Finite Group Databasebeta

← C37×#61857 #22683110

Subgroups — C37×#61857 #22683110

Order 9472.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3554C211yesmaximal, characteristic, complemented
2C37×#3503C211yesmaximal, characteristic, complemented
3C37×#3389C212yesmaximal, complemented
4C37×#3386C211yesmaximal, characteristic, complemented
5C37×#3386C211yesmaximal, characteristic, complemented
6C37×#3385C212yesmaximal, complemented
7C37×#3383C211yesmaximal, characteristic, complemented
8Q8×D8×C37C211yesmaximal, characteristic, complemented
9C37×#3375C212yesmaximal, complemented
10C37×#3373C211yesmaximal, characteristic, complemented
11C37×#3370C212yesmaximal, complemented
12C37×#3368C211yesmaximal, characteristic, complemented
13C37×#3365C211yesmaximal, characteristic, complemented
14C37×#3358C211yesmaximal, characteristic, complemented
15C37×#3243C212yesmaximal, complemented
16C37×#3241C212yesmaximal, complemented
17C37×#3239C211yesmaximal, characteristic, complemented
18C37×#3226C211yesmaximal, characteristic, complemented
19C37×#3124C212yesmaximal, complemented
20C37×#3119C212yesmaximal, complemented
21C37×#3115C211yesmaximal, characteristic, complemented
22C37×#3102C211yesmaximal, characteristic, complemented
23C37×#2985C211yesmaximal, characteristic, complemented
24C37×#562—22no—
25C37×#559C2212yes—
26C37×#559C2211yescharacteristic
27Q82×C37C2212yes—
28C37×#557C2211yescharacteristic
29C37×#557C2211yescharacteristic
30C37×#557C2211yescharacteristic
31C37×#554—22no—
32C37×#554C2212yes—
33C37×#554C2212yes—
34C37×#550C2211yescharacteristic
35D4×Q8×C37—21no—
36D4×Q8×C37—21no—
37D4×Q8×C37C2211yescharacteristic
38D4×Q8×C37C2211yescharacteristic
39D4×Q8×C37C2211yescharacteristic
40C37×#548—21no—
41C37×#547—21no—
42C37×#544—22no—
43C37×#544C2212yes—
44C37×#542—21no—
45C37×#542C2212yes—
46C37×#540C2212yes—
47C37×#539—22no—
48C37×#536—21no—
49C37×#533—21no—
50C37×#533C2211yescharacteristic
51C37×#532C2211yescharacteristic
52C2×C4⋊Q8×C37—21no—
53C2×C4⋊Q8×C37C2211yescharacteristic
54C37×#529C2211yescharacteristic
55C37×#520C2212yes—
56C4×#41×C37C2211yescharacteristic
57C37×#501C2212yes—
58C37×#501C2212yes—
59C37×#501C2212yes—
60C37×#500C2211yescharacteristic
61C37×#500C2212yes—
62C37×#500C2211yescharacteristic
63C37×#499C2212yes—
64C37×#490C2212yes—
65C37×#489C2212yes—
66C37×#489C2212yes—
67C37×#488C2212yes—
68C37×#486C2212yes—
69C37×#486C2211yescharacteristic
70C37×#486C2211yescharacteristic
71C37×#485C2211yescharacteristic
72C37×#484C2212yes—
73C37×#482C2211yescharacteristic
74C37×#482C2212yes—
75C37×#481C2212yes—
76C37×#480C2212yes—
77C37×#480C2212yes—
78C37×#479C2212yes—
79C37×#479C2212yes—
80C37×#479C2211yescharacteristic
81C37×#478C2212yes—
82C37×#478C2212yes—
83C37×#478C2211yescharacteristic
84C37×#478C2212yes—
85C37×#478C2212yes—
86C37×#477C2212yes—
87C37×#477C2212yes—
88C37×#476C2212yes—
89C37×#475C2211yescharacteristic
90C37×#475C2211yescharacteristic
91C37×#475C2211yescharacteristic
92C37×#474C2212yes—
93C37×#474C2212yes—
94C37×#474C2212yes—
95C37×#474C2211yescharacteristic
96C37×#474C2211yescharacteristic
97C37×#474C2212yes—
98C37×#474C2212yes—
99C37×#474C2211yescharacteristic
100C37×#464C2211yescharacteristic
101C37×#464C2212yes—
102C37×#463C2212yes—
103C37×#463C2211yescharacteristic
104C37×#460C2212yes—
105C37×#460C2211yescharacteristic
106C37×#459C2212yes—
107C37×#459C2211yescharacteristic
108C37×#452C2211yescharacteristic
109C37×#449C2211yescharacteristic
110C37×#449C2212yes—
111C37×#446C2212yes—
112C37×#446C2212yes—
113C37×#446C2211yescharacteristic
114C37×#446C2211yescharacteristic
115C8×Q8×C37C2211yescharacteristic
116C8×Q8×C37C2211yescharacteristic
117C37×#442C2212yes—
118C37×#442C2212yes—
119C37×#440C2212yes—
120C37×#440C2212yes—
121C37×#440C2212yes—
122C37×#440C2212yes—
123C4×Q16×C37C2212yes—
124C4×Q16×C37C2211yescharacteristic
125C4×SD16×C37C2212yes—
126C4×SD16×C37C2211yescharacteristic
127C4×SD16×C37C2211yescharacteristic
128C4×D8×C37C2212yes—
129C4×D8×C37C2211yescharacteristic
130C4×D8×C37C2212yes—
131C37×#433C2212yes—
132C37×#433C2212yes—
133C37×#432C2211yescharacteristic
134C37×#431C2211yescharacteristic
135C2×#41×C37—21no—
136C2×#41×C37—21no—
137C2×#41×C37C2311yescharacteristic
138C22×Q8×C37—21no—
139C22×Q8×C37—21no—
140C22×Q8×C37—21no—
141C22×Q8×C37—21no—
142C2×Q16×C37C2311yescharacteristic
143C2×SD16×C37C2312yes—
144C2×SD16×C37C2311yescharacteristic
145C2×SD16×C37C2311yescharacteristic
146C2×D8×C37C2311yescharacteristic
147C2×D8×C37C2312yes—
148C4⋊Q8×C37—21no—
149C4⋊Q8×C37—21no—
150C4⋊Q8×C37—21no—
151C4⋊Q8×C37—22no—
152C4⋊Q8×C37—22no—
153C4⋊Q8×C37—22no—
154C4⋊Q8×C37—22no—
155C4⋊Q8×C37—21no—
156C4⋊Q8×C37—21no—
157C4⋊Q8×C37D411yescharacteristic
158C4⋊Q8×C37D411yescharacteristic
159C4⋊Q8×C37C2311yescharacteristic
160C4⋊Q8×C37C2311yescharacteristic
161C4⋊Q8×C37C2312yes—
162C4⋊Q8×C37C2311yescharacteristic
163C4⋊Q8×C37C2312yes—
164C4⋊Q8×C37C2312yes—
165C4⋊Q8×C37C2312yes—
166#127×C37C2311yescharacteristic
167#127×C37C2312yes—
168#126×C37—22no—
169#126×C37—21no—
170#125×C37—22no—
171#125×C37—22no—
172#125×C37—22no—
173#125×C37—22no—
174#125×C37D412yes—
175#125×C37C2311yescharacteristic
176#125×C37C2312yes—
177#125×C37C2312yes—
178#125×C37C2312yes—
179#124×C37—21no—
180#124×C37—22no—
181#124×C37—22no—
182#124×C37—21no—
183#124×C37C2311yescharacteristic
184#124×C37C2312yes—
185#123×C37—21no—
186#123×C37—22no—
187#123×C37—22no—
188#123×C37—22no—
189#123×C37—22no—
190#123×C37—22no—
191#123×C37—22no—
192C22⋊Q8×C37—22no—
193C22⋊Q8×C37—22no—
194C22⋊Q8×C37—21no—
195C22⋊Q8×C37—21no—
196C22⋊Q8×C37—22no—
197C22⋊Q8×C37—22no—
198C22⋊Q8×C37—22no—
199C22⋊Q8×C37—22no—
200C22⋊Q8×C37—21no—
201C22⋊Q8×C37—22no—
202C22⋊Q8×C37—22no—
203C22⋊Q8×C37—22no—
204C22⋊Q8×C37—22no—
205C22⋊Q8×C37—22no—
206C22⋊Q8×C37—22no—
207C22⋊Q8×C37D411yescharacteristic
208C22⋊Q8×C37D411yescharacteristic
209C22⋊Q8×C37D412yes—
210C22⋊Q8×C37C2311yescharacteristic
211#121×C37—21no—
212#121×C37—22no—
213#121×C37—21no—
214#121×C37—22no—
215#121×C37—22no—
216#121×C37C2311yescharacteristic
217#121×C37C2312yes—
218C4×Q8×C37—22no—
219C4×Q8×C37—21no—
220C4×Q8×C37—21no—
221C4×Q8×C37—21no—
222C4×Q8×C37C2312yes—
223C4×Q8×C37C2312yes—
224C4×Q8×C37C2311yescharacteristic
225C4×Q8×C37C2312yes—
226C4×Q8×C37C2311yescharacteristic
227C4×Q8×C37C2311yescharacteristic
228C4×Q8×C37C2311yescharacteristic
229C4×Q8×C37C2311yescharacteristic
230C4×Q8×C37C2312yes—
231C4×D4×C37—21no—
232C4×D4×C37—21no—
233C4×D4×C37—21no—
234C4×D4×C37—22no—
235C4×D4×C37—21no—
236C4×D4×C37—22no—
237C4×D4×C37—22no—
238C4×D4×C37—21no—
239C4×D4×C37C2312yes—
240C4×D4×C37C2312yes—
241C4×D4×C37C2311yescharacteristic
242C4×D4×C37C2312yes—
243C4×D4×C37C2312yes—
244C4×D4×C37C2312yes—
245C4×D4×C37C2312yes—
246C4×D4×C37C2311yescharacteristic
247C4×D4×C37C2311yescharacteristic
248#117×C37—22no—
249#117×C37—21no—
250#117×C37—21no—
251#117×C37C2311yescharacteristic
252#117×C37C2312yes—
253C2×C4⋊C4×C37—21no—
254C2×C4⋊C4×C37—22no—
255C2×C4⋊C4×C37—22no—
256C2×C4⋊C4×C37—22no—
257C2×C4⋊C4×C37C2312yes—
258C2×C42×C37—21no—
259C2×C42×C37C2311yescharacteristic
260#107×C37C2312yes—
261#107×C37C2311yescharacteristic
262#107×C37C2312yes—
263#107×C37C2312yes—
264#107×C37C2311yescharacteristic
265#107×C37C2312yes—
266#107×C37C2312yes—
267#107×C37C2312yes—
268#107×C37C2312yes—
269#106×C37C2312yes—
270#106×C37C2311yescharacteristic
271#106×C37C2311yescharacteristic
272#106×C37C2312yes—
273#106×C37C2312yes—
274C4⋊C8×C37C2311yescharacteristic
275C4⋊C8×C37C2311yescharacteristic
276C4⋊C8×C37C2311yescharacteristic
277C4⋊C8×C37C2311yescharacteristic
278C4⋊C8×C37C2312yes—
279C4⋊C8×C37C2312yes—
280C4⋊C8×C37C2312yes—
281C4⋊C8×C37C2312yes—
282#103×C37C2311yescharacteristic
283#103×C37C2311yescharacteristic
284#103×C37C2311yescharacteristic
285#103×C37C2312yes—
286#103×C37C2312yes—
287#103×C37C2311yescharacteristic
288#103×C37C2312yes—
289#102×C37C2311yescharacteristic
290#102×C37C2312yes—
291#102×C37C2312yes—
292#102×C37C2311yescharacteristic
293#102×C37C2312yes—
294#102×C37C2311yescharacteristic
295#102×C37C2312yes—
296#102×C37C2311yescharacteristic
297#102×C37C2312yes—
298#102×C37C2312yes—
299#102×C37C2312yes—
300#102×C37C2312yes—
301#102×C37C2312yes—
302C22⋊C8×C37C2311yescharacteristic
303C22⋊C8×C37C2311yescharacteristic
304C22⋊C8×C37C2312yes—
305#97×C37C2312yes—
306#97×C37C2312yes—
307#97×C37C2312yes—
308C4×C8×C37C2311yescharacteristic
309C4×C8×C37C2311yescharacteristic
310C4×C8×C37C2312yes—
311C4×C8×C37C2312yes—
312#41×C37—22no—
313#41×C37—22no—
314#41×C37—82no—
315#41×C37—82no—
316C2×Q8×C37—21no—
317C2×Q8×C37—21no—
318C2×Q8×C37—21no—
319C2×Q8×C37—22no—
320C2×Q8×C37—22no—
321C2×Q8×C37—22no—
322C2×Q8×C37—22no—
323C2×Q8×C37—82no—
324C2×Q8×C37—82no—
325C2×Q8×C37—82no—
326C2×Q8×C37—82no—
327C2×Q8×C37C2×D411yescharacteristic
328C2×Q8×C37C2×D411yescharacteristic
329C2×Q8×C37C2×D412yes—
330C2×Q8×C37C2411yescharacteristic
331C2×Q8×C37C2411yescharacteristic
332C2×D4×C37—21no—
333C2×D4×C37—21no—
334C2×D4×C37—22no—
335C2×D4×C37—21no—
336C2×D4×C37—21no—
337C2×D4×C37—22no—
338C2×D4×C37—22no—
339C2×D4×C37C2411yescharacteristic
340C2×D4×C37C2412yes—
341C2×D4×C37C2411yescharacteristic
342C22×C4×C37—21no—
343C22×C4×C37—22no—
344C22×C4×C37—21no—
345C22×C4×C37—21no—
346C22×C4×C37—21no—
347C22×C4×C37—22no—
348C22×C4×C37—22no—
349C22×C4×C37—22no—
350C22×C4×C37—22no—
351C22×C4×C37—22no—
352C22×C4×C37—22no—
353C22×C4×C37C2×D411yescharacteristic
354C22×C4×C37C2×D411yescharacteristic
355C22×C4×C37C2411yescharacteristic
356Q16×C37—22no—
357SD16×C37—24no—
358SD16×C37—22no—
359SD16×C37—22no—
360D8×C37—22no—
361D8×C37—24no—
362C2×C8×C37C2411yescharacteristic
363C2×C8×C37C2411yescharacteristic
364C2×C8×C37C2411yescharacteristic
365C2×C8×C37C2411yescharacteristic
366C2×C8×C37C2412yes—
367C2×C8×C37C2412yes—
368C4⋊C4×C37—21no—
369C4⋊C4×C37—22no—
370C4⋊C4×C37—22no—
371C4⋊C4×C37—22no—
372C4⋊C4×C37—22no—
373C4⋊C4×C37—22no—
374C4⋊C4×C37—22no—
375C4⋊C4×C37—21no—
376C4⋊C4×C37—21no—
377C4⋊C4×C37—22no—
378C4⋊C4×C37—22no—
379C4⋊C4×C37—21no—
380C4⋊C4×C37—21no—
381C4⋊C4×C37—21no—
382C4⋊C4×C37—21no—
383C4⋊C4×C37—21no—
384C4⋊C4×C37—22no—
385C4⋊C4×C37—22no—
386C4⋊C4×C37—22no—
387C4⋊C4×C37—22no—
388C4⋊C4×C37—22no—
389C4⋊C4×C37—22no—
390C4⋊C4×C37—21no—
391C4⋊C4×C37C2×D412yes—
392C4⋊C4×C37C2×D412yes—
393C4⋊C4×C37C2×D412yes—
394C4⋊C4×C37C2×D412yes—
395C4⋊C4×C37C2×D411yescharacteristic
396C4⋊C4×C37C2×D412yes—
397C4⋊C4×C37C2×D411yescharacteristic
398C4⋊C4×C37C2×D412yes—
399C4⋊C4×C37C2×D412yes—
400C4⋊C4×C37C2411yescharacteristic
401C4⋊C4×C37C2412yes—
402C4⋊C4×C37C2412yes—
403C4⋊C4×C37C2411yescharacteristic
404C4⋊C4×C37C2411yescharacteristic
405C4⋊C4×C37C2411yescharacteristic
406C4⋊C4×C37C2412yes—
407C22⋊C4×C37—21no—
408C22⋊C4×C37—21no—
409C22⋊C4×C37—21no—
410C22⋊C4×C37—21no—
411C22⋊C4×C37—22no—
412C22⋊C4×C37—22no—
413C22⋊C4×C37—21no—
414C22⋊C4×C37—21no—
415C22⋊C4×C37—21no—
416C22⋊C4×C37—22no—
417C22⋊C4×C37—22no—
418C22⋊C4×C37—22no—
419C22⋊C4×C37—21no—
420C22⋊C4×C37—22no—
421C22⋊C4×C37—22no—
422C22⋊C4×C37—22no—
423C22⋊C4×C37—22no—
424C22⋊C4×C37C2×D412yes—
425C22⋊C4×C37C2×D412yes—
426C42×C37—21no—
427C42×C37—21no—
428C42×C37—21no—
429C42×C37—21no—
430C42×C37—22no—
431C42×C37—22no—
432C42×C37—22no—
433C42×C37C2×D411yescharacteristic
434C42×C37C2×D411yescharacteristic
435C42×C37C2411yescharacteristic
436C42×C37C2412yes—
437C42×C37C2412yes—
438C42×C37C2411yescharacteristic
439C23×C37—21no—
440C23×C37—22no—
441C23×C37—21no—
442C23×C37C22×D411yescharacteristic
443Q8×C37—22no—
444Q8×C37—22no—
445Q8×C37—21no—
446Q8×C37—21no—
447Q8×C37—21no—
448Q8×C37—42no—
449Q8×C37—42no—
450Q8×C37—42no—
451Q8×C37—42no—
452Q8×C37—82no—
453Q8×C37—82no—
454Q8×C37—82no—
455Q8×C37—82no—
456Q8×C372−1+412yes—
457D4×C37—24no—
458D4×C37—21no—
459D4×C37—21no—
460D4×C37—22no—
461D4×C37—21no—
462D4×C37—22no—
463D4×C37—42no—
464D4×C37—81no—
465D4×C37—82no—
466D4×C37—82no—
467D4×C37—81no—
468D4×C37—82no—
469D4×C372−1+412yes—
470C2×C4×C37—24no—
471C2×C4×C37—21no—
472C2×C4×C37—22no—
473C2×C4×C37—21no—
474C2×C4×C37—21no—
475C2×C4×C37—21no—
476C2×C4×C37—21no—
477C2×C4×C37—21no—
478C2×C4×C37—21no—
479C2×C4×C37—22no—
480C2×C4×C37—22no—
481C2×C4×C37—22no—
482C2×C4×C37—21no—
483C2×C4×C37—41no—
484C2×C4×C37—42no—
485C2×C4×C37—42no—
486C2×C4×C37—42no—
487C2×C4×C37—82no—
488C2×C4×C37—82no—
489C2×C4×C37—82no—
490C2×C4×C37—82no—
491C2×C4×C37—82no—
492C2×C4×C37—82no—
493C2×C4×C37—82no—
494C2×C4×C37C22×D412yes—
495C2×C4×C37C22×D411yescharacteristic
496C2×C4×C37C22×D411yescharacteristic
497C2×C4×C37C22×D412yes—
498C2×C4×C37C22×D411yescharacteristic
499C2×C4×C37C22×D411yescharacteristic
500C2×C4×C37C22×D412yes—
501C2×C4×C37C22×D412yes—
502C2×C4×C37C22×D411yescharacteristic
503C2×C4×C37C2511yescharacteristic
504C8×C37—21no—
505C8×C37—22no—
506C8×C37—21no—
507C8×C37—22no—
508C8×C37—21no—
509C8×C37—21no—
510#61857C3711yesmaximal, characteristic, direct product factor, Sylow
511C22×C37—21no—
512C22×C37—21no—
513C22×C37—22no—
514C22×C37—21no—
515C22×C37—41no—
516C22×C37—41no—
517C22×C37—42no—
518C22×C37—41no—
519C22×C37—42no—
520C22×C37—41no—
521C22×C37—41no—
522C22×C37—42no—
523C22×C37C23×D411yescharacteristic
524C4×C37—21no—
525C4×C37—21no—
526C4×C37—22no—
527C4×C37—22no—
528C4×C37—21no—
529C4×C37—22no—
530C4×C37—21no—
531C4×C37—22no—
532C4×C37—22no—
533C4×C37—41no—
534C4×C37—41no—
535C4×C37—41no—
536C4×C37—41no—
537C4×C37—41no—
538C4×C37—42no—
539C4×C37—42no—
540C4×C37—42no—
541C4×C37#57612yes—
542C4×C37C2×2−1+411yescharacteristic
543C4×C37C2×2−1+411yescharacteristic
544#3554C2×C3711yescharacteristic, complemented
545#3503C2×C3711yescharacteristic, complemented
546#3389C2×C3712yescomplemented
547#3386C2×C3711yescharacteristic, complemented
548#3386C2×C3711yescharacteristic, complemented
549#3385C2×C3712yescomplemented
550#3383C2×C3711yescharacteristic, complemented
551Q8×D8C2×C3711yescharacteristic, complemented
552#3375C2×C3712yescomplemented
553#3373C2×C3711yescharacteristic, complemented
554#3370C2×C3712yescomplemented
555#3368C2×C3711yescharacteristic, complemented
556#3365C2×C3711yescharacteristic, complemented
557#3358C2×C3711yescharacteristic, complemented
558#3243C2×C3712yescomplemented
559#3241C2×C3712yescomplemented
560#3239C2×C3711yescharacteristic, complemented
561#3226C2×C3711yescharacteristic, complemented
562#3124C2×C3712yescomplemented
563#3119C2×C3712yescomplemented
564#3115C2×C3711yescharacteristic, complemented
565#3102C2×C3711yescharacteristic, complemented
566#2985C2×C3711yescharacteristic, complemented
567C2×C37—41no—
568C2×C37—42no—
569C2×C37—82no—
570C2×C37—81no—
571C2×C37#348611yescharacteristic
572C2×C37C2×#57611yescharacteristic
573C2×C37#358611yescharacteristic
574#562—22no—
575#559C22×C3711yescharacteristic
576#559C22×C3712yes—
577Q82C22×C3712yes—
578#557C22×C3711yescharacteristic
579#557C22×C3711yescharacteristic
580#557C22×C3711yescharacteristic
581#554—22no—
582#554C22×C3712yes—
583#554C22×C3712yes—
584#550C22×C3711yescharacteristic
585D4×Q8—21no—
586D4×Q8—21no—
587D4×Q8C22×C3711yescharacteristic
588D4×Q8C22×C3711yescharacteristic
589D4×Q8C22×C3711yescharacteristic
590#548—21no—
591#547—21no—
592#544—22no—
593#544C22×C3712yes—
594#542—21no—
595#542C22×C3712yes—
596#540C22×C3712yes—
597#539—22no—
598#536—21no—
599#533—21no—
600#533C22×C3711yescharacteristic
601#532C22×C3711yescharacteristic
602C2×C4⋊Q8—21no—
603C2×C4⋊Q8C22×C3711yescharacteristic
604#529C22×C3711yescharacteristic
605#520C22×C3712yes—
606C4×#41C22×C3711yescharacteristic
607#501C22×C3712yes—
608#501C22×C3712yes—
609#501C22×C3712yes—
610#500C22×C3711yescharacteristic
611#500C22×C3712yes—
612#500C22×C3711yescharacteristic
613#499C22×C3712yes—
614#490C22×C3712yes—
615#489C22×C3712yes—
616#489C22×C3712yes—
617#488C22×C3712yes—
618#486C22×C3711yescharacteristic
619#486C22×C3712yes—
620#486C22×C3711yescharacteristic
621#485C22×C3711yescharacteristic
622#484C22×C3712yes—
623#482C22×C3711yescharacteristic
624#482C22×C3712yes—
625#481C22×C3712yes—
626#480C22×C3712yes—
627#480C22×C3712yes—
628#479C22×C3711yescharacteristic
629#479C22×C3712yes—
630#479C22×C3712yes—
631#478C22×C3711yescharacteristic
632#478C22×C3712yes—
633#478C22×C3712yes—
634#478C22×C3712yes—
635#478C22×C3712yes—
636#477C22×C3712yes—
637#477C22×C3712yes—
638#476C22×C3712yes—
639#475C22×C3711yescharacteristic
640#475C22×C3711yescharacteristic
641#475C22×C3711yescharacteristic
642#474C22×C3712yes—
643#474C22×C3711yescharacteristic
644#474C22×C3711yescharacteristic
645#474C22×C3712yes—
646#474C22×C3711yescharacteristic
647#474C22×C3712yes—
648#474C22×C3712yes—
649#474C22×C3712yes—
650#464C22×C3711yescharacteristic
651#464C22×C3712yes—
652#463C22×C3711yescharacteristic
653#463C22×C3712yes—
654#460C22×C3711yescharacteristic
655#460C22×C3712yes—
656#459C22×C3712yes—
657#459C22×C3711yescharacteristic
658#452C22×C3711yescharacteristic
659#449C22×C3711yescharacteristic
660#449C22×C3712yes—
661#446C22×C3711yescharacteristic
662#446C22×C3712yes—
663#446C22×C3711yescharacteristic
664#446C22×C3712yes—
665C8×Q8C22×C3711yescharacteristic
666C8×Q8C22×C3711yescharacteristic
667#442C22×C3712yes—
668#442C22×C3712yes—
669#440C22×C3712yes—
670#440C22×C3712yes—
671#440C22×C3712yes—
672#440C22×C3712yes—
673C4×Q16C22×C3711yescharacteristic
674C4×Q16C22×C3712yes—
675C4×SD16C22×C3711yescharacteristic
676C4×SD16C22×C3711yescharacteristic
677C4×SD16C22×C3712yes—
678C4×D8C22×C3711yescharacteristic
679C4×D8C22×C3712yes—
680C4×D8C22×C3712yes—
681#433C22×C3712yes—
682#433C22×C3712yes—
683#432C22×C3711yescharacteristic
684#431C22×C3711yescharacteristic
685C37#6185711yescharacteristic, direct product factor, Sylow
686C2×#41—21no—
687C2×#41—21no—
688C2×#41C23×C3711yescharacteristic
689C22×Q8—21no—
690C22×Q8—21no—
691C22×Q8—21no—
692C22×Q8—21no—
693C2×Q16C23×C3711yescharacteristic
694C2×SD16C23×C3711yescharacteristic
695C2×SD16C23×C3712yes—
696C2×SD16C23×C3711yescharacteristic
697C2×D8C23×C3711yescharacteristic
698C2×D8C23×C3712yes—
699C4⋊Q8—21no—
700C4⋊Q8—21no—
701C4⋊Q8—21no—
702C4⋊Q8—22no—
703C4⋊Q8—22no—
704C4⋊Q8—22no—
705C4⋊Q8—22no—
706C4⋊Q8—21no—
707C4⋊Q8—21no—
708C4⋊Q8D4×C3711yescharacteristic
709C4⋊Q8D4×C3711yescharacteristic
710C4⋊Q8C23×C3711yescharacteristic
711C4⋊Q8C23×C3711yescharacteristic
712C4⋊Q8C23×C3712yes—
713C4⋊Q8C23×C3711yescharacteristic
714C4⋊Q8C23×C3712yes—
715C4⋊Q8C23×C3712yes—
716C4⋊Q8C23×C3712yes—
717#127C23×C3711yescharacteristic
718#127C23×C3712yes—
719#126—22no—
720#126—21no—
721#125—22no—
722#125—22no—
723#125—22no—
724#125—22no—
725#125D4×C3712yes—
726#125C23×C3711yescharacteristic
727#125C23×C3712yes—
728#125C23×C3712yes—
729#125C23×C3712yes—
730#124—21no—
731#124—22no—
732#124—22no—
733#124—21no—
734#124C23×C3711yescharacteristic
735#124C23×C3712yes—
736#123—21no—
737#123—22no—
738#123—22no—
739#123—22no—
740#123—22no—
741#123—22no—
742#123—22no—
743C22⋊Q8—22no—
744C22⋊Q8—22no—
745C22⋊Q8—21no—
746C22⋊Q8—21no—
747C22⋊Q8—22no—
748C22⋊Q8—22no—
749C22⋊Q8—22no—
750C22⋊Q8—22no—
751C22⋊Q8—21no—
752C22⋊Q8—22no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8—22no—
756C22⋊Q8—22no—
757C22⋊Q8—22no—
758C22⋊Q8D4×C3711yescharacteristic
759C22⋊Q8D4×C3711yescharacteristic
760C22⋊Q8D4×C3712yes—
761C22⋊Q8C23×C3711yescharacteristic
762#121—21no—
763#121—22no—
764#121—21no—
765#121—22no—
766#121—22no—
767#121C23×C3711yescharacteristic
768#121C23×C3712yes—
769C4×Q8—22no—
770C4×Q8—21no—
771C4×Q8—21no—
772C4×Q8—21no—
773C4×Q8C23×C3711yescharacteristic
774C4×Q8C23×C3711yescharacteristic
775C4×Q8C23×C3712yes—
776C4×Q8C23×C3712yes—
777C4×Q8C23×C3711yescharacteristic
778C4×Q8C23×C3712yes—
779C4×Q8C23×C3711yescharacteristic
780C4×Q8C23×C3711yescharacteristic
781C4×Q8C23×C3712yes—
782C4×D4—21no—
783C4×D4—21no—
784C4×D4—21no—
785C4×D4—22no—
786C4×D4—21no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—21no—
790C4×D4C23×C3711yescharacteristic
791C4×D4C23×C3711yescharacteristic
792C4×D4C23×C3712yes—
793C4×D4C23×C3712yes—
794C4×D4C23×C3711yescharacteristic
795C4×D4C23×C3712yes—
796C4×D4C23×C3712yes—
797C4×D4C23×C3712yes—
798C4×D4C23×C3712yes—
799#117—22no—
800#117—21no—
801#117—21no—
802#117C23×C3711yescharacteristic
803#117C23×C3712yes—
804C2×C4⋊C4—21no—
805C2×C4⋊C4—22no—
806C2×C4⋊C4—22no—
807C2×C4⋊C4—22no—
808C2×C4⋊C4C23×C3712yes—
809C2×C42—21no—
810C2×C42C23×C3711yescharacteristic
811#107C23×C3712yes—
812#107C23×C3711yescharacteristic
813#107C23×C3712yes—
814#107C23×C3712yes—
815#107C23×C3711yescharacteristic
816#107C23×C3712yes—
817#107C23×C3712yes—
818#107C23×C3712yes—
819#107C23×C3712yes—
820#106C23×C3712yes—
821#106C23×C3711yescharacteristic
822#106C23×C3711yescharacteristic
823#106C23×C3712yes—
824#106C23×C3712yes—
825C4⋊C8C23×C3711yescharacteristic
826C4⋊C8C23×C3711yescharacteristic
827C4⋊C8C23×C3711yescharacteristic
828C4⋊C8C23×C3711yescharacteristic
829C4⋊C8C23×C3712yes—
830C4⋊C8C23×C3712yes—
831C4⋊C8C23×C3712yes—
832C4⋊C8C23×C3712yes—
833#103C23×C3711yescharacteristic
834#103C23×C3711yescharacteristic
835#103C23×C3711yescharacteristic
836#103C23×C3712yes—
837#103C23×C3712yes—
838#103C23×C3711yescharacteristic
839#103C23×C3712yes—
840#102C23×C3711yescharacteristic
841#102C23×C3712yes—
842#102C23×C3712yes—
843#102C23×C3711yescharacteristic
844#102C23×C3712yes—
845#102C23×C3711yescharacteristic
846#102C23×C3712yes—
847#102C23×C3711yescharacteristic
848#102C23×C3712yes—
849#102C23×C3712yes—
850#102C23×C3712yes—
851#102C23×C3712yes—
852#102C23×C3712yes—
853C22⋊C8C23×C3711yescharacteristic
854C22⋊C8C23×C3711yescharacteristic
855C22⋊C8C23×C3712yes—
856#97C23×C3712yes—
857#97C23×C3712yes—
858#97C23×C3712yes—
859C4×C8C23×C3711yescharacteristic
860C4×C8C23×C3711yescharacteristic
861C4×C8C23×C3712yes—
862C4×C8C23×C3712yes—
863#41—22no—
864#41—22no—
865#41—82no—
866#41—82no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—22no—
871C2×Q8—22no—
872C2×Q8—22no—
873C2×Q8—22no—
874C2×Q8—82no—
875C2×Q8—82no—
876C2×Q8—82no—
877C2×Q8—82no—
878C2×Q8C2×D4×C3711yescharacteristic
879C2×Q8C2×D4×C3711yescharacteristic
880C2×Q8C2×D4×C3712yes—
881C2×Q8C24×C3711yescharacteristic
882C2×Q8C24×C3711yescharacteristic
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—22no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4C24×C3711yescharacteristic
891C2×D4C24×C3712yes—
892C2×D4C24×C3711yescharacteristic
893C22×C4—21no—
894C22×C4—22no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4C2×D4×C3711yescharacteristic
905C22×C4C2×D4×C3711yescharacteristic
906C22×C4C24×C3711yescharacteristic
907Q16—22no—
908SD16—22no—
909SD16—24no—
910SD16—22no—
911D8—22no—
912D8—24no—
913C2×C8C24×C3711yescharacteristic
914C2×C8C24×C3711yescharacteristic
915C2×C8C24×C3711yescharacteristic
916C2×C8C24×C3711yescharacteristic
917C2×C8C24×C3712yes—
918C2×C8C24×C3712yes—
919C4⋊C4—21no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4C2×D4×C3712yes—
943C4⋊C4C2×D4×C3712yes—
944C4⋊C4C2×D4×C3712yes—
945C4⋊C4C2×D4×C3712yes—
946C4⋊C4C2×D4×C3711yescharacteristic
947C4⋊C4C2×D4×C3712yes—
948C4⋊C4C2×D4×C3711yescharacteristic
949C4⋊C4C2×D4×C3712yes—
950C4⋊C4C2×D4×C3712yes—
951C4⋊C4C24×C3711yescharacteristic
952C4⋊C4C24×C3712yes—
953C4⋊C4C24×C3712yes—
954C4⋊C4C24×C3711yescharacteristic
955C4⋊C4C24×C3711yescharacteristic
956C4⋊C4C24×C3711yescharacteristic
957C4⋊C4C24×C3712yes—
958C22⋊C4—21no—
959C22⋊C4—21no—
960C22⋊C4—21no—
961C22⋊C4—21no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—21no—
965C22⋊C4—21no—
966C22⋊C4—21no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—21no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4C2×D4×C3712yes—
976C22⋊C4C2×D4×C3712yes—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—22no—
982C42—22no—
983C42—22no—
984C42C2×D4×C3711yescharacteristic
985C42C2×D4×C3711yescharacteristic
986C42C24×C3711yescharacteristic
987C42C24×C3712yes—
988C42C24×C3712yes—
989C42C24×C3711yescharacteristic
990C23—21no—
991C23—21no—
992C23—22no—
993C23C22×D4×C3711yescharacteristic
994Q8—22no—
995Q8—22no—
996Q8—21no—
997Q8—21no—
998Q8—21no—
999Q8—42no—
1000Q8—42no—
1001Q8—42no—
1002Q8—42no—
1003Q8—82no—
1004Q8—82no—
1005Q8—82no—
1006Q8—82no—
1007Q82−1+4×C3712yes—
1008D4—24no—
1009D4—21no—
1010D4—21no—
1011D4—22no—
1012D4—21no—
1013D4—22no—
1014D4—42no—
1015D4—82no—
1016D4—81no—
1017D4—82no—
1018D4—82no—
1019D4—81no—
1020D42−1+4×C3712yes—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—41no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—82no—
1039C2×C4—82no—
1040C2×C4—82no—
1041C2×C4—82no—
1042C2×C4—82no—
1043C2×C4—82no—
1044C2×C4—82no—
1045C2×C4C22×D4×C3712yes—
1046C2×C4C22×D4×C3711yescharacteristic
1047C2×C4C22×D4×C3711yescharacteristic
1048C2×C4C22×D4×C3712yes—
1049C2×C4C22×D4×C3711yescharacteristic
1050C2×C4C22×D4×C3711yescharacteristic
1051C2×C4C22×D4×C3712yes—
1052C2×C4C22×D4×C3712yes—
1053C2×C4C22×D4×C3711yescharacteristic
1054C2×C4C25×C3711yescharacteristic
1055C8—21no—
1056C8—22no—
1057C8—21no—
1058C8—22no—
1059C8—21no—
1060C8—21no—
1061C22—21no—
1062C22—22no—
1063C22—21no—
1064C22—21no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—42no—
1069C22—41no—
1070C22—42no—
1071C22—42no—
1072C22—41no—
1073C22C23×D4×C3711yescharacteristic
1074C4—21no—
1075C4—22no—
1076C4—21no—
1077C4—22no—
1078C4—22no—
1079C4—21no—
1080C4—21no—
1081C4—22no—
1082C4—22no—
1083C4—41no—
1084C4—41no—
1085C4—41no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—41no—
1090C4—41no—
1091C4C37×#57612yes—
1092C4C2×2−1+4×C3711yescharacteristic
1093C4C2×2−1+4×C3711yescharacteristic
1094C2—41no—
1095C2—42no—
1096C2—81no—
1097C2—82no—
1098C2C37×#348611yescharacteristic
1099C2C2×C37×#57611yescharacteristic
1100C2C37×#358611yescharacteristic
subgroupG/H
center, socleC22×C37C23×D4
commutator, Frattini, cosocleC2×C4C25×C37
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C37×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3554C2semidirect
2. C37×#3503C2semidirect
3. C37×#3389C2semidirect
4. C37×#3386C2semidirect
5. C37×#3386C2semidirect
6. C37×#3385C2semidirect
7. C37×#3383C2semidirect
8. Q8×D8×C37C2semidirect
9. C37×#3375C2semidirect
10. C37×#3373C2semidirect
11. C37×#3370C2semidirect
12. C37×#3368C2semidirect
13. C37×#3365C2semidirect
14. C37×#3358C2semidirect
15. C37×#3243C2semidirect
16. C37×#3241C2semidirect
17. C37×#3239C2semidirect
18. C37×#3226C2semidirect
19. C37×#3124C2semidirect
20. C37×#3119C2semidirect
21. C37×#3115C2semidirect
22. C37×#3102C2semidirect
23. C37×#2985C2semidirect
510. #61857C37direct (N × H)
544. #3554C2×C37semidirect
545. #3503C2×C37semidirect
546. #3389C2×C37semidirect
547. #3386C2×C37semidirect
548. #3386C2×C37semidirect
549. #3385C2×C37semidirect
550. #3383C2×C37semidirect
551. Q8×D8C2×C37semidirect
552. #3375C2×C37semidirect
553. #3373C2×C37semidirect
554. #3370C2×C37semidirect
555. #3368C2×C37semidirect
556. #3365C2×C37semidirect
557. #3358C2×C37semidirect
558. #3243C2×C37semidirect
559. #3241C2×C37semidirect
560. #3239C2×C37semidirect
561. #3226C2×C37semidirect
562. #3124C2×C37semidirect
563. #3119C2×C37semidirect
564. #3115C2×C37semidirect
565. #3102C2×C37semidirect
566. #2985C2×C37semidirect
685. C37#61857direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35542
C37×#35032
C37×#33892
C37×#33862
C37×#33852
C37×#33832
Q8×D8×C372
C37×#33752
C37×#33732
C37×#33702
C37×#33682
C37×#33652
C37×#33582
C37×#32432
C37×#32412
C37×#32392
C37×#32262
C37×#31242
C37×#31192
C37×#31152
C37×#31022
C37×#29852
#6185737