Finite Group Databasebeta

← C37×#34422 #22655675

Subgroups — C37×#34422 #22655675

Order 9472.

2182 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#542C211yesmaximal, characteristic
2C37×#2383C212yesmaximal, complemented
3C37×#2378C212yesmaximal, complemented
4C37×#2373C212yesmaximal, complemented
5C37×#2369C211yesmaximal, characteristic, complemented
6C37×#2367C211yesmaximal, characteristic, complemented
7C37×#2367C211yesmaximal, characteristic, complemented
8C37×#2365C211yesmaximal, characteristic, complemented
9C37×#2360C212yesmaximal, complemented
10C37×#2357C211yesmaximal, characteristic, complemented
11C37×#2356C211yesmaximal, characteristic, complemented
12Q8×C4⋊C4×C37C211yesmaximal, characteristic, complemented
13D4×C4⋊C4×C37C211yesmaximal, characteristic, complemented
14C37×#2337C212yesmaximal, complemented
15C37×#2335C212yesmaximal, complemented
16C37×#2326C212yesmaximal, complemented
17C37×#2324C211yesmaximal, characteristic
18C37×#2323C211yesmaximal, characteristic, complemented
19C37×#2322C212yesmaximal, complemented
20C37×#2314C211yesmaximal, characteristic, complemented
21C4×C22⋊Q8×C37C211yesmaximal, characteristic, complemented
22C4×#121×C37C211yesmaximal, characteristic
23C37×#2296C211yesmaximal, characteristic, complemented
24C37×#542C4116yescomplemented
25C2×C4⋊Q8×C37C2211yescharacteristic
26C2×#126×C37C2212yes—
27C2×#124×C37C2211yescharacteristic
28C2×#124×C37C2212yes—
29C2×#123×C37C2212yes—
30C2×C22⋊Q8×C37C2212yes—
31C2×C22⋊Q8×C37C2211yescharacteristic
32C2×#121×C37C2211yescharacteristic
33C2×C4×Q8×C37C2211yescharacteristic
34C2×C4×Q8×C37C2211yescharacteristic
35C2×C4×Q8×C37C2212yes—
36C2×C4×Q8×C37C2211yescharacteristic
37C2×C4×D4×C37C2211yescharacteristic
38C2×C4×D4×C37C2211yescharacteristic
39C2×C4×D4×C37C2212yes—
40C2×C4×D4×C37C2211yescharacteristic
41C2×#117×C37C2211yescharacteristic
42C2×#117×C37C2211yescharacteristic
43C22×C4⋊C4×C37C2212yes—
44C22×C42×C37C2211yescharacteristic
45C37×#391C2211yescharacteristic
46C37×#391C2211yescharacteristic
47C37×#391C2212yes—
48C37×#391C2212yes—
49C37×#391C2212yes—
50C37×#390C2211yescharacteristic
51C37×#390C2211yescharacteristic
52C37×#390C2212yes—
53C37×#389C2212yes—
54C37×#389C2211yescharacteristic
55C37×#389C2211yescharacteristic
56C37×#389C2212yes—
57C37×#389C2211yescharacteristic
58C37×#389C2212yes—
59C37×#389C2211yescharacteristic
60C37×#389C2212yes—
61C37×#389C2211yescharacteristic
62C37×#389C2211yescharacteristic
63C37×#389C2211yescharacteristic
64C37×#389C2211yescharacteristic
65C37×#388C2212yes—
66C37×#388C2212yes—
67C37×#388C2212yes—
68C37×#388C2212yes—
69C37×#388C2212yes—
70C37×#388C2212yes—
71C37×#388C2212yes—
72C37×#388C2212yes—
73C37×#388C2212yes—
74C37×#388C2212yes—
75C37×#388C2212yes—
76C37×#388C2212yes—
77C37×#387C2212yes—
78C37×#387C2212yes—
79C37×#387C2212yes—
80C37×#387C2212yes—
81C37×#387C2212yes—
82C37×#387C2212yes—
83C37×#387C2212yes—
84C37×#387C2212yes—
85C37×#386C2212yes—
86C37×#386C2212yes—
87C37×#385C2212yes—
88C37×#385C2212yes—
89C37×#385C2212yes—
90C37×#385C2212yes—
91C37×#385C2212yes—
92C37×#385C2211yescharacteristic
93C37×#385C2211yescharacteristic
94C37×#385C2211yescharacteristic
95C37×#385C2211yescharacteristic
96C37×#385C2212yes—
97C37×#384C2212yes—
98C37×#384C2211yescharacteristic
99C37×#383C2212yes—
100C37×#382C2211yescharacteristic
101C37×#381C2212yes—
102C37×#380C2212yes—
103C37×#380C2211yescharacteristic
104C37×#380C2211yescharacteristic
105C4×C4⋊C4×C37C2211yescharacteristic
106C4×C4⋊C4×C37C2212yes—
107C4×C4⋊C4×C37C2211yescharacteristic
108C4×C4⋊C4×C37C2211yescharacteristic
109C4×C4⋊C4×C37C2211yescharacteristic
110C4×C4⋊C4×C37C2211yescharacteristic
111C4×C4⋊C4×C37C2211yescharacteristic
112C4×C4⋊C4×C37C2212yes—
113C4×C4⋊C4×C37C2211yescharacteristic
114C4×C4⋊C4×C37C2211yescharacteristic
115C4×C4⋊C4×C37C2211yescharacteristic
116C4×C4⋊C4×C37C2211yescharacteristic
117C4×C4⋊C4×C37C2212yes—
118C4×C22⋊C4×C37C2212yes—
119C4×C22⋊C4×C37C2212yes—
120C4×C22⋊C4×C37C2212yes—
121C4×C22⋊C4×C37C2212yes—
122C4×C22⋊C4×C37C2212yes—
123C37×#376C2212yes—
124C22×Q8×C37C2311yescharacteristic
125C22×Q8×C37C2312yes—
126C22×D4×C37C2311yescharacteristic
127C22×D4×C37C2312yes—
128C23×C4×C37C2311yescharacteristic
129C23×C4×C37C2311yescharacteristic
130C23×C4×C37C2312yes—
131C23×C4×C37C2311yescharacteristic
132C23×C4×C37C2312yes—
133C23×C4×C37C2312yes—
134C4⋊Q8×C37C2×C418yescomplemented
135#126×C37C2×C4116yescomplemented
136#124×C37C2×C418yescomplemented
137#124×C37C2×C4116yescomplemented
138#123×C37C2×C4116yescomplemented
139C22⋊Q8×C37C2×C4116yescomplemented
140C22⋊Q8×C37C2×C418yescomplemented
141#121×C37C2×C418yes—
142C4×Q8×C37—44no—
143C4×Q8×C37—42no—
144C4×Q8×C37—42no—
145C4×Q8×C37C2×C418yescomplemented
146C4×D4×C37—42no—
147C4×D4×C37—42no—
148C4×D4×C37—44no—
149C4×D4×C37C2×C418yescomplemented
150#117×C37—42no—
151#117×C37C2×C418yescomplemented
152C2×C4⋊C4×C37—44no—
153C2×C4⋊C4×C37C2311yescharacteristic
154C2×C4⋊C4×C37C2311yescharacteristic
155C2×C4⋊C4×C37C2311yescharacteristic
156C2×C4⋊C4×C37C2311yescharacteristic
157C2×C4⋊C4×C37C2311yescharacteristic
158C2×C4⋊C4×C37C2311yescharacteristic
159C2×C4⋊C4×C37C2311yescharacteristic
160C2×C4⋊C4×C37C2312yes—
161C2×C4⋊C4×C37C2311yescharacteristic
162C2×C4⋊C4×C37C2311yescharacteristic
163C2×C4⋊C4×C37C2312yes—
164C2×C4⋊C4×C37C2311yescharacteristic
165C2×C4⋊C4×C37C2311yescharacteristic
166C2×C4⋊C4×C37C2311yescharacteristic
167C2×C4⋊C4×C37C2312yes—
168C2×C4⋊C4×C37C2312yes—
169C2×C4⋊C4×C37C2312yes—
170C2×C4⋊C4×C37C2312yes—
171C2×C4⋊C4×C37C2312yes—
172C2×C4⋊C4×C37C2311yescharacteristic
173C2×C4⋊C4×C37C2312yes—
174C2×C4⋊C4×C37C2311yescharacteristic
175C2×C4⋊C4×C37C2311yescharacteristic
176C2×C4⋊C4×C37C2312yes—
177C2×C4⋊C4×C37C2311yescharacteristic
178C2×C4⋊C4×C37C2312yes—
179C2×C4⋊C4×C37C2311yescharacteristic
180C2×C4⋊C4×C37C2312yes—
181C2×C4⋊C4×C37C2311yescharacteristic
182C2×C22⋊C4×C37C2312yes—
183C2×C22⋊C4×C37C2312yes—
184C2×C22⋊C4×C37C2312yes—
185C2×C22⋊C4×C37C2312yes—
186C2×C22⋊C4×C37C2312yes—
187C2×C22⋊C4×C37C2312yes—
188C2×C22⋊C4×C37C2312yes—
189C2×C22⋊C4×C37C2312yes—
190C2×C22⋊C4×C37C2311yescharacteristic
191C2×C22⋊C4×C37C2311yescharacteristic
192C2×C22⋊C4×C37C2312yes—
193C2×C22⋊C4×C37C2312yes—
194C2×C22⋊C4×C37C2312yes—
195C2×C22⋊C4×C37C2311yescharacteristic
196C2×C22⋊C4×C37C2312yes—
197C2×C22⋊C4×C37C2311yescharacteristic
198C2×C22⋊C4×C37C2312yes—
199C2×C42×C37—42no—
200C2×C42×C37C2312yes—
201C2×C42×C37C2311yescharacteristic
202C2×C42×C37C2311yescharacteristic
203C2×C42×C37C2311yescharacteristic
204C2×C42×C37C2311yescharacteristic
205C2×C42×C37C2312yes—
206C2×C42×C37C2312yes—
207C2×C42×C37C2312yes—
208C2×C42×C37C2311yescharacteristic
209C2×C42×C37C2312yes—
210C2×C42×C37C2312yes—
211C2×C42×C37C2312yes—
212C2×C42×C37C2312yes—
213C2×C42×C37C2311yescharacteristic
214C2×C42×C37C2312yes—
215C2×C42×C37C2311yescharacteristic
216C2×C42×C37C2311yescharacteristic
217#95×C37C2311yescharacteristic
218#95×C37C2312yes—
219#95×C37C2312yes—
220#95×C37C2312yes—
221#95×C37C2311yescharacteristic
222#95×C37C2311yescharacteristic
223#95×C37C2311yescharacteristic
224#95×C37C2312yes—
225#95×C37C2312yes—
226#95×C37C2312yes—
227#95×C37C2312yes—
228#95×C37C2312yes—
229#95×C37C2312yes—
230#95×C37C2312yes—
231#95×C37C2312yes—
232#95×C37C2311yescharacteristic
233#95×C37C2312yes—
234#95×C37C2312yes—
235#95×C37C2311yescharacteristic
236#95×C37C2312yes—
237#95×C37C2312yes—
238#95×C37C2312yes—
239#95×C37C2311yescharacteristic
240#95×C37C2312yes—
241#95×C37C2311yescharacteristic
242#95×C37C2312yes—
243C24×C37C2411yescharacteristic
244C24×C37C2412yes—
245C2×Q8×C37—22no—
246C2×Q8×C37—22no—
247C2×Q8×C37—42no—
248C2×Q8×C37—42no—
249C2×Q8×C37C22×C414yes—
250C2×Q8×C37C22×C418yes—
251C2×D4×C37—22no—
252C2×D4×C37—22no—
253C2×D4×C37—42no—
254C2×D4×C37—42no—
255C2×D4×C37C22×C414yes—
256C2×D4×C37C22×C418yes—
257C22×C4×C37—22no—
258C22×C4×C37—22no—
259C22×C4×C37—22no—
260C22×C4×C37—22no—
261C22×C4×C37—24no—
262C22×C4×C37—41no—
263C22×C4×C37—41no—
264C22×C4×C37—42no—
265C22×C4×C37—41no—
266C22×C4×C37—42no—
267C22×C4×C37—41no—
268C22×C4×C37—42no—
269C22×C4×C37—42no—
270C22×C4×C37—42no—
271C22×C4×C37—42no—
272C22×C4×C37—42no—
273C22×C4×C37C22×C414yes—
274C22×C4×C37C22×C418yes—
275C22×C4×C37C2412yes—
276C22×C4×C37C2412yes—
277C22×C4×C37C2411yescharacteristic
278C22×C4×C37C2411yescharacteristic
279C22×C4×C37C2411yescharacteristic
280C22×C4×C37C2411yescharacteristic
281C22×C4×C37C2411yescharacteristic
282C22×C4×C37C2412yes—
283C22×C4×C37C2412yes—
284C22×C4×C37C2411yescharacteristic
285C22×C4×C37C2411yescharacteristic
286C22×C4×C37C2411yescharacteristic
287C22×C4×C37C2412yes—
288C22×C4×C37C2411yescharacteristic
289C22×C4×C37C2412yes—
290C22×C4×C37C2411yescharacteristic
291C22×C4×C37C2412yes—
292C22×C4×C37C2411yescharacteristic
293C22×C4×C37C2411yescharacteristic
294C22×C4×C37C2411yescharacteristic
295C22×C4×C37C2411yescharacteristic
296C4⋊C4×C37—22no—
297C4⋊C4×C37—24no—
298C4⋊C4×C37—22no—
299C4⋊C4×C37—22no—
300C4⋊C4×C37—22no—
301C4⋊C4×C37—22no—
302C4⋊C4×C37—22no—
303C4⋊C4×C37—22no—
304C4⋊C4×C37—22no—
305C4⋊C4×C37—42no—
306C4⋊C4×C37—42no—
307C4⋊C4×C37—41no—
308C4⋊C4×C37—42no—
309C4⋊C4×C37—41no—
310C4⋊C4×C37—41no—
311C4⋊C4×C37—41no—
312C4⋊C4×C37—41no—
313C4⋊C4×C37—41no—
314C4⋊C4×C37—42no—
315C4⋊C4×C37—42no—
316C4⋊C4×C37—42no—
317C4⋊C4×C37—42no—
318C4⋊C4×C37C22×C414yes—
319C4⋊C4×C37C22×C414yes—
320C4⋊C4×C37C22×C414yes—
321C4⋊C4×C37C22×C414yes—
322C4⋊C4×C37C22×C418yes—
323C4⋊C4×C37C22×C418yes—
324C4⋊C4×C37C22×C418yes—
325C22⋊C4×C37—24no—
326C22⋊C4×C37—42no—
327C22⋊C4×C37—42no—
328C22⋊C4×C37—42no—
329C22⋊C4×C37—41no—
330C22⋊C4×C37—41no—
331C22⋊C4×C37—42no—
332C22⋊C4×C37—42no—
333C22⋊C4×C37—42no—
334C22⋊C4×C37—42no—
335C22⋊C4×C37C22×C414yes—
336C22⋊C4×C37C22×C414yes—
337C22⋊C4×C37C22×C418yes—
338C22⋊C4×C37C22×C418yes—
339C22⋊C4×C37C22×C418yes—
340C22⋊C4×C37C22×C418yes—
341C22⋊C4×C37C22×C418yes—
342C42×C37—22no—
343C42×C37—22no—
344C42×C37—22no—
345C42×C37—22no—
346C42×C37—24no—
347C42×C37—41no—
348C42×C37—41no—
349C42×C37—42no—
350C42×C37—42no—
351C42×C37—42no—
352C42×C37—42no—
353C42×C37—42no—
354C42×C37—42no—
355C42×C37—42no—
356C42×C37C22×C414yes—
357C42×C37C22×C414yes—
358C42×C37C22×C418yes—
359C23×C37—21no—
360C23×C37—21no—
361C23×C37—22no—
362C23×C37—22no—
363C23×C37—22no—
364C23×C37—21no—
365C23×C37—21no—
366C23×C37—22no—
367C23×C37—21no—
368C23×C37—22no—
369C23×C37—22no—
370C23×C37—21no—
371C23×C37C23×C412yes—
372C23×C37C23×C414yes—
373C23×C37C2511yescharacteristic
374Q8×C37—28no—
375Q8×C37—48no—
376D4×C37—28no—
377D4×C37—48no—
378C2×C4×C37—21no—
379C2×C4×C37—21no—
380C2×C4×C37—22no—
381C2×C4×C37—21no—
382C2×C4×C37—21no—
383C2×C4×C37—22no—
384C2×C4×C37—22no—
385C2×C4×C37—21no—
386C2×C4×C37—21no—
387C2×C4×C37—21no—
388C2×C4×C37—21no—
389C2×C4×C37—22no—
390C2×C4×C37—21no—
391C2×C4×C37—21no—
392C2×C4×C37—22no—
393C2×C4×C37—22no—
394C2×C4×C37—21no—
395C2×C4×C37—21no—
396C2×C4×C37—21no—
397C2×C4×C37—21no—
398C2×C4×C37—28no—
399C2×C4×C37—22no—
400C2×C4×C37—21no—
401C2×C4×C37—21no—
402C2×C4×C37—21no—
403C2×C4×C37—21no—
404C2×C4×C37—21no—
405C2×C4×C37—21no—
406C2×C4×C37—21no—
407C2×C4×C37—22no—
408C2×C4×C37—22no—
409C2×C4×C37—22no—
410C2×C4×C37—21no—
411C2×C4×C37—22no—
412C2×C4×C37—21no—
413C2×C4×C37—22no—
414C2×C4×C37—21no—
415C2×C4×C37—21no—
416C2×C4×C37—22no—
417C2×C4×C37—22no—
418C2×C4×C37—21no—
419C2×C4×C37—22no—
420C2×C4×C37—21no—
421C2×C4×C37—22no—
422C2×C4×C37—22no—
423C2×C4×C37—21no—
424C2×C4×C37—21no—
425C2×C4×C37—22no—
426C2×C4×C37—21no—
427C2×C4×C37—21no—
428C2×C4×C37—21no—
429C2×C4×C37—48no—
430C2×C4×C37—44no—
431C2×C4×C37—44no—
432C2×C4×C37—84no—
433C2×C4×C37—84no—
434C2×C4×C37C23×C412yes—
435C2×C4×C37C23×C412yes—
436C2×C4×C37C23×C414yes—
437C2×C4×C37C23×C412yes—
438C2×C4×C37C23×C412yes—
439C2×C4×C37C23×C414yes—
440C2×C4×C37C23×C412yes—
441C2×C4×C37C23×C414yes—
442C2×C4×C37C23×C412yes—
443C2×C4×C37H(5,𝔽2)12yes—
444C2×C4×C37H(5,𝔽2)12yes—
445C2×C4×C372−1+412yes—
446C2×C4×C372−1+412yes—
447#34422C3711yesmaximal, characteristic, direct product factor, Sylow
448C22×C37—22no—
449C22×C37—24no—
450C22×C37—24no—
451C22×C37—22no—
452C22×C37—24no—
453C22×C37—22no—
454C22×C37—41no—
455C22×C37—42no—
456C22×C37—41no—
457C22×C37—42no—
458C22×C37—41no—
459C22×C37—42no—
460C22×C37—41no—
461C22×C37—42no—
462C22×C37C24×C411yescharacteristic
463C22×C37C2×H(5,𝔽2)11yescharacteristic
464C22×C37C2×H(5,𝔽2)11yescharacteristic
465C22×C37C2×2−1+411yescharacteristic
466C22×C37C2×2−1+411yescharacteristic
467C22×C37#58511yescharacteristic
468C22×C37#58511yescharacteristic
469C4×C37—22no—
470C4×C37—24no—
471C4×C37—22no—
472C4×C37—24no—
473C4×C37—24no—
474C4×C37—22no—
475C4×C37—22no—
476C4×C37—22no—
477C4×C37—22no—
478C4×C37—22no—
479C4×C37—41no—
480C4×C37—41no—
481C4×C37—41no—
482C4×C37—41no—
483C4×C37—41no—
484C4×C37—42no—
485C4×C37—42no—
486C4×C37—41no—
487C4×C37—42no—
488C4×C37—42no—
489C4×C37#52014yes—
490C2×#542C2×C3711yescharacteristic
491#2383C2×C3712yescomplemented
492#2378C2×C3712yescomplemented
493#2373C2×C3712yescomplemented
494#2369C2×C3711yescharacteristic, complemented
495#2367C2×C3711yescharacteristic, complemented
496#2367C2×C3711yescharacteristic, complemented
497#2365C2×C3711yescharacteristic, complemented
498#2360C2×C3712yescomplemented
499#2357C2×C3711yescharacteristic, complemented
500#2356C2×C3711yescharacteristic, complemented
501Q8×C4⋊C4C2×C3711yescharacteristic, complemented
502D4×C4⋊C4C2×C3711yescharacteristic, complemented
503#2337C2×C3712yescomplemented
504#2335C2×C3712yescomplemented
505#2326C2×C3712yescomplemented
506#2324C2×C3711yescharacteristic
507#2323C2×C3711yescharacteristic, complemented
508#2322C2×C3712yescomplemented
509#2314C2×C3711yescharacteristic, complemented
510C4×C22⋊Q8C2×C3711yescharacteristic, complemented
511C4×#121C2×C3711yescharacteristic
512#2296C2×C3711yescharacteristic, complemented
513C2×C37—42no—
514C2×C37—44no—
515C2×C37C2×#52011yescharacteristic
516C2×C37C4×H(5,𝔽2)11yescharacteristic
517C2×C37C4×2−1+411yescharacteristic
518C2×C37#354111yescharacteristic
519C2×C37#354211yescharacteristic
520C2×C37#355011yescharacteristic
521C2×C37#355711yescharacteristic
522#542C4×C37116yescomplemented
523C2×C4⋊Q8C22×C3711yescharacteristic
524C2×#126C22×C3712yes—
525C2×#124C22×C3712yes—
526C2×#124C22×C3711yescharacteristic
527C2×#123C22×C3712yes—
528C2×C22⋊Q8C22×C3711yescharacteristic
529C2×C22⋊Q8C22×C3712yes—
530C2×#121C22×C3711yescharacteristic
531C2×C4×Q8C22×C3711yescharacteristic
532C2×C4×Q8C22×C3712yes—
533C2×C4×Q8C22×C3711yescharacteristic
534C2×C4×Q8C22×C3711yescharacteristic
535C2×C4×D4C22×C3712yes—
536C2×C4×D4C22×C3711yescharacteristic
537C2×C4×D4C22×C3711yescharacteristic
538C2×C4×D4C22×C3711yescharacteristic
539C2×#117C22×C3711yescharacteristic
540C2×#117C22×C3711yescharacteristic
541C22×C4⋊C4C22×C3712yes—
542C22×C42C22×C3711yescharacteristic
543#391C22×C3711yescharacteristic
544#391C22×C3712yes—
545#391C22×C3712yes—
546#391C22×C3712yes—
547#391C22×C3711yescharacteristic
548#390C22×C3712yes—
549#390C22×C3711yescharacteristic
550#390C22×C3711yescharacteristic
551#389C22×C3712yes—
552#389C22×C3712yes—
553#389C22×C3711yescharacteristic
554#389C22×C3712yes—
555#389C22×C3711yescharacteristic
556#389C22×C3712yes—
557#389C22×C3711yescharacteristic
558#389C22×C3711yescharacteristic
559#389C22×C3711yescharacteristic
560#389C22×C3711yescharacteristic
561#389C22×C3711yescharacteristic
562#389C22×C3711yescharacteristic
563#388C22×C3712yes—
564#388C22×C3712yes—
565#388C22×C3712yes—
566#388C22×C3712yes—
567#388C22×C3712yes—
568#388C22×C3712yes—
569#388C22×C3712yes—
570#388C22×C3712yes—
571#388C22×C3712yes—
572#388C22×C3712yes—
573#388C22×C3712yes—
574#388C22×C3712yes—
575#387C22×C3712yes—
576#387C22×C3712yes—
577#387C22×C3712yes—
578#387C22×C3712yes—
579#387C22×C3712yes—
580#387C22×C3712yes—
581#387C22×C3712yes—
582#387C22×C3712yes—
583#386C22×C3712yes—
584#386C22×C3712yes—
585#385C22×C3711yescharacteristic
586#385C22×C3712yes—
587#385C22×C3712yes—
588#385C22×C3712yes—
589#385C22×C3711yescharacteristic
590#385C22×C3712yes—
591#385C22×C3712yes—
592#385C22×C3711yescharacteristic
593#385C22×C3711yescharacteristic
594#385C22×C3712yes—
595#384C22×C3711yescharacteristic
596#384C22×C3712yes—
597#383C22×C3712yes—
598#382C22×C3711yescharacteristic
599#381C22×C3712yes—
600#380C22×C3711yescharacteristic
601#380C22×C3711yescharacteristic
602#380C22×C3712yes—
603C4×C4⋊C4C22×C3711yescharacteristic
604C4×C4⋊C4C22×C3711yescharacteristic
605C4×C4⋊C4C22×C3711yescharacteristic
606C4×C4⋊C4C22×C3711yescharacteristic
607C4×C4⋊C4C22×C3712yes—
608C4×C4⋊C4C22×C3712yes—
609C4×C4⋊C4C22×C3711yescharacteristic
610C4×C4⋊C4C22×C3711yescharacteristic
611C4×C4⋊C4C22×C3711yescharacteristic
612C4×C4⋊C4C22×C3711yescharacteristic
613C4×C4⋊C4C22×C3712yes—
614C4×C4⋊C4C22×C3711yescharacteristic
615C4×C4⋊C4C22×C3711yescharacteristic
616C4×C22⋊C4C22×C3712yes—
617C4×C22⋊C4C22×C3712yes—
618C4×C22⋊C4C22×C3712yes—
619C4×C22⋊C4C22×C3712yes—
620C4×C22⋊C4C22×C3712yes—
621#376C22×C3712yes—
622C37#3442211yescharacteristic, direct product factor, Sylow
623C22×Q8C23×C3711yescharacteristic
624C22×Q8C23×C3712yes—
625C22×D4C23×C3711yescharacteristic
626C22×D4C23×C3712yes—
627C23×C4C23×C3711yescharacteristic
628C23×C4C23×C3712yes—
629C23×C4C23×C3711yescharacteristic
630C23×C4C23×C3711yescharacteristic
631C23×C4C23×C3712yes—
632C23×C4C23×C3712yes—
633C4⋊Q8C2×C4×C3718yescomplemented
634#126C2×C4×C37116yescomplemented
635#124C2×C4×C3718yescomplemented
636#124C2×C4×C37116yescomplemented
637#123C2×C4×C37116yescomplemented
638C22⋊Q8C2×C4×C37116yescomplemented
639C22⋊Q8C2×C4×C3718yescomplemented
640#121C2×C4×C3718yes—
641C4×Q8—44no—
642C4×Q8—42no—
643C4×Q8—42no—
644C4×Q8C2×C4×C3718yescomplemented
645C4×D4—42no—
646C4×D4—42no—
647C4×D4—44no—
648C4×D4C2×C4×C3718yescomplemented
649#117—42no—
650#117C2×C4×C3718yescomplemented
651C2×C4⋊C4—44no—
652C2×C4⋊C4C23×C3711yescharacteristic
653C2×C4⋊C4C23×C3712yes—
654C2×C4⋊C4C23×C3711yescharacteristic
655C2×C4⋊C4C23×C3711yescharacteristic
656C2×C4⋊C4C23×C3711yescharacteristic
657C2×C4⋊C4C23×C3711yescharacteristic
658C2×C4⋊C4C23×C3711yescharacteristic
659C2×C4⋊C4C23×C3711yescharacteristic
660C2×C4⋊C4C23×C3711yescharacteristic
661C2×C4⋊C4C23×C3712yes—
662C2×C4⋊C4C23×C3712yes—
663C2×C4⋊C4C23×C3711yescharacteristic
664C2×C4⋊C4C23×C3711yescharacteristic
665C2×C4⋊C4C23×C3712yes—
666C2×C4⋊C4C23×C3712yes—
667C2×C4⋊C4C23×C3712yes—
668C2×C4⋊C4C23×C3712yes—
669C2×C4⋊C4C23×C3711yescharacteristic
670C2×C4⋊C4C23×C3712yes—
671C2×C4⋊C4C23×C3711yescharacteristic
672C2×C4⋊C4C23×C3711yescharacteristic
673C2×C4⋊C4C23×C3711yescharacteristic
674C2×C4⋊C4C23×C3711yescharacteristic
675C2×C4⋊C4C23×C3711yescharacteristic
676C2×C4⋊C4C23×C3711yescharacteristic
677C2×C4⋊C4C23×C3711yescharacteristic
678C2×C4⋊C4C23×C3712yes—
679C2×C4⋊C4C23×C3712yes—
680C2×C4⋊C4C23×C3712yes—
681C2×C22⋊C4C23×C3712yes—
682C2×C22⋊C4C23×C3711yescharacteristic
683C2×C22⋊C4C23×C3711yescharacteristic
684C2×C22⋊C4C23×C3712yes—
685C2×C22⋊C4C23×C3712yes—
686C2×C22⋊C4C23×C3712yes—
687C2×C22⋊C4C23×C3712yes—
688C2×C22⋊C4C23×C3712yes—
689C2×C22⋊C4C23×C3712yes—
690C2×C22⋊C4C23×C3712yes—
691C2×C22⋊C4C23×C3711yescharacteristic
692C2×C22⋊C4C23×C3711yescharacteristic
693C2×C22⋊C4C23×C3712yes—
694C2×C22⋊C4C23×C3712yes—
695C2×C22⋊C4C23×C3712yes—
696C2×C22⋊C4C23×C3712yes—
697C2×C22⋊C4C23×C3712yes—
698C2×C42—42no—
699C2×C42C23×C3711yescharacteristic
700C2×C42C23×C3711yescharacteristic
701C2×C42C23×C3712yes—
702C2×C42C23×C3711yescharacteristic
703C2×C42C23×C3711yescharacteristic
704C2×C42C23×C3712yes—
705C2×C42C23×C3712yes—
706C2×C42C23×C3712yes—
707C2×C42C23×C3712yes—
708C2×C42C23×C3712yes—
709C2×C42C23×C3712yes—
710C2×C42C23×C3711yescharacteristic
711C2×C42C23×C3712yes—
712C2×C42C23×C3711yescharacteristic
713C2×C42C23×C3711yescharacteristic
714C2×C42C23×C3711yescharacteristic
715C2×C42C23×C3712yes—
716#95C23×C3711yescharacteristic
717#95C23×C3712yes—
718#95C23×C3712yes—
719#95C23×C3712yes—
720#95C23×C3711yescharacteristic
721#95C23×C3711yescharacteristic
722#95C23×C3711yescharacteristic
723#95C23×C3712yes—
724#95C23×C3712yes—
725#95C23×C3712yes—
726#95C23×C3712yes—
727#95C23×C3712yes—
728#95C23×C3712yes—
729#95C23×C3712yes—
730#95C23×C3712yes—
731#95C23×C3711yescharacteristic
732#95C23×C3712yes—
733#95C23×C3712yes—
734#95C23×C3711yescharacteristic
735#95C23×C3712yes—
736#95C23×C3712yes—
737#95C23×C3712yes—
738#95C23×C3711yescharacteristic
739#95C23×C3712yes—
740#95C23×C3711yescharacteristic
741#95C23×C3712yes—
742C24C24×C3711yescharacteristic
743C24C24×C3712yes—
744C2×Q8—22no—
745C2×Q8—22no—
746C2×Q8—42no—
747C2×Q8—42no—
748C2×Q8C22×C4×C3714yes—
749C2×Q8C22×C4×C3718yes—
750C2×D4—22no—
751C2×D4—22no—
752C2×D4—42no—
753C2×D4—42no—
754C2×D4C22×C4×C3714yes—
755C2×D4C22×C4×C3718yes—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—24no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—42no—
764C22×C4—41no—
765C22×C4—42no—
766C22×C4—41no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4C22×C4×C3714yes—
773C22×C4C22×C4×C3718yes—
774C22×C4C24×C3712yes—
775C22×C4C24×C3712yes—
776C22×C4C24×C3711yescharacteristic
777C22×C4C24×C3711yescharacteristic
778C22×C4C24×C3711yescharacteristic
779C22×C4C24×C3711yescharacteristic
780C22×C4C24×C3711yescharacteristic
781C22×C4C24×C3712yes—
782C22×C4C24×C3712yes—
783C22×C4C24×C3711yescharacteristic
784C22×C4C24×C3711yescharacteristic
785C22×C4C24×C3711yescharacteristic
786C22×C4C24×C3712yes—
787C22×C4C24×C3711yescharacteristic
788C22×C4C24×C3712yes—
789C22×C4C24×C3711yescharacteristic
790C22×C4C24×C3712yes—
791C22×C4C24×C3711yescharacteristic
792C22×C4C24×C3711yescharacteristic
793C22×C4C24×C3711yescharacteristic
794C22×C4C24×C3711yescharacteristic
795C4⋊C4—22no—
796C4⋊C4—24no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—42no—
805C4⋊C4—42no—
806C4⋊C4—41no—
807C4⋊C4—42no—
808C4⋊C4—41no—
809C4⋊C4—41no—
810C4⋊C4—41no—
811C4⋊C4—41no—
812C4⋊C4—41no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4C22×C4×C3714yes—
818C4⋊C4C22×C4×C3714yes—
819C4⋊C4C22×C4×C3714yes—
820C4⋊C4C22×C4×C3714yes—
821C4⋊C4C22×C4×C3718yes—
822C4⋊C4C22×C4×C3718yes—
823C4⋊C4C22×C4×C3718yes—
824C22⋊C4—24no—
825C22⋊C4—42no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—41no—
829C22⋊C4—41no—
830C22⋊C4—42no—
831C22⋊C4—42no—
832C22⋊C4—42no—
833C22⋊C4—42no—
834C22⋊C4C22×C4×C3714yes—
835C22⋊C4C22×C4×C3714yes—
836C22⋊C4C22×C4×C3718yes—
837C22⋊C4C22×C4×C3718yes—
838C22⋊C4C22×C4×C3718yes—
839C22⋊C4C22×C4×C3718yes—
840C22⋊C4C22×C4×C3718yes—
841C42—22no—
842C42—22no—
843C42—22no—
844C42—22no—
845C42—24no—
846C42—41no—
847C42—41no—
848C42—42no—
849C42—42no—
850C42—42no—
851C42—42no—
852C42—42no—
853C42—42no—
854C42—42no—
855C42C22×C4×C3714yes—
856C42C22×C4×C3714yes—
857C42C22×C4×C3718yes—
858C23—21no—
859C23—21no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—21no—
864C23—21no—
865C23—22no—
866C23—21no—
867C23—22no—
868C23—22no—
869C23—21no—
870C23C23×C4×C3712yes—
871C23C23×C4×C3714yes—
872C23C25×C3711yescharacteristic
873Q8—28no—
874Q8—48no—
875D4—28no—
876D4—48no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—28no—
898C2×C4—22no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—48no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—84no—
932C2×C4—84no—
933C2×C4C23×C4×C3712yes—
934C2×C4C23×C4×C3712yes—
935C2×C4C23×C4×C3714yes—
936C2×C4C23×C4×C3712yes—
937C2×C4C23×C4×C3712yes—
938C2×C4C23×C4×C3714yes—
939C2×C4C23×C4×C3712yes—
940C2×C4C23×C4×C3714yes—
941C2×C4C23×C4×C3712yes—
942C2×C4H(5,𝔽2)×C3712yes—
943C2×C4H(5,𝔽2)×C3712yes—
944C2×C42−1+4×C3712yes—
945C2×C42−1+4×C3712yes—
946C22—22no—
947C22—24no—
948C22—24no—
949C22—22no—
950C22—24no—
951C22—22no—
952C22—41no—
953C22—42no—
954C22—41no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—41no—
959C22—42no—
960C22C24×C4×C3711yescharacteristic
961C22C2×H(5,𝔽2)×C3711yescharacteristic
962C22C2×H(5,𝔽2)×C3711yescharacteristic
963C22C2×2−1+4×C3711yescharacteristic
964C22C2×2−1+4×C3711yescharacteristic
965C22C37×#58511yescharacteristic
966C22C37×#58511yescharacteristic
967C4—22no—
968C4—24no—
969C4—22no—
970C4—24no—
971C4—24no—
972C4—22no—
973C4—22no—
974C4—22no—
975C4—22no—
976C4—22no—
977C4—41no—
978C4—41no—
979C4—41no—
980C4—41no—
981C4—41no—
982C4—42no—
983C4—42no—
984C4—41no—
985C4—42no—
986C4—42no—
987C4C37×#52014yes—
988C2—42no—
989C2—44no—
990C2C2×C37×#52011yescharacteristic
991C2C4×H(5,𝔽2)×C3711yescharacteristic
992C2C4×2−1+4×C3711yescharacteristic
993C2C37×#354111yescharacteristic
994C2C37×#354211yescharacteristic
995C2C37×#355011yescharacteristic
996C2C37×#355711yescharacteristic
subgroupG/H
center, socleC23×C37C25
commutatorC22C24×C4×C37
Frattini, cosocleC23C25×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2383C2semidirect
3. C37×#2378C2semidirect
4. C37×#2373C2semidirect
5. C37×#2369C2semidirect
6. C37×#2367C2semidirect
7. C37×#2367C2semidirect
8. C37×#2365C2semidirect
9. C37×#2360C2semidirect
10. C37×#2357C2semidirect
11. C37×#2356C2semidirect
12. Q8×C4⋊C4×C37C2semidirect
13. D4×C4⋊C4×C37C2semidirect
14. C37×#2337C2semidirect
15. C37×#2335C2semidirect
16. C37×#2326C2semidirect
18. C37×#2323C2semidirect
19. C37×#2322C2semidirect
20. C37×#2314C2semidirect
21. C4×C22⋊Q8×C37C2semidirect
23. C37×#2296C2semidirect
24. C37×#542C4semidirect
134. C4⋊Q8×C37C2×C4semidirect
135. #126×C37C2×C4semidirect
136. #124×C37C2×C4semidirect
137. #124×C37C2×C4semidirect
138. #123×C37C2×C4semidirect
139. C22⋊Q8×C37C2×C4semidirect
140. C22⋊Q8×C37C2×C4semidirect
145. C4×Q8×C37C2×C4semidirect
149. C4×D4×C37C2×C4semidirect
151. #117×C37C2×C4semidirect
447. #34422C37direct (N × H)
491. #2383C2×C37semidirect
492. #2378C2×C37semidirect
493. #2373C2×C37semidirect
494. #2369C2×C37semidirect
495. #2367C2×C37semidirect
496. #2367C2×C37semidirect
497. #2365C2×C37semidirect
498. #2360C2×C37semidirect
499. #2357C2×C37semidirect
500. #2356C2×C37semidirect
501. Q8×C4⋊C4C2×C37semidirect
502. D4×C4⋊C4C2×C37semidirect
503. #2337C2×C37semidirect
504. #2335C2×C37semidirect
505. #2326C2×C37semidirect
507. #2323C2×C37semidirect
508. #2322C2×C37semidirect
509. #2314C2×C37semidirect
510. C4×C22⋊Q8C2×C37semidirect
512. #2296C2×C37semidirect
522. #542C4×C37semidirect
622. C37#34422direct (N × H)
633. C4⋊Q8C2×C4×C37semidirect
634. #126C2×C4×C37semidirect
635. #124C2×C4×C37semidirect
636. #124C2×C4×C37semidirect
637. #123C2×C4×C37semidirect
638. C22⋊Q8C2×C4×C37semidirect
639. C22⋊Q8C2×C4×C37semidirect
644. C4×Q8C2×C4×C37semidirect
648. C4×D4C2×C4×C37semidirect
650. #117C2×C4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5422
C37×#23832
C37×#23782
C37×#23732
C37×#23692
C37×#23672
C37×#23652
C37×#23602
C37×#23572
C37×#23562
Q8×C4⋊C4×C372
D4×C4⋊C4×C372
C37×#23372
C37×#23352
C37×#23262
C37×#23242
C37×#23232
C37×#23222
C37×#23142
C4×C22⋊Q8×C372
C4×#121×C372
C37×#22962
#3442237