Finite Group Databasebeta

← C37×#25543 #22646796

Subgroups — C37×#25543 #22646796

Order 9472.

1228 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#554C211yesmaximal, characteristic, complemented
2C2×C37×#481C211yesmaximal, characteristic, complemented
3C2×C37×#465C211yesmaximal, characteristic, complemented
4C37×#2416C211yesmaximal, characteristic
5C37×#2058C211yesmaximal, characteristic, complemented
6C37×#2035C211yesmaximal, characteristic, complemented
7C37×#2023C211yesmaximal, characteristic, complemented
8C37×#2000C211yesmaximal, characteristic, complemented
9C37×#1880C211yesmaximal, characteristic, complemented
10C37×#1874C211yesmaximal, characteristic, complemented
11C37×#1872C211yesmaximal, characteristic, complemented
12C37×#1869C211yesmaximal, characteristic, complemented
13C37×#1865C211yesmaximal, characteristic, complemented
14C37×#1853C211yesmaximal, characteristic, complemented
15C2×C37×#340C211yesmaximal, characteristic, complemented
16C22×SD16×C37C2211yescharacteristic
17C23×C8×C37C2211yescharacteristic
18C37×#554—24no—
19C37×#554—24no—
20C2×C4⋊Q8×C37C2211yescharacteristic
21C2×#125×C37—21no—
22C2×C22⋊Q8×C37—21no—
23C2×C22⋊Q8×C37—21no—
24C2×C22⋊Q8×C37C2211yescharacteristic
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×#121×C37—21no—
27C2×#121×C37C2211yescharacteristic
28C2×#121×C37C2211yescharacteristic
29C2×C4×Q8×C37C2211yescharacteristic
30C2×C4×D4×C37—21no—
31C2×C4×D4×C37C2211yescharacteristic
32C22×C4⋊C4×C37C2211yescharacteristic
33C22×C4⋊C4×C37C2211yescharacteristic
34C22×C4⋊C4×C37C2211yescharacteristic
35C37×#481—24no—
36C37×#465—24no—
37C2×#106×C37C2211yescharacteristic
38C2×#106×C37C2211yescharacteristic
39C2×#106×C37C2211yescharacteristic
40C2×#103×C37C2211yescharacteristic
41C2×#103×C37C2211yescharacteristic
42C2×#103×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×C22⋊C8×C37C2211yescharacteristic
47C2×C22⋊C8×C37C2211yescharacteristic
48C2×C22⋊C8×C37C2211yescharacteristic
49C37×#396—21no—
50C37×#394—21no—
51C37×#390C2211yescharacteristic
52C37×#389C2211yescharacteristic
53C37×#386—21no—
54C37×#380C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C22×Q8×C37—21no—
64C22×Q8×C37C2311yescharacteristic
65C22×D4×C37—21no—
66C22×D4×C37—21no—
67C22×D4×C37D411yescharacteristic
68C22×D4×C37C2311yescharacteristic
69C23×C4×C37—21no—
70C23×C4×C37—21no—
71C23×C4×C37—21no—
72C23×C4×C37C2311yescharacteristic
73C23×C4×C37C2311yescharacteristic
74C2×SD16×C37—22no—
75C2×SD16×C37—22no—
76C2×SD16×C37—41no—
77C22×C8×C37—22no—
78C22×C8×C37—22no—
79C22×C8×C37—41no—
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84C4⋊Q8×C37—22no—
85C4⋊Q8×C37—22no—
86#125×C37—28no—
87C22⋊Q8×C37—28no—
88C22⋊Q8×C37—28no—
89C22⋊Q8×C37—22no—
90C22⋊Q8×C37—22no—
91C22⋊Q8×C37—22no—
92C22⋊Q8×C37D414yescomplemented
93#121×C37—22no—
94#121×C37—22no—
95#121×C37—22no—
96#121×C37—41no—
97#121×C37—44no—
98C4×Q8×C37—22no—
99C4×Q8×C37—22no—
100C4×D4×C37—28no—
101C4×D4×C37—22no—
102C4×D4×C37—22no—
103C2×C4⋊C4×C37—21no—
104C2×C4⋊C4×C37—21no—
105C2×C4⋊C4×C37—21no—
106C2×C4⋊C4×C37—21no—
107C2×C4⋊C4×C37—21no—
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—22no—
110C2×C4⋊C4×C37—22no—
111C2×C4⋊C4×C37—22no—
112C2×C4⋊C4×C37—22no—
113C2×C4⋊C4×C37—21no—
114C2×C4⋊C4×C37—21no—
115C2×C4⋊C4×C37—41no—
116C2×C4⋊C4×C37D411yescharacteristic
117C2×C4⋊C4×C37D414yescomplemented
118C2×C4⋊C4×C37C2311yescharacteristic
119C2×C4⋊C4×C37C2311yescharacteristic
120C2×C4⋊C4×C37C2311yescharacteristic
121C2×C4⋊C4×C37C2311yescharacteristic
122C2×C4⋊C4×C37C2311yescharacteristic
123C2×C4⋊C4×C37C2311yescharacteristic
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37—21no—
127C2×C22⋊C4×C37—21no—
128C2×C22⋊C4×C37—21no—
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37—21no—
131C2×C22⋊C4×C37D411yescharacteristic
132C2×C22⋊C4×C37D411yescharacteristic
133C2×C42×C37—21no—
134C2×C42×C37C2311yescharacteristic
135#106×C37—22no—
136#106×C37—22no—
137#106×C37—22no—
138#103×C37—22no—
139#103×C37—22no—
140#103×C37—41no—
141#102×C37—22no—
142#102×C37—22no—
143#102×C37—22no—
144C22⋊C8×C37—22no—
145C22⋊C8×C37—22no—
146C22⋊C8×C37—41no—
147#95×C37—21no—
148#95×C37—21no—
149C24×C37—21no—
150C24×C37C2×D411yescharacteristic
151C24×C37C2×D411yescharacteristic
152C2×Q8×C37—24no—
153C2×Q8×C37—21no—
154C2×Q8×C37—21no—
155C2×Q8×C37—21no—
156C2×Q8×C37—21no—
157C2×Q8×C37—21no—
158C2×Q8×C37—81no—
159C2×Q8×C37—81no—
160C2×Q8×C37C2×D412yes—
161C2×D4×C37—22no—
162C2×D4×C37—22no—
163C2×D4×C37—21no—
164C2×D4×C37—21no—
165C2×D4×C37—21no—
166C2×D4×C37—21no—
167C2×D4×C37—21no—
168C2×D4×C37—21no—
169C2×D4×C37—42no—
170C2×D4×C37—42no—
171C2×D4×C37—42no—
172C2×D4×C37—42no—
173C2×D4×C37—42no—
174C2×D4×C37—81no—
175C2×D4×C37SD1614yescomplemented
176C22×C4×C37—21no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—21no—
183C22×C4×C37—21no—
184C22×C4×C37—21no—
185C22×C4×C37—24no—
186C22×C4×C37—24no—
187C22×C4×C37—21no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—21no—
191C22×C4×C37—21no—
192C22×C4×C37—21no—
193C22×C4×C37—21no—
194C22×C4×C37—21no—
195C22×C4×C37—42no—
196C22×C4×C37—42no—
197C22×C4×C37—81no—
198C22×C4×C37—81no—
199C22×C4×C37—81no—
200C22×C4×C37—81no—
201C22×C4×C37—81no—
202C22×C4×C37C2×D411yescharacteristic
203C22×C4×C37C2×D411yescharacteristic
204C22×C4×C37C2×D411yescharacteristic
205C22×C4×C37C2×D412yes—
206C22×C4×C37C2×D412yes—
207C22×C4×C37C2×D411yescharacteristic
208C22×C4×C37C2411yescharacteristic
209SD16×C37—44no—
210C2×C8×C37—21no—
211C2×C8×C37—21no—
212C2×C8×C37—21no—
213C2×C8×C37—21no—
214C2×C8×C37—21no—
215C2×C8×C37—21no—
216C2×C8×C37—21no—
217C2×C8×C37—21no—
218C2×C8×C37—21no—
219C2×C8×C37—21no—
220C2×C8×C37—21no—
221C2×C8×C37—44no—
222C2×C8×C37#4112yes—
223C4⋊C4×C37—24no—
224C4⋊C4×C37—24no—
225C4⋊C4×C37—24no—
226C4⋊C4×C37—24no—
227C4⋊C4×C37—24no—
228C4⋊C4×C37—24no—
229C4⋊C4×C37—22no—
230C4⋊C4×C37—21no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—21no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—42no—
239C4⋊C4×C37—42no—
240C4⋊C4×C37C2×D412yes—
241C4⋊C4×C37C2×D412yes—
242C4⋊C4×C37C2×D412yes—
243C4⋊C4×C37#4112yes—
244C22⋊C4×C37—24no—
245C22⋊C4×C37—24no—
246C22⋊C4×C37—22no—
247C22⋊C4×C37—22no—
248C22⋊C4×C37—42no—
249C22⋊C4×C37—42no—
250C22⋊C4×C37—42no—
251C22⋊C4×C37—42no—
252C22⋊C4×C37—81no—
253C42×C37—24no—
254C42×C37—21no—
255C42×C37—21no—
256C23×C37—21no—
257C23×C37—21no—
258C23×C37—21no—
259C23×C37—21no—
260C23×C37—21no—
261C23×C37—21no—
262C23×C37—21no—
263C23×C37—21no—
264C23×C37—21no—
265C23×C37—21no—
266C23×C37—41no—
267C23×C37—41no—
268C23×C37—41no—
269C23×C37—41no—
270C23×C37—41no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37#12012yes—
274C23×C37C2×SD1612yes—
275C23×C37C2×SD1612yes—
276C23×C37#13712yes—
277C23×C37C22×D411yescharacteristic
278Q8×C37—22no—
279Q8×C37—22no—
280Q8×C37—41no—
281Q8×C37—41no—
282Q8×C37—84no—
283D4×C37—28no—
284D4×C37—41no—
285D4×C37—41no—
286D4×C37—41no—
287D4×C37—41no—
288D4×C37—84no—
289D4×C37—84no—
290C2×C4×C37—21no—
291C2×C4×C37—21no—
292C2×C4×C37—21no—
293C2×C4×C37—21no—
294C2×C4×C37—22no—
295C2×C4×C37—22no—
296C2×C4×C37—22no—
297C2×C4×C37—22no—
298C2×C4×C37—22no—
299C2×C4×C37—21no—
300C2×C4×C37—22no—
301C2×C4×C37—21no—
302C2×C4×C37—22no—
303C2×C4×C37—22no—
304C2×C4×C37—21no—
305C2×C4×C37—22no—
306C2×C4×C37—21no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—41no—
310C2×C4×C37—41no—
311C2×C4×C37—41no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
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—41no—
329C2×C4×C37—84no—
330C2×C4×C37—84no—
331C2×C4×C37—84no—
332C2×C4×C37#12012yes—
333C2×C4×C37C2×SD1612yes—
334C2×C4×C37C22×D411yescharacteristic
335C2×C4×C37C22×D411yescharacteristic
336C2×C4×C37C2×#4111yescharacteristic
337C2×C4×C37C2×#4111yescharacteristic
338C2×C4×C37H(5,𝔽2)11yescharacteristic
339C2×C4×C372−1+411yescharacteristic
340C8×C37—22no—
341C8×C37—41no—
342C8×C37—41no—
343C8×C37—41no—
344#25543C3711yesmaximal, characteristic, direct product factor, Sylow
345C22×C37—22no—
346C22×C37—22no—
347C22×C37—22no—
348C22×C37—22no—
349C22×C37—22no—
350C22×C37—22no—
351C22×C37—22no—
352C22×C37—22no—
353C22×C37—22no—
354C22×C37—41no—
355C22×C37—41no—
356C22×C37—41no—
357C22×C37—41no—
358C22×C37—81no—
359C22×C37—81no—
360C22×C37—81no—
361C22×C37—81no—
362C22×C37—81no—
363C22×C37—81no—
364C22×C37—81no—
365C22×C37#44814yes—
366C22×C37C2×#12011yescharacteristic
367C22×C37#54611yescharacteristic
368C22×C37#54711yescharacteristic
369C22×C37C22×SD1611yescharacteristic
370C22×C37C2×#13711yescharacteristic
371C22×C37#57611yescharacteristic
372C22×C37#57711yescharacteristic
373C4×C37—22no—
374C4×C37—22no—
375C4×C37—41no—
376C4×C37—42no—
377C4×C37—41no—
378C4×C37—42no—
379C4×C37—42no—
380C4×C37—42no—
381C4×C37—42no—
382C4×C37—81no—
383C4×C37—81no—
384C4×C37#53211yescharacteristic
385C4×C37#53711yescharacteristic
386C4×C37#54611yescharacteristic
387C4×C37#54711yescharacteristic
388C2×#554C2×C3711yescharacteristic, complemented
389C2×#481C2×C3711yescharacteristic, complemented
390C2×#465C2×C3711yescharacteristic, complemented
391#2416C2×C3711yescharacteristic
392#2058C2×C3711yescharacteristic, complemented
393#2035C2×C3711yescharacteristic, complemented
394#2023C2×C3711yescharacteristic, complemented
395#2000C2×C3711yescharacteristic, complemented
396#1880C2×C3711yescharacteristic, complemented
397#1874C2×C3711yescharacteristic, complemented
398#1872C2×C3711yescharacteristic, complemented
399#1869C2×C3711yescharacteristic, complemented
400#1865C2×C3711yescharacteristic, complemented
401#1853C2×C3711yescharacteristic, complemented
402C2×#340C2×C3711yescharacteristic, complemented
403C2×C37—24no—
404C2×C37—42no—
405C2×C37—161no—
406C2×C37#243011yescharacteristic
407C2×C37C2×#44811yescharacteristic
408C2×C37#301211yescharacteristic
409C2×C37#329511yescharacteristic
410C2×C37#331611yescharacteristic
411C2×C37#333511yescharacteristic
412C2×C37#334611yescharacteristic
413C22×SD16C22×C3711yescharacteristic
414C23×C8C22×C3711yescharacteristic
415#554—24no—
416#554—24no—
417C2×C4⋊Q8C22×C3711yescharacteristic
418C2×#125—21no—
419C2×C22⋊Q8—21no—
420C2×C22⋊Q8—21no—
421C2×C22⋊Q8C22×C3711yescharacteristic
422C2×C22⋊Q8C22×C3711yescharacteristic
423C2×#121—21no—
424C2×#121C22×C3711yescharacteristic
425C2×#121C22×C3711yescharacteristic
426C2×C4×Q8C22×C3711yescharacteristic
427C2×C4×D4—21no—
428C2×C4×D4C22×C3711yescharacteristic
429C22×C4⋊C4C22×C3711yescharacteristic
430C22×C4⋊C4C22×C3711yescharacteristic
431C22×C4⋊C4C22×C3711yescharacteristic
432#481—24no—
433#465—24no—
434C2×#106C22×C3711yescharacteristic
435C2×#106C22×C3711yescharacteristic
436C2×#106C22×C3711yescharacteristic
437C2×#103C22×C3711yescharacteristic
438C2×#103C22×C3711yescharacteristic
439C2×#103C22×C3711yescharacteristic
440C2×#102C22×C3711yescharacteristic
441C2×#102C22×C3711yescharacteristic
442C2×#102C22×C3711yescharacteristic
443C2×C22⋊C8C22×C3711yescharacteristic
444C2×C22⋊C8C22×C3711yescharacteristic
445C2×C22⋊C8C22×C3711yescharacteristic
446#396—21no—
447#394—21no—
448#390C22×C3711yescharacteristic
449#389C22×C3711yescharacteristic
450#386—21no—
451#380C22×C3711yescharacteristic
452#340C22×C3711yescharacteristic
453#340C22×C3711yescharacteristic
454#340C22×C3711yescharacteristic
455#340C22×C3711yescharacteristic
456#340C22×C3711yescharacteristic
457#340C22×C3711yescharacteristic
458#336C22×C3711yescharacteristic
459#336C22×C3711yescharacteristic
460C37#2554311yescharacteristic, direct product factor, Sylow
461C22×Q8—21no—
462C22×Q8C23×C3711yescharacteristic
463C22×D4—21no—
464C22×D4—21no—
465C22×D4D4×C3711yescharacteristic
466C22×D4C23×C3711yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4—21no—
470C23×C4C23×C3711yescharacteristic
471C23×C4C23×C3711yescharacteristic
472C2×SD16—22no—
473C2×SD16—22no—
474C2×SD16—41no—
475C22×C8—22no—
476C22×C8—22no—
477C22×C8—41no—
478C22×C8C23×C3711yescharacteristic
479C22×C8C23×C3711yescharacteristic
480C22×C8C23×C3711yescharacteristic
481C22×C8C23×C3711yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8—22no—
484#125—28no—
485C22⋊Q8—28no—
486C22⋊Q8—28no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8D4×C3714yescomplemented
491#121—22no—
492#121—22no—
493#121—22no—
494#121—41no—
495#121—44no—
496C4×Q8—22no—
497C4×Q8—22no—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4D4×C3711yescharacteristic
515C2×C4⋊C4D4×C3714yescomplemented
516C2×C4⋊C4C23×C3711yescharacteristic
517C2×C4⋊C4C23×C3711yescharacteristic
518C2×C4⋊C4C23×C3711yescharacteristic
519C2×C4⋊C4C23×C3711yescharacteristic
520C2×C4⋊C4C23×C3711yescharacteristic
521C2×C4⋊C4C23×C3711yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4D4×C3711yescharacteristic
530C2×C22⋊C4D4×C3711yescharacteristic
531C2×C42—21no—
532C2×C42C23×C3711yescharacteristic
533#106—22no—
534#106—22no—
535#106—22no—
536#103—22no—
537#103—22no—
538#103—41no—
539#102—22no—
540#102—22no—
541#102—22no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544C22⋊C8—41no—
545#95—21no—
546#95—21no—
547C24—21no—
548C24C2×D4×C3711yescharacteristic
549C24C2×D4×C3711yescharacteristic
550C2×Q8—24no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—81no—
557C2×Q8—81no—
558C2×Q8C2×D4×C3712yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4SD16×C3714yescomplemented
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4—81no—
600C22×C4C2×D4×C3711yescharacteristic
601C22×C4C2×D4×C3711yescharacteristic
602C22×C4C2×D4×C3711yescharacteristic
603C22×C4C2×D4×C3712yes—
604C22×C4C2×D4×C3712yes—
605C22×C4C2×D4×C3711yescharacteristic
606C22×C4C24×C3711yescharacteristic
607SD16—44no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—44no—
620C2×C8#41×C3712yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4C2×D4×C3712yes—
639C4⋊C4C2×D4×C3712yes—
640C4⋊C4C2×D4×C3712yes—
641C4⋊C4#41×C3712yes—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—81no—
651C42—24no—
652C42—21no—
653C42—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#120×C3712yes—
672C23C2×SD16×C3712yes—
673C23C2×SD16×C3712yes—
674C23#137×C3712yes—
675C23C22×D4×C3711yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—41no—
679Q8—41no—
680Q8—84no—
681D4—28no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—84no—
687D4—84no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4#120×C3712yes—
731C2×C4C2×SD16×C3712yes—
732C2×C4C22×D4×C3711yescharacteristic
733C2×C4C22×D4×C3711yescharacteristic
734C2×C4C2×#41×C3711yescharacteristic
735C2×C4C2×#41×C3711yescharacteristic
736C2×C4H(5,𝔽2)×C3711yescharacteristic
737C2×C42−1+4×C3711yescharacteristic
738C8—22no—
739C8—41no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22C37×#44814yes—
763C22C2×#120×C3711yescharacteristic
764C22C37×#54611yescharacteristic
765C22C37×#54711yescharacteristic
766C22C22×SD16×C3711yescharacteristic
767C22C2×#137×C3711yescharacteristic
768C22C37×#57611yescharacteristic
769C22C37×#57711yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—42no—
774C4—41no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—81no—
780C4—81no—
781C4C37×#53211yescharacteristic
782C4C37×#53711yescharacteristic
783C4C37×#54611yescharacteristic
784C4C37×#54711yescharacteristic
785C2—24no—
786C2—42no—
787C2—161no—
788C2C37×#243011yescharacteristic
789C2C2×C37×#44811yescharacteristic
790C2C37×#301211yescharacteristic
791C2C37×#329511yescharacteristic
792C2C37×#331611yescharacteristic
793C2C37×#333511yescharacteristic
794C2C37×#334611yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#554C2semidirect
2. C2×C37×#481C2semidirect
3. C2×C37×#465C2semidirect
5. C37×#2058C2semidirect
6. C37×#2035C2semidirect
7. C37×#2023C2semidirect
8. C37×#2000C2semidirect
9. C37×#1880C2semidirect
10. C37×#1874C2semidirect
11. C37×#1872C2semidirect
12. C37×#1869C2semidirect
13. C37×#1865C2semidirect
14. C37×#1853C2semidirect
15. C2×C37×#340C2semidirect
92. C22⋊Q8×C37D4semidirect
117. C2×C4⋊C4×C37D4semidirect
175. C2×D4×C37SD16semidirect
344. #25543C37direct (N × H)
388. C2×#554C2×C37semidirect
389. C2×#481C2×C37semidirect
390. C2×#465C2×C37semidirect
392. #2058C2×C37semidirect
393. #2035C2×C37semidirect
394. #2023C2×C37semidirect
395. #2000C2×C37semidirect
396. #1880C2×C37semidirect
397. #1874C2×C37semidirect
398. #1872C2×C37semidirect
399. #1869C2×C37semidirect
400. #1865C2×C37semidirect
401. #1853C2×C37semidirect
402. C2×#340C2×C37semidirect
460. C37#25543direct (N × H)
490. C22⋊Q8D4×C37semidirect
515. C2×C4⋊C4D4×C37semidirect
573. C2×D4SD16×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5542
C2×C37×#4812
C2×C37×#4652
C37×#24162
C37×#20582
C37×#20352
C37×#20232
C37×#20002
C37×#18802
C37×#18742
C37×#18722
C37×#18692
C37×#18652
C37×#18532
C2×C37×#3402
#2554337