Finite Group Databasebeta

← #33103244

Subgroups — #33103244

Order 18688.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988591C211yesmaximal, characteristic
2C22⋊C4×D292C211yesmaximal, characteristic
3#22610627C211yesmaximal, characteristic, complemented
4#22610613C211yesmaximal, characteristic, complemented
5#22610558C211yesmaximal, characteristic, complemented
6#22610551C211yesmaximal, characteristic, complemented
7#22610191C211yesmaximal, characteristic, complemented
8#22610177C211yesmaximal, characteristic, complemented
9#22610026C211yesmaximal, characteristic, complemented
10#22609962C211yesmaximal, characteristic, complemented
11#22609861C211yesmaximal, characteristic
12#22609759C211yesmaximal, characteristic, complemented
13C4×#14556511C211yesmaximal, characteristic, complemented
14#22609715C211yesmaximal, characteristic, complemented
15C73×#2347C211yesmaximal, characteristic, complemented
16C23×D292C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C2×C4×D292C2211yescharacteristic
19C2×C4×D292C2211yescharacteristic
20C2×C22⋊C4×D73—21no—
21C2×#14556524C2211yescharacteristic, complemented
22C2×#14556522C2211yescharacteristic, complemented
23#17988591C418yescomplemented
24C2×#14556511C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556511C2211yescharacteristic
29C2×#14556511C2211yescharacteristic
30C2×#14556511C2211yescharacteristic
31C2×#14556511C2211yescharacteristic
32C2×C22⋊#10596831C2211yescharacteristic
33C2×#14556502C2211yescharacteristic, complemented
34C2×C4×#10596831C2211yescharacteristic, complemented
35#17988489C2211yescharacteristic
36#17988489C2211yescharacteristic
37#17988465—21no—
38#17988465—21no—
39#17988447C2211yescharacteristic
40#17988442—21no—
41#17988349C2211yescharacteristic, complemented
42#17988349C2211yescharacteristic, complemented
43#17988349C2211yescharacteristic, complemented
44#17988349C2211yescharacteristic, complemented
45#17988349C2211yescharacteristic, complemented
46#17988349C2211yescharacteristic, complemented
47#17988342C2211yescharacteristic, complemented
48#17988342C2211yescharacteristic, complemented
49C2×#117×C73C2211yescharacteristic
50#389×C73C2211yescharacteristic, complemented
51#389×C73C2211yescharacteristic, complemented
52#388×C73—21no—
53#388×C73—21no—
54#383×C73—21no—
55#380×C73C2211yescharacteristic
56C4×C4⋊C4×C73—21no—
57C4×C4⋊C4×C73C2211yescharacteristic, complemented
58C4×C4⋊C4×C73C2211yescharacteristic, complemented
59C4×C22⋊C4×C73C2211yescharacteristic
60C24×D73—21no—
61C22×D292—22no—
62C22×D292—22no—
63C22×D292—21no—
64C22×D292—22no—
65C22×D292—41no—
66C22×D292—41no—
67C22×D292C2×C414yes—
68C22×D292C2311yescharacteristic
69C22×D292C2311yescharacteristic
70C22×C4×D73—21no—
71C22×C4×D73—21no—
72C2×#11924012—41no—
73C2×#11924012—41no—
74C2×#11924012C2×C414yescomplemented
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C4×D292—22no—
80C4×D292—22no—
81C4×D292—41no—
82C4×D292—41no—
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C22⋊Dic73—21no—
86C2×#11924005—21no—
87C2×#11924005—21no—
88C2×#11924005—21no—
89C2×#11924005—21no—
90C2×#11924005—21no—
91C2×#11924005—21no—
92C22⋊C4×D73—44no—
93#14556524—41no—
94#14556522—41no—
95#14556511—22no—
96#14556511—22no—
97#14556511—41no—
98#14556511—41no—
99#14556511C2×C414yes—
100#14556511C2×C414yes—
101#14556511C2×C414yescomplemented
102#14556511C2×C414yescomplemented
103C22⋊#10596831—22no—
104#14556502—41no—
105C4×#10596831—41no—
106#14556498—21no—
107C23×C4×C73C2311yescharacteristic
108#117×C73—22no—
109#117×C73C2×C414yescomplemented
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73D411yescharacteristic
119C2×C22⋊C4×C73D411yescharacteristic
120C2×C42×C73—21no—
121C2×C42×C73—21no—
122C2×C42×C73—21no—
123C2×C42×C73C2311yescharacteristic
124C2×C42×C73C2311yescharacteristic
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73D411yescharacteristic
131#95×C73D411yescharacteristic
132C23×D73—21no—
133C23×D73—21no—
134C23×D73—24no—
135C23×D73—42no—
136C23×D73—42no—
137C23×D73—42no—
138C23×D73—42no—
139C23×D73—81no—
140C23×D73—81no—
141C2×D292—21no—
142C2×D292—21no—
143C2×D292—21no—
144C2×D292—21no—
145C2×D292—21no—
146C2×D292—21no—
147C2×D292—21no—
148C2×D292—28no—
149C2×D292—24no—
150C2×D292—21no—
151C2×D292—44no—
152C2×D292—44no—
153C2×D292—44no—
154C2×D292—42no—
155C2×D292—42no—
156C2×D292C22×C412yes—
157C2×D292C22×C412yes—
158C2×D292#4112yes—
159C2×D292#4112yes—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C2×C4×D73—42no—
163C2×C4×D73—42no—
164C2×C4×D73—42no—
165C2×C4×D73—42no—
166C2×C4×D73—81no—
167C2×C4×D73—81no—
168#11924012—44no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831C22×C412yes—
180C2×#10596831C22×C412yes—
181C4⋊Dic73—21no—
182C4⋊Dic73—21no—
183C4⋊Dic73—21no—
184C4⋊Dic73—21no—
185C22⋊Dic73—42no—
186#11924005—42no—
187#11924005—42no—
188#11924005—42no—
189#11924005—42no—
190#11924005—81no—
191#11924005—81no—
192C24×C73C2×D411yescharacteristic
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73C22×C412yes—
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73#4112yes—
208C22×C4×C73C2411yescharacteristic
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73—42no—
217C4⋊C4×C73C22×C412yes—
218C4⋊C4×C73C22×C412yes—
219C22⋊C4×C73—24no—
220C22⋊C4×C73—22no—
221C22⋊C4×C73—41no—
222C22⋊C4×C73—81no—
223C42×C73—24no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—81no—
229C42×C73—81no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73C4×D412yes—
237C23×C73C22×D411yescharacteristic
238C22×D73—22no—
239C22×D73—22no—
240C22×D73—22no—
241C22×D73—22no—
242C22×D73—48no—
243C22×D73—41no—
244C22×D73—41no—
245C22×D73—41no—
246C22×D73—41no—
247C22×D73—48no—
248C22×D73—41no—
249C22×D73—41no—
250C22×D73—41no—
251C22×D73—41no—
252C22×D73—41no—
253C22×D73—41no—
254C22×D73—84no—
255C22×D73—84no—
256C22×D73—84no—
257C22×D73—84no—
258C22×D73—84no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
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×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73C4×D412yes—
289C2×C4×C73AGL(1,ℤ/8)12yes—
290C2×C4×C73C23×C411yescharacteristic
291C2×C4×C73C2×#4111yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73H(5,𝔽2)11yescharacteristic
295C2×C4×C73H(5,𝔽2)11yescharacteristic
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—41no—
299C2×Dic73—41no—
300C2×Dic73—41no—
301C2×Dic73—41no—
302D292—22no—
303D292—22no—
304D292—22no—
305D292—22no—
306D292—22no—
307D292—48no—
308D292—41no—
309D292—41no—
310D292#11714yes—
311C4×D73—84no—
312C4×D73—84no—
313#10596831—22no—
314#10596831—22no—
315#10596831—41no—
316#10596831—41no—
317C22×C73—22no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—41no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73C2×C4×D411yescharacteristic
325C22×C73#54611yescharacteristic
326C22×C73#54611yescharacteristic
327C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C73#57511yescharacteristic
329C22×C73#57611yescharacteristic
330C22×C73#57711yescharacteristic
331C2×D73—24no—
332C2×D73—42no—
333C2×D73—42no—
334C2×D73—42no—
335C2×D73—42no—
336C2×D73—42no—
337C2×D73—42no—
338C2×D73—42no—
339C2×D73—42no—
340C2×D73—42no—
341C2×D73—816no—
342C2×D73—81no—
343C2×D73—81no—
344C2×D73—81no—
345C2×D73—81no—
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—42no—
349C4×C73—42no—
350C4×C73—41no—
351C4×C73—41no—
352C4×C73—41no—
353C4×C73—81no—
354C4×C73—81no—
355C4×C73C2×#11711yescharacteristic
356C4×C73#51811yescharacteristic
357C4×C73#55111yescharacteristic
358C4×C73#55111yescharacteristic
359Dic73—81no—
360Dic73—81no—
361#22580—731nomaximal, Sylow
362C2×C73—42no—
363C2×C73#234211yescharacteristic
364C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
365C2×C73#294611yescharacteristic
366C2×C73#331111yescharacteristic
367C2×C73#331811yescharacteristic
368C2×C73#332211yescharacteristic
369C2×C73#332411yescharacteristic
370D73—44no—
371D73—82no—
372C2×#418—731no—
373#2347D7311yescharacteristic, complemented
374D4×C22⋊C4—731no—
375#1936—731no—
376#1934—731no—
377#1926—731no—
378#1925—731no—
379#1864—731no—
380#1862—731no—
381#1825—731no—
382#1809—731no—
383#1786—731no—
384#1762—731no—
385C4×#102—731no—
386#1753—731no—
387C73#2258011yescharacteristic, complemented, Sylow
388C23×D4—731no—
389C22×M16—731no—
390C2×C4×D4—731no—
391C2×C4×D4—731no—
392C2×#117C2×D7311yescharacteristic
393C22×C22⋊C4—1461no—
394C2×#107—731no—
395C2×#106—731no—
396#418—738no—
397C2×#102—731no—
398C2×#102—731no—
399C2×#102—731no—
400C2×#102—731no—
401C2×#102—731no—
402C2×#102—731no—
403C2×#102—731no—
404C2×#102—731no—
405C2×C22⋊C8—731no—
406C2×#97—731no—
407C2×C4×C8—731no—
408#390—731no—
409#390—731no—
410#389C2×D7311yescharacteristic, complemented
411#389C2×D7311yescharacteristic, complemented
412#388—21no—
413#388—21no—
414#386—1461no—
415#386—1461no—
416#383—21no—
417#380—731no—
418#380C2×D7311yescharacteristic
419#379—1461no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4C2×D7311yescharacteristic, complemented
422C4×C4⋊C4C2×D7311yescharacteristic, complemented
423C4×C22⋊C4C2×D7311yescharacteristic
424#340—731no—
425#340—731no—
426#340—731no—
427#340—731no—
428#340—731no—
429#340—731no—
430#336—731no—
431#336—731no—
432C25—1461no—
433C22×D4—2921no—
434C22×D4—2921no—
435C22×D4—734no—
436C22×D4—731no—
437C22×D4—731no—
438C22×D4—1462no—
439C22×D4—1462no—
440C22×D4—1461no—
441C22×D4—1462no—
442C23×C4—1461no—
443C23×C4—1461no—
444C23×C4C22×D7311yescharacteristic
445C2×M16—2921no—
446C2×M16—2921no—
447C2×M16—734no—
448C22×C8—731no—
449C22×C8—731no—
450C22×C8—731no—
451C22×C8—731no—
452C4×D4—2921no—
453C4×D4—2921no—
454C4×D4—1462no—
455C4×D4—1462no—
456#117—22no—
457#117C4×D7314yescomplemented
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4C22×D7311yescharacteristic
463C2×C4⋊C4C22×D7311yescharacteristic
464C2×C4⋊C4C22×D7311yescharacteristic
465C2×C4⋊C4C22×D7311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—2924no—
469C2×C22⋊C4—1461no—
470C2×C22⋊C4—1461no—
471C2×C22⋊C4—1461no—
472C2×C22⋊C4—1461no—
473C2×C22⋊C4—1461no—
474C2×C22⋊C4—1461no—
475C2×C22⋊C4—1461no—
476C2×C22⋊C4C22⋊D7311yescharacteristic
477C2×C22⋊C4C22⋊D7311yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C22×D7311yescharacteristic
482C2×C42C22×D7311yescharacteristic
483#107—2921no—
484#106—2921no—
485#102—2921no—
486#102—2921no—
487#102—734no—
488#102—734no—
489#102—734no—
490#102—734no—
491#102—1462no—
492#102—1462no—
493C22⋊C8—1462no—
494#97—2921no—
495C4×C8—2921no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—1461no—
502#95C22⋊D7311yescharacteristic
503#95C22⋊D7311yescharacteristic
504C24—2922no—
505C24—2922no—
506C24—2922no—
507C24—2922no—
508C24—5841no—
509C24—5841no—
510C24—1461no—
511C24—1464no—
512C24—1461no—
513C24C2×C22⋊D7311yescharacteristic
514C2×D4—2922no—
515C2×D4—2922no—
516C2×D4—2924no—
517C2×D4—2924no—
518C2×D4—2924no—
519C2×D4—732no—
520C2×D4—732no—
521C2×D4—732no—
522C2×D4—732no—
523C2×D4—1468no—
524C2×D4—1464no—
525C2×D4—1461no—
526C2×D4—1461no—
527C2×D4—1461no—
528C2×D4—1461no—
529C2×D4—1461no—
530C2×D4—1461no—
531C2×D4—1461no—
532C2×D4—1461no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—2922no—
542C22×C4—2922no—
543C22×C4—2922no—
544C22×C4—2922no—
545C22×C4—5841no—
546C22×C4—5841no—
547C22×C4—1461no—
548C22×C4—1461no—
549C22×C4C2×C4×D7312yes—
550C22×C4C2×C22⋊D7311yescharacteristic
551C22×C4C2×C22⋊D7311yescharacteristic
552C22×C4C2×C22⋊D7311yescharacteristic
553C22×C4C2×C22⋊D7311yescharacteristic
554C22×C4C2×C22⋊D7311yescharacteristic
555C22×C4#1192402812yes—
556C22×C4C23×D7311yescharacteristic
557M16—2924no—
558C2×C8—732no—
559C2×C8—732no—
560C2×C8—1461no—
561C2×C8—1461no—
562C2×C8—1461no—
563C2×C8—1461no—
564C2×C8—1461no—
565C2×C8—1461no—
566C2×C8—1461no—
567C2×C8—1461no—
568C2×C8—1461no—
569C2×C8—1461no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—1461no—
579C4⋊C4—1461no—
580C4⋊C4—1461no—
581C4⋊C4—1461no—
582C4⋊C4C2×C4×D7312yes—
583C4⋊C4C2×C4×D7312yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—81no—
588C22⋊C4—2922no—
589C22⋊C4—2922no—
590C22⋊C4—2922no—
591C22⋊C4—2922no—
592C22⋊C4—2922no—
593C22⋊C4—5841no—
594C22⋊C4—5841no—
595C42—24no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—81no—
601C42—81no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—2928no—
609C23—2928no—
610C23—2921no—
611C23—2921no—
612C23—2921no—
613C23—2921no—
614C23—2921no—
615C23—2921no—
616C23—2921no—
617C23—2921no—
618C23—2921no—
619C23—2921no—
620C23—5844no—
621C23—5844no—
622C23—5844no—
623C23—5844no—
624C23—5844no—
625C23—1462no—
626C23—1462no—
627C23—1462no—
628C23—1462no—
629C23C4×C22⋊D7312yes—
630C23C22×C22⋊D7311yescharacteristic
631D4—2928no—
632D4—2921no—
633D4—2921no—
634D4—734no—
635D4—1462no—
636D4—1462no—
637D4—1462no—
638D4—1462no—
639D4—1462no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—5844no—
676C2×C4—5844no—
677C2×C4C4×C22⋊D7312yes—
678C2×C4#1455661612yes—
679C2×C4C22×C4×D7311yescharacteristic
680C2×C4#41×D7311yescharacteristic
681C2×C4#41×D7311yescharacteristic
682C2×C4C2×#1192402811yescharacteristic
683C2×C4#1455663711yescharacteristic
684C2×C4#1455663711yescharacteristic
685C8—2921no—
686C8—2921no—
687C8—1462no—
688C8—1462no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—2922no—
697C22—2922no—
698C22—2922no—
699C22—2922no—
700C22—2922no—
701C22—2922no—
702C22—2922no—
703C22—2922no—
704C22—2922no—
705C22—58416no—
706C22—5841no—
707C22—5841no—
708C22—5841no—
709C22—5841no—
710C22—1464no—
711C22C2×C4×C22⋊D7311yescharacteristic
712C22#1798922511yescharacteristic
713C22#1798922511yescharacteristic
714C22C2×#1455661611yescharacteristic
715C22#1798938511yescharacteristic
716C22#1798939011yescharacteristic
717C22#1798939511yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—41no—
724C4—41no—
725C4—81no—
726C4—81no—
727C4—5841no—
728C4—5841no—
729C4#117×D7311yescharacteristic
730C4#1798906111yescharacteristic
731C4#1798926111yescharacteristic
732C4#1798926111yescharacteristic
733C2—42no—
734C2—2924no—
735C2—5842no—
736C2#2261278111yescharacteristic
737C2C4×#1455661611yescharacteristic
738C2#2261875911yescharacteristic
739C2#2262196111yescharacteristic
740C2#2262206611yescharacteristic
741C2#2262212611yescharacteristic
742C2#2262215611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2347C2
socleC23×C73C22×D4
prime radicalC23×D292C22
cosocleC22×C4×C73C24
hypercenter#2347D73
hypocenterC73#22580
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2347

Complements

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

NH ≅ G/Ntype
3. #22610627C2semidirect
4. #22610613C2semidirect
5. #22610558C2semidirect
6. #22610551C2semidirect
7. #22610191C2semidirect
8. #22610177C2semidirect
9. #22610026C2semidirect
10. #22609962C2semidirect
12. #22609759C2semidirect
13. C4×#14556511C2semidirect
14. #22609715C2semidirect
15. C73×#2347C2semidirect
21. C2×#14556524C22semidirect
22. C2×#14556522C22semidirect
23. #17988591C4semidirect
33. C2×#14556502C22semidirect
34. C2×C4×#10596831C22semidirect
41. #17988349C22semidirect
42. #17988349C22semidirect
43. #17988349C22semidirect
44. #17988349C22semidirect
45. #17988349C22semidirect
46. #17988349C22semidirect
47. #17988342C22semidirect
48. #17988342C22semidirect
50. #389×C73C22semidirect
51. #389×C73C22semidirect
57. C4×C4⋊C4×C73C22semidirect
58. C4×C4⋊C4×C73C22semidirect
74. C2×#11924012C2×C4semidirect
101. #14556511C2×C4semidirect
102. #14556511C2×C4semidirect
109. #117×C73C2×C4semidirect
373. #2347D73semidirect
387. C73#22580semidirect
410. #389C2×D73semidirect
411. #389C2×D73semidirect
421. C4×C4⋊C4C2×D73semidirect
422. C4×C4⋊C4C2×D73semidirect
457. #117C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179885912
C22⋊C4×D2922
#226106272
#226106132
#226105582
#226105512
#226101912
#226101772
#226100262
#226099622
#226098612
#226097592
C4×#145565112
#226097152
C73×#23472
#2258073