Finite Group Databasebeta

← C137×#18416 #46867802

Subgroups — C137×#18416 #46867802

Order 35072.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3535×C137C211yesmaximal, characteristic, complemented
2#3194×C137C211yesmaximal, characteristic, complemented
3#3187×C137C211yesmaximal, characteristic, complemented
4#2661×C137C211yesmaximal, characteristic, complemented
5#1612×C137C211yesmaximal, characteristic, complemented
6#1611×C137C211yesmaximal, characteristic, complemented
7#1609×C137C211yesmaximal, characteristic, complemented
8#1608×C137C211yesmaximal, characteristic, complemented
9#1600×C137C211yesmaximal, characteristic, complemented
10#1599×C137C211yesmaximal, characteristic, complemented
11#1597×C137C211yesmaximal, characteristic, complemented
12#1596×C137C211yesmaximal, characteristic, complemented
13#1508×C137C211yesmaximal, characteristic, complemented
14#1501×C137C211yesmaximal, characteristic, complemented
15#1468×C137C211yesmaximal, characteristic, complemented
16#563×C137—21no—
17#562×C137—21no—
18#554×C137—21no—
19#552×C137—21no—
20#551×C137—21no—
21#551×C137—21no—
22#547×C137—21no—
23#546×C137—21no—
24#544×C137C2211yescharacteristic
25#543×C137C2211yescharacteristic
26#542×C137—21no—
27#539×C137—21no—
28#539×C137—21no—
29#539×C137C2211yescharacteristic
30#538×C137C2211yescharacteristic
31#536×C137—21no—
32#525×C137C2211yescharacteristic
33C2×#123×C137C2211yescharacteristic
34C2×C22⋊Q8×C137C2211yescharacteristic
35C2×#121×C137C2211yescharacteristic
36#483×C137C2211yescharacteristic
37#483×C137C2211yescharacteristic
38#483×C137C2211yescharacteristic
39#482×C137—21no—
40#481×C137—21no—
41#480×C137C2211yescharacteristic
42#469×C137—21no—
43#468×C137—21no—
44#465×C137—21no—
45#465×C137—21no—
46#450×C137C2211yescharacteristic
47#450×C137C2211yescharacteristic
48#450×C137C2211yescharacteristic
49#449×C137—21no—
50#448×C137—21no—
51#447×C137C2211yescharacteristic
52#407×C137C2211yescharacteristic
53C2×C22⋊C8×C137C2211yescharacteristic
54#398×C137C2211yescharacteristic
55#397×C137C2211yescharacteristic
56#394×C137—21no—
57#394×C137C2211yescharacteristic
58#392×C137—21no—
59#392×C137C2211yescharacteristic
60#390×C137—21no—
61#388×C137—21no—
62C4×C22⋊C4×C137C2211yescharacteristic
63#328×C137C2211yescharacteristic
64#328×C137C2211yescharacteristic
65#328×C137C2211yescharacteristic
66#328×C137C2211yescharacteristic
67#328×C137C2211yescharacteristic
68#328×C137C2211yescharacteristic
69#327×C137C2211yescharacteristic
70#327×C137C2211yescharacteristic
71#324×C137C2211yescharacteristic
72#324×C137C2211yescharacteristic
73#323×C137C2211yescharacteristic
74#323×C137C2211yescharacteristic
75C2×#41×C137—21no—
76C2×#41×C137D411yescharacteristic, complemented
77C22×Q8×C137D411yescharacteristic, complemented
78C22×D4×C137—21no—
79C22×D4×C137—21no—
80C22×D4×C137D411yescharacteristic
81C22×D4×C137C2311yescharacteristic
82C23×C4×C137C2311yescharacteristic
83C2×SD16×C137—21no—
84C2×SD16×C137—21no—
85C2×SD16×C137—21no—
86C2×D8×C137—21no—
87C2×M16×C137—21no—
88C22×C8×C137—21no—
89C4⋊Q8×C137—21no—
90C4⋊Q8×C137—21no—
91C4⋊Q8×C137—21no—
92#126×C137—21no—
93#126×C137—21no—
94#126×C137—21no—
95#126×C137—21no—
96#126×C137—21no—
97#126×C137—21no—
98#125×C137—21no—
99#125×C137—21no—
100#125×C137—21no—
101#125×C137—21no—
102#125×C137—21no—
103#124×C137—21no—
104#124×C137—21no—
105#124×C137—21no—
106#124×C137—21no—
107#123×C137—21no—
108#123×C137—21no—
109#123×C137—21no—
110#123×C137—21no—
111#123×C137—21no—
112#123×C137—21no—
113#123×C137—21no—
114#123×C137—21no—
115#123×C137—21no—
116#123×C137—21no—
117#123×C137—21no—
118#123×C137—21no—
119#123×C137—21no—
120#123×C137—21no—
121C22⋊Q8×C137—21no—
122C22⋊Q8×C137—21no—
123C22⋊Q8×C137—21no—
124C22⋊Q8×C137—21no—
125C22⋊Q8×C137—21no—
126C22⋊Q8×C137—21no—
127C22⋊Q8×C137—21no—
128C22⋊Q8×C137—21no—
129C22⋊Q8×C137—21no—
130C22⋊Q8×C137—21no—
131C22⋊Q8×C137—21no—
132C22⋊Q8×C137—21no—
133C22⋊Q8×C137—21no—
134C22⋊Q8×C137—21no—
135C22⋊Q8×C137D411yescharacteristic, complemented
136C22⋊Q8×C137D411yescharacteristic, complemented
137C22⋊Q8×C137D411yescharacteristic, complemented
138C22⋊Q8×C137C2311yescharacteristic
139C22⋊Q8×C137C2311yescharacteristic
140C22⋊Q8×C137C2311yescharacteristic
141#121×C137—21no—
142#121×C137—21no—
143#121×C137—21no—
144#121×C137—21no—
145#121×C137—21no—
146#121×C137—21no—
147#121×C137—21no—
148#121×C137—21no—
149#121×C137D411yescharacteristic, complemented
150#121×C137C2311yescharacteristic
151#120×C137—21no—
152#120×C137—21no—
153C4×Q8×C137—21no—
154C4×D4×C137—21no—
155C4×D4×C137—21no—
156C4×D4×C137—21no—
157C4×D4×C137—21no—
158C4×D4×C137—21no—
159C4×D4×C137—21no—
160C4×D4×C137—21no—
161#117×C137—21no—
162#117×C137—21no—
163#117×C137—21no—
164#117×C137D411yescharacteristic, complemented
165C2×C4⋊C4×C137—21no—
166C2×C4⋊C4×C137—21no—
167C2×C4⋊C4×C137—21no—
168C2×C4⋊C4×C137D411yescharacteristic
169C2×C4⋊C4×C137D411yescharacteristic, complemented
170C2×C4⋊C4×C137C2311yescharacteristic
171C2×C4⋊C4×C137C2311yescharacteristic
172C2×C22⋊C4×C137—21no—
173C2×C22⋊C4×C137—21no—
174C2×C22⋊C4×C137—21no—
175C2×C22⋊C4×C137—21no—
176C2×C22⋊C4×C137—21no—
177C2×C22⋊C4×C137—21no—
178C2×C22⋊C4×C137—21no—
179C2×C22⋊C4×C137—21no—
180C2×C22⋊C4×C137D411yescharacteristic
181C2×C22⋊C4×C137D411yescharacteristic
182C2×C22⋊C4×C137C2311yescharacteristic
183C2×C42×C137—21no—
184#107×C137—21no—
185#106×C137—21no—
186#106×C137—21no—
187#106×C137—21no—
188#103×C137—21no—
189#103×C137—21no—
190#103×C137—21no—
191#102×C137—21no—
192#102×C137—21no—
193#102×C137—21no—
194#102×C137—21no—
195#102×C137—21no—
196C22⋊C8×C137—21no—
197C22⋊C8×C137—21no—
198C22⋊C8×C137C2311yescharacteristic
199C22⋊C8×C137C2311yescharacteristic
200C22⋊C8×C137C2311yescharacteristic
201C22⋊C8×C137C2311yescharacteristic
202#95×C137—21no—
203#95×C137—21no—
204#95×C137C2311yescharacteristic
205#95×C137C2311yescharacteristic
206C24×C137—21no—
207C24×C137C2×D411yescharacteristic
208C24×C137C2×D411yescharacteristic
209#41×C137—82no—
210#41×C137—81no—
211C2×Q8×C137—21no—
212C2×Q8×C137—21no—
213C2×Q8×C137—21no—
214C2×Q8×C137—81no—
215C2×Q8×C137C2×D411yescharacteristic
216C2×Q8×C137C2×D411yescharacteristic
217C2×Q8×C137C2×D411yescharacteristic
218C2×D4×C137—21no—
219C2×D4×C137—21no—
220C2×D4×C137—21no—
221C2×D4×C137—21no—
222C2×D4×C137—21no—
223C2×D4×C137—21no—
224C2×D4×C137—21no—
225C2×D4×C137—21no—
226C2×D4×C137—21no—
227C2×D4×C137—42no—
228C2×D4×C137—41no—
229C2×D4×C137—41no—
230C2×D4×C137—81no—
231C2×D4×C137—81no—
232C2×D4×C137—81no—
233C2×D4×C137—81no—
234C2×D4×C137—81no—
235C2×D4×C137—81no—
236C2×D4×C137C2×D411yescharacteristic
237C22×C4×C137—21no—
238C22×C4×C137—21no—
239C22×C4×C137—21no—
240C22×C4×C137—21no—
241C22×C4×C137—21no—
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—21no—
245C22×C4×C137—21no—
246C22×C4×C137—21no—
247C22×C4×C137—81no—
248C22×C4×C137C2×D411yescharacteristic
249C22×C4×C137C2×D411yescharacteristic
250C22×C4×C137C2×D411yescharacteristic
251C22×C4×C137C2×D411yescharacteristic
252C22×C4×C137C2×D411yescharacteristic
253C22×C4×C137C2×D411yescharacteristic
254C22×C4×C137C2×D411yescharacteristic
255C22×C4×C137C2×D411yescharacteristic
256C22×C4×C137C2411yescharacteristic
257SD16×C137—81no—
258SD16×C137—81no—
259SD16×C137—81no—
260D8×C137—81no—
261M16×C137—81no—
262C2×C8×C137—21no—
263C2×C8×C137—21no—
264C2×C8×C137—21no—
265C2×C8×C137—21no—
266C2×C8×C137—81no—
267C4⋊C4×C137—21no—
268C4⋊C4×C137—21no—
269C4⋊C4×C137—21no—
270C4⋊C4×C137—21no—
271C4⋊C4×C137—21no—
272C4⋊C4×C137—21no—
273C4⋊C4×C137—21no—
274C4⋊C4×C137—21no—
275C4⋊C4×C137—21no—
276C4⋊C4×C137—21no—
277C4⋊C4×C137—21no—
278C4⋊C4×C137—21no—
279C4⋊C4×C137—21no—
280C4⋊C4×C137—21no—
281C4⋊C4×C137—21no—
282C4⋊C4×C137—21no—
283C4⋊C4×C137—21no—
284C4⋊C4×C137—21no—
285C4⋊C4×C137—21no—
286C4⋊C4×C137—21no—
287C4⋊C4×C137—21no—
288C4⋊C4×C137—21no—
289C4⋊C4×C137—21no—
290C4⋊C4×C137—21no—
291C4⋊C4×C137—21no—
292C4⋊C4×C137—81no—
293C4⋊C4×C137C2×D411yescharacteristic
294C4⋊C4×C137C2×D411yescharacteristic
295C4⋊C4×C137C2×D411yescharacteristic
296C4⋊C4×C137C2×D411yescharacteristic
297C22⋊C4×C137—21no—
298C22⋊C4×C137—21no—
299C22⋊C4×C137—21no—
300C22⋊C4×C137—21no—
301C22⋊C4×C137—21no—
302C22⋊C4×C137—21no—
303C22⋊C4×C137—21no—
304C22⋊C4×C137—21no—
305C22⋊C4×C137—21no—
306C22⋊C4×C137—21no—
307C22⋊C4×C137—21no—
308C22⋊C4×C137—21no—
309C22⋊C4×C137—21no—
310C22⋊C4×C137—21no—
311C22⋊C4×C137—21no—
312C22⋊C4×C137—21no—
313C22⋊C4×C137—21no—
314C22⋊C4×C137—21no—
315C22⋊C4×C137—21no—
316C22⋊C4×C137—21no—
317C22⋊C4×C137—21no—
318C22⋊C4×C137—21no—
319C22⋊C4×C137—21no—
320C22⋊C4×C137—42no—
321C22⋊C4×C137—42no—
322C22⋊C4×C137—41no—
323C22⋊C4×C137—41no—
324C22⋊C4×C137—81no—
325C22⋊C4×C137—81no—
326C22⋊C4×C137—81no—
327C42×C137—21no—
328C42×C137—21no—
329C42×C137—21no—
330C42×C137—21no—
331C42×C137—21no—
332C42×C137—81no—
333C23×C137—21no—
334C23×C137—21no—
335C23×C137—21no—
336C23×C137—21no—
337C23×C137—21no—
338C23×C137—21no—
339C23×C137—41no—
340C23×C137—41no—
341C23×C137—41no—
342C23×C137—41no—
343C23×C137—41no—
344C23×C137—41no—
345C23×C137—41no—
346C23×C137—41no—
347C23×C137—41no—
348C23×C137—41no—
349C23×C137—41no—
350C23×C137#12011yescharacteristic
351C23×C137#12011yescharacteristic
352C23×C137C22×D411yescharacteristic
353Q8×C137—41no—
354Q8×C137—41no—
355Q8×C137—41no—
356Q8×C137—81no—
357Q8×C137—81no—
358Q8×C137—81no—
359D4×C137—41no—
360D4×C137—41no—
361D4×C137—41no—
362D4×C137—41no—
363D4×C137—41no—
364D4×C137—42no—
365D4×C137—42no—
366D4×C137—41no—
367D4×C137—41no—
368D4×C137—81no—
369D4×C137—81no—
370D4×C137—81no—
371D4×C137—81no—
372D4×C137—84no—
373D4×C137—82no—
374D4×C137—82no—
375C2×C4×C137—22no—
376C2×C4×C137—21no—
377C2×C4×C137—21no—
378C2×C4×C137—21no—
379C2×C4×C137—21no—
380C2×C4×C137—21no—
381C2×C4×C137—21no—
382C2×C4×C137—21no—
383C2×C4×C137—21no—
384C2×C4×C137—21no—
385C2×C4×C137—21no—
386C2×C4×C137—21no—
387C2×C4×C137—21no—
388C2×C4×C137—41no—
389C2×C4×C137—41no—
390C2×C4×C137—41no—
391C2×C4×C137—41no—
392C2×C4×C137—41no—
393C2×C4×C137—41no—
394C2×C4×C137—41no—
395C2×C4×C137—42no—
396C2×C4×C137—41no—
397C2×C4×C137—41no—
398C2×C4×C137—41no—
399C2×C4×C137—41no—
400C2×C4×C137—41no—
401C2×C4×C137—41no—
402C2×C4×C137—41no—
403C2×C4×C137—41no—
404C2×C4×C137—41no—
405C2×C4×C137—81no—
406C2×C4×C137—81no—
407C2×C4×C137—81no—
408C2×C4×C137—81no—
409C2×C4×C137—81no—
410C2×C4×C137—81no—
411C2×C4×C137#12011yescharacteristic
412C2×C4×C137#12011yescharacteristic
413C2×C4×C137C22×D411yescharacteristic
414C2×C4×C137C22×D411yescharacteristic
415C8×C137—41no—
416C8×C137—41no—
417C8×C137—41no—
418C8×C137—41no—
419C22×C137—21no—
420C22×C137—21no—
421C22×C137—21no—
422C22×C137—21no—
423C22×C137—21no—
424C22×C137—21no—
425C22×C137—21no—
426C22×C137—21no—
427C22×C137—41no—
428C22×C137—41no—
429C22×C137—41no—
430C22×C137—41no—
431C22×C137—41no—
432C22×C137—41no—
433C22×C137—81no—
434C22×C137—81no—
435C22×C137—81no—
436C22×C137—81no—
437C22×C137—81no—
438C22×C137—81no—
439C22×C137—81no—
440C22×C137—81no—
441C22×C137—81no—
442C22×C137—81no—
443C22×C137—81no—
444C22×C137C2×#12011yescharacteristic
445C22×C137#57711yescharacteristic
446C22×C137#57711yescharacteristic
447C4×C137—21no—
448C4×C137—21no—
449C4×C137—21no—
450C4×C137—21no—
451C4×C137—42no—
452C4×C137—41no—
453C4×C137—41no—
454C4×C137—41no—
455C4×C137—41no—
456C4×C137—41no—
457C4×C137—41no—
458C4×C137—41no—
459C4×C137—41no—
460C4×C137—41no—
461C4×C137—41no—
462C4×C137—81no—
463C4×C137—81no—
464C2×C137—21no—
465C2×C137—21no—
466C2×C137—41no—
467C2×C137—41no—
468C2×C137—81no—
469C2×C137—81no—
470C2×C137—161no—
471C2×C137#301011yescharacteristic
472C2×C137#301811yescharacteristic
473C2×C137#302611yescharacteristic
474#18416C13711yesmaximal, characteristic, direct product factor, Sylow
475C137#1841611yescharacteristic, direct product factor, Sylow
476#3535C2×C13711yescharacteristic, complemented
477#3194C2×C13711yescharacteristic, complemented
478#3187C2×C13711yescharacteristic, complemented
479#2661C2×C13711yescharacteristic, complemented
480#1612C2×C13711yescharacteristic, complemented
481#1611C2×C13711yescharacteristic, complemented
482#1609C2×C13711yescharacteristic, complemented
483#1608C2×C13711yescharacteristic, complemented
484#1600C2×C13711yescharacteristic, complemented
485#1599C2×C13711yescharacteristic, complemented
486#1597C2×C13711yescharacteristic, complemented
487#1596C2×C13711yescharacteristic, complemented
488#1508C2×C13711yescharacteristic, complemented
489#1501C2×C13711yescharacteristic, complemented
490#1468C2×C13711yescharacteristic, complemented
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C13711yescharacteristic
500#543C22×C13711yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C13711yescharacteristic
505#538C22×C13711yescharacteristic
506#536—21no—
507#525C22×C13711yescharacteristic
508C2×#123C22×C13711yescharacteristic
509C2×C22⋊Q8C22×C13711yescharacteristic
510C2×#121C22×C13711yescharacteristic
511#483C22×C13711yescharacteristic
512#483C22×C13711yescharacteristic
513#483C22×C13711yescharacteristic
514#482—21no—
515#481—21no—
516#480C22×C13711yescharacteristic
517#469—21no—
518#468—21no—
519#465—21no—
520#465—21no—
521#450C22×C13711yescharacteristic
522#450C22×C13711yescharacteristic
523#450C22×C13711yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C13711yescharacteristic
527#407C22×C13711yescharacteristic
528C2×C22⋊C8C22×C13711yescharacteristic
529#398C22×C13711yescharacteristic
530#397C22×C13711yescharacteristic
531#394—21no—
532#394C22×C13711yescharacteristic
533#392—21no—
534#392C22×C13711yescharacteristic
535#390—21no—
536#388—21no—
537C4×C22⋊C4C22×C13711yescharacteristic
538#328C22×C13711yescharacteristic
539#328C22×C13711yescharacteristic
540#328C22×C13711yescharacteristic
541#328C22×C13711yescharacteristic
542#328C22×C13711yescharacteristic
543#328C22×C13711yescharacteristic
544#327C22×C13711yescharacteristic
545#327C22×C13711yescharacteristic
546#324C22×C13711yescharacteristic
547#324C22×C13711yescharacteristic
548#323C22×C13711yescharacteristic
549#323C22×C13711yescharacteristic
550C2×#41—21no—
551C2×#41D4×C13711yescharacteristic, complemented
552C22×Q8D4×C13711yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C13711yescharacteristic
556C22×D4C23×C13711yescharacteristic
557C23×C4C23×C13711yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C13711yescharacteristic, complemented
611C22⋊Q8D4×C13711yescharacteristic, complemented
612C22⋊Q8D4×C13711yescharacteristic, complemented
613C22⋊Q8C23×C13711yescharacteristic
614C22⋊Q8C23×C13711yescharacteristic
615C22⋊Q8C23×C13711yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C13711yescharacteristic, complemented
625#121C23×C13711yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C13711yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C13711yescharacteristic
644C2×C4⋊C4D4×C13711yescharacteristic, complemented
645C2×C4⋊C4C23×C13711yescharacteristic
646C2×C4⋊C4C23×C13711yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C13711yescharacteristic
656C2×C22⋊C4D4×C13711yescharacteristic
657C2×C22⋊C4C23×C13711yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C13711yescharacteristic
674C22⋊C8C23×C13711yescharacteristic
675C22⋊C8C23×C13711yescharacteristic
676C22⋊C8C23×C13711yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C13711yescharacteristic
680#95C23×C13711yescharacteristic
681C24—21no—
682C24C2×D4×C13711yescharacteristic
683C24C2×D4×C13711yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C13711yescharacteristic
691C2×Q8C2×D4×C13711yescharacteristic
692C2×Q8C2×D4×C13711yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C13711yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C13711yescharacteristic
724C22×C4C2×D4×C13711yescharacteristic
725C22×C4C2×D4×C13711yescharacteristic
726C22×C4C2×D4×C13711yescharacteristic
727C22×C4C2×D4×C13711yescharacteristic
728C22×C4C2×D4×C13711yescharacteristic
729C22×C4C2×D4×C13711yescharacteristic
730C22×C4C2×D4×C13711yescharacteristic
731C22×C4C24×C13711yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C13711yescharacteristic
769C4⋊C4C2×D4×C13711yescharacteristic
770C4⋊C4C2×D4×C13711yescharacteristic
771C4⋊C4C2×D4×C13711yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C13711yescharacteristic
826C23#120×C13711yescharacteristic
827C23C22×D4×C13711yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C13711yescharacteristic
887C2×C4#120×C13711yescharacteristic
888C2×C4C22×D4×C13711yescharacteristic
889C2×C4C22×D4×C13711yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C13711yescharacteristic
920C22#577×C13711yescharacteristic
921C22#577×C13711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2#3010×C13711yescharacteristic
947C2#3018×C13711yescharacteristic
948C2#3026×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3535×C137C2semidirect
2. #3194×C137C2semidirect
3. #3187×C137C2semidirect
4. #2661×C137C2semidirect
5. #1612×C137C2semidirect
6. #1611×C137C2semidirect
7. #1609×C137C2semidirect
8. #1608×C137C2semidirect
9. #1600×C137C2semidirect
10. #1599×C137C2semidirect
11. #1597×C137C2semidirect
12. #1596×C137C2semidirect
13. #1508×C137C2semidirect
14. #1501×C137C2semidirect
15. #1468×C137C2semidirect
76. C2×#41×C137D4semidirect
77. C22×Q8×C137D4semidirect
135. C22⋊Q8×C137D4semidirect
136. C22⋊Q8×C137D4semidirect
137. C22⋊Q8×C137D4semidirect
149. #121×C137D4semidirect
164. #117×C137D4semidirect
169. C2×C4⋊C4×C137D4semidirect
474. #18416C137direct (N × H)
475. C137#18416direct (N × H)
476. #3535C2×C137semidirect
477. #3194C2×C137semidirect
478. #3187C2×C137semidirect
479. #2661C2×C137semidirect
480. #1612C2×C137semidirect
481. #1611C2×C137semidirect
482. #1609C2×C137semidirect
483. #1608C2×C137semidirect
484. #1600C2×C137semidirect
485. #1599C2×C137semidirect
486. #1597C2×C137semidirect
487. #1596C2×C137semidirect
488. #1508C2×C137semidirect
489. #1501C2×C137semidirect
490. #1468C2×C137semidirect
551. C2×#41D4×C137semidirect
552. C22×Q8D4×C137semidirect
610. C22⋊Q8D4×C137semidirect
611. C22⋊Q8D4×C137semidirect
612. C22⋊Q8D4×C137semidirect
624. #121D4×C137semidirect
639. #117D4×C137semidirect
644. C2×C4⋊C4D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3535×C1372
#3194×C1372
#3187×C1372
#2661×C1372
#1612×C1372
#1611×C1372
#1609×C1372
#1608×C1372
#1600×C1372
#1599×C1372
#1597×C1372
#1596×C1372
#1508×C1372
#1501×C1372
#1468×C1372
#18416137