Finite Group Databasebeta

← C37×#33553 #22654806

Subgroups — C37×#33553 #22654806

Order 9472.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3537C211yesmaximal, characteristic, complemented
2C37×#3027C211yesmaximal, characteristic, complemented
3C37×#3025C211yesmaximal, characteristic, complemented
4C37×#3021C211yesmaximal, characteristic, complemented
5C37×#2200C214yesmaximal, complemented
6C37×#2196C214yesmaximal, complemented
7C37×#2128C211yesmaximal, characteristic, complemented
8C37×#2122C211yesmaximal, characteristic, complemented
9C37×#2120C211yesmaximal, characteristic, complemented
10C37×#585C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C37—21no—
12C37×#560—21no—
13C37×#560C2212yescomplemented
14C37×#553—21no—
15C37×#553—21no—
16D42×C37—21no—
17D42×C37—21no—
18D42×C37—21no—
19D42×C37C2212yescomplemented
20C37×#540—21no—
21C37×#538—22no—
22C37×#535—21no—
23C37×#535C2211yescharacteristic
24C37×#535C2211yescharacteristic
25C37×#534—22no—
26C37×#525—21no—
27C37×#525C2211yescharacteristic
28C2×#121×C37—21no—
29C37×#458—21no—
30C37×#458C2212yescomplemented
31C37×B(4,𝔽2)—21no—
32C37×B(4,𝔽2)—22no—
33C37×B(4,𝔽2)C2212yescomplemented
34C37×B(4,𝔽2)C2214yescomplemented
35C37×#454—22no—
36C37×#453C2214yescomplemented
37C37×#421—21no—
38C37×#413C2211yescharacteristic, complemented
39C37×#410—21no—
40C37×#410—21no—
41C37×#410C2211yescharacteristic, complemented
42C37×#410C2211yescharacteristic, complemented
43C37×#353C2214yescomplemented
44C37×#352C2212yescomplemented
45C37×AΣL(1,𝔽16)C2212yescomplemented
46C37×AΣL(1,𝔽16)C2214yescomplemented
472−1+4×C37—21no—
482−1+4×C37—41no—
49H(5,𝔽2)×C37—21no—
50H(5,𝔽2)×C37—21no—
51H(5,𝔽2)×C37—41no—
52H(5,𝔽2)×C37C2312yes—
53C2×#41×C37—21no—
54C2×#41×C37—21no—
55C2×#41×C37—21no—
56C2×#41×C37—42no—
57C2×#41×C37C2311yescharacteristic
58C22×D4×C37—21no—
59C22×D4×C37—22no—
60C22×D4×C37—22no—
61C22×D4×C37—22no—
62C22×D4×C37D411yescharacteristic, complemented
63C22×D4×C37D411yescharacteristic, complemented
64C23×C4×C37D411yescharacteristic, complemented
65AGL(1,ℤ/8)×C37—24no—
66AGL(1,ℤ/8)×C37—42no—
67C2×SD16×C37—41no—
68C2×D8×C37—41no—
69C2×M16×C37—21no—
70#127×C37—21no—
71#127×C37—21no—
72#127×C37—41no—
73#127×C37C2312yes—
74#126×C37—22no—
75#126×C37—22no—
76#125×C37—21no—
77#124×C37—21no—
78#124×C37—41no—
79#124×C37D412yescomplemented
80#123×C37—22no—
81#123×C37—22no—
82#123×C37—22no—
83#123×C37—22no—
84#123×C37—22no—
85#123×C37D411yescharacteristic, complemented
86#123×C37C2311yescharacteristic
87C22⋊Q8×C37—21no—
88C22⋊Q8×C37—41no—
89#121×C37—22no—
90#121×C37—21no—
91#121×C37—21no—
92#121×C37—22no—
93#121×C37—22no—
94#121×C37—21no—
95#121×C37—22no—
96#121×C37—21no—
97#121×C37—21no—
98#121×C37—22no—
99#121×C37—21no—
100#121×C37—21no—
101#121×C37—22no—
102#121×C37—22no—
103#121×C37—22no—
104#121×C37—42no—
105#121×C37—41no—
106#120×C37—22no—
107#120×C37—22no—
108#120×C37—22no—
109#120×C37—21no—
110#120×C37—21no—
111#120×C37—22no—
112#120×C37—22no—
113#120×C37—24no—
114#120×C37D411yescharacteristic, complemented
115#120×C37D412yescomplemented
116#120×C37C2311yescharacteristic
117#120×C37C2312yes—
118C4×D4×C37—22no—
119C4×D4×C37—21no—
120C4×D4×C37—21no—
121C4×D4×C37—21no—
122C4×D4×C37—21no—
123C4×D4×C37—22no—
124C4×D4×C37—42no—
125#117×C37—21no—
126#117×C37—21no—
127#117×C37D411yescharacteristic, complemented
128#117×C37D411yescharacteristic, complemented
129#117×C37D411yescharacteristic, complemented
130C2×C4⋊C4×C37—21no—
131C2×C22⋊C4×C37—22no—
132#104×C37—24no—
133#101×C37—21no—
134#100×C37C2312yes—
135#99×C37—21no—
136#99×C37—21no—
137#99×C37—24no—
138#99×C37—22no—
139#99×C37—22no—
140#99×C37C2312yes—
141#99×C37C2312yes—
142C24×C37—22no—
143C24×C37—21no—
144C24×C37C2×D411yescharacteristic
145C24×C37C2×D412yes—
146#41×C37—22no—
147#41×C37—22no—
148#41×C37—41no—
149#41×C37—41no—
150#41×C37—42no—
151#41×C37—41no—
152#41×C37—41no—
153#41×C37—41no—
154#41×C37—41no—
155#41×C37—41no—
156#41×C37—42no—
157#41×C37—42no—
158#41×C37—42no—
159#41×C37—41no—
160#41×C37—41no—
161#41×C37—41no—
162C2×Q8×C37—21no—
163C2×Q8×C37—21no—
164C2×Q8×C37—21no—
165C2×Q8×C37—42no—
166C2×Q8×C37C2×D411yescharacteristic
167C2×D4×C37—21no—
168C2×D4×C37—22no—
169C2×D4×C37—22no—
170C2×D4×C37—21no—
171C2×D4×C37—21no—
172C2×D4×C37—21no—
173C2×D4×C37—22no—
174C2×D4×C37—22no—
175C2×D4×C37—21no—
176C2×D4×C37—22no—
177C2×D4×C37—22no—
178C2×D4×C37—22no—
179C2×D4×C37—22no—
180C2×D4×C37—22no—
181C2×D4×C37—22no—
182C2×D4×C37—22no—
183C2×D4×C37—21no—
184C2×D4×C37—21no—
185C2×D4×C37—21no—
186C2×D4×C37—41no—
187C2×D4×C37—41no—
188C2×D4×C37—41no—
189C2×D4×C37—41no—
190C2×D4×C37—42no—
191C2×D4×C37—42no—
192C2×D4×C37—42no—
193C2×D4×C37—41no—
194C2×D4×C37—42no—
195C2×D4×C37—44no—
196C2×D4×C37—81no—
197C2×D4×C37—81no—
198C2×D4×C37—84no—
199C2×D4×C37—84no—
200C2×D4×C37—84no—
201C2×D4×C37C2×D411yescharacteristic
202C2×D4×C37C2×D411yescharacteristic
203C2×D4×C37C2×D412yes—
204C2×D4×C37C2411yescharacteristic
205C22×C4×C37—22no—
206C22×C4×C37—22no—
207C22×C4×C37—22no—
208C22×C4×C37—22no—
209C22×C4×C37—22no—
210C22×C4×C37—21no—
211C22×C4×C37—21no—
212C22×C4×C37—41no—
213C22×C4×C37—41no—
214C22×C4×C37—41no—
215C22×C4×C37C2×D411yescharacteristic
216C22×C4×C37C2×D411yescharacteristic
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2×D411yescharacteristic
219SD16×C37—44no—
220D8×C37—44no—
221M16×C37—22no—
222M16×C37—41no—
223C2×C8×C37—41no—
224C4⋊C4×C37—22no—
225C4⋊C4×C37—22no—
226C4⋊C4×C37—22no—
227C4⋊C4×C37—21no—
228C4⋊C4×C37—21no—
229C4⋊C4×C37—21no—
230C4⋊C4×C37—21no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—41no—
233C4⋊C4×C37—41no—
234C4⋊C4×C37—42no—
235C22⋊C4×C37—22no—
236C22⋊C4×C37—22no—
237C22⋊C4×C37—22no—
238C22⋊C4×C37—22no—
239C22⋊C4×C37—21no—
240C22⋊C4×C37—21no—
241C22⋊C4×C37—21no—
242C22⋊C4×C37—22no—
243C22⋊C4×C37—22no—
244C22⋊C4×C37—21no—
245C22⋊C4×C37—22no—
246C22⋊C4×C37—21no—
247C22⋊C4×C37—22no—
248C22⋊C4×C37—22no—
249C22⋊C4×C37—22no—
250C22⋊C4×C37—42no—
251C22⋊C4×C37—44no—
252C22⋊C4×C37—42no—
253C22⋊C4×C37C2×D412yes—
254C22⋊C4×C37C2×D411yescharacteristic
255C22⋊C4×C37C2×D411yescharacteristic
256C42×C37—21no—
257C42×C37—21no—
258C42×C37—41no—
259C42×C37—41no—
260C42×C37C2×D412yes—
261C23×C37—21no—
262C23×C37—22no—
263C23×C37—22no—
264C23×C37—22no—
265C23×C37—22no—
266C23×C37—41no—
267C23×C37—42no—
268C23×C37—41no—
269C23×C37—44no—
270C23×C37—42no—
271C23×C37—81no—
272C23×C37—82no—
273C23×C37—82no—
274C23×C37—82no—
275C23×C37—82no—
276C23×C37#12011yescharacteristic
277C23×C37C22×D411yescharacteristic
278C23×C37C22×D411yescharacteristic
279Q8×C37—22no—
280Q8×C37—41no—
281Q8×C37—41no—
282Q8×C37—41no—
283Q8×C37—41no—
284D4×C37—22no—
285D4×C37—41no—
286D4×C37—41no—
287D4×C37—41no—
288D4×C37—42no—
289D4×C37—41no—
290D4×C37—41no—
291D4×C37—42no—
292D4×C37—42no—
293D4×C37—42no—
294D4×C37—42no—
295D4×C37—44no—
296D4×C37—44no—
297D4×C37—42no—
298D4×C37—42no—
299D4×C37—41no—
300D4×C37—41no—
301D4×C37—41no—
302D4×C37—41no—
303D4×C37—41no—
304D4×C37—81no—
305D4×C37—82no—
306D4×C37—82no—
307D4×C37—82no—
308D4×C37—82no—
309D4×C37—82no—
310D4×C37—82no—
311D4×C37—82no—
312D4×C37—84no—
313D4×C37—164no—
314C2×C4×C37—21no—
315C2×C4×C37—21no—
316C2×C4×C37—21no—
317C2×C4×C37—21no—
318C2×C4×C37—21no—
319C2×C4×C37—21no—
320C2×C4×C37—22no—
321C2×C4×C37—22no—
322C2×C4×C37—22no—
323C2×C4×C37—21no—
324C2×C4×C37—21no—
325C2×C4×C37—22no—
326C2×C4×C37—21no—
327C2×C4×C37—42no—
328C2×C4×C37—42no—
329C2×C4×C37—42no—
330C2×C4×C37—41no—
331C2×C4×C37—42no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
335C2×C4×C37—42no—
336C2×C4×C37—42no—
337C2×C4×C37—81no—
338C2×C4×C37—82no—
339C2×C4×C37—82no—
340C2×C4×C37—82no—
341C2×C4×C37#12011yescharacteristic
342C2×C4×C37#12011yescharacteristic
343C2×C4×C37#12011yescharacteristic
344C2×C4×C37C22×D411yescharacteristic
345C8×C37—42no—
346#33553C3711yesmaximal, characteristic, direct product factor, Sylow
347C22×C37—22no—
348C22×C37—21no—
349C22×C37—21no—
350C22×C37—21no—
351C22×C37—41no—
352C22×C37—41no—
353C22×C37—41no—
354C22×C37—41no—
355C22×C37—42no—
356C22×C37—42no—
357C22×C37—42no—
358C22×C37—42no—
359C22×C37—42no—
360C22×C37—41no—
361C22×C37—42no—
362C22×C37—42no—
363C22×C37—42no—
364C22×C37—81no—
365C22×C37—82no—
366C22×C37—82no—
367C22×C37—84no—
368C22×C37—161no—
369C22×C37—164no—
370C22×C37—162no—
371C22×C37C2×#12011yescharacteristic
372C4×C37—21no—
373C4×C37—21no—
374C4×C37—21no—
375C4×C37—42no—
376C4×C37—41no—
377C4×C37—41no—
378C4×C37—42no—
379C4×C37—42no—
380C4×C37—41no—
381C4×C37—82no—
382C4×C37—82no—
383C4×C37B(4,𝔽2)11yescharacteristic
384C4×C37B(4,𝔽2)11yescharacteristic
385#3537C2×C3711yescharacteristic, complemented
386#3027C2×C3711yescharacteristic, complemented
387#3025C2×C3711yescharacteristic, complemented
388#3021C2×C3711yescharacteristic, complemented
389#2200C2×C3714yescomplemented
390#2196C2×C3714yescomplemented
391#2128C2×C3711yescharacteristic, complemented
392#2122C2×C3711yescharacteristic, complemented
393#2120C2×C3711yescharacteristic, complemented
394C2×C37—21no—
395C2×C37—41no—
396C2×C37—41no—
397C2×C37—42no—
398C2×C37—41no—
399C2×C37—82no—
400C2×C37—82no—
401C2×C37—82no—
402C2×C37C2×B(4,𝔽2)11yescharacteristic
403#585C22×C3711yescharacteristic, complemented
404C2×AGL(1,ℤ/8)—21no—
405#560—21no—
406#560C22×C3712yescomplemented
407#553—21no—
408#553—21no—
409D42—21no—
410D42—21no—
411D42—21no—
412D42C22×C3712yescomplemented
413#540—21no—
414#538—22no—
415#535—21no—
416#535C22×C3711yescharacteristic
417#535C22×C3711yescharacteristic
418#534—22no—
419#525—21no—
420#525C22×C3711yescharacteristic
421C2×#121—21no—
422#458—21no—
423#458C22×C3712yescomplemented
424B(4,𝔽2)—21no—
425B(4,𝔽2)—22no—
426B(4,𝔽2)C22×C3712yescomplemented
427B(4,𝔽2)C22×C3714yescomplemented
428#454—22no—
429#453C22×C3714yescomplemented
430#421—21no—
431#413C22×C3711yescharacteristic, complemented
432#410—21no—
433#410—21no—
434#410C22×C3711yescharacteristic, complemented
435#410C22×C3711yescharacteristic, complemented
436#353C22×C3714yescomplemented
437#352C22×C3712yescomplemented
438AΣL(1,𝔽16)C22×C3712yescomplemented
439AΣL(1,𝔽16)C22×C3714yescomplemented
440C37#3355311yescharacteristic, direct product factor, Sylow
4412−1+4—21no—
4422−1+4—41no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—21no—
445H(5,𝔽2)—41no—
446H(5,𝔽2)C23×C3712yes—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—42no—
451C2×#41C23×C3711yescharacteristic
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4D4×C3711yescharacteristic, complemented
457C22×D4D4×C3711yescharacteristic, complemented
458C23×C4D4×C3711yescharacteristic, complemented
459AGL(1,ℤ/8)—24no—
460AGL(1,ℤ/8)—42no—
461C2×SD16—41no—
462C2×D8—41no—
463C2×M16—21no—
464#127—21no—
465#127—21no—
466#127—41no—
467#127C23×C3712yes—
468#126—22no—
469#126—22no—
470#125—21no—
471#124—21no—
472#124—41no—
473#124D4×C3712yescomplemented
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123D4×C3711yescharacteristic, complemented
480#123C23×C3711yescharacteristic
481C22⋊Q8—21no—
482C22⋊Q8—41no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—42no—
499#121—41no—
500#120—22no—
501#120—22no—
502#120—22no—
503#120—21no—
504#120—21no—
505#120—22no—
506#120—22no—
507#120—24no—
508#120D4×C3711yescharacteristic, complemented
509#120D4×C3712yescomplemented
510#120C23×C3711yescharacteristic
511#120C23×C3712yes—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—22no—
518C4×D4—42no—
519#117—21no—
520#117—21no—
521#117D4×C3711yescharacteristic, complemented
522#117D4×C3711yescharacteristic, complemented
523#117D4×C3711yescharacteristic, complemented
524C2×C4⋊C4—21no—
525C2×C22⋊C4—22no—
526#104—24no—
527#101—21no—
528#100C23×C3712yes—
529#99—21no—
530#99—21no—
531#99—24no—
532#99—22no—
533#99—22no—
534#99C23×C3712yes—
535#99C23×C3712yes—
536C24—22no—
537C24—21no—
538C24C2×D4×C3711yescharacteristic
539C24C2×D4×C3712yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C3711yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C3711yescharacteristic
596C2×D4C2×D4×C3711yescharacteristic
597C2×D4C2×D4×C3712yes—
598C2×D4C24×C3711yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C3711yescharacteristic
610C22×C4C2×D4×C3711yescharacteristic
611C22×C4C2×D4×C3711yescharacteristic
612C22×C4C2×D4×C3711yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C3712yes—
648C22⋊C4C2×D4×C3711yescharacteristic
649C22⋊C4C2×D4×C3711yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C3712yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23#120×C3711yescharacteristic
671C23C22×D4×C3711yescharacteristic
672C23C22×D4×C3711yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4#120×C3711yescharacteristic
736C2×C4#120×C3711yescharacteristic
737C2×C4#120×C3711yescharacteristic
738C2×C4C22×D4×C3711yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×#120×C3711yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4C37×B(4,𝔽2)11yescharacteristic
777C4C37×B(4,𝔽2)11yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×C37×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C37C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C37
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C2×#41×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3537C2semidirect
2. C37×#3027C2semidirect
3. C37×#3025C2semidirect
4. C37×#3021C2semidirect
5. C37×#2200C2semidirect
6. C37×#2196C2semidirect
7. C37×#2128C2semidirect
8. C37×#2122C2semidirect
9. C37×#2120C2semidirect
10. C37×#585C22semidirect
13. C37×#560C22semidirect
19. D42×C37C22semidirect
30. C37×#458C22semidirect
33. C37×B(4,𝔽2)C22semidirect
34. C37×B(4,𝔽2)C22semidirect
36. C37×#453C22semidirect
38. C37×#413C22semidirect
41. C37×#410C22semidirect
42. C37×#410C22semidirect
43. C37×#353C22semidirect
44. C37×#352C22semidirect
45. C37×AΣL(1,𝔽16)C22semidirect
46. C37×AΣL(1,𝔽16)C22semidirect
62. C22×D4×C37D4semidirect
63. C22×D4×C37D4semidirect
64. C23×C4×C37D4semidirect
79. #124×C37D4semidirect
85. #123×C37D4semidirect
114. #120×C37D4semidirect
115. #120×C37D4semidirect
127. #117×C37D4semidirect
128. #117×C37D4semidirect
129. #117×C37D4semidirect
346. #33553C37direct (N × H)
385. #3537C2×C37semidirect
386. #3027C2×C37semidirect
387. #3025C2×C37semidirect
388. #3021C2×C37semidirect
389. #2200C2×C37semidirect
390. #2196C2×C37semidirect
391. #2128C2×C37semidirect
392. #2122C2×C37semidirect
393. #2120C2×C37semidirect
403. #585C22×C37semidirect
406. #560C22×C37semidirect
412. D42C22×C37semidirect
423. #458C22×C37semidirect
426. B(4,𝔽2)C22×C37semidirect
427. B(4,𝔽2)C22×C37semidirect
429. #453C22×C37semidirect
431. #413C22×C37semidirect
434. #410C22×C37semidirect
435. #410C22×C37semidirect
436. #353C22×C37semidirect
437. #352C22×C37semidirect
438. AΣL(1,𝔽16)C22×C37semidirect
439. AΣL(1,𝔽16)C22×C37semidirect
440. C37#33553direct (N × H)
456. C22×D4D4×C37semidirect
457. C22×D4D4×C37semidirect
458. C23×C4D4×C37semidirect
473. #124D4×C37semidirect
479. #123D4×C37semidirect
508. #120D4×C37semidirect
509. #120D4×C37semidirect
521. #117D4×C37semidirect
522. #117D4×C37semidirect
523. #117D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35372
C37×#30272
C37×#30252
C37×#30212
C37×#22002
C37×#21962
C37×#21282
C37×#21222
C37×#21202
#3355337