Finite Group Databasebeta

← C37×#22398 #22643651

Subgroups — C37×#22398 #22643651

Order 9472.

1630 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#525C211yesmaximal, characteristic
2C2×C37×#435C211yesmaximal, characteristic, complemented
3C2×C8×D4×C37C211yesmaximal, characteristic, complemented
4C2×C37×#408C211yesmaximal, characteristic, complemented
5C22×C22⋊C8×C37C211yesmaximal, characteristic, complemented
6C37×#1955C211yesmaximal, characteristic, complemented
7C37×#1954C211yesmaximal, characteristic, complemented
8C37×#1870C211yesmaximal, characteristic, complemented
9C37×#1869C211yesmaximal, characteristic, complemented
10C37×#1869C211yesmaximal, characteristic, complemented
11C37×#1869C211yesmaximal, characteristic, complemented
12C37×#1798C211yesmaximal, characteristic, complemented
13C37×#1780C211yesmaximal, characteristic, complemented
14C37×#1779C211yesmaximal, characteristic, complemented
15C37×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C24×C4×C37C2211yescharacteristic
18C22×M16×C37C2211yescharacteristic, complemented
19C23×C8×C37C2211yescharacteristic
20C23×C8×C37C2211yescharacteristic
21C23×C8×C37C2211yescharacteristic, complemented
22C37×#525—24no—
23C37×#525—24no—
24C2×#123×C37C411yescharacteristic
25C2×#123×C37C411yescharacteristic
26C2×C22⋊Q8×C37C411yescharacteristic
27C2×C22⋊Q8×C37C411yescharacteristic
28C2×#121×C37C411yescharacteristic
29C2×#121×C37C411yescharacteristic
30C2×#120×C37C411yescharacteristic
31C2×#120×C37C411yescharacteristic
32C2×C4×D4×C37C2211yescharacteristic
33C2×C4×D4×C37C2211yescharacteristic
34C2×C4×D4×C37C2211yescharacteristic
35C2×C4×D4×C37C2211yescharacteristic
36C2×#117×C37C2211yescharacteristic
37C37×#435—24no—
38C8×D4×C37—24no—
39C2×C4⋊C8×C37C2211yescharacteristic, complemented
40C2×C4⋊C8×C37C2211yescharacteristic, complemented
41C37×#408—24no—
42C2×C22⋊C8×C37—24no—
43C2×C22⋊C8×C37C2211yescharacteristic
44C2×C22⋊C8×C37C2211yescharacteristic
45C2×C22⋊C8×C37C2211yescharacteristic
46C2×C22⋊C8×C37C2211yescharacteristic
47C2×C22⋊C8×C37C2211yescharacteristic
48C2×C22⋊C8×C37C2211yescharacteristic
49C2×C22⋊C8×C37C2211yescharacteristic
50C2×C22⋊C8×C37C2211yescharacteristic
51C2×C22⋊C8×C37C2211yescharacteristic
52C2×C22⋊C8×C37C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C2×C22⋊C8×C37C2211yescharacteristic, complemented
55C2×C22⋊C8×C37C2211yescharacteristic, complemented
56C2×C22⋊C8×C37C2211yescharacteristic, complemented
57C2×C22⋊C8×C37C2211yescharacteristic, complemented
58C2×C22⋊C8×C37C2211yescharacteristic, complemented
59C2×#97×C37C2211yescharacteristic, complemented
60C2×C4×C8×C37C2211yescharacteristic, complemented
61C37×#336C2211yescharacteristic, complemented
62C37×#336C2211yescharacteristic, complemented
63C37×#336C2211yescharacteristic, complemented
64C37×#336C2211yescharacteristic, complemented
65C25×C37C2×C411yescharacteristic
66C2×#41×C37—22no—
67C2×#41×C37—22no—
68C2×#41×C37—22no—
69C2×#41×C37—22no—
70C2×#41×C37—41no—
71C2×#41×C37—41no—
72C22×Q8×C37C2×C411yescharacteristic
73C22×D4×C37C2×C411yescharacteristic
74C22×D4×C37C2×C411yescharacteristic
75C22×D4×C37C2×C411yescharacteristic
76C22×D4×C37C2×C411yescharacteristic
77C22×D4×C37C2×C411yescharacteristic
78C22×D4×C37C2×C411yescharacteristic
79C22×D4×C37C2×C411yescharacteristic
80C23×C4×C37—22no—
81C23×C4×C37—22no—
82C23×C4×C37—22no—
83C23×C4×C37—22no—
84C23×C4×C37—41no—
85C23×C4×C37—41no—
86C23×C4×C37C2×C411yescharacteristic
87C23×C4×C37C2×C411yescharacteristic
88C23×C4×C37C2×C411yescharacteristic
89C23×C4×C37C2311yescharacteristic
90C23×C4×C37C2311yescharacteristic
91C23×C4×C37C2311yescharacteristic
92C23×C4×C37C2311yescharacteristic
93C23×C4×C37C2311yescharacteristic
94C2×M16×C37—22no—
95C2×M16×C37—22no—
96C2×M16×C37—41no—
97C22×C8×C37—22no—
98C22×C8×C37—22no—
99C22×C8×C37—22no—
100C22×C8×C37—22no—
101C22×C8×C37—22no—
102C22×C8×C37—22no—
103C22×C8×C37—41no—
104C22×C8×C37—41no—
105C22×C8×C37—41no—
106C22×C8×C37C2311yescharacteristic
107C22×C8×C37C2311yescharacteristic
108C22×C8×C37C2311yescharacteristic
109C22×C8×C37C2311yescharacteristic
110C22×C8×C37C2311yescharacteristic
111C22×C8×C37C2311yescharacteristic
112C22×C8×C37C2311yescharacteristic
113C22×C8×C37C2311yescharacteristic
114#123×C37—24no—
115#123×C37—24no—
116C22⋊Q8×C37—24no—
117C22⋊Q8×C37—24no—
118#121×C37—24no—
119#121×C37—24no—
120#120×C37—24no—
121#120×C37—24no—
122C4×D4×C37—22no—
123C4×D4×C37—22no—
124C4×D4×C37—22no—
125C4×D4×C37—22no—
126C4×D4×C37—22no—
127C4×D4×C37—22no—
128C4×D4×C37D414yes—
129C4×D4×C37D414yes—
130#117×C37—22no—
131#117×C37—22no—
132C2×C4⋊C4×C37C2×C411yescharacteristic
133C2×C4⋊C4×C37C2×C411yescharacteristic
134C2×C4⋊C4×C37C2×C411yescharacteristic
135C2×C4⋊C4×C37C2×C411yescharacteristic
136C2×C4⋊C4×C37C2×C411yescharacteristic
137C2×C4⋊C4×C37C2×C411yescharacteristic
138C2×C22⋊C4×C37C2×C411yescharacteristic
139C2×C22⋊C4×C37C2×C411yescharacteristic
140C2×C22⋊C4×C37C2×C411yescharacteristic
141C2×C22⋊C4×C37C2×C411yescharacteristic
142C2×C22⋊C4×C37C2×C411yescharacteristic
143C2×C22⋊C4×C37C2×C411yescharacteristic
144C2×C22⋊C4×C37C2×C411yescharacteristic
145C2×C22⋊C4×C37C2×C411yescharacteristic
146C2×C22⋊C4×C37C2×C411yescharacteristic
147C2×C22⋊C4×C37C2×C411yescharacteristic
148C2×C42×C37C2311yescharacteristic
149C2×C42×C37C2311yescharacteristic
150C4⋊C8×C37—22no—
151C4⋊C8×C37—22no—
152C22⋊C8×C37—22no—
153C22⋊C8×C37—22no—
154C22⋊C8×C37—22no—
155C22⋊C8×C37—22no—
156C22⋊C8×C37—22no—
157C22⋊C8×C37—22no—
158C22⋊C8×C37—22no—
159C22⋊C8×C37—22no—
160C22⋊C8×C37—22no—
161C22⋊C8×C37—22no—
162C22⋊C8×C37—22no—
163C22⋊C8×C37—41no—
164C22⋊C8×C37—41no—
165C22⋊C8×C37—41no—
166C22⋊C8×C37—41no—
167C22⋊C8×C37D414yescomplemented
168#97×C37—22no—
169C4×C8×C37—22no—
170C24×C37—22no—
171C24×C37—22no—
172C24×C37—22no—
173C24×C37—22no—
174C24×C37—22no—
175C24×C37—41no—
176C24×C37—41no—
177C24×C37C22×C411yescharacteristic
178C24×C37C22×C411yescharacteristic
179C24×C37C22×C411yescharacteristic
180C24×C37C22×C411yescharacteristic
181C24×C37C22×C411yescharacteristic
182#41×C37—44no—
183#41×C37—44no—
184#41×C37—44no—
185#41×C37—44no—
186C2×Q8×C37—22no—
187C2×Q8×C37—22no—
188C2×Q8×C37—41no—
189C2×D4×C37—22no—
190C2×D4×C37—22no—
191C2×D4×C37—22no—
192C2×D4×C37—22no—
193C2×D4×C37—22no—
194C2×D4×C37—22no—
195C2×D4×C37—22no—
196C2×D4×C37—22no—
197C2×D4×C37—22no—
198C2×D4×C37—22no—
199C2×D4×C37—22no—
200C2×D4×C37—22no—
201C2×D4×C37—22no—
202C2×D4×C37—22no—
203C2×D4×C37—22no—
204C2×D4×C37—41no—
205C2×D4×C37—41no—
206C2×D4×C37—41no—
207C2×D4×C37—41no—
208C2×D4×C37—41no—
209C2×D4×C37C22⋊C414yes—
210C22×C4×C37—21no—
211C22×C4×C37—21no—
212C22×C4×C37—21no—
213C22×C4×C37—21no—
214C22×C4×C37—21no—
215C22×C4×C37—21no—
216C22×C4×C37—21no—
217C22×C4×C37—21no—
218C22×C4×C37—21no—
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—21no—
222C22×C4×C37—22no—
223C22×C4×C37—22no—
224C22×C4×C37—22no—
225C22×C4×C37—22no—
226C22×C4×C37—22no—
227C22×C4×C37—22no—
228C22×C4×C37—21no—
229C22×C4×C37—21no—
230C22×C4×C37—21no—
231C22×C4×C37—21no—
232C22×C4×C37—21no—
233C22×C4×C37—21no—
234C22×C4×C37—21no—
235C22×C4×C37—21no—
236C22×C4×C37—21no—
237C22×C4×C37—21no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—41no—
241C22×C4×C37—41no—
242C22×C4×C37—41no—
243C22×C4×C37—44no—
244C22×C4×C37—44no—
245C22×C4×C37—44no—
246C22×C4×C37—44no—
247C22×C4×C37C22×C411yescharacteristic
248C22×C4×C37C22×C411yescharacteristic
249C22×C4×C37C22×C411yescharacteristic
250C22×C4×C37C22×C411yescharacteristic
251C22×C4×C37C22×C411yescharacteristic
252C22×C4×C37C22×C411yescharacteristic
253C22×C4×C37C22×C411yescharacteristic
254C22×C4×C37C22×C411yescharacteristic
255C22×C4×C37C22×C411yescharacteristic
256C22×C4×C37C2×D412yes—
257C22×C4×C37C2×D412yes—
258C22×C4×C37C2×D412yes—
259C22×C4×C37C2×D412yes—
260C22×C4×C37C2×D412yes—
261C22×C4×C37#4112yes—
262C22×C4×C37C2411yescharacteristic
263M16×C37—44no—
264C2×C8×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—21no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—21no—
270C2×C8×C37—21no—
271C2×C8×C37—21no—
272C2×C8×C37—21no—
273C2×C8×C37—21no—
274C2×C8×C37—21no—
275C2×C8×C37—21no—
276C2×C8×C37—21no—
277C2×C8×C37—21no—
278C2×C8×C37—21no—
279C2×C8×C37—21no—
280C2×C8×C37—21no—
281C2×C8×C37—21no—
282C2×C8×C37—21no—
283C2×C8×C37—21no—
284C2×C8×C37—21no—
285C2×C8×C37—21no—
286C2×C8×C37—44no—
287C2×C8×C37—44no—
288C2×C8×C37—44no—
289C2×C8×C37C2×D412yes—
290C2×C8×C37C2×D412yes—
291C4⋊C4×C37—22no—
292C4⋊C4×C37—22no—
293C4⋊C4×C37—22no—
294C4⋊C4×C37—22no—
295C4⋊C4×C37—22no—
296C4⋊C4×C37C22⋊C414yes—
297C22⋊C4×C37—22no—
298C22⋊C4×C37—22no—
299C22⋊C4×C37—22no—
300C22⋊C4×C37—22no—
301C22⋊C4×C37—22no—
302C22⋊C4×C37—22no—
303C22⋊C4×C37—22no—
304C22⋊C4×C37—22no—
305C22⋊C4×C37C22⋊C414yes—
306C22⋊C4×C37C22⋊C414yes—
307C42×C37—21no—
308C42×C37—21no—
309C42×C37C2×D412yes—
310C42×C37C2×D412yes—
311C23×C37—21no—
312C23×C37—21no—
313C23×C37—21no—
314C23×C37—21no—
315C23×C37—28no—
316C23×C37—21no—
317C23×C37—21no—
318C23×C37—21no—
319C23×C37—21no—
320C23×C37—21no—
321C23×C37—21no—
322C23×C37—21no—
323C23×C37—21no—
324C23×C37—21no—
325C23×C37—21no—
326C23×C37—21no—
327C23×C37—21no—
328C23×C37—21no—
329C23×C37—21no—
330C23×C37—21no—
331C23×C37—21no—
332C23×C37—21no—
333C23×C37—21no—
334C23×C37—21no—
335C23×C37—21no—
336C23×C37—21no—
337C23×C37—21no—
338C23×C37—21no—
339C23×C37—21no—
340C23×C37—21no—
341C23×C37—44no—
342C23×C37—44no—
343C23×C37—44no—
344C23×C37—44no—
345C23×C37—44no—
346C23×C37—44no—
347C23×C37C2×C22⋊C412yes—
348C23×C37C2×C22⋊C412yes—
349C23×C37C4×D412yes—
350C23×C37#13112yes—
351C23×C37#13112yes—
352C23×C37#13112yes—
353C23×C37C23×C411yescharacteristic
354Q8×C37—44no—
355D4×C37—28no—
356D4×C37—44no—
357D4×C37—44no—
358D4×C37—44no—
359D4×C37—44no—
360D4×C37—44no—
361D4×C37—44no—
362C2×C4×C37—21no—
363C2×C4×C37—21no—
364C2×C4×C37—21no—
365C2×C4×C37—21no—
366C2×C4×C37—21no—
367C2×C4×C37—21no—
368C2×C4×C37—21no—
369C2×C4×C37—21no—
370C2×C4×C37—21no—
371C2×C4×C37—21no—
372C2×C4×C37—22no—
373C2×C4×C37—22no—
374C2×C4×C37—22no—
375C2×C4×C37—22no—
376C2×C4×C37—22no—
377C2×C4×C37—22no—
378C2×C4×C37—22no—
379C2×C4×C37—22no—
380C2×C4×C37—22no—
381C2×C4×C37—22no—
382C2×C4×C37—22no—
383C2×C4×C37—22no—
384C2×C4×C37—21no—
385C2×C4×C37—21no—
386C2×C4×C37—21no—
387C2×C4×C37—21no—
388C2×C4×C37—21no—
389C2×C4×C37—21no—
390C2×C4×C37—21no—
391C2×C4×C37—21no—
392C2×C4×C37—21no—
393C2×C4×C37—21no—
394C2×C4×C37—21no—
395C2×C4×C37—21no—
396C2×C4×C37—44no—
397C2×C4×C37—44no—
398C2×C4×C37—44no—
399C2×C4×C37—41no—
400C2×C4×C37—41no—
401C2×C4×C37—41no—
402C2×C4×C37—41no—
403C2×C4×C37—41no—
404C2×C4×C37—41no—
405C2×C4×C37—41no—
406C2×C4×C37—41no—
407C2×C4×C37C2×C22⋊C412yes—
408C2×C4×C37C2×C22⋊C412yes—
409C2×C4×C37C2×C22⋊C412yes—
410C2×C4×C37C2×C22⋊C412yes—
411C2×C4×C37C4×D412yes—
412C2×C4×C37C22×D411yescharacteristic
413C2×C4×C37C22×D411yescharacteristic
414C2×C4×C37C22×D411yescharacteristic
415C2×C4×C37C2×#4111yescharacteristic
416C2×C4×C37H(5,𝔽2)11yescharacteristic
417C2×C4×C37H(5,𝔽2)11yescharacteristic
418C8×C37—22no—
419C8×C37—22no—
420C8×C37—41no—
421C8×C37—41no—
422C8×C37—41no—
423C8×C37—41no—
424C8×C37—41no—
425C8×C37—41no—
426#22398C3711yesmaximal, characteristic, direct product factor, Sylow
427C22×C37—22no—
428C22×C37—22no—
429C22×C37—22no—
430C22×C37—22no—
431C22×C37—22no—
432C22×C37—22no—
433C22×C37—22no—
434C22×C37—22no—
435C22×C37—22no—
436C22×C37—22no—
437C22×C37—22no—
438C22×C37—22no—
439C22×C37—22no—
440C22×C37—22no—
441C22×C37—22no—
442C22×C37—416no—
443C22×C37—41no—
444C22×C37—41no—
445C22×C37—41no—
446C22×C37—41no—
447C22×C37—41no—
448C22×C37—41no—
449C22×C37—41no—
450C22×C37—41no—
451C22×C37—41no—
452C22×C37—41no—
453C22×C37—41no—
454C22×C37—41no—
455C22×C37—41no—
456C22×C37—41no—
457C22×C37—41no—
458C22×C37—41no—
459C22×C37—41no—
460C22×C37—41no—
461C22×C37—41no—
462C22×C37#40814yescomplemented
463C22×C37C22×C22⋊C411yescharacteristic
464C22×C37C2×C4×D411yescharacteristic
465C22×C37#51811yescharacteristic
466C22×C37C2×#13111yescharacteristic
467C22×C37C2×#13111yescharacteristic
468C22×C37C2×#13111yescharacteristic
469C22×C37#56811yescharacteristic
470C4×C37—22no—
471C4×C37—22no—
472C4×C37—22no—
473C4×C37—22no—
474C4×C37—22no—
475C4×C37—41no—
476C4×C37—41no—
477C4×C37—41no—
478C4×C37—41no—
479C4×C37D4211yescharacteristic
480C4×C37D4211yescharacteristic
481C4×C37#54611yescharacteristic
482C4×C37#54611yescharacteristic
483C2×#525C2×C3711yescharacteristic
484C2×#435C2×C3711yescharacteristic, complemented
485C2×C8×D4C2×C3711yescharacteristic, complemented
486C2×#408C2×C3711yescharacteristic, complemented
487C22×C22⋊C8C2×C3711yescharacteristic, complemented
488#1955C2×C3711yescharacteristic, complemented
489#1954C2×C3711yescharacteristic, complemented
490#1870C2×C3711yescharacteristic, complemented
491#1869C2×C3711yescharacteristic, complemented
492#1869C2×C3711yescharacteristic, complemented
493#1869C2×C3711yescharacteristic, complemented
494#1798C2×C3711yescharacteristic, complemented
495#1780C2×C3711yescharacteristic, complemented
496#1779C2×C3711yescharacteristic, complemented
497#1750C2×C3711yescharacteristic, complemented
498C2×C37—24no—
499C2×C37—42no—
500C2×C37—42no—
501C2×C37—42no—
502C2×C37—81no—
503C2×C37D4×C22⋊C411yescharacteristic
504C2×C37C2×#40811yescharacteristic
505C2×C37#288011yescharacteristic
506C2×C37#292911yescharacteristic
507C2×C37#293311yescharacteristic
508C2×C37#297611yescharacteristic
509C2×C37#297711yescharacteristic
510C22×#41C22×C3711yescharacteristic
511C24×C4C22×C3711yescharacteristic
512C22×M16C22×C3711yescharacteristic, complemented
513C23×C8C22×C3711yescharacteristic
514C23×C8C22×C3711yescharacteristic
515C23×C8C22×C3711yescharacteristic, complemented
516#525—24no—
517#525—24no—
518C2×#123C4×C3711yescharacteristic
519C2×#123C4×C3711yescharacteristic
520C2×C22⋊Q8C4×C3711yescharacteristic
521C2×C22⋊Q8C4×C3711yescharacteristic
522C2×#121C4×C3711yescharacteristic
523C2×#121C4×C3711yescharacteristic
524C2×#120C4×C3711yescharacteristic
525C2×#120C4×C3711yescharacteristic
526C2×C4×D4C22×C3711yescharacteristic
527C2×C4×D4C22×C3711yescharacteristic
528C2×C4×D4C22×C3711yescharacteristic
529C2×C4×D4C22×C3711yescharacteristic
530C2×#117C22×C3711yescharacteristic
531#435—24no—
532C8×D4—24no—
533C2×C4⋊C8C22×C3711yescharacteristic, complemented
534C2×C4⋊C8C22×C3711yescharacteristic, complemented
535#408—24no—
536C2×C22⋊C8—24no—
537C2×C22⋊C8C22×C3711yescharacteristic
538C2×C22⋊C8C22×C3711yescharacteristic
539C2×C22⋊C8C22×C3711yescharacteristic
540C2×C22⋊C8C22×C3711yescharacteristic
541C2×C22⋊C8C22×C3711yescharacteristic
542C2×C22⋊C8C22×C3711yescharacteristic
543C2×C22⋊C8C22×C3711yescharacteristic
544C2×C22⋊C8C22×C3711yescharacteristic
545C2×C22⋊C8C22×C3711yescharacteristic
546C2×C22⋊C8C22×C3711yescharacteristic
547C2×C22⋊C8C22×C3711yescharacteristic, complemented
548C2×C22⋊C8C22×C3711yescharacteristic, complemented
549C2×C22⋊C8C22×C3711yescharacteristic, complemented
550C2×C22⋊C8C22×C3711yescharacteristic, complemented
551C2×C22⋊C8C22×C3711yescharacteristic, complemented
552C2×C22⋊C8C22×C3711yescharacteristic, complemented
553C2×#97C22×C3711yescharacteristic, complemented
554C2×C4×C8C22×C3711yescharacteristic, complemented
555#336C22×C3711yescharacteristic, complemented
556#336C22×C3711yescharacteristic, complemented
557#336C22×C3711yescharacteristic, complemented
558#336C22×C3711yescharacteristic, complemented
559C37#2239811yescharacteristic, direct product factor, Sylow
560C25C2×C4×C3711yescharacteristic
561C2×#41—22no—
562C2×#41—22no—
563C2×#41—22no—
564C2×#41—22no—
565C2×#41—41no—
566C2×#41—41no—
567C22×Q8C2×C4×C3711yescharacteristic
568C22×D4C2×C4×C3711yescharacteristic
569C22×D4C2×C4×C3711yescharacteristic
570C22×D4C2×C4×C3711yescharacteristic
571C22×D4C2×C4×C3711yescharacteristic
572C22×D4C2×C4×C3711yescharacteristic
573C22×D4C2×C4×C3711yescharacteristic
574C22×D4C2×C4×C3711yescharacteristic
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—41no—
580C23×C4—41no—
581C23×C4C2×C4×C3711yescharacteristic
582C23×C4C2×C4×C3711yescharacteristic
583C23×C4C2×C4×C3711yescharacteristic
584C23×C4C23×C3711yescharacteristic
585C23×C4C23×C3711yescharacteristic
586C23×C4C23×C3711yescharacteristic
587C23×C4C23×C3711yescharacteristic
588C23×C4C23×C3711yescharacteristic
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—41no—
592C22×C8—22no—
593C22×C8—22no—
594C22×C8—22no—
595C22×C8—22no—
596C22×C8—22no—
597C22×C8—22no—
598C22×C8—41no—
599C22×C8—41no—
600C22×C8—41no—
601C22×C8C23×C3711yescharacteristic
602C22×C8C23×C3711yescharacteristic
603C22×C8C23×C3711yescharacteristic
604C22×C8C23×C3711yescharacteristic
605C22×C8C23×C3711yescharacteristic
606C22×C8C23×C3711yescharacteristic
607C22×C8C23×C3711yescharacteristic
608C22×C8C23×C3711yescharacteristic
609#123—24no—
610#123—24no—
611C22⋊Q8—24no—
612C22⋊Q8—24no—
613#121—24no—
614#121—24no—
615#120—24no—
616#120—24no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4D4×C3714yes—
624C4×D4D4×C3714yes—
625#117—22no—
626#117—22no—
627C2×C4⋊C4C2×C4×C3711yescharacteristic
628C2×C4⋊C4C2×C4×C3711yescharacteristic
629C2×C4⋊C4C2×C4×C3711yescharacteristic
630C2×C4⋊C4C2×C4×C3711yescharacteristic
631C2×C4⋊C4C2×C4×C3711yescharacteristic
632C2×C4⋊C4C2×C4×C3711yescharacteristic
633C2×C22⋊C4C2×C4×C3711yescharacteristic
634C2×C22⋊C4C2×C4×C3711yescharacteristic
635C2×C22⋊C4C2×C4×C3711yescharacteristic
636C2×C22⋊C4C2×C4×C3711yescharacteristic
637C2×C22⋊C4C2×C4×C3711yescharacteristic
638C2×C22⋊C4C2×C4×C3711yescharacteristic
639C2×C22⋊C4C2×C4×C3711yescharacteristic
640C2×C22⋊C4C2×C4×C3711yescharacteristic
641C2×C22⋊C4C2×C4×C3711yescharacteristic
642C2×C22⋊C4C2×C4×C3711yescharacteristic
643C2×C42C23×C3711yescharacteristic
644C2×C42C23×C3711yescharacteristic
645C4⋊C8—22no—
646C4⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8—22no—
650C22⋊C8—22no—
651C22⋊C8—22no—
652C22⋊C8—22no—
653C22⋊C8—22no—
654C22⋊C8—22no—
655C22⋊C8—22no—
656C22⋊C8—22no—
657C22⋊C8—22no—
658C22⋊C8—41no—
659C22⋊C8—41no—
660C22⋊C8—41no—
661C22⋊C8—41no—
662C22⋊C8D4×C3714yescomplemented
663#97—22no—
664C4×C8—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—41no—
671C24—41no—
672C24C22×C4×C3711yescharacteristic
673C24C22×C4×C3711yescharacteristic
674C24C22×C4×C3711yescharacteristic
675C24C22×C4×C3711yescharacteristic
676C24C22×C4×C3711yescharacteristic
677#41—44no—
678#41—44no—
679#41—44no—
680#41—44no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—41no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4C22⋊C4×C3714yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—41no—
736C22×C4—41no—
737C22×C4—41no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4C22×C4×C3711yescharacteristic
743C22×C4C22×C4×C3711yescharacteristic
744C22×C4C22×C4×C3711yescharacteristic
745C22×C4C22×C4×C3711yescharacteristic
746C22×C4C22×C4×C3711yescharacteristic
747C22×C4C22×C4×C3711yescharacteristic
748C22×C4C22×C4×C3711yescharacteristic
749C22×C4C22×C4×C3711yescharacteristic
750C22×C4C22×C4×C3711yescharacteristic
751C22×C4C2×D4×C3712yes—
752C22×C4C2×D4×C3712yes—
753C22×C4C2×D4×C3712yes—
754C22×C4C2×D4×C3712yes—
755C22×C4C2×D4×C3712yes—
756C22×C4#41×C3712yes—
757C22×C4C24×C3711yescharacteristic
758M16—44no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8—44no—
783C2×C8—44no—
784C2×C8C2×D4×C3712yes—
785C2×C8C2×D4×C3712yes—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4C22⋊C4×C3714yes—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4C22⋊C4×C3714yes—
801C22⋊C4C22⋊C4×C3714yes—
802C42—21no—
803C42—21no—
804C42C2×D4×C3712yes—
805C42C2×D4×C3712yes—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—28no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—44no—
837C23—44no—
838C23—44no—
839C23—44no—
840C23—44no—
841C23—44no—
842C23C2×C22⋊C4×C3712yes—
843C23C2×C22⋊C4×C3712yes—
844C23C4×D4×C3712yes—
845C23#131×C3712yes—
846C23#131×C3712yes—
847C23#131×C3712yes—
848C23C23×C4×C3711yescharacteristic
849Q8—44no—
850D4—28no—
851D4—44no—
852D4—44no—
853D4—44no—
854D4—44no—
855D4—44no—
856D4—44no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4C2×C22⋊C4×C3712yes—
903C2×C4C2×C22⋊C4×C3712yes—
904C2×C4C2×C22⋊C4×C3712yes—
905C2×C4C2×C22⋊C4×C3712yes—
906C2×C4C4×D4×C3712yes—
907C2×C4C22×D4×C3711yescharacteristic
908C2×C4C22×D4×C3711yescharacteristic
909C2×C4C22×D4×C3711yescharacteristic
910C2×C4C2×#41×C3711yescharacteristic
911C2×C4H(5,𝔽2)×C3711yescharacteristic
912C2×C4H(5,𝔽2)×C3711yescharacteristic
913C8—22no—
914C8—22no—
915C8—41no—
916C8—41no—
917C8—41no—
918C8—41no—
919C8—41no—
920C8—41no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—416no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22C37×#40814yescomplemented
957C22C22×C22⋊C4×C3711yescharacteristic
958C22C2×C4×D4×C3711yescharacteristic
959C22C37×#51811yescharacteristic
960C22C2×#131×C3711yescharacteristic
961C22C2×#131×C3711yescharacteristic
962C22C2×#131×C3711yescharacteristic
963C22C37×#56811yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—22no—
968C4—22no—
969C4—41no—
970C4—41no—
971C4—41no—
972C4—41no—
973C4D42×C3711yescharacteristic
974C4D42×C3711yescharacteristic
975C4C37×#54611yescharacteristic
976C4C37×#54611yescharacteristic
977C2—24no—
978C2—42no—
979C2—42no—
980C2—42no—
981C2—81no—
982C2D4×C22⋊C4×C3711yescharacteristic
983C2C2×C37×#40811yescharacteristic
984C2C37×#288011yescharacteristic
985C2C37×#292911yescharacteristic
986C2C37×#293311yescharacteristic
987C2C37×#297611yescharacteristic
988C2C37×#297711yescharacteristic
subgroupG/H
centerC22×C4×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC22×C4C24×C37
socleC23×C37C23×C4
prime radicalC2×C37×#525C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#435C2semidirect
3. C2×C8×D4×C37C2semidirect
4. C2×C37×#408C2semidirect
5. C22×C22⋊C8×C37C2semidirect
6. C37×#1955C2semidirect
7. C37×#1954C2semidirect
8. C37×#1870C2semidirect
9. C37×#1869C2semidirect
10. C37×#1869C2semidirect
11. C37×#1869C2semidirect
12. C37×#1798C2semidirect
13. C37×#1780C2semidirect
14. C37×#1779C2semidirect
15. C37×#1750C2semidirect
18. C22×M16×C37C22semidirect
21. C23×C8×C37C22semidirect
39. C2×C4⋊C8×C37C22semidirect
40. C2×C4⋊C8×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
54. C2×C22⋊C8×C37C22semidirect
55. C2×C22⋊C8×C37C22semidirect
56. C2×C22⋊C8×C37C22semidirect
57. C2×C22⋊C8×C37C22semidirect
58. C2×C22⋊C8×C37C22semidirect
59. C2×#97×C37C22semidirect
60. C2×C4×C8×C37C22semidirect
61. C37×#336C22semidirect
62. C37×#336C22semidirect
63. C37×#336C22semidirect
64. C37×#336C22semidirect
167. C22⋊C8×C37D4semidirect
426. #22398C37direct (N × H)
462. C22×C37#408semidirect
484. C2×#435C2×C37semidirect
485. C2×C8×D4C2×C37semidirect
486. C2×#408C2×C37semidirect
487. C22×C22⋊C8C2×C37semidirect
488. #1955C2×C37semidirect
489. #1954C2×C37semidirect
490. #1870C2×C37semidirect
491. #1869C2×C37semidirect
492. #1869C2×C37semidirect
493. #1869C2×C37semidirect
494. #1798C2×C37semidirect
495. #1780C2×C37semidirect
496. #1779C2×C37semidirect
497. #1750C2×C37semidirect
512. C22×M16C22×C37semidirect
515. C23×C8C22×C37semidirect
533. C2×C4⋊C8C22×C37semidirect
534. C2×C4⋊C8C22×C37semidirect
547. C2×C22⋊C8C22×C37semidirect
548. C2×C22⋊C8C22×C37semidirect
549. C2×C22⋊C8C22×C37semidirect
550. C2×C22⋊C8C22×C37semidirect
551. C2×C22⋊C8C22×C37semidirect
552. C2×C22⋊C8C22×C37semidirect
553. C2×#97C22×C37semidirect
554. C2×C4×C8C22×C37semidirect
555. #336C22×C37semidirect
556. #336C22×C37semidirect
557. #336C22×C37semidirect
558. #336C22×C37semidirect
559. C37#22398direct (N × H)
662. C22⋊C8D4×C37semidirect
956. C22C37×#408semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5252
C2×C37×#4352
C2×C8×D4×C372
C2×C37×#4082
C22×C22⋊C8×C372
C37×#19552
C37×#19542
C37×#18702
C37×#18692
C37×#17982
C37×#17802
C37×#17792
C37×#17502
#2239837