Finite Group Databasebeta

← C37×#21874 #22643127

Subgroups — C37×#21874 #22643127

Order 9472.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#525C211yesmaximal, characteristic
2C37×#2280C211yesmaximal, characteristic, complemented
3C2×C37×#380C211yesmaximal, characteristic, complemented
4C37×#1996C212yesmaximal, complemented
5C37×#1964C212yesmaximal, complemented
6C37×#1898C214yesmaximal, complemented
7C37×#1799C214yesmaximal, complemented
8C22×#41×C37C411yescharacteristic, complemented
9C24×C4×C37C2211yescharacteristic
10C37×#525—21no—
11C37×#525—21no—
12C37×#525—21no—
13C37×#525—21no—
14C37×#525—21no—
15C37×#525—21no—
16C37×#525—21no—
17C37×#525—21no—
18C2×#123×C37C412yescomplemented
19C2×C22⋊Q8×C37C411yescharacteristic, complemented
20C2×C22⋊Q8×C37C2211yescharacteristic
21C2×#121×C37C411yescharacteristic, complemented
22C2×#121×C37C2211yescharacteristic
23C2×#120×C37C2212yes—
24C2×C4×D4×C37C412yescomplemented
25C2×C4×D4×C37C2212yes—
26C2×#117×C37—21no—
27C2×#117×C37C411yescharacteristic, complemented
28C22×C4⋊C4×C37—21no—
29C22×C22⋊C4×C37C2212yes—
30C2×#99×C37C2218yes—
31C37×#381—21no—
32C37×#380—21no—
33C37×#380—21no—
34C37×#380—21no—
35C37×#380C2212yes—
36C37×#380C2212yes—
37C37×#380C2212yes—
38C37×#379C2212yes—
39C4×C22⋊C4×C37—21no—
40C4×C22⋊C4×C37C2212yes—
41C2×#95×C37—21no—
42C37×#342C2218yes—
43C25×C37C2311yescharacteristic
44C2×#41×C37—21no—
45C2×#41×C37—21no—
46C2×#41×C37—21no—
47C2×#41×C37—21no—
48C2×#41×C37—44no—
49C22×Q8×C37C2×C411yescharacteristic, complemented
50C22×D4×C37C2×C412yes—
51C22×D4×C37C2×C412yes—
52C22×D4×C37C2×C411yescharacteristic, complemented
53C22×D4×C37C2312yes—
54C23×C4×C37—22no—
55C23×C4×C37—44no—
56C23×C4×C37C2×C411yescharacteristic
57C23×C4×C37C2×C411yescharacteristic
58C23×C4×C37C2×C411yescharacteristic
59C23×C4×C37C2×C411yescharacteristic
60C23×C4×C37C2×C412yescomplemented
61C23×C4×C37D411yescharacteristic
62C23×C4×C37D411yescharacteristic
63C23×C4×C37D411yescharacteristic
64C23×C4×C37D411yescharacteristic
65C23×C4×C37D411yescharacteristic
66C23×C4×C37D411yescharacteristic
67C23×C4×C37D411yescharacteristic
68C23×C4×C37D411yescharacteristic
69C23×C4×C37C2311yescharacteristic
70C23×C4×C37C2311yescharacteristic
71#123×C37—22no—
72#123×C37—22no—
73#123×C37—22no—
74#123×C37—22no—
75C22⋊Q8×C37—21no—
76C22⋊Q8×C37—21no—
77C22⋊Q8×C37—21no—
78C22⋊Q8×C37—21no—
79C22⋊Q8×C37—21no—
80C22⋊Q8×C37—21no—
81C22⋊Q8×C37—21no—
82C22⋊Q8×C37—21no—
83#121×C37—21no—
84#121×C37—21no—
85#121×C37—21no—
86#121×C37—21no—
87#121×C37—21no—
88#121×C37—21no—
89#121×C37—21no—
90#121×C37—21no—
91#120×C37—22no—
92#120×C37—22no—
93#120×C37—22no—
94#120×C37—22no—
95C4×D4×C37—22no—
96C4×D4×C37—22no—
97C4×D4×C37—22no—
98C4×D4×C37—22no—
99C4×D4×C37—22no—
100C4×D4×C37—22no—
101C4×D4×C37—22no—
102C4×D4×C37—22no—
103#117×C37—21no—
104#117×C37—21no—
105#117×C37—21no—
106#117×C37—21no—
107#117×C37—44no—
108C2×C4⋊C4×C37—22no—
109C2×C4⋊C4×C37—22no—
110C2×C4⋊C4×C37—22no—
111C2×C4⋊C4×C37—44no—
112C2×C4⋊C4×C37C2×C411yescharacteristic, complemented
113C2×C4⋊C4×C37C2×C411yescharacteristic, complemented
114C2×C4⋊C4×C37C2×C412yescomplemented
115C2×C4⋊C4×C37C2×C412yescomplemented
116C2×C22⋊C4×C37—22no—
117C2×C22⋊C4×C37—22no—
118C2×C22⋊C4×C37—22no—
119C2×C22⋊C4×C37—44no—
120C2×C22⋊C4×C37C2×C412yes—
121C2×C22⋊C4×C37C2×C412yes—
122C2×C22⋊C4×C37C2×C412yescomplemented
123C2×C22⋊C4×C37C2×C412yescomplemented
124C2×C22⋊C4×C37C2314yes—
125C2×C22⋊C4×C37C2314yes—
126C2×C22⋊C4×C37C2312yes—
127C2×C42×C37—22no—
128C2×C42×C37C2×C412yescomplemented
129#99×C37—48no—
130#95×C37—22no—
131#95×C37—22no—
132#95×C37—22no—
133#95×C37—22no—
134C24×C37—22no—
135C24×C37—22no—
136C24×C37—42no—
137C24×C37—42no—
138C24×C37C22×C411yescharacteristic
139C24×C37C22×C411yescharacteristic
140C24×C37C22×C412yes—
141C24×C37C2×D411yescharacteristic
142C24×C37C2×D411yescharacteristic
143C24×C37C2×D411yescharacteristic
144C24×C37C2×D411yescharacteristic
145C24×C37C2411yescharacteristic
146#41×C37—44no—
147#41×C37—44no—
148#41×C37—44no—
149#41×C37—44no—
150C2×Q8×C37—21no—
151C2×Q8×C37—21no—
152C2×Q8×C37—42no—
153C2×D4×C37—22no—
154C2×D4×C37—22no—
155C2×D4×C37—22no—
156C2×D4×C37—22no—
157C2×D4×C37—22no—
158C2×D4×C37—22no—
159C2×D4×C37—24no—
160C2×D4×C37—24no—
161C2×D4×C37—21no—
162C2×D4×C37—21no—
163C2×D4×C37—42no—
164C2×D4×C37—44no—
165C2×D4×C37—44no—
166C22×C4×C37—24no—
167C22×C4×C37—24no—
168C22×C4×C37—24no—
169C22×C4×C37—22no—
170C22×C4×C37—22no—
171C22×C4×C37—24no—
172C22×C4×C37—24no—
173C22×C4×C37—42no—
174C22×C4×C37—42no—
175C22×C4×C37—42no—
176C22×C4×C37—42no—
177C22×C4×C37—42no—
178C22×C4×C37—42no—
179C22×C4×C37—42no—
180C22×C4×C37—42no—
181C22×C4×C37—42no—
182C22×C4×C37—42no—
183C22×C4×C37—42no—
184C22×C4×C37—44no—
185C22×C4×C37—44no—
186C22×C4×C37—44no—
187C22×C4×C37—44no—
188C22×C4×C37C22⋊C411yescharacteristic
189C22×C4×C37C22⋊C411yescharacteristic
190C22×C4×C37C22⋊C411yescharacteristic
191C22×C4×C37C22⋊C411yescharacteristic
192C22×C4×C37C22⋊C411yescharacteristic
193C22×C4×C37C22⋊C411yescharacteristic
194C22×C4×C37C22⋊C411yescharacteristic
195C22×C4×C37C22⋊C411yescharacteristic
196C22×C4×C37C22⋊C411yescharacteristic
197C22×C4×C37C22⋊C411yescharacteristic
198C22×C4×C37C22⋊C411yescharacteristic
199C22×C4×C37C22⋊C411yescharacteristic
200C22×C4×C37C22⋊C411yescharacteristic
201C22×C4×C37C22⋊C411yescharacteristic
202C22×C4×C37C22⋊C411yescharacteristic
203C22×C4×C37C22⋊C411yescharacteristic
204C22×C4×C37C22×C412yes—
205C22×C4×C37C22×C411yescharacteristic
206C22×C4×C37C22×C411yescharacteristic
207C22×C4×C37C22×C412yes—
208C22×C4×C37C22×C412yes—
209C22×C4×C37C22×C411yescharacteristic
210C22×C4×C37C22×C411yescharacteristic
211C22×C4×C37C2×D411yescharacteristic
212C22×C4×C37C2×D411yescharacteristic
213C22×C4×C37C2×D411yescharacteristic
214C22×C4×C37C2×D411yescharacteristic
215C22×C4×C37C2×D411yescharacteristic
216C22×C4×C37C2×D411yescharacteristic
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2×D411yescharacteristic
219C4⋊C4×C37—21no—
220C4⋊C4×C37—21no—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—21no—
223C4⋊C4×C37—22no—
224C4⋊C4×C37—22no—
225C4⋊C4×C37—22no—
226C4⋊C4×C37—22no—
227C4⋊C4×C37—44no—
228C4⋊C4×C37—44no—
229C4⋊C4×C37—44no—
230C22⋊C4×C37—22no—
231C22⋊C4×C37—22no—
232C22⋊C4×C37—22no—
233C22⋊C4×C37—22no—
234C22⋊C4×C37—22no—
235C22⋊C4×C37—22no—
236C22⋊C4×C37—22no—
237C22⋊C4×C37—22no—
238C22⋊C4×C37—22no—
239C22⋊C4×C37—22no—
240C22⋊C4×C37—24no—
241C22⋊C4×C37—28no—
242C22⋊C4×C37—24no—
243C22⋊C4×C37—44no—
244C22⋊C4×C37—44no—
245C22⋊C4×C37—44no—
246C42×C37—22no—
247C42×C37—22no—
248C42×C37—44no—
249C23×C37—21no—
250C23×C37—21no—
251C23×C37—22no—
252C23×C37—22no—
253C23×C37—22no—
254C23×C37—22no—
255C23×C37—21no—
256C23×C37—21no—
257C23×C37—22no—
258C23×C37—22no—
259C23×C37—22no—
260C23×C37—22no—
261C23×C37—22no—
262C23×C37—22no—
263C23×C37—22no—
264C23×C37—24no—
265C23×C37—41no—
266C23×C37—41no—
267C23×C37—41no—
268C23×C37—41no—
269C23×C37—41no—
270C23×C37—41no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37—48no—
274C23×C37—48no—
275C23×C37—42no—
276C23×C37—42no—
277C23×C37C2×C22⋊C411yescharacteristic
278C23×C37C2×C22⋊C411yescharacteristic
279C23×C37C2×C22⋊C411yescharacteristic
280C23×C37C2×C22⋊C411yescharacteristic
281C23×C37C23×C411yescharacteristic
282C23×C37C22×D411yescharacteristic
283C23×C37C22×D411yescharacteristic
284C23×C37H(5,𝔽2)12yes—
285C23×C372−1+412yes—
286Q8×C37—42no—
287Q8×C37—42no—
288D4×C37—42no—
289D4×C37—44no—
290D4×C37—44no—
291D4×C37—42no—
292D4×C37—42no—
293D4×C37—44no—
294D4×C37—44no—
295D4×C37—44no—
296D4×C37—42no—
297C2×C4×C37—22no—
298C2×C4×C37—22no—
299C2×C4×C37—22no—
300C2×C4×C37—22no—
301C2×C4×C37—22no—
302C2×C4×C37—22no—
303C2×C4×C37—22no—
304C2×C4×C37—22no—
305C2×C4×C37—22no—
306C2×C4×C37—22no—
307C2×C4×C37—22no—
308C2×C4×C37—22no—
309C2×C4×C37—22no—
310C2×C4×C37—22no—
311C2×C4×C37—22no—
312C2×C4×C37—22no—
313C2×C4×C37—22no—
314C2×C4×C37—22no—
315C2×C4×C37—24no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—41no—
322C2×C4×C37—41no—
323C2×C4×C37—41no—
324C2×C4×C37—41no—
325C2×C4×C37—41no—
326C2×C4×C37—41no—
327C2×C4×C37—41no—
328C2×C4×C37—44no—
329C2×C4×C37—44no—
330C2×C4×C37—42no—
331C2×C4×C37—42no—
332C2×C4×C37—44no—
333C2×C4×C37—44no—
334C2×C4×C37—44no—
335C2×C4×C37—44no—
336C2×C4×C37—44no—
337C2×C4×C37—44no—
338C2×C4×C37—88no—
339C2×C4×C37#9914yescomplemented
340C2×C4×C37C2×C22⋊C411yescharacteristic
341C2×C4×C37C2×C22⋊C411yescharacteristic
342C2×C4×C37C2×C22⋊C411yescharacteristic
343C2×C4×C37C2×C22⋊C411yescharacteristic
344C2×C4×C37C2×C22⋊C411yescharacteristic
345C2×C4×C37C2×C22⋊C411yescharacteristic
346C2×C4×C37C2×C22⋊C411yescharacteristic
347C2×C4×C37C2×C22⋊C411yescharacteristic
348#21874C3711yesmaximal, characteristic, direct product factor, Sylow
349C22×C37—24no—
350C22×C37—24no—
351C22×C37—21no—
352C22×C37—21no—
353C22×C37—21no—
354C22×C37—21no—
355C22×C37—21no—
356C22×C37—21no—
357C22×C37—21no—
358C22×C37—21no—
359C22×C37—21no—
360C22×C37—21no—
361C22×C37—21no—
362C22×C37—21no—
363C22×C37—21no—
364C22×C37—21no—
365C22×C37—21no—
366C22×C37—21no—
367C22×C37—42no—
368C22×C37—42no—
369C22×C37—44no—
370C22×C37—44no—
371C22×C37—44no—
372C22×C37—44no—
373C22×C37—42no—
374C22×C37—42no—
375C22×C37—42no—
376C22×C37—42no—
377C22×C37—42no—
378C22×C37—84no—
379C22×C37C2×#9912yes—
380C22×C37#41012yes—
381C22×C37C22×C22⋊C411yescharacteristic
382C22×C37#52012yes—
383C22×C37#53511yescharacteristic
384C22×C37#53611yescharacteristic
385C22×C37#53712yes—
386C4×C37—21no—
387C4×C37—21no—
388C4×C37—21no—
389C4×C37—21no—
390C4×C37—21no—
391C4×C37—21no—
392C4×C37—42no—
393C4×C37—42no—
394C4×C37—42no—
395C4×C37—84no—
396C4×C37—84no—
397C4×C37C2×#9912yes—
398C4×C37C2×#9912yes—
399C2×#525C2×C3711yescharacteristic
400#2280C2×C3711yescharacteristic, complemented
401C2×#380C2×C3711yescharacteristic, complemented
402#1996C2×C3712yescomplemented
403#1964C2×C3712yescomplemented
404#1898C2×C3714yescomplemented
405#1799C2×C3714yescomplemented
406C2×C37—21no—
407C2×C37—22no—
408C2×C37—21no—
409C2×C37—22no—
410C2×C37—22no—
411C2×C37—22no—
412C2×C37—41no—
413C2×C37—41no—
414C2×C37—82no—
415C2×C37#231111yescharacteristic
416C2×C37C22×#9911yescharacteristic
417C2×C37C2×#41011yescharacteristic
418C22×#41C4×C3711yescharacteristic, complemented
419C24×C4C22×C3711yescharacteristic
420#525—21no—
421#525—21no—
422#525—21no—
423#525—21no—
424#525—21no—
425#525—21no—
426#525—21no—
427#525—21no—
428C2×#123C4×C3712yescomplemented
429C2×C22⋊Q8C4×C3711yescharacteristic, complemented
430C2×C22⋊Q8C22×C3711yescharacteristic
431C2×#121C4×C3711yescharacteristic, complemented
432C2×#121C22×C3711yescharacteristic
433C2×#120C22×C3712yes—
434C2×C4×D4C4×C3712yescomplemented
435C2×C4×D4C22×C3712yes—
436C2×#117—21no—
437C2×#117C4×C3711yescharacteristic, complemented
438C22×C4⋊C4—21no—
439C22×C22⋊C4C22×C3712yes—
440C2×#99C22×C3718yes—
441#381—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380C22×C3712yes—
446#380C22×C3712yes—
447#380C22×C3712yes—
448#379C22×C3712yes—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C22×C3712yes—
451C2×#95—21no—
452#342C22×C3718yes—
453C37#2187411yescharacteristic, direct product factor, Sylow
454C25C23×C3711yescharacteristic
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—44no—
460C22×Q8C2×C4×C3711yescharacteristic, complemented
461C22×D4C2×C4×C3712yes—
462C22×D4C2×C4×C3712yes—
463C22×D4C2×C4×C3711yescharacteristic, complemented
464C22×D4C23×C3712yes—
465C23×C4—22no—
466C23×C4—44no—
467C23×C4C2×C4×C3711yescharacteristic
468C23×C4C2×C4×C3711yescharacteristic
469C23×C4C2×C4×C3711yescharacteristic
470C23×C4C2×C4×C3711yescharacteristic
471C23×C4C2×C4×C3712yescomplemented
472C23×C4D4×C3711yescharacteristic
473C23×C4D4×C3711yescharacteristic
474C23×C4D4×C3711yescharacteristic
475C23×C4D4×C3711yescharacteristic
476C23×C4D4×C3711yescharacteristic
477C23×C4D4×C3711yescharacteristic
478C23×C4D4×C3711yescharacteristic
479C23×C4D4×C3711yescharacteristic
480C23×C4C23×C3711yescharacteristic
481C23×C4C23×C3711yescharacteristic
482#123—22no—
483#123—22no—
484#123—22no—
485#123—22no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#120—22no—
503#120—22no—
504#120—22no—
505#120—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117—44no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—44no—
523C2×C4⋊C4C2×C4×C3711yescharacteristic, complemented
524C2×C4⋊C4C2×C4×C3711yescharacteristic, complemented
525C2×C4⋊C4C2×C4×C3712yescomplemented
526C2×C4⋊C4C2×C4×C3712yescomplemented
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—44no—
531C2×C22⋊C4C2×C4×C3712yes—
532C2×C22⋊C4C2×C4×C3712yes—
533C2×C22⋊C4C2×C4×C3712yescomplemented
534C2×C22⋊C4C2×C4×C3712yescomplemented
535C2×C22⋊C4C23×C3714yes—
536C2×C22⋊C4C23×C3714yes—
537C2×C22⋊C4C23×C3712yes—
538C2×C42—22no—
539C2×C42C2×C4×C3712yescomplemented
540#99—48no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24C22×C4×C3711yescharacteristic
550C24C22×C4×C3711yescharacteristic
551C24C22×C4×C3712yes—
552C24C2×D4×C3711yescharacteristic
553C24C2×D4×C3711yescharacteristic
554C24C2×D4×C3711yescharacteristic
555C24C2×D4×C3711yescharacteristic
556C24C24×C3711yescharacteristic
557#41—44no—
558#41—44no—
559#41—44no—
560#41—44no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—44no—
576C2×D4—44no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4C22⋊C4×C3711yescharacteristic
600C22×C4C22⋊C4×C3711yescharacteristic
601C22×C4C22⋊C4×C3711yescharacteristic
602C22×C4C22⋊C4×C3711yescharacteristic
603C22×C4C22⋊C4×C3711yescharacteristic
604C22×C4C22⋊C4×C3711yescharacteristic
605C22×C4C22⋊C4×C3711yescharacteristic
606C22×C4C22⋊C4×C3711yescharacteristic
607C22×C4C22⋊C4×C3711yescharacteristic
608C22×C4C22⋊C4×C3711yescharacteristic
609C22×C4C22⋊C4×C3711yescharacteristic
610C22×C4C22⋊C4×C3711yescharacteristic
611C22×C4C22⋊C4×C3711yescharacteristic
612C22×C4C22⋊C4×C3711yescharacteristic
613C22×C4C22⋊C4×C3711yescharacteristic
614C22×C4C22⋊C4×C3711yescharacteristic
615C22×C4C22×C4×C3712yes—
616C22×C4C22×C4×C3711yescharacteristic
617C22×C4C22×C4×C3711yescharacteristic
618C22×C4C22×C4×C3712yes—
619C22×C4C22×C4×C3712yes—
620C22×C4C22×C4×C3711yescharacteristic
621C22×C4C22×C4×C3711yescharacteristic
622C22×C4C2×D4×C3711yescharacteristic
623C22×C4C2×D4×C3711yescharacteristic
624C22×C4C2×D4×C3711yescharacteristic
625C22×C4C2×D4×C3711yescharacteristic
626C22×C4C2×D4×C3711yescharacteristic
627C22×C4C2×D4×C3711yescharacteristic
628C22×C4C2×D4×C3711yescharacteristic
629C22×C4C2×D4×C3711yescharacteristic
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—28no—
653C22⋊C4—24no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C42—22no—
658C42—22no—
659C42—44no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—48no—
685C23—48no—
686C23—42no—
687C23—42no—
688C23C2×C22⋊C4×C3711yescharacteristic
689C23C2×C22⋊C4×C3711yescharacteristic
690C23C2×C22⋊C4×C3711yescharacteristic
691C23C2×C22⋊C4×C3711yescharacteristic
692C23C23×C4×C3711yescharacteristic
693C23C22×D4×C3711yescharacteristic
694C23C22×D4×C3711yescharacteristic
695C23H(5,𝔽2)×C3712yes—
696C232−1+4×C3712yes—
697Q8—42no—
698Q8—42no—
699D4—42no—
700D4—44no—
701D4—44no—
702D4—42no—
703D4—42no—
704D4—44no—
705D4—44no—
706D4—44no—
707D4—42no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—88no—
750C2×C4#99×C3714yescomplemented
751C2×C4C2×C22⋊C4×C3711yescharacteristic
752C2×C4C2×C22⋊C4×C3711yescharacteristic
753C2×C4C2×C22⋊C4×C3711yescharacteristic
754C2×C4C2×C22⋊C4×C3711yescharacteristic
755C2×C4C2×C22⋊C4×C3711yescharacteristic
756C2×C4C2×C22⋊C4×C3711yescharacteristic
757C2×C4C2×C22⋊C4×C3711yescharacteristic
758C2×C4C2×C22⋊C4×C3711yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22C2×#99×C3712yes—
790C22C37×#41012yes—
791C22C22×C22⋊C4×C3711yescharacteristic
792C22C37×#52012yes—
793C22C37×#53511yescharacteristic
794C22C37×#53611yescharacteristic
795C22C37×#53712yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—84no—
806C4—84no—
807C4C2×#99×C3712yes—
808C4C2×#99×C3712yes—
809C2—21no—
810C2—22no—
811C2—21no—
812C2—22no—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2C37×#231111yescharacteristic
819C2C22×#99×C3711yescharacteristic
820C2C2×C37×#41011yescharacteristic
subgroupG/H
center, socleC22×C37C22×C22⋊C4
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
prime radicalC2×C37×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C24×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2280C2semidirect
3. C2×C37×#380C2semidirect
4. C37×#1996C2semidirect
5. C37×#1964C2semidirect
6. C37×#1898C2semidirect
7. C37×#1799C2semidirect
8. C22×#41×C37C4semidirect
18. C2×#123×C37C4semidirect
19. C2×C22⋊Q8×C37C4semidirect
21. C2×#121×C37C4semidirect
24. C2×C4×D4×C37C4semidirect
27. C2×#117×C37C4semidirect
49. C22×Q8×C37C2×C4semidirect
52. C22×D4×C37C2×C4semidirect
60. C23×C4×C37C2×C4semidirect
112. C2×C4⋊C4×C37C2×C4semidirect
113. C2×C4⋊C4×C37C2×C4semidirect
114. C2×C4⋊C4×C37C2×C4semidirect
115. C2×C4⋊C4×C37C2×C4semidirect
122. C2×C22⋊C4×C37C2×C4semidirect
123. C2×C22⋊C4×C37C2×C4semidirect
128. C2×C42×C37C2×C4semidirect
339. C2×C4×C37#99semidirect
348. #21874C37direct (N × H)
400. #2280C2×C37semidirect
401. C2×#380C2×C37semidirect
402. #1996C2×C37semidirect
403. #1964C2×C37semidirect
404. #1898C2×C37semidirect
405. #1799C2×C37semidirect
418. C22×#41C4×C37semidirect
428. C2×#123C4×C37semidirect
429. C2×C22⋊Q8C4×C37semidirect
431. C2×#121C4×C37semidirect
434. C2×C4×D4C4×C37semidirect
437. C2×#117C4×C37semidirect
453. C37#21874direct (N × H)
460. C22×Q8C2×C4×C37semidirect
463. C22×D4C2×C4×C37semidirect
471. C23×C4C2×C4×C37semidirect
523. C2×C4⋊C4C2×C4×C37semidirect
524. C2×C4⋊C4C2×C4×C37semidirect
525. C2×C4⋊C4C2×C4×C37semidirect
526. C2×C4⋊C4C2×C4×C37semidirect
533. C2×C22⋊C4C2×C4×C37semidirect
534. C2×C22⋊C4C2×C4×C37semidirect
539. C2×C42C2×C4×C37semidirect
750. C2×C4#99×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5252
C37×#22802
C2×C37×#3802
C37×#19962
C37×#19642
C37×#18982
C37×#17992
#2187437