D4×C3711yescharacteristic
497Q8—24no—
498Q8—24no—
499Q8—42no—
500Q8—42no—
501Q8—42no—
502Q8—44no—
503Q8—44no—
504Q8—81no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—44no—
509D4—81no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—44no—
528C2×C4—48no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—81no—
540C2×C4—84no—
541C2×C4#120×C3711yescharacteristic
542C2×C4#120×C3711yescharacteristic
543C2×C4C22×D4×C3711yescharacteristic
544C2×C4C22×D4×C3711yescharacteristic
545C8—42no—
546C8—42no—
547C22—24no—
548C22—24no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—84no—
557C22C37×#45212yes—
558C22C37×#45212yes—
559C22C37×#45612yes—
560C22C37×B(4,𝔽2)12yes—
561C22C2×#120×C3711yescharacteristic
562C22C2×#135×C3711yescharacteristic
563C22C2×#137×C3711yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—44no—
569C4—42no—
570C4—42no—
571C4—42no—
572C4—44no—
573C4—42no—
574C4—42no—
575C2—21no—
576C2—21no—
577C2—22no—
578C2—82no—
579C2C37×#160314yesdirect product factor
580C2C2×C37×#45211yescharacteristic
581C2C2×C37×#45611yescharacteristic
582C2C2×C37×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC23×C37#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#451C2semidirect
4. C2×C37×#395C2semidirect
5. C37×#1603C2direct (N × H)
6. C2×C37×#328C2semidirect
8. C2×C37×#324C2semidirect
27. C37×#451C22semidirect
35. C37×#395C22semidirect
38. C37×#328C22semidirect
40. C37×#324C22semidirect
255. C2×#1603C37direct (N × H)
285. C2×#451C2×C37semidirect
287. C2×#395C2×C37semidirect
288. #1603C2×C37direct (N × H)
289. C2×#328C2×C37semidirect
291. C2×#324C2×C37semidirect
296. C2×C37#1603direct (N × H)
318. #451C22×C37semidirect
326. #395C22×C37semidirect
329. #328C22×C37semidirect
331. #324C22×C37semidirect
332. C37C2×#1603direct (N × H)
579. C2C37×#1603direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5392
C2×C37×#4512
C2×C37×#4482
C2×C37×#3952
C37×#16032
C2×C37×#3282
C2×C37×#3272
C2×C37×#3242
C2×#160337