Finite Group Databasebeta

← C137×#22678 #46872064

Subgroups — C137×#22678 #46872064

Order 35072.

982 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#440×C137C211yesmaximal, characteristic
2C2×#440×C137C211yesmaximal, characteristic
3C2×C4×SD16×C137C211yesmaximal, characteristic
4Q8×C4⋊C4×C137C211yesmaximal, characteristic, complemented
5#2349×C137C211yesmaximal, characteristic
6#1943×C137C211yesmaximal, characteristic, complemented
7#1942×C137C211yesmaximal, characteristic, complemented
8#1865×C137C211yesmaximal, characteristic, complemented
9#1864×C137C211yesmaximal, characteristic
10#1863×C137C211yesmaximal, characteristic, complemented
11#1862×C137C211yesmaximal, characteristic
12#1847×C137C211yesmaximal, characteristic, complemented
13#1805×C137C211yesmaximal, characteristic, complemented
14#1802×C137C211yesmaximal, characteristic
15#1771×C137C211yesmaximal, characteristic, complemented
16C22×SD16×C137C2211yescharacteristic
17C2×C4×Q8×C137C2211yescharacteristic
18C2×C4×Q8×C137C2211yescharacteristic
19C2×C4×Q8×C137C2211yescharacteristic
20C2×C4×D4×C137C2211yescharacteristic
21C2×C4×D4×C137C2211yescharacteristic
22C2×C4×D4×C137C2211yescharacteristic
23#440×C137—24no—
24#440×C137C418yescomplemented
25C4×SD16×C137—24no—
26C2×#107×C137C2211yescharacteristic
27C2×#107×C137C2211yescharacteristic
28C2×#107×C137C2211yescharacteristic
29C2×#106×C137C2211yescharacteristic
30C2×#106×C137C2211yescharacteristic
31C2×C4⋊C8×C137C2211yescharacteristic
32C2×#103×C137C2211yescharacteristic
33C2×#103×C137C2211yescharacteristic
34C2×#103×C137C2211yescharacteristic
35C2×#102×C137C2211yescharacteristic
36C2×#102×C137C2211yescharacteristic
37C2×#102×C137C2211yescharacteristic
38C2×#97×C137C2211yescharacteristic
39C2×#97×C137C2211yescharacteristic
40C2×C4×C8×C137C2211yescharacteristic
41#389×C137—21no—
42#389×C137—21no—
43#389×C137C2211yescharacteristic
44#389×C137C2211yescharacteristic
45#389×C137C2211yescharacteristic
46#389×C137C2211yescharacteristic
47#385×C137—21no—
48#385×C137—21no—
49#384×C137—21no—
50#384×C137C2211yescharacteristic
51#382×C137C2211yescharacteristic
52#380×C137—21no—
53C4×C4⋊C4×C137—21no—
54C4×C4⋊C4×C137C2211yescharacteristic
55C2×#95×C137—21no—
56#340×C137C2211yescharacteristic
57#340×C137C2211yescharacteristic
58#340×C137C2211yescharacteristic
59#340×C137C2211yescharacteristic
60#336×C137C2211yescharacteristic
61#336×C137C2211yescharacteristic
62C22×Q8×C137C2311yescharacteristic
63C22×D4×C137C2311yescharacteristic
64C23×C4×C137—21no—
65C23×C4×C137—21no—
66C23×C4×C137—21no—
67C2×SD16×C137C2×C414yes—
68C2×SD16×C137D414yes—
69C2×SD16×C137Q814yes—
70C22×C8×C137C2311yescharacteristic
71C22×C8×C137C2311yescharacteristic
72C22×C8×C137C2311yescharacteristic
73C22×C8×C137C2311yescharacteristic
74C4×Q8×C137—22no—
75C4×Q8×C137—22no—
76C4×Q8×C137—22no—
77C4×Q8×C137—41no—
78C4×Q8×C137—41no—
79C4×Q8×C137C2×C414yescomplemented
80C4×D4×C137—22no—
81C4×D4×C137—22no—
82C4×D4×C137—22no—
83C4×D4×C137—41no—
84C4×D4×C137—41no—
85C4×D4×C137C2×C414yes—
86C2×C4⋊C4×C137—21no—
87C2×C4⋊C4×C137—21no—
88C2×C4⋊C4×C137—21no—
89C2×C4⋊C4×C137—21no—
90C2×C4⋊C4×C137—21no—
91C2×C4⋊C4×C137—21no—
92C2×C4⋊C4×C137—21no—
93C2×C4⋊C4×C137—21no—
94C2×C4⋊C4×C137—21no—
95C2×C4⋊C4×C137D411yescharacteristic
96C2×C4⋊C4×C137D411yescharacteristic
97C2×C4⋊C4×C137C2311yescharacteristic
98C2×C4⋊C4×C137C2311yescharacteristic
99C2×C4⋊C4×C137C2311yescharacteristic
100C2×C4⋊C4×C137C2311yescharacteristic
101C2×C4⋊C4×C137C2311yescharacteristic
102C2×C4⋊C4×C137C2311yescharacteristic
103C2×C22⋊C4×C137—21no—
104C2×C22⋊C4×C137—21no—
105C2×C22⋊C4×C137—21no—
106C2×C42×C137—21no—
107C2×C42×C137—21no—
108C2×C42×C137—21no—
109C2×C42×C137C2311yescharacteristic
110C2×C42×C137C2311yescharacteristic
111C2×C42×C137C2311yescharacteristic
112#107×C137—22no—
113#107×C137—41no—
114#107×C137C2×C414yescomplemented
115#106×C137—22no—
116#106×C137—41no—
117C4⋊C8×C137—22no—
118#103×C137—22no—
119#103×C137—22no—
120#103×C137C2×C414yescomplemented
121#102×C137—22no—
122#102×C137—22no—
123#102×C137C2×C414yes—
124#97×C137—22no—
125#97×C137C2×C414yescomplemented
126C4×C8×C137—22no—
127#95×C137—21no—
128#95×C137—21no—
129#95×C137—21no—
130#95×C137—21no—
131#95×C137—21no—
132#95×C137—21no—
133#95×C137D411yescharacteristic
134#95×C137D411yescharacteristic
135C24×C137—21no—
136C2×Q8×C137—21no—
137C2×Q8×C137—21no—
138C2×Q8×C137—21no—
139C2×Q8×C137C22×C412yes—
140C2×Q8×C137C2×D412yes—
141C2×Q8×C137C2×Q812yes—
142C2×D4×C137—21no—
143C2×D4×C137—21no—
144C2×D4×C137—21no—
145C2×D4×C137C22×C412yes—
146C2×D4×C137C2×D412yes—
147C2×D4×C137C2×Q812yes—
148C22×C4×C137—21no—
149C22×C4×C137—21no—
150C22×C4×C137—21no—
151C22×C4×C137—24no—
152C22×C4×C137—21no—
153C22×C4×C137—21no—
154C22×C4×C137—21no—
155C22×C4×C137—21no—
156C22×C4×C137—42no—
157C22×C4×C137—42no—
158C22×C4×C137—42no—
159C22×C4×C137—42no—
160C22×C4×C137—81no—
161C22×C4×C137—81no—
162C22×C4×C137—81no—
163C22×C4×C137—81no—
164C22×C4×C137C2×D411yescharacteristic
165C22×C4×C137C2×D411yescharacteristic
166C22×C4×C137C2×D411yescharacteristic
167C22×C4×C137C2×D411yescharacteristic
168C22×C4×C137C2×D411yescharacteristic
169C22×C4×C137C2×D411yescharacteristic
170C22×C4×C137C2411yescharacteristic
171SD16×C137C4⋊C4116yescomplemented
172C2×C8×C137—21no—
173C2×C8×C137—21no—
174C2×C8×C137—21no—
175C2×C8×C137—21no—
176C2×C8×C137—21no—
177C2×C8×C137—21no—
178C2×C8×C137—21no—
179C2×C8×C137—21no—
180C2×C8×C137C22×C412yes—
181C2×C8×C137C22×C412yes—
182C2×C8×C137C2×D412yes—
183C2×C8×C137C2×Q812yes—
184C4⋊C4×C137—24no—
185C4⋊C4×C137—22no—
186C4⋊C4×C137—21no—
187C4⋊C4×C137—21no—
188C4⋊C4×C137—21no—
189C4⋊C4×C137—21no—
190C4⋊C4×C137—21no—
191C4⋊C4×C137—21no—
192C4⋊C4×C137—21no—
193C4⋊C4×C137—21no—
194C4⋊C4×C137—21no—
195C4⋊C4×C137—21no—
196C4⋊C4×C137—41no—
197C4⋊C4×C137—42no—
198C4⋊C4×C137—42no—
199C4⋊C4×C137—42no—
200C4⋊C4×C137—81no—
201C4⋊C4×C137—81no—
202C4⋊C4×C137—81no—
203C4⋊C4×C137—81no—
204C4⋊C4×C137—81no—
205C4⋊C4×C137C22×C412yes—
206C4⋊C4×C137C22×C412yes—
207C22⋊C4×C137—24no—
208C22⋊C4×C137—42no—
209C22⋊C4×C137—42no—
210C42×C137—24no—
211C42×C137—21no—
212C42×C137—21no—
213C42×C137—21no—
214C42×C137—21no—
215C42×C137—42no—
216C42×C137—42no—
217C42×C137C22×C412yes—
218C42×C137#4112yes—
219C23×C137—22no—
220C23×C137—22no—
221C23×C137—22no—
222C23×C137—41no—
223C23×C137—41no—
224C23×C137—41no—
225C23×C137—41no—
226C23×C137C22×D411yescharacteristic
227Q8×C137—22no—
228Q8×C137—22no—
229Q8×C137—22no—
230Q8×C137C2×C4⋊C414yes—
231D4×C137—22no—
232D4×C137—22no—
233D4×C137—22no—
234D4×C137C2×C4⋊C414yes—
235C2×C4×C137—22no—
236C2×C4×C137—21no—
237C2×C4×C137—22no—
238C2×C4×C137—22no—
239C2×C4×C137—21no—
240C2×C4×C137—21no—
241C2×C4×C137—21no—
242C2×C4×C137—21no—
243C2×C4×C137—21no—
244C2×C4×C137—22no—
245C2×C4×C137—22no—
246C2×C4×C137—21no—
247C2×C4×C137—21no—
248C2×C4×C137—21no—
249C2×C4×C137—21no—
250C2×C4×C137—21no—
251C2×C4×C137—21no—
252C2×C4×C137—21no—
253C2×C4×C137—21no—
254C2×C4×C137—21no—
255C2×C4×C137—41no—
256C2×C4×C137—41no—
257C2×C4×C137—41no—
258C2×C4×C137—41no—
259C2×C4×C137—41no—
260C2×C4×C137—41no—
261C2×C4×C137—41no—
262C2×C4×C137—41no—
263C2×C4×C137—41no—
264C2×C4×C137—41no—
265C2×C4×C137—41no—
266C2×C4×C137—41no—
267C2×C4×C137—41no—
268C2×C4×C137—41no—
269C2×C4×C137—41no—
270C2×C4×C137—41no—
271C2×C4×C137—84no—
272C2×C4×C137—84no—
273C2×C4×C137—84no—
274C2×C4×C137C4×D412yes—
275C2×C4×C137C4×D412yes—
276C2×C4×C137#13712yes—
277C2×C4×C137C23×C411yescharacteristic
278C2×C4×C137C22×D411yescharacteristic
279C2×C4×C137C22×Q811yescharacteristic
280C2×C4×C137C2×#4111yescharacteristic
281C2×C4×C137H(5,𝔽2)11yescharacteristic
282C2×C4×C1372−1+411yescharacteristic
283C8×C137—22no—
284C8×C137—41no—
285C8×C137—41no—
286C8×C137C2×C4⋊C414yes—
287C22×C137—24no—
288C22×C137—42no—
289C22×C137—42no—
290C22×C137—42no—
291C22×C137—42no—
292C22×C137—42no—
293C22×C137—42no—
294C22×C137C2×C4×D411yescharacteristic
295C22×C137D4211yescharacteristic
296C22×C137D4×Q811yescharacteristic
297C22×C137C2×#13711yescharacteristic
298C22×C137#57511yescharacteristic
299C22×C137#57611yescharacteristic
300C22×C137#57711yescharacteristic
301C4×C137—24no—
302C4×C137—22no—
303C4×C137—22no—
304C4×C137—22no—
305C4×C137—42no—
306C4×C137—42no—
307C4×C137—41no—
308C4×C137—41no—
309C4×C137—41no—
310C4×C137—81no—
311C4×C137—81no—
312C4×C137—81no—
313C4×C137—81no—
314C4×C137C22×C4⋊C411yescharacteristic
315C4×C137#52011yescharacteristic
316C4×C137#54711yescharacteristic
317C4×C137#55411yescharacteristic
318C2×C137—44no—
319C2×C137D4×C4⋊C411yescharacteristic
320C2×C137C4×#13711yescharacteristic
321C2×C137#294611yescharacteristic
322C2×C137#326611yescharacteristic
323C2×C137#326811yescharacteristic
324C2×C137#338511yescharacteristic
325C2×C137#338811yescharacteristic
326#22678C13711yesmaximal, characteristic, direct product factor, Sylow
327C137#2267811yescharacteristic, direct product factor, Sylow
328C2×#440C2×C13711yescharacteristic
329C2×#440C2×C13711yescharacteristic
330C2×C4×SD16C2×C13711yescharacteristic
331Q8×C4⋊C4C2×C13711yescharacteristic, complemented
332#2349C2×C13711yescharacteristic
333#1943C2×C13711yescharacteristic, complemented
334#1942C2×C13711yescharacteristic, complemented
335#1865C2×C13711yescharacteristic, complemented
336#1864C2×C13711yescharacteristic
337#1863C2×C13711yescharacteristic, complemented
338#1862C2×C13711yescharacteristic
339#1847C2×C13711yescharacteristic, complemented
340#1805C2×C13711yescharacteristic, complemented
341#1802C2×C13711yescharacteristic
342#1771C2×C13711yescharacteristic, complemented
343C22×SD16C22×C13711yescharacteristic
344C2×C4×Q8C22×C13711yescharacteristic
345C2×C4×Q8C22×C13711yescharacteristic
346C2×C4×Q8C22×C13711yescharacteristic
347C2×C4×D4C22×C13711yescharacteristic
348C2×C4×D4C22×C13711yescharacteristic
349C2×C4×D4C22×C13711yescharacteristic
350#440—24no—
351#440C4×C13718yescomplemented
352C4×SD16—24no—
353C2×#107C22×C13711yescharacteristic
354C2×#107C22×C13711yescharacteristic
355C2×#107C22×C13711yescharacteristic
356C2×#106C22×C13711yescharacteristic
357C2×#106C22×C13711yescharacteristic
358C2×C4⋊C8C22×C13711yescharacteristic
359C2×#103C22×C13711yescharacteristic
360C2×#103C22×C13711yescharacteristic
361C2×#103C22×C13711yescharacteristic
362C2×#102C22×C13711yescharacteristic
363C2×#102C22×C13711yescharacteristic
364C2×#102C22×C13711yescharacteristic
365C2×#97C22×C13711yescharacteristic
366C2×#97C22×C13711yescharacteristic
367C2×C4×C8C22×C13711yescharacteristic
368#389—21no—
369#389—21no—
370#389C22×C13711yescharacteristic
371#389C22×C13711yescharacteristic
372#389C22×C13711yescharacteristic
373#389C22×C13711yescharacteristic
374#385—21no—
375#385—21no—
376#384—21no—
377#384C22×C13711yescharacteristic
378#382C22×C13711yescharacteristic
379#380—21no—
380C4×C4⋊C4—21no—
381C4×C4⋊C4C22×C13711yescharacteristic
382C2×#95—21no—
383#340C22×C13711yescharacteristic
384#340C22×C13711yescharacteristic
385#340C22×C13711yescharacteristic
386#340C22×C13711yescharacteristic
387#336C22×C13711yescharacteristic
388#336C22×C13711yescharacteristic
389C22×Q8C23×C13711yescharacteristic
390C22×D4C23×C13711yescharacteristic
391C23×C4—21no—
392C23×C4—21no—
393C23×C4—21no—
394C2×SD16C2×C4×C13714yes—
395C2×SD16D4×C13714yes—
396C2×SD16Q8×C13714yes—
397C22×C8C23×C13711yescharacteristic
398C22×C8C23×C13711yescharacteristic
399C22×C8C23×C13711yescharacteristic
400C22×C8C23×C13711yescharacteristic
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—41no—
405C4×Q8—41no—
406C4×Q8C2×C4×C13714yescomplemented
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—41no—
411C4×D4—41no—
412C4×D4C2×C4×C13714yes—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4D4×C13711yescharacteristic
423C2×C4⋊C4D4×C13711yescharacteristic
424C2×C4⋊C4C23×C13711yescharacteristic
425C2×C4⋊C4C23×C13711yescharacteristic
426C2×C4⋊C4C23×C13711yescharacteristic
427C2×C4⋊C4C23×C13711yescharacteristic
428C2×C4⋊C4C23×C13711yescharacteristic
429C2×C4⋊C4C23×C13711yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42C23×C13711yescharacteristic
437C2×C42C23×C13711yescharacteristic
438C2×C42C23×C13711yescharacteristic
439#107—22no—
440#107—41no—
441#107C2×C4×C13714yescomplemented
442#106—22no—
443#106—41no—
444C4⋊C8—22no—
445#103—22no—
446#103—22no—
447#103C2×C4×C13714yescomplemented
448#102—22no—
449#102—22no—
450#102C2×C4×C13714yes—
451#97—22no—
452#97C2×C4×C13714yescomplemented
453C4×C8—22no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95D4×C13711yescharacteristic
461#95D4×C13711yescharacteristic
462C24—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8C22×C4×C13712yes—
467C2×Q8C2×D4×C13712yes—
468C2×Q8C2×Q8×C13712yes—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4C22×C4×C13712yes—
473C2×D4C2×D4×C13712yes—
474C2×D4C2×Q8×C13712yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—24no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4C2×D4×C13711yescharacteristic
492C22×C4C2×D4×C13711yescharacteristic
493C22×C4C2×D4×C13711yescharacteristic
494C22×C4C2×D4×C13711yescharacteristic
495C22×C4C2×D4×C13711yescharacteristic
496C22×C4C2×D4×C13711yescharacteristic
497C22×C4C24×C13711yescharacteristic
498SD16C4⋊C4×C137116yescomplemented
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8C22×C4×C13712yes—
508C2×C8C22×C4×C13712yes—
509C2×C8C2×D4×C13712yes—
510C2×C8C2×Q8×C13712yes—
511C4⋊C4—24no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—41no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—81no—
528C4⋊C4—81no—
529C4⋊C4—81no—
530C4⋊C4—81no—
531C4⋊C4—81no—
532C4⋊C4C22×C4×C13712yes—
533C4⋊C4C22×C4×C13712yes—
534C22⋊C4—24no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C42—24no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—42no—
543C42—42no—
544C42C22×C4×C13712yes—
545C42#41×C13712yes—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23C22×D4×C13711yescharacteristic
554Q8—22no—
555Q8—22no—
556Q8—22no—
557Q8C2×C4⋊C4×C13714yes—
558D4—22no—
559D4—22no—
560D4—22no—
561D4C2×C4⋊C4×C13714yes—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—84no—
599C2×C4—84no—
600C2×C4—84no—
601C2×C4C4×D4×C13712yes—
602C2×C4C4×D4×C13712yes—
603C2×C4#137×C13712yes—
604C2×C4C23×C4×C13711yescharacteristic
605C2×C4C22×D4×C13711yescharacteristic
606C2×C4C22×Q8×C13711yescharacteristic
607C2×C4C2×#41×C13711yescharacteristic
608C2×C4H(5,𝔽2)×C13711yescharacteristic
609C2×C42−1+4×C13711yescharacteristic
610C8—22no—
611C8—41no—
612C8—41no—
613C8C2×C4⋊C4×C13714yes—
614C22—24no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22C2×C4×D4×C13711yescharacteristic
622C22D42×C13711yescharacteristic
623C22D4×Q8×C13711yescharacteristic
624C22C2×#137×C13711yescharacteristic
625C22#575×C13711yescharacteristic
626C22#576×C13711yescharacteristic
627C22#577×C13711yescharacteristic
628C4—24no—
629C4—22no—
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—81no—
640C4—81no—
641C4C22×C4⋊C4×C13711yescharacteristic
642C4#520×C13711yescharacteristic
643C4#547×C13711yescharacteristic
644C4#554×C13711yescharacteristic
645C2—44no—
646C2D4×C4⋊C4×C13711yescharacteristic
647C2C4×#137×C13711yescharacteristic
648C2#2946×C13711yescharacteristic
649C2#3266×C13711yescharacteristic
650C2#3268×C13711yescharacteristic
651C2#3385×C13711yescharacteristic
652C2#3388×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutatorC2×C4C23×C4×C137
Frattini, cosocleC22×C4C24×C137
prime radicalC22×D4×C137C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C4×C4⋊C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
4. Q8×C4⋊C4×C137C2semidirect
6. #1943×C137C2semidirect
7. #1942×C137C2semidirect
8. #1865×C137C2semidirect
10. #1863×C137C2semidirect
12. #1847×C137C2semidirect
13. #1805×C137C2semidirect
15. #1771×C137C2semidirect
24. #440×C137C4semidirect
79. C4×Q8×C137C2×C4semidirect
114. #107×C137C2×C4semidirect
120. #103×C137C2×C4semidirect
125. #97×C137C2×C4semidirect
171. SD16×C137C4⋊C4semidirect
326. #22678C137direct (N × H)
327. C137#22678direct (N × H)
331. Q8×C4⋊C4C2×C137semidirect
333. #1943C2×C137semidirect
334. #1942C2×C137semidirect
335. #1865C2×C137semidirect
337. #1863C2×C137semidirect
339. #1847C2×C137semidirect
340. #1805C2×C137semidirect
342. #1771C2×C137semidirect
351. #440C4×C137semidirect
406. C4×Q8C2×C4×C137semidirect
441. #107C2×C4×C137semidirect
447. #103C2×C4×C137semidirect
452. #97C2×C4×C137semidirect
498. SD16C4⋊C4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#440×C1372
C2×C4×SD16×C1372
Q8×C4⋊C4×C1372
#2349×C1372
#1943×C1372
#1942×C1372
#1865×C1372
#1864×C1372
#1863×C1372
#1862×C1372
#1847×C1372
#1805×C1372
#1802×C1372
#1771×C1372
#22678137