Finite Group Databasebeta

← C37×#14017 #22635270

Subgroups — C37×#14017 #22635270

Order 9472.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C37C211yesmaximal, characteristic
2C2×C37×#391C211yesmaximal, characteristic
3C2×C37×#391C211yesmaximal, characteristic
4C2×C37×#389C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C37C211yesmaximal, characteristic
6C37×#1444C212yesmaximal
7C37×#1442C212yesmaximal
8C37×#1436C212yesmaximal
9C37×#1436C212yesmaximal
10C37×C4⋊#95C211yesmaximal, characteristic
11C37×C4⋊#95C211yesmaximal, characteristic
12C23×Q8×C37C2211yescharacteristic
13C2×C4×Q8×C37—24no—
14C2×C4×Q8×C37—24no—
15C2×C4×Q8×C37—24no—
16C22×C4⋊C4×C37C2212yes—
17C22×C4⋊C4×C37C2211yescharacteristic
18C22×C4⋊C4×C37C2211yescharacteristic
19C22×C4⋊C4×C37C2212yes—
20C22×C4⋊C4×C37C2211yescharacteristic
21C22×C4⋊C4×C37C2211yescharacteristic
22C22×C4⋊C4×C37C2211yescharacteristic
23C22×C42×C37C2212yes—
24C22×C42×C37C2211yescharacteristic
25C22×C42×C37C2211yescharacteristic
26C22×C42×C37C2211yescharacteristic
27C37×#391—24no—
28C37×#391C418yescomplemented
29C37×#389—24no—
30C4×C4⋊C4×C37—24no—
31C2×#95×C37C2212yes—
32C2×#95×C37C2212yes—
33C2×#95×C37C2211yescharacteristic
34C2×#95×C37C2212yes—
35C2×#95×C37C2212yes—
36C2×#95×C37C2212yes—
37C2×#95×C37C2211yescharacteristic
38C2×#95×C37C2212yes—
39C2×#95×C37C2212yes—
40C2×#95×C37C2212yes—
41C2×#95×C37C2212yes—
42C22×Q8×C37—22no—
43C22×Q8×C37—22no—
44C22×Q8×C37—22no—
45C22×Q8×C37—22no—
46C22×Q8×C37C2×C414yes—
47C22×Q8×C37D414yes—
48C22×Q8×C37Q814yes—
49C23×C4×C37C2312yes—
50C23×C4×C37C2311yescharacteristic
51C23×C4×C37C2312yes—
52C23×C4×C37C2312yes—
53C23×C4×C37C2311yescharacteristic
54C23×C4×C37C2311yescharacteristic
55C23×C4×C37C2311yescharacteristic
56C23×C4×C37C2312yes—
57C23×C4×C37C2311yescharacteristic
58C23×C4×C37C2311yescharacteristic
59C23×C4×C37C2311yescharacteristic
60C4×Q8×C37—232no—
61C2×C4⋊C4×C37—22no—
62C2×C4⋊C4×C37—22no—
63C2×C4⋊C4×C37—22no—
64C2×C4⋊C4×C37—24no—
65C2×C4⋊C4×C37—24no—
66C2×C4⋊C4×C37—24no—
67C2×C4⋊C4×C37—22no—
68C2×C4⋊C4×C37—22no—
69C2×C4⋊C4×C37—22no—
70C2×C4⋊C4×C37—22no—
71C2×C4⋊C4×C37—22no—
72C2×C4⋊C4×C37—22no—
73C2×C4⋊C4×C37—24no—
74C2×C4⋊C4×C37—22no—
75C2×C4⋊C4×C37—24no—
76C2×C4⋊C4×C37—22no—
77C2×C4⋊C4×C37—22no—
78C2×C4⋊C4×C37—42no—
79C2×C4⋊C4×C37C2×C414yes—
80C2×C4⋊C4×C37D414yes—
81C2×C4⋊C4×C37Q814yescomplemented
82C2×C42×C37—22no—
83C2×C42×C37—24no—
84C2×C42×C37—24no—
85C2×C42×C37—24no—
86C2×C42×C37—22no—
87C2×C42×C37—22no—
88C2×C42×C37—22no—
89C2×C42×C37—22no—
90C2×C42×C37—22no—
91C2×C42×C37—22no—
92C2×C42×C37C2×C414yes—
93C2×C42×C37D414yes—
94#95×C37—22no—
95#95×C37—22no—
96#95×C37—24no—
97#95×C37—24no—
98#95×C37—24no—
99#95×C37—24no—
100#95×C37—24no—
101#95×C37—42no—
102#95×C37—42no—
103#95×C37C2×C418yes—
104#95×C37C2×C418yes—
105C24×C37C2411yescharacteristic
106C2×Q8×C37—28no—
107C2×Q8×C37—28no—
108C2×Q8×C37—28no—
109C2×Q8×C37—28no—
110C2×Q8×C37—28no—
111C2×Q8×C37—28no—
112C2×Q8×C37C4⋊C4116yescomplemented
113C22×C4×C37—21no—
114C22×C4×C37—21no—
115C22×C4×C37—21no—
116C22×C4×C37—22no—
117C22×C4×C37—22no—
118C22×C4×C37—21no—
119C22×C4×C37—21no—
120C22×C4×C37—21no—
121C22×C4×C37—22no—
122C22×C4×C37—22no—
123C22×C4×C37—21no—
124C22×C4×C37—21no—
125C22×C4×C37—21no—
126C22×C4×C37—21no—
127C22×C4×C37—21no—
128C22×C4×C37—21no—
129C22×C4×C37—21no—
130C22×C4×C37—21no—
131C22×C4×C37—22no—
132C22×C4×C37—22no—
133C22×C4×C37—21no—
134C22×C4×C37—22no—
135C22×C4×C37—21no—
136C22×C4×C37—21no—
137C22×C4×C37—22no—
138C22×C4×C37—22no—
139C22×C4×C37—21no—
140C22×C4×C37—22no—
141C22×C4×C37—22no—
142C22×C4×C37—21no—
143C22×C4×C37—21no—
144C22×C4×C37—21no—
145C22×C4×C37—21no—
146C22×C4×C37—22no—
147C22×C4×C37—21no—
148C22×C4×C37—21no—
149C22×C4×C37—22no—
150C22×C4×C37—22no—
151C22×C4×C37—21no—
152C22×C4×C37—21no—
153C22×C4×C37—21no—
154C22×C4×C37—21no—
155C22×C4×C37—22no—
156C22×C4×C37—21no—
157C22×C4×C37—22no—
158C22×C4×C37—21no—
159C22×C4×C37—21no—
160C22×C4×C37—21no—
161C22×C4×C37—22no—
162C22×C4×C37—22no—
163C22×C4×C37—22no—
164C22×C4×C37—22no—
165C22×C4×C37—22no—
166C22×C4×C37—22no—
167C22×C4×C37—22no—
168C22×C4×C37C22×C412yes—
169C22×C4×C37C22×C414yes—
170C22×C4×C37C22×C414yes—
171C22×C4×C37C22×C412yes—
172C22×C4×C37C22×C412yes—
173C22×C4×C37C2×D414yes—
174C22×C4×C37C2×D412yes—
175C22×C4×C37C2×D414yes—
176C22×C4×C37C2×D412yes—
177C22×C4×C37C2×D412yes—
178C22×C4×C37C2×D412yes—
179C22×C4×C37C2×D412yes—
180C22×C4×C37C2×Q812yes—
181C22×C4×C37C2×Q814yes—
182C22×C4×C37C2×Q812yes—
183C22×C4×C37C2×Q812yes—
184C22×C4×C37C2×Q812yes—
185C22×C4×C37#4112yes—
186C22×C4×C37#4112yes—
187C22×C4×C37#4112yes—
188C22×C4×C37#4112yes—
189C22×C4×C37#4112yes—
190C4⋊C4×C37—28no—
191C4⋊C4×C37—216no—
192C4⋊C4×C37—28no—
193C4⋊C4×C37—28no—
194C4⋊C4×C37—28no—
195C4⋊C4×C37—48no—
196C4⋊C4×C37—44no—
197C42×C37—216no—
198C42×C37—28no—
199C42×C37—28no—
200C42×C37—44no—
201C23×C37C23×C411yescharacteristic
202C23×C37C22×D411yescharacteristic
203C23×C37C22×D411yescharacteristic
204C23×C37C22×D411yescharacteristic
205C23×C37C22×Q811yescharacteristic
206C23×C37C22×Q811yescharacteristic
207C23×C37C2×#4111yescharacteristic
208C23×C37C2×#4111yescharacteristic
209C23×C37C2×#4111yescharacteristic
210C23×C37C2×#4111yescharacteristic
211C23×C37C2×#4111yescharacteristic
212C23×C37H(5,𝔽2)11yescharacteristic
213C23×C372−1+411yescharacteristic
214C23×C372−1+411yescharacteristic
215C23×C372−1+411yescharacteristic
216Q8×C37—232no—
217C2×C4×C37—22no—
218C2×C4×C37—24no—
219C2×C4×C37—24no—
220C2×C4×C37—22no—
221C2×C4×C37—22no—
222C2×C4×C37—24no—
223C2×C4×C37—22no—
224C2×C4×C37—24no—
225C2×C4×C37—24no—
226C2×C4×C37—24no—
227C2×C4×C37—22no—
228C2×C4×C37—22no—
229C2×C4×C37—22no—
230C2×C4×C37—22no—
231C2×C4×C37—22no—
232C2×C4×C37—22no—
233C2×C4×C37—22no—
234C2×C4×C37—22no—
235C2×C4×C37—22no—
236C2×C4×C37—24no—
237C2×C4×C37—24no—
238C2×C4×C37—22no—
239C2×C4×C37—22no—
240C2×C4×C37—24no—
241C2×C4×C37—24no—
242C2×C4×C37—22no—
243C2×C4×C37—22no—
244C2×C4×C37—22no—
245C2×C4×C37—22no—
246C2×C4×C37—22no—
247C2×C4×C37—22no—
248C2×C4×C37—24no—
249C2×C4×C37—24no—
250C2×C4×C37—22no—
251C2×C4×C37—22no—
252C2×C4×C37—22no—
253C2×C4×C37—41no—
254C2×C4×C37—41no—
255C2×C4×C37—42no—
256C2×C4×C37—41no—
257C2×C4×C37—41no—
258C2×C4×C37—41no—
259C2×C4×C37—41no—
260C2×C4×C37—42no—
261C2×C4×C37—41no—
262C2×C4×C37—41no—
263C2×C4×C37—42no—
264C2×C4×C37—41no—
265C2×C4×C37—41no—
266C2×C4×C37—41no—
267C2×C4×C37—42no—
268C2×C4×C37—41no—
269C2×C4×C37—42no—
270C2×C4×C37—41no—
271C2×C4×C37—41no—
272C2×C4×C37—41no—
273C2×C4×C37—42no—
274C2×C4×C37—41no—
275C2×C4×C37—42no—
276C2×C4×C37—42no—
277C2×C4×C37—42no—
278C2×C4×C37—42no—
279C2×C4×C37—42no—
280C2×C4×C37—42no—
281C2×C4×C37—42no—
282C2×C4×C37—42no—
283C2×C4×C37—42no—
284C2×C4×C37C2×C4⋊C418yes—
285C2×C4×C37C2×C4⋊C414yes—
286C2×C4×C37C4×D414yes—
287C2×C4×C37C4×D414yes—
288C2×C4×C37C4×Q814yescomplemented
289C2×C4×C37#12014yes—
290C2×C4×C37C22⋊Q814yes—
291C2×C4×C37C22⋊Q814yes—
292C2×C4×C37C22⋊Q814yes—
293C2×C4×C37#12314yes—
294#14017C3711yesmaximal, characteristic, direct product factor, Sylow
295C22×C37C22×C4⋊C411yescharacteristic
296C22×C37C2×C4×D411yescharacteristic
297C22×C37C2×C4×D411yescharacteristic
298C22×C37C2×C4×Q811yescharacteristic
299C22×C37C4×#4111yescharacteristic
300C22×C37#51911yescharacteristic
301C22×C37#52011yescharacteristic
302C22×C37C2×#12011yescharacteristic
303C22×C37C2×C22⋊Q811yescharacteristic
304C22×C37C2×C22⋊Q811yescharacteristic
305C22×C37C2×C22⋊Q811yescharacteristic
306C22×C37C2×#12311yescharacteristic
307C22×C37#52511yescharacteristic
308C22×C37#52911yescharacteristic
309C22×C37#53311yescharacteristic
310C22×C37#53611yescharacteristic
311C22×C37#53711yescharacteristic
312C22×C37#54111yescharacteristic
313C22×C37#54211yescharacteristic
314C22×C37#54611yescharacteristic
315C22×C37#54711yescharacteristic
316C22×C37#54811yescharacteristic
317C22×C37#54811yescharacteristic
318C22×C37#54811yescharacteristic
319C22×C37D4×Q811yescharacteristic
320C22×C37D4×Q811yescharacteristic
321C22×C37#55011yescharacteristic
322C22×C37#55611yescharacteristic
323C22×C37#55611yescharacteristic
324C22×C37#55711yescharacteristic
325C22×C37#55711yescharacteristic
326C22×C37#55711yescharacteristic
327C22×C37#55711yescharacteristic
328C22×C37Q8211yescharacteristic
329C22×C37#55911yescharacteristic
330C4×C37—24no—
331C4×C37—28no—
332C4×C37—24no—
333C4×C37—42no—
334C4×C37—44no—
335C4×C37—42no—
336C4×C37—44no—
337C4×C37—42no—
338C4×C37—42no—
339C4×C37—82no—
340C4×C37#38518yes—
341C22×C4×Q8C2×C3711yescharacteristic
342C2×#391C2×C3711yescharacteristic
343C2×#391C2×C3711yescharacteristic
344C2×#389C2×C3711yescharacteristic
345C2×C4×C4⋊C4C2×C3711yescharacteristic
346#1444C2×C3712yes—
347#1442C2×C3712yes—
348#1436C2×C3712yes—
349#1436C2×C3712yes—
350C4⋊#95C2×C3711yescharacteristic
351C4⋊#95C2×C3711yescharacteristic
352C2×C37C2×#38511yescharacteristic
353C2×C37C4×C22⋊Q811yescharacteristic
354C2×C37#232311yescharacteristic
355C2×C37Q8×C4⋊C411yescharacteristic
356C2×C37#235111yescharacteristic
357C2×C37#236511yescharacteristic
358C2×C37#236711yescharacteristic
359C2×C37#240711yescharacteristic
360C2×C37#240911yescharacteristic
361C2×C37#244611yescharacteristic
362C2×C37#244811yescharacteristic
363C2×C37#245111yescharacteristic
364C2×C37#245311yescharacteristic
365C2×C37#258111yescharacteristic
366C2×C37#258211yescharacteristic
367C23×Q8C22×C3711yescharacteristic
368C2×C4×Q8—24no—
369C2×C4×Q8—24no—
370C2×C4×Q8—24no—
371C22×C4⋊C4C22×C3712yes—
372C22×C4⋊C4C22×C3711yescharacteristic
373C22×C4⋊C4C22×C3711yescharacteristic
374C22×C4⋊C4C22×C3712yes—
375C22×C4⋊C4C22×C3711yescharacteristic
376C22×C4⋊C4C22×C3711yescharacteristic
377C22×C4⋊C4C22×C3711yescharacteristic
378C22×C42C22×C3712yes—
379C22×C42C22×C3711yescharacteristic
380C22×C42C22×C3711yescharacteristic
381C22×C42C22×C3711yescharacteristic
382#391—24no—
383#391C4×C3718yescomplemented
384#389—24no—
385C4×C4⋊C4—24no—
386C2×#95C22×C3712yes—
387C2×#95C22×C3712yes—
388C2×#95C22×C3711yescharacteristic
389C2×#95C22×C3712yes—
390C2×#95C22×C3712yes—
391C2×#95C22×C3712yes—
392C2×#95C22×C3711yescharacteristic
393C2×#95C22×C3712yes—
394C2×#95C22×C3712yes—
395C2×#95C22×C3712yes—
396C2×#95C22×C3712yes—
397C37#1401711yescharacteristic, direct product factor, Sylow
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8C2×C4×C3714yes—
403C22×Q8D4×C3714yes—
404C22×Q8Q8×C3714yes—
405C23×C4C23×C3712yes—
406C23×C4C23×C3712yes—
407C23×C4C23×C3711yescharacteristic
408C23×C4C23×C3712yes—
409C23×C4C23×C3711yescharacteristic
410C23×C4C23×C3711yescharacteristic
411C23×C4C23×C3711yescharacteristic
412C23×C4C23×C3712yes—
413C23×C4C23×C3711yescharacteristic
414C23×C4C23×C3711yescharacteristic
415C23×C4C23×C3711yescharacteristic
416C4×Q8—232no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4C2×C4×C3714yes—
436C2×C4⋊C4D4×C3714yes—
437C2×C4⋊C4Q8×C3714yescomplemented
438C2×C42—24no—
439C2×C42—24no—
440C2×C42—24no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42C2×C4×C3714yes—
449C2×C42D4×C3714yes—
450#95—22no—
451#95—22no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—42no—
458#95—42no—
459#95C2×C4×C3718yes—
460#95C2×C4×C3718yes—
461C24C24×C3711yescharacteristic
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8C4⋊C4×C37116yescomplemented
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4C22×C4×C3712yes—
525C22×C4C22×C4×C3714yes—
526C22×C4C22×C4×C3714yes—
527C22×C4C22×C4×C3712yes—
528C22×C4C22×C4×C3712yes—
529C22×C4C2×D4×C3714yes—
530C22×C4C2×D4×C3712yes—
531C22×C4C2×D4×C3714yes—
532C22×C4C2×D4×C3712yes—
533C22×C4C2×D4×C3712yes—
534C22×C4C2×D4×C3712yes—
535C22×C4C2×D4×C3712yes—
536C22×C4C2×Q8×C3712yes—
537C22×C4C2×Q8×C3714yes—
538C22×C4C2×Q8×C3712yes—
539C22×C4C2×Q8×C3712yes—
540C22×C4C2×Q8×C3712yes—
541C22×C4#41×C3712yes—
542C22×C4#41×C3712yes—
543C22×C4#41×C3712yes—
544C22×C4#41×C3712yes—
545C22×C4#41×C3712yes—
546C4⋊C4—28no—
547C4⋊C4—216no—
548C4⋊C4—28no—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—48no—
552C4⋊C4—44no—
553C42—216no—
554C42—28no—
555C42—28no—
556C42—44no—
557C23C23×C4×C3711yescharacteristic
558C23C22×D4×C3711yescharacteristic
559C23C22×D4×C3711yescharacteristic
560C23C22×D4×C3711yescharacteristic
561C23C22×Q8×C3711yescharacteristic
562C23C22×Q8×C3711yescharacteristic
563C23C2×#41×C3711yescharacteristic
564C23C2×#41×C3711yescharacteristic
565C23C2×#41×C3711yescharacteristic
566C23C2×#41×C3711yescharacteristic
567C23C2×#41×C3711yescharacteristic
568C23H(5,𝔽2)×C3711yescharacteristic
569C232−1+4×C3711yescharacteristic
570C232−1+4×C3711yescharacteristic
571C232−1+4×C3711yescharacteristic
572Q8—232no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4C2×C4⋊C4×C3718yes—
641C2×C4C2×C4⋊C4×C3714yes—
642C2×C4C4×D4×C3714yes—
643C2×C4C4×D4×C3714yes—
644C2×C4C4×Q8×C3714yescomplemented
645C2×C4#120×C3714yes—
646C2×C4C22⋊Q8×C3714yes—
647C2×C4C22⋊Q8×C3714yes—
648C2×C4C22⋊Q8×C3714yes—
649C2×C4#123×C3714yes—
650C22C22×C4⋊C4×C3711yescharacteristic
651C22C2×C4×D4×C3711yescharacteristic
652C22C2×C4×D4×C3711yescharacteristic
653C22C2×C4×Q8×C3711yescharacteristic
654C22C4×#41×C3711yescharacteristic
655C22C37×#51911yescharacteristic
656C22C37×#52011yescharacteristic
657C22C2×#120×C3711yescharacteristic
658C22C2×C22⋊Q8×C3711yescharacteristic
659C22C2×C22⋊Q8×C3711yescharacteristic
660C22C2×C22⋊Q8×C3711yescharacteristic
661C22C2×#123×C3711yescharacteristic
662C22C37×#52511yescharacteristic
663C22C37×#52911yescharacteristic
664C22C37×#53311yescharacteristic
665C22C37×#53611yescharacteristic
666C22C37×#53711yescharacteristic
667C22C37×#54111yescharacteristic
668C22C37×#54211yescharacteristic
669C22C37×#54611yescharacteristic
670C22C37×#54711yescharacteristic
671C22C37×#54811yescharacteristic
672C22C37×#54811yescharacteristic
673C22C37×#54811yescharacteristic
674C22D4×Q8×C3711yescharacteristic
675C22D4×Q8×C3711yescharacteristic
676C22C37×#55011yescharacteristic
677C22C37×#55611yescharacteristic
678C22C37×#55611yescharacteristic
679C22C37×#55711yescharacteristic
680C22C37×#55711yescharacteristic
681C22C37×#55711yescharacteristic
682C22C37×#55711yescharacteristic
683C22Q82×C3711yescharacteristic
684C22C37×#55911yescharacteristic
685C4—24no—
686C4—28no—
687C4—24no—
688C4—44no—
689C4—42no—
690C4—44no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—82no—
695C4C37×#38518yes—
696C2C2×C37×#38511yescharacteristic
697C2C4×C22⋊Q8×C3711yescharacteristic
698C2C37×#232311yescharacteristic
699C2Q8×C4⋊C4×C3711yescharacteristic
700C2C37×#235111yescharacteristic
701C2C37×#236511yescharacteristic
702C2C37×#236711yescharacteristic
703C2C37×#240711yescharacteristic
704C2C37×#240911yescharacteristic
705C2C37×#244611yescharacteristic
706C2C37×#244811yescharacteristic
707C2C37×#245111yescharacteristic
708C2C37×#245311yescharacteristic
709C2C37×#258111yescharacteristic
710C2C37×#258211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
28. C37×#391C4semidirect
81. C2×C4⋊C4×C37Q8semidirect
112. C2×Q8×C37C4⋊C4semidirect
288. C2×C4×C37C4×Q8semidirect
294. #14017C37direct (N × H)
383. #391C4×C37semidirect
397. C37#14017direct (N × H)
437. C2×C4⋊C4Q8×C37semidirect
468. C2×Q8C4⋊C4×C37semidirect
644. C2×C4C4×Q8×C37semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C372
C2×C37×#3912
C2×C37×#3892
C2×C4×C4⋊C4×C372
C37×#14442
C37×#14422
C37×#14362
C37×C4⋊#952
#1401737