Finite Group Databasebeta

← C137×#18434 #46867820

Subgroups — C137×#18434 #46867820

Order 35072.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3560×C137C211yesmaximal, characteristic, complemented
2#3213×C137C211yesmaximal, characteristic, complemented
3#3211×C137C211yesmaximal, characteristic, complemented
4#2662×C137C211yesmaximal, characteristic, complemented
5#1606×C137C211yesmaximal, characteristic, complemented
6#1604×C137C211yesmaximal, characteristic, complemented
7#1603×C137C211yesmaximal, characteristic, complemented
8#1601×C137C211yesmaximal, characteristic, complemented
9#1600×C137C211yesmaximal, characteristic, complemented
10#1598×C137C211yesmaximal, characteristic, complemented
11#1597×C137C211yesmaximal, characteristic, complemented
12#1595×C137C211yesmaximal, characteristic, complemented
13#1509×C137C211yesmaximal, characteristic, complemented
14#1502×C137C211yesmaximal, characteristic, complemented
15#1473×C137C211yesmaximal, characteristic, complemented
16#563×C137—21no—
17#560×C137—21no—
18#553×C137—21no—
19#553×C137—21no—
20#551×C137—21no—
21#547×C137—21no—
22#546×C137—21no—
23#546×C137—21no—
24#542×C137—21no—
25#539×C137—21no—
26#539×C137C2211yescharacteristic
27#538×C137—21no—
28#538×C137—21no—
29#538×C137C2211yescharacteristic
30#537×C137C2211yescharacteristic
31#534×C137C2211yescharacteristic
32#532×C137C2211yescharacteristic
33#529×C137C2211yescharacteristic
34C2×#126×C137C2211yescharacteristic
35C2×#124×C137C2211yescharacteristic, complemented
36#496×C137—21no—
37#495×C137—21no—
38#489×C137—21no—
39#488×C137—21no—
40#464×C137—21no—
41#463×C137—21no—
42#463×C137—21no—
43#463×C137—21no—
44#451×C137C2211yescharacteristic, complemented
45#450×C137C2211yescharacteristic, complemented
46#448×C137C2211yescharacteristic
47#448×C137C2211yescharacteristic
48#448×C137C2211yescharacteristic, complemented
49#447×C137C2211yescharacteristic
50#447×C137C2211yescharacteristic
51#447×C137C2211yescharacteristic, complemented
52#432×C137C2211yescharacteristic, complemented
53#431×C137C2211yescharacteristic, complemented
54#396×C137—21no—
55#395×C137C2211yescharacteristic, complemented
56#394×C137—21no—
57#394×C137C2211yescharacteristic, complemented
58#393×C137C2211yescharacteristic
59#392×C137C2211yescharacteristic
60#390×C137—21no—
61#388×C137—21no—
62C4×C4⋊C4×C137C2211yescharacteristic, complemented
63#328×C137C2211yescharacteristic, complemented
64#328×C137C2211yescharacteristic, complemented
65#327×C137C2211yescharacteristic
66#327×C137C2211yescharacteristic
67#327×C137C2211yescharacteristic
68#327×C137C2211yescharacteristic
69#327×C137C2211yescharacteristic, complemented
70#327×C137C2211yescharacteristic, complemented
71#324×C137C2211yescharacteristic, complemented
72#324×C137C2211yescharacteristic, complemented
73#323×C137C2211yescharacteristic
74#323×C137C2211yescharacteristic
75C2×#41×C137—21no—
76C2×#41×C137—21no—
77C22×Q8×C137C2311yescharacteristic
78C22×D4×C137—21no—
79C22×D4×C137—21no—
80C22×D4×C137C2311yescharacteristic
81C2×Q16×C137—21no—
82C2×SD16×C137—21no—
83C2×SD16×C137—21no—
84C2×SD16×C137—21no—
85C2×SD16×C137—21no—
86C2×D8×C137—21no—
87C2×D8×C137—21no—
88C2×D8×C137—21no—
89C4⋊Q8×C137—21no—
90C4⋊Q8×C137D411yescharacteristic, complemented
91#127×C137D411yescharacteristic, complemented
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#126×C137—21no—
99#126×C137—21no—
100#126×C137—21no—
101#125×C137—21no—
102#125×C137—21no—
103#125×C137D411yescharacteristic, complemented
104#124×C137—21no—
105#124×C137—21no—
106#124×C137—21no—
107#124×C137—21no—
108#124×C137—21no—
109#124×C137—21no—
110#124×C137—21no—
111#124×C137—21no—
112#124×C137D411yescharacteristic, complemented
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—
121#123×C137—21no—
122#123×C137—21no—
123#123×C137—21no—
124#123×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×C137C2311yescharacteristic
133#121×C137—21no—
134#121×C137—21no—
135#121×C137—21no—
136#121×C137—21no—
137#121×C137—21no—
138#121×C137—21no—
139#121×C137—21no—
140#121×C137—21no—
141#121×C137—21no—
142#121×C137—21no—
143#121×C137—21no—
144#121×C137—21no—
145#121×C137C2311yescharacteristic
146#121×C137C2311yescharacteristic
147#121×C137C2311yescharacteristic
148#120×C137—21no—
149#120×C137—21no—
150#120×C137—21no—
151#120×C137—21no—
152#120×C137—21no—
153C4×Q8×C137D411yescharacteristic, complemented
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—
161C4×D4×C137—21no—
162C4×D4×C137D411yescharacteristic, complemented
163C4×D4×C137D411yescharacteristic, complemented
164C4×D4×C137D411yescharacteristic, complemented
165#117×C137—21no—
166#117×C137—21no—
167C2×C4⋊C4×C137—21no—
168C2×C4⋊C4×C137—21no—
169C2×C4⋊C4×C137—21no—
170C2×C4⋊C4×C137D411yescharacteristic
171C2×C4⋊C4×C137D411yescharacteristic
172C2×C4⋊C4×C137C2311yescharacteristic
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×C137—21no—
181C2×C22⋊C4×C137D411yescharacteristic
182C2×C22⋊C4×C137D411yescharacteristic
183C2×C22⋊C4×C137C2311yescharacteristic
184C2×C42×C137—21no—
185C2×C42×C137C2311yescharacteristic
186C4⋊C8×C137—21no—
187C4⋊C8×C137—21no—
188#103×C137—21no—
189#103×C137—21no—
190#103×C137—21no—
191#103×C137—21no—
192#102×C137—21no—
193#102×C137—21no—
194#102×C137—21no—
195#102×C137—21no—
196C22⋊C8×C137C2311yescharacteristic
197C22⋊C8×C137C2311yescharacteristic
198C22⋊C8×C137C2311yescharacteristic
199C22⋊C8×C137C2311yescharacteristic
200#97×C137—21no—
201C4×C8×C137—21no—
202#95×C137—21no—
203#95×C137—21no—
204#95×C137C2311yescharacteristic
205#95×C137C2311yescharacteristic
206C24×C137—21no—
207C24×C137—21no—
208C24×C137C2×D411yescharacteristic
209#41×C137—81no—
210#41×C137—81no—
211#41×C137—81no—
212#41×C137—81no—
213C2×Q8×C137—21no—
214C2×Q8×C137—21no—
215C2×Q8×C137—21no—
216C2×Q8×C137—21no—
217C2×Q8×C137—81no—
218C2×Q8×C137C2×D411yescharacteristic
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—21no—
228C2×D4×C137—21no—
229C2×D4×C137—21no—
230C2×D4×C137—21no—
231C2×D4×C137—21no—
232C2×D4×C137—21no—
233C2×D4×C137—42no—
234C2×D4×C137—81no—
235C2×D4×C137—81no—
236C2×D4×C137—81no—
237C2×D4×C137—81no—
238C2×D4×C137—81no—
239C2×D4×C137C2×D411yescharacteristic
240C2×D4×C137C2×D411yescharacteristic
241C2×D4×C137C2×D411yescharacteristic
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—21no—
245C22×C4×C137—21no—
246C22×C4×C137—21no—
247C22×C4×C137—21no—
248C22×C4×C137—21no—
249C22×C4×C137—21no—
250C22×C4×C137—21no—
251C22×C4×C137—21no—
252C22×C4×C137—21no—
253C22×C4×C137C2×D411yescharacteristic
254C22×C4×C137C2×D411yescharacteristic
255C22×C4×C137C2×D411yescharacteristic
256C22×C4×C137C2×D411yescharacteristic
257C22×C4×C137C2×D411yescharacteristic
258C22×C4×C137C2411yescharacteristic
259Q16×C137—81no—
260SD16×C137—81no—
261SD16×C137—81no—
262SD16×C137—81no—
263SD16×C137—81no—
264D8×C137—81no—
265D8×C137—81no—
266D8×C137—81no—
267C2×C8×C137—21no—
268C2×C8×C137—21no—
269C2×C8×C137—21no—
270C2×C8×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—42no—
289C4⋊C4×C137—81no—
290C4⋊C4×C137C2×D411yescharacteristic
291C4⋊C4×C137C2×D411yescharacteristic
292C4⋊C4×C137C2×D411yescharacteristic
293C4⋊C4×C137C2×D411yescharacteristic
294C22⋊C4×C137—21no—
295C22⋊C4×C137—21no—
296C22⋊C4×C137—21no—
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—42no—
320C22⋊C4×C137—41no—
321C22⋊C4×C137—41no—
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—81no—
331C42×C137C2×D411yescharacteristic
332C42×C137C2×D411yescharacteristic
333C42×C137C2×D411yescharacteristic
334C42×C137C2×D411yescharacteristic
335C23×C137—21no—
336C23×C137—21no—
337C23×C137—21no—
338C23×C137—21no—
339C23×C137—21no—
340C23×C137—21no—
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—81no—
351C23×C137—81no—
352C23×C137—81no—
353C23×C137C22×D411yescharacteristic
354Q8×C137—41no—
355Q8×C137—41no—
356Q8×C137—41no—
357Q8×C137—41no—
358Q8×C137—41no—
359Q8×C137—81no—
360Q8×C137—81no—
361D4×C137—41no—
362D4×C137—41no—
363D4×C137—41no—
364D4×C137—41no—
365D4×C137—41no—
366D4×C137—41no—
367D4×C137—41no—
368D4×C137—41no—
369D4×C137—41no—
370D4×C137—41no—
371D4×C137—41no—
372D4×C137—41no—
373D4×C137—41no—
374D4×C137—81no—
375D4×C137—81no—
376D4×C137—81no—
377D4×C137—81no—
378D4×C137—81no—
379D4×C137—81no—
380D4×C137—81no—
381D4×C137—81no—
382D4×C137—81no—
383D4×C137—84no—
384C2×C4×C137—21no—
385C2×C4×C137—21no—
386C2×C4×C137—22no—
387C2×C4×C137—21no—
388C2×C4×C137—21no—
389C2×C4×C137—21no—
390C2×C4×C137—21no—
391C2×C4×C137—21no—
392C2×C4×C137—21no—
393C2×C4×C137—21no—
394C2×C4×C137—21no—
395C2×C4×C137—21no—
396C2×C4×C137—21no—
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—41no—
406C2×C4×C137—41no—
407C2×C4×C137—41no—
408C2×C4×C137—41no—
409C2×C4×C137—81no—
410C2×C4×C137—81no—
411C2×C4×C137—81no—
412C2×C4×C137—81no—
413C2×C4×C137—81no—
414C2×C4×C137—81no—
415C2×C4×C137—81no—
416C2×C4×C137—81no—
417C2×C4×C137#12011yescharacteristic
418C2×C4×C137#12011yescharacteristic
419C2×C4×C137#12011yescharacteristic
420C2×C4×C137#12011yescharacteristic
421C2×C4×C137C22×D411yescharacteristic
422C2×C4×C137C22×D411yescharacteristic
423C8×C137—41no—
424C8×C137—41no—
425C8×C137—41no—
426C8×C137—41no—
427C22×C137—21no—
428C22×C137—21no—
429C22×C137—41no—
430C22×C137—41no—
431C22×C137—41no—
432C22×C137—41no—
433C22×C137—41no—
434C22×C137—41no—
435C22×C137—41no—
436C22×C137—41no—
437C22×C137—41no—
438C22×C137—41no—
439C22×C137—41no—
440C22×C137—41no—
441C22×C137—81no—
442C22×C137—81no—
443C22×C137—81no—
444C22×C137—81no—
445C22×C137—81no—
446C22×C137—81no—
447C22×C137—81no—
448C22×C137—81no—
449C22×C137—81no—
450C22×C137—162no—
451C22×C137C2×#12011yescharacteristic
452C22×C137#57611yescharacteristic
453C22×C137#57711yescharacteristic
454C4×C137—21no—
455C4×C137—21no—
456C4×C137—21no—
457C4×C137—21no—
458C4×C137—21no—
459C4×C137—21no—
460C4×C137—42no—
461C4×C137—41no—
462C4×C137—41no—
463C4×C137—41no—
464C4×C137—41no—
465C4×C137—41no—
466C4×C137—41no—
467C4×C137—41no—
468C4×C137—41no—
469C4×C137—81no—
470C4×C137—81no—
471C2×C137—21no—
472C2×C137—21no—
473C2×C137—81no—
474C2×C137—81no—
475C2×C137—81no—
476C2×C137—81no—
477C2×C137—161no—
478C2×C137#301211yescharacteristic
479C2×C137#301811yescharacteristic
480C2×C137#302711yescharacteristic
481#18434C13711yesmaximal, characteristic, direct product factor, Sylow
482C137#1843411yescharacteristic, direct product factor, Sylow
483#3560C2×C13711yescharacteristic, complemented
484#3213C2×C13711yescharacteristic, complemented
485#3211C2×C13711yescharacteristic, complemented
486#2662C2×C13711yescharacteristic, complemented
487#1606C2×C13711yescharacteristic, complemented
488#1604C2×C13711yescharacteristic, complemented
489#1603C2×C13711yescharacteristic, complemented
490#1601C2×C13711yescharacteristic, complemented
491#1600C2×C13711yescharacteristic, complemented
492#1598C2×C13711yescharacteristic, complemented
493#1597C2×C13711yescharacteristic, complemented
494#1595C2×C13711yescharacteristic, complemented
495#1509C2×C13711yescharacteristic, complemented
496#1502C2×C13711yescharacteristic, complemented
497#1473C2×C13711yescharacteristic, complemented
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C13711yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C13711yescharacteristic
512#537C22×C13711yescharacteristic
513#534C22×C13711yescharacteristic
514#532C22×C13711yescharacteristic
515#529C22×C13711yescharacteristic
516C2×#126C22×C13711yescharacteristic
517C2×#124C22×C13711yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C13711yescharacteristic, complemented
527#450C22×C13711yescharacteristic, complemented
528#448C22×C13711yescharacteristic
529#448C22×C13711yescharacteristic
530#448C22×C13711yescharacteristic, complemented
531#447C22×C13711yescharacteristic
532#447C22×C13711yescharacteristic
533#447C22×C13711yescharacteristic, complemented
534#432C22×C13711yescharacteristic, complemented
535#431C22×C13711yescharacteristic, complemented
536#396—21no—
537#395C22×C13711yescharacteristic, complemented
538#394—21no—
539#394C22×C13711yescharacteristic, complemented
540#393C22×C13711yescharacteristic
541#392C22×C13711yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C13711yescharacteristic, complemented
545#328C22×C13711yescharacteristic, complemented
546#328C22×C13711yescharacteristic, complemented
547#327C22×C13711yescharacteristic
548#327C22×C13711yescharacteristic
549#327C22×C13711yescharacteristic
550#327C22×C13711yescharacteristic
551#327C22×C13711yescharacteristic, complemented
552#327C22×C13711yescharacteristic, complemented
553#324C22×C13711yescharacteristic, complemented
554#324C22×C13711yescharacteristic, complemented
555#323C22×C13711yescharacteristic
556#323C22×C13711yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C13711yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C13711yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C13711yescharacteristic, complemented
573#127D4×C13711yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C13711yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C13711yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C13711yescharacteristic
615#121—21no—
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#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C13711yescharacteristic
628#121C23×C13711yescharacteristic
629#121C23×C13711yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C13711yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C13711yescharacteristic, complemented
645C4×D4D4×C13711yescharacteristic, complemented
646C4×D4D4×C13711yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C13711yescharacteristic
653C2×C4⋊C4D4×C13711yescharacteristic
654C2×C4⋊C4C23×C13711yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C13711yescharacteristic
664C2×C22⋊C4D4×C13711yescharacteristic
665C2×C22⋊C4C23×C13711yescharacteristic
666C2×C42—21no—
667C2×C42C23×C13711yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C13711yescharacteristic
679C22⋊C8C23×C13711yescharacteristic
680C22⋊C8C23×C13711yescharacteristic
681C22⋊C8C23×C13711yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C13711yescharacteristic
687#95C23×C13711yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C13711yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C13711yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C13711yescharacteristic
722C2×D4C2×D4×C13711yescharacteristic
723C2×D4C2×D4×C13711yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C13711yescharacteristic
736C22×C4C2×D4×C13711yescharacteristic
737C22×C4C2×D4×C13711yescharacteristic
738C22×C4C2×D4×C13711yescharacteristic
739C22×C4C2×D4×C13711yescharacteristic
740C22×C4C24×C13711yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—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—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C13711yescharacteristic
773C4⋊C4C2×D4×C13711yescharacteristic
774C4⋊C4C2×D4×C13711yescharacteristic
775C4⋊C4C2×D4×C13711yescharacteristic
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—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C13711yescharacteristic
814C42C2×D4×C13711yescharacteristic
815C42C2×D4×C13711yescharacteristic
816C42C2×D4×C13711yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C13711yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C13711yescharacteristic
900C2×C4#120×C13711yescharacteristic
901C2×C4#120×C13711yescharacteristic
902C2×C4#120×C13711yescharacteristic
903C2×C4C22×D4×C13711yescharacteristic
904C2×C4C22×D4×C13711yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C13711yescharacteristic
934C22#576×C13711yescharacteristic
935C22#577×C13711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2#3012×C13711yescharacteristic
961C2#3018×C13711yescharacteristic
962C2#3027×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3560×C137C2semidirect
2. #3213×C137C2semidirect
3. #3211×C137C2semidirect
4. #2662×C137C2semidirect
5. #1606×C137C2semidirect
6. #1604×C137C2semidirect
7. #1603×C137C2semidirect
8. #1601×C137C2semidirect
9. #1600×C137C2semidirect
10. #1598×C137C2semidirect
11. #1597×C137C2semidirect
12. #1595×C137C2semidirect
13. #1509×C137C2semidirect
14. #1502×C137C2semidirect
15. #1473×C137C2semidirect
35. C2×#124×C137C22semidirect
44. #451×C137C22semidirect
45. #450×C137C22semidirect
48. #448×C137C22semidirect
51. #447×C137C22semidirect
52. #432×C137C22semidirect
53. #431×C137C22semidirect
55. #395×C137C22semidirect
57. #394×C137C22semidirect
62. C4×C4⋊C4×C137C22semidirect
63. #328×C137C22semidirect
64. #328×C137C22semidirect
69. #327×C137C22semidirect
70. #327×C137C22semidirect
71. #324×C137C22semidirect
72. #324×C137C22semidirect
90. C4⋊Q8×C137D4semidirect
91. #127×C137D4semidirect
103. #125×C137D4semidirect
112. #124×C137D4semidirect
153. C4×Q8×C137D4semidirect
162. C4×D4×C137D4semidirect
163. C4×D4×C137D4semidirect
164. C4×D4×C137D4semidirect
481. #18434C137direct (N × H)
482. C137#18434direct (N × H)
483. #3560C2×C137semidirect
484. #3213C2×C137semidirect
485. #3211C2×C137semidirect
486. #2662C2×C137semidirect
487. #1606C2×C137semidirect
488. #1604C2×C137semidirect
489. #1603C2×C137semidirect
490. #1601C2×C137semidirect
491. #1600C2×C137semidirect
492. #1598C2×C137semidirect
493. #1597C2×C137semidirect
494. #1595C2×C137semidirect
495. #1509C2×C137semidirect
496. #1502C2×C137semidirect
497. #1473C2×C137semidirect
517. C2×#124C22×C137semidirect
526. #451C22×C137semidirect
527. #450C22×C137semidirect
530. #448C22×C137semidirect
533. #447C22×C137semidirect
534. #432C22×C137semidirect
535. #431C22×C137semidirect
537. #395C22×C137semidirect
539. #394C22×C137semidirect
544. C4×C4⋊C4C22×C137semidirect
545. #328C22×C137semidirect
546. #328C22×C137semidirect
551. #327C22×C137semidirect
552. #327C22×C137semidirect
553. #324C22×C137semidirect
554. #324C22×C137semidirect
572. C4⋊Q8D4×C137semidirect
573. #127D4×C137semidirect
585. #125D4×C137semidirect
594. #124D4×C137semidirect
635. C4×Q8D4×C137semidirect
644. C4×D4D4×C137semidirect
645. C4×D4D4×C137semidirect
646. C4×D4D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3560×C1372
#3213×C1372
#3211×C1372
#2662×C1372
#1606×C1372
#1604×C1372
#1603×C1372
#1601×C1372
#1600×C1372
#1598×C1372
#1597×C1372
#1595×C1372
#1509×C1372
#1502×C1372
#1473×C1372
#18434137