Finite Group Databasebeta

← #32015608

Subgroups — #32015608

Order 18176.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986071C211yesmaximal, characteristic
2C2×#17986042C211yesmaximal, characteristic, complemented
3C22×#14556059C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic71C211yesmaximal, characteristic
5#22589106C211yesmaximal, characteristic, complemented
6#22589103C211yesmaximal, characteristic, complemented
7#22588539C211yesmaximal, characteristic, complemented
8#22588533C211yesmaximal, characteristic, complemented
9#22588532C211yesmaximal, characteristic, complemented
10#22588527C211yesmaximal, characteristic, complemented
11#22588509C211yesmaximal, characteristic, complemented
12#22588371C211yesmaximal, characteristic, complemented
13#22588367C211yesmaximal, characteristic, complemented
14#22588238C211yesmaximal, characteristic, complemented
15C71×#2352C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×D4×Dic71—21no—
19C22×C4⋊Dic71C2211yescharacteristic
20C22×C4⋊Dic71C2211yescharacteristic
21#17986071C418yescomplemented
22#17986042—24no—
23C2×#14556061C2211yescharacteristic
24C2×#14556061C2211yescharacteristic
25C2×#14556061C2211yescharacteristic
26C2×#14556061C2211yescharacteristic
27C2×#14556059—24no—
28C2×#14556059C2211yescharacteristic
29C2×#14556059C2211yescharacteristic
30C2×#14556059C2211yescharacteristic
31C2×#14556059C2211yescharacteristic
32C2×#14556059C2211yescharacteristic
33C2×#14556059C2211yescharacteristic
34C2×C4⋊(C71⋊C8)C2211yescharacteristic
35C2×C22⋊(C71⋊C8)C2211yescharacteristic
36C2×C22⋊(C71⋊C8)C2211yescharacteristic
37C2×#14556039C2211yescharacteristic
38#17985898—21no—
39#17985874—21no—
40#17985874—21no—
41#17985869C2211yescharacteristic
42#17985859C2211yescharacteristic
43#17985859C2211yescharacteristic
44C4×C4⋊Dic71C2211yescharacteristic
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—
62C23×Dic71—21no—
63C23×Dic71—21no—
64C2×#11765849—22no—
65C2×#11765849—22no—
66C2×#11765849C2×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
74D4×Dic71—44no—
75C2×C4⋊Dic71—22no—
76C2×C4⋊Dic71—22no—
77C2×C4⋊Dic71—21no—
78C2×C4⋊Dic71—21no—
79C2×C4⋊Dic71—21no—
80C2×C4⋊Dic71—21no—
81C2×C4⋊Dic71—41no—
82C2×C4⋊Dic71—41no—
83C2×C4⋊Dic71C2311yescharacteristic
84C2×C4⋊Dic71C2311yescharacteristic
85C2×C4⋊Dic71C2311yescharacteristic
86C2×C4⋊Dic71C2311yescharacteristic
87C2×C22⋊Dic71—21no—
88C2×C22⋊Dic71—21no—
89C2×C4×Dic71—21no—
90#14556061—22no—
91#14556061—22no—
92#14556061—22no—
93#14556061—41no—
94#14556059—22no—
95#14556059—22no—
96#14556059—22no—
97#14556059—22no—
98#14556059—41no—
99#14556059D414yescomplemented
100C4⋊(C71⋊C8)C2×C414yescomplemented
101C22⋊(C71⋊C8)C2×C414yescomplemented
102C22⋊(C71⋊C8)C2×C414yescomplemented
103#14556039C2×C414yescomplemented
104C71⋊#95—21no—
105C71⋊#95—21no—
106C71⋊#95—21no—
107C22×D4×C71D411yescharacteristic
108C23×C4×C71—21no—
109C23×C4×C71C2311yescharacteristic
110C23×C4×C71C2311yescharacteristic
111C4×D4×C71C2×C414yes—
112C4×D4×C71Q814yes—
113#117×C71—22no—
114#117×C71—41no—
115C2×C4⋊C4×C71—22no—
116C2×C4⋊C4×C71—21no—
117C2×C4⋊C4×C71—41no—
118C2×C4⋊C4×C71D411yescharacteristic
119C2×C4⋊C4×C71C2311yescharacteristic
120C2×C4⋊C4×C71C2311yescharacteristic
121C2×C4⋊C4×C71C2311yescharacteristic
122C2×C4⋊C4×C71C2311yescharacteristic
123C2×C22⋊C4×C71—21no—
124C2×C22⋊C4×C71—21no—
125C2×C22⋊C4×C71—21no—
126C2×C22⋊C4×C71D411yescharacteristic
127C2×C22⋊C4×C71D411yescharacteristic
128C2×C42×C71—21no—
129C2×C42×C71—21no—
130C2×C42×C71C2311yescharacteristic
131#95×C71—21no—
132#95×C71—21no—
133#95×C71—21no—
134#95×C71—21no—
135#95×C71—21no—
136C22×Dic71—21no—
137C22×Dic71—21no—
138C22×Dic71—21no—
139C22×Dic71—21no—
140C22×Dic71—42no—
141C22×Dic71—42no—
142C22×Dic71—42no—
143C22×Dic71—42no—
144C22×Dic71—81no—
145C22×Dic71—81no—
146#11765849—28no—
147C2×C71⋊C8—21no—
148C2×C71⋊C8—21no—
149C2×C71⋊C8—21no—
150C2×C71⋊C8—21no—
151C2×C71⋊C8—21no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—28no—
154C2×C71⋊C8C22×C412yes—
155C2×C71⋊C8C22×C412yes—
156C2×C71⋊C8C22×C412yes—
157C2×C71⋊C8C22×C412yes—
158C2×C71⋊C8C2×D412yes—
159C2×C71⋊C8#4112yes—
160C4⋊Dic71—21no—
161C4⋊Dic71—21no—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71—21no—
166C4⋊Dic71—21no—
167C4⋊Dic71—42no—
168C4⋊Dic71—42no—
169C4⋊Dic71—42no—
170C4⋊Dic71—81no—
171C4⋊Dic71C2×D412yes—
172C22⋊Dic71—42no—
173C22⋊Dic71—42no—
174C4×Dic71—42no—
175C24×C71C2×D411yescharacteristic
176C24×C71C2×D411yescharacteristic
177C2×D4×C71—22no—
178C2×D4×C71—22no—
179C2×D4×C71C4⋊C414yes—
180C22×C4×C71—21no—
181C22×C4×C71—21no—
182C22×C4×C71—21no—
183C22×C4×C71—21no—
184C22×C4×C71—21no—
185C22×C4×C71—21no—
186C22×C4×C71—21no—
187C22×C4×C71—21no—
188C22×C4×C71—21no—
189C22×C4×C71—21no—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—42no—
193C22×C4×C71—42no—
194C22×C4×C71—81no—
195C22×C4×C71C22×C412yes—
196C22×C4×C71C22×C412yes—
197C22×C4×C71C2×D411yescharacteristic
198C22×C4×C71C2×D411yescharacteristic
199C22×C4×C71C2×D411yescharacteristic
200C22×C4×C71C2×D411yescharacteristic
201C22×C4×C71C2×Q812yes—
202C22×C4×C71C2×Q812yes—
203C22×C4×C71C2411yescharacteristic
204C4⋊C4×C71—21no—
205C4⋊C4×C71—21no—
206C4⋊C4×C71—21no—
207C4⋊C4×C71—21no—
208C4⋊C4×C71—21no—
209C4⋊C4×C71—21no—
210C4⋊C4×C71—21no—
211C4⋊C4×C71—42no—
212C4⋊C4×C71C4⋊C414yes—
213C4⋊C4×C71C2×D412yes—
214C22⋊C4×C71—42no—
215C22⋊C4×C71—42no—
216C22⋊C4×C71—81no—
217C22⋊C4×C71C4⋊C414yes—
218C22⋊C4×C71C4⋊C414yes—
219C42×C71—42no—
220C42×C71—81no—
221C42×C71C22×C412yes—
222C42×C71C2×Q812yes—
223C23×C71—21no—
224C23×C71—21no—
225C23×C71—21no—
226C23×C71—21no—
227C23×C71—21no—
228C23×C71—21no—
229C23×C71—21no—
230C23×C71—21no—
231C23×C71—21no—
232C23×C71—21no—
233C23×C71C2×C4⋊C412yes—
234C23×C71C2×C4⋊C412yes—
235C23×C71AGL(1,ℤ/8)12yes—
236C23×C71#13712yes—
237C23×C71C22×D411yescharacteristic
238D4×C71—28no—
239C2×C4×C71—21no—
240C2×C4×C71—21no—
241C2×C4×C71—21no—
242C2×C4×C71—21no—
243C2×C4×C71—21no—
244C2×C4×C71—21no—
245C2×C4×C71—21no—
246C2×C4×C71—21no—
247C2×C4×C71—22no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—22no—
251C2×C4×C71—22no—
252C2×C4×C71—22no—
253C2×C4×C71—22no—
254C2×C4×C71—22no—
255C2×C4×C71—22no—
256C2×C4×C71—41no—
257C2×C4×C71—41no—
258C2×C4×C71—41no—
259C2×C4×C71—41no—
260C2×C4×C71—41no—
261C2×C4×C71—41no—
262C2×C4×C71—41no—
263C2×C4×C71—41no—
264C2×C4×C71—41no—
265C2×C4×C71—41no—
266C2×C4×C71—41no—
267C2×C4×C71—84no—
268C2×C4×C71C2×C4⋊C412yes—
269C2×C4×C71C2×C4⋊C412yes—
270C2×C4×C71C2×C4⋊C412yes—
271C2×C4×C71C2×C4⋊C412yes—
272C2×C4×C71C23×C411yescharacteristic
273C2×C4×C71C22×D411yescharacteristic
274C2×C4×C71C22×Q811yescharacteristic
275C2×C4×C71C2×#4111yescharacteristic
276C2×C4×C71H(5,𝔽2)11yescharacteristic
277C2×C4×C712−1+411yescharacteristic
278C2×Dic71—22no—
279C2×Dic71—41no—
280C2×Dic71—41no—
281C2×Dic71—41no—
282C2×Dic71—41no—
283C2×Dic71—41no—
284C2×Dic71—41no—
285C2×Dic71—41no—
286C2×Dic71—41no—
287C2×Dic71—41no—
288C2×Dic71—41no—
289C2×Dic71—41no—
290C2×Dic71—84no—
291C2×Dic71—84no—
292C71⋊C8—22no—
293C71⋊C8—22no—
294C71⋊C8—22no—
295C71⋊C8C4×D414yescomplemented
296C22×C71—22no—
297C22×C71—22no—
298C22×C71—22no—
299C22×C71—22no—
300C22×C71—22no—
301C22×C71—22no—
302C22×C71—22no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71—41no—
306C22×C71—41no—
307C22×C71—41no—
308C22×C71—41no—
309C22×C71#42814yescomplemented
310C22×C71C22×C4⋊C411yescharacteristic
311C22×C71D4211yescharacteristic
312C22×C71#54711yescharacteristic
313C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C71C2×#13711yescharacteristic
315C22×C71#57711yescharacteristic
316C22×C71#57711yescharacteristic
317C4×C71—22no—
318C4×C71—22no—
319C4×C71—22no—
320C4×C71—22no—
321C4×C71—42no—
322C4×C71—81no—
323C4×C71—81no—
324C4×C71—81no—
325C4×C71C2×C4×D411yescharacteristic
326C4×C71#52011yescharacteristic
327C4×C71D4×Q811yescharacteristic
328C4×C71#55411yescharacteristic
329Dic71—42no—
330Dic71—81no—
331Dic71—81no—
332Dic71—81no—
333#22659—711nomaximal, Sylow
334C2×C71—24no—
335C2×C71—42no—
336C2×C71D4×C4⋊C411yescharacteristic
337C2×C71C2×#42811yescharacteristic
338C2×C71#291211yescharacteristic
339C2×C71#326511yescharacteristic
340C2×C71#326611yescharacteristic
341C2×C71#334411yescharacteristic
342C2×C71#334511yescharacteristic
343C2×#435—711no—
344C2×#428—711no—
345C22×#106—711no—
346#2352D7111yescharacteristic
347D4×C4⋊C4—711no—
348#1949—711no—
349#1948—711no—
350#1854—711no—
351#1853—711no—
352#1853—711no—
353#1852—711no—
354#1847—711no—
355#1809—711no—
356#1808—711no—
357#1776—711no—
358C71#2265911yescharacteristic, complemented, Sylow
359C22×M16—711no—
360C23×C8—711no—
361C2×C4×D4—1421no—
362C2×C4×D4C2×D7111yescharacteristic
363C2×#117C2×D7111yescharacteristic
364C22×C4⋊C4—711no—
365C22×C4⋊C4—711no—
366C22×C4⋊C4C2×D7111yescharacteristic
367#435—718no—
368#428—1424no—
369C2×#107—711no—
370C2×#107—711no—
371C2×#107—711no—
372C2×#107—711no—
373C2×#106—711no—
374C2×#106—711no—
375C2×#106—711no—
376C2×#106—711no—
377C2×#106—711no—
378C2×#106—711no—
379C2×#106—1424no—
380C2×C4⋊C8—711no—
381C2×C22⋊C8—711no—
382C2×C22⋊C8—711no—
383C2×#97—711no—
384#389—1421no—
385#388—21no—
386#387—21no—
387#386—21no—
388#385—1421no—
389#385—1421no—
390#384—711no—
391#382C2×D7111yescharacteristic
392#380—711no—
393#380—711no—
394#380C2×D7111yescharacteristic
395#380C2×D7111yescharacteristic
396C4×C4⋊C4—711no—
397C4×C4⋊C4C2×D7111yescharacteristic
398C4×C22⋊C4—21no—
399#340—711no—
400#340—711no—
401#340—711no—
402#340—711no—
403#340—711no—
404#340—711no—
405C22×D4C22⋊D7111yescharacteristic
406C23×C4—21no—
407C23×C4—1421no—
408C23×C4—1421no—
409C23×C4C22×D7111yescharacteristic
410C23×C4C22×D7111yescharacteristic
411C2×M16—714no—
412C2×M16—1422no—
413C2×M16—1422no—
414C22×C8—711no—
415C22×C8—714no—
416C22×C8—711no—
417C22×C8—711no—
418C22×C8—711no—
419C22×C8—1422no—
420C22×C8—1422no—
421C4×D4—2844no—
422C4×D4Dic14214yes—
423C4×D4C4×D7114yes—
424#117—22no—
425#117—41no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—2841no—
430C2×C4⋊C4—2841no—
431C2×C4⋊C4—711no—
432C2×C4⋊C4—711no—
433C2×C4⋊C4—711no—
434C2×C4⋊C4—711no—
435C2×C4⋊C4—1421no—
436C2×C4⋊C4—1421no—
437C2×C4⋊C4—1421no—
438C2×C4⋊C4—1422no—
439C2×C4⋊C4—1422no—
440C2×C4⋊C4—1421no—
441C2×C4⋊C4C22⋊D7111yescharacteristic
442C2×C4⋊C4C22×D7111yescharacteristic
443C2×C4⋊C4C22×D7111yescharacteristic
444C2×C4⋊C4C22×D7111yescharacteristic
445C2×C4⋊C4C22×D7111yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—1421no—
450C2×C22⋊C4—1421no—
451C2×C22⋊C4C22⋊D7111yescharacteristic
452C2×C22⋊C4C22⋊D7111yescharacteristic
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—1421no—
456C2×C42C22×D7111yescharacteristic
457#107—2841no—
458#107—1422no—
459#107—1422no—
460#107—1422no—
461#106—2841no—
462#106—714no—
463#106—1422no—
464#106—1422no—
465#106—1422no—
466#106—1422no—
467C4⋊C8—714no—
468C22⋊C8—714no—
469C22⋊C8—714no—
470#97—714no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—1421no—
477#95—1421no—
478#95—1421no—
479C24C2×C22⋊D7111yescharacteristic
480C24C2×C22⋊D7111yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4Dic71⋊C414yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—2842no—
500C22×C4—2842no—
501C22×C4—2842no—
502C22×C4—2842no—
503C22×C4—5681no—
504C22×C4—5681no—
505C22×C4—1421no—
506C22×C4—1421no—
507C22×C4—1421no—
508C22×C4—1421no—
509C22×C4C2×C4×D7112yes—
510C22×C4C2×C4×D7112yes—
511C22×C4C2×C22⋊D7111yescharacteristic
512C22×C4C2×C22⋊D7111yescharacteristic
513C22×C4C2×C22⋊D7111yescharacteristic
514C22×C4C2×C22⋊D7111yescharacteristic
515C22×C4C2×Dic14212yes—
516C22×C4C2×Dic14212yes—
517C22×C4C23×D7111yescharacteristic
518M16—1428no—
519C2×C8—712no—
520C2×C8—712no—
521C2×C8—712no—
522C2×C8—712no—
523C2×C8—712no—
524C2×C8—712no—
525C2×C8—1428no—
526C2×C8—1421no—
527C2×C8—1421no—
528C2×C8—1421no—
529C2×C8—1421no—
530C2×C8—1421no—
531C2×C8—1421no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—2842no—
541C4⋊C4—2842no—
542C4⋊C4—2842no—
543C4⋊C4—5681no—
544C4⋊C4—712no—
545C4⋊C4—1421no—
546C4⋊C4—1421no—
547C4⋊C4—1421no—
548C4⋊C4—1421no—
549C4⋊C4—1421no—
550C4⋊C4—1421no—
551C4⋊C4—1421no—
552C4⋊C4Dic71⋊C414yes—
553C4⋊C4D4×D7112yes—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4—2842no—
558C22⋊C4—2842no—
559C22⋊C4Dic71⋊C414yes—
560C22⋊C4Dic71⋊C414yes—
561C42—42no—
562C42—81no—
563C42—2842no—
564C42C2×C4×D7112yes—
565C42C2×Dic14212yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×Dic71⋊C412yes—
577C23C2×Dic71⋊C412yes—
578C23#1455615312yes—
579C23#1455615812yes—
580C23C22×C22⋊D7111yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
611C2×C4—2841no—
612C2×C4—2841no—
613C2×C4—2841no—
614C2×C4—2841no—
615C2×C4—2841no—
616C2×C4—2841no—
617C2×C4—2841no—
618C2×C4—2841no—
619C2×C4—2841no—
620C2×C4—2841no—
621C2×C4—2841no—
622C2×C4—5684no—
623C2×C4—5684no—
624C2×C4—1422no—
625C2×C4C2×Dic71⋊C412yes—
626C2×C4C2×Dic71⋊C412yes—
627C2×C4C2×Dic71⋊C412yes—
628C2×C4C2×Dic71⋊C412yes—
629C2×C4C22×C4×D7111yescharacteristic
630C2×C4C2×D4×D7111yescharacteristic
631C2×C4C22×Dic14211yescharacteristic
632C2×C4#41×D7111yescharacteristic
633C2×C4#1455617311yescharacteristic
634C2×C4#1455617511yescharacteristic
635C8—714no—
636C8—1422no—
637C8—1422no—
638C8—1422no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#1798604214yescomplemented
653C22C22×Dic71⋊C411yescharacteristic
654C22D4×C22⋊D7111yescharacteristic
655C22#1798664811yescharacteristic
656C22C2×#1455615311yescharacteristic
657C22C2×#1455615811yescharacteristic
658C22#1798680711yescharacteristic
659C22#1798681011yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—42no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—2842no—
669C4—5681no—
670C4—5681no—
671C4—5681no—
672C4C4×D4×D7111yescharacteristic
673C4#1798647811yescharacteristic
674C4D4×Dic14211yescharacteristic
675C4#1798670811yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×Dic71⋊C411yescharacteristic
679C2C2×#1798604211yescharacteristic
680C2#2259693311yescharacteristic
681C2#2259983611yescharacteristic
682C2#2259984611yescharacteristic
683C2#2260079511yescharacteristic
684C2#2260080411yescharacteristic
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#22659
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
2. C2×#17986042C2semidirect
3. C22×#14556059C2semidirect
5. #22589106C2semidirect
6. #22589103C2semidirect
7. #22588539C2semidirect
8. #22588533C2semidirect
9. #22588532C2semidirect
10. #22588527C2semidirect
11. #22588509C2semidirect
12. #22588371C2semidirect
13. #22588367C2semidirect
14. #22588238C2semidirect
21. #17986071C4semidirect
66. C2×#11765849C2×C4semidirect
69. C22×C71⋊C8C2×C4semidirect
99. #14556059D4semidirect
100. C4⋊(C71⋊C8)C2×C4semidirect
101. C22⋊(C71⋊C8)C2×C4semidirect
102. C22⋊(C71⋊C8)C2×C4semidirect
103. #14556039C2×C4semidirect
295. C71⋊C8C4×D4semidirect
309. C22×C71#428semidirect
358. C71#22659semidirect
652. C22#17986042semidirect

Maximal subgroups

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

subgroupindex
C2×#179860712
C2×#179860422
C22×#145560592
D4×C4⋊Dic712
#225891062
#225891032
#225885392
#225885332
#225885322
#225885272
#225885092
#225883712
#225883672
#225882382
C71×#23522
#2265971