Finite Group Databasebeta

← #32014365

Subgroups — #32014365

Order 18176.

1280 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986050C211yesmaximal, characteristic, complemented
2C22×(C2×D71)⋊C8C211yesmaximal, characteristic
3C4×C22⋊C4×D71C211yesmaximal, characteristic
4#22588946C211yesmaximal, characteristic, complemented
5#22588946C211yesmaximal, characteristic, complemented
6#22588944C211yesmaximal, characteristic, complemented
7#22588944C211yesmaximal, characteristic, complemented
8#22588518C211yesmaximal, characteristic, complemented
9#22588517C211yesmaximal, characteristic, complemented
10#22588407C211yesmaximal, characteristic, complemented
11#22588319C211yesmaximal, characteristic, complemented
12#22588249C211yesmaximal, characteristic
13C22⋊C4×C71⋊C8C211yesmaximal, characteristic, complemented
14C4×(C2×D71)⋊C8C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C71C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×C22⋊C4×D71C411yescharacteristic
19C2×C22⋊C4×D71C411yescharacteristic
20C2×C42×D71C2211yescharacteristic
21C2×C42×D71C2211yescharacteristic
22#17986050—24no—
23C2×Dic71⋊C8C2211yescharacteristic, complemented
24C2×Dic71⋊C8C2211yescharacteristic, complemented
25C2×Dic71⋊C8C2211yescharacteristic, complemented
26C2×Dic71⋊C8C2211yescharacteristic, complemented
27C2×C22⋊(C71⋊C8)C2211yescharacteristic
28C2×(C2×D71)⋊C8—24no—
29C2×(C2×D71)⋊C8C2211yescharacteristic
30C2×(C2×D71)⋊C8C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×(C2×D71)⋊C8C2211yescharacteristic
35C2×(C2×D71)⋊C8C2211yescharacteristic
36C2×(C2×D71)⋊C8C2211yescharacteristic
37C2×C4×C71⋊C8C2211yescharacteristic, complemented
38C2×C4×C71⋊C8C2211yescharacteristic, complemented
39C22⋊C4×Dic71C411yescharacteristic
40C22⋊C4×Dic71C411yescharacteristic
41C4×(C2×D71)⋊C4C2211yescharacteristic
42C4×(C2×D71)⋊C4C2211yescharacteristic
43C4×C22⋊Dic71C2211yescharacteristic
44#17985846C411yescharacteristic
45#17985846C411yescharacteristic
46#95×D71C411yescharacteristic
47#95×D71C411yescharacteristic
48#17985754C2211yescharacteristic, complemented
49#17985754C2211yescharacteristic, complemented
50#17985753C2211yescharacteristic, complemented
51#17985753C2211yescharacteristic, complemented
52#17985753C2211yescharacteristic, complemented
53#17985753C2211yescharacteristic, complemented
54C23×C8×C71C2211yescharacteristic
55C2×C22⋊C8×C71C2211yescharacteristic
56C2×C4×C8×C71C2211yescharacteristic, complemented
57C2×C4×C8×C71C2211yescharacteristic, complemented
58C4×C22⋊C4×C71C2211yescharacteristic
59#336×C71C2211yescharacteristic, complemented
60#336×C71C2211yescharacteristic, complemented
61C24×D71C2×C411yescharacteristic
62C23×Dic71C2×C411yescharacteristic
63C22×C4×D71—22no—
64C22×C4×D71—22no—
65C22×C4×D71—22no—
66C22×C4×D71—22no—
67C22×C4×D71—41no—
68C22×C4×D71—41no—
69C22×C4×D71C2×C411yescharacteristic
70C22×C4×D71C2×C411yescharacteristic
71C22×C4×D71C2×C411yescharacteristic
72C22×C4×D71C2×C411yescharacteristic
73C22×C4×D71C2×C411yescharacteristic
74C22×C4×D71C2×C411yescharacteristic
75C22×C4×D71C2311yescharacteristic
76C22×C4×D71C2311yescharacteristic
77C22×C71⋊C8—22no—
78C22×C71⋊C8—22no—
79C22×C71⋊C8—41no—
80C22×C71⋊C8C2311yescharacteristic
81C22×C71⋊C8C2311yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C22×C71⋊C8C2311yescharacteristic
84C2×C22⋊Dic71C2×C411yescharacteristic
85C2×C22⋊Dic71C2×C411yescharacteristic
86C2×(C2×D71)⋊C4C2×C411yescharacteristic
87C2×(C2×D71)⋊C4C2×C411yescharacteristic
88C2×(C2×D71)⋊C4C2×C411yescharacteristic
89C2×(C2×D71)⋊C4C2×C411yescharacteristic
90C22⋊C4×D71—24no—
91C22⋊C4×D71C818yescomplemented
92C2×C4×Dic71C2×C411yescharacteristic
93C2×C4×Dic71C2×C411yescharacteristic
94C2×C4×Dic71C2×C411yescharacteristic
95C2×C4×Dic71C2×C411yescharacteristic
96C2×C4×Dic71C2311yescharacteristic
97C2×C4×Dic71C2311yescharacteristic
98C42×D71—22no—
99C42×D71—22no—
100C42×D71—41no—
101C42×D71—41no—
102Dic71⋊C8—22no—
103Dic71⋊C8—22no—
104Dic71⋊C8—41no—
105Dic71⋊C8—41no—
106C22⋊(C71⋊C8)—22no—
107(C2×D71)⋊C8—22no—
108(C2×D71)⋊C8—22no—
109(C2×D71)⋊C8—22no—
110(C2×D71)⋊C8—22no—
111(C2×D71)⋊C8—22no—
112(C2×D71)⋊C8—41no—
113(C2×D71)⋊C8—41no—
114(C2×D71)⋊C8D414yes—
115C4×C71⋊C8—22no—
116C4×C71⋊C8—41no—
117C71⋊#95C2×C411yescharacteristic
118C71⋊#95C2×C411yescharacteristic
119C71⋊#95C2×C411yescharacteristic
120C71⋊#95C2×C411yescharacteristic
121C71⋊#95C2×C411yescharacteristic
122C71⋊#95C2×C411yescharacteristic
123C23×C4×C71C2311yescharacteristic
124C22×C8×C71—22no—
125C22×C8×C71—22no—
126C22×C8×C71—41no—
127C22×C8×C71C2311yescharacteristic
128C22×C8×C71C2311yescharacteristic
129C22×C8×C71C2311yescharacteristic
130C22×C8×C71C2311yescharacteristic
131C2×C22⋊C4×C71C2×C411yescharacteristic
132C2×C22⋊C4×C71C2×C411yescharacteristic
133C2×C42×C71C2311yescharacteristic
134C2×C42×C71C2311yescharacteristic
135C22⋊C8×C71—22no—
136C4×C8×C71—22no—
137C4×C8×C71—41no—
138#95×C71C2×C411yescharacteristic
139#95×C71C2×C411yescharacteristic
140C23×D71—22no—
141C23×D71—22no—
142C23×D71—22no—
143C23×D71—22no—
144C23×D71—41no—
145C23×D71—41no—
146C23×D71C2×C814yes—
147C23×D71C22×C411yescharacteristic
148C23×D71C22×C411yescharacteristic
149C22×Dic71—22no—
150C22×Dic71—22no—
151C22×Dic71—41no—
152C22×Dic71C22×C411yescharacteristic
153C22×Dic71C22×C411yescharacteristic
154C22×Dic71C22×C411yescharacteristic
155C22×Dic71C22×C411yescharacteristic
156C22×Dic71C22×C411yescharacteristic
157C22×Dic71C22×C411yescharacteristic
158C2×C4×D71—22no—
159C2×C4×D71—22no—
160C2×C4×D71—21no—
161C2×C4×D71—21no—
162C2×C4×D71—21no—
163C2×C4×D71—21no—
164C2×C4×D71—22no—
165C2×C4×D71—22no—
166C2×C4×D71—22no—
167C2×C4×D71—22no—
168C2×C4×D71—22no—
169C2×C4×D71—22no—
170C2×C4×D71—22no—
171C2×C4×D71—21no—
172C2×C4×D71—21no—
173C2×C4×D71—21no—
174C2×C4×D71—21no—
175C2×C4×D71—21no—
176C2×C4×D71—21no—
177C2×C4×D71—22no—
178C2×C4×D71—44no—
179C2×C4×D71—44no—
180C2×C4×D71—44no—
181C2×C4×D71—44no—
182C2×C4×D71—41no—
183C2×C4×D71—41no—
184C2×C4×D71—41no—
185C2×C4×D71—41no—
186C2×C4×D71—41no—
187C2×C4×D71—41no—
188C2×C4×D71C2×C814yescomplemented
189C2×C4×D71C2×C814yescomplemented
190C2×C4×D71C2×D412yes—
191C2×C4×D71#4112yes—
192C2×C71⋊C8—21no—
193C2×C71⋊C8—21no—
194C2×C71⋊C8—21no—
195C2×C71⋊C8—21no—
196C2×C71⋊C8—21no—
197C2×C71⋊C8—21no—
198C2×C71⋊C8—21no—
199C2×C71⋊C8—21no—
200C2×C71⋊C8—21no—
201C2×C71⋊C8—21no—
202C2×C71⋊C8—21no—
203C2×C71⋊C8—44no—
204C2×C71⋊C8C2×D412yes—
205C22⋊Dic71—22no—
206C22⋊Dic71C2×C814yes—
207(C2×D71)⋊C4—22no—
208(C2×D71)⋊C4—22no—
209(C2×D71)⋊C4C2×C814yescomplemented
210(C2×D71)⋊C4C2×C814yescomplemented
211C4×Dic71—21no—
212C4×Dic71—21no—
213C4×Dic71—21no—
214C4×Dic71—21no—
215C4×Dic71—22no—
216C4×Dic71—22no—
217C4×Dic71—41no—
218C4×Dic71—41no—
219C24×C71C22×C411yescharacteristic
220C22×C4×C71—21no—
221C22×C4×C71—21no—
222C22×C4×C71—21no—
223C22×C4×C71—21no—
224C22×C4×C71C22×C411yescharacteristic
225C22×C4×C71C22×C411yescharacteristic
226C22×C4×C71C22×C411yescharacteristic
227C22×C4×C71C22×C411yescharacteristic
228C22×C4×C71C22×C411yescharacteristic
229C22×C4×C71#4112yes—
230C22×C4×C71#4112yes—
231C22×C4×C71C2411yescharacteristic
232C2×C8×C71—21no—
233C2×C8×C71—21no—
234C2×C8×C71—21no—
235C2×C8×C71—21no—
236C2×C8×C71—21no—
237C2×C8×C71—21no—
238C2×C8×C71—21no—
239C2×C8×C71—21no—
240C2×C8×C71—21no—
241C2×C8×C71—21no—
242C2×C8×C71—21no—
243C2×C8×C71—44no—
244C2×C8×C71C2×D412yes—
245C22⋊C4×C71C2×C814yes—
246C22⋊C4×C71M1614yes—
247C42×C71—21no—
248C42×C71—21no—
249C42×C71—21no—
250C42×C71—21no—
251C23×C71—21no—
252C23×C71—21no—
253C23×C71—21no—
254C23×C71—21no—
255C23×C71#11712yes—
256C23×C71C22×C812yes—
257C23×C71C2×M1612yes—
258C23×C71C23×C411yescharacteristic
259C22×D71—21no—
260C22×D71—21no—
261C22×D71—21no—
262C22×D71—21no—
263C22×D71—21no—
264C22×D71—21no—
265C22×D71—21no—
266C22×D71—21no—
267C22×D71—21no—
268C22×D71—21no—
269C22×D71—28no—
270C22×D71—28no—
271C22×D71—44no—
272C22×D71—44no—
273C22×D71—44no—
274C22×D71—44no—
275C22×D71—44no—
276C22×D71C4×D412yes—
277C22×D71C22×C812yes—
278C22×D71C22×C812yes—
279C22×D71#13112yes—
280C2×C4×C71—21no—
281C2×C4×C71—21no—
282C2×C4×C71—21no—
283C2×C4×C71—21no—
284C2×C4×C71—21no—
285C2×C4×C71—21no—
286C2×C4×C71—21no—
287C2×C4×C71—21no—
288C2×C4×C71—21no—
289C2×C4×C71—21no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71#11712yes—
295C2×C4×C71C22×C812yes—
296C2×C4×C71C22×C812yes—
297C2×C4×C71C2×M1612yes—
298C2×C4×C71C2×M1612yes—
299C2×C4×C71C22×D411yescharacteristic
300C2×C4×C71C2×#4111yescharacteristic
301C2×C4×C71C2×#4111yescharacteristic
302C2×C4×C71C2×#4111yescharacteristic
303C2×C4×C71H(5,𝔽2)11yescharacteristic
304C2×C4×C71H(5,𝔽2)11yescharacteristic
305C2×Dic71—21no—
306C2×Dic71—21no—
307C2×Dic71—21no—
308C2×Dic71—21no—
309C2×Dic71—21no—
310C2×Dic71—21no—
311C2×Dic71—21no—
312C2×Dic71—21no—
313C2×Dic71—21no—
314C2×Dic71—21no—
315C2×Dic71—21no—
316C2×Dic71—21no—
317C2×Dic71—21no—
318C2×Dic71—21no—
319C2×Dic71—21no—
320C2×Dic71—44no—
321C2×Dic71C4×D412yes—
322C2×Dic71C22×C812yes—
323C2×Dic71C22×C812yes—
324C4×D71—28no—
325C4×D71—22no—
326C4×D71—22no—
327C4×D71—22no—
328C4×D71—22no—
329C4×D71—44no—
330C4×D71—44no—
331C4×D71—44no—
332C4×D71—44no—
333C4×D71—44no—
334C4×D71—41no—
335C4×D71—41no—
336C4×D71—41no—
337C4×D71—41no—
338C8×C71—22no—
339C8×C71—41no—
340C8×C71—41no—
341C8×C71—41no—
342C71⋊C8—22no—
343C71⋊C8—41no—
344C71⋊C8—41no—
345C71⋊C8—41no—
346C22×C71—22no—
347C22×C71—22no—
348C22×C71—22no—
349C22×C71—22no—
350C22×C71—22no—
351C22×C71—22no—
352C22×C71#43114yescomplemented
353C22×C71C2×#11711yescharacteristic
354C22×C71C2×C4×D411yescharacteristic
355C22×C71#51811yescharacteristic
356C22×C71C23×C811yescharacteristic
357C22×C71C22×M1611yescharacteristic
358C22×C71C2×#13111yescharacteristic
359C22×C71#56811yescharacteristic
360C2×D71—22no—
361C2×D71—22no—
362C2×D71—22no—
363C2×D71—22no—
364C2×D71—22no—
365C2×D71—22no—
366C2×D71—22no—
367C2×D71—22no—
368C2×D71—22no—
369C2×D71—416no—
370C2×D71—41no—
371C2×D71—41no—
372C2×D71—41no—
373C2×D71—41no—
374C2×D71C8×D414yes—
375C4×C71—22no—
376C4×C71—22no—
377C4×C71—22no—
378C4×C71—22no—
379C4×C71—22no—
380C4×C71#54611yescharacteristic
381C4×C71#54611yescharacteristic
382C4×C71#55111yescharacteristic
383C4×C71#55111yescharacteristic
384Dic71—22no—
385Dic71—22no—
386Dic71—22no—
387Dic71—41no—
388Dic71—41no—
389Dic71—41no—
390#22552—711nomaximal, Sylow
391C2×C71—24no—
392C2×C71#234211yescharacteristic
393C2×C71C2×#43111yescharacteristic
394C2×C71#292411yescharacteristic
395C2×C71C2×C8×D411yescharacteristic
396C2×C71D4×M1611yescharacteristic
397C2×C71#297211yescharacteristic
398C2×C71#297411yescharacteristic
399D71—24no—
400D71—42no—
401C2×#431—711no—
402C22×C22⋊C8—711no—
403C2×C4×C22⋊C4—711no—
404#1923—711no—
405#1923—711no—
406#1923—711no—
407#1923—711no—
408#1850—711no—
409#1850—711no—
410#1817—711no—
411#1797—711no—
412#1779—711no—
413C8×C22⋊C4—711no—
414C8×C22⋊C4D7111yescharacteristic, complemented
415C4×C22⋊C8—711no—
416C71#2255211yescharacteristic, complemented, Sylow
417C24×C4—711no—
418C23×C8—711no—
419C23×C8C2×D7111yescharacteristic
420C22×C22⋊C4—711no—
421C22×C22⋊C4—711no—
422C22×C42—711no—
423C22×C42—711no—
424#431—1424no—
425C2×C4⋊C8—711no—
426C2×C4⋊C8—711no—
427C2×C4⋊C8—711no—
428C2×C4⋊C8—711no—
429C2×C22⋊C8—711no—
430C2×C22⋊C8—711no—
431C2×C22⋊C8—711no—
432C2×C22⋊C8—711no—
433C2×C22⋊C8—711no—
434C2×C22⋊C8—711no—
435C2×C22⋊C8—711no—
436C2×C22⋊C8—711no—
437C2×C22⋊C8—711no—
438C2×C22⋊C8—1424no—
439C2×C22⋊C8C2×D7111yescharacteristic
440C2×C4×C8—711no—
441C2×C4×C8—711no—
442C2×C4×C8C2×D7111yescharacteristic, complemented
443C2×C4×C8C2×D7111yescharacteristic, complemented
444C4×C22⋊C4—711no—
445C4×C22⋊C4—711no—
446C4×C22⋊C4—711no—
447C4×C22⋊C4—711no—
448C4×C22⋊C4—711no—
449C4×C22⋊C4—711no—
450C4×C22⋊C4—711no—
451C4×C22⋊C4C2×D7111yescharacteristic
452C2×#95—711no—
453C2×#95—711no—
454#336—711no—
455#336—711no—
456#336—711no—
457#336—711no—
458#336—711no—
459#336—711no—
460#336C2×D7111yescharacteristic, complemented
461#336C2×D7111yescharacteristic, complemented
462C25—711no—
463C23×C4—2841no—
464C23×C4—2841no—
465C23×C4—711no—
466C23×C4—711no—
467C23×C4—711no—
468C23×C4—711no—
469C23×C4—711no—
470C23×C4—711no—
471C23×C4—711no—
472C23×C4—711no—
473C23×C4—711no—
474C23×C4—1422no—
475C23×C4—1422no—
476C23×C4—1422no—
477C23×C4—1422no—
478C23×C4C22×D7111yescharacteristic
479C22×C8—22no—
480C22×C8—22no—
481C22×C8—41no—
482C22×C8—2841no—
483C22×C8—711no—
484C22×C8—711no—
485C22×C8—711no—
486C22×C8—711no—
487C22×C8—1422no—
488C22×C8—1422no—
489C22×C8C22×D7111yescharacteristic
490C22×C8C22×D7111yescharacteristic
491C22×C8C22×D7111yescharacteristic
492C22×C8C22×D7111yescharacteristic
493C2×C22⋊C4—711no—
494C2×C22⋊C4—711no—
495C2×C22⋊C4—711no—
496C2×C22⋊C4—718no—
497C2×C22⋊C4—711no—
498C2×C22⋊C4—711no—
499C2×C22⋊C4—711no—
500C2×C22⋊C4—1424no—
501C2×C22⋊C4C4×D7111yescharacteristic
502C2×C22⋊C4C4×D7111yescharacteristic
503C2×C42—2841no—
504C2×C42—2841no—
505C2×C42—711no—
506C2×C42—711no—
507C2×C42—711no—
508C2×C42—711no—
509C2×C42—711no—
510C2×C42—711no—
511C2×C42—1422no—
512C2×C42—1422no—
513C2×C42C22×D7111yescharacteristic
514C2×C42C22×D7111yescharacteristic
515C4⋊C8—2841no—
516C4⋊C8—2841no—
517C4⋊C8—1422no—
518C4⋊C8—1422no—
519C22⋊C8—22no—
520C22⋊C8—2841no—
521C22⋊C8—2841no—
522C22⋊C8—714no—
523C22⋊C8—1422no—
524C22⋊C8—1422no—
525C22⋊C8—1422no—
526C22⋊C8—1422no—
527C22⋊C8—1422no—
528C22⋊C8—1422no—
529C4×C8—22no—
530C4×C8—41no—
531C4×C8—2841no—
532C4×C8—1422no—
533#95—711no—
534#95—711no—
535#95—711no—
536#95—711no—
537#95—711no—
538#95—711no—
539#95C4×D7111yescharacteristic
540#95C4×D7111yescharacteristic
541C24—2841no—
542C24—2841no—
543C24—714no—
544C24—711no—
545C24—711no—
546C24—1422no—
547C24—1422no—
548C24—1422no—
549C24—1422no—
550C24C2×C4×D7111yescharacteristic
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—2844no—
556C22×C4—2844no—
557C22×C4—2844no—
558C22×C4—2844no—
559C22×C4—2841no—
560C22×C4—2841no—
561C22×C4—2841no—
562C22×C4—2841no—
563C22×C4—2841no—
564C22×C4—2841no—
565C22×C4—2841no—
566C22×C4—714no—
567C22×C4—711no—
568C22×C4—711no—
569C22×C4—711no—
570C22×C4—712no—
571C22×C4—712no—
572C22×C4—714no—
573C22×C4—711no—
574C22×C4—711no—
575C22×C4—711no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1421no—
585C22×C4—1421no—
586C22×C4—1421no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1421no—
590C22×C4—1422no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1421no—
595C22×C4—1421no—
596C22×C4—1421no—
597C22×C4—1421no—
598C22×C4C2×C4×D7111yescharacteristic
599C22×C4C2×C4×D7111yescharacteristic
600C22×C4C2×C4×D7111yescharacteristic
601C22×C4C2×C4×D7111yescharacteristic
602C22×C4C2×C4×D7111yescharacteristic
603C22×C4#1176586512yes—
604C22×C4#1176586512yes—
605C22×C4C23×D7111yescharacteristic
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—44no—
618C2×C8—2844no—
619C2×C8—712no—
620C2×C8—1421no—
621C2×C8—1421no—
622C2×C8—1421no—
623C2×C8—1421no—
624C2×C8—1421no—
625C2×C8—1421no—
626C2×C8—1421no—
627C2×C8—1421no—
628C2×C8—1421no—
629C2×C8—1421no—
630C2×C8—1421no—
631C2×C8D4×D7112yes—
632C22⋊C4—714no—
633C22⋊C4—714no—
634C22⋊C4—714no—
635C22⋊C4—1422no—
636C22⋊C4—1422no—
637C22⋊C4—1422no—
638C22⋊C4C8×D7114yes—
639C22⋊C4#1176584814yes—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—2841no—
645C42—2841no—
646C42—1422no—
647C42—1422no—
648C42—1421no—
649C42—1421no—
650C42—1421no—
651C42—1421no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—2844no—
657C23—2844no—
658C23—2844no—
659C23—2844no—
660C23—2844no—
661C23—712no—
662C23—712no—
663C23—712no—
664C23—712no—
665C23—1428no—
666C23—1428no—
667C23—1421no—
668C23—1421no—
669C23—1421no—
670C23—1421no—
671C23—1421no—
672C23—1421no—
673C23—1421no—
674C23—1421no—
675C23—1421no—
676C23—1421no—
677C23#1455608512yes—
678C23C2×C8×D7112yes—
679C23C2×#1176584812yes—
680C23C22×C4×D7111yescharacteristic
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—2844no—
696C2×C4—2844no—
697C2×C4—2844no—
698C2×C4—2844no—
699C2×C4—2844no—
700C2×C4—2844no—
701C2×C4—2841no—
702C2×C4—2841no—
703C2×C4—2841no—
704C2×C4—2841no—
705C2×C4—712no—
706C2×C4—712no—
707C2×C4—712no—
708C2×C4—1428no—
709C2×C4—1421no—
710C2×C4—1421no—
711C2×C4—1421no—
712C2×C4—1421no—
713C2×C4—1421no—
714C2×C4—1421no—
715C2×C4—1421no—
716C2×C4—1421no—
717C2×C4—1421no—
718C2×C4—1421no—
719C2×C4—1421no—
720C2×C4—1421no—
721C2×C4—1421no—
722C2×C4—1421no—
723C2×C4—1421no—
724C2×C4—1422no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4—1422no—
728C2×C4#1455608512yes—
729C2×C4C2×C8×D7112yes—
730C2×C4C2×C8×D7112yes—
731C2×C4C2×#1176584812yes—
732C2×C4C2×#1176584812yes—
733C2×C4C2×D4×D7111yescharacteristic
734C2×C4#41×D7111yescharacteristic
735C2×C4C2×#1176586511yescharacteristic
736C2×C4C2×#1176586511yescharacteristic
737C2×C4#1455617311yescharacteristic
738C2×C4#1455617411yescharacteristic
739C8—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—2841no—
744C8—2841no—
745C8—2841no—
746C8—1422no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—28416no—
754C22—2841no—
755C22—2841no—
756C22—2841no—
757C22—2841no—
758C22—714no—
759C22—1422no—
760C22—1422no—
761C22—1422no—
762C22—1422no—
763C22—1422no—
764C22—1422no—
765C22—1422no—
766C22—1422no—
767C22—1422no—
768C22#1798605014yescomplemented
769C22C2×#1455608511yescharacteristic
770C22C4×D4×D7111yescharacteristic
771C22#1798647111yescharacteristic
772C22C22×C8×D7111yescharacteristic
773C22C22×#1176584811yescharacteristic
774C22#131×D7111yescharacteristic
775C22#1798676411yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—22no—
781C4—2841no—
782C4—2841no—
783C4—2841no—
784C4—1422no—
785C4—1422no—
786C4—1422no—
787C4#1798663911yescharacteristic
788C4#1798664511yescharacteristic
789C4#1798667311yescharacteristic
790C4#1798667811yescharacteristic
791C2—24no—
792C2—2842no—
793C2—1424no—
794C2#2259118311yescharacteristic
795C2C2×#1798605011yescharacteristic
796C2#2259699511yescharacteristic
797C2C8×D4×D7111yescharacteristic
798C2D4×#1176584811yescharacteristic
799C2#2259736111yescharacteristic
800C2#2259737311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC8×C22⋊C4×C71C2
socleC23×C71C23×C4
prime radicalC24×D71C2×C4
cosocleC22×C4×C71C24
hypercenterC8×C22⋊C4D71
hypocenterC71#22552
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#17986050C2semidirect
4. #22588946C2semidirect
5. #22588946C2semidirect
6. #22588944C2semidirect
7. #22588944C2semidirect
8. #22588518C2semidirect
9. #22588517C2semidirect
10. #22588407C2semidirect
11. #22588319C2semidirect
13. C22⋊C4×C71⋊C8C2semidirect
14. C4×(C2×D71)⋊C8C2semidirect
15. C8×C22⋊C4×C71C2semidirect
23. C2×Dic71⋊C8C22semidirect
24. C2×Dic71⋊C8C22semidirect
25. C2×Dic71⋊C8C22semidirect
26. C2×Dic71⋊C8C22semidirect
37. C2×C4×C71⋊C8C22semidirect
38. C2×C4×C71⋊C8C22semidirect
48. #17985754C22semidirect
49. #17985754C22semidirect
50. #17985753C22semidirect
51. #17985753C22semidirect
52. #17985753C22semidirect
53. #17985753C22semidirect
56. C2×C4×C8×C71C22semidirect
57. C2×C4×C8×C71C22semidirect
59. #336×C71C22semidirect
60. #336×C71C22semidirect
91. C22⋊C4×D71C8semidirect
188. C2×C4×D71C2×C8semidirect
189. C2×C4×D71C2×C8semidirect
209. (C2×D71)⋊C4C2×C8semidirect
210. (C2×D71)⋊C4C2×C8semidirect
352. C22×C71#431semidirect
414. C8×C22⋊C4D71semidirect
416. C71#22552semidirect
442. C2×C4×C8C2×D71semidirect
443. C2×C4×C8C2×D71semidirect
460. #336C2×D71semidirect
461. #336C2×D71semidirect
768. C22#17986050semidirect

Maximal subgroups

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

subgroupindex
C2×#179860502
C22×(C2×D71)⋊C82
C4×C22⋊C4×D712
#225889462
#225889442
#225885182
#225885172
#225884072
#225883192
#225882492
C22⋊C4×C71⋊C82
C4×(C2×D71)⋊C82
C8×C22⋊C4×C712
#2255271