Finite Group Databasebeta

← C37×#22054 #22643307

Subgroups — C37×#22054 #22643307

Order 9472.

920 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#451C211yesmaximal, characteristic
2C37×#2323C211yesmaximal, characteristic
3C37×#2310C211yesmaximal, characteristic
4C37×#1971C211yesmaximal, characteristic, complemented
5C37×#1969C211yesmaximal, characteristic, complemented
6C37×#1935C211yesmaximal, characteristic, complemented
7C37×#1933C211yesmaximal, characteristic, complemented
8C37×#1928C211yesmaximal, characteristic, complemented
9C37×#1927C211yesmaximal, characteristic, complemented
10C37×#1878C211yesmaximal, characteristic, complemented
11C37×#1878C211yesmaximal, characteristic, complemented
12C37×#1873C211yesmaximal, characteristic
13C37×#1854C211yesmaximal, characteristic
14C37×#1787C211yesmaximal, characteristic
15C37×#1750C211yesmaximal, characteristic
16C23×Q8×C37C2211yescharacteristic
17C22×Q16×C37C2211yescharacteristic
18C22×Q16×C37C2211yescharacteristic
19C2×C22⋊Q8×C37C2211yescharacteristic
20C2×C4×Q8×C37C2211yescharacteristic
21C2×#117×C37C2211yescharacteristic
22C2×#117×C37C2211yescharacteristic
23C37×#451C418yescomplemented
24C2×#107×C37C2211yescharacteristic
25C2×#106×C37C2211yescharacteristic
26C2×#103×C37C2211yescharacteristic
27C2×#103×C37C2211yescharacteristic
28C2×#103×C37C2211yescharacteristic
29C2×#103×C37C2211yescharacteristic
30C2×#103×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×C22⋊C8×C37C2211yescharacteristic
35C2×C22⋊C8×C37C2211yescharacteristic
36C2×#97×C37C2211yescharacteristic
37C2×C4×C8×C37C2211yescharacteristic
38C37×#391—21no—
39C37×#391—21no—
40C37×#391C2211yescharacteristic
41C37×#391C2211yescharacteristic
42C37×#391C2211yescharacteristic
43C37×#391C2211yescharacteristic
44C37×#391C2211yescharacteristic
45C37×#389—21no—
46C37×#389C2211yescharacteristic
47C37×#388—21no—
48C37×#388—21no—
49C37×#387—21no—
50C37×#381—21no—
51C37×#381—21no—
52C37×#380C2211yescharacteristic
53C4×C4⋊C4×C37C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C22×Q8×C37—21no—
61C22×Q8×C37—22no—
62C22×Q8×C37—41no—
63C22×Q8×C37—41no—
64C22×Q8×C37—41no—
65C22×Q8×C37—41no—
66C22×Q8×C37C2×C414yes—
67C22×Q8×C37C2311yescharacteristic
68C22×Q8×C37C2311yescharacteristic
69C22×Q8×C37C2311yescharacteristic
70C23×C4×C37—21no—
71C23×C4×C37C2311yescharacteristic
72C2×Q16×C37—41no—
73C2×Q16×C37—41no—
74C2×Q16×C37—41no—
75C2×Q16×C37—41no—
76C2×Q16×C37C2×C414yes—
77C2×Q16×C37C2×C414yes—
78C22×C8×C37C2311yescharacteristic
79C22×C8×C37C2311yescharacteristic
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37C2×C414yes—
84C4×Q8×C37—41no—
85C4×Q8×C37—41no—
86#117×C37—41no—
87#117×C37—41no—
88#117×C37—41no—
89#117×C37—41no—
90C2×C4⋊C4×C37—21no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—21no—
93C2×C4⋊C4×C37D411yescharacteristic
94C2×C4⋊C4×C37D411yescharacteristic
95C2×C4⋊C4×C37C2311yescharacteristic
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C22⋊C4×C37—21no—
101C2×C22⋊C4×C37—21no—
102C2×C22⋊C4×C37—21no—
103C2×C22⋊C4×C37D411yescharacteristic
104C2×C22⋊C4×C37D411yescharacteristic
105C2×C42×C37—21no—
106C2×C42×C37—21no—
107C2×C42×C37—21no—
108C2×C42×C37C2311yescharacteristic
109C2×C42×C37C2311yescharacteristic
110#107×C37—41no—
111#106×C37—41no—
112#103×C37—41no—
113#103×C37—41no—
114#103×C37—41no—
115#103×C37—41no—
116#103×C37—41no—
117#103×C37—41no—
118#103×C37C2×C414yes—
119#103×C37C2×C414yes—
120C22⋊C8×C37—22no—
121C22⋊C8×C37C2×C414yes—
122#97×C37—41no—
123C4×C8×C37—41no—
124#95×C37—21no—
125#95×C37—21no—
126#95×C37—21no—
127#95×C37—21no—
128#95×C37—21no—
129#95×C37—21no—
130#95×C37—21no—
131#95×C37—21no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137C24×C37C2×D411yescharacteristic
138C2×Q8×C37—24no—
139C2×Q8×C37—21no—
140C2×Q8×C37—21no—
141C2×Q8×C37—21no—
142C2×Q8×C37—21no—
143C2×Q8×C37—21no—
144C2×Q8×C37—21no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—21no—
150C2×Q8×C37—21no—
151C2×Q8×C37—21no—
152C2×Q8×C37—21no—
153C2×Q8×C37—21no—
154C2×Q8×C37—44no—
155C2×Q8×C37—44no—
156C2×Q8×C37—42no—
157C2×Q8×C37—42no—
158C2×Q8×C37—44no—
159C2×Q8×C37—44no—
160C2×Q8×C37C22×C412yes—
161C2×Q8×C37C22×C412yes—
162C2×Q8×C37C22×C412yes—
163C22×C4×C37—21no—
164C22×C4×C37—21no—
165C22×C4×C37—21no—
166C22×C4×C37—21no—
167C22×C4×C37—24no—
168C22×C4×C37—21no—
169C22×C4×C37—21no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—42no—
177C22×C4×C37—42no—
178C22×C4×C37C22×C412yes—
179C22×C4×C37C2×D411yescharacteristic
180C22×C4×C37C2×D411yescharacteristic
181C22×C4×C37C2×D411yescharacteristic
182C22×C4×C37C2×D411yescharacteristic
183C22×C4×C37C2×D411yescharacteristic
184C22×C4×C37#4112yes—
185C22×C4×C37C2411yescharacteristic
186Q16×C37—44no—
187Q16×C37—44no—
188C2×C8×C37—21no—
189C2×C8×C37—21no—
190C2×C8×C37—21no—
191C2×C8×C37—21no—
192C2×C8×C37—21no—
193C2×C8×C37—21no—
194C2×C8×C37—21no—
195C2×C8×C37—21no—
196C2×C8×C37—21no—
197C2×C8×C37—21no—
198C2×C8×C37C22×C412yes—
199C2×C8×C37C22×C412yes—
200C4⋊C4×C37—24no—
201C4⋊C4×C37—21no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37—21no—
205C4⋊C4×C37—21no—
206C4⋊C4×C37—21no—
207C4⋊C4×C37—21no—
208C4⋊C4×C37—21no—
209C4⋊C4×C37—21no—
210C4⋊C4×C37—41no—
211C4⋊C4×C37—41no—
212C4⋊C4×C37—42no—
213C4⋊C4×C37—81no—
214C4⋊C4×C37C22×C412yes—
215C22⋊C4×C37—24no—
216C22⋊C4×C37—41no—
217C22⋊C4×C37—41no—
218C22⋊C4×C37—42no—
219C22⋊C4×C37—81no—
220C42×C37—21no—
221C42×C37—21no—
222C42×C37—21no—
223C42×C37—21no—
224C42×C37—42no—
225C42×C37—42no—
226C42×C37—81no—
227C23×C37—21no—
228C23×C37—21no—
229C23×C37—21no—
230C23×C37—21no—
231C23×C37—21no—
232C23×C37—21no—
233C23×C37C4×D412yes—
234C23×C37C22×D411yescharacteristic
235Q8×C37—22no—
236Q8×C37—22no—
237Q8×C37—22no—
238Q8×C37—22no—
239Q8×C37—22no—
240Q8×C37—22no—
241Q8×C37—48no—
242Q8×C37—41no—
243Q8×C37—41no—
244Q8×C37—41no—
245Q8×C37—41no—
246Q8×C37—41no—
247Q8×C37—41no—
248C2×C4×C37—21no—
249C2×C4×C37—21no—
250C2×C4×C37—22no—
251C2×C4×C37—22no—
252C2×C4×C37—22no—
253C2×C4×C37—22no—
254C2×C4×C37—22no—
255C2×C4×C37—22no—
256C2×C4×C37—22no—
257C2×C4×C37—22no—
258C2×C4×C37—21no—
259C2×C4×C37—21no—
260C2×C4×C37—21no—
261C2×C4×C37—21no—
262C2×C4×C37—21no—
263C2×C4×C37—21no—
264C2×C4×C37—21no—
265C2×C4×C37—21no—
266C2×C4×C37—21no—
267C2×C4×C37—21no—
268C2×C4×C37—21no—
269C2×C4×C37—21no—
270C2×C4×C37—48no—
271C2×C4×C37—41no—
272C2×C4×C37—41no—
273C2×C4×C37—41no—
274C2×C4×C37—41no—
275C2×C4×C37—41no—
276C2×C4×C37—41no—
277C2×C4×C37—41no—
278C2×C4×C37—41no—
279C2×C4×C37—41no—
280C2×C4×C37—41no—
281C2×C4×C37—41no—
282C2×C4×C37—41no—
283C2×C4×C37—41no—
284C2×C4×C37—41no—
285C2×C4×C37—41no—
286C2×C4×C37—41no—
287C2×C4×C37—41no—
288C2×C4×C37—41no—
289C2×C4×C37—41no—
290C2×C4×C37—41no—
291C2×C4×C37C4×D412yes—
292C2×C4×C37C23×C411yescharacteristic
293C2×C4×C37C2×#4111yescharacteristic
294C2×C4×C37H(5,𝔽2)11yescharacteristic
295C2×C4×C37H(5,𝔽2)11yescharacteristic
296C2×C4×C37H(5,𝔽2)11yescharacteristic
297C2×C4×C37H(5,𝔽2)11yescharacteristic
298C8×C37—22no—
299C8×C37—22no—
300C8×C37—41no—
301C8×C37—41no—
302#22054C3711yesmaximal, characteristic, direct product factor, Sylow
303C22×C37—22no—
304C22×C37—22no—
305C22×C37—22no—
306C22×C37—41no—
307C22×C37—41no—
308C22×C37—41no—
309C22×C37—41no—
310C22×C37C2×C4×D411yescharacteristic
311C22×C37#53411yescharacteristic
312C22×C37#53511yescharacteristic
313C22×C37#57711yescharacteristic
314C22×C37#57811yescharacteristic
315C22×C37#57811yescharacteristic
316C22×C37#57811yescharacteristic
317C4×C37—22no—
318C4×C37—42no—
319C4×C37—42no—
320C4×C37—42no—
321C4×C37—41no—
322C4×C37—41no—
323C4×C37—41no—
324C4×C37—41no—
325C4×C37—42no—
326C4×C37—81no—
327C4×C37—81no—
328C4×C37—81no—
329C4×C37—81no—
330C4×C37#51811yescharacteristic
331C4×C37#51811yescharacteristic
332C4×C37#53811yescharacteristic
333C4×C37#53811yescharacteristic
334C2×#451C2×C3711yescharacteristic
335#2323C2×C3711yescharacteristic
336#2310C2×C3711yescharacteristic
337#1971C2×C3711yescharacteristic, complemented
338#1969C2×C3711yescharacteristic, complemented
339#1935C2×C3711yescharacteristic, complemented
340#1933C2×C3711yescharacteristic, complemented
341#1928C2×C3711yescharacteristic, complemented
342#1927C2×C3711yescharacteristic, complemented
343#1878C2×C3711yescharacteristic, complemented
344#1878C2×C3711yescharacteristic, complemented
345#1873C2×C3711yescharacteristic
346#1854C2×C3711yescharacteristic
347#1787C2×C3711yescharacteristic
348#1750C2×C3711yescharacteristic
349C2×C37—42no—
350C2×C37#232111yescharacteristic
351C2×C37#294711yescharacteristic
352C2×C37#295011yescharacteristic
353C2×C37#320111yescharacteristic
354C2×C37#320211yescharacteristic
355C2×C37#322311yescharacteristic
356C2×C37#322511yescharacteristic
357C23×Q8C22×C3711yescharacteristic
358C22×Q16C22×C3711yescharacteristic
359C22×Q16C22×C3711yescharacteristic
360C2×C22⋊Q8C22×C3711yescharacteristic
361C2×C4×Q8C22×C3711yescharacteristic
362C2×#117C22×C3711yescharacteristic
363C2×#117C22×C3711yescharacteristic
364#451C4×C3718yescomplemented
365C2×#107C22×C3711yescharacteristic
366C2×#106C22×C3711yescharacteristic
367C2×#103C22×C3711yescharacteristic
368C2×#103C22×C3711yescharacteristic
369C2×#103C22×C3711yescharacteristic
370C2×#103C22×C3711yescharacteristic
371C2×#103C22×C3711yescharacteristic
372C2×#103C22×C3711yescharacteristic
373C2×#103C22×C3711yescharacteristic
374C2×#103C22×C3711yescharacteristic
375C2×C22⋊C8C22×C3711yescharacteristic
376C2×C22⋊C8C22×C3711yescharacteristic
377C2×#97C22×C3711yescharacteristic
378C2×C4×C8C22×C3711yescharacteristic
379#391—21no—
380#391—21no—
381#391C22×C3711yescharacteristic
382#391C22×C3711yescharacteristic
383#391C22×C3711yescharacteristic
384#391C22×C3711yescharacteristic
385#391C22×C3711yescharacteristic
386#389—21no—
387#389C22×C3711yescharacteristic
388#388—21no—
389#388—21no—
390#387—21no—
391#381—21no—
392#381—21no—
393#380C22×C3711yescharacteristic
394C4×C4⋊C4C22×C3711yescharacteristic
395#340C22×C3711yescharacteristic
396#340C22×C3711yescharacteristic
397#340C22×C3711yescharacteristic
398#340C22×C3711yescharacteristic
399#336C22×C3711yescharacteristic
400#336C22×C3711yescharacteristic
401C37#2205411yescharacteristic, direct product factor, Sylow
402C22×Q8—21no—
403C22×Q8—22no—
404C22×Q8—41no—
405C22×Q8—41no—
406C22×Q8—41no—
407C22×Q8—41no—
408C22×Q8C2×C4×C3714yes—
409C22×Q8C23×C3711yescharacteristic
410C22×Q8C23×C3711yescharacteristic
411C22×Q8C23×C3711yescharacteristic
412C23×C4—21no—
413C23×C4C23×C3711yescharacteristic
414C2×Q16—41no—
415C2×Q16—41no—
416C2×Q16—41no—
417C2×Q16—41no—
418C2×Q16C2×C4×C3714yes—
419C2×Q16C2×C4×C3714yes—
420C22×C8C23×C3711yescharacteristic
421C22×C8C23×C3711yescharacteristic
422C22×C8C23×C3711yescharacteristic
423C22×C8C23×C3711yescharacteristic
424C22⋊Q8—22no—
425C22⋊Q8C2×C4×C3714yes—
426C4×Q8—41no—
427C4×Q8—41no—
428#117—41no—
429#117—41no—
430#117—41no—
431#117—41no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4D4×C3711yescharacteristic
436C2×C4⋊C4D4×C3711yescharacteristic
437C2×C4⋊C4C23×C3711yescharacteristic
438C2×C4⋊C4C23×C3711yescharacteristic
439C2×C4⋊C4C23×C3711yescharacteristic
440C2×C4⋊C4C23×C3711yescharacteristic
441C2×C4⋊C4C23×C3711yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4D4×C3711yescharacteristic
446C2×C22⋊C4D4×C3711yescharacteristic
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42C23×C3711yescharacteristic
451C2×C42C23×C3711yescharacteristic
452#107—41no—
453#106—41no—
454#103—41no—
455#103—41no—
456#103—41no—
457#103—41no—
458#103—41no—
459#103—41no—
460#103C2×C4×C3714yes—
461#103C2×C4×C3714yes—
462C22⋊C8—22no—
463C22⋊C8C2×C4×C3714yes—
464#97—41no—
465C4×C8—41no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479C24C2×D4×C3711yescharacteristic
480C2×Q8—24no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8C22×C4×C3712yes—
503C2×Q8C22×C4×C3712yes—
504C2×Q8C22×C4×C3712yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4C22×C4×C3712yes—
521C22×C4C2×D4×C3711yescharacteristic
522C22×C4C2×D4×C3711yescharacteristic
523C22×C4C2×D4×C3711yescharacteristic
524C22×C4C2×D4×C3711yescharacteristic
525C22×C4C2×D4×C3711yescharacteristic
526C22×C4#41×C3712yes—
527C22×C4C24×C3711yescharacteristic
528Q16—44no—
529Q16—44no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8C22×C4×C3712yes—
541C2×C8C22×C4×C3712yes—
542C4⋊C4—24no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—42no—
555C4⋊C4—81no—
556C4⋊C4C22×C4×C3712yes—
557C22⋊C4—24no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C22⋊C4—42no—
561C22⋊C4—81no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—42no—
568C42—81no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23C4×D4×C3712yes—
576C23C22×D4×C3711yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—48no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—48no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4C4×D4×C3712yes—
634C2×C4C23×C4×C3711yescharacteristic
635C2×C4C2×#41×C3711yescharacteristic
636C2×C4H(5,𝔽2)×C3711yescharacteristic
637C2×C4H(5,𝔽2)×C3711yescharacteristic
638C2×C4H(5,𝔽2)×C3711yescharacteristic
639C2×C4H(5,𝔽2)×C3711yescharacteristic
640C8—22no—
641C8—22no—
642C8—41no—
643C8—41no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×C4×D4×C3711yescharacteristic
652C22C37×#53411yescharacteristic
653C22C37×#53511yescharacteristic
654C22C37×#57711yescharacteristic
655C22C37×#57811yescharacteristic
656C22C37×#57811yescharacteristic
657C22C37×#57811yescharacteristic
658C4—22no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4C37×#51811yescharacteristic
672C4C37×#51811yescharacteristic
673C4C37×#53811yescharacteristic
674C4C37×#53811yescharacteristic
675C2—42no—
676C2C37×#232111yescharacteristic
677C2C37×#294711yescharacteristic
678C2C37×#295011yescharacteristic
679C2C37×#320111yescharacteristic
680C2C37×#320211yescharacteristic
681C2C37×#322311yescharacteristic
682C2C37×#322511yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutatorC2×C4C23×C4×C37
Frattini, cosocleC22×C4C24×C37
prime radicalC24×C37C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×#117×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C37×#1971C2semidirect
5. C37×#1969C2semidirect
6. C37×#1935C2semidirect
7. C37×#1933C2semidirect
8. C37×#1928C2semidirect
9. C37×#1927C2semidirect
10. C37×#1878C2semidirect
11. C37×#1878C2semidirect
23. C37×#451C4semidirect
302. #22054C37direct (N × H)
337. #1971C2×C37semidirect
338. #1969C2×C37semidirect
339. #1935C2×C37semidirect
340. #1933C2×C37semidirect
341. #1928C2×C37semidirect
342. #1927C2×C37semidirect
343. #1878C2×C37semidirect
344. #1878C2×C37semidirect
364. #451C4×C37semidirect
401. C37#22054direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4512
C37×#23232
C37×#23102
C37×#19712
C37×#19692
C37×#19352
C37×#19332
C37×#19282
C37×#19272
C37×#18782
C37×#18732
C37×#18542
C37×#17872
C37×#17502
#2205437