Finite Group Databasebeta

← #32020042

Subgroups — #32020042

Order 18176.

1066 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986226C211yesmaximal, characteristic
2C2×C4×#11765853C211yesmaximal, characteristic, complemented
3C22×#14556059C211yesmaximal, characteristic, complemented
4#22591343C211yesmaximal, characteristic, complemented
5#22589193C211yesmaximal, characteristic, complemented
6#22589065C211yesmaximal, characteristic, complemented
7#22588974C211yesmaximal, characteristic, complemented
8#22588964C211yesmaximal, characteristic, complemented
9#22588658C211yesmaximal, characteristic
10#22588647C211yesmaximal, characteristic, complemented
11#22588607C211yesmaximal, characteristic, complemented
12#22588601C211yesmaximal, characteristic, complemented
13C4×#14556059C211yesmaximal, characteristic, complemented
14C22⋊C4×C71⋊C8C211yesmaximal, characteristic, complemented
15C71×#2361C211yesmaximal, characteristic
16C22×#11765853C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×#14556107C2211yescharacteristic
19C2×C4×Dic142C2211yescharacteristic
20C22×C4⋊Dic71C2211yescharacteristic
21#17986226C418yescomplemented
22C4×#11765853—24no—
23C2×#14556059—24no—
24C2×#14556059C2211yescharacteristic
25C2×#14556059C2211yescharacteristic
26C2×#14556059C2211yescharacteristic
27C2×#14556059C2211yescharacteristic
28C2×#14556059C2211yescharacteristic
29C2×#14556051C2211yescharacteristic
30C2×#14556051C2211yescharacteristic
31C2×#14556051C2211yescharacteristic
32C2×#14556049C2211yescharacteristic
33C2×#14556049C2211yescharacteristic
34C2×#14556049C2211yescharacteristic
35C2×C22⋊(C71⋊C8)C2211yescharacteristic
36C2×C4×C71⋊C8C2211yescharacteristic
37C2×C4×C71⋊C8C2211yescharacteristic
38#17985905C2211yescharacteristic
39#17985897C2211yescharacteristic
40#17985896—21no—
41#17985886—21no—
42#17985871—21no—
43C4×C4⋊Dic71C2211yescharacteristic
44C22⋊C4×Dic71—21no—
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#17985754C2211yescharacteristic
50#17985754C2211yescharacteristic
51C2×#121×C71C2211yescharacteristic
52C2×C4×D4×C71—21no—
53C2×C4×D4×C71C2211yescharacteristic
54C22×C4⋊C4×C71C2211yescharacteristic
55#390×C71C2211yescharacteristic
56#389×C71C2211yescharacteristic
57#388×C71—21no—
58#386×C71—21no—
59#385×C71—21no—
60C4×C4⋊C4×C71C2211yescharacteristic
61C4×C22⋊C4×C71C2211yescharacteristic
62C22×Dic142C2311yescharacteristic
63C23×Dic71—21no—
64C2×#11765853—22no—
65C2×#11765853—22no—
66C2×#11765853C2×C414yescomplemented
67C22×C71⋊C8—22no—
68C22×C71⋊C8—22no—
69C22×C71⋊C8C2×C414yescomplemented
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74#14556107—22no—
75#14556107C2×C414yescomplemented
76C4×Dic142—22no—
77C4×Dic142—41no—
78C2×C4⋊Dic71—22no—
79C2×C4⋊Dic71—21no—
80C2×C4⋊Dic71—41no—
81C2×C4⋊Dic71C2311yescharacteristic
82C2×C4⋊Dic71C2311yescharacteristic
83C2×C4⋊Dic71C2311yescharacteristic
84C2×Dic71⋊C4—21no—
85C2×Dic71⋊C4—21no—
86C2×Dic71⋊C4—21no—
87C2×C22⋊Dic71—21no—
88C2×C4×Dic71—21no—
89C2×C4×Dic71—21no—
90#14556059—22no—
91#14556059—22no—
92#14556059—22no—
93#14556059C2×C414yescomplemented
94#14556059D414yescomplemented
95#14556051—22no—
96#14556051—41no—
97#14556051C2×C414yescomplemented
98#14556049—22no—
99#14556049—41no—
100#14556049C2×C414yescomplemented
101C22⋊(C71⋊C8)—22no—
102C4×C71⋊C8—22no—
103C4×C71⋊C8—22no—
104C71⋊#95—21no—
105C71⋊#95—21no—
106C71⋊#95—21no—
107C71⋊#95—21no—
108C22×D4×C71—21no—
109C22×D4×C71C2311yescharacteristic
110C23×C4×C71—21no—
111C23×C4×C71—21no—
112C23×C4×C71C2311yescharacteristic
113#121×C71—22no—
114#121×C71C2×C414yes—
115C4×D4×C71—22no—
116C4×D4×C71—41no—
117C4×D4×C71—44no—
118C2×C4⋊C4×C71—22no—
119C2×C4⋊C4×C71—21no—
120C2×C4⋊C4×C71—21no—
121C2×C4⋊C4×C71—41no—
122C2×C4⋊C4×C71C2311yescharacteristic
123C2×C4⋊C4×C71C2311yescharacteristic
124C2×C4⋊C4×C71C2311yescharacteristic
125C2×C22⋊C4×C71—21no—
126C2×C22⋊C4×C71—21no—
127C2×C22⋊C4×C71—21no—
128C2×C22⋊C4×C71—21no—
129C2×C22⋊C4×C71D411yescharacteristic
130C2×C22⋊C4×C71D411yescharacteristic
131C2×C42×C71—21no—
132C2×C42×C71C2311yescharacteristic
133C2×C42×C71C2311yescharacteristic
134#95×C71—21no—
135#95×C71—21no—
136#95×C71D411yescharacteristic
137#95×C71D411yescharacteristic
138C2×Dic142—21no—
139C2×Dic142—21no—
140C2×Dic142—21no—
141C2×Dic142—21no—
142C2×Dic142—21no—
143C2×Dic142C22×C412yes—
144C22×Dic71—21no—
145C22×Dic71—21no—
146C22×Dic71—21no—
147C22×Dic71—21no—
148C22×Dic71—42no—
149C22×Dic71—42no—
150C22×Dic71—81no—
151#11765853—28no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—28no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8—21no—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—21no—
161C2×C71⋊C8C22×C412yes—
162C2×C71⋊C8C22×C412yes—
163C2×C71⋊C8C2×D412yes—
164C2×C71⋊C8#4112yes—
165C4⋊Dic71—21no—
166C4⋊Dic71—21no—
167C4⋊Dic71—21no—
168C4⋊Dic71—21no—
169C4⋊Dic71—42no—
170C4⋊Dic71C22×C412yes—
171C4⋊Dic71C2×D412yes—
172Dic71⋊C4—24no—
173Dic71⋊C4—42no—
174Dic71⋊C4—81no—
175C22⋊Dic71—24no—
176C4×Dic71—42no—
177C4×Dic71—81no—
178C24×C71—21no—
179C24×C71C2×D411yescharacteristic
180C2×D4×C71—24no—
181C2×D4×C71—21no—
182C2×D4×C71—21no—
183C2×D4×C71—21no—
184C2×D4×C71—21no—
185C2×D4×C71—21no—
186C2×D4×C71—42no—
187C2×D4×C71—42no—
188C2×D4×C71C22×C412yes—
189C22×C4×C71—21no—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—42no—
197C22×C4×C71—42no—
198C22×C4×C71—42no—
199C22×C4×C71—42no—
200C22×C4×C71—81no—
201C22×C4×C71—81no—
202C22×C4×C71C22×C412yes—
203C22×C4×C71C2×D411yescharacteristic
204C22×C4×C71C2×D411yescharacteristic
205C22×C4×C71C2×D411yescharacteristic
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71#4112yes—
209C22×C4×C71C2411yescharacteristic
210C4⋊C4×C71—21no—
211C4⋊C4×C71—21no—
212C4⋊C4×C71—21no—
213C4⋊C4×C71—21no—
214C4⋊C4×C71—42no—
215C4⋊C4×C71—42no—
216C4⋊C4×C71C22×C412yes—
217C4⋊C4×C71C2×D412yes—
218C22⋊C4×C71—22no—
219C22⋊C4×C71—24no—
220C22⋊C4×C71—42no—
221C22⋊C4×C71—42no—
222C22⋊C4×C71—81no—
223C22⋊C4×C71SD1614yescomplemented
224C42×C71—21no—
225C42×C71—21no—
226C42×C71—21no—
227C42×C71—21no—
228C42×C71—42no—
229C23×C71—21no—
230C23×C71—21no—
231C23×C71—21no—
232C23×C71—21no—
233C23×C71—22no—
234C23×C71—41no—
235C23×C71—41no—
236C23×C71—41no—
237C23×C71—41no—
238C23×C71—41no—
239C23×C71—41no—
240C23×C71C4×D412yes—
241C23×C71C2×SD1612yes—
242C23×C71#13512yes—
243C23×C71C22×D411yescharacteristic
244D4×C71—22no—
245D4×C71—22no—
246D4×C71—48no—
247D4×C71—41no—
248D4×C71—41no—
249C2×C4×C71—21no—
250C2×C4×C71—21no—
251C2×C4×C71—21no—
252C2×C4×C71—21no—
253C2×C4×C71—21no—
254C2×C4×C71—21no—
255C2×C4×C71—22no—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—22no—
259C2×C4×C71—22no—
260C2×C4×C71—21no—
261C2×C4×C71—22no—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—21no—
266C2×C4×C71—21no—
267C2×C4×C71—41no—
268C2×C4×C71—41no—
269C2×C4×C71—41no—
270C2×C4×C71—41no—
271C2×C4×C71—41no—
272C2×C4×C71—41no—
273C2×C4×C71—41no—
274C2×C4×C71—84no—
275C2×C4×C71—84no—
276C2×C4×C71C4×D412yes—
277C2×C4×C71C2×SD1612yes—
278C2×C4×C71C2×SD1612yes—
279C2×C4×C71C23×C411yescharacteristic
280C2×C4×C71C22×D411yescharacteristic
281C2×C4×C71C2×#4111yescharacteristic
282C2×C4×C71C2×#4111yescharacteristic
283C2×C4×C71H(5,𝔽2)11yescharacteristic
284C2×C4×C712−1+411yescharacteristic
285C2×Dic71—22no—
286C2×Dic71—22no—
287C2×Dic71—22no—
288C2×Dic71—41no—
289C2×Dic71—41no—
290C2×Dic71—41no—
291C2×Dic71—41no—
292C2×Dic71—41no—
293C2×Dic71—41no—
294C2×Dic71—41no—
295C2×Dic71—41no—
296C2×Dic71—41no—
297C2×Dic71—84no—
298Dic142—22no—
299Dic142—22no—
300Dic142—41no—
301Dic142—41no—
302C71⋊C8—22no—
303C71⋊C8—41no—
304C71⋊C8—41no—
305C71⋊C8C4×D414yescomplemented
306C22×C71—22no—
307C22×C71—22no—
308C22×C71—22no—
309C22×C71—22no—
310C22×C71—22no—
311C22×C71—22no—
312C22×C71—42no—
313C22×C71—42no—
314C22×C71—42no—
315C22×C71—81no—
316C22×C71—81no—
317C22×C71—81no—
318C22×C71—81no—
319C22×C71C4×SD1614yescomplemented
320C22×C71C2×C4×D411yescharacteristic
321C22×C71D4211yescharacteristic
322C22×C71#54711yescharacteristic
323C22×C71C22×SD1611yescharacteristic
324C22×C71C2×#13511yescharacteristic
325C22×C71#57711yescharacteristic
326C22×C71#57711yescharacteristic
327C4×C71—22no—
328C4×C71—22no—
329C4×C71—22no—
330C4×C71—41no—
331C4×C71—42no—
332C4×C71—42no—
333C4×C71—41no—
334C4×C71—81no—
335C4×C71C2×C4×D411yescharacteristic
336C4×C71#52011yescharacteristic
337C4×C71#54811yescharacteristic
338C4×C71#55311yescharacteristic
339Dic71—42no—
340Dic71—42no—
341Dic71—42no—
342Dic71—81no—
343#23022—711nomaximal, Sylow
344C2×C71—24no—
345C2×C71—82no—
346C2×C71#236111yescharacteristic
347C2×C71C2×C4×SD1611yescharacteristic
348C2×C71#295211yescharacteristic
349C2×C71D4×SD1611yescharacteristic
350C2×C71#328211yescharacteristic
351C2×C71#333511yescharacteristic
352C2×C71#333711yescharacteristic
353C2×#465—711no—
354C2×C4×SD16—711no—
355C22×#106—711no—
356#2361D7111yescharacteristic
357#2360—711no—
358#1968—711no—
359#1941—711no—
360#1927—711no—
361#1926—711no—
362#1874—711no—
363#1872—711no—
364#1865—711no—
365#1864—711no—
366C4×#106—711no—
367C8×C22⋊C4—711no—
368C71#2302211yescharacteristic, complemented, Sylow
369C22×SD16—711no—
370C23×C8—711no—
371C2×C22⋊Q8—711no—
372C2×#121C2×D7111yescharacteristic
373C2×C4×Q8—711no—
374C2×C4×D4—21no—
375C2×C4×D4C2×D7111yescharacteristic
376C22×C4⋊C4—711no—
377C22×C4⋊C4C2×D7111yescharacteristic
378#465—718no—
379C4×SD16—1424no—
380C2×#106—711no—
381C2×#106—711no—
382C2×#106—711no—
383C2×#106—711no—
384C2×#106—711no—
385C2×#106—1424no—
386C2×#103—711no—
387C2×#103—711no—
388C2×#103—711no—
389C2×#102—711no—
390C2×#102—711no—
391C2×#102—711no—
392C2×C22⋊C8—711no—
393C2×C4×C8—711no—
394C2×C4×C8—711no—
395#391—711no—
396#390C2×D7111yescharacteristic
397#389—711no—
398#389—1421no—
399#389C2×D7111yescharacteristic
400#388—21no—
401#387—1421no—
402#386—21no—
403#385—21no—
404#385—1421no—
405C4×C4⋊C4—711no—
406C4×C4⋊C4C2×D7111yescharacteristic
407C4×C22⋊C4—1421no—
408C4×C22⋊C4C2×D7111yescharacteristic
409#340—711no—
410#340—711no—
411#340—711no—
412#340—711no—
413#336—711no—
414#336—711no—
415C22×Q8—711no—
416C22×D4—21no—
417C22×D4C22×D7111yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—1421no—
421C23×C4C22×D7111yescharacteristic
422C2×SD16—714no—
423C2×SD16—1422no—
424C2×SD16—1422no—
425C22×C8—711no—
426C22×C8—714no—
427C22×C8—711no—
428C22×C8—711no—
429C22×C8—711no—
430C22×C8—1422no—
431C22×C8—1422no—
432C22⋊Q8—714no—
433C22⋊Q8—1422no—
434#121—22no—
435#121C4×D7114yes—
436C4×Q8—2841no—
437C4×Q8—1422no—
438C4×D4—22no—
439C4×D4—41no—
440C4×D4—44no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—2841no—
446C2×C4⋊C4—711no—
447C2×C4⋊C4—711no—
448C2×C4⋊C4—711no—
449C2×C4⋊C4—1421no—
450C2×C4⋊C4—1421no—
451C2×C4⋊C4—1422no—
452C2×C4⋊C4—1421no—
453C2×C4⋊C4—1421no—
454C2×C4⋊C4C22×D7111yescharacteristic
455C2×C4⋊C4C22×D7111yescharacteristic
456C2×C4⋊C4C22×D7111yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—1421no—
462C2×C22⋊C4C22⋊D7111yescharacteristic
463C2×C22⋊C4C22⋊D7111yescharacteristic
464C2×C42—21no—
465C2×C42—1421no—
466C2×C42—1421no—
467C2×C42C22×D7111yescharacteristic
468C2×C42C22×D7111yescharacteristic
469#106—714no—
470#106—714no—
471#106—1422no—
472#106—1422no—
473#106—1422no—
474#103—2841no—
475#103—714no—
476#103—1422no—
477#102—2841no—
478#102—714no—
479#102—1422no—
480C22⋊C8—1422no—
481C4×C8—1422no—
482C4×C8—1422no—
483#95—21no—
484#95—21no—
485#95—1421no—
486#95—1421no—
487#95—1421no—
488#95—1421no—
489#95C22⋊D7111yescharacteristic
490#95C22⋊D7111yescharacteristic
491C24—21no—
492C24C2×C22⋊D7111yescharacteristic
493C2×Q8—712no—
494C2×Q8—1421no—
495C2×Q8—1421no—
496C2×Q8—1421no—
497C2×Q8—1421no—
498C2×Q8—1421no—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C2×C4×D7112yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—2842no—
522C22×C4—2842no—
523C22×C4—5681no—
524C22×C4—1421no—
525C22×C4—1421no—
526C22×C4—1421no—
527C22×C4—1421no—
528C22×C4C2×C4×D7112yes—
529C22×C4C2×C22⋊D7111yescharacteristic
530C22×C4C2×C22⋊D7111yescharacteristic
531C22×C4C2×C22⋊D7111yescharacteristic
532C22×C4C2×C22⋊D7111yescharacteristic
533C22×C4C2×C22⋊D7111yescharacteristic
534C22×C4#1176586512yes—
535C22×C4C23×D7111yescharacteristic
536SD16—1428no—
537C2×C8—712no—
538C2×C8—712no—
539C2×C8—712no—
540C2×C8—712no—
541C2×C8—1421no—
542C2×C8—1421no—
543C2×C8—1421no—
544C2×C8—1421no—
545C2×C8—1421no—
546C2×C8—1421no—
547C2×C8—1428no—
548C2×C8—1421no—
549C2×C8—1421no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—2842no—
557C4⋊C4—2842no—
558C4⋊C4—5681no—
559C4⋊C4—712no—
560C4⋊C4—712no—
561C4⋊C4—1421no—
562C4⋊C4—1421no—
563C4⋊C4—1421no—
564C4⋊C4—1421no—
565C4⋊C4—1424no—
566C4⋊C4C2×C4×D7112yes—
567C4⋊C4D4×D7112yes—
568C22⋊C4—22no—
569C22⋊C4—24no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—1424no—
574C22⋊C4#1176585314yescomplemented
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—2842no—
581C42—5681no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C4×C22⋊D7112yes—
594C23C2×#1176585312yes—
595C23#1455614812yes—
596C23C22×C22⋊D7111yescharacteristic
597Q8—2841no—
598Q8—2841no—
599Q8—1422no—
600Q8—1422no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—41no—
605D4—41no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—2841no—
634C2×C4—2841no—
635C2×C4—2841no—
636C2×C4—2841no—
637C2×C4—2841no—
638C2×C4—2841no—
639C2×C4—2841no—
640C2×C4—2841no—
641C2×C4—2841no—
642C2×C4—5684no—
643C2×C4—1422no—
644C2×C4—1422no—
645C2×C4—1422no—
646C2×C4C4×C22⋊D7112yes—
647C2×C4C2×#1176585312yes—
648C2×C4C2×#1176585312yes—
649C2×C4C22×C4×D7111yescharacteristic
650C2×C4C2×D4×D7111yescharacteristic
651C2×C4#41×D7111yescharacteristic
652C2×C4C2×#1176586511yescharacteristic
653C2×C4#1455617311yescharacteristic
654C2×C4#1455617511yescharacteristic
655C8—2841no—
656C8—2841no—
657C8—714no—
658C8—1422no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22C4×#1176585314yescomplemented
673C22C2×C4×C22⋊D7111yescharacteristic
674C22D4×C22⋊D7111yescharacteristic
675C22#1798664811yescharacteristic
676C22C22×#1176585311yescharacteristic
677C22C2×#1455614811yescharacteristic
678C22#1798680711yescharacteristic
679C22#1798681011yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—42no—
687C4—81no—
688C4—2842no—
689C4—2842no—
690C4—2842no—
691C4—5681no—
692C4C4×D4×D7111yescharacteristic
693C4#1798647811yescharacteristic
694C4#1798665811yescharacteristic
695C4#1798669811yescharacteristic
696C2—24no—
697C2—82no—
698C2#2259135711yescharacteristic
699C2C2×C4×#1176585311yescharacteristic
700C2#2259722111yescharacteristic
701C2D4×#1176585311yescharacteristic
702C2#2260004811yescharacteristic
703C2#2260069711yescharacteristic
704C2#2260071311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#2361C2
socleC23×C71C22×D4
prime radicalC2×#121×C71C22
cosocleC22×C4×C71C24
hypercenter#2361D71
hypocenterC71#23022
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11765853C2semidirect
3. C22×#14556059C2semidirect
4. #22591343C2semidirect
5. #22589193C2semidirect
6. #22589065C2semidirect
7. #22588974C2semidirect
8. #22588964C2semidirect
10. #22588647C2semidirect
11. #22588607C2semidirect
12. #22588601C2semidirect
13. C4×#14556059C2semidirect
14. C22⋊C4×C71⋊C8C2semidirect
21. #17986226C4semidirect
66. C2×#11765853C2×C4semidirect
69. C22×C71⋊C8C2×C4semidirect
75. #14556107C2×C4semidirect
93. #14556059C2×C4semidirect
94. #14556059D4semidirect
97. #14556051C2×C4semidirect
100. #14556049C2×C4semidirect
223. C22⋊C4×C71SD16semidirect
305. C71⋊C8C4×D4semidirect
319. C22×C71C4×SD16semidirect
368. C71#23022semidirect
574. C22⋊C4#11765853semidirect
672. C22C4×#11765853semidirect

Maximal subgroups

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

subgroupindex
C2×#179862262
C2×C4×#117658532
C22×#145560592
#225913432
#225891932
#225890652
#225889742
#225889642
#225886582
#225886472
#225886072
#225886012
C4×#145560592
C22⋊C4×C71⋊C82
C71×#23612
#2302271