Finite Group Databasebeta

← #33106387

Subgroups — #33106387

Order 18688.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988738C211yesmaximal, characteristic
2C2×#17988687C211yesmaximal, characteristic, complemented
3C2×#17988592C211yesmaximal, characteristic
4#22612956C211yesmaximal, characteristic, complemented
5#22610784C211yesmaximal, characteristic, complemented
6#22610631C211yesmaximal, characteristic, complemented
7#22610548C211yesmaximal, characteristic, complemented
8#22610362C211yesmaximal, characteristic, complemented
9#22610289C211yesmaximal, characteristic, complemented
10#22610265C211yesmaximal, characteristic, complemented
11#22610192C211yesmaximal, characteristic, complemented
12#22610128C211yesmaximal, characteristic, complemented
13C4×#14556512C211yesmaximal, characteristic, complemented
14#22609715C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C73C211yesmaximal, characteristic
16C22×#11924016C2211yescharacteristic
17C22×#11924016C2211yescharacteristic
18C22×#11924012C2211yescharacteristic
19C2×#14556570C2211yescharacteristic
20C2×C4×Dic146C2211yescharacteristic, complemented
21C2×#14556550C2211yescharacteristic
22#17988738C418yescomplemented
23#17988687—24no—
24C2×#14556524C2211yescharacteristic, complemented
25C2×#14556522C2211yescharacteristic, complemented
26#17988592—24no—
27C2×#14556514C2211yescharacteristic, complemented
28C2×#14556514C2211yescharacteristic, complemented
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556512C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×#14556502C2211yescharacteristic, complemented
37C2×C4×#10596831C2211yescharacteristic, complemented
38#17988493C2211yescharacteristic, complemented
39#17988485C2211yescharacteristic, complemented
40#17988481—21no—
41#17988475—21no—
42#17988469—21no—
43C4×C4⋊Dic73C2211yescharacteristic, complemented
44#17988438—21no—
45#17988349C2211yescharacteristic, complemented
46#17988349C2211yescharacteristic, complemented
47#17988349C2211yescharacteristic, complemented
48#17988349C2211yescharacteristic, complemented
49#17988342C2211yescharacteristic, complemented
50#17988342C2211yescharacteristic, complemented
51C23×D4×C73C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54C22×C22⋊C4×C73—21no—
55#390×C73C2211yescharacteristic
56#390×C73C2211yescharacteristic
57#386×C73—21no—
58#386×C73—21no—
59#380×C73C2211yescharacteristic
60#379×C73—21no—
61C4×C22⋊C4×C73C2211yescharacteristic
62C22×Dic146C2311yescharacteristic
63C2×#11924016—22no—
64C2×#11924016—22no—
65C2×#11924016—41no—
66C2×#11924016—41no—
67C2×#11924016C2×C414yes—
68C2×#11924016C2×C414yescomplemented
69C2×#11924012—22no—
70C2×#11924012—22no—
71C2×#11924012—41no—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76#14556570—22no—
77#14556570C2×C414yescomplemented
78C4×Dic146—22no—
79C4×Dic146—41no—
80#14556550—22no—
81#14556550—41no—
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×C22⋊Dic73—21no—
89C2×C22⋊Dic73—21no—
90C2×C4×Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93#14556524—22no—
94#14556522—41no—
95#14556514—22no—
96#14556514—41no—
97#14556512—22no—
98#14556512—22no—
99#14556512—22no—
100#14556512C2×C414yes—
101#14556512C2×C414yescomplemented
102#14556512D414yes—
103C22⋊#10596831C2×C414yescomplemented
104#14556502—22no—
105C4×#10596831—41no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110C25×C73—21no—
111C22×D4×C73—22no—
112C22×D4×C73—22no—
113C22×D4×C73—21no—
114C22×D4×C73—22no—
115C22×D4×C73—41no—
116C22×D4×C73—41no—
117C22×D4×C73C2×C414yes—
118C22×D4×C73C2311yescharacteristic
119C22×D4×C73C2311yescharacteristic
120C23×C4×C73—21no—
121C23×C4×C73—21no—
122C23×C4×C73C2311yescharacteristic
123C4×D4×C73—22no—
124C4×D4×C73—22no—
125C4×D4×C73—41no—
126C4×D4×C73—41no—
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73—21no—
136C2×C22⋊C4×C73—44no—
137C2×C22⋊C4×C73D411yescharacteristic
138C2×C22⋊C4×C73D411yescharacteristic
139C2×C42×C73C2311yescharacteristic
140C2×C42×C73C2311yescharacteristic
141#95×C73—21no—
142#95×C73D411yescharacteristic
143#95×C73D411yescharacteristic
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146—21no—
149C2×Dic146C22×C412yes—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154#11924016—28no—
155#11924016—44no—
156#11924012—44no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831C22×C412yes—
167C2×#10596831C22×C412yes—
168C2×#10596831C2×D412yes—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73C22×C412yes—
174C4⋊Dic73C2×D412yes—
175#11924007—24no—
176#11924007—42no—
177#11924007—42no—
178C22⋊Dic73—24no—
179C22⋊Dic73—42no—
180C4×Dic73—42no—
181C4×Dic73—42no—
182C4×Dic73—42no—
183C24×C73—21no—
184C24×C73—21no—
185C24×C73—24no—
186C24×C73—42no—
187C24×C73—42no—
188C24×C73—42no—
189C24×C73—42no—
190C24×C73—81no—
191C24×C73—81no—
192C24×C73C2×D411yescharacteristic
193C2×D4×C73—28no—
194C2×D4×C73—24no—
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×C73—44no—
204C2×D4×C73—44no—
205C2×D4×C73—44no—
206C2×D4×C73—42no—
207C2×D4×C73—42no—
208C2×D4×C73C22×C412yes—
209C2×D4×C73C22×C412yes—
210C2×D4×C73C2×D412yes—
211C2×D4×C73#4112yes—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—42no—
219C22×C4×C73—42no—
220C22×C4×C73—42no—
221C22×C4×C73—42no—
222C22×C4×C73—81no—
223C22×C4×C73—81no—
224C22×C4×C73C22×C412yes—
225C22×C4×C73C2×D411yescharacteristic
226C22×C4×C73C2×D411yescharacteristic
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73C2×D411yescharacteristic
230C22×C4×C73#4112yes—
231C22×C4×C73C2411yescharacteristic
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C22⋊C4×C73—22no—
237C22⋊C4×C73—41no—
238C22⋊C4×C73—42no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—42no—
241C22⋊C4×C73—42no—
242C22⋊C4×C73—42no—
243C22⋊C4×C73—81no—
244C22⋊C4×C73—81no—
245C42×C73—21no—
246C42×C73—21no—
247C42×C73—21no—
248C42×C73—21no—
249C23×C73—22no—
250C23×C73—22no—
251C23×C73—21no—
252C23×C73—22no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—22no—
259C23×C73—48no—
260C23×C73—48no—
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×C73—41no—
270C23×C73—41no—
271C23×C73—84no—
272C23×C73—84no—
273C23×C73—84no—
274C23×C73—84no—
275C23×C73—84no—
276C23×C73C4×D412yes—
277C23×C73C22×D411yescharacteristic
278D4×C73—22no—
279D4×C73—22no—
280D4×C73—22no—
281D4×C73—22no—
282D4×C73—22no—
283D4×C73—48no—
284D4×C73—41no—
285D4×C73—41no—
286D4×C73C4×D414yes—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—84no—
311C2×C4×C73—84no—
312C2×C4×C73C4×D412yes—
313C2×C4×C73AGL(1,ℤ/8)12yes—
314C2×C4×C73C23×C411yescharacteristic
315C2×C4×C73C22×D411yescharacteristic
316C2×C4×C73C2×#4111yescharacteristic
317C2×C4×C73C2×#4111yescharacteristic
318C2×C4×C73H(5,𝔽2)11yescharacteristic
319C2×C4×C73H(5,𝔽2)11yescharacteristic
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—41no—
324C2×Dic73—41no—
325C2×Dic73—41no—
326C2×Dic73—41no—
327C2×Dic73—41no—
328C2×Dic73—41no—
329C2×Dic73—41no—
330C2×Dic73—41no—
331C2×Dic73—41no—
332Dic146—22no—
333Dic146—22no—
334Dic146—41no—
335Dic146—41no—
336#10596831—22no—
337#10596831—22no—
338#10596831—22no—
339#10596831—41no—
340C22×C73—22no—
341C22×C73—24no—
342C22×C73—22no—
343C22×C73—22no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—42no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—42no—
354C22×C73—42no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—816no—
358C22×C73—81no—
359C22×C73—81no—
360C22×C73—81no—
361C22×C73—81no—
362C22×C73C2×C4×D411yescharacteristic
363C22×C73D4211yescharacteristic
364C22×C73#54611yescharacteristic
365C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C73#57511yescharacteristic
367C22×C73#57711yescharacteristic
368C22×C73#57711yescharacteristic
369C4×C73—22no—
370C4×C73—22no—
371C4×C73—41no—
372C4×C73—41no—
373C4×C73—41no—
374C4×C73—81no—
375C4×C73—81no—
376C4×C73C2×C4×D411yescharacteristic
377C4×C73#51811yescharacteristic
378C4×C73#54611yescharacteristic
379C4×C73#55111yescharacteristic
380Dic73—42no—
381Dic73—42no—
382Dic73—42no—
383Dic73—81no—
384#22864—731nomaximal, Sylow
385C2×C73—42no—
386C2×C73—44no—
387C2×C73—82no—
388C2×C73#235811yescharacteristic
389C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
390C2×C73#294911yescharacteristic
391C2×C73#327211yescharacteristic
392C2×C73#327511yescharacteristic
393C2×C73#331011yescharacteristic
394C2×C73#331111yescharacteristic
395C2×#450—731no—
396C2×#440—731no—
397C2×#418—731no—
398#2362—731no—
399D4×C22⋊C4D7311yescharacteristic
400#1968—731no—
401#1936—731no—
402#1925—731no—
403#1894—731no—
404#1880—731no—
405#1877—731no—
406#1864—731no—
407#1854—731no—
408C4×#102—731no—
409#1753—731no—
410C73#2286411yescharacteristic, complemented, Sylow
411C23×D4C2×D7311yescharacteristic
412C22×SD16—731no—
413C22×SD16—731no—
414C22×M16—731no—
415C2×C22⋊Q8—731no—
416C2×C4×Q8—731no—
417C2×C4×D4C2×D7311yescharacteristic
418C2×C4×D4C2×D7311yescharacteristic
419C2×#117—731no—
420C22×C22⋊C4—21no—
421#450—738no—
422#440—1464no—
423C2×#107—731no—
424C2×#106—731no—
425#418—1464no—
426C2×#103—731no—
427C2×#103—731no—
428C2×#102—731no—
429C2×#102—731no—
430C2×#102—731no—
431C2×#102—731no—
432C2×#102—731no—
433C2×#102—731no—
434C2×C22⋊C8—731no—
435C2×#97—731no—
436C2×C4×C8—731no—
437#391—731no—
438#390C2×D7311yescharacteristic
439#390C2×D7311yescharacteristic
440#389—731no—
441#388—1461no—
442#388—1461no—
443#387—1461no—
444#386—21no—
445#386—21no—
446#380C2×D7311yescharacteristic
447#379—21no—
448C4×C4⋊C4—731no—
449C4×C4⋊C4—1461no—
450C4×C22⋊C4C2×D7311yescharacteristic
451#340—731no—
452#340—731no—
453#340—731no—
454#340—731no—
455#336—731no—
456#336—731no—
457C25—21no—
458C22×Q8—731no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—21no—
462C22×D4—22no—
463C22×D4—41no—
464C22×D4—41no—
465C22×D4C4×D7314yes—
466C22×D4C22×D7311yescharacteristic
467C22×D4C22×D7311yescharacteristic
468C23×C4—21no—
469C23×C4—21no—
470C23×C4C22×D7311yescharacteristic
471C2×SD16—2921no—
472C2×SD16—2921no—
473C2×SD16—734no—
474C2×SD16—734no—
475C2×SD16—1462no—
476C2×SD16—1462no—
477C2×M16—2921no—
478C2×M16—1462no—
479C2×M16—1462no—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8—731no—
483C22×C8—731no—
484C22⋊Q8—734no—
485C22⋊Q8—1462no—
486C4×Q8—2921no—
487C4×Q8—1462no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—41no—
491C4×D4—41no—
492#117—2921no—
493#117—1462no—
494C2×C4⋊C4—731no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—1461no—
498C2×C4⋊C4—1461no—
499C2×C4⋊C4—1461no—
500C2×C4⋊C4C22×D7311yescharacteristic
501C2×C4⋊C4C22×D7311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4—1461no—
511C2×C22⋊C4—1461no—
512C2×C22⋊C4C22⋊D7311yescharacteristic
513C2×C22⋊C4C22⋊D7311yescharacteristic
514C2×C42—1461no—
515C2×C42—1461no—
516C2×C42—1461no—
517C2×C42C22×D7311yescharacteristic
518C2×C42C22×D7311yescharacteristic
519#107—1462no—
520#106—2921no—
521#103—2921no—
522#103—1462no—
523#102—734no—
524#102—734no—
525#102—734no—
526#102—1462no—
527#102—1462no—
528#102—1462no—
529C22⋊C8—734no—
530#97—1462no—
531C4×C8—2921no—
532#95—21no—
533#95—1461no—
534#95—1461no—
535#95—1461no—
536#95—1461no—
537#95C22⋊D7311yescharacteristic
538#95C22⋊D7311yescharacteristic
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—42no—
545C24—42no—
546C24—81no—
547C24—81no—
548C24C2×C22⋊D7311yescharacteristic
549C2×Q8—732no—
550C2×Q8—1461no—
551C2×Q8—1461no—
552C2×Q8—1461no—
553C2×Q8—1461no—
554C2×Q8—1461no—
555C2×D4—28no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4C2×C4×D7312yes—
571C2×D4C2×C4×D7312yes—
572C2×D4D4×D7312yes—
573C2×D4#1192402712yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4C2×C4×D7312yes—
591C22×C4C2×C22⋊D7311yescharacteristic
592C22×C4C2×C22⋊D7311yescharacteristic
593C22×C4C2×C22⋊D7311yescharacteristic
594C22×C4C2×C22⋊D7311yescharacteristic
595C22×C4C2×C22⋊D7311yescharacteristic
596C22×C4#1192402812yes—
597C22×C4C23×D7311yescharacteristic
598SD16—2924no—
599SD16—1468no—
600M16—2924no—
601C2×C8—732no—
602C2×C8—732no—
603C2×C8—732no—
604C2×C8—1461no—
605C2×C8—1461no—
606C2×C8—1461no—
607C2×C8—1461no—
608C2×C8—1461no—
609C2×C8—1461no—
610C2×C8—1461no—
611C2×C8—1461no—
612C2×C8—1461no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—2922no—
618C4⋊C4—2922no—
619C4⋊C4—732no—
620C4⋊C4—732no—
621C4⋊C4—1461no—
622C4⋊C4—1461no—
623C4⋊C4—1464no—
624C4⋊C4—1461no—
625C4⋊C4—1461no—
626C22⋊C4—22no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—2922no—
636C22⋊C4—1464no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—2922no—
642C42—2922no—
643C42—2922no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—22no—
650C23—21no—
651C23—22no—
652C23—21no—
653C23—22no—
654C23—48no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23C4×C22⋊D7312yes—
672C23C22×C22⋊D7311yescharacteristic
673Q8—2921no—
674Q8—2921no—
675Q8—1462no—
676Q8—1462no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4#1455655114yes—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4—2921no—
712C2×C4—2921no—
713C2×C4—2921no—
714C2×C4—2921no—
715C2×C4—2921no—
716C2×C4—2921no—
717C2×C4—2921no—
718C2×C4—2921no—
719C2×C4—2921no—
720C2×C4—1462no—
721C2×C4—1462no—
722C2×C4—1462no—
723C2×C4C4×C22⋊D7312yes—
724C2×C4#1455661712yes—
725C2×C4C22×C4×D7311yescharacteristic
726C2×C4C2×D4×D7311yescharacteristic
727C2×C4C2×#1192402711yescharacteristic
728C2×C4C2×#1192402811yescharacteristic
729C2×C4#1455663611yescharacteristic
730C2×C4#1455663611yescharacteristic
731C8—2921no—
732C8—1462no—
733C8—1462no—
734C8—1462no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—24no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—42no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—816no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×C4×C22⋊D7311yescharacteristic
758C22D4×C22⋊D7311yescharacteristic
759C22#1798923111yescharacteristic
760C22C2×#1455661711yescharacteristic
761C22#1798938511yescharacteristic
762C22#1798939811yescharacteristic
763C22#1798939811yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4—81no—
771C4—2922no—
772C4—2922no—
773C4—2922no—
774C4—5841no—
775C4C2×#1455655111yescharacteristic
776C4#1798906011yescharacteristic
777C4#1798922711yescharacteristic
778C4#1798926311yescharacteristic
779C2—42no—
780C2—44no—
781C2—82no—
782C2#2261291011yescharacteristic
783C2C4×#1455661711yescharacteristic
784C2#2261878811yescharacteristic
785C2#2262152711yescharacteristic
786C2#2262155811yescharacteristic
787C2#2262195211yescharacteristic
788C2#2262196711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingD4×C22⋊C4×C73C2
socleC23×C73C22×D4
prime radicalC23×D4×C73C22
cosocleC22×C4×C73C24
hypercenterD4×C22⋊C4D73
hypocenterC73#22864
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#17988687C2semidirect
4. #22612956C2semidirect
5. #22610784C2semidirect
6. #22610631C2semidirect
7. #22610548C2semidirect
8. #22610362C2semidirect
9. #22610289C2semidirect
10. #22610265C2semidirect
11. #22610192C2semidirect
12. #22610128C2semidirect
13. C4×#14556512C2semidirect
14. #22609715C2semidirect
20. C2×C4×Dic146C22semidirect
22. #17988738C4semidirect
24. C2×#14556524C22semidirect
25. C2×#14556522C22semidirect
27. C2×#14556514C22semidirect
28. C2×#14556514C22semidirect
36. C2×#14556502C22semidirect
37. C2×C4×#10596831C22semidirect
38. #17988493C22semidirect
39. #17988485C22semidirect
43. C4×C4⋊Dic73C22semidirect
45. #17988349C22semidirect
46. #17988349C22semidirect
47. #17988349C22semidirect
48. #17988349C22semidirect
49. #17988342C22semidirect
50. #17988342C22semidirect
68. C2×#11924016C2×C4semidirect
77. #14556570C2×C4semidirect
101. #14556512C2×C4semidirect
103. C22⋊#10596831C2×C4semidirect
410. C73#22864semidirect

Maximal subgroups

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

subgroupindex
C2×#179887382
C2×#179886872
C2×#179885922
#226129562
#226107842
#226106312
#226105482
#226103622
#226102892
#226102652
#226101922
#226101282
C4×#145565122
#226097152
D4×C22⋊C4×C732
#2286473