Finite Group Databasebeta

← #33106350

Subgroups — #33106350

Order 18688.

1090 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988694C211yesmaximal, characteristic, complemented
2C2×#17988583C211yesmaximal, characteristic
3#22612962C211yesmaximal, characteristic, complemented
4#22612772C211yesmaximal, characteristic
5#22610814C211yesmaximal, characteristic, complemented
6#22610630C211yesmaximal, characteristic, complemented
7#22610560C211yesmaximal, characteristic, complemented
8#22610355C211yesmaximal, characteristic, complemented
9#22610288C211yesmaximal, characteristic, complemented
10#22610274C211yesmaximal, characteristic, complemented
11#22610187C211yesmaximal, characteristic, complemented
12#22610132C211yesmaximal, characteristic, complemented
13#22609763C211yesmaximal, characteristic, complemented
14#22609710C211yesmaximal, characteristic, complemented
15C2×#452×C73C211yesmaximal, characteristic
16C23×#10596831C2211yescharacteristic
17C2×Q8×Dic73C2211yescharacteristic
18C2×Q8×Dic73C2211yescharacteristic
19C2×Q8×Dic73C2211yescharacteristic
20C2×#14556550C2211yescharacteristic
21#17988694—24no—
22C2×#14556525C2211yescharacteristic
23C2×#14556523C2211yescharacteristic
24#17988583—24no—
25C2×#14556515C2211yescharacteristic
26C2×#14556515C2211yescharacteristic
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556501C2211yescharacteristic
32C2×#14556501C2211yescharacteristic
33#17988494C2211yescharacteristic
34#17988490—21no—
35#17988490—21no—
36#17988490C2211yescharacteristic
37#17988490C2211yescharacteristic
38#17988486C2211yescharacteristic
39#17988480—21no—
40#17988480—21no—
41#17988473—21no—
42#17988447—21no—
43#17988447C2211yescharacteristic
44C4⋊C4×Dic73—21no—
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×Q16×C73C2211yescharacteristic
56C22×SD16×C73C2211yescharacteristic
57C2×C22⋊Q8×C73C2211yescharacteristic
58#452×C73C418yescomplemented
59C2×#103×C73C2211yescharacteristic
60C2×#102×C73C2211yescharacteristic
61C2×C22⋊C8×C73C2211yescharacteristic
62C22×#10596831—22no—
63C22×#10596831—22no—
64C22×#10596831—41no—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67Q8×Dic73—22no—
68Q8×Dic73—22no—
69Q8×Dic73—22no—
70Q8×Dic73—41no—
71Q8×Dic73—41no—
72Q8×Dic73—41no—
73#14556550—22no—
74#14556550—41no—
75C2×C4⋊Dic73—21no—
76C2×C4⋊Dic73—21no—
77C2×C4⋊Dic73—21no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C22⋊Dic73—21no—
84C2×C22⋊Dic73—21no—
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C22⋊Dic73—21no—
88C2×C22⋊Dic73—21no—
89C2×C22⋊Dic73D411yescharacteristic
90C2×C22⋊Dic73D411yescharacteristic
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93C2×C4×Dic73—21no—
94C2×C4×Dic73—21no—
95C2×C4×Dic73—21no—
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98#14556525—41no—
99#14556523—22no—
100#14556515—22no—
101#14556515—22no—
102#14556515—41no—
103#14556515D414yes—
104#14556512—22no—
105#14556512—22no—
106#14556501—22no—
107#14556501—41no—
108#14556498—21no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498D411yescharacteristic
114#14556498D411yescharacteristic
115C2×#41×C73—22no—
116C2×#41×C73—22no—
117C2×#41×C73—22no—
118C2×#41×C73—41no—
119C2×#41×C73—41no—
120C2×#41×C73C2×C414yes—
121C22×Q8×C73C2311yescharacteristic
122C22×Q8×C73C2311yescharacteristic
123C22×D4×C73—21no—
124C22×D4×C73C2311yescharacteristic
125C23×C4×C73—21no—
126C23×C4×C73C2311yescharacteristic
127C2×Q16×C73—22no—
128C2×Q16×C73—22no—
129C2×Q16×C73C2×C414yes—
130C2×SD16×C73—41no—
131C2×SD16×C73—41no—
132C2×SD16×C73C2×C414yes—
133C22×C8×C73C2311yescharacteristic
134C22×C8×C73C2311yescharacteristic
135C22⋊Q8×C73—22no—
136C22⋊Q8×C73C2×C414yes—
137C2×C4⋊C4×C73—21no—
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73—21no—
140#103×C73C2×C414yes—
141#102×C73C2×C414yes—
142C22⋊C8×C73C2×C414yes—
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73C2×D411yescharacteristic
148C22×Dic73C2×D411yescharacteristic
149C22×Dic73C2×D411yescharacteristic
150C22×Dic73C2×D411yescharacteristic
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—44no—
157C2×#10596831C2×D412yes—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—42no—
166C4⋊Dic73—42no—
167C4⋊Dic73—42no—
168C4⋊Dic73—42no—
169C4⋊Dic73C2×D412yes—
170C22⋊Dic73—41no—
171C22⋊Dic73—41no—
172C22⋊Dic73—42no—
173C22⋊Dic73—42no—
174C22⋊Dic73—42no—
175C22⋊Dic73—81no—
176C22⋊Dic73—81no—
177C22⋊Dic73—81no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—42no—
183C4×Dic73—42no—
184C4×Dic73—42no—
185C4×Dic73—42no—
186C4×Dic73—42no—
187C24×C73—21no—
188C24×C73C2×D411yescharacteristic
189#41×C73—28no—
190#41×C73—44no—
191#41×C73—44no—
192#41×C73—44no—
193C2×Q8×C73—21no—
194C2×Q8×C73—21no—
195C2×Q8×C73—21no—
196C2×Q8×C73—21no—
197C2×Q8×C73—21no—
198C2×Q8×C73—21no—
199C2×Q8×C73—21no—
200C2×Q8×C73—21no—
201C2×Q8×C73C22×C412yes—
202C2×Q8×C73C22×C412yes—
203C2×Q8×C73C2×D412yes—
204C2×Q8×C73#4112yes—
205C2×D4×C73—24no—
206C2×D4×C73—21no—
207C2×D4×C73—21no—
208C2×D4×C73—21no—
209C2×D4×C73—21no—
210C2×D4×C73—21no—
211C2×D4×C73—42no—
212C2×D4×C73—42no—
213C2×D4×C73C22×C412yes—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—24no—
222C22×C4×C73—42no—
223C22×C4×C73—42no—
224C22×C4×C73C22×C412yes—
225C22×C4×C73C2×D411yescharacteristic
226C22×C4×C73#4112yes—
227C22×C4×C73C2411yescharacteristic
228Q16×C73—28no—
229SD16×C73—44no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73C22×C412yes—
235C2×C8×C73C22×C412yes—
236C4⋊C4×C73—24no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73C22×C412yes—
239C22⋊C4×C73—24no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—22no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73C4×D412yes—
254C23×C73C22×D411yescharacteristic
255Q8×C73—22no—
256Q8×C73—22no—
257Q8×C73—22no—
258Q8×C73—22no—
259Q8×C73—22no—
260Q8×C73—41no—
261Q8×C73—41no—
262Q8×C73C4×D414yes—
263D4×C73—22no—
264D4×C73—22no—
265D4×C73—48no—
266D4×C73—41no—
267D4×C73—41no—
268C2×C4×C73—22no—
269C2×C4×C73—21no—
270C2×C4×C73—22no—
271C2×C4×C73—21no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—48no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73C4×D412yes—
285C2×C4×C73C23×C411yescharacteristic
286C2×C4×C73C22×D411yescharacteristic
287C2×C4×C73C2×#4111yescharacteristic
288C2×C4×C73C2×#4111yescharacteristic
289C2×C4×C73H(5,𝔽2)11yescharacteristic
290C2×C4×C73H(5,𝔽2)11yescharacteristic
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—22no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C8×C73—22no—
316C8×C73—22no—
317#10596831—22no—
318#10596831—41no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—22no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—42no—
327C22×C73—42no—
328C22×C73—42no—
329C22×C73—81no—
330C22×C73—81no—
331C22×C73—81no—
332C22×C73—81no—
333C22×C73C2×C4×D411yescharacteristic
334C22×C73D4211yescharacteristic
335C22×C73#54611yescharacteristic
336C22×C73#57511yescharacteristic
337C22×C73#57511yescharacteristic
338C22×C73#57711yescharacteristic
339C22×C73#57811yescharacteristic
340C4×C73—22no—
341C4×C73—24no—
342C4×C73—42no—
343C4×C73—42no—
344C4×C73C2×C4×D411yescharacteristic
345C4×C73#51811yescharacteristic
346C4×C73#54611yescharacteristic
347C4×C73#55111yescharacteristic
348Dic73—41no—
349Dic73—42no—
350Dic73—41no—
351Dic73—41no—
352Dic73—41no—
353Dic73—81no—
354Dic73—81no—
355Dic73—81no—
356#22861—731nomaximal, Sylow
357C2×C73—42no—
358C2×C73—82no—
359C2×C73#235811yescharacteristic
360C2×C73#294311yescharacteristic
361C2×C73#294711yescharacteristic
362C2×C73#326911yescharacteristic
363C2×C73#327111yescharacteristic
364C2×C73#331311yescharacteristic
365C2×C73#331711yescharacteristic
366C2×#452D7311yescharacteristic
367C2×#441—731no—
368C2×#416—731no—
369#2362—731no—
370#2341—731no—
371#1973—731no—
372#1936—731no—
373#1926—731no—
374#1892—731no—
375#1880—731no—
376#1878—731no—
377#1863—731no—
378#1854—731no—
379#1763—731no—
380#1752—731no—
381C73#2286111yescharacteristic, complemented, Sylow
382C22×#41C2×D7311yescharacteristic
383C22×Q16C2×D7311yescharacteristic
384C22×SD16C2×D7311yescharacteristic
385C23×C8—731no—
386C2×C22⋊Q8C2×D7311yescharacteristic
387C2×C4×Q8—731no—
388C2×C4×Q8—731no—
389C2×C4×Q8—731no—
390C2×#117—731no—
391#452Dic7318yescomplemented
392#441—1464no—
393C2×#107—731no—
394C2×#106—731no—
395#416—1464no—
396C2×#103—731no—
397C2×#103—731no—
398C2×#103—731no—
399C2×#103—731no—
400C2×#103C2×D7311yescharacteristic
401C2×#102—731no—
402C2×#102—731no—
403C2×#102C2×D7311yescharacteristic
404C2×C22⋊C8C2×D7311yescharacteristic
405C2×#97—731no—
406C2×#97—731no—
407#391—731no—
408#390—731no—
409#390—731no—
410#390—1461no—
411#390—1461no—
412#389—731no—
413#388—1461no—
414#388—1461no—
415#387—1461no—
416#380—731no—
417#380—1461no—
418C4×C4⋊C4—731no—
419C4×C4⋊C4—1461no—
420C4×C22⋊C4—731no—
421C4×C22⋊C4—1461no—
422#340—731no—
423#340—731no—
424#340—731no—
425#340—731no—
426#336—731no—
427#336—731no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41—22no—
431C2×#41—41no—
432C2×#41—41no—
433C2×#41C2×Dic7314yes—
434C22×Q8C22×D7311yescharacteristic
435C22×Q8C22×D7311yescharacteristic
436C22×D4—21no—
437C22×D4C22×D7311yescharacteristic
438C23×C4—21no—
439C23×C4C22×D7311yescharacteristic
440C2×Q16—22no—
441C2×Q16—22no—
442C2×Q16C2×Dic7314yes—
443C2×SD16—41no—
444C2×SD16—41no—
445C2×SD16C2×Dic7314yes—
446C22×C8—2921no—
447C22×C8—731no—
448C22×C8—731no—
449C22×C8—1462no—
450C22×C8—1462no—
451C22×C8C22×D7311yescharacteristic
452C22×C8C22×D7311yescharacteristic
453C22⋊Q8—22no—
454C22⋊Q8C2×Dic7314yes—
455C4×Q8—2921no—
456C4×Q8—2921no—
457C4×Q8—2921no—
458C4×Q8—1462no—
459C4×Q8—1462no—
460C4×Q8—1462no—
461#117—2921no—
462#117—1462no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—731no—
465C2×C4⋊C4—731no—
466C2×C4⋊C4—731no—
467C2×C4⋊C4—731no—
468C2×C4⋊C4—1461no—
469C2×C4⋊C4—1461no—
470C2×C4⋊C4—1461no—
471C2×C4⋊C4—1461no—
472C2×C4⋊C4C22×D7311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—731no—
475C2×C22⋊C4—731no—
476C2×C22⋊C4—1461no—
477C2×C22⋊C4—1461no—
478C2×C22⋊C4—1461no—
479C2×C22⋊C4—1461no—
480C2×C22⋊C4—1461no—
481C2×C22⋊C4—1461no—
482C2×C42—731no—
483C2×C42—731no—
484C2×C42—1461no—
485C2×C42—1461no—
486C2×C42—1461no—
487C2×C42—1461no—
488C2×C42—1461no—
489#107—2921no—
490#106—1462no—
491#103—2921no—
492#103—734no—
493#103—1462no—
494#103—1462no—
495#103C2×Dic7314yes—
496#102—1462no—
497#102—1462no—
498#102C2×Dic7314yes—
499C22⋊C8C2×Dic7314yes—
500#97—2921no—
501#97—1462no—
502#95—731no—
503#95—731no—
504#95—1461no—
505#95—1461no—
506#95—1461no—
507#95—1461no—
508#95—1461no—
509C24—21no—
510C24D4×D7311yescharacteristic
511#41—28no—
512#41—44no—
513#41—44no—
514#41—44no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8C22×Dic7312yes—
524C2×Q8C22×Dic7312yes—
525C2×Q8D4×D7312yes—
526C2×Q8#1192402712yes—
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4C22×Dic7312yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—24no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—731no—
547C22×C4—731no—
548C22×C4—731no—
549C22×C4—731no—
550C22×C4—1461no—
551C22×C4—1461no—
552C22×C4—1461no—
553C22×C4—1461no—
554C22×C4C22×Dic7312yes—
555C22×C4D4×D7311yescharacteristic
556C22×C4#1192402712yes—
557C22×C4C23×D7311yescharacteristic
558Q16—28no—
559SD16—44no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—2924no—
565C2×C8—732no—
566C2×C8—1461no—
567C2×C8—1461no—
568C2×C8—1461no—
569C2×C8—1461no—
570C2×C8—1461no—
571C2×C8C22×Dic7312yes—
572C2×C8C22×Dic7312yes—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—2922no—
576C4⋊C4—2922no—
577C4⋊C4—2922no—
578C4⋊C4—2922no—
579C4⋊C4—732no—
580C4⋊C4—1461no—
581C4⋊C4—1461no—
582C4⋊C4—1461no—
583C4⋊C4—1461no—
584C4⋊C4—1461no—
585C4⋊C4—1461no—
586C4⋊C4—1461no—
587C4⋊C4C22×Dic7312yes—
588C22⋊C4—24no—
589C22⋊C4—2922no—
590C22⋊C4—2922no—
591C22⋊C4—2922no—
592C22⋊C4—2921no—
593C22⋊C4—2921no—
594C22⋊C4—5841no—
595C22⋊C4—5841no—
596C22⋊C4—5841no—
597C42—2922no—
598C42—2922no—
599C42—2922no—
600C42—2922no—
601C42—2922no—
602C42—1461no—
603C42—1461no—
604C42—1461no—
605C42—1461no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23D4×Dic7312yes—
620C23C2×D4×D7311yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—22no—
626Q8—41no—
627Q8—41no—
628Q8D4×Dic7314yes—
629D4—22no—
630D4—22no—
631D4—48no—
632D4—41no—
633D4—41no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—2921no—
651C2×C4—2921no—
652C2×C4—2921no—
653C2×C4—2921no—
654C2×C4—2921no—
655C2×C4—2921no—
656C2×C4—2921no—
657C2×C4—2921no—
658C2×C4—2921no—
659C2×C4—2921no—
660C2×C4—2921no—
661C2×C4—1461no—
662C2×C4—1461no—
663C2×C4—1461no—
664C2×C4—1461no—
665C2×C4—1461no—
666C2×C4—1461no—
667C2×C4—1461no—
668C2×C4—1461no—
669C2×C4—1461no—
670C2×C4—1461no—
671C2×C4—1462no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4D4×Dic7312yes—
675C2×C4C23×Dic7311yescharacteristic
676C2×C4C2×D4×D7311yescharacteristic
677C2×C4C2×#1192402711yescharacteristic
678C2×C4C2×#1192402711yescharacteristic
679C2×C4#1455663611yescharacteristic
680C2×C4#1455663611yescharacteristic
681C8—22no—
682C8—22no—
683C8—2921no—
684C8—1462no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22C2×D4×Dic7311yescharacteristic
700C22#1798921911yescharacteristic
701C22#1798922411yescharacteristic
702C22#1798938411yescharacteristic
703C22#1798938411yescharacteristic
704C22#1798939611yescharacteristic
705C22#1798940311yescharacteristic
706C4—22no—
707C4—24no—
708C4—42no—
709C4—42no—
710C4—2922no—
711C4—2921no—
712C4—2921no—
713C4—2921no—
714C4—2921no—
715C4—5841no—
716C4—5841no—
717C4—5841no—
718C4C2×D4×Dic7311yescharacteristic
719C4#1798906211yescharacteristic
720C4#1798922411yescharacteristic
721C4#1798926811yescharacteristic
722C2—42no—
723C2—82no—
724C2#2261291511yescharacteristic
725C2#2261873211yescharacteristic
726C2#2261877511yescharacteristic
727C2#2262147911yescharacteristic
728C2#2262152011yescharacteristic
729C2#2262200111yescharacteristic
730C2#2262206111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#452×C73C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#452D73
hypocenterC73#22861
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#17988694C2semidirect
3. #22612962C2semidirect
5. #22610814C2semidirect
6. #22610630C2semidirect
7. #22610560C2semidirect
8. #22610355C2semidirect
9. #22610288C2semidirect
10. #22610274C2semidirect
11. #22610187C2semidirect
12. #22610132C2semidirect
13. #22609763C2semidirect
14. #22609710C2semidirect
58. #452×C73C4semidirect
381. C73#22861semidirect
391. #452Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886942
C2×#179885832
#226129622
#226127722
#226108142
#226106302
#226105602
#226103552
#226102882
#226102742
#226101872
#226101322
#226097632
#226097102
C2×#452×C732
#2286173