Finite Group Databasebeta

← C2×#22591735 #32165016

Subgroups — C2×#22591735 #32165016

Order 18176.

5162 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556110C211yesmaximal, characteristic, complemented
2C22×#14556096C211yesmaximal, characteristic
3C23×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D71C211yesmaximal, characteristic, complemented
5#22591735C2116yesmaximal, direct product factor
6C2×#17985928C211yesmaximal, characteristic, complemented
7C2×#17985926C211yesmaximal, characteristic, complemented
8C2×#17985915C211yesmaximal, characteristic, complemented
9C2×#17985914C211yesmaximal, characteristic, complemented
10C2×#17985879C211yesmaximal, characteristic, complemented
11C2×#17985875C211yesmaximal, characteristic, complemented
12C2×#17985873C211yesmaximal, characteristic, complemented
13C2×#17985861C211yesmaximal, characteristic, complemented
14C2×#17985859C211yesmaximal, characteristic, complemented
15C2×#17985857C211yesmaximal, characteristic, complemented
16C2×#386×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C24×Dic71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C2×#14556110—28no—
24C2×#14556110C2218yescomplemented
25C2×#14556096—28no—
26C2×#14556096C2218yes—
27C22×C4⋊Dic71C2211yescharacteristic, complemented
28C22×C4⋊Dic71C2211yescharacteristic, complemented
29C22×Dic71⋊C4C2211yescharacteristic, complemented
30C22×Dic71⋊C4C2211yescharacteristic, complemented
31C22×C22⋊Dic71C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic
33C22×C22⋊Dic71C2211yescharacteristic, complemented
34C22×C22⋊Dic71C2211yescharacteristic, complemented
35C22×(C2×D71)⋊C4—28no—
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×(C2×D71)⋊C4C2211yescharacteristic
43C22×(C2×D71)⋊C4C2211yescharacteristic
44C22×(C2×D71)⋊C4C2218yescomplemented
45C2×C22⋊C4×D71—28no—
46C2×C22⋊C4×D71C2218yescomplemented
47#17985928C2218yescomplemented
48#17985926C2218yescomplemented
49#17985915C2218yescomplemented
50#17985914C2218yescomplemented
51#17985879C2218yescomplemented
52#17985875C2218yescomplemented
53#17985873C2218yescomplemented
54#17985861C2218yescomplemented
55#17985859C2218yescomplemented
56#17985857C2218yescomplemented
57C2×C71⋊#95C2211yescharacteristic, complemented
58C2×C71⋊#95C2211yescharacteristic, complemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C2×C71⋊#95C2211yescharacteristic, complemented
62C2×C71⋊#95C2211yescharacteristic, complemented
63C23×D4×C71C2211yescharacteristic
64C24×C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic, complemented
67C22×C22⋊C4×C71C2211yescharacteristic, complemented
68#386×C71C2218yescomplemented
69C2×#95×C71C2211yescharacteristic, complemented
70C2×#95×C71C2211yescharacteristic, complemented
71C24×D71—24no—
72C24×D71—24no—
73C24×D71—24no—
74C24×D71—24no—
75C24×D71—42no—
76C24×D71—42no—
77C24×D71D418yes—
78C24×D71C2311yescharacteristic
79C24×D71C2314yes—
80C24×D71C2311yescharacteristic
81C22×C22⋊D71—24no—
82C22×C22⋊D71—24no—
83C22×C22⋊D71—24no—
84C22×C22⋊D71—24no—
85C22×C22⋊D71—42no—
86C22×C22⋊D71—42no—
87C22×C22⋊D71C2314yes—
88C22×C22⋊D71C2314yes—
89C23×Dic71—24no—
90C23×Dic71—24no—
91C23×Dic71—42no—
92C23×Dic71C2311yescharacteristic
93C23×Dic71C2311yescharacteristic
94C23×Dic71C2311yescharacteristic
95C23×Dic71C2311yescharacteristic
96C23×Dic71C2311yescharacteristic
97C23×Dic71C2314yes—
98C23×Dic71C2311yescharacteristic
99C22×C4×D71—24no—
100C22×C4×D71—24no—
101C22×C4×D71—24no—
102C22×C4×D71—24no—
103C22×C4×D71—42no—
104C22×C4×D71—42no—
105C22×C4×D71C2314yes—
106C22×C4×D71C2314yes—
107#14556110—232no—
108#14556096—232no—
109C2×C4⋊Dic71—24no—
110C2×C4⋊Dic71—42no—
111C2×C4⋊Dic71C2314yescomplemented
112C2×C4⋊Dic71C2314yescomplemented
113C2×Dic71⋊C4—24no—
114C2×Dic71⋊C4—42no—
115C2×Dic71⋊C4C2314yescomplemented
116C2×Dic71⋊C4C2314yescomplemented
117C2×C22⋊Dic71—24no—
118C2×C22⋊Dic71—24no—
119C2×C22⋊Dic71—24no—
120C2×C22⋊Dic71—42no—
121C2×C22⋊Dic71C2314yes—
122C2×C22⋊Dic71C2314yes—
123C2×C22⋊Dic71C2314yescomplemented
124C2×C22⋊Dic71C2314yescomplemented
125C2×(C2×D71)⋊C4—24no—
126C2×(C2×D71)⋊C4—24no—
127C2×(C2×D71)⋊C4—24no—
128C2×(C2×D71)⋊C4—24no—
129C2×(C2×D71)⋊C4—24no—
130C2×(C2×D71)⋊C4—24no—
131C2×(C2×D71)⋊C4—232no—
132C2×(C2×D71)⋊C4—24no—
133C2×(C2×D71)⋊C4D418yescomplemented
134C2×(C2×D71)⋊C4C2314yes—
135C2×(C2×D71)⋊C4C2314yes—
136C2×(C2×D71)⋊C4C2314yes—
137C2×(C2×D71)⋊C4C2314yes—
138C2×(C2×D71)⋊C4C2314yes—
139C2×(C2×D71)⋊C4C2314yes—
140C2×(C2×D71)⋊C4C2314yes—
141C2×(C2×D71)⋊C4C2314yes—
142C22⋊C4×D71—232no—
143C71⋊#95C2314yescomplemented
144C71⋊#95C2314yescomplemented
145C71⋊#95C2314yescomplemented
146C71⋊#95C2314yescomplemented
147C71⋊#95C2314yescomplemented
148C71⋊#95C2314yescomplemented
149C25×C71C2311yescharacteristic
150C25×C71C2311yescharacteristic
151C22×D4×C71—24no—
152C22×D4×C71—24no—
153C22×D4×C71—24no—
154C22×D4×C71C2314yes—
155C23×C4×C71—24no—
156C23×C4×C71—24no—
157C23×C4×C71—42no—
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C23×C4×C71C2311yescharacteristic
162C23×C4×C71C2314yes—
163C23×C4×C71C2311yescharacteristic
164C2×C22⋊C4×C71—24no—
165C2×C22⋊C4×C71—24no—
166C2×C22⋊C4×C71—42no—
167C2×C22⋊C4×C71C2314yes—
168C2×C22⋊C4×C71C2314yescomplemented
169C2×C22⋊C4×C71C2314yescomplemented
170#95×C71C2314yescomplemented
171#95×C71C2314yescomplemented
172C23×D71—22no—
173C23×D71—22no—
174C23×D71—22no—
175C23×D71—22no—
176C23×D71—232no—
177C23×D71—22no—
178C23×D71—22no—
179C23×D71—28no—
180C23×D71—22no—
181C23×D71—28no—
182C23×D71—22no—
183C23×D71—22no—
184C23×D71—22no—
185C23×D71—232no—
186C23×D71—28no—
187C23×D71—28no—
188C23×D71—416no—
189C23×D71—44no—
190C23×D71—44no—
191C23×D71—416no—
192C23×D71—416no—
193C23×D71—416no—
194C23×D71—416no—
195C23×D71C2×D414yes—
196C23×D71C2×D4116yes—
197C23×D71C2×D414yes—
198C23×D71C2×D414yes—
199C23×D71#4114yes—
200C23×D71C2412yes—
201C23×D71C2412yes—
202C2×C22⋊D71—28no—
203C2×C22⋊D71—28no—
204C2×C22⋊D71—28no—
205C2×C22⋊D71—28no—
206C2×C22⋊D71—44no—
207C2×C22⋊D71—44no—
208C2×C22⋊D71—416no—
209C2×C22⋊D71—416no—
210C22×Dic71—22no—
211C22×Dic71—22no—
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—28no—
221C22×Dic71—22no—
222C22×Dic71—22no—
223C22×Dic71—22no—
224C22×Dic71—22no—
225C22×Dic71—22no—
226C22×Dic71—22no—
227C22×Dic71—22no—
228C22×Dic71—28no—
229C22×Dic71—44no—
230C22×Dic71—416no—
231C22×Dic71C2×D414yes—
232C22×Dic71C2412yes—
233C22×Dic71C2412yes—
234C22×Dic71C2412yes—
235C22×Dic71C2412yes—
236C22×Dic71C2412yes—
237C22×Dic71C2412yes—
238C2×C4×D71—28no—
239C2×C4×D71—28no—
240C2×C4×D71—28no—
241C2×C4×D71—28no—
242C2×C4×D71—44no—
243C2×C4×D71—44no—
244C2×C4×D71—416no—
245C2×C4×D71—416no—
246C4⋊Dic71—28no—
247C4⋊Dic71—44no—
248Dic71⋊C4—28no—
249Dic71⋊C4—44no—
250C22⋊Dic71—28no—
251C22⋊Dic71—28no—
252C22⋊Dic71—28no—
253C22⋊Dic71—44no—
254(C2×D71)⋊C4—28no—
255(C2×D71)⋊C4—28no—
256(C2×D71)⋊C4—28no—
257(C2×D71)⋊C4—28no—
258(C2×D71)⋊C4—28no—
259(C2×D71)⋊C4—28no—
260(C2×D71)⋊C4—28no—
261(C2×D71)⋊C4C2×D4116yescomplemented
262C24×C71—22no—
263C24×C71—22no—
264C24×C71—22no—
265C24×C71—22no—
266C24×C71—22no—
267C24×C71—22no—
268C24×C71—22no—
269C24×C71—22no—
270C24×C71—22no—
271C24×C71—22no—
272C24×C71—22no—
273C24×C71C2×D414yes—
274C24×C71#4114yes—
275C24×C71#4114yes—
276C24×C71C2412yes—
277C24×C71C2412yes—
278C24×C71C2411yescharacteristic
279C2×D4×C71—28no—
280C2×D4×C71—28no—
281C2×D4×C71—28no—
282C2×D4×C71—416no—
283C22×C4×C71—22no—
284C22×C4×C71—22no—
285C22×C4×C71—22no—
286C22×C4×C71—22no—
287C22×C4×C71—22no—
288C22×C4×C71—22no—
289C22×C4×C71—22no—
290C22×C4×C71—22no—
291C22×C4×C71—28no—
292C22×C4×C71—22no—
293C22×C4×C71—22no—
294C22×C4×C71—22no—
295C22×C4×C71—22no—
296C22×C4×C71—22no—
297C22×C4×C71—22no—
298C22×C4×C71—28no—
299C22×C4×C71—44no—
300C22×C4×C71—416no—
301C22×C4×C71C2×D414yes—
302C22×C4×C71C2412yes—
303C22×C4×C71C2412yes—
304C22×C4×C71C2412yes—
305C22×C4×C71C2412yes—
306C22×C4×C71C2412yes—
307C22⋊C4×C71—28no—
308C22⋊C4×C71—28no—
309C22⋊C4×C71—44no—
310C23×C71—28no—
311C23×C71—28no—
312C23×C71—28no—
313C23×C71—28no—
314C23×C71—28no—
315C23×C71—28no—
316C23×C71—22no—
317C23×C71—22no—
318C23×C71—22no—
319C23×C71—22no—
320C23×C71—22no—
321C23×C71—22no—
322C23×C71—22no—
323C23×C71—22no—
324C23×C71—22no—
325C23×C71—22no—
326C23×C71—22no—
327C23×C71—44no—
328C23×C71—44no—
329C23×C71—44no—
330C23×C71—44no—
331C23×C71—44no—
332C23×C71—44no—
333C23×C71—44no—
334C23×C71#123116yescomplemented
335C23×C71C22×D414yes—
336C23×C71C22×D412yes—
337C23×C71C22×D412yes—
338C23×C71C2×#4112yes—
339C23×C71C2×#4114yes—
340C23×C71C2×#4112yes—
341C23×C71C2×#4114yes—
342C23×C71C2×#4112yes—
343C23×C71H(5,𝔽2)12yes—
344C23×C71H(5,𝔽2)12yes—
345C23×C71C2511yescharacteristic
346C22×D71—28no—
347C22×D71—28no—
348C22×D71—28no—
349C22×D71—28no—
350C22×D71—28no—
351C22×D71—28no—
352C22×D71—22no—
353C22×D71—22no—
354C22×D71—22no—
355C22×D71—22no—
356C22×D71—28no—
357C22×D71—28no—
358C22×D71—232no—
359C22×D71—28no—
360C22×D71—22no—
361C22×D71—22no—
362C22×D71—22no—
363C22×D71—22no—
364C22×D71—22no—
365C22×D71—22no—
366C22×D71—232no—
367C22×D71—416no—
368C22×D71—4128no—
369C22×D71—416no—
370C22×D71—416no—
371C22×D71—416no—
372C22×D71—416no—
373C22×D71—44no—
374C22×D71—44no—
375C22×D71—44no—
376C22×D71—44no—
377C22×D71#121116yes—
378C22×D71C22×D414yes—
379C22×D71C22×D414yes—
380C22×D71C22×D414yes—
381C22×D71C2×#4114yes—
382D4×C71—416no—
383C2×C4×C71—28no—
384C2×C4×C71—22no—
385C2×C4×C71—22no—
386C2×C4×C71—22no—
387C2×C4×C71—22no—
388C2×C4×C71—22no—
389C2×C4×C71—22no—
390C2×C4×C71—22no—
391C2×C4×C71—22no—
392C2×C4×C71—22no—
393C2×C4×C71—22no—
394C2×C4×C71—22no—
395C2×C4×C71—22no—
396C2×C4×C71—22no—
397C2×C4×C71—22no—
398C2×C4×C71—416no—
399C2×C4×C71—44no—
400C2×C4×C71—44no—
401C2×C4×C71—44no—
402C2×C4×C71—44no—
403C2×C4×C71C22×D414yes—
404C22⋊D71—416no—
405C22⋊D71—416no—
406C2×Dic71—28no—
407C2×Dic71—22no—
408C2×Dic71—22no—
409C2×Dic71—22no—
410C2×Dic71—22no—
411C2×Dic71—22no—
412C2×Dic71—22no—
413C2×Dic71—22no—
414C2×Dic71—22no—
415C2×Dic71—22no—
416C2×Dic71—22no—
417C2×Dic71—22no—
418C2×Dic71—22no—
419C2×Dic71—22no—
420C2×Dic71—22no—
421C2×Dic71—22no—
422C2×Dic71—22no—
423C2×Dic71—22no—
424C2×Dic71—416no—
425C2×Dic71—44no—
426C2×Dic71—44no—
427C2×Dic71—44no—
428C2×Dic71—44no—
429C2×Dic71—44no—
430C2×Dic71C22×D414yes—
431C4×D71—416no—
432C4×D71—416no—
433C22×C71—24no—
434C22×C71—232no—
435C22×C71—24no—
436C22×C71—24no—
437C22×C71—24no—
438C22×C71—24no—
439C22×C71—24no—
440C22×C71—42no—
441C22×C71—42no—
442C22×C71—42no—
443C22×C71—42no—
444C22×C71—42no—
445C22×C71—42no—
446C22×C71—42no—
447C22×C71—88no—
448C22×C71C2×#12114yes—
449C22×C71C2×#12314yes—
450C22×C71C2×#12318yescomplemented
451C22×C71#53414yes—
452C22×C71#54614yes—
453C22×C71#54614yes—
454C22×C71#55114yes—
455C22×C71#55114yes—
456C22×C71C23×D411yescharacteristic
457C22×C71C23×D411yescharacteristic
458C22×C71C22×#4111yescharacteristic
459C22×C71C22×#4111yescharacteristic
460C22×C71C22×#4111yescharacteristic
461C22×C71C2×H(5,𝔽2)11yescharacteristic
462C22×C71C2×H(5,𝔽2)11yescharacteristic
463C2×D71—24no—
464C2×D71—232no—
465C2×D71—24no—
466C2×D71—24no—
467C2×D71—24no—
468C2×D71—24no—
469C2×D71—24no—
470C2×D71—24no—
471C2×D71—24no—
472C2×D71—24no—
473C2×D71—464no—
474C2×D71—416no—
475C2×D71—42no—
476C2×D71—42no—
477C2×D71—42no—
478C2×D71—42no—
479C2×D71C2×#12118yes—
480C4×C71—24no—
481C4×C71—42no—
482C4×C71—42no—
483C4×C71—42no—
484C4×C71—42no—
485Dic71—24no—
486Dic71—42no—
487Dic71—42no—
488Dic71—42no—
489Dic71—42no—
490Dic71—42no—
491C2×#2412—711nomaximal, Sylow
492C2×C71—28no—
493C2×C71—82no—
494C2×C71#241218yescomplemented
495C2×C71C22×#12111yescharacteristic
496C2×C71C22×#12311yescharacteristic
497C2×C71C2×#53411yescharacteristic
498C2×C71C2×#54611yescharacteristic
499C2×C71C2×#54611yescharacteristic
500C2×C71C2×#55111yescharacteristic
501C2×C71C2×#55111yescharacteristic
502D71—28no—
503D71—44no—
504C22×#123—711no—
505C22×#120—711no—
506C23×C22⋊C4—711no—
507C23×C22⋊C4—711no—
508#2412—7116no—
509C2×#397—711no—
510C2×#397—711no—
511C2×#394—711no—
512C2×#394—711no—
513C2×#386—711no—
514C2×#386—711no—
515C2×#386D7111yescharacteristic, complemented
516C2×#385—711no—
517C2×#381—711no—
518C2×#380—711no—
519C2×#380—711no—
520C71C2×#241211yescharacteristic, complemented, Sylow
521C26—711no—
522C23×D4—711no—
523C23×D4—711no—
524C23×D4C2×D7111yescharacteristic
525C24×C4—711no—
526C24×C4—711no—
527C24×C4—711no—
528C24×C4C2×D7111yescharacteristic
529C2×#123—718no—
530C2×#123—1428no—
531C2×#120—718no—
532C2×#120—1428no—
533C22×C4⋊C4—711no—
534C22×C4⋊C4—711no—
535C22×C4⋊C4—711no—
536C22×C4⋊C4—711no—
537C22×C22⋊C4—711no—
538C22×C22⋊C4—711no—
539C22×C22⋊C4—711no—
540C22×C22⋊C4—711no—
541C22×C22⋊C4—711no—
542C22×C22⋊C4—711no—
543C22×C22⋊C4—711no—
544C22×C22⋊C4—711no—
545C22×C22⋊C4—711no—
546C22×C22⋊C4—711no—
547C22×C22⋊C4—718no—
548C22×C22⋊C4—711no—
549C22×C22⋊C4—711no—
550C22×C22⋊C4—718no—
551C22×C22⋊C4—1428no—
552C22×C22⋊C4—1428no—
553C22×C22⋊C4C2×D7111yescharacteristic
554C22×C22⋊C4C2×D7111yescharacteristic, complemented
555C22×C22⋊C4C2×D7111yescharacteristic, complemented
556#397—718no—
557#397—718no—
558#394—718no—
559#394—718no—
560#386—718no—
561#386—718no—
562#386C2×D7118yescomplemented
563#385—718no—
564#381—718no—
565#380—718no—
566#380—718no—
567C2×#95—711no—
568C2×#95—711no—
569C2×#95—711no—
570C2×#95—711no—
571C2×#95—711no—
572C2×#95—711no—
573C2×#95C2×D7111yescharacteristic, complemented
574C2×#95C2×D7111yescharacteristic, complemented
575C25—2842no—
576C25—2842no—
577C25—718no—
578C25—714no—
579C25—711no—
580C25—711no—
581C25—1424no—
582C25—1424no—
583C25—1424no—
584C25—1424no—
585C25C22×D7111yescharacteristic
586C25C22×D7111yescharacteristic
587C22×D4—24no—
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—2842no—
591C22×D4—2842no—
592C22×D4—714no—
593C22×D4—714no—
594C22×D4—1424no—
595C22×D4—1424no—
596C22×D4—1424no—
597C22×D4—1424no—
598C22×D4C22×D7114yes—
599C23×C4—24no—
600C23×C4—24no—
601C23×C4—42no—
602C23×C4—2842no—
603C23×C4—2842no—
604C23×C4—2842no—
605C23×C4—714no—
606C23×C4—714no—
607C23×C4—711no—
608C23×C4—711no—
609C23×C4—711no—
610C23×C4—711no—
611C23×C4—711no—
612C23×C4—711no—
613C23×C4—714no—
614C23×C4—1424no—
615C23×C4—1424no—
616C23×C4—1424no—
617C23×C4—1424no—
618C23×C4—1424no—
619C23×C4—1424no—
620C23×C4C22×D7111yescharacteristic
621C23×C4C22×D7111yescharacteristic
622C23×C4C22×D7111yescharacteristic
623C23×C4C22×D7111yescharacteristic
624C23×C4C22×D7114yes—
625C23×C4C22×D7111yescharacteristic
626#123—14232no—
627#120—14232no—
628C2×C4⋊C4—2842no—
629C2×C4⋊C4—2842no—
630C2×C4⋊C4—714no—
631C2×C4⋊C4—714no—
632C2×C4⋊C4—714no—
633C2×C4⋊C4—714no—
634C2×C4⋊C4—1424no—
635C2×C4⋊C4—1424no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—2842no—
640C2×C22⋊C4—714no—
641C2×C22⋊C4—718no—
642C2×C22⋊C4—714no—
643C2×C22⋊C4—714no—
644C2×C22⋊C4—714no—
645C2×C22⋊C4—714no—
646C2×C22⋊C4—714no—
647C2×C22⋊C4—714no—
648C2×C22⋊C4—714no—
649C2×C22⋊C4—714no—
650C2×C22⋊C4—714no—
651C2×C22⋊C4—714no—
652C2×C22⋊C4—714no—
653C2×C22⋊C4—14232no—
654C2×C22⋊C4—14232no—
655C2×C22⋊C4—1424no—
656C2×C22⋊C4—1424no—
657C2×C22⋊C4—1424no—
658C2×C22⋊C4—1424no—
659C2×C22⋊C4—1424no—
660C2×C22⋊C4—1424no—
661C2×C22⋊C4—1424no—
662C2×C22⋊C4—1424no—
663C2×C22⋊C4—1424no—
664C2×C22⋊C4—1424no—
665C2×C22⋊C4C22×D7114yes—
666C2×C22⋊C4C22×D7114yescomplemented
667C2×C22⋊C4C22×D7114yescomplemented
668#95—714no—
669#95—714no—
670#95—714no—
671#95—714no—
672#95—714no—
673#95—714no—
674#95C22×D7114yescomplemented
675#95C22×D7114yescomplemented
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—28416no—
688C24—28416no—
689C24—28416no—
690C24—28416no—
691C24—2844no—
692C24—2844no—
693C24—28416no—
694C24—7116no—
695C24—714no—
696C24—714no—
697C24—714no—
698C24—712no—
699C24—714no—
700C24—712no—
701C24—1428no—
702C24—1428no—
703C24—14232no—
704C24—1422no—
705C24—1422no—
706C24—1428no—
707C24—1422no—
708C24—1428no—
709C24—1422no—
710C24—1422no—
711C24—1422no—
712C24—14232no—
713C24—1422no—
714C24—1422no—
715C24—1422no—
716C24—1422no—
717C24D4×D7114yes—
718C24#1176586414yes—
719C24#1176586514yes—
720C24C23×D7112yes—
721C24C23×D7112yes—
722C24C23×D7111yescharacteristic
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—416no—
727C2×D4—28416no—
728C2×D4—28416no—
729C2×D4—2844no—
730C2×D4—2844no—
731C2×D4—1428no—
732C2×D4—1428no—
733C2×D4—1428no—
734C2×D4—1428no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—28no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—28no—
751C22×C4—44no—
752C22×C4—416no—
753C22×C4—2844no—
754C22×C4—2844no—
755C22×C4—28416no—
756C22×C4—28416no—
757C22×C4—28416no—
758C22×C4—2844no—
759C22×C4—714no—
760C22×C4—712no—
761C22×C4—712no—
762C22×C4—712no—
763C22×C4—712no—
764C22×C4—712no—
765C22×C4—712no—
766C22×C4—1428no—
767C22×C4—1428no—
768C22×C4—1428no—
769C22×C4—1428no—
770C22×C4—1428no—
771C22×C4—1422no—
772C22×C4—1422no—
773C22×C4—1422no—
774C22×C4—1422no—
775C22×C4—1422no—
776C22×C4—1422no—
777C22×C4—1422no—
778C22×C4—1422no—
779C22×C4—1422no—
780C22×C4—1422no—
781C22×C4—1428no—
782C22×C4—1422no—
783C22×C4—1422no—
784C22×C4—1422no—
785C22×C4—1422no—
786C22×C4—1422no—
787C22×C4—1422no—
788C22×C4—1422no—
789C22×C4D4×D7114yes—
790C22×C4C23×D7112yes—
791C22×C4C23×D7112yes—
792C22×C4C23×D7112yes—
793C22×C4C23×D7112yes—
794C22×C4C23×D7112yes—
795C4⋊C4—2844no—
796C4⋊C4—2844no—
797C4⋊C4—1428no—
798C4⋊C4—1428no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—2844no—
803C22⋊C4—7116no—
804C22⋊C4—1428no—
805C22⋊C4—1428no—
806C22⋊C4—1428no—
807C22⋊C4—1428no—
808C22⋊C4—1428no—
809C22⋊C4—1428no—
810C22⋊C4—1428no—
811C22⋊C4—1428no—
812C22⋊C4—1428no—
813C22⋊C4—1428no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—28no—
819C23—28no—
820C23—28no—
821C23—28no—
822C23—28no—
823C23—28no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—28416no—
839C23—28416no—
840C23—28416no—
841C23—28416no—
842C23—284128no—
843C23—28416no—
844C23—2844no—
845C23—2844no—
846C23—2844no—
847C23—2844no—
848C23—714no—
849C23—714no—
850C23—714no—
851C23—7116no—
852C23—714no—
853C23—14232no—
854C23—1422no—
855C23—1422no—
856C23—1422no—
857C23—1422no—
858C23—1422no—
859C23—1422no—
860C23—1428no—
861C23—1428no—
862C23—14232no—
863C23—1428no—
864C23—1422no—
865C23—1422no—
866C23—1422no—
867C23—1422no—
868C23—1428no—
869C23—1428no—
870C23—1428no—
871C23—1428no—
872C23—1428no—
873C23—1428no—
874C23#14556110116yescomplemented
875C23C2×D4×D7114yes—
876C23C2×D4×D7112yes—
877C23C2×D4×D7112yes—
878C23#41×D7112yes—
879C23C2×#1176586414yes—
880C23C2×#1176586412yes—
881C23C2×#1176586514yes—
882C23C2×#1176586512yes—
883C23#1455617312yes—
884C23#1455617412yes—
885C23C24×D7111yescharacteristic
886D4—416no—
887D4—28416no—
888D4—28416no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—28no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—416no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—28416no—
910C2×C4—28416no—
911C2×C4—2844no—
912C2×C4—2844no—
913C2×C4—2844no—
914C2×C4—2844no—
915C2×C4—2844no—
916C2×C4—28416no—
917C2×C4—714no—
918C2×C4—1422no—
919C2×C4—1422no—
920C2×C4—1422no—
921C2×C4—1422no—
922C2×C4—1422no—
923C2×C4—1422no—
924C2×C4—1422no—
925C2×C4—1422no—
926C2×C4—1422no—
927C2×C4—1422no—
928C2×C4—1422no—
929C2×C4—1422no—
930C2×C4—1422no—
931C2×C4—1422no—
932C2×C4—1422no—
933C2×C4—1422no—
934C2×C4—1422no—
935C2×C4—1428no—
936C2×C4C2×D4×D7114yes—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—232no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—88no—
952C22—28464no—
953C22—2842no—
954C22—2842no—
955C22—2842no—
956C22—2842no—
957C22—28416no—
958C22—718no—
959C22—1424no—
960C22—1424no—
961C22—1424no—
962C22—1424no—
963C22—1424no—
964C22—1424no—
965C22—1424no—
966C22—1424no—
967C22—1424no—
968C22—14232no—
969C22#121×D7114yes—
970C22C2×#1455611014yes—
971C22C2×#1455611018yescomplemented
972C22#1798655714yes—
973C22#1798663614yes—
974C22#1798664514yes—
975C22#1798667214yes—
976C22#1798667814yes—
977C22C22×D4×D7111yescharacteristic
978C22C22×D4×D7111yescharacteristic
979C22C2×#41×D7111yescharacteristic
980C22C22×#1176586411yescharacteristic
981C22C22×#1176586511yescharacteristic
982C22C2×#1455617311yescharacteristic
983C22C2×#1455617411yescharacteristic
984C4—24no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—2842no—
990C4—2842no—
991C4—2842no—
992C4—2842no—
993C4—2842no—
994C4—1424no—
995C2—28no—
996C2—82no—
997C2—2844no—
998C2—1428no—
999C2#2259173518yesdirect product factor
1000C2C2×#121×D7111yescharacteristic
1001C2C22×#1455611011yescharacteristic
1002C2C2×#1798655711yescharacteristic
1003C2C2×#1798663611yescharacteristic
1004C2C2×#1798664511yescharacteristic
1005C2C2×#1798667211yescharacteristic
1006C2C2×#1798667811yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#386×C71C2
socleC24×C71C24
prime radicalC22×#14556096C2
hypercenterC2×#386D71
hypocenterC71C2×#2412
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#14556110C2semidirect
3. C23×(C2×D71)⋊C4C2semidirect
4. C22×C22⋊C4×D71C2semidirect
5. #22591735C2direct (N × H)
6. C2×#17985928C2semidirect
7. C2×#17985926C2semidirect
8. C2×#17985915C2semidirect
9. C2×#17985914C2semidirect
10. C2×#17985879C2semidirect
11. C2×#17985875C2semidirect
12. C2×#17985873C2semidirect
13. C2×#17985861C2semidirect
14. C2×#17985859C2semidirect
15. C2×#17985857C2semidirect
16. C2×#386×C71C2semidirect
24. C2×#14556110C22semidirect
27. C22×C4⋊Dic71C22semidirect
28. C22×C4⋊Dic71C22semidirect
29. C22×Dic71⋊C4C22semidirect
30. C22×Dic71⋊C4C22semidirect
33. C22×C22⋊Dic71C22semidirect
34. C22×C22⋊Dic71C22semidirect
44. C22×(C2×D71)⋊C4C22semidirect
46. C2×C22⋊C4×D71C22semidirect
47. #17985928C22semidirect
48. #17985926C22semidirect
49. #17985915C22semidirect
50. #17985914C22semidirect
51. #17985879C22semidirect
52. #17985875C22semidirect
53. #17985873C22semidirect
54. #17985861C22semidirect
55. #17985859C22semidirect
56. #17985857C22semidirect
57. C2×C71⋊#95C22semidirect
58. C2×C71⋊#95C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
61. C2×C71⋊#95C22semidirect
62. C2×C71⋊#95C22semidirect
66. C22×C22⋊C4×C71C22semidirect
67. C22×C22⋊C4×C71C22semidirect
68. #386×C71C22semidirect
69. C2×#95×C71C22semidirect
70. C2×#95×C71C22semidirect
111. C2×C4⋊Dic71C23semidirect
112. C2×C4⋊Dic71C23semidirect
115. C2×Dic71⋊C4C23semidirect
116. C2×Dic71⋊C4C23semidirect
123. C2×C22⋊Dic71C23semidirect
124. C2×C22⋊Dic71C23semidirect
133. C2×(C2×D71)⋊C4D4semidirect
143. C71⋊#95C23semidirect
144. C71⋊#95C23semidirect
145. C71⋊#95C23semidirect
146. C71⋊#95C23semidirect
147. C71⋊#95C23semidirect
148. C71⋊#95C23semidirect
168. C2×C22⋊C4×C71C23semidirect
169. C2×C22⋊C4×C71C23semidirect
170. #95×C71C23semidirect
171. #95×C71C23semidirect
261. (C2×D71)⋊C4C2×D4semidirect
334. C23×C71#123semidirect
450. C22×C71C2×#123semidirect
494. C2×C71#2412semidirect
515. C2×#386D71semidirect
520. C71C2×#2412semidirect
554. C22×C22⋊C4C2×D71semidirect
555. C22×C22⋊C4C2×D71semidirect
562. #386C2×D71semidirect
573. C2×#95C2×D71semidirect
574. C2×#95C2×D71semidirect
666. C2×C22⋊C4C22×D71semidirect
667. C2×C22⋊C4C22×D71semidirect
674. #95C22×D71semidirect
675. #95C22×D71semidirect
874. C23#14556110semidirect
971. C22C2×#14556110semidirect
999. C2#22591735direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561102
C22×#145560962
C23×(C2×D71)⋊C42
C22×C22⋊C4×D712
#225917352
C2×#179859282
C2×#179859262
C2×#179859152
C2×#179859142
C2×#179858792
C2×#179858752
C2×#179858732
C2×#179858612
C2×#179858592
C2×#179858572
C2×#386×C712
C2×#241271