Finite Group Databasebeta

← #33106380

Subgroups — #33106380

Order 18688.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988688C211yesmaximal, characteristic, complemented
2C2×#17988588C211yesmaximal, characteristic, complemented
3#22612951C211yesmaximal, characteristic, complemented
4#22612772C211yesmaximal, characteristic, complemented
5#22610798C211yesmaximal, characteristic, complemented
6#22610630C211yesmaximal, characteristic, complemented
7#22610553C211yesmaximal, characteristic, complemented
8#22610370C211yesmaximal, characteristic, complemented
9#22610288C211yesmaximal, characteristic, complemented
10#22610281C211yesmaximal, characteristic, complemented
11#22610187C211yesmaximal, characteristic, complemented
12#22610121C211yesmaximal, characteristic, complemented
13#103×Dic73C211yesmaximal, characteristic, complemented
14#22609717C211yesmaximal, characteristic, complemented
15C2×#449×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C2×Q8×Dic73C2211yescharacteristic
18C2×Q8×Dic73C2211yescharacteristic
19C2×D4×Dic73—21no—
20C2×D4×Dic73C2211yescharacteristic
21C22×C4⋊Dic73C2211yescharacteristic
22#17988688—24no—
23C2×#14556525C2211yescharacteristic
24C2×#14556525C2211yescharacteristic
25#17988588—24no—
26C2×#14556515C2211yescharacteristic
27C2×#14556515C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32C2×#14556501C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34#17988490—21no—
35#17988490—21no—
36#17988490C2211yescharacteristic
37#17988490C2211yescharacteristic
38#17988490C2211yescharacteristic
39#17988486C2211yescharacteristic
40#17988480—21no—
41#17988467—21no—
42#17988462—21no—
43#17988447—21no—
44#17988447C2211yescharacteristic
45C4⋊C4×Dic73C2211yescharacteristic
46C4×C22⋊Dic73—21no—
47C4×C22⋊Dic73C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C22×#41×C73C2211yescharacteristic
55C22×SD16×C73C2211yescharacteristic
56C22×D8×C73C2211yescharacteristic
57C2×#121×C73C2211yescharacteristic
58#449×C73C418yescomplemented
59C2×#103×C73C2211yescharacteristic
60C2×#102×C73C2211yescharacteristic
61C2×C22⋊C8×C73C2211yescharacteristic
62C23×Dic73—21no—
63C23×Dic73—21no—
64C2×#11924012—22no—
65C2×#11924012—22no—
66C2×#11924012—41no—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69Q8×Dic73—22no—
70Q8×Dic73—22no—
71Q8×Dic73—41no—
72Q8×Dic73—41no—
73D4×Dic73—22no—
74D4×Dic73—41no—
75D4×Dic73—44no—
76C2×C4⋊Dic73—22no—
77C2×C4⋊Dic73—21no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73—21no—
81C2×C4⋊Dic73—41no—
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×C22⋊Dic73—21no—
87C2×C22⋊Dic73—21no—
88C2×C22⋊Dic73—21no—
89C2×C22⋊Dic73—21no—
90C2×C22⋊Dic73—21no—
91C2×C22⋊Dic73—21no—
92C2×C22⋊Dic73—21no—
93C2×C22⋊Dic73—21no—
94C2×C22⋊Dic73D411yescharacteristic
95C2×C22⋊Dic73D411yescharacteristic
96C2×C4×Dic73—21no—
97C2×C4×Dic73—21no—
98C2×C4×Dic73—21no—
99C2×C4×Dic73C2311yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101#14556525—22no—
102#14556525—41no—
103#14556515—22no—
104#14556515D414yescomplemented
105#14556512—22no—
106#14556512—22no—
107#14556512—22no—
108#14556512—41no—
109#14556501—22no—
110C8×Dic73—41no—
111#14556498—21no—
112#14556498—21no—
113#14556498—21no—
114#14556498D411yescharacteristic
115#14556498D411yescharacteristic
116C2×#41×C73—22no—
117C2×#41×C73—22no—
118C2×#41×C73—22no—
119C2×#41×C73—41no—
120C2×#41×C73—41no—
121C2×#41×C73C2×C414yescomplemented
122C22×Q8×C73C2311yescharacteristic
123C22×D4×C73—21no—
124C22×D4×C73—21no—
125C22×D4×C73C2311yescharacteristic
126C22×D4×C73C2311yescharacteristic
127C23×C4×C73—21no—
128C23×C4×C73C2311yescharacteristic
129C2×SD16×C73—22no—
130C2×SD16×C73—22no—
131C2×SD16×C73C2×C414yescomplemented
132C2×D8×C73—41no—
133C2×D8×C73—41no—
134C2×D8×C73C2×C414yescomplemented
135C22×C8×C73C2311yescharacteristic
136C22×C8×C73C2311yescharacteristic
137#121×C73—22no—
138#121×C73C2×C414yes—
139C2×C4⋊C4×C73C2311yescharacteristic
140C2×C22⋊C4×C73—21no—
141#103×C73C2×C414yescomplemented
142#102×C73C2×C414yescomplemented
143C22⋊C8×C73C2×C414yescomplemented
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—42no—
149C22×Dic73—42no—
150C22×Dic73—42no—
151C22×Dic73—42no—
152C22×Dic73—81no—
153C22×Dic73—81no—
154C22×Dic73C2×D411yescharacteristic
155C22×Dic73C2×D411yescharacteristic
156C22×Dic73C2×D411yescharacteristic
157C22×Dic73C2×D411yescharacteristic
158#11924012—44no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831C2×D412yes—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—42no—
173C4⋊Dic73—42no—
174C4⋊Dic73—42no—
175C4⋊Dic73—42no—
176C4⋊Dic73C2×D412yes—
177C22⋊Dic73—22no—
178C22⋊Dic73—41no—
179C22⋊Dic73—42no—
180C22⋊Dic73—42no—
181C22⋊Dic73—42no—
182C22⋊Dic73—42no—
183C22⋊Dic73—81no—
184C22⋊Dic73—81no—
185C22⋊Dic73—81no—
186C22⋊Dic73—81no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—42no—
192C4×Dic73—42no—
193C4×Dic73—42no—
194C24×C73—21no—
195C24×C73—21no—
196C24×C73C2×D411yescharacteristic
197#41×C73—28no—
198#41×C73—44no—
199#41×C73—44no—
200#41×C73—44no—
201C2×Q8×C73—21no—
202C2×Q8×C73—21no—
203C2×Q8×C73—21no—
204C2×Q8×C73C22×C412yes—
205C2×Q8×C73C2×D412yes—
206C2×Q8×C73#4112yes—
207C2×D4×C73—24no—
208C2×D4×C73—24no—
209C2×D4×C73—21no—
210C2×D4×C73—21no—
211C2×D4×C73—21no—
212C2×D4×C73—21no—
213C2×D4×C73—21no—
214C2×D4×C73—21no—
215C2×D4×C73—21no—
216C2×D4×C73—21no—
217C2×D4×C73—21no—
218C2×D4×C73—21no—
219C2×D4×C73—42no—
220C2×D4×C73—42no—
221C2×D4×C73—42no—
222C2×D4×C73—42no—
223C2×D4×C73C22×C412yes—
224C2×D4×C73C22×C412yes—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—24no—
232C22×C4×C73—42no—
233C22×C4×C73—42no—
234C22×C4×C73C22×C412yes—
235C22×C4×C73C2×D411yescharacteristic
236C22×C4×C73#4112yes—
237C22×C4×C73C2411yescharacteristic
238SD16×C73—28no—
239D8×C73—44no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73C22×C412yes—
245C2×C8×C73C22×C412yes—
246C4⋊C4×C73—21no—
247C4⋊C4×C73C22×C412yes—
248C22⋊C4×C73—24no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—22no—
256C23×C73—22no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73—41no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73C4×D412yes—
270C23×C73C22×D411yescharacteristic
271Q8×C73—22no—
272Q8×C73—22no—
273Q8×C73—22no—
274Q8×C73C4×D414yescomplemented
275D4×C73—22no—
276D4×C73—22no—
277D4×C73—22no—
278D4×C73—22no—
279D4×C73—48no—
280D4×C73—48no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—41no—
284D4×C73—41no—
285C2×C4×C73—22no—
286C2×C4×C73—21no—
287C2×C4×C73—22no—
288C2×C4×C73—21no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—48no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73C4×D412yes—
299C2×C4×C73C23×C411yescharacteristic
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73C2×#4111yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C2×C4×C73H(5,𝔽2)11yescharacteristic
305C2×Dic73—21no—
306C2×Dic73—21no—
307C2×Dic73—21no—
308C2×Dic73—21no—
309C2×Dic73—22no—
310C2×Dic73—21no—
311C2×Dic73—21no—
312C2×Dic73—21no—
313C2×Dic73—21no—
314C2×Dic73—21no—
315C2×Dic73—21no—
316C2×Dic73—21no—
317C2×Dic73—41no—
318C2×Dic73—41no—
319C2×Dic73—41no—
320C2×Dic73—41no—
321C2×Dic73—41no—
322C2×Dic73—41no—
323C2×Dic73—41no—
324C2×Dic73—41no—
325C2×Dic73—41no—
326C2×Dic73—41no—
327C2×Dic73—41no—
328C2×Dic73—84no—
329C2×Dic73—84no—
330C2×Dic73AGL(1,ℤ/8)12yes—
331C8×C73—22no—
332C8×C73—22no—
333#10596831—22no—
334#10596831—41no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—22no—
338C22×C73—41no—
339C22×C73—41no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—42no—
347C22×C73—42no—
348C22×C73—81no—
349C22×C73—81no—
350C22×C73—81no—
351C22×C73—81no—
352C22×C73—81no—
353C22×C73—81no—
354C22×C73—81no—
355C22×C73—81no—
356C22×C73C2×C4×D411yescharacteristic
357C22×C73D4211yescharacteristic
358C22×C73#54611yescharacteristic
359C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C73#57511yescharacteristic
361C22×C73#57611yescharacteristic
362C22×C73#57811yescharacteristic
363C4×C73—22no—
364C4×C73—24no—
365C4×C73—42no—
366C4×C73C2×C4×D411yescharacteristic
367C4×C73#51811yescharacteristic
368C4×C73#54611yescharacteristic
369C4×C73#55111yescharacteristic
370Dic73—22no—
371Dic73—41no—
372Dic73—42no—
373Dic73—41no—
374Dic73—41no—
375Dic73—81no—
376Dic73—81no—
377Dic73—81no—
378#22863—731nomaximal, Sylow
379C2×C73—42no—
380C2×C73—82no—
381C2×C73—82no—
382C2×C73#235811yescharacteristic
383C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
384C2×C73#295111yescharacteristic
385C2×C73#327411yescharacteristic
386C2×C73#327711yescharacteristic
387C2×C73#330811yescharacteristic
388C2×C73#330911yescharacteristic
389C2×#449D7311yescharacteristic
390C2×#440—731no—
391C2×#417—731no—
392#2361—731no—
393#2341—731no—
394#1970—731no—
395#1936—731no—
396#1925—731no—
397#1895—731no—
398#1880—731no—
399#1879—731no—
400#1863—731no—
401#1852—731no—
402C4×#103—731no—
403#1753—731no—
404C73#2286311yescharacteristic, complemented, Sylow
405C22×#41C2×D7311yescharacteristic
406C22×SD16C2×D7311yescharacteristic
407C22×D8C2×D7311yescharacteristic
408C22×M16—731no—
409C2×#121C2×D7311yescharacteristic
410C2×C4×Q8—731no—
411C2×C4×Q8—731no—
412C2×C4×D4—731no—
413C2×C4×D4—1461no—
414C22×C4⋊C4—731no—
415#449Dic7318yescomplemented
416#440—1464no—
417C2×#107—731no—
418C2×#107—731no—
419#417—1464no—
420C2×#103—731no—
421C2×#103—731no—
422C2×#103C2×D7311yescharacteristic
423C2×#102—731no—
424C2×#102—731no—
425C2×#102—731no—
426C2×#102—731no—
427C2×#102C2×D7311yescharacteristic
428C2×C22⋊C8C2×D7311yescharacteristic
429C2×#97—731no—
430C2×C4×C8—731no—
431#390—731no—
432#390—731no—
433#390—731no—
434#390—1461no—
435#390—1461no—
436#389—731no—
437#388—1461no—
438#386—1461no—
439#385—1461no—
440#380—731no—
441#380—1461no—
442C4×C4⋊C4—731no—
443C4×C22⋊C4—731no—
444C4×C22⋊C4—1461no—
445#340—731no—
446#340—731no—
447#340—731no—
448#340—731no—
449#336—731no—
450#336—731no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41C2×Dic7314yescomplemented
457C22×Q8C22×D7311yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4C22×D7311yescharacteristic
461C22×D4C22×D7311yescharacteristic
462C23×C4—21no—
463C23×C4—1461no—
464C23×C4—1461no—
465C23×C4C22×D7311yescharacteristic
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16C2×Dic7314yescomplemented
469C2×D8—41no—
470C2×D8—41no—
471C2×D8C2×Dic7314yescomplemented
472C2×M16—2921no—
473C2×M16—1462no—
474C2×M16—1462no—
475C22×C8—731no—
476C22×C8—731no—
477C22×C8C22×D7311yescharacteristic
478C22×C8C22×D7311yescharacteristic
479#121—22no—
480#121C2×Dic7314yes—
481C4×Q8—2921no—
482C4×Q8—2921no—
483C4×Q8—1462no—
484C4×Q8—1462no—
485C4×D4—2924no—
486C4×D4—2921no—
487C4×D4—1462no—
488C2×C4⋊C4—2921no—
489C2×C4⋊C4—731no—
490C2×C4⋊C4—731no—
491C2×C4⋊C4—731no—
492C2×C4⋊C4—731no—
493C2×C4⋊C4—1461no—
494C2×C4⋊C4—1461no—
495C2×C4⋊C4—1461no—
496C2×C4⋊C4—1461no—
497C2×C4⋊C4—1462no—
498C2×C4⋊C4C22×D7311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—731no—
501C2×C22⋊C4—731no—
502C2×C22⋊C4—1461no—
503C2×C22⋊C4—1461no—
504C2×C22⋊C4—1461no—
505C2×C22⋊C4—1461no—
506C2×C22⋊C4—1461no—
507C2×C22⋊C4—1461no—
508C2×C22⋊C4—1461no—
509C2×C22⋊C4—1461no—
510C2×C42—731no—
511C2×C42—731no—
512C2×C42—1461no—
513C2×C42—1461no—
514C2×C42—1461no—
515#107—2921no—
516#107—1462no—
517#103—734no—
518#103—1462no—
519#103C2×Dic7314yescomplemented
520#102—2921no—
521#102—1462no—
522#102—1462no—
523#102—1462no—
524#102C2×Dic7314yescomplemented
525C22⋊C8C2×Dic7314yescomplemented
526#97—1462no—
527C4×C8—2921no—
528#95—731no—
529#95—731no—
530#95—1461no—
531#95—1461no—
532#95—1461no—
533C24—21no—
534C24—21no—
535C24D4×D7311yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C22×Dic7312yes—
544C2×Q8D4×D7312yes—
545C2×Q8#1192402712yes—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4C22×Dic7312yes—
563C2×D4C22×Dic7312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—2922no—
574C22×C4—2922no—
575C22×C4—2922no—
576C22×C4—2922no—
577C22×C4—5841no—
578C22×C4—5841no—
579C22×C4—731no—
580C22×C4—731no—
581C22×C4—731no—
582C22×C4—731no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4C22×Dic7312yes—
588C22×C4D4×D7311yescharacteristic
589C22×C4#1192402712yes—
590C22×C4C23×D7311yescharacteristic
591SD16—28no—
592D8—44no—
593M16—2924no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—732no—
599C2×C8—1461no—
600C2×C8—1461no—
601C2×C8—1461no—
602C2×C8—1461no—
603C2×C8—1461no—
604C2×C8C22×Dic7312yes—
605C2×C8C22×Dic7312yes—
606C4⋊C4—21no—
607C4⋊C4—2922no—
608C4⋊C4—2922no—
609C4⋊C4—2922no—
610C4⋊C4—2922no—
611C4⋊C4—732no—
612C4⋊C4—1461no—
613C4⋊C4—1461no—
614C4⋊C4—1461no—
615C4⋊C4—1461no—
616C4⋊C4—1461no—
617C4⋊C4—1461no—
618C4⋊C4—1461no—
619C4⋊C4C22×Dic7312yes—
620C22⋊C4—24no—
621C22⋊C4—2922no—
622C22⋊C4—2922no—
623C22⋊C4—2922no—
624C22⋊C4—2921no—
625C22⋊C4—2922no—
626C22⋊C4—5841no—
627C22⋊C4—5841no—
628C22⋊C4—5841no—
629C22⋊C4—5841no—
630C22⋊C4—1462no—
631C42—2922no—
632C42—2922no—
633C42—2922no—
634C42—1461no—
635C42—1461no—
636C42—1461no—
637C42—1461no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23D4×Dic7312yes—
659C23C2×D4×D7311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8D4×Dic7314yescomplemented
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—48no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—2921no—
688C2×C4—2921no—
689C2×C4—2921no—
690C2×C4—2921no—
691C2×C4—2921no—
692C2×C4—2921no—
693C2×C4—2921no—
694C2×C4—2921no—
695C2×C4—2921no—
696C2×C4—2921no—
697C2×C4—2921no—
698C2×C4—5844no—
699C2×C4—5844no—
700C2×C4—732no—
701C2×C4—1461no—
702C2×C4—1461no—
703C2×C4—1461no—
704C2×C4—1461no—
705C2×C4—1461no—
706C2×C4—1461no—
707C2×C4—1461no—
708C2×C4—1462no—
709C2×C4—1461no—
710C2×C4—1461no—
711C2×C4—1461no—
712C2×C4—1461no—
713C2×C4D4×Dic7312yes—
714C2×C4C23×Dic7311yescharacteristic
715C2×C4C2×D4×D7311yescharacteristic
716C2×C4C2×#1192402711yescharacteristic
717C2×C4C2×#1192402711yescharacteristic
718C2×C4#1455663611yescharacteristic
719C2×C4#1455663611yescharacteristic
720C8—22no—
721C8—22no—
722C8—2921no—
723C8—1462no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22C2×D4×Dic7311yescharacteristic
746C22#1798921911yescharacteristic
747C22#1798922411yescharacteristic
748C22AGL(1,ℤ/8)×D7311yescharacteristic
749C22#1798938311yescharacteristic
750C22#1798938911yescharacteristic
751C22#1798940111yescharacteristic
752C4—22no—
753C4—24no—
754C4—42no—
755C4—2922no—
756C4—2921no—
757C4—2921no—
758C4—2921no—
759C4—5841no—
760C4—5841no—
761C4—5841no—
762C4—1462no—
763C4C2×D4×Dic7311yescharacteristic
764C4#1798906211yescharacteristic
765C4#1798922411yescharacteristic
766C4#1798926811yescharacteristic
767C2—42no—
768C2—82no—
769C2—82no—
770C2#2261291511yescharacteristic
771C2AGL(1,ℤ/8)×Dic7311yescharacteristic
772C2#2261880711yescharacteristic
773C2#2262154411yescharacteristic
774C2#2262158111yescharacteristic
775C2#2262191511yescharacteristic
776C2#2262193011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
Fitting, prime radicalC2×#449×C73C2
socleC23×C73C22×D4
cosocleC22×C4×C73C24
hypercenterC2×#449D73
hypocenterC73#22863
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#17988688C2semidirect
2. C2×#17988588C2semidirect
3. #22612951C2semidirect
4. #22612772C2semidirect
5. #22610798C2semidirect
6. #22610630C2semidirect
7. #22610553C2semidirect
8. #22610370C2semidirect
9. #22610288C2semidirect
10. #22610281C2semidirect
11. #22610187C2semidirect
12. #22610121C2semidirect
13. #103×Dic73C2semidirect
14. #22609717C2semidirect
58. #449×C73C4semidirect
104. #14556515D4semidirect
121. C2×#41×C73C2×C4semidirect
131. C2×SD16×C73C2×C4semidirect
134. C2×D8×C73C2×C4semidirect
141. #103×C73C2×C4semidirect
142. #102×C73C2×C4semidirect
143. C22⋊C8×C73C2×C4semidirect
274. Q8×C73C4×D4semidirect
404. C73#22863semidirect
415. #449Dic73semidirect
456. C2×#41C2×Dic73semidirect
468. C2×SD16C2×Dic73semidirect
471. C2×D8C2×Dic73semidirect
519. #103C2×Dic73semidirect
524. #102C2×Dic73semidirect
525. C22⋊C8C2×Dic73semidirect
663. Q8D4×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886882
C2×#179885882
#226129512
#226127722
#226107982
#226106302
#226105532
#226103702
#226102882
#226102812
#226101872
#226101212
#103×Dic732
#226097172
C2×#449×C732
#2286373