Finite Group Databasebeta

← C2×#22591480 #32160030

Subgroups — C2×#22591480 #32160030

Order 18176.

4246 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556098C211yesmaximal, characteristic
2#22591480C2116yesmaximal, direct product factor
3C2×#17985901C211yesmaximal, characteristic, complemented
4C2×#17985900C211yesmaximal, characteristic, complemented
5C2×#17985899C211yesmaximal, characteristic, complemented
6C2×#17985892C211yesmaximal, characteristic, complemented
7C2×#17985891C211yesmaximal, characteristic, complemented
8C2×#17985890C211yesmaximal, characteristic, complemented
9C2×#17985889C211yesmaximal, characteristic, complemented
10C2×#17985888C211yesmaximal, characteristic, complemented
11C2×#17985877C211yesmaximal, characteristic, complemented
12C2×#17985877C211yesmaximal, characteristic, complemented
13C2×#17985875C211yesmaximal, characteristic, complemented
14C2×#17985854C211yesmaximal, characteristic, complemented
15C2×#17985854C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C23×D284C2211yescharacteristic
20C23×C22⋊D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic, complemented
22C2×#14556098C4116yescomplemented
23C2×#14556098C2218yes—
24C22×C4⋊Dic71C2211yescharacteristic, complemented
25C22×Dic71⋊C4C2211yescharacteristic, complemented
26C22×C22⋊Dic71C2211yescharacteristic
27C22×C22⋊Dic71C2211yescharacteristic
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
39C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
41C22×C4×Dic71C2211yescharacteristic, complemented
42C22×C4×Dic71C2211yescharacteristic, complemented
43#17985901C2218yescomplemented
44#17985900C2218yescomplemented
45#17985899C2218yescomplemented
46#17985892C2218yescomplemented
47#17985891C2218yescomplemented
48#17985890C2218yescomplemented
49#17985889C2218yescomplemented
50#17985888C2218yescomplemented
51#17985877C2218yescomplemented
52#17985877C2218yescomplemented
53#17985875C2218yescomplemented
54#17985854C2218yescomplemented
55#17985854C2218yescomplemented
56C2×C71⋊#95C2211yescharacteristic, complemented
57C2×C71⋊#95C2211yescharacteristic, complemented
58C2×C71⋊#95C2211yescharacteristic, complemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C22×C4⋊C4×C71C2211yescharacteristic, complemented
61C22×C22⋊C4×C71C2211yescharacteristic
62C22×C22⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C42×C71C2211yescharacteristic, complemented
65#388×C71C2218yescomplemented
66C2×#95×C71C2211yescharacteristic, complemented
67C2×#95×C71C2211yescharacteristic, complemented
68C24×D71—42no—
69C24×D71—42no—
70C24×D71—42no—
71C24×D71—42no—
72C24×D71—42no—
73C24×D71—42no—
74C24×D71C2×C418yescomplemented
75C24×D71C2311yescharacteristic
76C24×D71C2311yescharacteristic
77C24×D71C2311yescharacteristic
78C24×D71C2314yes—
79C22×D284—42no—
80C22×D284—42no—
81C22×D284—42no—
82C22×D284—42no—
83C22×D284C2×C418yes—
84C22×D284C2×C418yes—
85C22×D284C2314yes—
86C22×D284C2314yes—
87C22×C22⋊D71—42no—
88C22×C22⋊D71—42no—
89C22×C22⋊D71C2×C418yes—
90C22×C22⋊D71C2314yes—
91C23×Dic71C2311yescharacteristic
92C23×Dic71C2311yescharacteristic
93C23×Dic71C2311yescharacteristic
94C23×Dic71C2311yescharacteristic
95C23×Dic71C2311yescharacteristic
96C22×C4×D71—42no—
97C22×C4×D71—42no—
98C22×C4×D71—42no—
99C22×C4×D71C2314yescomplemented
100#14556098C2×C4164yescomplemented
101C2×C4⋊Dic71—42no—
102C2×C4⋊Dic71C2314yescomplemented
103C2×Dic71⋊C4—42no—
104C2×Dic71⋊C4C2314yescomplemented
105C2×C22⋊Dic71—42no—
106C2×C22⋊Dic71—42no—
107C2×C22⋊Dic71C2314yes—
108C2×C22⋊Dic71C2314yes—
109C2×(C2×D71)⋊C4—42no—
110C2×(C2×D71)⋊C4—42no—
111C2×(C2×D71)⋊C4—42no—
112C2×(C2×D71)⋊C4—42no—
113C2×(C2×D71)⋊C4—42no—
114C2×(C2×D71)⋊C4—42no—
115C2×(C2×D71)⋊C4—42no—
116C2×(C2×D71)⋊C4—42no—
117C2×(C2×D71)⋊C4—42no—
118C2×(C2×D71)⋊C4—42no—
119C2×(C2×D71)⋊C4—42no—
120C2×(C2×D71)⋊C4C2×C418yescomplemented
121C2×(C2×D71)⋊C4C2×C418yescomplemented
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2314yes—
130C2×(C2×D71)⋊C4C2314yes—
131C2×(C2×D71)⋊C4C2314yes—
132C2×(C2×D71)⋊C4C2314yescomplemented
133C2×(C2×D71)⋊C4C2314yescomplemented
134C2×(C2×D71)⋊C4C2314yescomplemented
135C2×C4×Dic71—42no—
136C2×C4×Dic71—42no—
137C2×C4×Dic71C2314yescomplemented
138C2×C4×Dic71C2314yescomplemented
139C71⋊#95C2314yescomplemented
140C71⋊#95C2314yescomplemented
141C71⋊#95C2314yescomplemented
142C71⋊#95C2314yescomplemented
143C25×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2311yescharacteristic
149C23×C4×C71C2311yescharacteristic
150C2×C4⋊C4×C71—42no—
151C2×C4⋊C4×C71C2314yescomplemented
152C2×C22⋊C4×C71—42no—
153C2×C22⋊C4×C71—42no—
154C2×C22⋊C4×C71C2×C418yescomplemented
155C2×C22⋊C4×C71C2314yes—
156C2×C22⋊C4×C71C2314yes—
157C2×C22⋊C4×C71C2314yes—
158C2×C42×C71—42no—
159C2×C42×C71C2314yescomplemented
160#95×C71C2314yescomplemented
161#95×C71C2314yescomplemented
162C23×D71—22no—
163C23×D71—22no—
164C23×D71—22no—
165C23×D71—22no—
166C23×D71—22no—
167C23×D71—22no—
168C23×D71—22no—
169C23×D71—22no—
170C23×D71—22no—
171C23×D71—22no—
172C23×D71—22no—
173C23×D71—22no—
174C23×D71—22no—
175C23×D71—22no—
176C23×D71—22no—
177C23×D71—22no—
178C23×D71—22no—
179C23×D71—22no—
180C23×D71—416no—
181C23×D71—416no—
182C23×D71—416no—
183C23×D71—44no—
184C23×D71—44no—
185C23×D71—44no—
186C23×D71—44no—
187C23×D71—44no—
188C23×D71—44no—
189C23×D71—416no—
190C23×D71—416no—
191C23×D71—416no—
192C23×D71—416no—
193C23×D71C22×C414yes—
194C23×D71C22×C414yes—
195C23×D71C22×C414yes—
196C23×D71C22×C4116yescomplemented
197C23×D71C2412yes—
198C23×D71C2412yes—
199C23×D71C2412yes—
200C2×D284—416no—
201C2×D284—416no—
202C2×D284—44no—
203C2×D284—44no—
204C2×D284—44no—
205C2×D284—44no—
206C2×D284C22×C4116yes—
207C2×D284C22×C4116yes—
208C2×C22⋊D71—416no—
209C2×C22⋊D71—44no—
210C2×C22⋊D71—44no—
211C2×C22⋊D71C22×C4116yes—
212C22×Dic71—22no—
213C22×Dic71—22no—
214C22×Dic71—22no—
215C22×Dic71—22no—
216C22×Dic71—22no—
217C22×Dic71—22no—
218C22×Dic71—22no—
219C22×Dic71—22no—
220C22×Dic71—22no—
221C22×Dic71—22no—
222C22×Dic71—22no—
223C22×Dic71—22no—
224C22×Dic71—22no—
225C22×Dic71—22no—
226C22×Dic71C22×C414yes—
227C22×Dic71C2412yes—
228C22×Dic71C2412yes—
229C22×Dic71C2412yes—
230C22×Dic71C2412yes—
231C22×Dic71C2412yes—
232C2×C4×D71—44no—
233C2×C4×D71—44no—
234C2×C4×D71—44no—
235C2×C4×D71—416no—
236C4⋊Dic71—44no—
237Dic71⋊C4—44no—
238C22⋊Dic71—44no—
239C22⋊Dic71—44no—
240(C2×D71)⋊C4—44no—
241(C2×D71)⋊C4—44no—
242(C2×D71)⋊C4—44no—
243(C2×D71)⋊C4—44no—
244(C2×D71)⋊C4—44no—
245(C2×D71)⋊C4—44no—
246(C2×D71)⋊C4—44no—
247(C2×D71)⋊C4—44no—
248(C2×D71)⋊C4—44no—
249(C2×D71)⋊C4—44no—
250(C2×D71)⋊C4—44no—
251(C2×D71)⋊C4C22×C4116yescomplemented
252(C2×D71)⋊C4C22×C4116yescomplemented
253C4×Dic71—44no—
254C4×Dic71—44no—
255C24×C71—22no—
256C24×C71—22no—
257C24×C71—22no—
258C24×C71—22no—
259C24×C71—22no—
260C24×C71—22no—
261C24×C71C22×C414yes—
262C24×C71C2412yes—
263C24×C71C2411yescharacteristic
264C22×C4×C71—22no—
265C22×C4×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71—22no—
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71—22no—
271C22×C4×C71—22no—
272C22×C4×C71—22no—
273C22×C4×C71—22no—
274C22×C4×C71—22no—
275C22×C4×C71—22no—
276C22×C4×C71—22no—
277C22×C4×C71—22no—
278C22×C4×C71—22no—
279C22×C4×C71—22no—
280C22×C4×C71C22×C414yes—
281C22×C4×C71C22×C414yes—
282C22×C4×C71C2412yes—
283C22×C4×C71C2412yes—
284C22×C4×C71C2412yes—
285C22×C4×C71C2412yes—
286C22×C4×C71C2412yes—
287C22×C4×C71C2412yes—
288C4⋊C4×C71—44no—
289C22⋊C4×C71—44no—
290C22⋊C4×C71—44no—
291C22⋊C4×C71C22×C4116yescomplemented
292C42×C71—44no—
293C23×C71—28no—
294C23×C71—28no—
295C23×C71—28no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—22no—
300C23×C71—22no—
301C23×C71—22no—
302C23×C71—44no—
303C23×C71—44no—
304C23×C71—44no—
305C23×C71—44no—
306C23×C71C23×C414yes—
307C23×C71C23×C412yes—
308C23×C71H(5,𝔽2)12yes—
309C23×C71H(5,𝔽2)12yes—
310C23×C71H(5,𝔽2)12yes—
311C23×C71H(5,𝔽2)12yes—
312C23×C71H(5,𝔽2)12yes—
313C23×C71H(5,𝔽2)12yes—
314C23×C71C2511yescharacteristic
315C22×D71—28no—
316C22×D71—28no—
317C22×D71—28no—
318C22×D71—28no—
319C22×D71—28no—
320C22×D71—28no—
321C22×D71—28no—
322C22×D71—28no—
323C22×D71—28no—
324C22×D71—22no—
325C22×D71—22no—
326C22×D71—22no—
327C22×D71—22no—
328C22×D71—22no—
329C22×D71—22no—
330C22×D71—22no—
331C22×D71—22no—
332C22×D71—22no—
333C22×D71—22no—
334C22×D71—22no—
335C22×D71—22no—
336C22×D71—22no—
337C22×D71—22no—
338C22×D71—22no—
339C22×D71—22no—
340C22×D71—22no—
341C22×D71—22no—
342C22×D71—416no—
343C22×D71—416no—
344C22×D71—416no—
345C22×D71—4128no—
346C22×D71—416no—
347C22×D71—416no—
348C22×D71—416no—
349C22×D71—416no—
350C22×D71—44no—
351C22×D71—44no—
352C22×D71—44no—
353C22×D71—44no—
354C22×D71—44no—
355C22×D71—44no—
356C22×D71—44no—
357C22×D71—44no—
358C22×D71—44no—
359C22×D71—44no—
360C22×D71—44no—
361C22×D71—44no—
362C22×D71C23×C414yes—
363C22×D71C23×C414yes—
364C22×D71C23×C414yes—
365C2×C4×C71—28no—
366C2×C4×C71—28no—
367C2×C4×C71—22no—
368C2×C4×C71—22no—
369C2×C4×C71—22no—
370C2×C4×C71—22no—
371C2×C4×C71—22no—
372C2×C4×C71—22no—
373C2×C4×C71—22no—
374C2×C4×C71—22no—
375C2×C4×C71—22no—
376C2×C4×C71—22no—
377C2×C4×C71—22no—
378C2×C4×C71—22no—
379C2×C4×C71—22no—
380C2×C4×C71—22no—
381C2×C4×C71—22no—
382C2×C4×C71—22no—
383C2×C4×C71—44no—
384C2×C4×C71—44no—
385C2×C4×C71—44no—
386C2×C4×C71—44no—
387C2×C4×C71C23×C414yes—
388C2×C4×C71C23×C414yes—
389C22⋊D71—416no—
390C2×Dic71—28no—
391C2×Dic71—22no—
392C2×Dic71—22no—
393C2×Dic71—22no—
394C2×Dic71—22no—
395C2×Dic71—22no—
396C2×Dic71—22no—
397C2×Dic71—22no—
398C2×Dic71—22no—
399C2×Dic71—22no—
400C2×Dic71—22no—
401C2×Dic71—22no—
402C2×Dic71—22no—
403C2×Dic71—22no—
404C2×Dic71—22no—
405C2×Dic71—44no—
406C2×Dic71—44no—
407C2×Dic71—44no—
408C2×Dic71—44no—
409C2×Dic71C23×C414yes—
410D284—416no—
411D284—416no—
412C4×D71—416no—
413C22×C71—24no—
414C22×C71—24no—
415C22×C71—24no—
416C22×C71—416no—
417C22×C71—42no—
418C22×C71—42no—
419C22×C71—42no—
420C22×C71—42no—
421C22×C71#51814yes—
422C22×C71#51814yes—
423C22×C71#51814yes—
424C22×C71#56014yes—
425C22×C71#56014yes—
426C22×C71#56014yes—
427C22×C71H(3,𝔽4)14yes—
428C22×C71C24×C411yescharacteristic
429C22×C71C2×H(5,𝔽2)11yescharacteristic
430C22×C71C2×H(5,𝔽2)11yescharacteristic
431C22×C71C2×H(5,𝔽2)11yescharacteristic
432C22×C71C2×H(5,𝔽2)11yescharacteristic
433C22×C71C2×H(5,𝔽2)11yescharacteristic
434C22×C71C2×H(5,𝔽2)11yescharacteristic
435C2×D71—24no—
436C2×D71—24no—
437C2×D71—24no—
438C2×D71—24no—
439C2×D71—24no—
440C2×D71—24no—
441C2×D71—24no—
442C2×D71—24no—
443C2×D71—24no—
444C2×D71—464no—
445C2×D71—416no—
446C2×D71—416no—
447C2×D71—416no—
448C2×D71—42no—
449C2×D71—42no—
450C2×D71—42no—
451C2×D71—42no—
452C2×D71—42no—
453C2×D71—42no—
454C2×D71—42no—
455C2×D71—42no—
456C2×D71—42no—
457C2×D71—42no—
458C2×D71—42no—
459C2×D71—42no—
460C4×C71—24no—
461C4×C71—24no—
462C4×C71—42no—
463C4×C71—42no—
464C4×C71—42no—
465C4×C71—42no—
466Dic71—24no—
467Dic71—42no—
468Dic71—42no—
469Dic71—42no—
470Dic71—42no—
471C2×#2375—711nomaximal, Sylow
472C2×C71—44no—
473C2×C71#237518yescomplemented
474C2×C71C2×#51811yescharacteristic
475C2×C71C2×#51811yescharacteristic
476C2×C71C2×#51811yescharacteristic
477C2×C71C2×#56011yescharacteristic
478C2×C71C2×#56011yescharacteristic
479C2×C71C2×#56011yescharacteristic
480C2×C71C2×H(3,𝔽4)11yescharacteristic
481D71—44no—
482D71—44no—
483D71—44no—
484C22×#120—711no—
485#2375—7116no—
486C2×#390—711no—
487C2×#390—711no—
488C2×#390—711no—
489C2×#388—711no—
490C2×#388—711no—
491C2×#388—711no—
492C2×#388—711no—
493C2×#388—711no—
494C2×#388D7111yescharacteristic, complemented
495C2×#386—711no—
496C2×#386—711no—
497C2×#386—711no—
498C2×#379—711no—
499C2×#379—711no—
500C71C2×#237511yescharacteristic, complemented, Sylow
501C26—711no—
502C23×D4—711no—
503C23×D4—711no—
504C23×D4—711no—
505C24×C4—711no—
506C2×#120—7116no—
507C2×#120—718no—
508C22×C4⋊C4—711no—
509C22×C4⋊C4—711no—
510C22×C4⋊C4C2×D7111yescharacteristic, complemented
511C22×C22⋊C4—711no—
512C22×C22⋊C4—711no—
513C22×C22⋊C4—711no—
514C22×C22⋊C4—711no—
515C22×C22⋊C4—711no—
516C22×C22⋊C4—711no—
517C22×C22⋊C4—711no—
518C22×C22⋊C4—711no—
519C22×C22⋊C4—711no—
520C22×C22⋊C4—711no—
521C22×C22⋊C4—711no—
522C22×C22⋊C4—711no—
523C22×C22⋊C4—711no—
524C22×C22⋊C4—711no—
525C22×C22⋊C4—711no—
526C22×C22⋊C4C2×D7111yescharacteristic
527C22×C22⋊C4C2×D7111yescharacteristic
528C22×C22⋊C4C2×D7111yescharacteristic
529C22×C42—711no—
530C22×C42—711no—
531C22×C42C2×D7111yescharacteristic, complemented
532#390—718no—
533#390—718no—
534#390—718no—
535#388—718no—
536#388—718no—
537#388—718no—
538#388—718no—
539#388—718no—
540#388C2×D7118yescomplemented
541#386—718no—
542#386—718no—
543#386—718no—
544#379—718no—
545#379—718no—
546C2×#95—711no—
547C2×#95—711no—
548C2×#95—711no—
549C2×#95—711no—
550C2×#95C2×D7111yescharacteristic, complemented
551C2×#95C2×D7111yescharacteristic, complemented
552C25—2842no—
553C25—2842no—
554C25—2842no—
555C25—2842no—
556C25—2842no—
557C25—2842no—
558C25—718no—
559C25—714no—
560C25—711no—
561C25—711no—
562C25—711no—
563C25C22×D7111yescharacteristic
564C22×D4—2842no—
565C22×D4—2842no—
566C22×D4—2842no—
567C22×D4—2842no—
568C22×D4—2842no—
569C22×D4—2842no—
570C22×D4—718no—
571C22×D4—714no—
572C22×D4—718no—
573C22×D4—718no—
574C22×D4—714no—
575C22×D4—714no—
576C23×C4—2842no—
577C23×C4—2842no—
578C23×C4—2842no—
579C23×C4—714no—
580C23×C4—711no—
581C23×C4—711no—
582C23×C4—711no—
583C23×C4—711no—
584C23×C4—711no—
585C23×C4C22×D7111yescharacteristic
586C23×C4C22×D7111yescharacteristic
587C23×C4C22×D7111yescharacteristic
588C23×C4C22×D7111yescharacteristic
589C23×C4C22×D7111yescharacteristic
590C23×C4C22×D7111yescharacteristic
591#120—7164no—
592C2×C4⋊C4—42no—
593C2×C4⋊C4—2842no—
594C2×C4⋊C4—2842no—
595C2×C4⋊C4—714no—
596C2×C4⋊C4—714no—
597C2×C4⋊C4C22×D7114yescomplemented
598C2×C22⋊C4—42no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—2842no—
601C2×C22⋊C4—2842no—
602C2×C22⋊C4—2842no—
603C2×C22⋊C4—2842no—
604C2×C22⋊C4—2842no—
605C2×C22⋊C4—2842no—
606C2×C22⋊C4—2842no—
607C2×C22⋊C4—2842no—
608C2×C22⋊C4—2842no—
609C2×C22⋊C4—2842no—
610C2×C22⋊C4—2842no—
611C2×C22⋊C4—2842no—
612C2×C22⋊C4—2842no—
613C2×C22⋊C4—714no—
614C2×C22⋊C4—714no—
615C2×C22⋊C4—714no—
616C2×C22⋊C4—714no—
617C2×C22⋊C4—714no—
618C2×C22⋊C4—714no—
619C2×C22⋊C4—714no—
620C2×C22⋊C4—714no—
621C2×C22⋊C4—714no—
622C2×C22⋊C4—714no—
623C2×C22⋊C4—714no—
624C2×C22⋊C4—714no—
625C2×C22⋊C4—714no—
626C2×C22⋊C4—718no—
627C2×C22⋊C4—718no—
628C2×C22⋊C4—714no—
629C2×C22⋊C4—714no—
630C2×C22⋊C4C4×D7118yescomplemented
631C2×C22⋊C4C22×D7114yes—
632C2×C22⋊C4C22×D7114yes—
633C2×C22⋊C4C22×D7114yes—
634C2×C42—42no—
635C2×C42—2842no—
636C2×C42—2842no—
637C2×C42—714no—
638C2×C42—714no—
639C2×C42C22×D7114yescomplemented
640#95—714no—
641#95—714no—
642#95—714no—
643#95—714no—
644#95C22×D7114yescomplemented
645#95C22×D7114yescomplemented
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—2844no—
653C24—2844no—
654C24—2844no—
655C24—2844no—
656C24—2844no—
657C24—2844no—
658C24—28416no—
659C24—28416no—
660C24—28416no—
661C24—28416no—
662C24—28416no—
663C24—28416no—
664C24—28416no—
665C24—7116no—
666C24—714no—
667C24—714no—
668C24—714no—
669C24—712no—
670C24—712no—
671C24—712no—
672C24—1422no—
673C24—1422no—
674C24—1422no—
675C24—1422no—
676C24—1422no—
677C24—1422no—
678C24—1422no—
679C24—1422no—
680C24—1422no—
681C24—1422no—
682C24—1422no—
683C24—1422no—
684C24—1422no—
685C24—1422no—
686C24—1422no—
687C24—1422no—
688C24—1422no—
689C24—1422no—
690C24C2×C4×D7114yes—
691C24C23×D7112yes—
692C24C23×D7111yescharacteristic
693C2×D4—2844no—
694C2×D4—2844no—
695C2×D4—2844no—
696C2×D4—2844no—
697C2×D4—28416no—
698C2×D4—28416no—
699C2×D4—2844no—
700C2×D4—2844no—
701C2×D4—28416no—
702C2×D4—7116no—
703C2×D4—7116no—
704C2×D4—7116no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—2844no—
722C22×C4—2844no—
723C22×C4—2844no—
724C22×C4—28416no—
725C22×C4—714no—
726C22×C4—712no—
727C22×C4—712no—
728C22×C4—712no—
729C22×C4—712no—
730C22×C4—712no—
731C22×C4—1422no—
732C22×C4—1422no—
733C22×C4—1422no—
734C22×C4—1422no—
735C22×C4—1422no—
736C22×C4—1422no—
737C22×C4—1422no—
738C22×C4—1422no—
739C22×C4—1422no—
740C22×C4—1422no—
741C22×C4—1422no—
742C22×C4—1422no—
743C22×C4—1422no—
744C22×C4—1422no—
745C22×C4C2×C4×D7114yes—
746C22×C4C2×C4×D7114yes—
747C22×C4C23×D7112yes—
748C22×C4C23×D7112yes—
749C22×C4C23×D7112yes—
750C22×C4C23×D7112yes—
751C22×C4C23×D7112yes—
752C22×C4C23×D7112yes—
753C4⋊C4—44no—
754C4⋊C4—2844no—
755C4⋊C4—2844no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4—2844no—
759C22⋊C4—2844no—
760C22⋊C4—2844no—
761C22⋊C4—2844no—
762C22⋊C4—2844no—
763C22⋊C4—2844no—
764C22⋊C4—2844no—
765C22⋊C4—2844no—
766C22⋊C4—2844no—
767C22⋊C4—2844no—
768C22⋊C4—2844no—
769C22⋊C4—2844no—
770C22⋊C4—2844no—
771C22⋊C4—7116no—
772C22⋊C4—7116no—
773C22⋊C4C2×C4×D71116yescomplemented
774C42—44no—
775C42—2844no—
776C42—2844no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—28no—
784C23—28no—
785C23—28no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—28416no—
791C23—28416no—
792C23—28416no—
793C23—28416no—
794C23—28416no—
795C23—28416no—
796C23—28416no—
797C23—284128no—
798C23—2844no—
799C23—2844no—
800C23—2844no—
801C23—2844no—
802C23—2844no—
803C23—2844no—
804C23—2844no—
805C23—2844no—
806C23—2844no—
807C23—2844no—
808C23—2844no—
809C23—2844no—
810C23—714no—
811C23—714no—
812C23—714no—
813C23—1422no—
814C23—1422no—
815C23—1422no—
816C23—1422no—
817C23—1422no—
818C23—1422no—
819C23—1422no—
820C23—1422no—
821C23—1422no—
822C23—1422no—
823C23—1422no—
824C23—1422no—
825C23—1422no—
826C23—1422no—
827C23—1422no—
828C23—1422no—
829C23—1422no—
830C23—1422no—
831C23—1428no—
832C23—1428no—
833C23—1428no—
834C23—1428no—
835C23—1428no—
836C23—1428no—
837C23—1428no—
838C23—1428no—
839C23—1428no—
840C23C22×C4×D7114yes—
841C23C22×C4×D7112yes—
842C23#1455617312yes—
843C23#1455617312yes—
844C23#1455617412yes—
845C23#1455617412yes—
846C23#1455617412yes—
847C23#1455617412yes—
848C23C24×D7111yescharacteristic
849D4—28416no—
850D4—28416no—
851D4—28416no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—28no—
857C2×C4—28no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—28416no—
875C2×C4—2844no—
876C2×C4—2844no—
877C2×C4—2844no—
878C2×C4—2844no—
879C2×C4—714no—
880C2×C4—1422no—
881C2×C4—1422no—
882C2×C4—1422no—
883C2×C4—1422no—
884C2×C4—1422no—
885C2×C4—1422no—
886C2×C4—1422no—
887C2×C4—1422no—
888C2×C4—1422no—
889C2×C4—1422no—
890C2×C4—1422no—
891C2×C4—1422no—
892C2×C4—1422no—
893C2×C4—1422no—
894C2×C4—1428no—
895C2×C4C22×C4×D7114yes—
896C2×C4C22×C4×D7114yes—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—416no—
905C22—28464no—
906C22—2842no—
907C22—2842no—
908C22—2842no—
909C22—2842no—
910C22—2842no—
911C22—2842no—
912C22—2842no—
913C22—2842no—
914C22—2842no—
915C22—2842no—
916C22—2842no—
917C22—2842no—
918C22—28416no—
919C22—28416no—
920C22—28416no—
921C22—1424no—
922C22—1424no—
923C22—1424no—
924C22—1424no—
925C22—1424no—
926C22—1424no—
927C22—1424no—
928C22—1424no—
929C22—1424no—
930C22#1798647114yes—
931C22#1798647114yes—
932C22#1798647314yes—
933C22#1798673714yes—
934C22#1798673914yes—
935C22#1798674014yes—
936C22#1798674114yes—
937C22C23×C4×D7111yescharacteristic
938C22C2×#1455617311yescharacteristic
939C22C2×#1455617311yescharacteristic
940C22C2×#1455617411yescharacteristic
941C22C2×#1455617411yescharacteristic
942C22C2×#1455617411yescharacteristic
943C22C2×#1455617411yescharacteristic
944C4—24no—
945C4—24no—
946C4—42no—
947C4—42no—
948C4—42no—
949C4—42no—
950C4—2842no—
951C4—2842no—
952C4—2842no—
953C4—2842no—
954C4—1424no—
955C2—44no—
956C2—2844no—
957C2—2844no—
958C2—2844no—
959C2#2259148018yesdirect product factor
960C2C2×#1798647111yescharacteristic
961C2C2×#1798647111yescharacteristic
962C2C2×#1798647311yescharacteristic
963C2C2×#1798673711yescharacteristic
964C2C2×#1798673911yescharacteristic
965C2C2×#1798674011yescharacteristic
966C2C2×#1798674111yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC22×#14556098C2
cosocleC23×C71C25
hypercenterC2×#388D71
hypocenterC71C2×#2375
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #22591480C2direct (N × H)
3. C2×#17985901C2semidirect
4. C2×#17985900C2semidirect
5. C2×#17985899C2semidirect
6. C2×#17985892C2semidirect
7. C2×#17985891C2semidirect
8. C2×#17985890C2semidirect
9. C2×#17985889C2semidirect
10. C2×#17985888C2semidirect
11. C2×#17985877C2semidirect
12. C2×#17985877C2semidirect
13. C2×#17985875C2semidirect
14. C2×#17985854C2semidirect
15. C2×#17985854C2semidirect
16. C2×#388×C71C2semidirect
21. C23×C4×D71C22semidirect
22. C2×#14556098C4semidirect
24. C22×C4⋊Dic71C22semidirect
25. C22×Dic71⋊C4C22semidirect
38. C22×(C2×D71)⋊C4C22semidirect
39. C22×(C2×D71)⋊C4C22semidirect
40. C22×(C2×D71)⋊C4C22semidirect
41. C22×C4×Dic71C22semidirect
42. C22×C4×Dic71C22semidirect
43. #17985901C22semidirect
44. #17985900C22semidirect
45. #17985899C22semidirect
46. #17985892C22semidirect
47. #17985891C22semidirect
48. #17985890C22semidirect
49. #17985889C22semidirect
50. #17985888C22semidirect
51. #17985877C22semidirect
52. #17985877C22semidirect
53. #17985875C22semidirect
54. #17985854C22semidirect
55. #17985854C22semidirect
56. C2×C71⋊#95C22semidirect
57. C2×C71⋊#95C22semidirect
58. C2×C71⋊#95C22semidirect
59. C2×C71⋊#95C22semidirect
60. C22×C4⋊C4×C71C22semidirect
64. C22×C42×C71C22semidirect
65. #388×C71C22semidirect
66. C2×#95×C71C22semidirect
67. C2×#95×C71C22semidirect
74. C24×D71C2×C4semidirect
99. C22×C4×D71C23semidirect
100. #14556098C2×C4semidirect
102. C2×C4⋊Dic71C23semidirect
104. C2×Dic71⋊C4C23semidirect
120. C2×(C2×D71)⋊C4C2×C4semidirect
121. C2×(C2×D71)⋊C4C2×C4semidirect
132. C2×(C2×D71)⋊C4C23semidirect
133. C2×(C2×D71)⋊C4C23semidirect
134. C2×(C2×D71)⋊C4C23semidirect
137. C2×C4×Dic71C23semidirect
138. C2×C4×Dic71C23semidirect
139. C71⋊#95C23semidirect
140. C71⋊#95C23semidirect
141. C71⋊#95C23semidirect
142. C71⋊#95C23semidirect
151. C2×C4⋊C4×C71C23semidirect
154. C2×C22⋊C4×C71C2×C4semidirect
159. C2×C42×C71C23semidirect
160. #95×C71C23semidirect
161. #95×C71C23semidirect
196. C23×D71C22×C4semidirect
251. (C2×D71)⋊C4C22×C4semidirect
252. (C2×D71)⋊C4C22×C4semidirect
291. C22⋊C4×C71C22×C4semidirect
473. C2×C71#2375semidirect
494. C2×#388D71semidirect
500. C71C2×#2375semidirect
510. C22×C4⋊C4C2×D71semidirect
531. C22×C42C2×D71semidirect
540. #388C2×D71semidirect
550. C2×#95C2×D71semidirect
551. C2×#95C2×D71semidirect
597. C2×C4⋊C4C22×D71semidirect
630. C2×C22⋊C4C4×D71semidirect
639. C2×C42C22×D71semidirect
644. #95C22×D71semidirect
645. #95C22×D71semidirect
773. C22⋊C4C2×C4×D71semidirect
959. C2#22591480direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145560982
#225914802
C2×#179859012
C2×#179859002
C2×#179858992
C2×#179858922
C2×#179858912
C2×#179858902
C2×#179858892
C2×#179858882
C2×#179858772
C2×#179858752
C2×#179858542
C2×#388×C712
C2×#237571