Finite Group Databasebeta

← #31996853

Subgroups — #31996853

Order 18176.

1690 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×#17986471C211yesmaximal, characteristic
2C2×#99×D71C212yesmaximal
3#22590953C212yesmaximal, complemented
4#22588328C211yesmaximal, characteristic, complemented
5#22588327C212yesmaximal, complemented
6#22588326C212yesmaximal, complemented
7#22588325C212yesmaximal, complemented
8#342×D71C212yesmaximal, complemented
9C71×#1799C211yesmaximal, characteristic, complemented
10C22×D4×D71C2211yescharacteristic
11#17986471—24no—
12#17986471—24no—
13C2×C4×D284C411yescharacteristic, complemented
14C2×D4×Dic71C2211yescharacteristic
15C2×#14556090C411yescharacteristic, complemented
16C2×C4×C22⋊D71C411yescharacteristic, complemented
17C2×C4×C22⋊D71C2211yescharacteristic
18C2×(C22⋊D71)⋊C4C411yescharacteristic, complemented
19C2×(C22⋊D71)⋊C4C2211yescharacteristic
20C2×#14556086C411yescharacteristic, complemented
21C2×#14556085C411yescharacteristic, complemented
22C22×(C2×D71)⋊C4C411yescharacteristic, complemented
23C22×(C2×D71)⋊C4C2211yescharacteristic
24C2×C22⋊C4×D71C411yescharacteristic, complemented
25C2×C22⋊C4×D71C2214yes—
26C2×C22⋊C4×D71C2211yescharacteristic
27C2×#14556043C2212yes—
28C2×#14556042C2214yes—
29#99×D71—28no—
30#17985873—24no—
31#17985870—24no—
32#17985859C2212yescomplemented
33#17985857C2214yescomplemented
34#17985766C2212yescomplemented
35#17985765C2214yescomplemented
36C2×C4×D4×C71C2211yescharacteristic
37C2×#99×C71C2212yes—
38#380×C71C2212yescomplemented
39#342×C71C2212yescomplemented
40C24×D71C2×C411yescharacteristic
41C24×D71C2311yescharacteristic
42C22×D284C2×C411yescharacteristic
43C22×C22⋊D71C2×C411yescharacteristic
44C22×C22⋊D71C2311yescharacteristic
45C2×D4×D71—24no—
46C2×D4×D71—24no—
47C2×D4×D71D414yes—
48C2×D4×D71Q814yes—
49C23×Dic71C2×C411yescharacteristic, complemented
50C23×Dic71C2311yescharacteristic
51C22×C4×D71—24no—
52C22×C4×D71C2×C411yescharacteristic
53C22×C4×D71C2×C411yescharacteristic
54C22×C4×D71C2×C411yescharacteristic
55C22×C4×D71C2×C411yescharacteristic, complemented
56C22×C4×D71C2×C411yescharacteristic, complemented
57C4×D284—22no—
58C4×D284—22no—
59D4×Dic71—24no—
60#14556090—24no—
61C4×C22⋊D71—22no—
62C4×C22⋊D71—22no—
63C4×C22⋊D71—22no—
64C4×C22⋊D71—22no—
65(C22⋊D71)⋊C4—24no—
66(C22⋊D71)⋊C4—24no—
67#14556086—24no—
68#14556085—22no—
69#14556085—22no—
70C2×C4⋊Dic71—22no—
71C2×C4⋊Dic71C2×C411yescharacteristic, complemented
72C2×Dic71⋊C4—24no—
73C2×Dic71⋊C4C2×C411yescharacteristic, complemented
74C2×Dic71⋊C4C2×C411yescharacteristic, complemented
75C2×C22⋊Dic71C2×C411yescharacteristic, complemented
76C2×C22⋊Dic71C2314yes—
77C2×C22⋊Dic71C2311yescharacteristic
78C2×(C2×D71)⋊C4—22no—
79C2×(C2×D71)⋊C4—22no—
80C2×(C2×D71)⋊C4—24no—
81C2×(C2×D71)⋊C4C2×C411yescharacteristic
82C2×(C2×D71)⋊C4C2×C411yescharacteristic
83C2×(C2×D71)⋊C4C2×C411yescharacteristic
84C2×(C2×D71)⋊C4C2×C411yescharacteristic
85C2×(C2×D71)⋊C4C2×C411yescharacteristic
86C2×(C2×D71)⋊C4C2×C411yescharacteristic
87C2×(C2×D71)⋊C4C2×C411yescharacteristic, complemented
88C2×(C2×D71)⋊C4C2×C411yescharacteristic, complemented
89C2×(C2×D71)⋊C4D414yes—
90C2×(C2×D71)⋊C4D414yes—
91C22⋊C4×D71—24no—
92C22⋊C4×D71—24no—
93C22⋊C4×D71—28no—
94C22⋊C4×D71—28no—
95C2×C4×Dic71C2×C411yescharacteristic, complemented
96C2×C4×Dic71C2×C411yescharacteristic, complemented
97C2×C4×Dic71C2×C411yescharacteristic, complemented
98#14556043—24no—
99#14556042—28no—
100C71⋊#95—24no—
101C71⋊#95—22no—
102C22×D4×C71C2311yescharacteristic
103C23×C4×C71C2×C411yescharacteristic, complemented
104C23×C4×C71C2311yescharacteristic
105C4×D4×C71—22no—
106C4×D4×C71—22no—
107C2×C4⋊C4×C71—22no—
108C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
109C2×C22⋊C4×C71C2×C411yescharacteristic, complemented
110C2×C22⋊C4×C71C2314yes—
111C2×C22⋊C4×C71C2311yescharacteristic
112C2×C42×C71C2×C411yescharacteristic, complemented
113#99×C71—24no—
114#95×C71—22no—
115C23×D71—22no—
116C23×D71—22no—
117C23×D71—81no—
118C23×D71—81no—
119C23×D71—81no—
120C23×D71—81no—
121C23×D71C4⋊C414yescomplemented
122C23×D71C22×C411yescharacteristic
123C23×D71C22×C411yescharacteristic
124C23×D71C22×C411yescharacteristic
125C23×D71C2×D414yes—
126C23×D71C2×D412yes—
127C23×D71C2×Q812yes—
128C23×D71#4114yes—
129C2×D284—22no—
130C2×D284—22no—
131C2×D284C4⋊C414yescomplemented
132C2×C22⋊D71—22no—
133C2×C22⋊D71—22no—
134C2×C22⋊D71—22no—
135C2×C22⋊D71—22no—
136C2×C22⋊D71C4⋊C414yescomplemented
137C2×C22⋊D71C2×D412yes—
138C2×C22⋊D71C2×Q812yes—
139D4×D71—216no—
140D4×D71—216no—
141C22×Dic71—22no—
142C22×Dic71—24no—
143C22×Dic71—81no—
144C22×Dic71—81no—
145C22×Dic71C22×C411yescharacteristic
146C22×Dic71C22×C411yescharacteristic
147C22×Dic71C22×C411yescharacteristic
148C22×Dic71C22×C411yescharacteristic
149C22×Dic71C22×C411yescharacteristic
150C22×Dic71C2×D414yes—
151C2×C4×D71—22no—
152C2×C4×D71—22no—
153C2×C4×D71—22no—
154C2×C4×D71—22no—
155C2×C4×D71—22no—
156C2×C4×D71—22no—
157C2×C4×D71—48no—
158C2×C4×D71—84no—
159C2×C4×D71—84no—
160C2×C4×D71—81no—
161C2×C4×D71—81no—
162C2×C4×D71—81no—
163C2×C4×D71—81no—
164C2×C4×D71C4⋊C414yescomplemented
165C4⋊Dic71—22no—
166C4⋊Dic71—82no—
167Dic71⋊C4—21no—
168Dic71⋊C4—21no—
169Dic71⋊C4—22no—
170Dic71⋊C4—84no—
171C22⋊Dic71—22no—
172C22⋊Dic71—22no—
173C22⋊Dic71—24no—
174C22⋊Dic71—24no—
175(C2×D71)⋊C4—22no—
176(C2×D71)⋊C4—22no—
177(C2×D71)⋊C4—21no—
178(C2×D71)⋊C4—21no—
179(C2×D71)⋊C4—22no—
180(C2×D71)⋊C4—48no—
181(C2×D71)⋊C4C22⋊C414yes—
182(C2×D71)⋊C4C22⋊C412yes—
183(C2×D71)⋊C4C22⋊C412yes—
184(C2×D71)⋊C4C22⋊C414yes—
185(C2×D71)⋊C4C22⋊C412yes—
186(C2×D71)⋊C4C22⋊C412yes—
187C4×Dic71—22no—
188C4×Dic71—22no—
189C4×Dic71—22no—
190C24×C71C22×C411yescharacteristic
191C24×C71C2411yescharacteristic
192C2×D4×C71—22no—
193C2×D4×C71—22no—
194C2×D4×C71C2×D412yes—
195C2×D4×C71C2×Q812yes—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—24no—
199C22×C4×C71—81no—
200C22×C4×C71—81no—
201C22×C4×C71C22×C411yescharacteristic
202C22×C4×C71C22×C411yescharacteristic
203C22×C4×C71C22×C411yescharacteristic
204C22×C4×C71C22×C411yescharacteristic
205C22×C4×C71C22×C411yescharacteristic
206C22×C4×C71C2×D412yes—
207C22×C4×C71C2×D412yes—
208C4⋊C4×C71—22no—
209C4⋊C4×C71—82no—
210C22⋊C4×C71—22no—
211C22⋊C4×C71—22no—
212C22⋊C4×C71—24no—
213C22⋊C4×C71—24no—
214C42×C71—21no—
215C42×C71—21no—
216C23×C71—21no—
217C23×C71—21no—
218C23×C71—41no—
219C23×C71—41no—
220C23×C71—41no—
221C23×C71—41no—
222C23×C71C2×C4⋊C412yes—
223C23×C71C23×C411yescharacteristic
224C23×C71C22×D412yes—
225C23×C71C22×D411yescharacteristic
226C23×C71C22×Q811yescharacteristic
227C23×C71C2×#4112yes—
228C22×D71—21no—
229C22×D71—21no—
230C22×D71—28no—
231C22×D71—41no—
232C22×D71—41no—
233C22×D71—44no—
234C22×D71—44no—
235C22×D71—41no—
236C22×D71—41no—
237C22×D71—41no—
238C22×D71—41no—
239C22×D71—82no—
240C22×D71—82no—
241C22×D71—82no—
242C22×D71—82no—
243C22×D71—84no—
244C22×D71—84no—
245C22×D71—84no—
246C22×D71C2×C22⋊C412yes—
247C22×D71C2×C22⋊C412yes—
248C22×D71C2×C4⋊C412yes—
249C22×D71C2×C4⋊C412yes—
250C22×D71C2×C4⋊C412yes—
251C22×D71#11712yes—
252C22×D71#11712yes—
253C22×D71#12118yes—
254C22×D71C22⋊Q818yes—
255D4×C71—24no—
256D4×C71—24no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—42no—
262C2×C4×C71—41no—
263C2×C4×C71—41no—
264C2×C4×C71—42no—
265C2×C4×C71—41no—
266C2×C4×C71—41no—
267C2×C4×C71—44no—
268C2×C4×C71—44no—
269C2×C4×C71—44no—
270C2×C4×C71—81no—
271C2×C4×C71—81no—
272C2×C4×C71C2×C22⋊C411yescharacteristic
273C2×C4×C71C2×C22⋊C411yescharacteristic
274C2×C4×C71C2×C22⋊C412yes—
275C2×C4×C71C2×C4⋊C412yes—
276C22⋊D71—24no—
277C22⋊D71—24no—
278C22⋊D71—28no—
279C2×Dic71—21no—
280C2×Dic71—21no—
281C2×Dic71—21no—
282C2×Dic71—21no—
283C2×Dic71—44no—
284C2×Dic71—41no—
285C2×Dic71—41no—
286C2×Dic71—41no—
287C2×Dic71—41no—
288C2×Dic71—44no—
289C2×Dic71—44no—
290C2×Dic71—44no—
291C2×Dic71—82no—
292C2×Dic71C2×C22⋊C412yes—
293C2×Dic71C2×C22⋊C412yes—
294C2×Dic71C2×C4⋊C412yes—
295D284—28no—
296C4×D71—28no—
297C4×D71—82no—
298C4×D71—82no—
299C4×D71—82no—
300C4×D71—82no—
301C4×D71—816no—
302C22×C71—22no—
303C22×C71—21no—
304C22×C71—22no—
305C22×C71—21no—
306C22×C71—22no—
307C22×C71—41no—
308C22×C71—41no—
309C22×C71—42no—
310C22×C71—42no—
311C22×C71—42no—
312C22×C71—41no—
313C22×C71—41no—
314C22×C71C22×C22⋊C411yescharacteristic
315C22×C71C22×C4⋊C411yescharacteristic
316C22×C71C2×#11711yescharacteristic
317C22×C71C2×#12112yes—
318C22×C71C2×C22⋊Q812yes—
319C2×D71—22no—
320C2×D71—22no—
321C2×D71—22no—
322C2×D71—22no—
323C2×D71—22no—
324C2×D71—48no—
325C2×D71—42no—
326C2×D71—42no—
327C2×D71—42no—
328C2×D71—42no—
329C2×D71—48no—
330C2×D71—42no—
331C2×D71—41no—
332C2×D71—41no—
333C2×D71—42no—
334C2×D71—88no—
335C2×D71#38014yes—
336C2×D71#38014yes—
337C4×C71—22no—
338C4×C71—21no—
339C4×C71—21no—
340C4×C71—22no—
341C4×C71—41no—
342C4×C71—41no—
343C4×C71—84no—
344Dic71—22no—
345Dic71—22no—
346Dic71—22no—
347Dic71—41no—
348Dic71—41no—
349Dic71—84no—
350#20633—711nomaximal, Sylow
351C2×C71—22no—
352C2×C71—21no—
353C2×C71—21no—
354C2×C71—22no—
355C2×C71—42no—
356C2×C71C2×#38011yescharacteristic
357C2×C71#288311yescharacteristic
358C2×C71#288311yescharacteristic
359D71—24no—
360D71—24no—
361D71—42no—
362C2×#518—711no—
363C22×#99—712no—
364#2315—712no—
365#1799—712no—
366#1799—712no—
367#1799—712no—
368#1799—711no—
369#1799D7111yescharacteristic, complemented
370C2×#342—712no—
371C71#2063311yescharacteristic, complemented, Sylow
372C23×D4—711no—
373#518—1424no—
374#518—1424no—
375C2×C4×D4—711no—
376C2×C4×D4—711no—
377C2×C4×D4—711no—
378C2×C4×D4—711no—
379C2×C4×D4—711no—
380C2×C4×D4—711no—
381C2×C4×D4—711no—
382C2×C4×D4C2×D7111yescharacteristic
383C2×#117—711no—
384C2×#117—711no—
385C22×C22⋊C4—711no—
386C22×C22⋊C4—711no—
387C22×C22⋊C4—711no—
388C22×C22⋊C4—711no—
389C22×C22⋊C4—714no—
390C2×#99—712no—
391C2×#99—714no—
392C2×#99—1428no—
393C2×#99C2×D7112yes—
394#385—1424no—
395#385—1424no—
396#380—712no—
397#380—714no—
398#380C2×D7112yescomplemented
399#342—714no—
400#342—712no—
401#342C2×D7112yescomplemented
402C25—711no—
403C25—711no—
404C22×D4—711no—
405C22×D4—711no—
406C22×D4—714no—
407C22×D4—714no—
408C22×D4—711no—
409C22×D4—1424no—
410C22×D4—1424no—
411C22×D4C22×D7111yescharacteristic
412C23×C4—711no—
413C23×C4—711no—
414C23×C4—711no—
415C23×C4—711no—
416C23×C4—711no—
417C23×C4—711no—
418C23×C4—711no—
419C23×C4—1424no—
420C23×C4C4×D7111yescharacteristic, complemented
421C23×C4C22×D7111yescharacteristic
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—1422no—
425C4×D4—1422no—
426C4×D4—1424no—
427C4×D4—1424no—
428C4×D4—1424no—
429C4×D4—1422no—
430C4×D4—1422no—
431C4×D4—1424no—
432C4×D4—1422no—
433C4×D4—1422no—
434#117—1422no—
435#117—1422no—
436#117—1424no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—711no—
439C2×C4⋊C4—711no—
440C2×C4⋊C4—711no—
441C2×C4⋊C4—1424no—
442C2×C4⋊C4—1422no—
443C2×C4⋊C4C4×D7111yescharacteristic, complemented
444C2×C22⋊C4—711no—
445C2×C22⋊C4—711no—
446C2×C22⋊C4—711no—
447C2×C22⋊C4—711no—
448C2×C22⋊C4—714no—
449C2×C22⋊C4—714no—
450C2×C22⋊C4—711no—
451C2×C22⋊C4—711no—
452C2×C22⋊C4—711no—
453C2×C22⋊C4—711no—
454C2×C22⋊C4—711no—
455C2×C22⋊C4—711no—
456C2×C22⋊C4—714no—
457C2×C22⋊C4—1428no—
458C2×C22⋊C4—1428no—
459C2×C22⋊C4—1424no—
460C2×C22⋊C4—1424no—
461C2×C22⋊C4—1424no—
462C2×C22⋊C4—1422no—
463C2×C22⋊C4—1422no—
464C2×C22⋊C4C4×D7111yescharacteristic, complemented
465C2×C22⋊C4C22×D7114yes—
466C2×C22⋊C4C22×D7111yescharacteristic
467C2×C42—711no—
468C2×C42—711no—
469C2×C42—711no—
470C2×C42C4×D7111yescharacteristic, complemented
471#99—24no—
472#99—1428no—
473#99—1424no—
474#95—22no—
475#95—1424no—
476#95—1422no—
477C24—5681no—
478C24—5681no—
479C24—5681no—
480C24—5681no—
481C24—711no—
482C24—711no—
483C24—714no—
484C24—711no—
485C24—712no—
486C24—712no—
487C24—714no—
488C24—714no—
489C24—1422no—
490C24—1422no—
491C24C2×C4×D7111yescharacteristic
492C24C23×D7111yescharacteristic
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—712no—
496C2×D4—712no—
497C2×D4—714no—
498C2×D4—714no—
499C2×D4—1422no—
500C2×D4—1422no—
501C2×D4—14216no—
502C2×D4—14216no—
503C2×D4—1422no—
504C2×D4—1422no—
505C2×D4—1422no—
506C2×D4—1422no—
507C2×D4D4×D7112yes—
508C2×D4Q8×D7112yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4—2848no—
515C22×C4—5684no—
516C22×C4—5684no—
517C22×C4—5681no—
518C22×C4—5681no—
519C22×C4—5681no—
520C22×C4—5681no—
521C22×C4—5681no—
522C22×C4—5681no—
523C22×C4—711no—
524C22×C4—711no—
525C22×C4—714no—
526C22×C4—711no—
527C22×C4—711no—
528C22×C4—711no—
529C22×C4—714no—
530C22×C4—1422no—
531C22×C4—1422no—
532C22×C4—1422no—
533C22×C4—1422no—
534C22×C4—1422no—
535C22×C4—1424no—
536C22×C4—1422no—
537C22×C4—1422no—
538C22×C4C2×C4×D7111yescharacteristic
539C22×C4C2×C4×D7111yescharacteristic
540C22×C4C2×C4×D7111yescharacteristic
541C22×C4C2×C4×D7111yescharacteristic
542C22×C4C2×C4×D7111yescharacteristic
543C22×C4D4×D7112yes—
544C22×C4D4×D7112yes—
545C4⋊C4—22no—
546C4⋊C4—82no—
547C4⋊C4—5684no—
548C4⋊C4—5682no—
549C4⋊C4—1422no—
550C4⋊C4—1422no—
551C4⋊C4—1421no—
552C4⋊C4—1421no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—2848no—
558C22⋊C4—712no—
559C22⋊C4—712no—
560C22⋊C4—714no—
561C22⋊C4—712no—
562C22⋊C4—712no—
563C22⋊C4—714no—
564C22⋊C4—1422no—
565C22⋊C4—1422no—
566C22⋊C4—1422no—
567C22⋊C4—1424no—
568C22⋊C4—1424no—
569C22⋊C4—1422no—
570C22⋊C4—1422no—
571C22⋊C4—1421no—
572C22⋊C4—1421no—
573C42—21no—
574C42—21no—
575C42—1422no—
576C42—1422no—
577C42—1422no—
578C23—21no—
579C23—21no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—2841no—
585C23—2841no—
586C23—2844no—
587C23—2841no—
588C23—2844no—
589C23—2841no—
590C23—2841no—
591C23—2841no—
592C23—5682no—
593C23—5682no—
594C23—5684no—
595C23—5684no—
596C23—5684no—
597C23—5682no—
598C23—5682no—
599C23—712no—
600C23—712no—
601C23—712no—
602C23—712no—
603C23—718no—
604C23—718no—
605C23—712no—
606C23—712no—
607C23—712no—
608C23—1428no—
609C23—1421no—
610C23—1421no—
611C23C4⋊C4×D7112yes—
612C23C22×C4×D7111yescharacteristic
613C23C2×D4×D7112yes—
614C23C2×D4×D7111yescharacteristic
615C23C2×Q8×D7111yescharacteristic
616C23#41×D7112yes—
617D4—24no—
618D4—24no—
619D4—1428no—
620D4—1428no—
621D4—1424no—
622D4—1424no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—44no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—2841no—
639C2×C4—2841no—
640C2×C4—2844no—
641C2×C4—2844no—
642C2×C4—2844no—
643C2×C4—2844no—
644C2×C4—2841no—
645C2×C4—2841no—
646C2×C4—5682no—
647C2×C4—5682no—
648C2×C4—5682no—
649C2×C4—5682no—
650C2×C4—56816no—
651C2×C4—5682no—
652C2×C4—712no—
653C2×C4—712no—
654C2×C4—712no—
655C2×C4—1428no—
656C2×C4—1421no—
657C2×C4—1421no—
658C2×C4—1421no—
659C2×C4—1421no—
660C2×C4C22⋊C4×D7111yescharacteristic
661C2×C4C22⋊C4×D7111yescharacteristic
662C2×C4C22⋊C4×D7112yes—
663C2×C4C4⋊C4×D7112yes—
664C22—22no—
665C22—21no—
666C22—22no—
667C22—21no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—41no—
675C22—41no—
676C22—2842no—
677C22—2842no—
678C22—2848no—
679C22—2842no—
680C22—2842no—
681C22—2842no—
682C22—2842no—
683C22—2848no—
684C22—2841no—
685C22—2841no—
686C22—5688no—
687C22—714no—
688C22—714no—
689C22—1422no—
690C22—1422no—
691C22—1422no—
692C22—1422no—
693C22—1422no—
694C22C2×C22⋊C4×D7111yescharacteristic
695C22C2×C4⋊C4×D7111yescharacteristic
696C22#117×D7111yescharacteristic
697C22#121×D7112yes—
698C22C22⋊Q8×D7112yes—
699C4—21no—
700C4—21no—
701C4—22no—
702C4—22no—
703C4—41no—
704C4—41no—
705C4—84no—
706C4—2841no—
707C4—2841no—
708C4—5684no—
709C4—1422no—
710C4—1422no—
711C4—1422no—
712C2—22no—
713C2—21no—
714C2—21no—
715C2—22no—
716C2—42no—
717C2—2842no—
718C2—1424no—
719C2—1424no—
720C2#380×D7111yescharacteristic
721C2#2259679811yescharacteristic
722C2#2259679911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D71
commutatorC23×C71C23×C4
FrattiniC24C23×D71
FittingC71×#1799C2
socleC22×C71C22×C22⋊C4
prime radicalC22×D4×D71C22
cosocleC24×C71C24
hypercenter#1799D71
hypocenterC71#20633
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #22590953C2semidirect
4. #22588328C2semidirect
5. #22588327C2semidirect
6. #22588326C2semidirect
7. #22588325C2semidirect
8. #342×D71C2semidirect
9. C71×#1799C2semidirect
13. C2×C4×D284C4semidirect
15. C2×#14556090C4semidirect
16. C2×C4×C22⋊D71C4semidirect
18. C2×(C22⋊D71)⋊C4C4semidirect
20. C2×#14556086C4semidirect
21. C2×#14556085C4semidirect
22. C22×(C2×D71)⋊C4C4semidirect
24. C2×C22⋊C4×D71C4semidirect
32. #17985859C22semidirect
33. #17985857C22semidirect
34. #17985766C22semidirect
35. #17985765C22semidirect
38. #380×C71C22semidirect
39. #342×C71C22semidirect
49. C23×Dic71C2×C4semidirect
55. C22×C4×D71C2×C4semidirect
56. C22×C4×D71C2×C4semidirect
71. C2×C4⋊Dic71C2×C4semidirect
73. C2×Dic71⋊C4C2×C4semidirect
74. C2×Dic71⋊C4C2×C4semidirect
75. C2×C22⋊Dic71C2×C4semidirect
87. C2×(C2×D71)⋊C4C2×C4semidirect
88. C2×(C2×D71)⋊C4C2×C4semidirect
95. C2×C4×Dic71C2×C4semidirect
96. C2×C4×Dic71C2×C4semidirect
97. C2×C4×Dic71C2×C4semidirect
103. C23×C4×C71C2×C4semidirect
108. C2×C4⋊C4×C71C2×C4semidirect
109. C2×C22⋊C4×C71C2×C4semidirect
112. C2×C42×C71C2×C4semidirect
121. C23×D71C4⋊C4semidirect
131. C2×D284C4⋊C4semidirect
136. C2×C22⋊D71C4⋊C4semidirect
164. C2×C4×D71C4⋊C4semidirect
369. #1799D71semidirect
371. C71#20633semidirect
398. #380C2×D71semidirect
401. #342C2×D71semidirect
420. C23×C4C4×D71semidirect
443. C2×C4⋊C4C4×D71semidirect
464. C2×C22⋊C4C4×D71semidirect
470. C2×C42C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179864712
C2×#99×D712
#225909532
#225883282
#225883272
#225883262
#225883252
#342×D712
C71×#17992
#2063371