Finite Group Databasebeta

← #33106275

Subgroups — #33106275

Order 18688.

1118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988688C211yesmaximal, characteristic, complemented
2C2×#17988583C211yesmaximal, characteristic
3#22612962C211yesmaximal, characteristic, complemented
4#22612761C211yesmaximal, characteristic
5#22610803C211yesmaximal, characteristic, complemented
6#22610623C211yesmaximal, characteristic, complemented
7#22610574C211yesmaximal, characteristic, complemented
8#22610355C211yesmaximal, characteristic, complemented
9#22610274C211yesmaximal, characteristic, complemented
10#22610267C211yesmaximal, characteristic, complemented
11#22610194C211yesmaximal, characteristic, complemented
12#22610132C211yesmaximal, characteristic, complemented
13#22609758C211yesmaximal, characteristic, complemented
14#22609710C211yesmaximal, characteristic, complemented
15C2×#452×C73C211yesmaximal, characteristic
16C23×#10596831C2211yescharacteristic
17C2×Q8×Dic73C2211yescharacteristic
18C2×D4×Dic73C2211yescharacteristic
19C2×D4×Dic73C2211yescharacteristic
20C2×#14556550C2211yescharacteristic
21#17988688—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#17988494C2211yescharacteristic
35#17988494C2211yescharacteristic
36#17988486C2211yescharacteristic
37#17988480—21no—
38#17988480—21no—
39#17988473—21no—
40#17988467—21no—
41#17988467—21no—
42#17988450—21no—
43#17988447C2211yescharacteristic
44C4⋊C4×Dic73—21no—
45C4⋊C4×Dic73C2211yescharacteristic
46C4×C22⋊Dic73C2211yescharacteristic
47C2×#14556498—21no—
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
62C23×Dic73—21no—
63C23×Dic73—21no—
64C22×#10596831—22no—
65C22×#10596831—22no—
66C22×#10596831—41no—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69Q8×Dic73—22no—
70Q8×Dic73—41no—
71D4×Dic73—22no—
72D4×Dic73—22no—
73D4×Dic73—41no—
74D4×Dic73—41no—
75#14556550—22no—
76#14556550—41no—
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⋊Dic73D411yescharacteristic
88C2×C22⋊Dic73D411yescharacteristic
89C2×C4×Dic73—21no—
90C2×C4×Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94#14556525—22no—
95#14556523—41no—
96#14556515—22no—
97#14556515—22no—
98#14556515—22no—
99#14556515—41no—
100#14556512—22no—
101#14556512D414yes—
102#14556501—22no—
103#14556501—41no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
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—41no—
128C2×Q16×C73—41no—
129C2×Q16×C73C2×C414yescomplemented
130C2×SD16×C73—22no—
131C2×SD16×C73—22no—
132C2×SD16×C73C2×C414yes—
133C22×C8×C73C2311yescharacteristic
134C22×C8×C73C2311yescharacteristic
135C22⋊Q8×C73—22no—
136C22⋊Q8×C73C2×C414yescomplemented
137C2×C4⋊C4×C73—21no—
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73—21no—
140#103×C73C2×C414yescomplemented
141#102×C73C2×C414yes—
142C22⋊C8×C73C2×C414yescomplemented
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—42no—
148C22×Dic73—42no—
149C22×Dic73—42no—
150C22×Dic73—42no—
151C22×Dic73—81no—
152C22×Dic73—81no—
153C22×Dic73C2×D411yescharacteristic
154C22×Dic73C2×D411yescharacteristic
155C22×Dic73C2×D411yescharacteristic
156C22×Dic73C2×D411yescharacteristic
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—44no—
163C2×#10596831C2×D412yes—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—42no—
172C4⋊Dic73—42no—
173C4⋊Dic73C2×D412yes—
174C22⋊Dic73—41no—
175C22⋊Dic73—41no—
176C22⋊Dic73—42no—
177C22⋊Dic73—42no—
178C22⋊Dic73—42no—
179C22⋊Dic73—81no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
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×C73—21no—
202C2×Q8×C73—21no—
203C2×Q8×C73C22×C412yes—
204C2×Q8×C73C22×C412yes—
205C2×D4×C73—24no—
206C2×D4×C73—21no—
207C2×D4×C73—21no—
208C2×D4×C73—21no—
209C2×D4×C73—42no—
210C2×D4×C73—42no—
211C2×D4×C73C22×C412yes—
212C2×D4×C73C2×D412yes—
213C2×D4×C73#4112yes—
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—44no—
229SD16×C73—28no—
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—22no—
241C23×C73—21no—
242C23×C73—22no—
243C23×C73—21no—
244C23×C73—22no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
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—41no—
260Q8×C73—41no—
261Q8×C73—41no—
262Q8×C73—41no—
263D4×C73—22no—
264D4×C73—22no—
265D4×C73—22no—
266D4×C73—48no—
267D4×C73C4×D414yes—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—48no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
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—
315C2×Dic73—84no—
316C2×Dic73—84no—
317C8×C73—22no—
318C8×C73—22no—
319#10596831—22no—
320#10596831—41no—
321C22×C73—22no—
322C22×C73—24no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—42no—
326C22×C73—42no—
327C22×C73—42no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—42no—
335C22×C73C2×C4×D411yescharacteristic
336C22×C73D4211yescharacteristic
337C22×C73#54611yescharacteristic
338C22×C73#57511yescharacteristic
339C22×C73#57511yescharacteristic
340C22×C73#57711yescharacteristic
341C22×C73#57811yescharacteristic
342C4×C73—22no—
343C4×C73—42no—
344C4×C73—42no—
345C4×C73—42no—
346C4×C73C2×C4×D411yescharacteristic
347C4×C73#51811yescharacteristic
348C4×C73#54611yescharacteristic
349C4×C73#55111yescharacteristic
350Dic73—41no—
351Dic73—42no—
352Dic73—41no—
353Dic73—41no—
354Dic73—41no—
355Dic73—81no—
356Dic73—81no—
357Dic73—81no—
358#22856—731nomaximal, Sylow
359C2×C73—42no—
360C2×C73—44no—
361C2×C73#235811yescharacteristic
362C2×C73#294311yescharacteristic
363C2×C73#294711yescharacteristic
364C2×C73#326711yescharacteristic
365C2×C73#326911yescharacteristic
366C2×C73#331111yescharacteristic
367C2×C73#331511yescharacteristic
368C2×#452D7311yescharacteristic
369C2×#440—731no—
370C2×#416—731no—
371#2362—731no—
372#2339—731no—
373#1971—731no—
374#1935—731no—
375#1928—731no—
376#1892—731no—
377#1878—731no—
378#1877—731no—
379#1864—731no—
380#1854—731no—
381#1762—731no—
382#1752—731no—
383C73#2285611yescharacteristic, complemented, Sylow
384C22×#41C2×D7311yescharacteristic
385C22×Q16C2×D7311yescharacteristic
386C22×SD16C2×D7311yescharacteristic
387C23×C8—731no—
388C2×C22⋊Q8C2×D7311yescharacteristic
389C2×C4×Q8—731no—
390C2×C4×D4—731no—
391C2×C4×D4—731no—
392C2×#117—731no—
393#452Dic7318yescomplemented
394#440—1464no—
395C2×#107—731no—
396C2×#106—731no—
397#416—1464no—
398C2×#103—731no—
399C2×#103—731no—
400C2×#103—731no—
401C2×#103—731no—
402C2×#103C2×D7311yescharacteristic
403C2×#102—731no—
404C2×#102—731no—
405C2×#102C2×D7311yescharacteristic
406C2×C22⋊C8C2×D7311yescharacteristic
407C2×#97—731no—
408C2×#97—731no—
409#391—731no—
410#391—731no—
411#391—731no—
412#389—731no—
413#388—1461no—
414#388—1461no—
415#387—1461no—
416#386—1461no—
417#386—1461no—
418#381—1461no—
419#380—731no—
420C4×C4⋊C4—731no—
421C4×C4⋊C4—1461no—
422C4×C22⋊C4—731no—
423C2×#95—1461no—
424#340—731no—
425#340—731no—
426#340—731no—
427#340—731no—
428#336—731no—
429#336—731no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41C2×Dic7314yes—
436C22×Q8C22×D7311yescharacteristic
437C22×Q8C22×D7311yescharacteristic
438C22×D4—21no—
439C22×D4C22×D7311yescharacteristic
440C23×C4—21no—
441C23×C4—1461no—
442C23×C4—1461no—
443C23×C4C22×D7311yescharacteristic
444C2×Q16—41no—
445C2×Q16—41no—
446C2×Q16C2×Dic7314yescomplemented
447C2×SD16—22no—
448C2×SD16—22no—
449C2×SD16C2×Dic7314yes—
450C22×C8—2921no—
451C22×C8—731no—
452C22×C8—731no—
453C22×C8—1462no—
454C22×C8—1462no—
455C22×C8C22×D7311yescharacteristic
456C22×C8C22×D7311yescharacteristic
457C22⋊Q8—22no—
458C22⋊Q8C2×Dic7314yescomplemented
459C4×Q8—2921no—
460C4×Q8—1462no—
461C4×D4—2921no—
462C4×D4—2921no—
463C4×D4—1462no—
464C4×D4—1462no—
465#117—2921no—
466#117—1462no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—731no—
469C2×C4⋊C4—731no—
470C2×C4⋊C4—731no—
471C2×C4⋊C4—731no—
472C2×C4⋊C4—1461no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4C22×D7311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—731no—
477C2×C22⋊C4—731no—
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—
487#107—1462no—
488#106—2921no—
489#103—2921no—
490#103—1462no—
491#103—1462no—
492#103—1462no—
493#103C2×Dic7314yescomplemented
494#102—734no—
495#102—1462no—
496#102C2×Dic7314yes—
497C22⋊C8C2×Dic7314yescomplemented
498#97—2921no—
499#97—1462no—
500#95—731no—
501#95—731no—
502#95—1461no—
503#95—1461no—
504#95—1461no—
505#95—1461no—
506#95—1461no—
507#95—1461no—
508#95—1461no—
509#95—1461no—
510#95—1461no—
511C24—21no—
512C24D4×D7311yescharacteristic
513#41—28no—
514#41—44no—
515#41—44no—
516#41—44no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8C22×Dic7312yes—
528C2×Q8C22×Dic7312yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4C22×Dic7312yes—
536C2×D4D4×D7312yes—
537C2×D4#1192402712yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—2922no—
549C22×C4—2922no—
550C22×C4—2922no—
551C22×C4—2922no—
552C22×C4—5841no—
553C22×C4—5841no—
554C22×C4—731no—
555C22×C4—731no—
556C22×C4—731no—
557C22×C4—731no—
558C22×C4—1461no—
559C22×C4—1461no—
560C22×C4—1461no—
561C22×C4—1461no—
562C22×C4C22×Dic7312yes—
563C22×C4D4×D7311yescharacteristic
564C22×C4#1192402712yes—
565C22×C4C23×D7311yescharacteristic
566Q16—44no—
567SD16—28no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—2924no—
573C2×C8—732no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C2×C8C22×Dic7312yes—
580C2×C8C22×Dic7312yes—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—2922no—
584C4⋊C4—2922no—
585C4⋊C4—732no—
586C4⋊C4—1461no—
587C4⋊C4—1461no—
588C4⋊C4—1461no—
589C4⋊C4—1461no—
590C4⋊C4—1461no—
591C4⋊C4—1461no—
592C4⋊C4—1461no—
593C4⋊C4C22×Dic7312yes—
594C22⋊C4—24no—
595C22⋊C4—2922no—
596C22⋊C4—2922no—
597C22⋊C4—2922no—
598C22⋊C4—2921no—
599C22⋊C4—2921no—
600C22⋊C4—5841no—
601C42—2922no—
602C42—2922no—
603C42—2922no—
604C42—1461no—
605C42—1461no—
606C42—1461no—
607C42—1461no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—22no—
615C23—21no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23D4×Dic7312yes—
622C23C2×D4×D7311yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—48no—
635D4D4×Dic7314yes—
636C2×C4—21no—
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—41no—
651C2×C4—41no—
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—2921no—
662C2×C4—2921no—
663C2×C4—5844no—
664C2×C4—5844no—
665C2×C4—1461no—
666C2×C4—1461no—
667C2×C4—1461no—
668C2×C4—1461no—
669C2×C4—1461no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1462no—
675C2×C4—1461no—
676C2×C4—1461no—
677C2×C4—1461no—
678C2×C4D4×Dic7312yes—
679C2×C4C23×Dic7311yescharacteristic
680C2×C4C2×D4×D7311yescharacteristic
681C2×C4C2×#1192402711yescharacteristic
682C2×C4C2×#1192402711yescharacteristic
683C2×C4#1455663611yescharacteristic
684C2×C4#1455663611yescharacteristic
685C8—22no—
686C8—22no—
687C8—2921no—
688C8—1462no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—24no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22C2×D4×Dic7311yescharacteristic
704C22#1798921911yescharacteristic
705C22#1798922411yescharacteristic
706C22#1798938411yescharacteristic
707C22#1798938411yescharacteristic
708C22#1798939611yescharacteristic
709C22#1798940311yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—2921no—
715C4—2922no—
716C4—2921no—
717C4—2921no—
718C4—2921no—
719C4—5841no—
720C4—5841no—
721C4—5841no—
722C4C2×D4×Dic7311yescharacteristic
723C4#1798906211yescharacteristic
724C4#1798922411yescharacteristic
725C4#1798926811yescharacteristic
726C2—42no—
727C2—44no—
728C2#2261291511yescharacteristic
729C2#2261873211yescharacteristic
730C2#2261877511yescharacteristic
731C2#2262146011yescharacteristic
732C2#2262149011yescharacteristic
733C2#2262197111yescharacteristic
734C2#2262203111yescharacteristic
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#22856
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×#17988688C2semidirect
3. #22612962C2semidirect
5. #22610803C2semidirect
6. #22610623C2semidirect
7. #22610574C2semidirect
8. #22610355C2semidirect
9. #22610274C2semidirect
10. #22610267C2semidirect
11. #22610194C2semidirect
12. #22610132C2semidirect
13. #22609758C2semidirect
14. #22609710C2semidirect
58. #452×C73C4semidirect
129. C2×Q16×C73C2×C4semidirect
136. C22⋊Q8×C73C2×C4semidirect
140. #103×C73C2×C4semidirect
142. C22⋊C8×C73C2×C4semidirect
383. C73#22856semidirect
393. #452Dic73semidirect
446. C2×Q16C2×Dic73semidirect
458. C22⋊Q8C2×Dic73semidirect
493. #103C2×Dic73semidirect
497. C22⋊C8C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886882
C2×#179885832
#226129622
#226127612
#226108032
#226106232
#226105742
#226103552
#226102742
#226102672
#226101942
#226101322
#226097582
#226097102
C2×#452×C732
#2285673