Finite Group Databasebeta

← #32007093

Subgroups — #32007093

Order 18176.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986060C211yesmaximal, characteristic, complemented
2C2×#17986026C211yesmaximal, characteristic, complemented
3#22589281C211yesmaximal, characteristic, complemented
4#22589277C211yesmaximal, characteristic, complemented
5#22589139C211yesmaximal, characteristic, complemented
6#22589135C211yesmaximal, characteristic, complemented
7#22588638C211yesmaximal, characteristic, complemented
8#22588638C211yesmaximal, characteristic, complemented
9#22588633C211yesmaximal, characteristic, complemented
10#22588633C211yesmaximal, characteristic, complemented
11#22588324C211yesmaximal, characteristic, complemented
12#22588324C211yesmaximal, characteristic, complemented
13#22588320C211yesmaximal, characteristic, complemented
14#22588320C211yesmaximal, characteristic, complemented
15C2×#529×C71C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18#17986060—24no—
19#17986026—24no—
20C2×C4⋊(C71⋊C8)C2211yescharacteristic
21C2×C4⋊(C71⋊C8)C2211yescharacteristic
22C2×C4⋊(C71⋊C8)C2211yescharacteristic
23C2×C4⋊(C71⋊C8)C2211yescharacteristic
24C2×C4⋊(C71⋊C8)C2211yescharacteristic
25C2×C4⋊(C71⋊C8)C2211yescharacteristic
26C2×C22⋊(C71⋊C8)C2211yescharacteristic
27C2×C22⋊(C71⋊C8)C2211yescharacteristic
28C2×C22⋊(C71⋊C8)C2211yescharacteristic
29C2×C22⋊(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×#14556039C2211yescharacteristic
37C2×C4×C71⋊C8C2211yescharacteristic
38#17985754C2211yescharacteristic
39#17985754C2211yescharacteristic
40#17985754C2211yescharacteristic
41#17985754C2211yescharacteristic
42#17985754C2211yescharacteristic
43#17985754C2211yescharacteristic
44#17985754C2211yescharacteristic
45#17985754C2211yescharacteristic
46#529×C71—24no—
47#529×C71—24no—
48C2×#126×C71C411yescharacteristic
49C2×#126×C71C411yescharacteristic
50C2×#125×C71C411yescharacteristic
51C2×#124×C71C411yescharacteristic
52C2×#123×C71C411yescharacteristic
53C2×#123×C71C411yescharacteristic
54C2×C22⋊Q8×C71C411yescharacteristic
55C2×#121×C71C411yescharacteristic
56C2×C4×Q8×C71C2211yescharacteristic
57C2×C4×D4×C71C2211yescharacteristic
58C2×C4×D4×C71C2211yescharacteristic
59C2×C4×D4×C71C2211yescharacteristic
60C2×#117×C71C2211yescharacteristic
61C2×#117×C71C2211yescharacteristic
62C22×C42×C71C2211yescharacteristic
63C2×#11765849—22no—
64C2×#11765849—41no—
65C2×#11765849—41no—
66C22×C71⋊C8—22no—
67C22×C71⋊C8—41no—
68C22×C71⋊C8—41no—
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74C22×C71⋊C8C2311yescharacteristic
75C22×C71⋊C8C2311yescharacteristic
76C22×C71⋊C8C2311yescharacteristic
77C4⋊(C71⋊C8)—22no—
78C4⋊(C71⋊C8)—22no—
79C4⋊(C71⋊C8)—22no—
80C4⋊(C71⋊C8)—22no—
81C4⋊(C71⋊C8)—22no—
82C4⋊(C71⋊C8)—22no—
83C22⋊(C71⋊C8)—22no—
84C22⋊(C71⋊C8)—22no—
85C22⋊(C71⋊C8)—41no—
86C22⋊(C71⋊C8)—41no—
87C22⋊(C71⋊C8)—41no—
88C22⋊(C71⋊C8)—41no—
89C22⋊(C71⋊C8)—41no—
90C22⋊(C71⋊C8)—41no—
91C22⋊(C71⋊C8)—41no—
92C22⋊(C71⋊C8)—41no—
93#14556039—22no—
94C4×C71⋊C8—22no—
95C22×Q8×C71C2×C411yescharacteristic
96C22×D4×C71C2×C411yescharacteristic
97C22×D4×C71C2×C411yescharacteristic
98C22×D4×C71C2×C411yescharacteristic
99C23×C4×C71C2×C411yescharacteristic
100C23×C4×C71C2×C411yescharacteristic
101C23×C4×C71C2311yescharacteristic
102C23×C4×C71C2311yescharacteristic
103C23×C4×C71C2311yescharacteristic
104#126×C71—24no—
105#126×C71—24no—
106#125×C71—24no—
107#124×C71—24no—
108#123×C71—24no—
109#123×C71—24no—
110C22⋊Q8×C71—24no—
111#121×C71—24no—
112C4×Q8×C71—22no—
113C4×Q8×C71—22no—
114C4×D4×C71—22no—
115C4×D4×C71—22no—
116C4×D4×C71—22no—
117C4×D4×C71—22no—
118C4×D4×C71—22no—
119C4×D4×C71—22no—
120#117×C71—22no—
121#117×C71—22no—
122#117×C71D414yes—
123#117×C71D414yes—
124C2×C4⋊C4×C71C2×C411yescharacteristic
125C2×C4⋊C4×C71C2×C411yescharacteristic
126C2×C4⋊C4×C71C2×C411yescharacteristic
127C2×C4⋊C4×C71C2×C411yescharacteristic
128C2×C4⋊C4×C71C2×C411yescharacteristic
129C2×C4⋊C4×C71C2×C411yescharacteristic
130C2×C4⋊C4×C71C2×C411yescharacteristic
131C2×C4⋊C4×C71C2×C411yescharacteristic
132C2×C4⋊C4×C71C2×C411yescharacteristic
133C2×C4⋊C4×C71C2×C411yescharacteristic
134C2×C22⋊C4×C71C2×C411yescharacteristic
135C2×C22⋊C4×C71C2×C411yescharacteristic
136C2×C22⋊C4×C71C2×C411yescharacteristic
137C2×C22⋊C4×C71C2×C411yescharacteristic
138C2×C22⋊C4×C71C2×C411yescharacteristic
139C2×C22⋊C4×C71C2×C411yescharacteristic
140C2×C22⋊C4×C71C2×C411yescharacteristic
141C2×C22⋊C4×C71C2×C411yescharacteristic
142C2×C22⋊C4×C71C2×C411yescharacteristic
143C2×C22⋊C4×C71C2×C411yescharacteristic
144C2×C42×C71—22no—
145C2×C42×C71—22no—
146C2×C42×C71C2×C411yescharacteristic
147C2×C42×C71C2×C411yescharacteristic
148C2×C42×C71C2311yescharacteristic
149C2×C42×C71C2311yescharacteristic
150C2×C42×C71C2311yescharacteristic
151C2×C42×C71C2311yescharacteristic
152#11765849—44no—
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—21no—
168C2×C71⋊C8—21no—
169C2×C71⋊C8—21no—
170C2×C71⋊C8—21no—
171C2×C71⋊C8—21no—
172C2×C71⋊C8—21no—
173C2×C71⋊C8—21no—
174C2×C71⋊C8—21no—
175C2×C71⋊C8—21no—
176C2×C71⋊C8—21no—
177C2×C71⋊C8—44no—
178C24×C71C22×C411yescharacteristic
179C24×C71C22×C411yescharacteristic
180C24×C71C22×C411yescharacteristic
181C2×Q8×C71—22no—
182C2×Q8×C71—22no—
183C2×Q8×C71—41no—
184C2×D4×C71—22no—
185C2×D4×C71—22no—
186C2×D4×C71—22no—
187C2×D4×C71—22no—
188C2×D4×C71—22no—
189C2×D4×C71—22no—
190C2×D4×C71—41no—
191C2×D4×C71—41no—
192C2×D4×C71—41no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—22no—
198C22×C4×C71—22no—
199C22×C4×C71—22no—
200C22×C4×C71—22no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—21no—
206C22×C4×C71—21no—
207C22×C4×C71—21no—
208C22×C4×C71—21no—
209C22×C4×C71—21no—
210C22×C4×C71—21no—
211C22×C4×C71—21no—
212C22×C4×C71—21no—
213C22×C4×C71—41no—
214C22×C4×C71—41no—
215C22×C4×C71C22×C411yescharacteristic
216C22×C4×C71C22×C411yescharacteristic
217C22×C4×C71C22×C411yescharacteristic
218C22×C4×C71C22×C411yescharacteristic
219C22×C4×C71C22×C411yescharacteristic
220C22×C4×C71C22×C411yescharacteristic
221C22×C4×C71C22×C411yescharacteristic
222C22×C4×C71C22×C411yescharacteristic
223C22×C4×C71C22×C411yescharacteristic
224C22×C4×C71C22×C411yescharacteristic
225C22×C4×C71C22×C411yescharacteristic
226C22×C4×C71C2×D412yes—
227C22×C4×C71C2×D412yes—
228C22×C4×C71C2411yescharacteristic
229C4⋊C4×C71—22no—
230C4⋊C4×C71—22no—
231C4⋊C4×C71—22no—
232C4⋊C4×C71—22no—
233C4⋊C4×C71—22no—
234C4⋊C4×C71—22no—
235C4⋊C4×C71—22no—
236C4⋊C4×C71—22no—
237C4⋊C4×C71C22⋊C414yes—
238C4⋊C4×C71C22⋊C414yes—
239C22⋊C4×C71—22no—
240C22⋊C4×C71—22no—
241C22⋊C4×C71—22no—
242C22⋊C4×C71—22no—
243C22⋊C4×C71—22no—
244C22⋊C4×C71—22no—
245C22⋊C4×C71—22no—
246C22⋊C4×C71—22no—
247C22⋊C4×C71C22⋊C414yes—
248C22⋊C4×C71C22⋊C414yes—
249C42×C71—22no—
250C42×C71—22no—
251C42×C71—21no—
252C42×C71—21no—
253C42×C71—21no—
254C42×C71—21no—
255C42×C71C2×D412yes—
256C42×C71C2×D412yes—
257C42×C71C2×D412yes—
258C42×C71C2×D412yes—
259C23×C71—21no—
260C23×C71—21no—
261C23×C71—21no—
262C23×C71—21no—
263C23×C71—21no—
264C23×C71—21no—
265C23×C71—21no—
266C23×C71—21no—
267C23×C71—21no—
268C23×C71—21no—
269C23×C71—21no—
270C23×C71—21no—
271C23×C71—21no—
272C23×C71—21no—
273C23×C71—21no—
274C23×C71—21no—
275C23×C71—21no—
276C23×C71—21no—
277C23×C71—21no—
278C23×C71C2×C22⋊C412yes—
279C23×C71#13112yes—
280C23×C71C23×C411yescharacteristic
281Q8×C71—44no—
282D4×C71—44no—
283D4×C71—44no—
284D4×C71—44no—
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—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—21no—
302C2×C4×C71—21no—
303C2×C4×C71—21no—
304C2×C4×C71—21no—
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—44no—
317C2×C4×C71—44no—
318C2×C4×C71—41no—
319C2×C4×C71—41no—
320C2×C4×C71—41no—
321C2×C4×C71—41no—
322C2×C4×C71—41no—
323C2×C4×C71—41no—
324C2×C4×C71—41no—
325C2×C4×C71—41no—
326C2×C4×C71C2×C22⋊C412yes—
327C2×C4×C71C2×C22⋊C412yes—
328C2×C4×C71C2×C22⋊C412yes—
329C2×C4×C71C2×C22⋊C412yes—
330C2×C4×C71C2×C22⋊C412yes—
331C2×C4×C71#13112yes—
332C2×C4×C71C22×D411yescharacteristic
333C2×C4×C71C22×D411yescharacteristic
334C2×C4×C71H(5,𝔽2)11yescharacteristic
335C2×C4×C71H(5,𝔽2)11yescharacteristic
336C2×C4×C712−1+411yescharacteristic
337C2×C4×C712−1+411yescharacteristic
338C71⋊C8—41no—
339C71⋊C8—41no—
340C71⋊C8—41no—
341C71⋊C8—41no—
342C71⋊C8—41no—
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—41no—
353C22×C71—41no—
354C22×C71—41no—
355C22×C71—41no—
356C22×C71—41no—
357C22×C71—41no—
358C22×C71—41no—
359C22×C71—41no—
360C22×C71—41no—
361C22×C71—41no—
362C22×C71—41no—
363C22×C71—41no—
364C22×C71—41no—
365C22×C71—41no—
366C22×C71—41no—
367C22×C71C22×C22⋊C411yescharacteristic
368C22×C71#52011yescharacteristic
369C22×C71#52011yescharacteristic
370C22×C71C2×#13111yescharacteristic
371C22×C71C2×#13111yescharacteristic
372C22×C71#56811yescharacteristic
373C22×C71#56811yescharacteristic
374C4×C71—22no—
375C4×C71—22no—
376C4×C71—22no—
377C4×C71—22no—
378C4×C71—22no—
379C4×C71—22no—
380C4×C71—41no—
381C4×C71—41no—
382C4×C71—41no—
383C4×C71—41no—
384C4×C71—41no—
385C4×C71#53511yescharacteristic
386C4×C71#53611yescharacteristic
387C4×C71#53711yescharacteristic
388C4×C71#53711yescharacteristic
389#21855—711nomaximal, Sylow
390C2×C71—42no—
391C2×C71—42no—
392C2×C71—81no—
393C2×C71#231111yescharacteristic
394C2×C71#288011yescharacteristic
395C2×C71#288011yescharacteristic
396C2×C71#299211yescharacteristic
397C2×C71#299311yescharacteristic
398C2×C71#299411yescharacteristic
399C2×C71#299511yescharacteristic
400C2×#529D7111yescharacteristic
401C2×#433—711no—
402C2×#424—711no—
403#1985—711no—
404#1984—711no—
405#1955—711no—
406#1954—711no—
407#1870—711no—
408#1870—711no—
409#1869—711no—
410#1869—711no—
411#1798—711no—
412#1798—711no—
413#1797—711no—
414#1797—711no—
415C71#2185511yescharacteristic, complemented, Sylow
416C22×M16—711no—
417C23×C8—711no—
418#529—24no—
419#529—24no—
420C2×#126Dic7111yescharacteristic
421C2×#126Dic7111yescharacteristic
422C2×#125Dic7111yescharacteristic
423C2×#124Dic7111yescharacteristic
424C2×#123Dic7111yescharacteristic
425C2×#123Dic7111yescharacteristic
426C2×C22⋊Q8Dic7111yescharacteristic
427C2×#121Dic7111yescharacteristic
428C2×C4×Q8C2×D7111yescharacteristic
429C2×C4×D4C2×D7111yescharacteristic
430C2×C4×D4C2×D7111yescharacteristic
431C2×C4×D4C2×D7111yescharacteristic
432C2×#117C2×D7111yescharacteristic
433C2×#117C2×D7111yescharacteristic
434C22×C42C2×D7111yescharacteristic
435#433—1424no—
436#424—1424no—
437C2×C4⋊C8—711no—
438C2×C4⋊C8—711no—
439C2×C4⋊C8—711no—
440C2×C4⋊C8—711no—
441C2×C4⋊C8—711no—
442C2×C4⋊C8—711no—
443C2×C22⋊C8—711no—
444C2×C22⋊C8—711no—
445C2×C22⋊C8—711no—
446C2×C22⋊C8—711no—
447C2×C22⋊C8—711no—
448C2×C22⋊C8—711no—
449C2×C22⋊C8—711no—
450C2×C22⋊C8—711no—
451C2×C22⋊C8—711no—
452C2×C22⋊C8—711no—
453C2×#97—711no—
454C2×C4×C8—711no—
455#336—711no—
456#336—711no—
457#336—711no—
458#336—711no—
459#336—711no—
460#336—711no—
461#336—711no—
462#336—711no—
463C22×Q8C2×Dic7111yescharacteristic
464C22×D4C2×Dic7111yescharacteristic
465C22×D4C2×Dic7111yescharacteristic
466C22×D4C2×Dic7111yescharacteristic
467C23×C4C2×Dic7111yescharacteristic
468C23×C4C2×Dic7111yescharacteristic
469C23×C4C22×D7111yescharacteristic
470C23×C4C22×D7111yescharacteristic
471C23×C4C22×D7111yescharacteristic
472C2×M16—2841no—
473C2×M16—2841no—
474C2×M16—1422no—
475C22×C8—2841no—
476C22×C8—2841no—
477C22×C8—711no—
478C22×C8—711no—
479C22×C8—711no—
480C22×C8—711no—
481C22×C8—711no—
482C22×C8—711no—
483C22×C8—711no—
484C22×C8—711no—
485C22×C8—1422no—
486#126—24no—
487#126—24no—
488#125—24no—
489#124—24no—
490#123—24no—
491#123—24no—
492C22⋊Q8—24no—
493#121—24no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—22no—
503#117—22no—
504#117C22⋊D7114yes—
505#117C22⋊D7114yes—
506C2×C4⋊C4C2×Dic7111yescharacteristic
507C2×C4⋊C4C2×Dic7111yescharacteristic
508C2×C4⋊C4C2×Dic7111yescharacteristic
509C2×C4⋊C4C2×Dic7111yescharacteristic
510C2×C4⋊C4C2×Dic7111yescharacteristic
511C2×C4⋊C4C2×Dic7111yescharacteristic
512C2×C4⋊C4C2×Dic7111yescharacteristic
513C2×C4⋊C4C2×Dic7111yescharacteristic
514C2×C4⋊C4C2×Dic7111yescharacteristic
515C2×C4⋊C4C2×Dic7111yescharacteristic
516C2×C22⋊C4C2×Dic7111yescharacteristic
517C2×C22⋊C4C2×Dic7111yescharacteristic
518C2×C22⋊C4C2×Dic7111yescharacteristic
519C2×C22⋊C4C2×Dic7111yescharacteristic
520C2×C22⋊C4C2×Dic7111yescharacteristic
521C2×C22⋊C4C2×Dic7111yescharacteristic
522C2×C22⋊C4C2×Dic7111yescharacteristic
523C2×C22⋊C4C2×Dic7111yescharacteristic
524C2×C22⋊C4C2×Dic7111yescharacteristic
525C2×C22⋊C4C2×Dic7111yescharacteristic
526C2×C42—22no—
527C2×C42—22no—
528C2×C42C2×Dic7111yescharacteristic
529C2×C42C2×Dic7111yescharacteristic
530C2×C42C22×D7111yescharacteristic
531C2×C42C22×D7111yescharacteristic
532C2×C42C22×D7111yescharacteristic
533C2×C42C22×D7111yescharacteristic
534C4⋊C8—1422no—
535C4⋊C8—1422no—
536C4⋊C8—1422no—
537C4⋊C8—1422no—
538C4⋊C8—1422no—
539C4⋊C8—1422no—
540C22⋊C8—2841no—
541C22⋊C8—2841no—
542C22⋊C8—2841no—
543C22⋊C8—2841no—
544C22⋊C8—2841no—
545C22⋊C8—2841no—
546C22⋊C8—2841no—
547C22⋊C8—2841no—
548C22⋊C8—1422no—
549C22⋊C8—1422no—
550#97—1422no—
551C4×C8—1422no—
552C24C22×Dic7111yescharacteristic
553C24C22×Dic7111yescharacteristic
554C24C22×Dic7111yescharacteristic
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—41no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4C22×Dic7111yescharacteristic
590C22×C4C22×Dic7111yescharacteristic
591C22×C4C22×Dic7111yescharacteristic
592C22×C4C22×Dic7111yescharacteristic
593C22×C4C22×Dic7111yescharacteristic
594C22×C4C22×Dic7111yescharacteristic
595C22×C4C22×Dic7111yescharacteristic
596C22×C4C22×Dic7111yescharacteristic
597C22×C4C22×Dic7111yescharacteristic
598C22×C4C22×Dic7111yescharacteristic
599C22×C4C22×Dic7111yescharacteristic
600C22×C4C2×C22⋊D7112yes—
601C22×C4C2×C22⋊D7112yes—
602C22×C4C23×D7111yescharacteristic
603M16—2844no—
604C2×C8—2844no—
605C2×C8—1421no—
606C2×C8—1421no—
607C2×C8—1421no—
608C2×C8—1421no—
609C2×C8—1421no—
610C2×C8—1421no—
611C2×C8—1421no—
612C2×C8—1421no—
613C2×C8—1421no—
614C2×C8—1421no—
615C2×C8—1421no—
616C2×C8—1421no—
617C2×C8—1421no—
618C2×C8—1421no—
619C2×C8—1421no—
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—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4C22⋊Dic7114yes—
638C4⋊C4C22⋊Dic7114yes—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4C22⋊Dic7114yes—
648C22⋊C4C22⋊Dic7114yes—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—22no—
654C42—22no—
655C42C2×C22⋊D7112yes—
656C42C2×C22⋊D7112yes—
657C42C2×C22⋊D7112yes—
658C42C2×C22⋊D7112yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23C2×C22⋊Dic7112yes—
679C23#1455613512yes—
680C23C23×Dic7111yescharacteristic
681Q8—44no—
682D4—44no—
683D4—44no—
684D4—44no—
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—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4C2×C22⋊Dic7112yes—
727C2×C4C2×C22⋊Dic7112yes—
728C2×C4C2×C22⋊Dic7112yes—
729C2×C4C2×C22⋊Dic7112yes—
730C2×C4C2×C22⋊Dic7112yes—
731C2×C4#1455613512yes—
732C2×C4C22×C22⋊D7111yescharacteristic
733C2×C4C22×C22⋊D7111yescharacteristic
734C2×C4#1455617411yescharacteristic
735C2×C4#1455617411yescharacteristic
736C2×C4#1455617511yescharacteristic
737C2×C4#1455617511yescharacteristic
738C8—2841no—
739C8—2841no—
740C8—2841no—
741C8—2841no—
742C8—2841no—
743C8—2841no—
744C8—2841no—
745C8—2841no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C22×C22⋊Dic7111yescharacteristic
768C22#1798648211yescharacteristic
769C22#1798648211yescharacteristic
770C22C2×#1455613511yescharacteristic
771C22C2×#1455613511yescharacteristic
772C22#1798676611yescharacteristic
773C22#1798676611yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4#1798656311yescharacteristic
786C4#1798657011yescharacteristic
787C4#1798657711yescharacteristic
788C4#1798657711yescharacteristic
789C2—42no—
790C2—42no—
791C2—81no—
792C2#2259093211yescharacteristic
793C2#2259678911yescharacteristic
794C2#2259678911yescharacteristic
795C2#2259747911yescharacteristic
796C2#2259748911yescharacteristic
797C2#2259750011yescharacteristic
798C2#2259751011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC2×#529×C71C2
prime radicalC2×#121×C71C4
cosocleC22×C4×C71C24
hypercenterC2×#529D71
hypocenterC71#21855
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#17986060C2semidirect
2. C2×#17986026C2semidirect
3. #22589281C2semidirect
4. #22589277C2semidirect
5. #22589139C2semidirect
6. #22589135C2semidirect
7. #22588638C2semidirect
8. #22588638C2semidirect
9. #22588633C2semidirect
10. #22588633C2semidirect
11. #22588324C2semidirect
12. #22588324C2semidirect
13. #22588320C2semidirect
14. #22588320C2semidirect
415. C71#21855semidirect

Maximal subgroups

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

subgroupindex
C2×#179860602
C2×#179860262
#225892812
#225892772
#225891392
#225891352
#225886382
#225886332
#225883242
#225883202
C2×#529×C712
#2185571