Finite Group Databasebeta

← #32017572

Subgroups — #32017572

Order 18176.

1396 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D284C211yesmaximal, characteristic, complemented
2C2×#17986064C211yesmaximal, characteristic, complemented
3C2×C22⋊C8×D71C211yesmaximal, characteristic, complemented
4C2×C22⋊C8×D71C211yesmaximal, characteristic, complemented
5C4×#14556098C211yesmaximal, characteristic
6#22589132C211yesmaximal, characteristic, complemented
7#22588948C211yesmaximal, characteristic, complemented
8#22588631C211yesmaximal, characteristic, complemented
9#22588631C211yesmaximal, characteristic, complemented
10#22588629C211yesmaximal, characteristic, complemented
11#22588519C211yesmaximal, characteristic, complemented
12#22588516C211yesmaximal, characteristic, complemented
13C8×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
14#22588110C211yesmaximal, characteristic, complemented
15C71×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20C22×C8×D71C2211yescharacteristic
21C22×C8×D71C2211yescharacteristic, complemented
22C2×#14556098C411yescharacteristic
23C2×C4×D284C2211yescharacteristic
24C2×C4×D284C2211yescharacteristic
25C2×C4×C22⋊D71C2211yescharacteristic
26C8×D284—24no—
27#17986064—24no—
28C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
29C2×Dic71⋊C8C2211yescharacteristic, complemented
30C2×C22⋊(C71⋊C8)C2211yescharacteristic
31C2×C22⋊(C71⋊C8)C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×(C2×D71)⋊C8C2211yescharacteristic
35C2×(C2×D71)⋊C8C2211yescharacteristic
36C2×(C2×D71)⋊C8C2211yescharacteristic, complemented
37C2×(C2×D71)⋊C8C2211yescharacteristic, complemented
38C2×(C2×D71)⋊C8C2211yescharacteristic, complemented
39C22⋊C8×D71—24no—
40C22⋊C8×D71—24no—
41C2×C4×C71⋊C8C2211yescharacteristic, complemented
42C2×C8×Dic71C2211yescharacteristic, complemented
43#17985877C411yescharacteristic
44#17985877C411yescharacteristic
45#17985876C411yescharacteristic
46#17985874C411yescharacteristic
47#17985873C411yescharacteristic
48#17985873C411yescharacteristic
49#17985854C411yescharacteristic
50C4×(C2×D71)⋊C4C2211yescharacteristic
51C4×(C2×D71)⋊C4C2211yescharacteristic
52#17985754C2211yescharacteristic, complemented
53#17985754C2211yescharacteristic, complemented
54#17985753C2211yescharacteristic, complemented
55#17985753C2211yescharacteristic, complemented
56C2×C4⋊C8×C71C2211yescharacteristic, complemented
57C2×C22⋊C8×C71C2211yescharacteristic
58C2×C22⋊C8×C71C2211yescharacteristic
59C2×C4×C8×C71C2211yescharacteristic, complemented
60C4×C22⋊C4×C71C2211yescharacteristic
61#336×C71C2211yescharacteristic, complemented
62#336×C71C2211yescharacteristic, complemented
63C24×D71C2×C411yescharacteristic
64C22×D284C2×C411yescharacteristic
65C22×D284C2×C411yescharacteristic
66C22×C22⋊D71C2×C411yescharacteristic
67C23×Dic71C2×C411yescharacteristic
68C22×C4×D71—22no—
69C22×C4×D71—22no—
70C22×C4×D71—22no—
71C22×C4×D71—22no—
72C22×C4×D71—41no—
73C22×C4×D71—41no—
74C22×C4×D71C2×C411yescharacteristic
75C22×C4×D71C2×C411yescharacteristic
76C22×C4×D71C2311yescharacteristic
77C22×C4×D71C2311yescharacteristic
78C22×C4×D71C2311yescharacteristic
79C22×C71⋊C8C2311yescharacteristic
80C22×C71⋊C8C2311yescharacteristic
81C22×C71⋊C8C2311yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C2×C8×D71—22no—
84C2×C8×D71—22no—
85C2×C8×D71—22no—
86C2×C8×D71—22no—
87C2×C8×D71—22no—
88C2×C8×D71—22no—
89C2×C8×D71—22no—
90C2×C8×D71—22no—
91C2×C8×D71—22no—
92C2×C8×D71—22no—
93C2×C8×D71—41no—
94C2×C8×D71—41no—
95C2×C8×D71—41no—
96C2×C8×D71—41no—
97C2×C8×D71—41no—
98#14556098C818yescomplemented
99C4×D284—22no—
100C4×D284—22no—
101C4×D284—22no—
102C4×D284—22no—
103C4×C22⋊D71—41no—
104C4×C22⋊D71—41no—
105C2×C4⋊Dic71C2×C411yescharacteristic
106C2×C4⋊Dic71C2×C411yescharacteristic
107C2×Dic71⋊C4C2×C411yescharacteristic
108C2×C22⋊Dic71C2×C411yescharacteristic
109C2×(C2×D71)⋊C4C2×C411yescharacteristic
110C2×(C2×D71)⋊C4C2×C411yescharacteristic
111C2×(C2×D71)⋊C4C2×C411yescharacteristic
112C2×(C2×D71)⋊C4C2×C411yescharacteristic
113C2×(C2×D71)⋊C4C2×C411yescharacteristic
114C2×(C2×D71)⋊C4C2×C411yescharacteristic
115C2×(C2×D71)⋊C4C2×C411yescharacteristic
116C2×(C2×D71)⋊C4C2×C411yescharacteristic
117C2×(C2×D71)⋊C4C2×C411yescharacteristic
118C2×C4×Dic71C2311yescharacteristic
119C4⋊(C71⋊C8)—22no—
120Dic71⋊C8—41no—
121C22⋊(C71⋊C8)—22no—
122C22⋊(C71⋊C8)—22no—
123(C2×D71)⋊C8—22no—
124(C2×D71)⋊C8—22no—
125(C2×D71)⋊C8—22no—
126(C2×D71)⋊C8—22no—
127(C2×D71)⋊C8—41no—
128(C2×D71)⋊C8D414yescomplemented
129(C2×D71)⋊C8D414yescomplemented
130C4×C71⋊C8—22no—
131C8×Dic71—41no—
132C71⋊#95C2×C411yescharacteristic
133C71⋊#95C2×C411yescharacteristic
134C71⋊#95C2×C411yescharacteristic
135C71⋊#95C2×C411yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C22×C8×C71C2311yescharacteristic
138C22×C8×C71C2311yescharacteristic
139C22×C8×C71C2311yescharacteristic
140C22×C8×C71C2311yescharacteristic
141C2×C22⋊C4×C71C2×C411yescharacteristic
142C2×C22⋊C4×C71C2×C411yescharacteristic
143C2×C42×C71C2311yescharacteristic
144C2×C42×C71C2311yescharacteristic
145C4⋊C8×C71—22no—
146C22⋊C8×C71—22no—
147C22⋊C8×C71—22no—
148C4×C8×C71—22no—
149#95×C71C2×C411yescharacteristic
150#95×C71C2×C411yescharacteristic
151C23×D71—22no—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—22no—
155C23×D71—41no—
156C23×D71—41no—
157C23×D71C2×C814yescomplemented
158C23×D71C22×C411yescharacteristic
159C23×D71C22×C411yescharacteristic
160C23×D71C22×C411yescharacteristic
161C2×D284—22no—
162C2×D284—22no—
163C2×D284—22no—
164C2×D284—22no—
165C2×D284C2×C814yescomplemented
166C2×D284C2×C814yescomplemented
167C2×C22⋊D71—41no—
168C2×C22⋊D71—41no—
169C2×C22⋊D71C2×C814yescomplemented
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—41no—
173C22×Dic71C22×C411yescharacteristic
174C22×Dic71C22×C411yescharacteristic
175C22×Dic71C22×C411yescharacteristic
176C22×Dic71C22×C411yescharacteristic
177C22×Dic71C22×C411yescharacteristic
178C2×C4×D71—21no—
179C2×C4×D71—21no—
180C2×C4×D71—21no—
181C2×C4×D71—21no—
182C2×C4×D71—21no—
183C2×C4×D71—21no—
184C2×C4×D71—21no—
185C2×C4×D71—21no—
186C2×C4×D71—22no—
187C2×C4×D71—22no—
188C2×C4×D71—21no—
189C2×C4×D71—21no—
190C2×C4×D71—21no—
191C2×C4×D71—21no—
192C2×C4×D71—21no—
193C2×C4×D71—21no—
194C2×C4×D71—22no—
195C2×C4×D71—22no—
196C2×C4×D71—44no—
197C2×C4×D71—44no—
198C2×C4×D71—44no—
199C2×C4×D71—44no—
200C2×C4×D71—41no—
201C2×C4×D71—41no—
202C2×C4×D71C2×D412yes—
203C2×C4×D71C2×D412yes—
204C2×C4×D71#4112yes—
205C2×C4×D71#4112yes—
206C2×C71⋊C8—21no—
207C2×C71⋊C8—21no—
208C2×C71⋊C8—21no—
209C2×C71⋊C8—21no—
210C2×C71⋊C8—21no—
211C2×C71⋊C8—21no—
212C2×C71⋊C8—21no—
213C2×C71⋊C8—21no—
214C2×C71⋊C8—21no—
215C2×C71⋊C8—21no—
216C2×C71⋊C8C2×D412yes—
217C2×C71⋊C8C2×D412yes—
218C8×D71—44no—
219C8×D71—44no—
220C8×D71—44no—
221C8×D71—44no—
222C8×D71—44no—
223C4⋊Dic71—22no—
224C4⋊Dic71—22no—
225Dic71⋊C4—41no—
226C22⋊Dic71—41no—
227(C2×D71)⋊C4—22no—
228(C2×D71)⋊C4—22no—
229(C2×D71)⋊C4—22no—
230(C2×D71)⋊C4—22no—
231(C2×D71)⋊C4—22no—
232(C2×D71)⋊C4—22no—
233(C2×D71)⋊C4—41no—
234(C2×D71)⋊C4C2×C814yescomplemented
235(C2×D71)⋊C4C2×C814yescomplemented
236C4×Dic71—21no—
237C4×Dic71—21no—
238C24×C71C22×C411yescharacteristic
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71C22×C411yescharacteristic
246C22×C4×C71C22×C411yescharacteristic
247C22×C4×C71C22×C411yescharacteristic
248C22×C4×C71C22×C411yescharacteristic
249C22×C4×C71C22×C411yescharacteristic
250C22×C4×C71C2411yescharacteristic
251C2×C8×C71—21no—
252C2×C8×C71—21no—
253C2×C8×C71—21no—
254C2×C8×C71—21no—
255C2×C8×C71—21no—
256C2×C8×C71—21no—
257C2×C8×C71—21no—
258C2×C8×C71—21no—
259C2×C8×C71—21no—
260C2×C8×C71—21no—
261C2×C8×C71C2×D412yes—
262C2×C8×C71C2×D412yes—
263C22⋊C4×C71—41no—
264C22⋊C4×C71C2×C814yescomplemented
265C42×C71—21no—
266C42×C71—21no—
267C42×C71—21no—
268C42×C71—21no—
269C23×C71—21no—
270C23×C71—21no—
271C23×C71—21no—
272C23×C71—21no—
273C23×C71—21no—
274C23×C71—21no—
275C23×C71C22×C812yes—
276C23×C71C23×C411yescharacteristic
277C22×D71—21no—
278C22×D71—21no—
279C22×D71—21no—
280C22×D71—21no—
281C22×D71—21no—
282C22×D71—21no—
283C22×D71—21no—
284C22×D71—21no—
285C22×D71—21no—
286C22×D71—21no—
287C22×D71—21no—
288C22×D71—21no—
289C22×D71—21no—
290C22×D71—21no—
291C22×D71—28no—
292C22×D71—28no—
293C22×D71—44no—
294C22×D71—44no—
295C22×D71—44no—
296C22×D71—44no—
297C22×D71—44no—
298C22×D71C4×D412yes—
299C22×D71C4×D412yes—
300C22×D71C22×C812yes—
301C22×D71C22×C812yes—
302C22×D71C22×C812yes—
303C22×D71#13112yes—
304C22×D71#13112yes—
305C2×C4×C71—21no—
306C2×C4×C71—21no—
307C2×C4×C71—21no—
308C2×C4×C71—21no—
309C2×C4×C71—21no—
310C2×C4×C71—21no—
311C2×C4×C71—21no—
312C2×C4×C71—21no—
313C2×C4×C71—21no—
314C2×C4×C71—21no—
315C2×C4×C71—21no—
316C2×C4×C71—21no—
317C2×C4×C71—21no—
318C2×C4×C71—41no—
319C2×C4×C71—41no—
320C2×C4×C71—41no—
321C2×C4×C71—41no—
322C2×C4×C71C22×C812yes—
323C2×C4×C71C22×C812yes—
324C2×C4×C71C22×D411yescharacteristic
325C2×C4×C71C22×D411yescharacteristic
326C2×C4×C71C2×#4111yescharacteristic
327C2×C4×C71C2×#4111yescharacteristic
328C2×C4×C71H(5,𝔽2)11yescharacteristic
329C2×C4×C71H(5,𝔽2)11yescharacteristic
330C22⋊D71—44no—
331C2×Dic71—21no—
332C2×Dic71—21no—
333C2×Dic71—21no—
334C2×Dic71—21no—
335C2×Dic71—21no—
336C2×Dic71—21no—
337C2×Dic71—21no—
338C2×Dic71—21no—
339C2×Dic71—21no—
340C2×Dic71—21no—
341C2×Dic71—21no—
342C2×Dic71—21no—
343C2×Dic71—44no—
344C2×Dic71C4×D412yes—
345C2×Dic71C4×D412yes—
346C2×Dic71C22×C812yes—
347D284—28no—
348D284—28no—
349C4×D71—22no—
350C4×D71—22no—
351C4×D71—22no—
352C4×D71—22no—
353C4×D71—22no—
354C4×D71—22no—
355C4×D71—22no—
356C4×D71—22no—
357C4×D71—44no—
358C4×D71—44no—
359C4×D71—41no—
360C4×D71—41no—
361C4×D71—41no—
362C4×D71—41no—
363C8×C71—22no—
364C8×C71—22no—
365C8×C71—41no—
366C8×C71—41no—
367C71⋊C8—22no—
368C71⋊C8—22no—
369C71⋊C8—41no—
370C71⋊C8—41no—
371C22×C71—22no—
372C22×C71—22no—
373C22×C71—22no—
374C22×C71—41no—
375C22×C71—41no—
376C22×C71—41no—
377C22×C71—41no—
378C22×C71C2×C4×D411yescharacteristic
379C22×C71C2×C4×D411yescharacteristic
380C22×C71#51811yescharacteristic
381C22×C71C23×C811yescharacteristic
382C22×C71C2×#13111yescharacteristic
383C22×C71C2×#13111yescharacteristic
384C22×C71#56811yescharacteristic
385C2×D71—22no—
386C2×D71—22no—
387C2×D71—22no—
388C2×D71—22no—
389C2×D71—22no—
390C2×D71—22no—
391C2×D71—22no—
392C2×D71—22no—
393C2×D71—22no—
394C2×D71—22no—
395C2×D71—22no—
396C2×D71—22no—
397C2×D71—22no—
398C2×D71—22no—
399C2×D71—22no—
400C2×D71—416no—
401C2×D71—41no—
402C2×D71—41no—
403C2×D71—41no—
404C2×D71—41no—
405C2×D71C8×D414yescomplemented
406C2×D71C8×D414yescomplemented
407C4×C71—22no—
408C4×C71—22no—
409C4×C71—41no—
410C4×C71—41no—
411C4×C71—41no—
412C4×C71D4211yescharacteristic
413C4×C71#54611yescharacteristic
414C4×C71#54611yescharacteristic
415C4×C71#55111yescharacteristic
416Dic71—22no—
417Dic71—22no—
418Dic71—22no—
419Dic71—41no—
420Dic71—41no—
421#22842—711nomaximal, Sylow
422C2×C71—42no—
423C2×C71#235811yescharacteristic
424C2×C71C2×C8×D411yescharacteristic
425C2×C71C2×C8×D411yescharacteristic
426C2×C71#293311yescharacteristic
427C2×C71#293311yescharacteristic
428C2×C71#297211yescharacteristic
429C2×C71#297711yescharacteristic
430D71—24no—
431D71—24no—
432D71—42no—
433C2×C8×D4—711no—
434C2×C8×D4—711no—
435C22×C22⋊C8—711no—
436C22×C22⋊C8—711no—
437C4×#120—711no—
438#1954—711no—
439#1923—711no—
440#1923D7111yescharacteristic, complemented
441#1869—711no—
442#1869—711no—
443#1869—711no—
444#1850—711no—
445#1850—711no—
446C8×C22⋊C4—711no—
447C8×C22⋊C4—711no—
448C71#2284211yescharacteristic, complemented, Sylow
449C24×C4—711no—
450C23×C8—711no—
451C23×C8—711no—
452C23×C8—711no—
453C23×C8—711no—
454C23×C8—711no—
455C2×#120—711no—
456C2×C4×D4—711no—
457C2×C4×D4—711no—
458C2×C4×D4—711no—
459C8×D4—1424no—
460C8×D4—1424no—
461C2×C4⋊C8—711no—
462C2×C4⋊C8—711no—
463C2×C4⋊C8C2×D7111yescharacteristic, complemented
464C2×C22⋊C8—711no—
465C2×C22⋊C8—711no—
466C2×C22⋊C8—711no—
467C2×C22⋊C8—711no—
468C2×C22⋊C8—711no—
469C2×C22⋊C8—711no—
470C2×C22⋊C8—711no—
471C2×C22⋊C8—711no—
472C2×C22⋊C8—711no—
473C2×C22⋊C8—1424no—
474C2×C22⋊C8—1424no—
475C2×C22⋊C8C2×D7111yescharacteristic
476C2×C22⋊C8C2×D7111yescharacteristic
477C2×C4×C8—711no—
478C2×C4×C8—711no—
479C2×C4×C8C2×D7111yescharacteristic, complemented
480#386—711no—
481#386—711no—
482#386—711no—
483#385—711no—
484#385—711no—
485#385—711no—
486#379—711no—
487C4×C22⋊C4—711no—
488C4×C22⋊C4—711no—
489C4×C22⋊C4C2×D7111yescharacteristic
490#336—711no—
491#336—711no—
492#336—711no—
493#336—711no—
494#336C2×D7111yescharacteristic, complemented
495#336C2×D7111yescharacteristic, complemented
496C25—711no—
497C22×D4—711no—
498C22×D4—711no—
499C22×D4—711no—
500C23×C4—2841no—
501C23×C4—2841no—
502C23×C4—711no—
503C23×C4—711no—
504C23×C4—711no—
505C23×C4—711no—
506C23×C4—711no—
507C23×C4—711no—
508C23×C4—1422no—
509C23×C4—1422no—
510C23×C4—1422no—
511C23×C4—1422no—
512C23×C4C22×D7111yescharacteristic
513C22×C8—2841no—
514C22×C8—2841no—
515C22×C8—2841no—
516C22×C8—2841no—
517C22×C8—2841no—
518C22×C8—711no—
519C22×C8—711no—
520C22×C8—711no—
521C22×C8—711no—
522C22×C8—1422no—
523C22×C8—1422no—
524C22×C8—1422no—
525C22×C8—1422no—
526C22×C8—1422no—
527C22×C8—1422no—
528C22×C8—1422no—
529C22×C8—1422no—
530C22×C8—1422no—
531C22×C8—1422no—
532C22×C8C22×D7111yescharacteristic
533C22×C8C22×D7111yescharacteristic
534C22×C8C22×D7111yescharacteristic
535C22×C8C22×D7111yescharacteristic
536#120—718no—
537C4×D4—2841no—
538C4×D4—2841no—
539C4×D4—1422no—
540C4×D4—1422no—
541C4×D4—1422no—
542C4×D4—1422no—
543C2×C4⋊C4—711no—
544C2×C4⋊C4—711no—
545C2×C4⋊C4—711no—
546C2×C22⋊C4—711no—
547C2×C22⋊C4—711no—
548C2×C22⋊C4—711no—
549C2×C22⋊C4—711no—
550C2×C22⋊C4—711no—
551C2×C22⋊C4—711no—
552C2×C22⋊C4—711no—
553C2×C22⋊C4—711no—
554C2×C22⋊C4—711no—
555C2×C22⋊C4—711no—
556C2×C22⋊C4C4×D7111yescharacteristic
557C2×C22⋊C4C4×D7111yescharacteristic
558C2×C42—711no—
559C2×C42C22×D7111yescharacteristic
560C2×C42C22×D7111yescharacteristic
561C4⋊C8—22no—
562C4⋊C8—2841no—
563C4⋊C8—1422no—
564C22⋊C8—22no—
565C22⋊C8—22no—
566C22⋊C8—2841no—
567C22⋊C8—714no—
568C22⋊C8—714no—
569C22⋊C8—1422no—
570C22⋊C8—1422no—
571C22⋊C8—1422no—
572C22⋊C8—1422no—
573C22⋊C8—1422no—
574C22⋊C8—1422no—
575C4×C8—22no—
576C4×C8—2841no—
577C4×C8—1422no—
578#95—711no—
579#95—711no—
580#95—711no—
581#95—711no—
582#95C4×D7111yescharacteristic
583#95C4×D7111yescharacteristic
584C24—2841no—
585C24—2841no—
586C24—714no—
587C24—711no—
588C24—711no—
589C24—711no—
590C24—1422no—
591C24—1422no—
592C24—1422no—
593C24—1422no—
594C24C2×C4×D7111yescharacteristic
595C2×D4—2841no—
596C2×D4—2841no—
597C2×D4—714no—
598C2×D4—714no—
599C2×D4—714no—
600C2×D4—1422no—
601C2×D4—1422no—
602C2×D4—1422no—
603C2×D4—1422no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—2841no—
611C22×C4—2841no—
612C22×C4—2844no—
613C22×C4—2844no—
614C22×C4—2844no—
615C22×C4—2844no—
616C22×C4—2841no—
617C22×C4—711no—
618C22×C4—711no—
619C22×C4—711no—
620C22×C4—712no—
621C22×C4—712no—
622C22×C4—712no—
623C22×C4—712no—
624C22×C4—711no—
625C22×C4—711no—
626C22×C4—1422no—
627C22×C4—1422no—
628C22×C4—1422no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4—1422no—
632C22×C4—1421no—
633C22×C4—1421no—
634C22×C4—1421no—
635C22×C4—1421no—
636C22×C4—1421no—
637C22×C4—1421no—
638C22×C4—1421no—
639C22×C4—1421no—
640C22×C4—1421no—
641C22×C4—1421no—
642C22×C4—1421no—
643C22×C4—1421no—
644C22×C4—1421no—
645C22×C4—1421no—
646C22×C4C2×C4×D7111yescharacteristic
647C22×C4C2×C4×D7111yescharacteristic
648C22×C4C2×C4×D7111yescharacteristic
649C22×C4C2×C4×D7111yescharacteristic
650C22×C4C2×C4×D7111yescharacteristic
651C22×C4C23×D7111yescharacteristic
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—2844no—
663C2×C8—2844no—
664C2×C8—2844no—
665C2×C8—2844no—
666C2×C8—2844no—
667C2×C8—712no—
668C2×C8—712no—
669C2×C8—1421no—
670C2×C8—1421no—
671C2×C8—1421no—
672C2×C8—1421no—
673C2×C8—1421no—
674C2×C8—1421no—
675C2×C8—1421no—
676C2×C8—1421no—
677C2×C8—1421no—
678C2×C8—1421no—
679C2×C8D4×D7112yes—
680C2×C8D4×D7112yes—
681C4⋊C4—2841no—
682C4⋊C4—1422no—
683C4⋊C4—1422no—
684C22⋊C4—41no—
685C22⋊C4—2841no—
686C22⋊C4—2841no—
687C22⋊C4—714no—
688C22⋊C4—714no—
689C22⋊C4—1422no—
690C22⋊C4—1422no—
691C22⋊C4—1422no—
692C22⋊C4—1422no—
693C22⋊C4—1422no—
694C22⋊C4—1422no—
695C22⋊C4C8×D7114yescomplemented
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—1421no—
701C42—1421no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—2844no—
709C23—2844no—
710C23—2844no—
711C23—2844no—
712C23—2844no—
713C23—712no—
714C23—712no—
715C23—712no—
716C23—712no—
717C23—712no—
718C23—712no—
719C23—712no—
720C23—1428no—
721C23—1428no—
722C23—1421no—
723C23—1421no—
724C23—1421no—
725C23—1421no—
726C23—1421no—
727C23—1421no—
728C23—1421no—
729C23—1421no—
730C23—1421no—
731C23—1421no—
732C23—1421no—
733C23—1421no—
734C23—1421no—
735C23—1421no—
736C23C2×C8×D7112yes—
737C23C22×C4×D7111yescharacteristic
738D4—2844no—
739D4—1428no—
740D4—1428no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—2844no—
759C2×C4—2844no—
760C2×C4—2841no—
761C2×C4—2841no—
762C2×C4—2841no—
763C2×C4—2841no—
764C2×C4—2844no—
765C2×C4—712no—
766C2×C4—712no—
767C2×C4—712no—
768C2×C4—1421no—
769C2×C4—1421no—
770C2×C4—1421no—
771C2×C4—1421no—
772C2×C4—1421no—
773C2×C4—1421no—
774C2×C4—1421no—
775C2×C4—1421no—
776C2×C4—1421no—
777C2×C4—1421no—
778C2×C4—1421no—
779C2×C4—1421no—
780C2×C4—1422no—
781C2×C4—1422no—
782C2×C4—1422no—
783C2×C4—1422no—
784C2×C4—1422no—
785C2×C4—1422no—
786C2×C4—1422no—
787C2×C4—1422no—
788C2×C4C2×C8×D7112yes—
789C2×C4C2×C8×D7112yes—
790C2×C4C2×D4×D7111yescharacteristic
791C2×C4C2×D4×D7111yescharacteristic
792C2×C4#41×D7111yescharacteristic
793C2×C4#41×D7111yescharacteristic
794C2×C4#1455617411yescharacteristic
795C2×C4#1455617411yescharacteristic
796C8—22no—
797C8—22no—
798C8—41no—
799C8—41no—
800C8—2841no—
801C8—2841no—
802C8—1422no—
803C8—1422no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—28416no—
812C22—2841no—
813C22—2841no—
814C22—2841no—
815C22—2841no—
816C22—714no—
817C22—714no—
818C22—1422no—
819C22—1422no—
820C22—1422no—
821C22—1422no—
822C22—1422no—
823C22—1422no—
824C22—1422no—
825C22—1422no—
826C22—1422no—
827C22—1422no—
828C22—1422no—
829C22—1422no—
830C22—1422no—
831C22—1422no—
832C22—1422no—
833C22C4×D4×D7111yescharacteristic
834C22C4×D4×D7111yescharacteristic
835C22#1798647311yescharacteristic
836C22C22×C8×D7111yescharacteristic
837C22#131×D7111yescharacteristic
838C22#131×D7111yescharacteristic
839C22#1798676511yescharacteristic
840C4—22no—
841C4—22no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—2841no—
846C4—2841no—
847C4—1422no—
848C4—1422no—
849C4—1422no—
850C4#1798663311yescharacteristic
851C4#1798664111yescharacteristic
852C4#1798664211yescharacteristic
853C4#1798667411yescharacteristic
854C2—42no—
855C2—2842no—
856C2—1424no—
857C2—1424no—
858C2#2259131811yescharacteristic
859C2C8×D4×D7111yescharacteristic
860C2C8×D4×D7111yescharacteristic
861C2#2259706311yescharacteristic
862C2#2259706911yescharacteristic
863C2#2259736311yescharacteristic
864C2#2259739511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC71×#1923C2
socleC23×C71C23×C4
prime radicalC2×#14556098C4
cosocleC22×C4×C71C24
hypercenter#1923D71
hypocenterC71#22842
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×C8×D284C2semidirect
2. C2×#17986064C2semidirect
3. C2×C22⋊C8×D71C2semidirect
4. C2×C22⋊C8×D71C2semidirect
6. #22589132C2semidirect
7. #22588948C2semidirect
8. #22588631C2semidirect
9. #22588631C2semidirect
10. #22588629C2semidirect
11. #22588519C2semidirect
12. #22588516C2semidirect
13. C8×(C2×D71)⋊C4C2semidirect
14. #22588110C2semidirect
15. C71×#1923C2semidirect
21. C22×C8×D71C22semidirect
28. C2×C4⋊(C71⋊C8)C22semidirect
29. C2×Dic71⋊C8C22semidirect
36. C2×(C2×D71)⋊C8C22semidirect
37. C2×(C2×D71)⋊C8C22semidirect
38. C2×(C2×D71)⋊C8C22semidirect
41. C2×C4×C71⋊C8C22semidirect
42. C2×C8×Dic71C22semidirect
52. #17985754C22semidirect
53. #17985754C22semidirect
54. #17985753C22semidirect
55. #17985753C22semidirect
56. C2×C4⋊C8×C71C22semidirect
59. C2×C4×C8×C71C22semidirect
61. #336×C71C22semidirect
62. #336×C71C22semidirect
98. #14556098C8semidirect
128. (C2×D71)⋊C8D4semidirect
129. (C2×D71)⋊C8D4semidirect
157. C23×D71C2×C8semidirect
165. C2×D284C2×C8semidirect
166. C2×D284C2×C8semidirect
169. C2×C22⋊D71C2×C8semidirect
234. (C2×D71)⋊C4C2×C8semidirect
235. (C2×D71)⋊C4C2×C8semidirect
264. C22⋊C4×C71C2×C8semidirect
405. C2×D71C8×D4semidirect
406. C2×D71C8×D4semidirect
440. #1923D71semidirect
448. C71#22842semidirect
463. C2×C4⋊C8C2×D71semidirect
479. C2×C4×C8C2×D71semidirect
494. #336C2×D71semidirect
495. #336C2×D71semidirect
695. C22⋊C4C8×D71semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D2842
C2×#179860642
C2×C22⋊C8×D712
C4×#145560982
#225891322
#225889482
#225886312
#225886292
#225885192
#225885162
C8×(C2×D71)⋊C42
#225881102
C71×#19232
#2284271