Finite Group Databasebeta

← C137×#24471 #46873857

Subgroups — C137×#24471 #46873857

Order 35072.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C137C211yesmaximal, characteristic
2#3056×C137C211yesmaximal, characteristic, complemented
3C2×#455×C137C211yesmaximal, characteristic, complemented
4#3007×C137C211yesmaximal, characteristic, complemented
5C2×#421×C137C211yesmaximal, characteristic, complemented
6#2620×C137C211yesmaximal, characteristic, complemented
7#2039×C137C211yesmaximal, characteristic, complemented
8#2037×C137C211yesmaximal, characteristic, complemented
9#2007×C137C211yesmaximal, characteristic, complemented
10#2004×C137C211yesmaximal, characteristic, complemented
11#1900×C137C211yesmaximal, characteristic, complemented
12#1897×C137C211yesmaximal, characteristic, complemented
13#1882×C137C211yesmaximal, characteristic, complemented
14#1859×C137C211yesmaximal, characteristic, complemented
15#1792×C137C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C137C2211yescharacteristic
17C22×#41×C137C2211yescharacteristic
18C2×#137×C137C2211yescharacteristic
19C2×#137×C137C2211yescharacteristic, complemented
20C2×#137×C137C2211yescharacteristic, complemented
21C22×M16×C137C2211yescharacteristic, complemented
22#550×C137—21no—
23#548×C137—21no—
24#546×C137—21no—
25#546×C137—22no—
26D42×C137—22no—
27D42×C137—21no—
28#537×C137—21no—
29#537×C137C2211yescharacteristic
30#535×C137—21no—
31#535×C137C2211yescharacteristic
32C2×#124×C137C2211yescharacteristic, complemented
33#525×C137—21no—
34#525×C137C2211yescharacteristic
35C2×C22⋊Q8×C137C2211yescharacteristic, complemented
36C2×#121×C137—21no—
37C2×#121×C137C2211yescharacteristic
38#520×C137C2211yescharacteristic
39C2×#117×C137C2211yescharacteristic, complemented
40#470×C137—21no—
41#468×C137—21no—
42#467×C137—21no—
43#465×C137—21no—
44#455×C137—24no—
45#452×C137—21no—
46#452×C137—21no—
47#451×C137—21no—
48#450×C137—21no—
49#428×C137C2211yescharacteristic, complemented
50#421×C137—24no—
51C2×#104×C137C2211yescharacteristic
52C2×#104×C137C2211yescharacteristic
53C2×#104×C137C2211yescharacteristic, complemented
54C2×#104×C137C2211yescharacteristic, complemented
55C2×#104×C137C2211yescharacteristic, complemented
56C2×#104×C137C2211yescharacteristic, complemented
57#419×C137C2211yescharacteristic, complemented
58#417×C137C2211yescharacteristic
59#417×C137C2211yescharacteristic, complemented
60#417×C137C2211yescharacteristic, complemented
61C2×#100×C137C2211yescharacteristic, complemented
62C2×#100×C137C2211yescharacteristic, complemented
63#407×C137C2211yescharacteristic, complemented
64#396×C137—22no—
65#394×C137—22no—
66#391×C137C2211yescharacteristic, complemented
67#390×C137C2211yescharacteristic, complemented
68#384×C137C2211yescharacteristic, complemented
69#343×C137C2211yescharacteristic, complemented
70#343×C137C2211yescharacteristic, complemented
71#339×C137C2211yescharacteristic, complemented
72#339×C137C2211yescharacteristic, complemented
73H(5,𝔽2)×C137—22no—
74H(5,𝔽2)×C137—22no—
75H(5,𝔽2)×C137—41no—
76H(5,𝔽2)×C137—41no—
77C2×#41×C137—21no—
78C2×#41×C137—21no—
79C2×#41×C137—21no—
80C2×#41×C137—21no—
81C2×#41×C137—22no—
82C2×#41×C137—22no—
83C2×#41×C137—41no—
84C2×#41×C137—41no—
85C2×#41×C137D411yescharacteristic
86C2×#41×C137D411yescharacteristic
87C2×#41×C137C2311yescharacteristic
88C2×#41×C137C2311yescharacteristic
89C2×#41×C137C2311yescharacteristic
90C22×Q8×C137D411yescharacteristic
91C22×Q8×C137C2311yescharacteristic
92C22×D4×C137—21no—
93C22×D4×C137—22no—
94C22×D4×C137—22no—
95C22×D4×C137—21no—
96C22×D4×C137—21no—
97C22×D4×C137D411yescharacteristic
98C22×D4×C137D412yes—
99C22×D4×C137C2311yescharacteristic
100C23×C4×C137—21no—
101C23×C4×C137C2311yescharacteristic
102#137×C137—22no—
103#137×C137—22no—
104#137×C137—22no—
105#137×C137—41no—
106#137×C137—41no—
107#137×C137—41no—
108C2×Q16×C137—21no—
109C2×Q16×C137—21no—
110C2×Q16×C137—21no—
111C2×SD16×C137—21no—
112C2×SD16×C137—21no—
113C2×SD16×C137—21no—
114C2×M16×C137—21no—
115C2×M16×C137—22no—
116C2×M16×C137—41no—
117C2×M16×C137C2311yescharacteristic
118C2×M16×C137C2311yescharacteristic
119C2×M16×C137C2311yescharacteristic
120C2×M16×C137C2311yescharacteristic
121C22×C8×C137—21no—
122#127×C137—22no—
123#127×C137—21no—
124#124×C137—22no—
125#124×C137—21no—
126#124×C137—22no—
127#124×C137—41no—
128#123×C137—22no—
129#123×C137—21no—
130C22⋊Q8×C137—22no—
131C22⋊Q8×C137—21no—
132C22⋊Q8×C137—21no—
133C22⋊Q8×C137—21no—
134C22⋊Q8×C137—21no—
135C22⋊Q8×C137—21no—
136C22⋊Q8×C137—21no—
137C22⋊Q8×C137D411yescharacteristic
138C22⋊Q8×C137D411yescharacteristic
139#121×C137—22no—
140#121×C137—22no—
141#121×C137—22no—
142#121×C137—22no—
143#121×C137—22no—
144#121×C137—21no—
145#121×C137—21no—
146#121×C137—21no—
147#121×C137—21no—
148#121×C137—21no—
149#121×C137—21no—
150#121×C137—22no—
151#121×C137—21no—
152#121×C137—21no—
153#121×C137D411yescharacteristic
154#121×C137D411yescharacteristic
155#120×C137—22no—
156#120×C137—22no—
157#120×C137—22no—
158#120×C137—21no—
159#120×C137—22no—
160C4×Q8×C137—21no—
161C4×D4×C137—22no—
162C4×D4×C137—22no—
163C4×D4×C137—21no—
164C4×D4×C137—22no—
165C4×D4×C137—21no—
166C4×D4×C137—21no—
167#117×C137—21no—
168#117×C137—22no—
169#117×C137—41no—
170#117×C137C2311yescharacteristic
171C2×C4⋊C4×C137—21no—
172C2×C4⋊C4×C137—21no—
173C2×C4⋊C4×C137—21no—
174C2×C4⋊C4×C137—22no—
175C2×C4⋊C4×C137C2311yescharacteristic
176C2×C4⋊C4×C137C2311yescharacteristic
177C2×C22⋊C4×C137—22no—
178C2×C22⋊C4×C137—21no—
179C2×C22⋊C4×C137—21no—
180C2×C22⋊C4×C137—22no—
181C2×C22⋊C4×C137—22no—
182C2×C22⋊C4×C137D412yes—
183C2×C42×C137C2311yescharacteristic
184C2×C42×C137C2311yescharacteristic
185#107×C137—21no—
186#106×C137—21no—
187#104×C137—22no—
188#104×C137—22no—
189#104×C137—22no—
190#104×C137—22no—
191#104×C137—41no—
192#104×C137D414yescomplemented
193#103×C137—21no—
194#103×C137—21no—
195#103×C137—21no—
196#103×C137—21no—
197#103×C137—21no—
198#102×C137—21no—
199#102×C137—21no—
200#102×C137—21no—
201#100×C137—22no—
202#100×C137—41no—
203C22⋊C8×C137—21no—
204C22⋊C8×C137—21no—
205#95×C137—22no—
206C24×C137—22no—
207C24×C137—21no—
208C24×C137C2×D412yes—
209C24×C137C2×D411yescharacteristic
210#41×C137—21no—
211#41×C137—21no—
212#41×C137—22no—
213#41×C137—22no—
214#41×C137—21no—
215#41×C137—21no—
216#41×C137—21no—
217#41×C137—21no—
218#41×C137—21no—
219#41×C137—21no—
220#41×C137—21no—
221#41×C137—21no—
222#41×C137—42no—
223#41×C137—42no—
224#41×C137—41no—
225#41×C137—41no—
226#41×C137—42no—
227#41×C137—42no—
228#41×C137—42no—
229#41×C137—42no—
230#41×C137—42no—
231#41×C137—42no—
232#41×C137C2×D412yes—
233#41×C137#4112yes—
234C2×Q8×C137—21no—
235C2×Q8×C137—22no—
236C2×Q8×C137—21no—
237C2×Q8×C137—21no—
238C2×Q8×C137—21no—
239C2×Q8×C137—21no—
240C2×Q8×C137—21no—
241C2×Q8×C137—21no—
242C2×Q8×C137—41no—
243C2×Q8×C137C2×D411yescharacteristic
244C2×Q8×C137C2×D411yescharacteristic
245C2×Q8×C137C2×D411yescharacteristic
246C2×D4×C137—21no—
247C2×D4×C137—22no—
248C2×D4×C137—22no—
249C2×D4×C137—22no—
250C2×D4×C137—22no—
251C2×D4×C137—21no—
252C2×D4×C137—21no—
253C2×D4×C137—21no—
254C2×D4×C137—21no—
255C2×D4×C137—21no—
256C2×D4×C137—22no—
257C2×D4×C137—22no—
258C2×D4×C137—22no—
259C2×D4×C137—21no—
260C2×D4×C137—22no—
261C2×D4×C137—21no—
262C2×D4×C137—21no—
263C2×D4×C137—21no—
264C2×D4×C137—21no—
265C2×D4×C137—21no—
266C2×D4×C137—21no—
267C2×D4×C137—21no—
268C2×D4×C137—41no—
269C2×D4×C137—42no—
270C2×D4×C137—42no—
271C2×D4×C137—42no—
272C2×D4×C137—42no—
273C2×D4×C137—44no—
274C2×D4×C137—44no—
275C2×D4×C137—42no—
276C2×D4×C137—42no—
277C2×D4×C137—82no—
278C2×D4×C137—84no—
279C2×D4×C137C2×D411yescharacteristic
280C2×D4×C137C2×D411yescharacteristic
281C2×D4×C137C2×D411yescharacteristic
282C22×C4×C137—21no—
283C22×C4×C137—21no—
284C22×C4×C137—21no—
285C22×C4×C137—21no—
286C22×C4×C137—21no—
287C22×C4×C137—22no—
288C22×C4×C137—21no—
289C22×C4×C137—21no—
290C22×C4×C137—22no—
291C22×C4×C137—21no—
292C22×C4×C137—21no—
293C22×C4×C137—21no—
294C22×C4×C137—21no—
295C22×C4×C137—21no—
296C22×C4×C137—21no—
297C22×C4×C137—21no—
298C22×C4×C137—42no—
299C22×C4×C137—42no—
300C22×C4×C137C2×D411yescharacteristic
301C22×C4×C137C2×D411yescharacteristic
302C22×C4×C137C2×D411yescharacteristic
303C22×C4×C137C2×D411yescharacteristic
304C22×C4×C137C2×D411yescharacteristic
305C22×C4×C137C2×D412yes—
306C22×C4×C137C2411yescharacteristic
307Q16×C137—42no—
308Q16×C137—42no—
309Q16×C137—42no—
310SD16×C137—42no—
311SD16×C137—42no—
312SD16×C137—42no—
313M16×C137—21no—
314M16×C137—21no—
315M16×C137—21no—
316M16×C137—21no—
317M16×C137—21no—
318M16×C137—21no—
319M16×C137—21no—
320M16×C137—42no—
321M16×C137C2×D412yescomplemented
322C2×C8×C137—21no—
323C2×C8×C137—21no—
324C2×C8×C137—21no—
325C2×C8×C137—21no—
326C2×C8×C137—42no—
327C4⋊C4×C137—22no—
328C4⋊C4×C137—22no—
329C4⋊C4×C137—21no—
330C4⋊C4×C137—21no—
331C4⋊C4×C137—21no—
332C4⋊C4×C137—21no—
333C4⋊C4×C137—21no—
334C4⋊C4×C137—21no—
335C4⋊C4×C137—42no—
336C4⋊C4×C137—41no—
337C4⋊C4×C137—41no—
338C4⋊C4×C137—82no—
339C4⋊C4×C137C2×D411yescharacteristic
340C4⋊C4×C137C2×D411yescharacteristic
341C22⋊C4×C137—22no—
342C22⋊C4×C137—22no—
343C22⋊C4×C137—22no—
344C22⋊C4×C137—22no—
345C22⋊C4×C137—22no—
346C22⋊C4×C137—21no—
347C22⋊C4×C137—21no—
348C22⋊C4×C137—21no—
349C22⋊C4×C137—21no—
350C22⋊C4×C137—22no—
351C22⋊C4×C137—22no—
352C22⋊C4×C137—21no—
353C22⋊C4×C137—42no—
354C22⋊C4×C137—44no—
355C22⋊C4×C137—41no—
356C22⋊C4×C137—41no—
357C22⋊C4×C137—82no—
358C42×C137—22no—
359C42×C137—21no—
360C42×C137—21no—
361C42×C137—21no—
362C42×C137—21no—
363C42×C137C2×D412yescomplemented
364C23×C137—21no—
365C23×C137—21no—
366C23×C137—21no—
367C23×C137—22no—
368C23×C137—21no—
369C23×C137—21no—
370C23×C137—22no—
371C23×C137—22no—
372C23×C137—41no—
373C23×C137—41no—
374C23×C137—42no—
375C23×C137—42no—
376C23×C137—44no—
377C23×C137—42no—
378C23×C137—42no—
379C23×C137—81no—
380C23×C137—82no—
381C23×C137—82no—
382C23×C137#12011yescharacteristic
383C23×C137#12011yescharacteristic
384C23×C137C22×D411yescharacteristic
385Q8×C137—21no—
386Q8×C137—21no—
387Q8×C137—21no—
388Q8×C137—21no—
389Q8×C137—21no—
390Q8×C137—42no—
391Q8×C137—41no—
392Q8×C137—41no—
393Q8×C137—41no—
394Q8×C137—41no—
395Q8×C137#12112yes—
396D4×C137—22no—
397D4×C137—22no—
398D4×C137—21no—
399D4×C137—21no—
400D4×C137—21no—
401D4×C137—21no—
402D4×C137—21no—
403D4×C137—42no—
404D4×C137—42no—
405D4×C137—44no—
406D4×C137—42no—
407D4×C137—44no—
408D4×C137—44no—
409D4×C137—42no—
410D4×C137—41no—
411D4×C137—41no—
412D4×C137—41no—
413D4×C137—41no—
414D4×C137—41no—
415D4×C137—41no—
416D4×C137—41no—
417D4×C137—41no—
418D4×C137—81no—
419D4×C137—82no—
420D4×C137—82no—
421D4×C137—82no—
422D4×C137—82no—
423D4×C137#12112yes—
424C2×C4×C137—21no—
425C2×C4×C137—21no—
426C2×C4×C137—21no—
427C2×C4×C137—21no—
428C2×C4×C137—21no—
429C2×C4×C137—21no—
430C2×C4×C137—21no—
431C2×C4×C137—21no—
432C2×C4×C137—21no—
433C2×C4×C137—22no—
434C2×C4×C137—21no—
435C2×C4×C137—21no—
436C2×C4×C137—22no—
437C2×C4×C137—21no—
438C2×C4×C137—22no—
439C2×C4×C137—21no—
440C2×C4×C137—21no—
441C2×C4×C137—21no—
442C2×C4×C137—22no—
443C2×C4×C137—42no—
444C2×C4×C137—42no—
445C2×C4×C137—42no—
446C2×C4×C137—44no—
447C2×C4×C137—41no—
448C2×C4×C137—41no—
449C2×C4×C137—41no—
450C2×C4×C137—41no—
451C2×C4×C137—41no—
452C2×C4×C137—41no—
453C2×C4×C137—42no—
454C2×C4×C137—41no—
455C2×C4×C137—42no—
456C2×C4×C137—41no—
457C2×C4×C137—41no—
458C2×C4×C137—41no—
459C2×C4×C137—41no—
460C2×C4×C137—41no—
461C2×C4×C137—41no—
462C2×C4×C137—82no—
463C2×C4×C137#12011yescharacteristic
464C2×C4×C137#12011yescharacteristic
465C2×C4×C137C22×D411yescharacteristic
466C2×C4×C137C22×D411yescharacteristic
467C2×C4×C137C22×D411yescharacteristic
468C2×C4×C137C2×#4111yescharacteristic
469C2×C4×C137H(5,𝔽2)11yescharacteristic
470C2×C4×C137H(5,𝔽2)11yescharacteristic
471C8×C137—22no—
472C8×C137—41no—
473C8×C137—41no—
474C8×C137—41no—
475C22×C137—21no—
476C22×C137—21no—
477C22×C137—21no—
478C22×C137—21no—
479C22×C137—22no—
480C22×C137—21no—
481C22×C137—21no—
482C22×C137—21no—
483C22×C137—21no—
484C22×C137—41no—
485C22×C137—41no—
486C22×C137—41no—
487C22×C137—41no—
488C22×C137—42no—
489C22×C137—42no—
490C22×C137—41no—
491C22×C137—41no—
492C22×C137—41no—
493C22×C137—42no—
494C22×C137—41no—
495C22×C137—81no—
496C22×C137—81no—
497C22×C137—82no—
498C22×C137—82no—
499C22×C137—84no—
500C22×C137—164no—
501C22×C137C2×#12011yescharacteristic
502C22×C137D4211yescharacteristic
503C22×C137#54611yescharacteristic
504C4×C137—21no—
505C4×C137—21no—
506C4×C137—22no—
507C4×C137—42no—
508C4×C137—41no—
509C4×C137—41no—
510C4×C137—42no—
511C4×C137—41no—
512C4×C137—41no—
513C4×C137—81no—
514C4×C137—81no—
515C4×C137—81no—
516C4×C137C2×#12111yescharacteristic
517C4×C137#53411yescharacteristic
518C4×C137D4211yescharacteristic
519C4×C137#54611yescharacteristic
520C2×C137—21no—
521C2×C137—21no—
522C2×C137—41no—
523C2×C137—41no—
524C2×C137—42no—
525C2×C137—81no—
526C2×C137—82no—
527C2×C137—81no—
528C2×C137#241011yescharacteristic
529C2×C137#301911yescharacteristic
530C2×C137#302211yescharacteristic
531#24471C13711yesmaximal, characteristic, direct product factor, Sylow
532C137#2447111yescharacteristic, direct product factor, Sylow
533#3488C2×C13711yescharacteristic
534#3056C2×C13711yescharacteristic, complemented
535C2×#455C2×C13711yescharacteristic, complemented
536#3007C2×C13711yescharacteristic, complemented
537C2×#421C2×C13711yescharacteristic, complemented
538#2620C2×C13711yescharacteristic, complemented
539#2039C2×C13711yescharacteristic, complemented
540#2037C2×C13711yescharacteristic, complemented
541#2007C2×C13711yescharacteristic, complemented
542#2004C2×C13711yescharacteristic, complemented
543#1900C2×C13711yescharacteristic, complemented
544#1897C2×C13711yescharacteristic, complemented
545#1882C2×C13711yescharacteristic, complemented
546#1859C2×C13711yescharacteristic, complemented
547#1792C2×C13711yescharacteristic, complemented
548C2×H(5,𝔽2)C22×C13711yescharacteristic
549C22×#41C22×C13711yescharacteristic
550C2×#137C22×C13711yescharacteristic
551C2×#137C22×C13711yescharacteristic, complemented
552C2×#137C22×C13711yescharacteristic, complemented
553C22×M16C22×C13711yescharacteristic, complemented
554#550—21no—
555#548—21no—
556#546—21no—
557#546—22no—
558D42—22no—
559D42—21no—
560#537—21no—
561#537C22×C13711yescharacteristic
562#535—21no—
563#535C22×C13711yescharacteristic
564C2×#124C22×C13711yescharacteristic, complemented
565#525—21no—
566#525C22×C13711yescharacteristic
567C2×C22⋊Q8C22×C13711yescharacteristic, complemented
568C2×#121—21no—
569C2×#121C22×C13711yescharacteristic
570#520C22×C13711yescharacteristic
571C2×#117C22×C13711yescharacteristic, complemented
572#470—21no—
573#468—21no—
574#467—21no—
575#465—21no—
576#455—24no—
577#452—21no—
578#452—21no—
579#451—21no—
580#450—21no—
581#428C22×C13711yescharacteristic, complemented
582#421—24no—
583C2×#104C22×C13711yescharacteristic
584C2×#104C22×C13711yescharacteristic
585C2×#104C22×C13711yescharacteristic, complemented
586C2×#104C22×C13711yescharacteristic, complemented
587C2×#104C22×C13711yescharacteristic, complemented
588C2×#104C22×C13711yescharacteristic, complemented
589#419C22×C13711yescharacteristic, complemented
590#417C22×C13711yescharacteristic
591#417C22×C13711yescharacteristic, complemented
592#417C22×C13711yescharacteristic, complemented
593C2×#100C22×C13711yescharacteristic, complemented
594C2×#100C22×C13711yescharacteristic, complemented
595#407C22×C13711yescharacteristic, complemented
596#396—22no—
597#394—22no—
598#391C22×C13711yescharacteristic, complemented
599#390C22×C13711yescharacteristic, complemented
600#384C22×C13711yescharacteristic, complemented
601#343C22×C13711yescharacteristic, complemented
602#343C22×C13711yescharacteristic, complemented
603#339C22×C13711yescharacteristic, complemented
604#339C22×C13711yescharacteristic, complemented
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C13711yescharacteristic
618C2×#41D4×C13711yescharacteristic
619C2×#41C23×C13711yescharacteristic
620C2×#41C23×C13711yescharacteristic
621C2×#41C23×C13711yescharacteristic
622C22×Q8D4×C13711yescharacteristic
623C22×Q8C23×C13711yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C13711yescharacteristic
630C22×D4D4×C13712yes—
631C22×D4C23×C13711yescharacteristic
632C23×C4—21no—
633C23×C4C23×C13711yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C13711yescharacteristic
650C2×M16C23×C13711yescharacteristic
651C2×M16C23×C13711yescharacteristic
652C2×M16C23×C13711yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C13711yescharacteristic
670C22⋊Q8D4×C13711yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C13711yescharacteristic
686#121D4×C13711yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C13711yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C13711yescharacteristic
708C2×C4⋊C4C23×C13711yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C13712yes—
715C2×C42C23×C13711yescharacteristic
716C2×C42C23×C13711yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C13714yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C13712yes—
741C24C2×D4×C13711yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C13712yes—
765#41#41×C13712yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C13711yescharacteristic
776C2×Q8C2×D4×C13711yescharacteristic
777C2×Q8C2×D4×C13711yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C13711yescharacteristic
812C2×D4C2×D4×C13711yescharacteristic
813C2×D4C2×D4×C13711yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C13711yescharacteristic
833C22×C4C2×D4×C13711yescharacteristic
834C22×C4C2×D4×C13711yescharacteristic
835C22×C4C2×D4×C13711yescharacteristic
836C22×C4C2×D4×C13711yescharacteristic
837C22×C4C2×D4×C13712yes—
838C22×C4C24×C13711yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C13712yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C13711yescharacteristic
872C4⋊C4C2×D4×C13711yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C13712yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C13711yescharacteristic
915C23#120×C13711yescharacteristic
916C23C22×D4×C13711yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C13712yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C13712yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C13711yescharacteristic
996C2×C4#120×C13711yescharacteristic
997C2×C4C22×D4×C13711yescharacteristic
998C2×C4C22×D4×C13711yescharacteristic
999C2×C4C22×D4×C13711yescharacteristic
1000C2×C4C2×#41×C13711yescharacteristic
1001C2×C4H(5,𝔽2)×C13711yescharacteristic
1002C2×C4H(5,𝔽2)×C13711yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C13711yescharacteristic
1034C22D42×C13711yescharacteristic
1035C22#546×C13711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C13711yescharacteristic
1049C4#534×C13711yescharacteristic
1050C4D42×C13711yescharacteristic
1051C4#546×C13711yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2#2410×C13711yescharacteristic
1061C2#3019×C13711yescharacteristic
1062C2#3022×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
prime radical#3488×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3056×C137C2semidirect
3. C2×#455×C137C2semidirect
4. #3007×C137C2semidirect
5. C2×#421×C137C2semidirect
6. #2620×C137C2semidirect
7. #2039×C137C2semidirect
8. #2037×C137C2semidirect
9. #2007×C137C2semidirect
10. #2004×C137C2semidirect
11. #1900×C137C2semidirect
12. #1897×C137C2semidirect
13. #1882×C137C2semidirect
14. #1859×C137C2semidirect
15. #1792×C137C2semidirect
19. C2×#137×C137C22semidirect
20. C2×#137×C137C22semidirect
21. C22×M16×C137C22semidirect
32. C2×#124×C137C22semidirect
35. C2×C22⋊Q8×C137C22semidirect
39. C2×#117×C137C22semidirect
49. #428×C137C22semidirect
53. C2×#104×C137C22semidirect
54. C2×#104×C137C22semidirect
55. C2×#104×C137C22semidirect
56. C2×#104×C137C22semidirect
57. #419×C137C22semidirect
59. #417×C137C22semidirect
60. #417×C137C22semidirect
61. C2×#100×C137C22semidirect
62. C2×#100×C137C22semidirect
63. #407×C137C22semidirect
66. #391×C137C22semidirect
67. #390×C137C22semidirect
68. #384×C137C22semidirect
69. #343×C137C22semidirect
70. #343×C137C22semidirect
71. #339×C137C22semidirect
72. #339×C137C22semidirect
192. #104×C137D4semidirect
321. M16×C137C2×D4semidirect
363. C42×C137C2×D4semidirect
531. #24471C137direct (N × H)
532. C137#24471direct (N × H)
534. #3056C2×C137semidirect
535. C2×#455C2×C137semidirect
536. #3007C2×C137semidirect
537. C2×#421C2×C137semidirect
538. #2620C2×C137semidirect
539. #2039C2×C137semidirect
540. #2037C2×C137semidirect
541. #2007C2×C137semidirect
542. #2004C2×C137semidirect
543. #1900C2×C137semidirect
544. #1897C2×C137semidirect
545. #1882C2×C137semidirect
546. #1859C2×C137semidirect
547. #1792C2×C137semidirect
551. C2×#137C22×C137semidirect
552. C2×#137C22×C137semidirect
553. C22×M16C22×C137semidirect
564. C2×#124C22×C137semidirect
567. C2×C22⋊Q8C22×C137semidirect
571. C2×#117C22×C137semidirect
581. #428C22×C137semidirect
585. C2×#104C22×C137semidirect
586. C2×#104C22×C137semidirect
587. C2×#104C22×C137semidirect
588. C2×#104C22×C137semidirect
589. #419C22×C137semidirect
591. #417C22×C137semidirect
592. #417C22×C137semidirect
593. C2×#100C22×C137semidirect
594. C2×#100C22×C137semidirect
595. #407C22×C137semidirect
598. #391C22×C137semidirect
599. #390C22×C137semidirect
600. #384C22×C137semidirect
601. #343C22×C137semidirect
602. #343C22×C137semidirect
603. #339C22×C137semidirect
604. #339C22×C137semidirect
724. #104D4×C137semidirect
853. M16C2×D4×C137semidirect
895. C42C2×D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3488×C1372
#3056×C1372
C2×#455×C1372
#3007×C1372
C2×#421×C1372
#2620×C1372
#2039×C1372
#2037×C1372
#2007×C1372
#2004×C1372
#1900×C1372
#1897×C1372
#1882×C1372
#1859×C1372
#1792×C1372
#24471137