Finite Group Databasebeta

← #32014370

Subgroups — #32014370

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×#17986051C211yesmaximal, characteristic, complemented
2C2×C22⋊C8×D71C211yesmaximal, characteristic
3C4×C22⋊C4×D71C211yesmaximal, characteristic
4#22588949C211yesmaximal, characteristic, complemented
5#22588948C211yesmaximal, characteristic, complemented
6#22588943C211yesmaximal, characteristic, complemented
7#22588519C211yesmaximal, characteristic, complemented
8#22588516C211yesmaximal, characteristic, complemented
9#22588407C211yesmaximal, characteristic, complemented
10#22588319C211yesmaximal, characteristic, complemented
11#22588249C211yesmaximal, characteristic
12C8×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
13#22588110C211yesmaximal, characteristic, complemented
14C4×(C2×D71)⋊C8C211yesmaximal, characteristic, complemented
15C71×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19C2×C22⋊C4×D71C411yescharacteristic
20C2×C22⋊C4×D71C411yescharacteristic
21C2×C42×D71C2211yescharacteristic
22C2×C42×D71C2211yescharacteristic
23#17986051—24no—
24C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
25C2×Dic71⋊C8C2211yescharacteristic, complemented
26C2×Dic71⋊C8C2211yescharacteristic, complemented
27C2×C22⋊(C71⋊C8)C2211yescharacteristic
28C2×C22⋊(C71⋊C8)C2211yescharacteristic
29C2×(C2×D71)⋊C8C2211yescharacteristic
30C2×(C2×D71)⋊C8C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×(C2×D71)⋊C8C2211yescharacteristic
35C22⋊C8×D71—24no—
36C2×C4×C71⋊C8C2211yescharacteristic, complemented
37C2×C8×Dic71C2211yescharacteristic, complemented
38C2×C8×Dic71C2211yescharacteristic, 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
54C2×C4⋊C8×C71C2211yescharacteristic, complemented
55C2×C22⋊C8×C71C2211yescharacteristic
56C2×C22⋊C8×C71C2211yescharacteristic
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⋊C8C2311yescharacteristic
78C22×C71⋊C8C2311yescharacteristic
79C22×C71⋊C8C2311yescharacteristic
80C22×C71⋊C8C2311yescharacteristic
81C2×C8×D71—22no—
82C2×C8×D71—22no—
83C2×C8×D71—22no—
84C2×C8×D71—22no—
85C2×C8×D71—41no—
86C2×C8×D71—41no—
87C2×C22⋊Dic71C2×C411yescharacteristic
88C2×C22⋊Dic71C2×C411yescharacteristic
89C2×(C2×D71)⋊C4C2×C411yescharacteristic
90C2×(C2×D71)⋊C4C2×C411yescharacteristic
91C2×(C2×D71)⋊C4C2×C411yescharacteristic
92C2×(C2×D71)⋊C4C2×C411yescharacteristic
93C22⋊C4×D71—24no—
94C22⋊C4×D71C818yescomplemented
95C2×C4×Dic71C2×C411yescharacteristic
96C2×C4×Dic71C2×C411yescharacteristic
97C2×C4×Dic71C2×C411yescharacteristic
98C2×C4×Dic71C2×C411yescharacteristic
99C2×C4×Dic71C2311yescharacteristic
100C2×C4×Dic71C2311yescharacteristic
101C42×D71—22no—
102C42×D71—22no—
103C42×D71—41no—
104C42×D71—41no—
105C4⋊(C71⋊C8)—22no—
106Dic71⋊C8—41no—
107Dic71⋊C8—41no—
108C22⋊(C71⋊C8)—22no—
109C22⋊(C71⋊C8)—41no—
110(C2×D71)⋊C8—22no—
111(C2×D71)⋊C8—22no—
112(C2×D71)⋊C8—22no—
113(C2×D71)⋊C8—22no—
114(C2×D71)⋊C8—22no—
115(C2×D71)⋊C8D414yes—
116C4×C71⋊C8—41no—
117C8×Dic71—22no—
118C8×Dic71—22no—
119C71⋊#95C2×C411yescharacteristic
120C71⋊#95C2×C411yescharacteristic
121C71⋊#95C2×C411yescharacteristic
122C71⋊#95C2×C411yescharacteristic
123C71⋊#95C2×C411yescharacteristic
124C71⋊#95C2×C411yescharacteristic
125C23×C4×C71C2311yescharacteristic
126C22×C8×C71C2311yescharacteristic
127C22×C8×C71C2311yescharacteristic
128C22×C8×C71C2311yescharacteristic
129C22×C8×C71C2311yescharacteristic
130C2×C22⋊C4×C71C2×C411yescharacteristic
131C2×C22⋊C4×C71C2×C411yescharacteristic
132C2×C42×C71C2311yescharacteristic
133C2×C42×C71C2311yescharacteristic
134C4⋊C8×C71—22no—
135C22⋊C8×C71—22no—
136C22⋊C8×C71—41no—
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—21no—
165C2×C4×D71—21no—
166C2×C4×D71—21no—
167C2×C4×D71—21no—
168C2×C4×D71—22no—
169C2×C4×D71—22no—
170C2×C4×D71—22no—
171C2×C4×D71—22no—
172C2×C4×D71—22no—
173C2×C4×D71—22no—
174C2×C4×D71—22no—
175C2×C4×D71—22no—
176C2×C4×D71—44no—
177C2×C4×D71—44no—
178C2×C4×D71—44no—
179C2×C4×D71—44no—
180C2×C4×D71—41no—
181C2×C4×D71—41no—
182C2×C4×D71—41no—
183C2×C4×D71—41no—
184C2×C4×D71—41no—
185C2×C4×D71—41no—
186C2×C4×D71C2×C814yescomplemented
187C2×C4×D71C2×C814yescomplemented
188C2×C4×D71C2×D412yes—
189C2×C4×D71#4112yes—
190C2×C4×D71#4112yes—
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⋊C8C2×D412yes—
204C8×D71—44no—
205C8×D71—44no—
206C22⋊Dic71—22no—
207C22⋊Dic71C2×C814yescomplemented
208(C2×D71)⋊C4—22no—
209(C2×D71)⋊C4C2×C814yes—
210(C2×D71)⋊C4C2×C814yes—
211(C2×D71)⋊C4M1614yes—
212C4×Dic71—21no—
213C4×Dic71—21no—
214C4×Dic71—21no—
215C4×Dic71—21no—
216C4×Dic71—22no—
217C4×Dic71—22no—
218C4×Dic71—41no—
219C4×Dic71—41no—
220C24×C71C22×C411yescharacteristic
221C22×C4×C71—21no—
222C22×C4×C71—21no—
223C22×C4×C71—21no—
224C22×C4×C71—21no—
225C22×C4×C71—21no—
226C22×C4×C71—21no—
227C22×C4×C71C22×C411yescharacteristic
228C22×C4×C71C22×C411yescharacteristic
229C22×C4×C71C22×C411yescharacteristic
230C22×C4×C71C22×C411yescharacteristic
231C22×C4×C71C22×C411yescharacteristic
232C22×C4×C71C2411yescharacteristic
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—21no—
244C2×C8×C71C2×D412yes—
245C22⋊C4×C71—22no—
246C22⋊C4×C71C2×C814yescomplemented
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—21no—
256C23×C71—21no—
257C23×C71C22×C812yes—
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—28no—
268C22×D71—28no—
269C22×D71—44no—
270C22×D71—44no—
271C22×D71—44no—
272C22×D71—44no—
273C22×D71—44no—
274C22×D71#11712yes—
275C22×D71C4×D412yes—
276C22×D71C22×C812yes—
277C22×D71C22×C812yes—
278C22×D71C2×M1612yes—
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—21no—
291C2×C4×C71—21no—
292C2×C4×C71—41no—
293C2×C4×C71—41no—
294C2×C4×C71—41no—
295C2×C4×C71—41no—
296C2×C4×C71C22×C812yes—
297C2×C4×C71C22×C812yes—
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—44no—
319C2×Dic71#11712yes—
320C2×Dic71C4×D412yes—
321C2×Dic71C22×C812yes—
322C2×Dic71C22×C812yes—
323C2×Dic71C2×M1612yes—
324C4×D71—28no—
325C4×D71—22no—
326C4×D71—22no—
327C4×D71—22no—
328C4×D71—22no—
329C4×D71—22no—
330C4×D71—22no—
331C4×D71—22no—
332C4×D71—22no—
333C4×D71—44no—
334C4×D71—44no—
335C4×D71—44no—
336C4×D71—44no—
337C4×D71—44no—
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—41no—
350C22×C71—41no—
351C22×C71—41no—
352C22×C71—41no—
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—22no—
370C2×D71—22no—
371C2×D71—22no—
372C2×D71—416no—
373C2×D71#43114yescomplemented
374C2×D71C8×D414yes—
375C4×C71—22no—
376C4×C71—22no—
377C4×C71—22no—
378C4×C71—41no—
379C4×C71—41no—
380C4×C71#54611yescharacteristic
381C4×C71#54611yescharacteristic
382C4×C71#55111yescharacteristic
383C4×C71#55111yescharacteristic
384Dic71—22no—
385Dic71—22no—
386Dic71—22no—
387Dic71—22no—
388Dic71—22no—
389Dic71—41no—
390#22552—711nomaximal, Sylow
391C2×C71—42no—
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—24no—
401C2×#431—711no—
402C22×C22⋊C8—711no—
403C2×C4×C22⋊C4—711no—
404#1923—711no—
405#1923—711no—
406#1923—711no—
407#1923D7111yescharacteristic, complemented
408#1850—711no—
409#1850—711no—
410#1817—711no—
411#1797—711no—
412#1779—711no—
413C8×C22⋊C4—711no—
414C8×C22⋊C4—711no—
415C4×C22⋊C8—711no—
416C71#2255211yescharacteristic, complemented, Sylow
417C24×C4—711no—
418C23×C8—711no—
419C23×C8—711no—
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⋊C8C2×D7111yescharacteristic, complemented
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—1424no—
438C2×C22⋊C8C2×D7111yescharacteristic
439C2×C22⋊C8C2×D7111yescharacteristic
440C2×C4×C8—711no—
441C2×C4×C8—711no—
442C2×C4×C8—711no—
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—2841no—
480C22×C8—2841no—
481C22×C8—711no—
482C22×C8—711no—
483C22×C8—711no—
484C22×C8—711no—
485C22×C8—1422no—
486C22×C8—1422no—
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—711no—
497C2×C22⋊C4—718no—
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—22no—
516C4⋊C8—2841no—
517C4⋊C8—2841no—
518C4⋊C8—1422no—
519C22⋊C8—22no—
520C22⋊C8—41no—
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—41no—
530C4×C8—2841no—
531C4×C8—1422no—
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—21no—
556C22×C4—21no—
557C22×C4—2841no—
558C22×C4—2841no—
559C22×C4—2841no—
560C22×C4—2841no—
561C22×C4—2841no—
562C22×C4—2841no—
563C22×C4—2844no—
564C22×C4—2844no—
565C22×C4—2844no—
566C22×C4—2844no—
567C22×C4—2841no—
568C22×C4—714no—
569C22×C4—711no—
570C22×C4—711no—
571C22×C4—711no—
572C22×C4—711no—
573C22×C4—711no—
574C22×C4—712no—
575C22×C4—712no—
576C22×C4—712no—
577C22×C4—712no—
578C22×C4—714no—
579C22×C4—711no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1422no—
586C22×C4—1422no—
587C22×C4—1422no—
588C22×C4—1422no—
589C22×C4—1422no—
590C22×C4—1422no—
591C22×C4—1422no—
592C22×C4—1421no—
593C22×C4—1421no—
594C22×C4—1421no—
595C22×C4—1421no—
596C22×C4—1421no—
597C22×C4—1421no—
598C22×C4—1421no—
599C22×C4—1421no—
600C22×C4C2×C4×D7111yescharacteristic
601C22×C4C2×C4×D7111yescharacteristic
602C22×C4C2×C4×D7111yescharacteristic
603C22×C4C2×C4×D7111yescharacteristic
604C22×C4C2×C4×D7111yescharacteristic
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—2844no—
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—22no—
633C22⋊C4—714no—
634C22⋊C4—714no—
635C22⋊C4—714no—
636C22⋊C4—714no—
637C22⋊C4—1422no—
638C22⋊C4—1422no—
639C22⋊C4C8×D7114yescomplemented
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—21no—
657C23—21no—
658C23—2844no—
659C23—2844no—
660C23—2844no—
661C23—2844no—
662C23—2844no—
663C23—712no—
664C23—712no—
665C23—712no—
666C23—712no—
667C23—712no—
668C23—712no—
669C23—1428no—
670C23—1428no—
671C23—1421no—
672C23—1421no—
673C23—1421no—
674C23—1421no—
675C23—1421no—
676C23—1421no—
677C23—1421no—
678C23—1421no—
679C23C2×C8×D7112yes—
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—21no—
692C2×C4—21no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—2844no—
698C2×C4—2844no—
699C2×C4—2844no—
700C2×C4—2844no—
701C2×C4—2844no—
702C2×C4—2844no—
703C2×C4—712no—
704C2×C4—712no—
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—1422no—
723C2×C4—1422no—
724C2×C4—1422no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4—1422no—
728C2×C4—1422no—
729C2×C4—1422no—
730C2×C4C2×C8×D7112yes—
731C2×C4C2×C8×D7112yes—
732C2×C4M16×D7112yes—
733C2×C4C2×D4×D7111yescharacteristic
734C2×C4#41×D7111yescharacteristic
735C2×C4#41×D7111yescharacteristic
736C2×C4#41×D7111yescharacteristic
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—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—28416no—
755C22—714no—
756C22—714no—
757C22—1422no—
758C22—1422no—
759C22—1422no—
760C22—1422no—
761C22—1422no—
762C22—1422no—
763C22—1422no—
764C22—1422no—
765C22—1422no—
766C22—1422no—
767C22—1422no—
768C22—1422no—
769C22#117×D7111yescharacteristic
770C22C4×D4×D7111yescharacteristic
771C22#1798647111yescharacteristic
772C22C22×C8×D7111yescharacteristic
773C22C2×M16×D7111yescharacteristic
774C22#131×D7111yescharacteristic
775C22#1798676411yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—41no—
780C4—41no—
781C4—2841no—
782C4—1422no—
783C4—1422no—
784C4—1422no—
785C4—1422no—
786C4—1422no—
787C4#1798663811yescharacteristic
788C4#1798664211yescharacteristic
789C4#1798667411yescharacteristic
790C4#1798667711yescharacteristic
791C2—42no—
792C2—1424no—
793C2—1424no—
794C2#2259118811yescharacteristic
795C2#431×D7111yescharacteristic
796C2#2259699611yescharacteristic
797C2C8×D4×D7111yescharacteristic
798C2#2259707611yescharacteristic
799C2#2259736111yescharacteristic
800C2#2259737011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC71×#1923C2
socleC23×C71C23×C4
prime radicalC24×D71C2×C4
cosocleC22×C4×C71C24
hypercenter#1923D71
hypocenterC71#22552
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#17986051C2semidirect
4. #22588949C2semidirect
5. #22588948C2semidirect
6. #22588943C2semidirect
7. #22588519C2semidirect
8. #22588516C2semidirect
9. #22588407C2semidirect
10. #22588319C2semidirect
12. C8×(C2×D71)⋊C4C2semidirect
13. #22588110C2semidirect
14. C4×(C2×D71)⋊C8C2semidirect
15. C71×#1923C2semidirect
24. C2×C4⋊(C71⋊C8)C22semidirect
25. C2×Dic71⋊C8C22semidirect
26. C2×Dic71⋊C8C22semidirect
36. C2×C4×C71⋊C8C22semidirect
37. C2×C8×Dic71C22semidirect
38. C2×C8×Dic71C22semidirect
48. #17985754C22semidirect
49. #17985754C22semidirect
50. #17985753C22semidirect
51. #17985753C22semidirect
52. #17985753C22semidirect
53. #17985753C22semidirect
54. C2×C4⋊C8×C71C22semidirect
57. C2×C4×C8×C71C22semidirect
59. #336×C71C22semidirect
60. #336×C71C22semidirect
94. C22⋊C4×D71C8semidirect
186. C2×C4×D71C2×C8semidirect
187. C2×C4×D71C2×C8semidirect
207. C22⋊Dic71C2×C8semidirect
246. C22⋊C4×C71C2×C8semidirect
373. C2×D71#431semidirect
407. #1923D71semidirect
416. C71#22552semidirect
428. C2×C4⋊C8C2×D71semidirect
443. C2×C4×C8C2×D71semidirect
460. #336C2×D71semidirect
461. #336C2×D71semidirect
639. C22⋊C4C8×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860512
C2×C22⋊C8×D712
C4×C22⋊C4×D712
#225889492
#225889482
#225889432
#225885192
#225885162
#225884072
#225883192
#225882492
C8×(C2×D71)⋊C42
#225881102
C4×(C2×D71)⋊C82
C71×#19232
#2255271