Finite Group Databasebeta

← #32016057

Subgroups — #32016057

Order 18176.

888 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986072C211yesmaximal, characteristic
2C2×#17986069C211yesmaximal, characteristic
3#22590801C211yesmaximal, characteristic
4#22589064C211yesmaximal, characteristic, complemented
5#22588524C211yesmaximal, characteristic, complemented
6#22588521C211yesmaximal, characteristic, complemented
7#22588519C211yesmaximal, characteristic, complemented
8#22588516C211yesmaximal, characteristic, complemented
9#22588456C211yesmaximal, characteristic, complemented
10#22588321C211yesmaximal, characteristic, complemented
11#22588321C211yesmaximal, characteristic, complemented
12#22588194C211yesmaximal, characteristic, complemented
13#22588035C211yesmaximal, characteristic, complemented
14#22588035C211yesmaximal, characteristic, complemented
15C71×#1940C211yesmaximal, characteristic, complemented
16C22×#11765848C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20C2×C4×D284C2211yescharacteristic
21C2×#14556085C2211yescharacteristic
22C2×#14556085C2211yescharacteristic
23#17986072—24no—
24#17986069—24no—
25C2×C4⋊(C71⋊C8)C2211yescharacteristic
26C2×C4⋊(C71⋊C8)C2211yescharacteristic
27C2×C4⋊(C71⋊C8)C2211yescharacteristic
28C2×Dic71⋊C8C2211yescharacteristic
29C2×Dic71⋊C8C2211yescharacteristic
30C2×(C2×D71)⋊C8C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×#14556039C2211yescharacteristic
35#17985900C411yescharacteristic
36#17985900C411yescharacteristic
37#17985895C411yescharacteristic
38#17985895C411yescharacteristic
39#17985888C411yescharacteristic
40#17985888C411yescharacteristic
41#17985888C411yescharacteristic
42#17985888C411yescharacteristic
43C4×(C2×D71)⋊C4C2211yescharacteristic
44C4×(C2×D71)⋊C4C2211yescharacteristic
45C42×Dic71C2211yescharacteristic
46#17985754C2211yescharacteristic
47#17985754C2211yescharacteristic
48#17985753C2211yescharacteristic
49#17985753C2211yescharacteristic
50#17985753C2211yescharacteristic
51#17985753C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54C2×C4⋊C8×C71C2211yescharacteristic
55C2×C4⋊C8×C71C2211yescharacteristic
56C2×C4⋊C8×C71C2211yescharacteristic
57C2×#97×C71C2211yescharacteristic
58C4×C4⋊C4×C71C2211yescharacteristic
59#336×C71C2211yescharacteristic
60#336×C71C2211yescharacteristic
61C22×D284C2×C411yescharacteristic
62C22×C4×D71C2311yescharacteristic
63C22×C4×D71C2311yescharacteristic
64C2×#11765848—22no—
65C2×#11765848—22no—
66C2×#11765848—22no—
67C2×#11765848—22no—
68C2×#11765848—41no—
69C2×#11765848—41no—
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74C2×C8×D71—22no—
75C2×C8×D71—22no—
76C2×C8×D71—22no—
77C2×C8×D71—22no—
78C2×C8×D71—41no—
79C2×C8×D71—41no—
80C4×D284D414yes—
81C4×D284Q814yes—
82#14556085—41no—
83#14556085—41no—
84#14556085—41no—
85#14556085—41no—
86C2×C4⋊Dic71C2×C411yescharacteristic
87C2×Dic71⋊C4C2×C411yescharacteristic
88C2×Dic71⋊C4C2×C411yescharacteristic
89C2×Dic71⋊C4C2×C411yescharacteristic
90C2×Dic71⋊C4C2×C411yescharacteristic
91C2×(C2×D71)⋊C4C2×C411yescharacteristic
92C2×(C2×D71)⋊C4C2×C411yescharacteristic
93C2×(C2×D71)⋊C4C2×C411yescharacteristic
94C2×(C2×D71)⋊C4C2×C411yescharacteristic
95C2×(C2×D71)⋊C4C2×C411yescharacteristic
96C2×(C2×D71)⋊C4C2×C411yescharacteristic
97C2×(C2×D71)⋊C4C2×C411yescharacteristic
98C2×(C2×D71)⋊C4C2×C411yescharacteristic
99C2×(C2×D71)⋊C4C2×C411yescharacteristic
100C2×(C2×D71)⋊C4C2×C411yescharacteristic
101C2×C4×Dic71C2×C411yescharacteristic
102C2×C4×Dic71C2×C411yescharacteristic
103C2×C4×Dic71C2×C411yescharacteristic
104C2×C4×Dic71C2×C411yescharacteristic
105C2×C4×Dic71C2311yescharacteristic
106C2×C4×Dic71C2311yescharacteristic
107C4⋊(C71⋊C8)—22no—
108C4⋊(C71⋊C8)—41no—
109C4⋊(C71⋊C8)—41no—
110Dic71⋊C8—22no—
111Dic71⋊C8—22no—
112(C2×D71)⋊C8—22no—
113(C2×D71)⋊C8—22no—
114(C2×D71)⋊C8—22no—
115(C2×D71)⋊C8—22no—
116#14556039—22no—
117C71⋊#95C2×C411yescharacteristic
118C71⋊#95C2×C411yescharacteristic
119C71⋊#95C2×C411yescharacteristic
120C71⋊#95C2×C411yescharacteristic
121C22×C8×C71C2311yescharacteristic
122C22×C8×C71C2311yescharacteristic
123C22×C8×C71C2311yescharacteristic
124C22×C8×C71C2311yescharacteristic
125C2×C4⋊C4×C71C2×C411yescharacteristic
126C2×C4⋊C4×C71C2×C411yescharacteristic
127C2×C42×C71C2311yescharacteristic
128C2×C42×C71C2311yescharacteristic
129C2×C42×C71C2311yescharacteristic
130C4⋊C8×C71—22no—
131C4⋊C8×C71—41no—
132C4⋊C8×C71—41no—
133#97×C71—22no—
134#95×C71C2×C411yescharacteristic
135#95×C71C2×C411yescharacteristic
136C23×D71C22×C411yescharacteristic
137C23×D71C22×C411yescharacteristic
138C2×D284—41no—
139C2×D284—41no—
140C2×D284C4⋊C414yes—
141C22×Dic71C22×C411yescharacteristic
142C22×Dic71C22×C411yescharacteristic
143C22×Dic71C22×C411yescharacteristic
144C22×Dic71C22×C411yescharacteristic
145C22×Dic71C22×C411yescharacteristic
146C22×Dic71C22×C411yescharacteristic
147C2×C4×D71—21no—
148C2×C4×D71—21no—
149C2×C4×D71—21no—
150C2×C4×D71—21no—
151C2×C4×D71—21no—
152C2×C4×D71—21no—
153C2×C4×D71—21no—
154C2×C4×D71—21no—
155C2×C4×D71C2×D412yes—
156C2×C4×D71C2×D412yes—
157C2×C4×D71C2×Q812yes—
158C2×C4×D71C2×Q812yes—
159#11765848—44no—
160#11765848—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#4112yes—
173C8×D71—44no—
174C8×D71—44no—
175C4⋊Dic71C4⋊C414yes—
176Dic71⋊C4—41no—
177Dic71⋊C4—41no—
178Dic71⋊C4—41no—
179Dic71⋊C4—41no—
180(C2×D71)⋊C4—22no—
181(C2×D71)⋊C4—22no—
182(C2×D71)⋊C4—41no—
183(C2×D71)⋊C4—41no—
184(C2×D71)⋊C4—41no—
185(C2×D71)⋊C4—41no—
186(C2×D71)⋊C4—41no—
187(C2×D71)⋊C4—41no—
188(C2×D71)⋊C4C4⋊C414yes—
189(C2×D71)⋊C4C4⋊C414yes—
190C4×Dic71—21no—
191C4×Dic71—21no—
192C4×Dic71—21no—
193C4×Dic71—21no—
194C4×Dic71—22no—
195C4×Dic71—41no—
196C4×Dic71—41no—
197C4×Dic71—41no—
198C22×C4×C71C22×C411yescharacteristic
199C22×C4×C71C22×C411yescharacteristic
200C22×C4×C71C22×C411yescharacteristic
201C22×C4×C71C22×C411yescharacteristic
202C22×C4×C71C22×C411yescharacteristic
203C22×C4×C71C22×C411yescharacteristic
204C22×C4×C71C2411yescharacteristic
205C2×C8×C71—21no—
206C2×C8×C71—21no—
207C2×C8×C71—21no—
208C2×C8×C71—21no—
209C2×C8×C71—21no—
210C2×C8×C71—21no—
211C2×C8×C71—21no—
212C2×C8×C71—21no—
213C2×C8×C71—21no—
214C2×C8×C71—21no—
215C2×C8×C71—21no—
216C2×C8×C71#4112yes—
217C4⋊C4×C71—41no—
218C4⋊C4×C71—41no—
219C42×C71—21no—
220C42×C71—21no—
221C42×C71—21no—
222C42×C71—21no—
223C42×C71C2×D412yes—
224C42×C71C2×Q812yes—
225C23×C71C23×C411yescharacteristic
226C22×D71—21no—
227C22×D71—21no—
228C22×D71—21no—
229C22×D71—21no—
230C22×D71—21no—
231C22×D71—21no—
232C22×D71—21no—
233C22×D71—21no—
234C22×D71—21no—
235C22×D71—21no—
236C22×D71—21no—
237C22×D71—21no—
238C22×D71C2×C4⋊C412yes—
239C22×D71C2×C4⋊C412yes—
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—21no—
248C2×C4×C71—21no—
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—21no—
256C2×C4×C71C2×C4⋊C412yes—
257C2×C4×C71C2×C4⋊C412yes—
258C2×C4×C71C22×D411yescharacteristic
259C2×C4×C71C22×Q811yescharacteristic
260C2×C4×C71C2×#4111yescharacteristic
261C2×C4×C71C2×#4111yescharacteristic
262C2×C4×C71H(5,𝔽2)11yescharacteristic
263C2×C4×C71H(5,𝔽2)11yescharacteristic
264C2×Dic71—21no—
265C2×Dic71—21no—
266C2×Dic71—21no—
267C2×Dic71—21no—
268C2×Dic71—21no—
269C2×Dic71—21no—
270C2×Dic71—21no—
271C2×Dic71—21no—
272C2×Dic71—21no—
273C2×Dic71—21no—
274C2×Dic71—21no—
275C2×Dic71—21no—
276C2×Dic71—21no—
277C2×Dic71—21no—
278C2×Dic71—21no—
279C2×Dic71C2×C4⋊C412yes—
280C2×Dic71C2×C4⋊C412yes—
281C2×Dic71#13112yes—
282D284—44no—
283C4×D71—22no—
284C4×D71—22no—
285C4×D71—22no—
286C4×D71—22no—
287C4×D71—22no—
288C4×D71—22no—
289C4×D71—22no—
290C4×D71—22no—
291C8×C71—22no—
292C8×C71—41no—
293C8×C71—41no—
294C8×C71—41no—
295C71⋊C8—22no—
296C71⋊C8—41no—
297C71⋊C8—41no—
298C71⋊C8—41no—
299C22×C71C22×C4⋊C411yescharacteristic
300C22×C71C4×#4111yescharacteristic
301C22×C71#51811yescharacteristic
302C22×C71C2×#13111yescharacteristic
303C22×C71#56811yescharacteristic
304C22×C71#56811yescharacteristic
305C22×C71#56811yescharacteristic
306C2×D71—22no—
307C2×D71—22no—
308C2×D71—22no—
309C2×D71—22no—
310C2×D71—22no—
311C2×D71—22no—
312C2×D71—41no—
313C2×D71—41no—
314C2×D71—41no—
315C2×D71—41no—
316C2×D71—41no—
317C2×D71—41no—
318C2×D71—41no—
319C2×D71—41no—
320C4×C71—22no—
321C4×C71—22no—
322C4×C71—41no—
323C4×C71—41no—
324C4×C71—41no—
325C4×C71—41no—
326C4×C71#54611yescharacteristic
327C4×C71#54611yescharacteristic
328C4×C71#55411yescharacteristic
329C4×C71#55411yescharacteristic
330Dic71—22no—
331Dic71—22no—
332Dic71—22no—
333Dic71—41no—
334Dic71—41no—
335Dic71—41no—
336#22702—711nomaximal, Sylow
337C2×C71#234911yescharacteristic
338C2×C71#290511yescharacteristic
339C2×C71#290611yescharacteristic
340C2×C71#296711yescharacteristic
341C2×C71#296811yescharacteristic
342C2×C71#298011yescharacteristic
343C2×C71#298111yescharacteristic
344D71—42no—
345D71—42no—
346C2×#435—711no—
347C2×#435—711no—
348#2293—711no—
349#1940—711no—
350#1940D7111yescharacteristic, complemented
351#1851—711no—
352#1851—711no—
353#1850—711no—
354#1850—711no—
355#1831—711no—
356#1798—711no—
357#1798—711no—
358#1767—711no—
359#1729—711no—
360#1729—711no—
361C71#2270211yescharacteristic, complemented, Sylow
362C22×M16—711no—
363C22×M16—711no—
364C23×C8—711no—
365C23×C8—711no—
366C2×C4×D4—711no—
367C2×#117—711no—
368C2×#117—711no—
369#435—1424no—
370#435—1424no—
371C2×C4⋊C8—711no—
372C2×C4⋊C8—711no—
373C2×C4⋊C8—711no—
374C2×C4⋊C8—711no—
375C2×C4⋊C8—711no—
376C2×C4⋊C8C2×D7111yescharacteristic
377C2×C4⋊C8C2×D7111yescharacteristic
378C2×C4⋊C8C2×D7111yescharacteristic
379C2×C22⋊C8—711no—
380C2×C22⋊C8—711no—
381C2×C22⋊C8—711no—
382C2×C22⋊C8—711no—
383C2×#97—711no—
384C2×#97C2×D7111yescharacteristic
385#390—711no—
386#390—711no—
387#389—711no—
388#389—711no—
389#388—711no—
390#388—711no—
391#388—711no—
392#388—711no—
393C4×C4⋊C4C2×D7111yescharacteristic
394C4×C22⋊C4—711no—
395C4×C22⋊C4—711no—
396C43—711no—
397#336—711no—
398#336—711no—
399#336—711no—
400#336—711no—
401#336—711no—
402#336—711no—
403#336—711no—
404#336—711no—
405#336C2×D7111yescharacteristic
406#336C2×D7111yescharacteristic
407C22×D4—711no—
408C23×C4—711no—
409C23×C4—711no—
410C2×M16—2841no—
411C2×M16—2841no—
412C2×M16—1422no—
413C2×M16—1422no—
414C2×M16—1422no—
415C2×M16—1422no—
416C22×C8—2841no—
417C22×C8—2841no—
418C22×C8—711no—
419C22×C8—711no—
420C22×C8—711no—
421C22×C8—711no—
422C22×C8—1422no—
423C22×C8—1422no—
424C22×C8—1422no—
425C22×C8—1422no—
426C22×C8C22×D7111yescharacteristic
427C22×C8C22×D7111yescharacteristic
428C22×C8C22×D7111yescharacteristic
429C22×C8C22×D7111yescharacteristic
430C4×D4—714no—
431C4×D4—714no—
432#117—2841no—
433#117—2841no—
434#117—2841no—
435#117—2841no—
436C2×C4⋊C4—711no—
437C2×C4⋊C4—711no—
438C2×C4⋊C4—711no—
439C2×C4⋊C4—711no—
440C2×C4⋊C4—711no—
441C2×C4⋊C4C4×D7111yescharacteristic
442C2×C4⋊C4C4×D7111yescharacteristic
443C2×C22⋊C4—711no—
444C2×C22⋊C4—711no—
445C2×C22⋊C4—711no—
446C2×C22⋊C4—711no—
447C2×C22⋊C4—711no—
448C2×C22⋊C4—711no—
449C2×C22⋊C4—711no—
450C2×C22⋊C4—711no—
451C2×C22⋊C4—711no—
452C2×C22⋊C4—711no—
453C2×C42—711no—
454C2×C42—711no—
455C2×C42—711no—
456C2×C42—711no—
457C2×C42—711no—
458C2×C42—711no—
459C2×C42C22×D7111yescharacteristic
460C2×C42C22×D7111yescharacteristic
461C2×C42C22×D7111yescharacteristic
462C4⋊C8—22no—
463C4⋊C8—41no—
464C4⋊C8—41no—
465C4⋊C8—2841no—
466C4⋊C8—2841no—
467C4⋊C8—1422no—
468C4⋊C8—1422no—
469C4⋊C8—1422no—
470C22⋊C8—1422no—
471C22⋊C8—1422no—
472C22⋊C8—1422no—
473C22⋊C8—1422no—
474#97—22no—
475#97—1422no—
476#95—711no—
477#95—711no—
478#95—711no—
479#95—711no—
480#95C4×D7111yescharacteristic
481#95C4×D7111yescharacteristic
482C24—711no—
483C24—711no—
484C2×D4—2841no—
485C2×D4—2841no—
486C2×D4—714no—
487C22×C4—711no—
488C22×C4—711no—
489C22×C4—711no—
490C22×C4—712no—
491C22×C4—712no—
492C22×C4—712no—
493C22×C4—712no—
494C22×C4—711no—
495C22×C4—711no—
496C22×C4—711no—
497C22×C4—1421no—
498C22×C4—1421no—
499C22×C4—1421no—
500C22×C4—1421no—
501C22×C4—1421no—
502C22×C4—1421no—
503C22×C4—1421no—
504C22×C4—1421no—
505C22×C4C2×C4×D7111yescharacteristic
506C22×C4C2×C4×D7111yescharacteristic
507C22×C4C2×C4×D7111yescharacteristic
508C22×C4C2×C4×D7111yescharacteristic
509C22×C4C2×C4×D7111yescharacteristic
510C22×C4C2×C4×D7111yescharacteristic
511C22×C4C23×D7111yescharacteristic
512M16—2844no—
513M16—2844no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—2844no—
526C2×C8—2844no—
527C2×C8—712no—
528C2×C8—1421no—
529C2×C8—1421no—
530C2×C8—1421no—
531C2×C8—1421no—
532C2×C8—1421no—
533C2×C8—1421no—
534C2×C8—1421no—
535C2×C8—1421no—
536C2×C8—1421no—
537C2×C8—1421no—
538C2×C8—1421no—
539C2×C8#1176586612yes—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—2841no—
543C4⋊C4—2841no—
544C4⋊C4—2841no—
545C4⋊C4—2841no—
546C4⋊C4—714no—
547C22⋊C4—2841no—
548C22⋊C4—2841no—
549C22⋊C4—2841no—
550C22⋊C4—2841no—
551C22⋊C4—2841no—
552C22⋊C4—2841no—
553C22⋊C4—714no—
554C22⋊C4—714no—
555C22⋊C4—1422no—
556C22⋊C4—1422no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—2841no—
562C42—2841no—
563C42—2841no—
564C42—1422no—
565C42—1421no—
566C42—1421no—
567C42—1421no—
568C42—1421no—
569C42D4×D7112yes—
570C42Q8×D7112yes—
571C23—712no—
572C23—712no—
573C23—1421no—
574C23—1421no—
575C23—1421no—
576C23—1421no—
577C23—1421no—
578C23—1421no—
579C23—1421no—
580C23—1421no—
581C23—1421no—
582C23—1421no—
583C23—1421no—
584C23—1421no—
585C23C22×C4×D7111yescharacteristic
586D4—2844no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—712no—
604C2×C4—712no—
605C2×C4—712no—
606C2×C4—1421no—
607C2×C4—1421no—
608C2×C4—1421no—
609C2×C4—1421no—
610C2×C4—1421no—
611C2×C4—1421no—
612C2×C4—1421no—
613C2×C4—1421no—
614C2×C4—1421no—
615C2×C4—1421no—
616C2×C4—1421no—
617C2×C4—1421no—
618C2×C4—1421no—
619C2×C4—1421no—
620C2×C4—1421no—
621C2×C4—1422no—
622C2×C4—1422no—
623C2×C4—1422no—
624C2×C4—1422no—
625C2×C4—1422no—
626C2×C4—1422no—
627C2×C4—1422no—
628C2×C4—1422no—
629C2×C4C4⋊C4×D7112yes—
630C2×C4C4⋊C4×D7112yes—
631C2×C4C2×D4×D7111yescharacteristic
632C2×C4C2×Q8×D7111yescharacteristic
633C2×C4#41×D7111yescharacteristic
634C2×C4C2×#1176586611yescharacteristic
635C2×C4#1455617311yescharacteristic
636C2×C4#1455617411yescharacteristic
637C8—22no—
638C8—41no—
639C8—41no—
640C8—41no—
641C8—2841no—
642C8—2841no—
643C8—2841no—
644C8—1422no—
645C22—2841no—
646C22—2841no—
647C22—2841no—
648C22—2841no—
649C22—2841no—
650C22—2841no—
651C22—2841no—
652C22—2841no—
653C22—1422no—
654C22—1422no—
655C22—1422no—
656C22—1422no—
657C22—1422no—
658C22—1422no—
659C22C2×C4⋊C4×D7111yescharacteristic
660C22C4×#1176586611yescharacteristic
661C22#1798647111yescharacteristic
662C22#131×D7111yescharacteristic
663C22#1798676411yescharacteristic
664C22#1798676511yescharacteristic
665C22#1798676511yescharacteristic
666C4—22no—
667C4—22no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—2841no—
673C4—2841no—
674C4—2841no—
675C4—1422no—
676C4—1422no—
677C4—1422no—
678C4#1798664011yescharacteristic
679C4#1798664611yescharacteristic
680C4#1798670511yescharacteristic
681C4#1798671011yescharacteristic
682C2—2842no—
683C2—2842no—
684C2#2259124911yescharacteristic
685C2#2259690211yescharacteristic
686C2#2259690711yescharacteristic
687C2#2259732411yescharacteristic
688C2#2259733311yescharacteristic
689C2#2259740811yescharacteristic
690C2#2259741211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1940C2
prime radicalC22×D284C2×C4
cosocleC22×C4×C71C24
hypercenter#1940D71
hypocenterC71#22702
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
4. #22589064C2semidirect
5. #22588524C2semidirect
6. #22588521C2semidirect
7. #22588519C2semidirect
8. #22588516C2semidirect
9. #22588456C2semidirect
10. #22588321C2semidirect
11. #22588321C2semidirect
12. #22588194C2semidirect
13. #22588035C2semidirect
14. #22588035C2semidirect
15. C71×#1940C2semidirect
350. #1940D71semidirect
361. C71#22702semidirect

Maximal subgroups

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

subgroupindex
C2×#179860722
C2×#179860692
#225908012
#225890642
#225885242
#225885212
#225885192
#225885162
#225884562
#225883212
#225881942
#225880352
C71×#19402
#2270271