Finite Group Databasebeta

← #32019681

Subgroups — #32019681

Order 18176.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986077C211yesmaximal, characteristic, complemented
2C2×#17986077C211yesmaximal, characteristic, complemented
3C2×#17986071C211yesmaximal, characteristic, complemented
4C2×#17986026C211yesmaximal, characteristic, complemented
5#22589139C211yesmaximal, characteristic, complemented
6#22589059C211yesmaximal, characteristic, complemented
7#22588955C211yesmaximal, characteristic, complemented
8#22588948C211yesmaximal, characteristic, complemented
9#22588638C211yesmaximal, characteristic, complemented
10#22588633C211yesmaximal, characteristic, complemented
11#22588525C211yesmaximal, characteristic, complemented
12#22588525C211yesmaximal, characteristic, complemented
13#22588215C211yesmaximal, characteristic, complemented
14#22588106C211yesmaximal, characteristic, complemented
15C71×#2392C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C22×#11765849C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19C23×C71⋊C8C2211yescharacteristic
20#17986077—24no—
21#17986077—24no—
22#17986071—24no—
23#17986026—24no—
24C2×C4⋊(C71⋊C8)C2211yescharacteristic
25C2×C4⋊(C71⋊C8)C2211yescharacteristic
26C2×C4⋊(C71⋊C8)C2211yescharacteristic
27C2×C4⋊(C71⋊C8)C2211yescharacteristic
28C2×C4⋊(C71⋊C8)C2211yescharacteristic
29C2×C4⋊(C71⋊C8)C2211yescharacteristic
30C2×C22⋊(C71⋊C8)C2211yescharacteristic
31C2×C22⋊(C71⋊C8)C2211yescharacteristic
32C2×C22⋊(C71⋊C8)C2211yescharacteristic
33C2×C22⋊(C71⋊C8)C2211yescharacteristic
34C2×C22⋊(C71⋊C8)C2211yescharacteristic
35C2×C22⋊(C71⋊C8)C2211yescharacteristic
36C2×C22⋊(C71⋊C8)C2211yescharacteristic
37C2×C22⋊(C71⋊C8)C2211yescharacteristic
38C2×#14556039C2211yescharacteristic
39C2×#14556039C2211yescharacteristic
40C2×C4×C71⋊C8C2211yescharacteristic
41C2×C4×C71⋊C8C2211yescharacteristic
42#17985754C2211yescharacteristic
43#17985754C2211yescharacteristic
44#17985754C2211yescharacteristic
45#17985754C2211yescharacteristic
46#17985754C2211yescharacteristic
47#17985754C2211yescharacteristic
48C2×C4×D4×C71C2211yescharacteristic
49C2×C4×D4×C71C2211yescharacteristic
50C2×C4×D4×C71C2211yescharacteristic
51C2×#117×C71C2211yescharacteristic
52#398×C71C411yescharacteristic
53#397×C71C411yescharacteristic
54#396×C71C411yescharacteristic
55#396×C71C411yescharacteristic
56#394×C71C411yescharacteristic
57#394×C71C411yescharacteristic
58#394×C71C411yescharacteristic
59#392×C71C411yescharacteristic
60C4×C4⋊C4×C71C2211yescharacteristic
61C4×C22⋊C4×C71C2211yescharacteristic
62C4×C22⋊C4×C71C2211yescharacteristic
63C2×#11765849—22no—
64C2×#11765849—22no—
65C2×#11765849—22no—
66C2×#11765849—22no—
67C2×#11765849—22no—
68C2×#11765849—22no—
69C2×#11765849—41no—
70C2×#11765849—41no—
71C2×#11765849—41no—
72C22×C71⋊C8—22no—
73C22×C71⋊C8—22no—
74C22×C71⋊C8—41no—
75C22×C71⋊C8C2311yescharacteristic
76C22×C71⋊C8C2311yescharacteristic
77C22×C71⋊C8C2311yescharacteristic
78C22×C71⋊C8C2311yescharacteristic
79C22×C71⋊C8C2311yescharacteristic
80C22×C71⋊C8C2311yescharacteristic
81C22×C71⋊C8C2311yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C4⋊(C71⋊C8)—22no—
84C4⋊(C71⋊C8)—22no—
85C4⋊(C71⋊C8)—22no—
86C4⋊(C71⋊C8)—22no—
87C4⋊(C71⋊C8)—22no—
88C4⋊(C71⋊C8)D414yescomplemented
89C22⋊(C71⋊C8)—22no—
90C22⋊(C71⋊C8)—22no—
91C22⋊(C71⋊C8)—22no—
92C22⋊(C71⋊C8)—22no—
93C22⋊(C71⋊C8)—22no—
94C22⋊(C71⋊C8)—41no—
95C22⋊(C71⋊C8)—41no—
96C22⋊(C71⋊C8)D414yescomplemented
97#14556039—22no—
98#14556039—22no—
99C4×C71⋊C8—22no—
100C4×C71⋊C8—22no—
101C22×D4×C71C2×C411yescharacteristic
102C22×D4×C71C2×C411yescharacteristic
103C22×D4×C71C2×C411yescharacteristic
104C23×C4×C71C2311yescharacteristic
105C23×C4×C71C2311yescharacteristic
106C23×C4×C71C2311yescharacteristic
107C4×D4×C71—22no—
108C4×D4×C71—22no—
109C4×D4×C71—22no—
110C4×D4×C71—22no—
111C4×D4×C71—22no—
112C4×D4×C71—22no—
113#117×C71—22no—
114#117×C71—22no—
115C2×C4⋊C4×C71C2×C411yescharacteristic
116C2×C4⋊C4×C71C2×C411yescharacteristic
117C2×C4⋊C4×C71C2×C411yescharacteristic
118C2×C4⋊C4×C71C2×C411yescharacteristic
119C2×C4⋊C4×C71C2×C411yescharacteristic
120C2×C4⋊C4×C71C2×C411yescharacteristic
121C2×C4⋊C4×C71C2×C411yescharacteristic
122C2×C22⋊C4×C71C2×C411yescharacteristic
123C2×C22⋊C4×C71C2×C411yescharacteristic
124C2×C22⋊C4×C71C2×C411yescharacteristic
125C2×C22⋊C4×C71C2×C411yescharacteristic
126C2×C22⋊C4×C71C2×C411yescharacteristic
127C2×C22⋊C4×C71C2×C411yescharacteristic
128C2×C22⋊C4×C71C2×C411yescharacteristic
129C2×C22⋊C4×C71C2×C411yescharacteristic
130C2×C22⋊C4×C71C2×C411yescharacteristic
131C2×C22⋊C4×C71C2×C411yescharacteristic
132C2×C22⋊C4×C71C2×C411yescharacteristic
133C2×C22⋊C4×C71C2×C411yescharacteristic
134C2×C42×C71C2311yescharacteristic
135C2×C42×C71C2311yescharacteristic
136C2×C42×C71C2311yescharacteristic
137C2×C42×C71C2311yescharacteristic
138#95×C71C2×C411yescharacteristic
139#95×C71C2×C411yescharacteristic
140#95×C71C2×C411yescharacteristic
141#95×C71C2×C411yescharacteristic
142#95×C71C2×C411yescharacteristic
143#95×C71C2×C411yescharacteristic
144#11765849—44no—
145#11765849—44no—
146#11765849—44no—
147C2×C71⋊C8—21no—
148C2×C71⋊C8—21no—
149C2×C71⋊C8—21no—
150C2×C71⋊C8—21no—
151C2×C71⋊C8—21no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8—21no—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—21no—
161C2×C71⋊C8—21no—
162C2×C71⋊C8—21no—
163C2×C71⋊C8—21no—
164C2×C71⋊C8—21no—
165C2×C71⋊C8—21no—
166C2×C71⋊C8—21no—
167C2×C71⋊C8—44no—
168C2×C71⋊C8C2×D412yes—
169C2×C71⋊C8C2×D412yes—
170C2×C71⋊C8C2×D412yes—
171C2×C71⋊C8C2×D412yes—
172C24×C71C22×C411yescharacteristic
173C24×C71C22×C411yescharacteristic
174C24×C71C22×C411yescharacteristic
175C2×D4×C71—22no—
176C2×D4×C71—22no—
177C2×D4×C71—22no—
178C2×D4×C71—22no—
179C2×D4×C71—41no—
180C2×D4×C71—41no—
181C2×D4×C71—41no—
182C2×D4×C71—41no—
183C2×D4×C71—41no—
184C22×C4×C71—21no—
185C22×C4×C71—21no—
186C22×C4×C71—21no—
187C22×C4×C71—21no—
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—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71C22×C411yescharacteristic
201C22×C4×C71C22×C411yescharacteristic
202C22×C4×C71C22×C411yescharacteristic
203C22×C4×C71C22×C411yescharacteristic
204C22×C4×C71C22×C411yescharacteristic
205C22×C4×C71C22×C411yescharacteristic
206C22×C4×C71C22×C411yescharacteristic
207C22×C4×C71C22×C411yescharacteristic
208C22×C4×C71C22×C411yescharacteristic
209C22×C4×C71C22×C411yescharacteristic
210C22×C4×C71C22×C411yescharacteristic
211C22×C4×C71C2×D412yes—
212C22×C4×C71#4112yes—
213C22×C4×C71C2411yescharacteristic
214C4⋊C4×C71—22no—
215C4⋊C4×C71—22no—
216C4⋊C4×C71—22no—
217C4⋊C4×C71—22no—
218C4⋊C4×C71—22no—
219C4⋊C4×C71—22no—
220C4⋊C4×C71—41no—
221C22⋊C4×C71—22no—
222C22⋊C4×C71—22no—
223C22⋊C4×C71—22no—
224C22⋊C4×C71—22no—
225C22⋊C4×C71—22no—
226C22⋊C4×C71—22no—
227C22⋊C4×C71—22no—
228C22⋊C4×C71—22no—
229C22⋊C4×C71—22no—
230C22⋊C4×C71—41no—
231C22⋊C4×C71—41no—
232C22⋊C4×C71—41no—
233C42×C71—21no—
234C42×C71—21no—
235C42×C71—21no—
236C42×C71—21no—
237C42×C71—21no—
238C42×C71—21no—
239C42×C71C2×D412yes—
240C42×C71#4112yes—
241C23×C71—21no—
242C23×C71—21no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71—21no—
246C23×C71—21no—
247C23×C71—21no—
248C23×C71—21no—
249C23×C71—21no—
250C23×C71—21no—
251C23×C71—21no—
252C23×C71—21no—
253C23×C71—21no—
254C23×C71—21no—
255C23×C71—21no—
256C23×C71—21no—
257C23×C71—21no—
258C23×C71—21no—
259C23×C71—21no—
260C23×C71—21no—
261C23×C71C4×D412yes—
262C23×C71C23×C411yescharacteristic
263D4×C71—44no—
264D4×C71—44no—
265D4×C71—44no—
266C2×C4×C71—21no—
267C2×C4×C71—21no—
268C2×C4×C71—21no—
269C2×C4×C71—21no—
270C2×C4×C71—21no—
271C2×C4×C71—21no—
272C2×C4×C71—21no—
273C2×C4×C71—21no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—21no—
279C2×C4×C71—21no—
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—21no—
293C2×C4×C71—21no—
294C2×C4×C71—21no—
295C2×C4×C71—21no—
296C2×C4×C71—21no—
297C2×C4×C71—21no—
298C2×C4×C71—21no—
299C2×C4×C71—41no—
300C2×C4×C71—41no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
303C2×C4×C71—41no—
304C2×C4×C71—41no—
305C2×C4×C71—41no—
306C2×C4×C71—41no—
307C2×C4×C71C4×D412yes—
308C2×C4×C71C4×D412yes—
309C2×C4×C71C4×D412yes—
310C2×C4×C71#13112yes—
311C2×C4×C71C22×D411yescharacteristic
312C2×C4×C71C22×D411yescharacteristic
313C2×C4×C71C2×#4111yescharacteristic
314C2×C4×C71C2×#4111yescharacteristic
315C2×C4×C71H(5,𝔽2)11yescharacteristic
316C2×C4×C712−1+411yescharacteristic
317C71⋊C8—22no—
318C71⋊C8—22no—
319C71⋊C8—22no—
320C71⋊C8—22no—
321C71⋊C8—41no—
322C71⋊C8—41no—
323C71⋊C8—41no—
324C71⋊C8—41no—
325C22×C71—22no—
326C22×C71—22no—
327C22×C71—22no—
328C22×C71—41no—
329C22×C71—41no—
330C22×C71—41no—
331C22×C71—41no—
332C22×C71—41no—
333C22×C71—41no—
334C22×C71—41no—
335C22×C71—41no—
336C22×C71—41no—
337C22×C71—41no—
338C22×C71—41no—
339C22×C71—41no—
340C22×C71—41no—
341C22×C71—41no—
342C22×C71—41no—
343C22×C71—41no—
344C22×C71—41no—
345C22×C71—41no—
346C22×C71C2×C4×D411yescharacteristic
347C22×C71C2×C4×D411yescharacteristic
348C22×C71#52011yescharacteristic
349C22×C71C2×#13111yescharacteristic
350C22×C71#56811yescharacteristic
351C22×C71#56811yescharacteristic
352C22×C71#56811yescharacteristic
353C4×C71—22no—
354C4×C71—22no—
355C4×C71—22no—
356C4×C71—22no—
357C4×C71—41no—
358C4×C71—41no—
359C4×C71—41no—
360C4×C71—41no—
361C4×C71—41no—
362C4×C71—41no—
363C4×C71—41no—
364C4×C71D4211yescharacteristic
365C4×C71#54711yescharacteristic
366C4×C71#54811yescharacteristic
367C4×C71#55311yescharacteristic
368#22994—711nomaximal, Sylow
369C2×C71—42no—
370C2×C71—81no—
371C2×C71—81no—
372C2×C71#236111yescharacteristic
373C2×C71#293011yescharacteristic
374C2×C71#293011yescharacteristic
375C2×C71#293311yescharacteristic
376C2×C71#293511yescharacteristic
377C2×C71#299311yescharacteristic
378C2×C71#299511yescharacteristic
379C2×#436—711no—
380C2×#436—711no—
381C2×#435—711no—
382C2×#424—711no—
383#2392D7111yescharacteristic
384#1955—711no—
385#1939—711no—
386#1924—711no—
387#1923—711no—
388#1870—711no—
389#1869—711no—
390#1851—711no—
391#1851—711no—
392#1771—711no—
393#1750—711no—
394C71#2299411yescharacteristic, complemented, Sylow
395C22×M16—711no—
396C22×M16—711no—
397C22×M16—711no—
398C23×C8—711no—
399C2×C4×D4C2×D7111yescharacteristic
400C2×C4×D4C2×D7111yescharacteristic
401C2×C4×D4C2×D7111yescharacteristic
402C2×#117C2×D7111yescharacteristic
403#436—1424no—
404#436—1424no—
405#435—1424no—
406#424—1424no—
407C2×C4⋊C8—711no—
408C2×C4⋊C8—711no—
409C2×C4⋊C8—711no—
410C2×C4⋊C8—711no—
411C2×C4⋊C8—711no—
412C2×C4⋊C8—711no—
413C2×C22⋊C8—711no—
414C2×C22⋊C8—711no—
415C2×C22⋊C8—711no—
416C2×C22⋊C8—711no—
417C2×C22⋊C8—711no—
418C2×C22⋊C8—711no—
419C2×C22⋊C8—711no—
420C2×C22⋊C8—711no—
421C2×#97—711no—
422C2×#97—711no—
423C2×C4×C8—711no—
424C2×C4×C8—711no—
425#398Dic7111yescharacteristic
426#397Dic7111yescharacteristic
427#396Dic7111yescharacteristic
428#396Dic7111yescharacteristic
429#394Dic7111yescharacteristic
430#394Dic7111yescharacteristic
431#394Dic7111yescharacteristic
432#392Dic7111yescharacteristic
433C4×C4⋊C4C2×D7111yescharacteristic
434C4×C22⋊C4C2×D7111yescharacteristic
435C4×C22⋊C4C2×D7111yescharacteristic
436#336—711no—
437#336—711no—
438#336—711no—
439#336—711no—
440#336—711no—
441#336—711no—
442C22×D4C2×Dic7111yescharacteristic
443C22×D4C2×Dic7111yescharacteristic
444C22×D4C2×Dic7111yescharacteristic
445C23×C4C22×D7111yescharacteristic
446C23×C4C22×D7111yescharacteristic
447C23×C4C22×D7111yescharacteristic
448C2×M16—2841no—
449C2×M16—2841no—
450C2×M16—2841no—
451C2×M16—1422no—
452C2×M16—1422no—
453C2×M16—1422no—
454C2×M16—1422no—
455C2×M16—1422no—
456C2×M16—1422no—
457C22×C8—2841no—
458C22×C8—711no—
459C22×C8—711no—
460C22×C8—711no—
461C22×C8—711no—
462C22×C8—711no—
463C22×C8—711no—
464C22×C8—711no—
465C22×C8—711no—
466C22×C8—1422no—
467C22×C8—1422no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4C2×Dic7111yescharacteristic
477C2×C4⋊C4C2×Dic7111yescharacteristic
478C2×C4⋊C4C2×Dic7111yescharacteristic
479C2×C4⋊C4C2×Dic7111yescharacteristic
480C2×C4⋊C4C2×Dic7111yescharacteristic
481C2×C4⋊C4C2×Dic7111yescharacteristic
482C2×C4⋊C4C2×Dic7111yescharacteristic
483C2×C22⋊C4C2×Dic7111yescharacteristic
484C2×C22⋊C4C2×Dic7111yescharacteristic
485C2×C22⋊C4C2×Dic7111yescharacteristic
486C2×C22⋊C4C2×Dic7111yescharacteristic
487C2×C22⋊C4C2×Dic7111yescharacteristic
488C2×C22⋊C4C2×Dic7111yescharacteristic
489C2×C22⋊C4C2×Dic7111yescharacteristic
490C2×C22⋊C4C2×Dic7111yescharacteristic
491C2×C22⋊C4C2×Dic7111yescharacteristic
492C2×C22⋊C4C2×Dic7111yescharacteristic
493C2×C22⋊C4C2×Dic7111yescharacteristic
494C2×C22⋊C4C2×Dic7111yescharacteristic
495C2×C42C22×D7111yescharacteristic
496C2×C42C22×D7111yescharacteristic
497C2×C42C22×D7111yescharacteristic
498C2×C42C22×D7111yescharacteristic
499C4⋊C8—714no—
500C4⋊C8—1422no—
501C4⋊C8—1422no—
502C4⋊C8—1422no—
503C4⋊C8—1422no—
504C4⋊C8—1422no—
505C22⋊C8—2841no—
506C22⋊C8—2841no—
507C22⋊C8—714no—
508C22⋊C8—1422no—
509C22⋊C8—1422no—
510C22⋊C8—1422no—
511C22⋊C8—1422no—
512C22⋊C8—1422no—
513#97—1422no—
514#97—1422no—
515C4×C8—1422no—
516C4×C8—1422no—
517#95C2×Dic7111yescharacteristic
518#95C2×Dic7111yescharacteristic
519#95C2×Dic7111yescharacteristic
520#95C2×Dic7111yescharacteristic
521#95C2×Dic7111yescharacteristic
522#95C2×Dic7111yescharacteristic
523C24C22×Dic7111yescharacteristic
524C24C22×Dic7111yescharacteristic
525C24C22×Dic7111yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4C22×Dic7111yescharacteristic
552C22×C4C22×Dic7111yescharacteristic
553C22×C4C22×Dic7111yescharacteristic
554C22×C4C22×Dic7111yescharacteristic
555C22×C4C22×Dic7111yescharacteristic
556C22×C4C22×Dic7111yescharacteristic
557C22×C4C22×Dic7111yescharacteristic
558C22×C4C22×Dic7111yescharacteristic
559C22×C4C22×Dic7111yescharacteristic
560C22×C4C22×Dic7111yescharacteristic
561C22×C4C22×Dic7111yescharacteristic
562C22×C4D4×D7112yes—
563C22×C4#1176586412yes—
564C22×C4C23×D7111yescharacteristic
565M16—2844no—
566M16—2844no—
567M16—2844no—
568C2×C8—2844no—
569C2×C8—712no—
570C2×C8—712no—
571C2×C8—712no—
572C2×C8—712no—
573C2×C8—1421no—
574C2×C8—1421no—
575C2×C8—1421no—
576C2×C8—1421no—
577C2×C8—1421no—
578C2×C8—1421no—
579C2×C8—1421no—
580C2×C8—1421no—
581C2×C8—1421no—
582C2×C8—1421no—
583C2×C8—1421no—
584C2×C8—1421no—
585C2×C8—1421no—
586C2×C8—1421no—
587C2×C8—1421no—
588C2×C8—1421no—
589C2×C8—1421no—
590C2×C8—1421no—
591C2×C8—1421no—
592C2×C8—1421no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—41no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42D4×D7112yes—
619C42#1176586412yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23D4×Dic7112yes—
641C23C23×Dic7111yescharacteristic
642D4—44no—
643D4—44no—
644D4—44no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4D4×Dic7112yes—
687C2×C4D4×Dic7112yes—
688C2×C4D4×Dic7112yes—
689C2×C4#1455613512yes—
690C2×C4C2×D4×D7111yescharacteristic
691C2×C4C2×D4×D7111yescharacteristic
692C2×C4C2×#1176586411yescharacteristic
693C2×C4C2×#1176586411yescharacteristic
694C2×C4#1455617411yescharacteristic
695C2×C4#1455617511yescharacteristic
696C8—2841no—
697C8—2841no—
698C8—2841no—
699C8—2841no—
700C8—1422no—
701C8—1422no—
702C8—1422no—
703C8—1422no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22C2×D4×Dic7111yescharacteristic
726C22C2×D4×Dic7111yescharacteristic
727C22#1798648211yescharacteristic
728C22C2×#1455613511yescharacteristic
729C22#1798676611yescharacteristic
730C22#1798676611yescharacteristic
731C22#1798676611yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4#1798663311yescharacteristic
744C4#1798664911yescharacteristic
745C4#1798665511yescharacteristic
746C4#1798670111yescharacteristic
747C2—42no—
748C2—81no—
749C2—81no—
750C2#2259136011yescharacteristic
751C2#2259704411yescharacteristic
752C2#2259704411yescharacteristic
753C2#2259706711yescharacteristic
754C2#2259708411yescharacteristic
755C2#2259748911yescharacteristic
756C2#2259751011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#2392C2
prime radical#392×C71C4
cosocleC22×C4×C71C24
hypercenter#2392D71
hypocenterC71#22994
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. C2×#17986077C2semidirect
2. C2×#17986077C2semidirect
3. C2×#17986071C2semidirect
4. C2×#17986026C2semidirect
5. #22589139C2semidirect
6. #22589059C2semidirect
7. #22588955C2semidirect
8. #22588948C2semidirect
9. #22588638C2semidirect
10. #22588633C2semidirect
11. #22588525C2semidirect
12. #22588525C2semidirect
13. #22588215C2semidirect
14. #22588106C2semidirect
88. C4⋊(C71⋊C8)D4semidirect
96. C22⋊(C71⋊C8)D4semidirect
394. C71#22994semidirect

Maximal subgroups

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

subgroupindex
C2×#179860772
C2×#179860712
C2×#179860262
#225891392
#225890592
#225889552
#225889482
#225886382
#225886332
#225885252
#225882152
#225881062
C71×#23922
#2299471