Finite Group Databasebeta

← #33108436

Subgroups — #33108436

Order 18688.

1058 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988688C211yesmaximal, characteristic, complemented
2C2×D8×Dic73C211yesmaximal, characteristic
3#22613006C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic73C211yesmaximal, characteristic, complemented
5#22610748C211yesmaximal, characteristic, complemented
6#22610690C211yesmaximal, characteristic, complemented
7#22610630C211yesmaximal, characteristic, complemented
8#22610609C211yesmaximal, characteristic, complemented
9#22610281C211yesmaximal, characteristic
10#22610267C211yesmaximal, characteristic, complemented
11#22610187C211yesmaximal, characteristic, complemented
12#22610180C211yesmaximal, characteristic, complemented
13#22609808C211yesmaximal, characteristic, complemented
14#22609756C211yesmaximal, characteristic, complemented
15C2×#463×C73C211yesmaximal, characteristic
16C2×Q8×Dic73C2211yescharacteristic
17C2×D4×Dic73C2211yescharacteristic
18C2×D4×Dic73C2211yescharacteristic
19C2×D4×Dic73C2211yescharacteristic
20C22×C4⋊Dic73—21no—
21#17988688—24no—
22D8×Dic73—24no—
23C2×#14556525C2211yescharacteristic
24C2×#14556525C2211yescharacteristic
25C2×#14556515C2211yescharacteristic
26C2×#14556515C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556502C2211yescharacteristic
32C2×#14556501C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34#17988494C2211yescharacteristic
35#17988490C2211yescharacteristic
36#17988486C2211yescharacteristic
37#17988486C2211yescharacteristic
38#17988480—21no—
39#17988480—21no—
40#17988462—21no—
41#17988462—21no—
42#17988462—21no—
43#17988457C2211yescharacteristic
44#17988447—21no—
45C4×C4⋊Dic73C2211yescharacteristic
46C4×C4⋊Dic73C2211yescharacteristic
47C22⋊C4×Dic73—21no—
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C22×SD16×C73C2211yescharacteristic
55C22×D8×C73C2211yescharacteristic
56C2×#124×C73C2211yescharacteristic
57C2×C4×D4×C73C2211yescharacteristic
58#463×C73C418yescomplemented
59C2×C4⋊C8×C73C2211yescharacteristic
60C2×#103×C73C2211yescharacteristic
61C2×#102×C73C2211yescharacteristic
62C23×Dic73—21no—
63C23×Dic73—21no—
64C23×Dic73—21no—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67Q8×Dic73—22no—
68Q8×Dic73—41no—
69D4×Dic73—22no—
70D4×Dic73—22no—
71D4×Dic73—22no—
72D4×Dic73—41no—
73D4×Dic73—41no—
74D4×Dic73—41no—
75C2×C4⋊Dic73—21no—
76C2×C4⋊Dic73—21no—
77C2×C4⋊Dic73—21no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73—44no—
81C2×C4⋊Dic73D411yescharacteristic
82C2×C4⋊Dic73D411yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×C4⋊Dic73C2311yescharacteristic
87C2×C22⋊Dic73—21no—
88C2×C22⋊Dic73—21no—
89C2×C22⋊Dic73—21no—
90C2×C22⋊Dic73—21no—
91C2×C22⋊Dic73—21no—
92C2×C4×Dic73—21no—
93C2×C4×Dic73—21no—
94C2×C4×Dic73C2311yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96#14556525—22no—
97#14556525—22no—
98#14556515—22no—
99#14556515—41no—
100#14556512—22no—
101#14556512—22no—
102#14556512—41no—
103#14556512D414yes—
104#14556502—22no—
105#14556501—22no—
106C8×Dic73—22no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498D411yescharacteristic
113#14556498D411yescharacteristic
114C22×Q8×C73C2311yescharacteristic
115C22×D4×C73C2311yescharacteristic
116C22×D4×C73C2311yescharacteristic
117C23×C4×C73—21no—
118C2×SD16×C73—22no—
119C2×SD16×C73—22no—
120C2×SD16×C73C2×C414yescomplemented
121C2×D8×C73—22no—
122C2×D8×C73—22no—
123C2×D8×C73C2×C414yes—
124C22×C8×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126#124×C73—22no—
127#124×C73C2×C414yescomplemented
128C4×D4×C73—22no—
129C4×D4×C73C2×C414yescomplemented
130C2×C4⋊C4×C73C2311yescharacteristic
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C42×C73C2311yescharacteristic
135C4⋊C8×C73C2×C414yescomplemented
136#103×C73C2×C414yescomplemented
137#102×C73C2×C414yescomplemented
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73—21no—
142C22×Dic73—42no—
143C22×Dic73—42no—
144C22×Dic73—42no—
145C22×Dic73—42no—
146C22×Dic73—42no—
147C22×Dic73—42no—
148C22×Dic73—81no—
149C22×Dic73—81no—
150C22×Dic73—81no—
151C22×Dic73C2×D411yescharacteristic
152C22×Dic73C2×D411yescharacteristic
153C22×Dic73C2×D411yescharacteristic
154C22×Dic73C2×D411yescharacteristic
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831C2×D412yes—
161C4⋊Dic73—21no—
162C4⋊Dic73—22no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—41no—
170C4⋊Dic73—42no—
171C4⋊Dic73—42no—
172C4⋊Dic73—42no—
173C4⋊Dic73—42no—
174C4⋊Dic73—81no—
175C4⋊Dic73C2×D412yes—
176C22⋊Dic73—42no—
177C22⋊Dic73—42no—
178C22⋊Dic73—42no—
179C22⋊Dic73—42no—
180C22⋊Dic73—81no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—42no—
186C4×Dic73—81no—
187C24×C73—21no—
188C24×C73—21no—
189C2×Q8×C73—21no—
190C2×Q8×C73—21no—
191C2×Q8×C73—21no—
192C2×Q8×C73—21no—
193C2×Q8×C73—21no—
194C2×Q8×C73C22×C412yes—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—21no—
203C2×D4×C73C22×C412yes—
204C2×D4×C73C22×C412yes—
205C2×D4×C73C2×D412yes—
206C2×D4×C73#4112yes—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—24no—
210C22×C4×C73—42no—
211C22×C4×C73—42no—
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2411yescharacteristic
215SD16×C73—28no—
216D8×C73—28no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73C22×C412yes—
222C2×C8×C73C22×C412yes—
223C4⋊C4×C73—21no—
224C4⋊C4×C73C22×C412yes—
225C22⋊C4×C73—24no—
226C22⋊C4×C73—24no—
227C22⋊C4×C73—24no—
228C42×C73C22×C412yes—
229C42×C73#4112yes—
230C23×C73—22no—
231C23×C73—22no—
232C23×C73—22no—
233C23×C73—22no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73C22×D411yescharacteristic
245Q8×C73—22no—
246Q8×C73—22no—
247Q8×C73—41no—
248Q8×C73—41no—
249D4×C73—22no—
250D4×C73—22no—
251D4×C73—22no—
252D4×C73—22no—
253D4×C73—22no—
254D4×C73—41no—
255D4×C73—41no—
256D4×C73C4×D414yes—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—48no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73C4×D412yes—
269C2×C4×C73C4×D412yes—
270C2×C4×C73C23×C411yescharacteristic
271C2×C4×C73C22×D411yescharacteristic
272C2×C4×C73C2×#4111yescharacteristic
273C2×C4×C73C2×#4111yescharacteristic
274C2×C4×C73H(5,𝔽2)11yescharacteristic
275C2×C4×C732−1+411yescharacteristic
276C2×Dic73—21no—
277C2×Dic73—21no—
278C2×Dic73—21no—
279C2×Dic73—21no—
280C2×Dic73—21no—
281C2×Dic73—22no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—41no—
289C2×Dic73—41no—
290C2×Dic73—41no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—41no—
299C2×Dic73—84no—
300C2×Dic73—84no—
301C2×Dic73—84no—
302C2×Dic73AGL(1,ℤ/8)12yes—
303C8×C73—22no—
304C8×C73—22no—
305#10596831—22no—
306#10596831—41no—
307C22×C73—24no—
308C22×C73—42no—
309C22×C73—42no—
310C22×C73—42no—
311C22×C73—42no—
312C22×C73—42no—
313C22×C73—42no—
314C22×C73—42no—
315C22×C73—42no—
316C22×C73—42no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73—81no—
320C22×C73—81no—
321C22×C73C2×C4×D411yescharacteristic
322C22×C73D4211yescharacteristic
323C22×C73#54811yescharacteristic
324C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C73#57511yescharacteristic
326C22×C73#57611yescharacteristic
327C22×C73#57811yescharacteristic
328C4×C73—22no—
329C4×C73—22no—
330C4×C73—42no—
331C4×C73—42no—
332C4×C73C2×C4×D411yescharacteristic
333C4×C73#52011yescharacteristic
334C4×C73#54711yescharacteristic
335C4×C73#55311yescharacteristic
336Dic73—22no—
337Dic73—41no—
338Dic73—42no—
339Dic73—41no—
340Dic73—41no—
341Dic73—81no—
342Dic73—81no—
343Dic73—81no—
344#23011—731nomaximal, Sylow
345C2×C73—44no—
346C2×C73—82no—
347C2×C73#236111yescharacteristic
348C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
349C2×C73#295111yescharacteristic
350C2×C73#326411yescharacteristic
351C2×C73#326911yescharacteristic
352C2×C73#336711yescharacteristic
353C2×C73#337011yescharacteristic
354C2×#463D7311yescharacteristic
355C2×#440—731no—
356C2×C4×D8—731no—
357#2367—731no—
358D4×C4⋊C4—731no—
359#1959—731no—
360#1947—731no—
361#1936—731no—
362#1933—731no—
363#1879—731no—
364#1877—731no—
365#1863—731no—
366#1862—731no—
367#1771—731no—
368#1762—731no—
369C73#2301111yescharacteristic, complemented, Sylow
370C22×SD16C2×D7311yescharacteristic
371C22×D8C2×D7311yescharacteristic
372C2×#124C2×D7311yescharacteristic
373C2×C4×Q8—731no—
374C2×C4×D4—731no—
375C2×C4×D4—731no—
376C2×C4×D4—731no—
377C2×C4×D4C2×D7311yescharacteristic
378C22×C4⋊C4—1461no—
379#463Dic7318yescomplemented
380#440—1464no—
381C4×D8—1464no—
382C2×#107—731no—
383C2×#107—731no—
384C2×C4⋊C8C2×D7311yescharacteristic
385C2×#103—731no—
386C2×#103—731no—
387C2×#103C2×D7311yescharacteristic
388C2×#102—731no—
389C2×#102—731no—
390C2×#102—731no—
391C2×#102—731no—
392C2×#102C2×D7311yescharacteristic
393C2×#97—731no—
394C2×#97—731no—
395C2×C4×C8—731no—
396#391—731no—
397#390—731no—
398#389—731no—
399#389—731no—
400#388—1461no—
401#388—1461no—
402#385—1461no—
403#385—1461no—
404#385—1461no—
405#384—731no—
406#380—1461no—
407C4×C4⋊C4—731no—
408C4×C4⋊C4—731no—
409C4×C22⋊C4—1461no—
410#340—731no—
411#340—731no—
412#340—731no—
413#340—731no—
414#336—731no—
415#336—731no—
416C22×Q8C22×D7311yescharacteristic
417C22×D4C22×D7311yescharacteristic
418C22×D4C22×D7311yescharacteristic
419C23×C4—21no—
420C23×C4—1461no—
421C23×C4—1461no—
422C23×C4—1461no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16C2×Dic7314yescomplemented
426C2×D8—22no—
427C2×D8—22no—
428C2×D8C2×Dic7314yes—
429C22×C8—731no—
430C22×C8—731no—
431C22×C8C22×D7311yescharacteristic
432C22×C8C22×D7311yescharacteristic
433#124—22no—
434#124C2×Dic7314yescomplemented
435C4×Q8—2921no—
436C4×Q8—1462no—
437C4×D4—22no—
438C4×D4—2921no—
439C4×D4—2921no—
440C4×D4—2921no—
441C4×D4—1462no—
442C4×D4—1462no—
443C4×D4—1462no—
444C4×D4C2×Dic7314yescomplemented
445C2×C4⋊C4—2924no—
446C2×C4⋊C4—731no—
447C2×C4⋊C4—731no—
448C2×C4⋊C4—731no—
449C2×C4⋊C4—731no—
450C2×C4⋊C4—731no—
451C2×C4⋊C4—731no—
452C2×C4⋊C4—1461no—
453C2×C4⋊C4—1461no—
454C2×C4⋊C4—1461no—
455C2×C4⋊C4—1461no—
456C2×C4⋊C4—1461no—
457C2×C4⋊C4C22×D7311yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—1461no—
462C2×C22⋊C4—1461no—
463C2×C22⋊C4—1461no—
464C2×C22⋊C4—1461no—
465C2×C22⋊C4—1461no—
466C2×C42—731no—
467C2×C42—731no—
468C2×C42—1461no—
469C2×C42—1461no—
470C2×C42C22×D7311yescharacteristic
471#107—1462no—
472#107—1462no—
473C4⋊C8C2×Dic7314yescomplemented
474#103—2921no—
475#103—1462no—
476#103C2×Dic7314yescomplemented
477#102—2921no—
478#102—734no—
479#102—1462no—
480#102—1462no—
481#102C2×Dic7314yescomplemented
482#97—1462no—
483#97—1462no—
484C4×C8—1462no—
485#95—731no—
486#95—731no—
487#95—1461no—
488#95—1461no—
489#95—1461no—
490#95—1461no—
491#95—1461no—
492C24—21no—
493C24—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C22×Dic7312yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C22×Dic7312yes—
509C2×D4C22×Dic7312yes—
510C2×D4D4×D7312yes—
511C2×D4#1192402712yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—24no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—2922no—
518C22×C4—2922no—
519C22×C4—2922no—
520C22×C4—2922no—
521C22×C4—2922no—
522C22×C4—2922no—
523C22×C4—5841no—
524C22×C4—5841no—
525C22×C4—5841no—
526C22×C4—731no—
527C22×C4—731no—
528C22×C4—731no—
529C22×C4—731no—
530C22×C4—1461no—
531C22×C4—1461no—
532C22×C4—1461no—
533C22×C4—1461no—
534C22×C4D4×D7311yescharacteristic
535C22×C4D4×D7311yescharacteristic
536C22×C4C23×D7311yescharacteristic
537SD16—28no—
538D8—28no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—732no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8—1461no—
548C2×C8—1461no—
549C2×C8C22×Dic7312yes—
550C2×C8C22×Dic7312yes—
551C4⋊C4—21no—
552C4⋊C4—2922no—
553C4⋊C4—2921no—
554C4⋊C4—2922no—
555C4⋊C4—2922no—
556C4⋊C4—2922no—
557C4⋊C4—5841no—
558C4⋊C4—732no—
559C4⋊C4—1462no—
560C4⋊C4—1461no—
561C4⋊C4—1461no—
562C4⋊C4—1461no—
563C4⋊C4—1461no—
564C4⋊C4—1461no—
565C4⋊C4—1461no—
566C4⋊C4—1461no—
567C4⋊C4C22×Dic7312yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—2922no—
572C22⋊C4—2922no—
573C22⋊C4—2922no—
574C22⋊C4—2922no—
575C22⋊C4—5841no—
576C42—2922no—
577C42—5841no—
578C42—1461no—
579C42—1461no—
580C42—1461no—
581C42—1461no—
582C42C22×Dic7312yes—
583C42#1192402712yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C2×D4×D7311yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4D4×Dic7314yes—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—48no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—2921no—
623C2×C4—2921no—
624C2×C4—2921no—
625C2×C4—2921no—
626C2×C4—2921no—
627C2×C4—2921no—
628C2×C4—2921no—
629C2×C4—2921no—
630C2×C4—2921no—
631C2×C4—2921no—
632C2×C4—2921no—
633C2×C4—5844no—
634C2×C4—5844no—
635C2×C4—5844no—
636C2×C4—732no—
637C2×C4—1461no—
638C2×C4—1461no—
639C2×C4—1461no—
640C2×C4—1461no—
641C2×C4—1461no—
642C2×C4—1461no—
643C2×C4—1462no—
644C2×C4—1461no—
645C2×C4—1461no—
646C2×C4—1461no—
647C2×C4—1461no—
648C2×C4—1461no—
649C2×C4D4×Dic7312yes—
650C2×C4D4×Dic7312yes—
651C2×C4C23×Dic7311yescharacteristic
652C2×C4C2×D4×D7311yescharacteristic
653C2×C4C2×#1192402711yescharacteristic
654C2×C4C2×#1192402711yescharacteristic
655C2×C4#1455663711yescharacteristic
656C2×C4#1455663811yescharacteristic
657C8—22no—
658C8—22no—
659C8—2921no—
660C8—1462no—
661C22—24no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×D4×Dic7311yescharacteristic
676C22#1798922111yescharacteristic
677C22#1798924311yescharacteristic
678C22AGL(1,ℤ/8)×D7311yescharacteristic
679C22#1798938311yescharacteristic
680C22#1798938911yescharacteristic
681C22#1798940111yescharacteristic
682C4—22no—
683C4—22no—
684C4—42no—
685C4—42no—
686C4—2921no—
687C4—2921no—
688C4—2922no—
689C4—2921no—
690C4—5841no—
691C4—5841no—
692C4—5841no—
693C4—1462no—
694C4C2×D4×Dic7311yescharacteristic
695C4#1798907011yescharacteristic
696C4#1798923711yescharacteristic
697C4#1798928911yescharacteristic
698C2—44no—
699C2—82no—
700C2#2261295111yescharacteristic
701C2AGL(1,ℤ/8)×Dic7311yescharacteristic
702C2#2261880711yescharacteristic
703C2#2262141711yescharacteristic
704C2#2262149211yescharacteristic
705C2#2262264411yescharacteristic
706C2#2262268111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#463×C73C2
socleC23×C73C22×D4
prime radicalC22×D8×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#463D73
hypocenterC73#23011
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#17988688C2semidirect
3. #22613006C2semidirect
4. D4×C4⋊Dic73C2semidirect
5. #22610748C2semidirect
6. #22610690C2semidirect
7. #22610630C2semidirect
8. #22610609C2semidirect
10. #22610267C2semidirect
11. #22610187C2semidirect
12. #22610180C2semidirect
13. #22609808C2semidirect
14. #22609756C2semidirect
58. #463×C73C4semidirect
120. C2×SD16×C73C2×C4semidirect
127. #124×C73C2×C4semidirect
129. C4×D4×C73C2×C4semidirect
135. C4⋊C8×C73C2×C4semidirect
136. #103×C73C2×C4semidirect
137. #102×C73C2×C4semidirect
369. C73#23011semidirect
379. #463Dic73semidirect
425. C2×SD16C2×Dic73semidirect
434. #124C2×Dic73semidirect
444. C4×D4C2×Dic73semidirect
473. C4⋊C8C2×Dic73semidirect
476. #103C2×Dic73semidirect
481. #102C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886882
C2×D8×Dic732
#226130062
D4×C4⋊Dic732
#226107482
#226106902
#226106302
#226106092
#226102812
#226102672
#226101872
#226101802
#226098082
#226097562
C2×#463×C732
#2301173