Finite Group Databasebeta

← #32013824

Subgroups — #32013824

Order 18176.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986706C211yesmaximal, characteristic
2C2×#17986071C211yesmaximal, characteristic
3#22589312C211yesmaximal, characteristic, complemented
4#22589292C211yesmaximal, characteristic, complemented
5#22588771C211yesmaximal, characteristic, complemented
6#22588761C211yesmaximal, characteristic, complemented
7#22588652C211yesmaximal, characteristic, complemented
8#22588647C211yesmaximal, characteristic, complemented
9#22588428C211yesmaximal, characteristic, complemented
10#22588424C211yesmaximal, characteristic, complemented
11#22588352C211yesmaximal, characteristic, complemented
12#22588173C211yesmaximal, characteristic, complemented
13#22588061C211yesmaximal, characteristic, complemented
14C2×#17985761C211yesmaximal, characteristic, complemented
15C71×#2352C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18#17986706—24no—
19#17986706C418yescomplemented
20C2×#14556128C2211yescharacteristic
21C2×#14556119—21no—
22C2×#14556107C2211yescharacteristic
23C2×#14556107C2211yescharacteristic
24C2×#14556105—21no—
25C2×#14556105—21no—
26C2×C4×Dic142C2211yescharacteristic
27C2×D4×Dic71—21no—
28C22×C4⋊Dic71C2211yescharacteristic
29C22×C4⋊Dic71C2211yescharacteristic
30#17986071—24no—
31C2×C4⋊(C71⋊C8)C2211yescharacteristic
32C2×#14556051C2211yescharacteristic
33C2×#14556051C2211yescharacteristic
34C2×#14556051C2211yescharacteristic
35C2×#14556051C2211yescharacteristic
36C2×C22⋊(C71⋊C8)C2211yescharacteristic
37C2×C22⋊(C71⋊C8)C2211yescharacteristic
38C2×#14556039C2211yescharacteristic
39#17985761C2211yescharacteristic
40#17985761C2211yescharacteristic
41#17985761C2211yescharacteristic
42#17985761C2211yescharacteristic
43#17985761C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#17985761C2211yescharacteristic
50#17985761C2211yescharacteristic
51C2×C4×D4×C71C2211yescharacteristic
52C2×#117×C71C2211yescharacteristic
53C22×C4⋊C4×C71C2211yescharacteristic
54#388×C71—21no—
55#387×C71—21no—
56#386×C71—21no—
57#382×C71C2211yescharacteristic
58#380×C71C2211yescharacteristic
59#380×C71C2211yescharacteristic
60C4×C4⋊C4×C71C2211yescharacteristic
61C4×C22⋊C4×C71—21no—
62C22×Dic142—21no—
63C22×Dic142C2311yescharacteristic
64C23×Dic71—21no—
65C23×Dic71—21no—
66C2×#11765849—22no—
67C2×#11765849—22no—
68C2×#11765849—41no—
69C22×C71⋊C8—22no—
70C22×C71⋊C8—22no—
71C22×C71⋊C8—41no—
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74C22×C71⋊C8C2311yescharacteristic
75C22×C71⋊C8C2311yescharacteristic
76#14556128—22no—
77#14556128C2×C414yescomplemented
78#14556119—28no—
79#14556107—22no—
80#14556107—22no—
81#14556107C2×C414yes—
82#14556107C2×C414yescomplemented
83#14556105—28no—
84#14556105—28no—
85C4×Dic142—22no—
86C4×Dic142C2×C414yescomplemented
87D4×Dic71—28no—
88C2×C4⋊Dic71—22no—
89C2×C4⋊Dic71—22no—
90C2×C4⋊Dic71—21no—
91C2×C4⋊Dic71—21no—
92C2×C4⋊Dic71—21no—
93C2×C4⋊Dic71C2×C414yes—
94C2×C4⋊Dic71C2×C414yescomplemented
95C2×C4⋊Dic71C2311yescharacteristic
96C2×C4⋊Dic71C2311yescharacteristic
97C2×C4⋊Dic71C2311yescharacteristic
98C2×Dic71⋊C4—21no—
99C2×Dic71⋊C4—21no—
100C2×Dic71⋊C4—21no—
101C2×C22⋊Dic71—21no—
102C2×C22⋊Dic71—21no—
103C2×C4×Dic71—21no—
104C4⋊(C71⋊C8)—22no—
105#14556051—22no—
106#14556051—22no—
107#14556051—41no—
108#14556051—41no—
109C22⋊(C71⋊C8)—22no—
110C22⋊(C71⋊C8)—22no—
111#14556039—22no—
112C22×D4×C71D411yescharacteristic
113C23×C4×C71—21no—
114C23×C4×C71C2311yescharacteristic
115C23×C4×C71C2311yescharacteristic
116C4×D4×C71C2×C414yes—
117C4×D4×C71D414yes—
118#117×C71—22no—
119#117×C71—41no—
120C2×C4⋊C4×C71—22no—
121C2×C4⋊C4×C71—21no—
122C2×C4⋊C4×C71—41no—
123C2×C4⋊C4×C71D411yescharacteristic
124C2×C4⋊C4×C71C2311yescharacteristic
125C2×C4⋊C4×C71C2311yescharacteristic
126C2×C4⋊C4×C71C2311yescharacteristic
127C2×C4⋊C4×C71C2311yescharacteristic
128C2×C22⋊C4×C71—21no—
129C2×C22⋊C4×C71—21no—
130C2×C22⋊C4×C71—21no—
131C2×C22⋊C4×C71D411yescharacteristic
132C2×C22⋊C4×C71D411yescharacteristic
133C2×C42×C71—21no—
134C2×C42×C71—21no—
135C2×C42×C71C2311yescharacteristic
136#95×C71—21no—
137#95×C71—21no—
138#95×C71—21no—
139#95×C71—21no—
140#95×C71—21no—
141C2×Dic142—21no—
142C2×Dic142—21no—
143C2×Dic142—21no—
144C2×Dic142—21no—
145C2×Dic142—21no—
146C2×Dic142—24no—
147C2×Dic142—81no—
148C2×Dic142—81no—
149C2×Dic142C22×C412yes—
150C22×Dic71—21no—
151C22×Dic71—21no—
152C22×Dic71—21no—
153C22×Dic71—21no—
154C22×Dic71—24no—
155C22×Dic71—24no—
156C22×Dic71—81no—
157C22×Dic71—81no—
158C22×Dic71—81no—
159C22×Dic71—81no—
160#11765849—44no—
161C2×C71⋊C8—21no—
162C2×C71⋊C8—21no—
163C2×C71⋊C8—21no—
164C2×C71⋊C8—21no—
165C2×C71⋊C8—21no—
166C2×C71⋊C8—21no—
167C2×C71⋊C8—21no—
168C2×C71⋊C8—21no—
169C2×C71⋊C8—21no—
170C2×C71⋊C8—21no—
171C2×C71⋊C8—21no—
172C2×C71⋊C8—44no—
173C2×C71⋊C8#4112yes—
174C4⋊Dic71—24no—
175C4⋊Dic71—24no—
176C4⋊Dic71—24no—
177C4⋊Dic71—21no—
178C4⋊Dic71—21no—
179C4⋊Dic71—21no—
180C4⋊Dic71C22×C412yes—
181C4⋊Dic71C22×C412yes—
182C4⋊Dic71C22×C412yes—
183Dic71⋊C4—24no—
184Dic71⋊C4—24no—
185Dic71⋊C4—24no—
186C22⋊Dic71—24no—
187C22⋊Dic71—24no—
188C4×Dic71—24no—
189C24×C71C2×D411yescharacteristic
190C24×C71C2×D411yescharacteristic
191C2×D4×C71—22no—
192C2×D4×C71—22no—
193C2×D4×C71C22⋊C414yes—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—21no—
206C22×C4×C71—42no—
207C22×C4×C71—42no—
208C22×C4×C71—81no—
209C22×C4×C71C22×C412yes—
210C22×C4×C71C22×C412yes—
211C22×C4×C71C2×D411yescharacteristic
212C22×C4×C71C2×D411yescharacteristic
213C22×C4×C71C2×D411yescharacteristic
214C22×C4×C71C2×D411yescharacteristic
215C22×C4×C71C2×D412yes—
216C22×C4×C71C2×D412yes—
217C22×C4×C71C2411yescharacteristic
218C4⋊C4×C71—21no—
219C4⋊C4×C71—21no—
220C4⋊C4×C71—21no—
221C4⋊C4×C71—21no—
222C4⋊C4×C71—21no—
223C4⋊C4×C71—21no—
224C4⋊C4×C71—21no—
225C4⋊C4×C71—42no—
226C4⋊C4×C71C22⋊C414yes—
227C4⋊C4×C71#4112yes—
228C22⋊C4×C71—42no—
229C22⋊C4×C71—42no—
230C22⋊C4×C71—81no—
231C22⋊C4×C71C22⋊C414yes—
232C22⋊C4×C71C22⋊C414yes—
233C42×C71—42no—
234C42×C71—81no—
235C42×C71C22×C412yes—
236C42×C71C2×D412yes—
237C23×C71—21no—
238C23×C71—21no—
239C23×C71—21no—
240C23×C71—21no—
241C23×C71—21no—
242C23×C71—21no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71—21no—
246C23×C71—21no—
247C23×C71C2×C22⋊C412yes—
248C23×C71C2×C22⋊C412yes—
249C23×C71#13712yes—
250C23×C71#13712yes—
251C23×C71C22×D411yescharacteristic
252D4×C71—28no—
253C2×C4×C71—21no—
254C2×C4×C71—21no—
255C2×C4×C71—21no—
256C2×C4×C71—21no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—22no—
266C2×C4×C71—22no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—41no—
271C2×C4×C71—41no—
272C2×C4×C71—41no—
273C2×C4×C71—41no—
274C2×C4×C71—41no—
275C2×C4×C71—41no—
276C2×C4×C71—41no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—84no—
282C2×C4×C71C2×C22⋊C412yes—
283C2×C4×C71C2×C22⋊C412yes—
284C2×C4×C71C2×C22⋊C412yes—
285C2×C4×C71C2×C22⋊C412yes—
286C2×C4×C71C23×C411yescharacteristic
287C2×C4×C71C22×D411yescharacteristic
288C2×C4×C71C2×#4111yescharacteristic
289C2×C4×C71C2×#4111yescharacteristic
290C2×C4×C71H(5,𝔽2)11yescharacteristic
291C2×C4×C712−1+411yescharacteristic
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—41no—
297C2×Dic71—41no—
298C2×Dic71—41no—
299C2×Dic71—41no—
300C2×Dic71—41no—
301C2×Dic71—41no—
302C2×Dic71—41no—
303C2×Dic71—41no—
304C2×Dic71—84no—
305C2×Dic71—84no—
306Dic142—22no—
307Dic142—22no—
308Dic142—41no—
309Dic142—41no—
310Dic142—84no—
311C71⋊C8—22no—
312C71⋊C8—41no—
313C71⋊C8—41no—
314C71⋊C8—41no—
315C22×C71—22no—
316C22×C71—22no—
317C22×C71—22no—
318C22×C71—22no—
319C22×C71—22no—
320C22×C71—22no—
321C22×C71—22no—
322C22×C71—22no—
323C22×C71—22no—
324C22×C71—41no—
325C22×C71—41no—
326C22×C71—41no—
327C22×C71—41no—
328C22×C71#41914yes—
329C22×C71C22×C22⋊C411yescharacteristic
330C22×C71#54611yescharacteristic
331C22×C71#54711yescharacteristic
332C22×C71C2×#13711yescharacteristic
333C22×C71C2×#13711yescharacteristic
334C22×C71#57611yescharacteristic
335C22×C71#57711yescharacteristic
336C4×C71—22no—
337C4×C71—22no—
338C4×C71—22no—
339C4×C71—22no—
340C4×C71—42no—
341C4×C71—81no—
342C4×C71—81no—
343C4×C71—81no—
344C4×C71C4×#4111yescharacteristic
345C4×C71#52011yescharacteristic
346C4×C71#54611yescharacteristic
347C4×C71#54711yescharacteristic
348Dic71—42no—
349Dic71—42no—
350Dic71—42no—
351Dic71—42no—
352#22497—711nomaximal, Sylow
353C2×C71—24no—
354C2×C71—42no—
355C2×C71#233911yescharacteristic
356C2×C71C2×#41911yescharacteristic
357C2×C71#289711yescharacteristic
358C2×C71#331411yescharacteristic
359C2×C71#331611yescharacteristic
360C2×C71#334411yescharacteristic
361C2×C71#334611yescharacteristic
362C2×#554—711no—
363C2×#435—711no—
364#2352D7111yescharacteristic
365#1993—711no—
366#1988—711no—
367#1894—711no—
368#1892—711no—
369#1873—711no—
370#1872—711no—
371#1824—711no—
372#1823—711no—
373#1805—711no—
374#1763—711no—
375#1736—711no—
376C2×#340—711no—
377C71#2249711yescharacteristic, complemented, Sylow
378C22×M16—711no—
379C23×C8—711no—
380#554—718no—
381#554—1424no—
382C2×C4⋊Q8—711no—
383C2×#125—1421no—
384C2×C22⋊Q8—711no—
385C2×C22⋊Q8—711no—
386C2×C22⋊Q8—1421no—
387C2×C22⋊Q8—1421no—
388C2×C4×Q8—711no—
389C2×C4×D4—1421no—
390C2×C4×D4C2×D7111yescharacteristic
391C2×#117C2×D7111yescharacteristic
392C22×C4⋊C4—711no—
393C22×C4⋊C4—711no—
394C22×C4⋊C4C2×D7111yescharacteristic
395#435—1424no—
396C2×C4⋊C8—711no—
397C2×#103—711no—
398C2×#103—711no—
399C2×#103—711no—
400C2×#103—711no—
401C2×C22⋊C8—711no—
402C2×C22⋊C8—711no—
403C2×#97—711no—
404#388—21no—
405#387—21no—
406#386—21no—
407#382C2×D7111yescharacteristic
408#380C2×D7111yescharacteristic
409#380C2×D7111yescharacteristic
410C4×C4⋊C4C2×D7111yescharacteristic
411C4×C22⋊C4—21no—
412#340—711no—
413#340—711no—
414#340—711no—
415#340—711no—
416#340—711no—
417#340—711no—
418#340—711no—
419#340—711no—
420#340—711no—
421#340—711no—
422#340—711no—
423#340—711no—
424C22×Q8—711no—
425C22×Q8—1421no—
426C22×D4C22⋊D7111yescharacteristic
427C23×C4—21no—
428C23×C4—1421no—
429C23×C4—1421no—
430C23×C4C22×D7111yescharacteristic
431C23×C4C22×D7111yescharacteristic
432C2×M16—2841no—
433C2×M16—1422no—
434C2×M16—1422no—
435C22×C8—2841no—
436C22×C8—711no—
437C22×C8—711no—
438C22×C8—711no—
439C22×C8—711no—
440C22×C8—1422no—
441C22×C8—1422no—
442C4⋊Q8—714no—
443C4⋊Q8—1422no—
444#125—1428no—
445C22⋊Q8—714no—
446C22⋊Q8—714no—
447C22⋊Q8—1422no—
448C22⋊Q8—1422no—
449C22⋊Q8—1428no—
450C22⋊Q8—1428no—
451C4×Q8—714no—
452C4×Q8—1422no—
453C4×D4—1428no—
454C4×D4C4×D7114yes—
455C4×D4D28414yes—
456#117—22no—
457#117—41no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—714no—
462C2×C4⋊C4—714no—
463C2×C4⋊C4—711no—
464C2×C4⋊C4—711no—
465C2×C4⋊C4—711no—
466C2×C4⋊C4—1421no—
467C2×C4⋊C4—1421no—
468C2×C4⋊C4—1421no—
469C2×C4⋊C4—1421no—
470C2×C4⋊C4—1421no—
471C2×C4⋊C4—1421no—
472C2×C4⋊C4—1422no—
473C2×C4⋊C4—1422no—
474C2×C4⋊C4C22⋊D7111yescharacteristic
475C2×C4⋊C4C22×D7111yescharacteristic
476C2×C4⋊C4C22×D7111yescharacteristic
477C2×C4⋊C4C22×D7111yescharacteristic
478C2×C4⋊C4C22×D7111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—1421no—
483C2×C22⋊C4—1421no—
484C2×C22⋊C4C22⋊D7111yescharacteristic
485C2×C22⋊C4C22⋊D7111yescharacteristic
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—1421no—
489C2×C42C22×D7111yescharacteristic
490C4⋊C8—1422no—
491#103—2841no—
492#103—2841no—
493#103—1422no—
494#103—1422no—
495C22⋊C8—1422no—
496C22⋊C8—1422no—
497#97—1422no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503C24C2×C22⋊D7111yescharacteristic
504C24C2×C22⋊D7111yescharacteristic
505C2×Q8—5681no—
506C2×Q8—5681no—
507C2×Q8—712no—
508C2×Q8—1421no—
509C2×Q8—1421no—
510C2×Q8—1421no—
511C2×Q8—1421no—
512C2×Q8—1421no—
513C2×Q8—1424no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4(C2×D71)⋊C414yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4—5681no—
533C22×C4—5681no—
534C22×C4—5681no—
535C22×C4—5681no—
536C22×C4—1421no—
537C22×C4—1421no—
538C22×C4—1421no—
539C22×C4—1421no—
540C22×C4—1424no—
541C22×C4—1424no—
542C22×C4C2×C4×D7112yes—
543C22×C4C2×C4×D7112yes—
544C22×C4C2×C22⋊D7111yescharacteristic
545C22×C4C2×C22⋊D7111yescharacteristic
546C22×C4C2×C22⋊D7111yescharacteristic
547C22×C4C2×C22⋊D7111yescharacteristic
548C22×C4C2×D28412yes—
549C22×C4C2×D28412yes—
550C22×C4C23×D7111yescharacteristic
551M16—2844no—
552C2×C8—2844no—
553C2×C8—712no—
554C2×C8—1421no—
555C2×C8—1421no—
556C2×C8—1421no—
557C2×C8—1421no—
558C2×C8—1421no—
559C2×C8—1421no—
560C2×C8—1421no—
561C2×C8—1421no—
562C2×C8—1421no—
563C2×C8—1421no—
564C2×C8—1421no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—42no—
573C4⋊C4—712no—
574C4⋊C4—712no—
575C4⋊C4—712no—
576C4⋊C4—1421no—
577C4⋊C4—1421no—
578C4⋊C4—1421no—
579C4⋊C4—1424no—
580C4⋊C4—1424no—
581C4⋊C4—1424no—
582C4⋊C4—1424no—
583C4⋊C4—1424no—
584C4⋊C4—1424no—
585C4⋊C4(C2×D71)⋊C414yes—
586C4⋊C4#1176586412yes—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—81no—
590C22⋊C4—1424no—
591C22⋊C4—1424no—
592C22⋊C4(C2×D71)⋊C414yes—
593C22⋊C4(C2×D71)⋊C414yes—
594C42—42no—
595C42—81no—
596C42—1424no—
597C42C2×C4×D7112yes—
598C42C2×D28412yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×(C2×D71)⋊C412yes—
610C23C2×(C2×D71)⋊C412yes—
611C23#1455615812yes—
612C23#1455615812yes—
613C23C22×C22⋊D7111yescharacteristic
614Q8—2841no—
615Q8—2841no—
616Q8—5684no—
617Q8—1422no—
618Q8—1422no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—2841no—
650C2×C4—2841no—
651C2×C4—2841no—
652C2×C4—2841no—
653C2×C4—2841no—
654C2×C4—2841no—
655C2×C4—2841no—
656C2×C4—2841no—
657C2×C4—5684no—
658C2×C4—5684no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4C2×(C2×D71)⋊C412yes—
664C2×C4C2×(C2×D71)⋊C412yes—
665C2×C4C2×(C2×D71)⋊C412yes—
666C2×C4C2×(C2×D71)⋊C412yes—
667C2×C4C22×C4×D7111yescharacteristic
668C2×C4C22×D28411yescharacteristic
669C2×C4#41×D7111yescharacteristic
670C2×C4C2×#1176586411yescharacteristic
671C2×C4#1455617311yescharacteristic
672C2×C4#1455617511yescharacteristic
673C8—2841no—
674C8—2841no—
675C8—2841no—
676C8—1422no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1798600714yes—
691C22C22×(C2×D71)⋊C411yescharacteristic
692C22#1798664311yescharacteristic
693C22#1798664811yescharacteristic
694C22C2×#1455615811yescharacteristic
695C22C2×#1455615811yescharacteristic
696C22#1798680211yescharacteristic
697C22#1798680711yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—2842no—
707C4—2842no—
708C4—2842no—
709C4—2842no—
710C4C4×#1176586411yescharacteristic
711C4#1798647811yescharacteristic
712C4#1798664411yescharacteristic
713C4#1798665311yescharacteristic
714C2—24no—
715C2—42no—
716C2#2259116511yescharacteristic
717C2C2×#1798600711yescharacteristic
718C2#2259686311yescharacteristic
719C2#2260042111yescharacteristic
720C2#2260045111yescharacteristic
721C2#2260079511yescharacteristic
722C2#2260082511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#2352C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
cosocleC22×C4×C71C24
hypercenter#2352D71
hypocenterC71#22497
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. #22589312C2semidirect
4. #22589292C2semidirect
5. #22588771C2semidirect
6. #22588761C2semidirect
7. #22588652C2semidirect
8. #22588647C2semidirect
9. #22588428C2semidirect
10. #22588424C2semidirect
11. #22588352C2semidirect
12. #22588173C2semidirect
13. #22588061C2semidirect
14. C2×#17985761C2semidirect
19. #17986706C4semidirect
77. #14556128C2×C4semidirect
82. #14556107C2×C4semidirect
86. C4×Dic142C2×C4semidirect
94. C2×C4⋊Dic71C2×C4semidirect
377. C71#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#179867062
C2×#179860712
#225893122
#225892922
#225887712
#225887612
#225886522
#225886472
#225884282
#225884242
#225883522
#225881732
#225880612
C2×#179857612
C71×#23522
#2249771