Finite Group Databasebeta

← #32015602

Subgroups — #32015602

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×#17986070C211yesmaximal, characteristic
2C2×#17986038C211yesmaximal, characteristic, complemented
3#22591265C211yesmaximal, characteristic
4C4⋊C4×C22⋊D71C211yesmaximal, characteristic
5#22589109C211yesmaximal, characteristic, complemented
6#22589100C211yesmaximal, characteristic, complemented
7#22588538C211yesmaximal, characteristic, complemented
8#22588533C211yesmaximal, characteristic, complemented
9#22588531C211yesmaximal, characteristic, complemented
10#22588528C211yesmaximal, characteristic, complemented
11#22588505C211yesmaximal, characteristic, complemented
12#22588370C211yesmaximal, characteristic, complemented
13#22588369C211yesmaximal, characteristic, complemented
14#22588240C211yesmaximal, characteristic, complemented
15C22×#106×C71C211yesmaximal, characteristic, complemented
16C22×#11765848C2211yescharacteristic
17C2×C4×C22⋊D71—21no—
18C2×C4×C22⋊D71C2211yescharacteristic
19C2×#14556086C2211yescharacteristic
20C2×C4⋊C4×D71C2211yescharacteristic
21#17986070C418yescomplemented
22#17986038—24no—
23C2×#14556062C2211yescharacteristic
24C2×#14556062C2211yescharacteristic
25C2×#14556061C2211yescharacteristic
26C2×#14556061C2211yescharacteristic
27C2×#14556059C2211yescharacteristic
28C2×#14556059C2211yescharacteristic
29C2×Dic71⋊C8C2211yescharacteristic
30C2×C22⋊(C71⋊C8)C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×#14556038C2211yescharacteristic
33#17985894—21no—
34#17985889—21no—
35#17985880—21no—
36#17985878—21no—
37#17985872—21no—
38#17985870—21no—
39#17985868C2211yescharacteristic
40#17985864C2211yescharacteristic
41#17985859C2211yescharacteristic
42#17985859C2211yescharacteristic
43#17985856C2211yescharacteristic
44#17985856C2211yescharacteristic
45C4⋊C4×Dic71C2211yescharacteristic
46C4⋊C4×Dic71C2211yescharacteristic
47C4×C22⋊Dic71—21no—
48#17985762C2211yescharacteristic
49#17985762C2211yescharacteristic
50#17985761C2211yescharacteristic
51#17985761C2211yescharacteristic
52#17985761C2211yescharacteristic
53#17985761C2211yescharacteristic
54C23×C8×C71C2211yescharacteristic
55C22×C4⋊C4×C71C2211yescharacteristic
56C22×C4⋊C4×C71C2211yescharacteristic
57C2×#106×C71—24no—
58C2×#106×C71C2211yescharacteristic
59C2×#106×C71C2211yescharacteristic
60C2×#106×C71C2211yescharacteristic
61C2×#106×C71C2211yescharacteristic
62C22×C22⋊D71D411yescharacteristic
63C22×C4×D71—21no—
64C22×C4×D71C2311yescharacteristic
65C2×#11765848—22no—
66C2×#11765848—22no—
67C2×#11765848C2×C414yescomplemented
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C4×C22⋊D71—44no—
71C4×C22⋊D71C2×C414yes—
72C4×C22⋊D71Q814yes—
73#14556086—22no—
74#14556086—41no—
75C2×C4⋊Dic71C2311yescharacteristic
76C2×C4⋊Dic71C2311yescharacteristic
77C2×C4⋊Dic71C2311yescharacteristic
78C2×C4⋊Dic71C2311yescharacteristic
79C2×Dic71⋊C4—21no—
80C2×Dic71⋊C4—21no—
81C2×Dic71⋊C4—21no—
82C2×Dic71⋊C4D411yescharacteristic
83C4⋊C4×D71—22no—
84C4⋊C4×D71—41no—
85C2×C22⋊Dic71—21no—
86C2×C22⋊Dic71—21no—
87C2×C22⋊Dic71D411yescharacteristic
88C2×(C2×D71)⋊C4—21no—
89C2×(C2×D71)⋊C4—21no—
90C2×(C2×D71)⋊C4—21no—
91C2×(C2×D71)⋊C4D411yescharacteristic
92C2×C4×Dic71—21no—
93C2×C4×Dic71—21no—
94C2×C4×Dic71—21no—
95C2×C4×Dic71C2311yescharacteristic
96#14556062—22no—
97#14556062—22no—
98#14556061—22no—
99#14556061—41no—
100#14556059—22no—
101#14556059—41no—
102Dic71⋊C8C2×C414yescomplemented
103C22⋊(C71⋊C8)C2×C414yescomplemented
104(C2×D71)⋊C8C2×C414yescomplemented
105#14556038C2×C414yescomplemented
106C71⋊#95—21no—
107C71⋊#95—21no—
108C71⋊#95—21no—
109C71⋊#95—21no—
110C71⋊#95—21no—
111C71⋊#95—21no—
112C71⋊#95—21no—
113C71⋊#95—21no—
114C23×C4×C71—21no—
115C23×C4×C71—21no—
116C23×C4×C71C2311yescharacteristic
117C22×C8×C71—22no—
118C22×C8×C71—22no—
119C22×C8×C71C2×C414yescomplemented
120C22×C8×C71C2311yescharacteristic
121C22×C8×C71C2311yescharacteristic
122C2×C4⋊C4×C71—22no—
123C2×C4⋊C4×C71—22no—
124C2×C4⋊C4×C71—21no—
125C2×C4⋊C4×C71—21no—
126C2×C4⋊C4×C71—41no—
127C2×C4⋊C4×C71—41no—
128C2×C4⋊C4×C71C2311yescharacteristic
129C2×C4⋊C4×C71C2311yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C4⋊C4×C71C2311yescharacteristic
132#106×C71—22no—
133#106×C71—22no—
134#106×C71—22no—
135#106×C71D414yescomplemented
136C23×D71C2×D411yescharacteristic
137C2×C22⋊D71—22no—
138C2×C22⋊D71—22no—
139C2×C22⋊D71C4⋊C414yes—
140C22×Dic71—21no—
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71C2×D411yescharacteristic
145C22×Dic71C2×D411yescharacteristic
146C22×Dic71C2×D411yescharacteristic
147C2×C4×D71—21no—
148C2×C4×D71—21no—
149C2×C4×D71—21no—
150C2×C4×D71—21no—
151C2×C4×D71—42no—
152C2×C4×D71—42no—
153C2×C4×D71—81no—
154C2×C4×D71C22×C412yes—
155C2×C4×D71C2×Q812yes—
156#11765848—28no—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—21no—
161C2×C71⋊C8C22×C412yes—
162C2×C71⋊C8C22×C412yes—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71—21no—
166C4⋊Dic71—21no—
167C4⋊Dic71—21no—
168C4⋊Dic71—21no—
169C4⋊Dic71—21no—
170C4⋊Dic71—21no—
171Dic71⋊C4—42no—
172Dic71⋊C4—42no—
173Dic71⋊C4—81no—
174Dic71⋊C4C4⋊C414yes—
175C22⋊Dic71—42no—
176C22⋊Dic71—42no—
177C22⋊Dic71C4⋊C414yes—
178(C2×D71)⋊C4—42no—
179(C2×D71)⋊C4—42no—
180(C2×D71)⋊C4—81no—
181(C2×D71)⋊C4C4⋊C414yes—
182C4×Dic71—42no—
183C4×Dic71—42no—
184C4×Dic71—81no—
185C4×Dic71C22×C412yes—
186C4×Dic71C2×Q812yes—
187C24×C71C2×D411yescharacteristic
188C22×C4×C71—21no—
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×Q812yes—
205C22×C4×C71C2411yescharacteristic
206C2×C8×C71—21no—
207C2×C8×C71—21no—
208C2×C8×C71—28no—
209C2×C8×C71C22×C412yes—
210C2×C8×C71C22×C412yes—
211C2×C8×C71C2×D412yes—
212C2×C8×C71#4112yes—
213C4⋊C4×C71—21no—
214C4⋊C4×C71—21no—
215C4⋊C4×C71—21no—
216C4⋊C4×C71—21no—
217C4⋊C4×C71—21no—
218C4⋊C4×C71—21no—
219C4⋊C4×C71—42no—
220C4⋊C4×C71—42no—
221C4⋊C4×C71C2×D412yes—
222C4⋊C4×C71C2×D412yes—
223C23×C71—21no—
224C23×C71—21no—
225C23×C71—21no—
226C23×C71—21no—
227C23×C71C2×C4⋊C412yes—
228C23×C71AGL(1,ℤ/8)12yes—
229C23×C71#13712yes—
230C23×C71C22×D411yescharacteristic
231C22×D71—21no—
232C22×D71—21no—
233C22×D71—21no—
234C22×D71—21no—
235C22×D71—21no—
236C22×D71—21no—
237C22×D71C2×C4⋊C412yes—
238C2×C4×C71—21no—
239C2×C4×C71—21no—
240C2×C4×C71—22no—
241C2×C4×C71—22no—
242C2×C4×C71—22no—
243C2×C4×C71—22no—
244C2×C4×C71—22no—
245C2×C4×C71—22no—
246C2×C4×C71—41no—
247C2×C4×C71—41no—
248C2×C4×C71—41no—
249C2×C4×C71—41no—
250C2×C4×C71—41no—
251C2×C4×C71—41no—
252C2×C4×C71—41no—
253C2×C4×C71—41no—
254C2×C4×C71—41no—
255C2×C4×C71—41no—
256C2×C4×C71—84no—
257C2×C4×C71—84no—
258C2×C4×C71C2×C4⋊C412yes—
259C2×C4×C71C23×C411yescharacteristic
260C2×C4×C71C22×D411yescharacteristic
261C2×C4×C71C22×Q811yescharacteristic
262C2×C4×C71C2×#4111yescharacteristic
263C2×C4×C71H(5,𝔽2)11yescharacteristic
264C2×C4×C712−1+411yescharacteristic
265C22⋊D71—28no—
266C2×Dic71—21no—
267C2×Dic71—21no—
268C2×Dic71—21no—
269C2×Dic71—21no—
270C2×Dic71—21no—
271C2×Dic71—21no—
272C2×Dic71—41no—
273C2×Dic71—41no—
274C2×Dic71—41no—
275C2×Dic71—41no—
276C2×Dic71—41no—
277C2×Dic71—41no—
278C2×Dic71—41no—
279C2×Dic71—41no—
280C2×Dic71—41no—
281C2×Dic71—41no—
282C2×Dic71—41no—
283C2×Dic71—41no—
284C2×Dic71C2×C4⋊C412yes—
285C2×Dic71C2×C4⋊C412yes—
286C2×Dic71C2×C4⋊C412yes—
287C4×D71—22no—
288C4×D71—22no—
289C4×D71—22no—
290C4×D71—22no—
291C4×D71—84no—
292C8×C71—22no—
293C8×C71C4×D414yescomplemented
294C71⋊C8—22no—
295C71⋊C8—22no—
296C22×C71—22no—
297C22×C71—22no—
298C22×C71—22no—
299C22×C71—22no—
300C22×C71—22no—
301C22×C71—22no—
302C22×C71#42814yescomplemented
303C22×C71C22×C4⋊C411yescharacteristic
304C22×C71D4211yescharacteristic
305C22×C71#54711yescharacteristic
306C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C71C2×#13711yescharacteristic
308C22×C71#57711yescharacteristic
309C22×C71#57711yescharacteristic
310C2×D71—22no—
311C2×D71—22no—
312C2×D71—22no—
313C2×D71—41no—
314C2×D71—41no—
315C2×D71—41no—
316C2×D71—41no—
317C4×C71—22no—
318C4×C71—42no—
319C4×C71—42no—
320C4×C71—81no—
321C4×C71—81no—
322C4×C71C2×C4×D411yescharacteristic
323C4×C71#52011yescharacteristic
324C4×C71D4×Q811yescharacteristic
325C4×C71#55411yescharacteristic
326Dic71—22no—
327Dic71—22no—
328Dic71—22no—
329Dic71—81no—
330Dic71—81no—
331Dic71—81no—
332Dic71—81no—
333#22659—711nomaximal, Sylow
334C2×C71—24no—
335C2×C71D4×C4⋊C411yescharacteristic
336C2×C71C2×#42811yescharacteristic
337C2×C71#291211yescharacteristic
338C2×C71#326511yescharacteristic
339C2×C71#326611yescharacteristic
340C2×C71#334411yescharacteristic
341C2×C71#334511yescharacteristic
342D71—42no—
343C2×#435—711no—
344C2×#428—711no—
345C22×#106D7111yescharacteristic, complemented
346#2352—711no—
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×C8C2×D7111yescharacteristic
361C2×C4×D4—711no—
362C2×C4×D4—1421no—
363C2×#117—711no—
364C22×C4⋊C4—711no—
365C22×C4⋊C4C2×D7111yescharacteristic
366C22×C4⋊C4C2×D7111yescharacteristic
367#435—718no—
368#428—1424no—
369C2×#107—711no—
370C2×#107—711no—
371C2×#107—711no—
372C2×#107—711no—
373C2×#106—24no—
374C2×#106—711no—
375C2×#106—711no—
376C2×#106C2×D7111yescharacteristic
377C2×#106C2×D7111yescharacteristic
378C2×#106C2×D7111yescharacteristic
379C2×#106C2×D7111yescharacteristic
380C2×C4⋊C8—711no—
381C2×C22⋊C8—711no—
382C2×C22⋊C8—711no—
383C2×#97—711no—
384#389—1421no—
385#388—1421no—
386#387—1421no—
387#386—1421no—
388#385—1421no—
389#385—1421no—
390#384—711no—
391#382—711no—
392#380—711no—
393#380—711no—
394#380—711no—
395#380—711no—
396C4×C4⋊C4—711no—
397C4×C4⋊C4—711no—
398C4×C22⋊C4—1421no—
399#340—711no—
400#340—711no—
401#340—711no—
402#340—711no—
403#340—711no—
404#340—711no—
405C22×D4—711no—
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—711no—
409C23×C4—1421no—
410C23×C4C22×D7111yescharacteristic
411C2×M16—714no—
412C2×M16—1422no—
413C2×M16—1422no—
414C22×C8—22no—
415C22×C8—22no—
416C22×C8—711no—
417C22×C8—711no—
418C22×C8C4×D7114yescomplemented
419C22×C8C22×D7111yescharacteristic
420C22×C8C22×D7111yescharacteristic
421C4×D4—2844no—
422C4×D4—714no—
423C4×D4—714no—
424#117—2841no—
425#117—1422no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—2841no—
433C2×C4⋊C4—711no—
434C2×C4⋊C4—711no—
435C2×C4⋊C4—711no—
436C2×C4⋊C4—711no—
437C2×C4⋊C4—711no—
438C2×C4⋊C4—1421no—
439C2×C4⋊C4—1421no—
440C2×C4⋊C4—1422no—
441C2×C4⋊C4—1421no—
442C2×C4⋊C4C22×D7111yescharacteristic
443C2×C4⋊C4C22×D7111yescharacteristic
444C2×C4⋊C4C22×D7111yescharacteristic
445C2×C4⋊C4C22×D7111yescharacteristic
446C2×C22⋊C4—711no—
447C2×C22⋊C4—711no—
448C2×C22⋊C4—1421no—
449C2×C22⋊C4—1421no—
450C2×C22⋊C4—1421no—
451C2×C22⋊C4—1421no—
452C2×C22⋊C4—1421no—
453C2×C42—711no—
454C2×C42—1421no—
455C2×C42—1421no—
456C2×C42—1421no—
457#107—2841no—
458#107—1422no—
459#107—1422no—
460#107—1422no—
461#106—22no—
462#106—22no—
463#106—22no—
464#106—2841no—
465#106—1422no—
466#106C22⋊D7114yescomplemented
467C4⋊C8—714no—
468C22⋊C8—714no—
469C22⋊C8—714no—
470#97—714no—
471#95—1421no—
472#95—1421no—
473#95—1421no—
474#95—1421no—
475#95—1421no—
476#95—1421no—
477#95—1421no—
478#95—1421no—
479C24—711no—
480C24D4×D7111yescharacteristic
481C2×D4—714no—
482C2×D4—1422no—
483C2×D4—1422no—
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—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—2842no—
499C22×C4—2842no—
500C22×C4—5681no—
501C22×C4—711no—
502C22×C4—711no—
503C22×C4—711no—
504C22×C4—712no—
505C22×C4—712no—
506C22×C4—1421no—
507C22×C4—1421no—
508C22×C4—1421no—
509C22×C4—1421no—
510C22×C4—1421no—
511C22×C4—1421no—
512C22×C4—1421no—
513C22×C4—1421no—
514C22×C4C2×C4×D7112yes—
515C22×C4D4×D7111yescharacteristic
516C22×C4Q8×D7112yes—
517C22×C4C23×D7111yescharacteristic
518M16—1428no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—28no—
522C2×C8—712no—
523C2×C8—712no—
524C2×C8—1421no—
525C2×C8—1421no—
526C2×C8—1421no—
527C2×C8—1421no—
528C2×C8C2×C4×D7112yes—
529C2×C8C2×C4×D7112yes—
530C2×C8C2×C22⋊D7112yes—
531C2×C8#1176586512yes—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—2842no—
541C4⋊C4—2842no—
542C4⋊C4—5681no—
543C4⋊C4—714no—
544C4⋊C4—1421no—
545C4⋊C4—1421no—
546C4⋊C4—1421no—
547C4⋊C4—1421no—
548C4⋊C4—1421no—
549C4⋊C4—1421no—
550C4⋊C4—1421no—
551C4⋊C4—1421no—
552C4⋊C4C2×C22⋊D7112yes—
553C4⋊C4C2×C22⋊D7112yes—
554C22⋊C4—2842no—
555C22⋊C4—2842no—
556C22⋊C4—2842no—
557C22⋊C4—2842no—
558C22⋊C4—5681no—
559C22⋊C4—714no—
560C22⋊C4—714no—
561C42—2842no—
562C42—2842no—
563C42—5681no—
564C42—712no—
565C42—712no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—712no—
571C23—1421no—
572C23—1421no—
573C23—1421no—
574C23—1421no—
575C23—1421no—
576C23—1421no—
577C23C4⋊C4×D7112yes—
578C23#1455615512yes—
579C23#1455615712yes—
580C23C2×D4×D7111yescharacteristic
581D4—1428no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4—2841no—
603C2×C4—2841no—
604C2×C4—2841no—
605C2×C4—2841no—
606C2×C4—2841no—
607C2×C4—2841no—
608C2×C4—2841no—
609C2×C4—2841no—
610C2×C4—2841no—
611C2×C4—2841no—
612C2×C4—2841no—
613C2×C4—2841no—
614C2×C4—5684no—
615C2×C4—712no—
616C2×C4—712no—
617C2×C4—712no—
618C2×C4—1421no—
619C2×C4—1421no—
620C2×C4—1421no—
621C2×C4—1421no—
622C2×C4—1421no—
623C2×C4—1421no—
624C2×C4—1422no—
625C2×C4—1422no—
626C2×C4—1422no—
627C2×C4—1422no—
628C2×C4C4⋊C4×D7112yes—
629C2×C4C22×C4×D7111yescharacteristic
630C2×C4C22×C22⋊D7111yescharacteristic
631C2×C4C2×Q8×D7111yescharacteristic
632C2×C4C2×#1176586511yescharacteristic
633C2×C4#1455617311yescharacteristic
634C2×C4#1455617611yescharacteristic
635C8—22no—
636C8—1422no—
637C8—1422no—
638C8C4×C22⋊D7114yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—2841no—
646C22—2841no—
647C22—2841no—
648C22—2841no—
649C22—1422no—
650C22—1422no—
651C22—1422no—
652C22#1798603814yescomplemented
653C22C2×C4⋊C4×D7111yescharacteristic
654C22D4×C22⋊D7111yescharacteristic
655C22#1798665011yescharacteristic
656C22C2×#1455615511yescharacteristic
657C22C2×#1455615711yescharacteristic
658C22#1798680511yescharacteristic
659C22#1798680511yescharacteristic
660C4—22no—
661C4—42no—
662C4—42no—
663C4—81no—
664C4—81no—
665C4—5681no—
666C4—5681no—
667C4—5681no—
668C4—5681no—
669C4—1422no—
670C4—1422no—
671C4—1422no—
672C4C2×C4×C22⋊D7111yescharacteristic
673C4#1798648011yescharacteristic
674C4Q8×C22⋊D7111yescharacteristic
675C4#1798670411yescharacteristic
676C2—24no—
677C2—2842no—
678C2C4⋊C4×C22⋊D7111yescharacteristic
679C2C2×#1798603811yescharacteristic
680C2#2259693111yescharacteristic
681C2#2259983511yescharacteristic
682C2#2259985011yescharacteristic
683C2#2260079111yescharacteristic
684C2#2260080611yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC22×#106×C71C2
socleC23×C71C22×D4
prime radicalC22×C22⋊D71D4
cosocleC22×C4×C71C24
hypercenterC22×#106D71
hypocenterC71#22659
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#17986038C2semidirect
5. #22589109C2semidirect
6. #22589100C2semidirect
7. #22588538C2semidirect
8. #22588533C2semidirect
9. #22588531C2semidirect
10. #22588528C2semidirect
11. #22588505C2semidirect
12. #22588370C2semidirect
13. #22588369C2semidirect
14. #22588240C2semidirect
15. C22×#106×C71C2semidirect
21. #17986070C4semidirect
67. C2×#11765848C2×C4semidirect
102. Dic71⋊C8C2×C4semidirect
103. C22⋊(C71⋊C8)C2×C4semidirect
104. (C2×D71)⋊C8C2×C4semidirect
105. #14556038C2×C4semidirect
119. C22×C8×C71C2×C4semidirect
135. #106×C71D4semidirect
293. C8×C71C4×D4semidirect
302. C22×C71#428semidirect
345. C22×#106D71semidirect
358. C71#22659semidirect
418. C22×C8C4×D71semidirect
466. #106C22⋊D71semidirect
638. C8C4×C22⋊D71semidirect
652. C22#17986038semidirect

Maximal subgroups

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

subgroupindex
C2×#179860702
C2×#179860382
#225912652
C4⋊C4×C22⋊D712
#225891092
#225891002
#225885382
#225885332
#225885312
#225885282
#225885052
#225883702
#225883692
#225882402
C22×#106×C712
#2265971