Finite Group Databasebeta

← #33108381

Subgroups — #33108381

Order 18688.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988779C211yesmaximal, characteristic
2C2×#17988697C211yesmaximal, characteristic, complemented
3C2×C4×#11924013C211yesmaximal, characteristic, complemented
4#22612842C211yesmaximal, characteristic, complemented
5#22610756C211yesmaximal, characteristic, complemented
6#22610699C211yesmaximal, characteristic, complemented
7#22610631C211yesmaximal, characteristic, complemented
8#22610617C211yesmaximal, characteristic, complemented
9#22610282C211yesmaximal, characteristic, complemented
10#22610282C211yesmaximal, characteristic, complemented
11#22610192C211yesmaximal, characteristic, complemented
12#22610178C211yesmaximal, characteristic, complemented
13#22609806C211yesmaximal, characteristic, complemented
14#22609759C211yesmaximal, characteristic, complemented
15C73×#2366C211yesmaximal, characteristic, complemented
16C22×#11924013C2211yescharacteristic
17C22×#11924013C2211yescharacteristic
18C2×C4×D292C2211yescharacteristic
19C2×C4×D292C2211yescharacteristic
20C2×C4×D292C2211yescharacteristic
21#17988779C418yescomplemented
22#17988697—24no—
23C4×#11924013—24no—
24C2×#14556524C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26C2×C4⋊#10596831C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556511C2211yescharacteristic
34C2×#14556511C2211yescharacteristic
35C2×#14556502C2211yescharacteristic
36C2×#14556502C2211yescharacteristic
37C2×C4×#10596831C2211yescharacteristic
38#17988485C2211yescharacteristic
39#17988485C2211yescharacteristic
40#17988458—21no—
41#17988458—21no—
42#17988453C2211yescharacteristic
43#17988446—21no—
44#95×D73—21no—
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51C2×#127×C73C2211yescharacteristic
52C2×C4×D4×C73—21no—
53C2×C4×D4×C73C2211yescharacteristic
54C2×C4×D4×C73C2211yescharacteristic
55#390×C73—21no—
56#390×C73C2211yescharacteristic
57#390×C73C2211yescharacteristic
58#386×C73—21no—
59#386×C73—21no—
60C4×C4⋊C4×C73C2211yescharacteristic
61C4×C4⋊C4×C73C2211yescharacteristic
62C22×D292C2311yescharacteristic
63C22×C4×D73—21no—
64C22×C4×D73—21no—
65C22×C4×D73—21no—
66C2×#11924013—22no—
67C2×#11924013—22no—
68C2×#11924013—22no—
69C2×#11924013—22no—
70C2×#11924013C2×C414yescomplemented
71C2×#11924013C2×C414yescomplemented
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C4×D292—22no—
77C4×D292—22no—
78C4×D292—22no—
79C4×D292—41no—
80C4×D292—41no—
81C4×D292C2×C414yescomplemented
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×#11924005—21no—
88C2×#11924005—21no—
89C2×#11924005—21no—
90#14556524—22no—
91#14556522—22no—
92C4⋊#10596831C2×C414yescomplemented
93#14556512—22no—
94#14556512—22no—
95#14556512—41no—
96#14556512—41no—
97#14556512C2×C414yescomplemented
98#14556512C2×C414yescomplemented
99#14556511—22no—
100#14556511D414yescomplemented
101#14556502—22no—
102#14556502—22no—
103C4×#10596831—22no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108C22×D4×C73—21no—
109C22×D4×C73—21no—
110C22×D4×C73C2311yescharacteristic
111C22×D4×C73C2311yescharacteristic
112C23×C4×C73—21no—
113C23×C4×C73—21no—
114#127×C73—22no—
115#127×C73C2×C414yescomplemented
116C4×D4×C73—22no—
117C4×D4×C73—22no—
118C4×D4×C73—41no—
119C4×D4×C73—41no—
120C4×D4×C73—44no—
121C2×C4⋊C4×C73D411yescharacteristic
122C2×C4⋊C4×C73D411yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C42×C73—21no—
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134C2×C42×C73C2311yescharacteristic
135#95×C73—21no—
136#95×C73D411yescharacteristic
137#95×C73D411yescharacteristic
138C23×D73—21no—
139C2×D292—21no—
140C2×D292—21no—
141C2×D292—21no—
142C2×D292C22×C412yes—
143C2×D292C2×D412yes—
144C2×D292#4112yes—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C2×C4×D73—24no—
149C2×C4×D73—42no—
150C2×C4×D73—42no—
151C2×C4×D73—42no—
152C2×C4×D73—42no—
153C2×C4×D73—81no—
154C2×C4×D73—81no—
155C2×C4×D73—81no—
156C2×C4×D73—81no—
157#11924013—28no—
158#11924013—28no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831C22×C412yes—
169C2×#10596831C22×C412yes—
170C2×#10596831C2×D412yes—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73C22×C412yes—
177#11924007—81no—
178#11924007—81no—
179#11924005—24no—
180#11924005—42no—
181#11924005—42no—
182C24×C73—21no—
183C24×C73—21no—
184C2×D4×C73—24no—
185C2×D4×C73—24no—
186C2×D4×C73—21no—
187C2×D4×C73—21no—
188C2×D4×C73—21no—
189C2×D4×C73—21no—
190C2×D4×C73—21no—
191C2×D4×C73—21no—
192C2×D4×C73—21no—
193C2×D4×C73—21no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73—42no—
197C2×D4×C73—42no—
198C2×D4×C73—81no—
199C2×D4×C73—81no—
200C2×D4×C73C22×C412yes—
201C2×D4×C73C22×C412yes—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—42no—
205C22×C4×C73—42no—
206C22×C4×C73—42no—
207C22×C4×C73—42no—
208C22×C4×C73—81no—
209C22×C4×C73—81no—
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2411yescharacteristic
217C4⋊C4×C73—22no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—41no—
222C4⋊C4×C73C2×D412yes—
223C22⋊C4×C73—42no—
224C22⋊C4×C73—42no—
225C22⋊C4×C73—42no—
226C22⋊C4×C73—42no—
227C22⋊C4×C73—81no—
228C22⋊C4×C73—81no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73—21no—
233C42×C73—42no—
234C42×C73C22×C412yes—
235C42×C73#4112yes—
236C23×C73—22no—
237C23×C73—22no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73C22×D411yescharacteristic
251C22×D73—22no—
252C22×D73—22no—
253C22×D73—22no—
254C22×D73—41no—
255C22×D73—41no—
256C22×D73—41no—
257C22×D73—41no—
258D4×C73—22no—
259D4×C73—22no—
260D4×C73—22no—
261D4×C73—22no—
262D4×C73—48no—
263D4×C73—41no—
264D4×C73—41no—
265D4×C73—41no—
266D4×C73—41no—
267D4×C73—84no—
268C2×C4×C73—21no—
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—22no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—84no—
290C2×C4×C73—84no—
291C2×C4×C73C4×D412yes—
292C2×C4×C73C4×D412yes—
293C2×C4×C73AGL(1,ℤ/8)12yes—
294C2×C4×C73C23×C411yescharacteristic
295C2×C4×C73C22×D411yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×C4×C73C2×#4111yescharacteristic
298C2×C4×C73H(5,𝔽2)11yescharacteristic
299C2×C4×C732−1+411yescharacteristic
300C2×Dic73—22no—
301C2×Dic73—41no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309D292—22no—
310D292—22no—
311D292—22no—
312D292C4×D414yescomplemented
313C4×D73—84no—
314C4×D73—84no—
315C4×D73—84no—
316#10596831—22no—
317#10596831—22no—
318#10596831—22no—
319#10596831—41no—
320C22×C73—42no—
321C22×C73—42no—
322C22×C73—42no—
323C22×C73—42no—
324C22×C73—42no—
325C22×C73—42no—
326C22×C73—81no—
327C22×C73—81no—
328C22×C73—81no—
329C22×C73—81no—
330C22×C73—81no—
331C22×C73—81no—
332C22×C73—81no—
333C22×C73—81no—
334C22×C73C2×C4×D411yescharacteristic
335C22×C73D4211yescharacteristic
336C22×C73#54811yescharacteristic
337C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C73#57511yescharacteristic
339C22×C73#57611yescharacteristic
340C22×C73#57611yescharacteristic
341C2×D73—24no—
342C2×D73—42no—
343C2×D73—42no—
344C2×D73—42no—
345C2×D73—42no—
346C2×D73—42no—
347C2×D73—42no—
348C4×C73—22no—
349C4×C73—22no—
350C4×C73—22no—
351C4×C73—41no—
352C4×C73—42no—
353C4×C73—41no—
354C4×C73—41no—
355C4×C73—81no—
356C4×C73C2×C4×D411yescharacteristic
357C4×C73#52011yescharacteristic
358C4×C73#54711yescharacteristic
359C4×C73#55311yescharacteristic
360Dic73—42no—
361Dic73—81no—
362Dic73—81no—
363#23008—731nomaximal, Sylow
364C2×C73—82no—
365C2×C73—82no—
366C2×C73#236111yescharacteristic
367C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
368C2×C73#294811yescharacteristic
369C2×C73#326411yescharacteristic
370C2×C73#326811yescharacteristic
371C2×C73#336611yescharacteristic
372C2×C73#337011yescharacteristic
373D73—44no—
374C2×#459—731no—
375C2×#442—731no—
376C2×C4×D8—731no—
377#2366D7311yescharacteristic, complemented
378#2349—731no—
379#1961—731no—
380#1949—731no—
381#1936—731no—
382#1934—731no—
383#1879—731no—
384#1879—731no—
385#1864—731no—
386#1862—731no—
387#1771—731no—
388#1762—731no—
389C73#2300811yescharacteristic, complemented, Sylow
390C22×D8—731no—
391C22×D8—731no—
392C2×#127C2×D7311yescharacteristic
393C2×C4×D4—21no—
394C2×C4×D4—731no—
395C2×C4×D4—731no—
396C2×C4×D4—731no—
397C2×C4×D4C2×D7311yescharacteristic
398C2×C4×D4C2×D7311yescharacteristic
399#459—738no—
400#442—1464no—
401C4×D8—1464no—
402C2×#107—731no—
403C2×#106—731no—
404C2×C4⋊C8—731no—
405C2×#102—731no—
406C2×#102—731no—
407C2×#102—731no—
408C2×#102—731no—
409C2×#102—731no—
410C2×#102—731no—
411C2×#102—731no—
412C2×#102—731no—
413C2×#97—731no—
414C2×#97—731no—
415C2×C4×C8—731no—
416#390—21no—
417#390C2×D7311yescharacteristic
418#390C2×D7311yescharacteristic
419#389—731no—
420#389—731no—
421#386—21no—
422#386—21no—
423#385—1461no—
424#385—1461no—
425#382—731no—
426#380—1461no—
427C4×C4⋊C4C2×D7311yescharacteristic
428C4×C4⋊C4C2×D7311yescharacteristic
429C2×#95—1461no—
430#340—731no—
431#340—731no—
432#340—731no—
433#340—731no—
434#336—731no—
435#336—731no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—731no—
439C22×D4C22×D7311yescharacteristic
440C22×D4C22×D7311yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—1461no—
444C23×C4—1461no—
445C23×C4—1461no—
446C2×D8—734no—
447C2×D8—734no—
448C2×D8—1462no—
449C2×D8—1462no—
450C2×D8—1462no—
451C2×D8—1462no—
452C22×C8—731no—
453C22×C8—731no—
454C22×C8—731no—
455C22×C8—731no—
456#127—22no—
457#127C4×D7314yescomplemented
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—41no—
461C4×D4—41no—
462C4×D4—44no—
463C4×D4—2921no—
464C4×D4—2921no—
465C4×D4—734no—
466C4×D4—1462no—
467C4×D4—1462no—
468C4×D4—1462no—
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×C4⋊C4C22⋊D7311yescharacteristic
476C2×C4⋊C4C22×D7311yescharacteristic
477C2×C4⋊C4C22×D7311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—1461no—
485C2×C22⋊C4—1461no—
486C2×C22⋊C4—1461no—
487C2×C42—21no—
488C2×C42C22×D7311yescharacteristic
489C2×C42C22×D7311yescharacteristic
490C2×C42C22×D7311yescharacteristic
491#107—1462no—
492#106—1462no—
493C4⋊C8—734no—
494#102—2921no—
495#102—2921no—
496#102—734no—
497#102—734no—
498#102—734no—
499#102—1462no—
500#102—1462no—
501#102—1462no—
502#97—1462no—
503#97—1462no—
504C4×C8—1462no—
505#95—21no—
506#95—1461no—
507#95—1461no—
508#95—1461no—
509#95—1461no—
510#95C22⋊D7311yescharacteristic
511#95C22⋊D7311yescharacteristic
512C24—21no—
513C24—21no—
514C24—1461no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4—732no—
532C2×D4—732no—
533C2×D4—732no—
534C2×D4—1461no—
535C2×D4—1461no—
536C2×D4—1461no—
537C2×D4C2×C4×D7312yes—
538C2×D4C2×C4×D7312yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—2922no—
548C22×C4—2922no—
549C22×C4—2922no—
550C22×C4—2922no—
551C22×C4—5841no—
552C22×C4—5841no—
553C22×C4—5841no—
554C22×C4—5841no—
555C22×C4—1461no—
556C22×C4—1461no—
557C22×C4—1461no—
558C22×C4—1464no—
559C22×C4C2×C22⋊D7311yescharacteristic
560C22×C4C2×C22⋊D7311yescharacteristic
561C22×C4C2×C22⋊D7311yescharacteristic
562C22×C4C2×C22⋊D7311yescharacteristic
563C22×C4C2×C22⋊D7311yescharacteristic
564C22×C4C2×C22⋊D7311yescharacteristic
565C22×C4C23×D7311yescharacteristic
566D8—1468no—
567D8—1468no—
568C2×C8—732no—
569C2×C8—732no—
570C2×C8—732no—
571C2×C8—1461no—
572C2×C8—1461no—
573C2×C8—1461no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C2×C8—1461no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—41no—
585C4⋊C4—5841no—
586C4⋊C4—5841no—
587C4⋊C4—732no—
588C4⋊C4—1461no—
589C4⋊C4—1461no—
590C4⋊C4—1461no—
591C4⋊C4—1461no—
592C4⋊C4—1461no—
593C4⋊C4D4×D7312yes—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C22⋊C4—2922no—
601C22⋊C4—2922no—
602C22⋊C4—1464no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—42no—
608C42C2×C4×D7312yes—
609C42#1192402812yes—
610C23—22no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—2921no—
625C23—2921no—
626C23—2921no—
627C23—2921no—
628C23—1462no—
629C23—1462no—
630C23—1462no—
631C23C22×C22⋊D7311yescharacteristic
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—84no—
642D4—734no—
643D4—1462no—
644D4—1462no—
645D4—1462no—
646C2×C4—21no—
647C2×C4—21no—
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—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—2921no—
677C2×C4—5844no—
678C2×C4—5844no—
679C2×C4—5844no—
680C2×C4—1462no—
681C2×C4C4×C22⋊D7312yes—
682C2×C4C4×C22⋊D7312yes—
683C2×C4#1455661712yes—
684C2×C4C22×C4×D7311yescharacteristic
685C2×C4C2×D4×D7311yescharacteristic
686C2×C4#41×D7311yescharacteristic
687C2×C4C2×#1192402811yescharacteristic
688C2×C4#1455663611yescharacteristic
689C2×C4#1455663811yescharacteristic
690C8—2921no—
691C8—1462no—
692C8—1462no—
693C8—1462no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—2922no—
709C22—2922no—
710C22—2922no—
711C22—2922no—
712C22—2922no—
713C22—2922no—
714C22—1464no—
715C22C2×C4×C22⋊D7311yescharacteristic
716C22D4×C22⋊D7311yescharacteristic
717C22#1798924411yescharacteristic
718C22C2×#1455661711yescharacteristic
719C22#1798938511yescharacteristic
720C22#1798939011yescharacteristic
721C22#1798939011yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—81no—
730C4—2922no—
731C4—5841no—
732C4—5841no—
733C4C4×D4×D7311yescharacteristic
734C4#1798906611yescharacteristic
735C4#1798924211yescharacteristic
736C4#1798928711yescharacteristic
737C2—82no—
738C2—82no—
739C2—2924no—
740C2#2261294311yescharacteristic
741C2C4×#1455661711yescharacteristic
742C2#2261878111yescharacteristic
743C2#2262140711yescharacteristic
744C2#2262147211yescharacteristic
745C2#2262263411yescharacteristic
746C2#2262267811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2366C2
socleC23×C73C22×D4
prime radicalC2×#17988779C2
cosocleC22×C4×C73C24
hypercenter#2366D73
hypocenterC73#23008
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
2. C2×#17988697C2semidirect
3. C2×C4×#11924013C2semidirect
4. #22612842C2semidirect
5. #22610756C2semidirect
6. #22610699C2semidirect
7. #22610631C2semidirect
8. #22610617C2semidirect
9. #22610282C2semidirect
10. #22610282C2semidirect
11. #22610192C2semidirect
12. #22610178C2semidirect
13. #22609806C2semidirect
14. #22609759C2semidirect
15. C73×#2366C2semidirect
21. #17988779C4semidirect
70. C2×#11924013C2×C4semidirect
71. C2×#11924013C2×C4semidirect
81. C4×D292C2×C4semidirect
92. C4⋊#10596831C2×C4semidirect
97. #14556512C2×C4semidirect
98. #14556512C2×C4semidirect
100. #14556511D4semidirect
115. #127×C73C2×C4semidirect
312. D292C4×D4semidirect
377. #2366D73semidirect
389. C73#23008semidirect
457. #127C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179887792
C2×#179886972
C2×C4×#119240132
#226128422
#226107562
#226106992
#226106312
#226106172
#226102822
#226101922
#226101782
#226098062
#226097592
C73×#23662
#2300873