Finite Group Databasebeta

← C2×#22591802 #32164886

Subgroups — C2×#22591802 #32164886

Order 18176.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556110C211yesmaximal, characteristic, complemented
2C22×#14556097C211yesmaximal, characteristic
3C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
4#22591802C2116yesmaximal, direct product factor
5C2×#17985935C211yesmaximal, characteristic, complemented
6C2×#17985927C211yesmaximal, characteristic, complemented
7C2×#17985915C211yesmaximal, characteristic, complemented
8C2×#17985914C211yesmaximal, characteristic, complemented
9C2×#17985893C211yesmaximal, characteristic, complemented
10C2×#17985892C211yesmaximal, characteristic, complemented
11C2×#17985878C211yesmaximal, characteristic, complemented
12C2×#17985875C211yesmaximal, characteristic, complemented
13C2×#17985872C211yesmaximal, characteristic, complemented
14C2×#17985859C211yesmaximal, characteristic, complemented
15C2×#17985855C211yesmaximal, characteristic, complemented
16C23×C22⋊C4×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic, complemented
21C2×#14556110—28no—
22C2×#14556110C2218yescomplemented
23C2×#14556097—28no—
24C2×#14556097C2218yes—
25C2×C4×C22⋊D71—28no—
26C2×C4×C22⋊D71C2218yescomplemented
27C22×C4⋊Dic71C2211yescharacteristic, complemented
28C22×C4⋊Dic71C2211yescharacteristic, complemented
29C22×Dic71⋊C4C2211yescharacteristic, complemented
30C22×Dic71⋊C4C2211yescharacteristic, complemented
31C22×Dic71⋊C4C2211yescharacteristic, complemented
32C22×C22⋊Dic71C2211yescharacteristic
33C22×C22⋊Dic71C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×C22⋊Dic71C2211yescharacteristic
37C22×C22⋊Dic71C2211yescharacteristic
38C22×C22⋊Dic71C2211yescharacteristic
39C22×C22⋊Dic71C2211yescharacteristic
40C22×C22⋊Dic71C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
44C22×C4×Dic71C2211yescharacteristic, complemented
45#17985935C2218yescomplemented
46#17985927C2218yescomplemented
47#17985915C2218yescomplemented
48#17985914C2218yescomplemented
49#17985893C2218yescomplemented
50#17985892C2218yescomplemented
51#17985878C2218yescomplemented
52#17985875C2218yescomplemented
53#17985872C2218yescomplemented
54#17985859C2218yescomplemented
55#17985855C2218yescomplemented
56C2×C71⋊#95C2211yescharacteristic, complemented
57C2×C71⋊#95C2211yescharacteristic, complemented
58C2×C71⋊#95C2211yescharacteristic, complemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C2×C71⋊#95C2211yescharacteristic, complemented
62C26×C71C2211yescharacteristic
63C24×C4×C71C2211yescharacteristic
64C24×C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71—28no—
66C22×C22⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68C22×C22⋊C4×C71C2211yescharacteristic
69C22×C22⋊C4×C71C2211yescharacteristic
70C22×C22⋊C4×C71C2218yescomplemented
71C24×D71C2311yescharacteristic
72C22×C22⋊D71—24no—
73C22×C22⋊D71—24no—
74C22×C22⋊D71—24no—
75C22×C22⋊D71—24no—
76C22×C22⋊D71—24no—
77C22×C22⋊D71—24no—
78C22×C22⋊D71—42no—
79C22×C22⋊D71—42no—
80C22×C22⋊D71D418yes—
81C22×C22⋊D71C2314yes—
82C22×C22⋊D71C2314yes—
83C22×C22⋊D71C2314yes—
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C22×C4×D71—24no—
92C22×C4×D71—24no—
93C22×C4×D71—42no—
94C22×C4×D71C2314yescomplemented
95#14556110—232no—
96#14556097—232no—
97C4×C22⋊D71—232no—
98C2×C4⋊Dic71—24no—
99C2×C4⋊Dic71—42no—
100C2×C4⋊Dic71C2314yescomplemented
101C2×C4⋊Dic71C2314yescomplemented
102C2×Dic71⋊C4—24no—
103C2×Dic71⋊C4—24no—
104C2×Dic71⋊C4—42no—
105C2×Dic71⋊C4C2314yescomplemented
106C2×Dic71⋊C4C2314yescomplemented
107C2×Dic71⋊C4C2314yescomplemented
108C2×C22⋊Dic71—24no—
109C2×C22⋊Dic71—24no—
110C2×C22⋊Dic71—24no—
111C2×C22⋊Dic71—24no—
112C2×C22⋊Dic71—24no—
113C2×C22⋊Dic71—24no—
114C2×C22⋊Dic71—24no—
115C2×C22⋊Dic71—42no—
116C2×C22⋊Dic71—42no—
117C2×C22⋊Dic71C2314yes—
118C2×C22⋊Dic71C2314yes—
119C2×C22⋊Dic71C2314yes—
120C2×C22⋊Dic71C2314yes—
121C2×C22⋊Dic71C2314yes—
122C2×C22⋊Dic71C2314yes—
123C2×C22⋊Dic71C2314yes—
124C2×C22⋊Dic71C2314yes—
125C2×C22⋊Dic71C2314yes—
126C2×(C2×D71)⋊C4—24no—
127C2×(C2×D71)⋊C4—24no—
128C2×(C2×D71)⋊C4—42no—
129C2×(C2×D71)⋊C4C2314yescomplemented
130C2×(C2×D71)⋊C4C2314yescomplemented
131C2×(C2×D71)⋊C4C2314yescomplemented
132C2×C4×Dic71—24no—
133C2×C4×Dic71C2314yescomplemented
134C71⋊#95C2314yescomplemented
135C71⋊#95C2314yescomplemented
136C71⋊#95C2314yescomplemented
137C71⋊#95C2314yescomplemented
138C71⋊#95C2314yescomplemented
139C71⋊#95C2314yescomplemented
140C25×C71—24no—
141C25×C71—24no—
142C25×C71—24no—
143C25×C71—24no—
144C25×C71—24no—
145C25×C71—42no—
146C25×C71—42no—
147C25×C71C2311yescharacteristic
148C25×C71C2311yescharacteristic
149C25×C71C2314yes—
150C25×C71C2311yescharacteristic
151C23×C4×C71—24no—
152C23×C4×C71—24no—
153C23×C4×C71—24no—
154C23×C4×C71—24no—
155C23×C4×C71—42no—
156C23×C4×C71—42no—
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2314yes—
160C23×C4×C71C2314yes—
161C23×C4×C71C2311yescharacteristic
162C23×C4×C71C2311yescharacteristic
163C2×C22⋊C4×C71—24no—
164C2×C22⋊C4×C71—24no—
165C2×C22⋊C4×C71—24no—
166C2×C22⋊C4×C71—232no—
167C2×C22⋊C4×C71D418yescomplemented
168C2×C22⋊C4×C71C2314yes—
169C2×C22⋊C4×C71C2314yes—
170C2×C22⋊C4×C71C2314yes—
171C2×C22⋊C4×C71C2314yes—
172C23×D71—22no—
173C23×D71—22no—
174C23×D71—22no—
175C23×D71—22no—
176C23×D71—22no—
177C23×D71—22no—
178C23×D71C2×D414yes—
179C23×D71C2412yes—
180C2×C22⋊D71—232no—
181C2×C22⋊D71—28no—
182C2×C22⋊D71—28no—
183C2×C22⋊D71—28no—
184C2×C22⋊D71—28no—
185C2×C22⋊D71—28no—
186C2×C22⋊D71—28no—
187C2×C22⋊D71—44no—
188C2×C22⋊D71—44no—
189C2×C22⋊D71—416no—
190C2×C22⋊D71—416no—
191C2×C22⋊D71C2×D4116yes—
192C22×Dic71—22no—
193C22×Dic71—22no—
194C22×Dic71—22no—
195C22×Dic71—22no—
196C22×Dic71—22no—
197C22×Dic71—22no—
198C22×Dic71—22no—
199C22×Dic71—22no—
200C22×Dic71—22no—
201C22×Dic71—22no—
202C22×Dic71—22no—
203C22×Dic71—22no—
204C22×Dic71—22no—
205C22×Dic71—22no—
206C22×Dic71—22no—
207C22×Dic71—22no—
208C22×Dic71—22no—
209C22×Dic71—22no—
210C22×Dic71—22no—
211C22×Dic71—22no—
212C22×Dic71C2×D414yes—
213C22×Dic71C2412yes—
214C22×Dic71C2412yes—
215C22×Dic71C2412yes—
216C22×Dic71C2412yes—
217C22×Dic71C2412yes—
218C22×Dic71C2412yes—
219C22×Dic71C2412yes—
220C2×C4×D71—28no—
221C2×C4×D71—28no—
222C2×C4×D71—44no—
223C2×C4×D71—416no—
224C4⋊Dic71—28no—
225C4⋊Dic71—44no—
226Dic71⋊C4—28no—
227Dic71⋊C4—28no—
228Dic71⋊C4—44no—
229C22⋊Dic71—28no—
230C22⋊Dic71—28no—
231C22⋊Dic71—28no—
232C22⋊Dic71—28no—
233C22⋊Dic71—28no—
234C22⋊Dic71—28no—
235C22⋊Dic71—28no—
236C22⋊Dic71—44no—
237C22⋊Dic71—44no—
238(C2×D71)⋊C4—28no—
239(C2×D71)⋊C4—28no—
240(C2×D71)⋊C4—44no—
241C4×Dic71—28no—
242C24×C71—22no—
243C24×C71—22no—
244C24×C71—22no—
245C24×C71—22no—
246C24×C71—232no—
247C24×C71—22no—
248C24×C71—22no—
249C24×C71—28no—
250C24×C71—22no—
251C24×C71—22no—
252C24×C71—22no—
253C24×C71—28no—
254C24×C71—28no—
255C24×C71—22no—
256C24×C71—22no—
257C24×C71—22no—
258C24×C71—22no—
259C24×C71—22no—
260C24×C71—22no—
261C24×C71—22no—
262C24×C71—28no—
263C24×C71—28no—
264C24×C71—44no—
265C24×C71—44no—
266C24×C71—416no—
267C24×C71—416no—
268C24×C71—416no—
269C24×C71—416no—
270C24×C71—416no—
271C24×C71—416no—
272C24×C71C2×D414yes—
273C24×C71C2×D414yes—
274C24×C71#4114yes—
275C24×C71#4114yes—
276C24×C71#4114yes—
277C24×C71C2412yes—
278C24×C71C2412yes—
279C24×C71C2412yes—
280C24×C71C2411yescharacteristic
281C22×C4×C71—22no—
282C22×C4×C71—22no—
283C22×C4×C71—22no—
284C22×C4×C71—22no—
285C22×C4×C71—22no—
286C22×C4×C71—22no—
287C22×C4×C71—22no—
288C22×C4×C71—28no—
289C22×C4×C71—28no—
290C22×C4×C71—22no—
291C22×C4×C71—22no—
292C22×C4×C71—22no—
293C22×C4×C71—28no—
294C22×C4×C71—28no—
295C22×C4×C71—44no—
296C22×C4×C71—44no—
297C22×C4×C71—416no—
298C22×C4×C71—416no—
299C22×C4×C71C2×D414yes—
300C22×C4×C71C2×D414yes—
301C22×C4×C71C2412yes—
302C22×C4×C71C2412yes—
303C22×C4×C71C2412yes—
304C22×C4×C71C2412yes—
305C22⋊C4×C71—28no—
306C22⋊C4×C71—28no—
307C22⋊C4×C71—28no—
308C22⋊C4×C71C2×D4116yescomplemented
309C23×C71—28no—
310C23×C71—28no—
311C23×C71—28no—
312C23×C71—28no—
313C23×C71—28no—
314C23×C71—28no—
315C23×C71—22no—
316C23×C71—22no—
317C23×C71—22no—
318C23×C71—22no—
319C23×C71—232no—
320C23×C71—28no—
321C23×C71—28no—
322C23×C71—28no—
323C23×C71—28no—
324C23×C71—28no—
325C23×C71—28no—
326C23×C71—22no—
327C23×C71—22no—
328C23×C71—22no—
329C23×C71—22no—
330C23×C71—22no—
331C23×C71—22no—
332C23×C71—22no—
333C23×C71—22no—
334C23×C71—22no—
335C23×C71—22no—
336C23×C71—22no—
337C23×C71—22no—
338C23×C71—416no—
339C23×C71—416no—
340C23×C71—416no—
341C23×C71—416no—
342C23×C71—4128no—
343C23×C71—416no—
344C23×C71—44no—
345C23×C71—44no—
346C23×C71—416no—
347C23×C71—44no—
348C23×C71—44no—
349C23×C71—44no—
350C23×C71—44no—
351C23×C71—44no—
352C23×C71—44no—
353C23×C71#123116yescomplemented
354C23×C71C22×D414yes—
355C23×C71C22×D412yes—
356C23×C71C22×D414yes—
357C23×C71C22×D412yes—
358C23×C71C2×#4114yes—
359C23×C71C2×#4112yes—
360C23×C71C2×#4114yes—
361C23×C71C2×#4114yes—
362C23×C71C2×#4112yes—
363C23×C71C2×#4112yes—
364C23×C71H(5,𝔽2)12yes—
365C23×C71H(5,𝔽2)12yes—
366C23×C71C2511yescharacteristic
367C22×D71—28no—
368C22×D71—28no—
369C22×D71—28no—
370C22×D71—22no—
371C22×D71—22no—
372C22×D71—22no—
373C22×D71—22no—
374C22×D71—22no—
375C22×D71—22no—
376C22×D71—44no—
377C22×D71—44no—
378C22×D71—44no—
379C22×D71—44no—
380C22×D71C22×D414yes—
381C2×C4×C71—28no—
382C2×C4×C71—28no—
383C2×C4×C71—22no—
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—416no—
394C2×C4×C71—416no—
395C2×C4×C71—44no—
396C2×C4×C71—44no—
397C2×C4×C71C22×D414yes—
398C2×C4×C71C22×D414yes—
399C22⋊D71—232no—
400C22⋊D71—416no—
401C22⋊D71—416no—
402C2×Dic71—28no—
403C2×Dic71—22no—
404C2×Dic71—22no—
405C2×Dic71—22no—
406C2×Dic71—22no—
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—44no—
424C2×Dic71—44no—
425C2×Dic71—44no—
426C2×Dic71—44no—
427C2×Dic71—44no—
428C2×Dic71—44no—
429C2×Dic71C22×D414yes—
430C4×D71—416no—
431C22×C71—24no—
432C22×C71—232no—
433C22×C71—24no—
434C22×C71—24no—
435C22×C71—24no—
436C22×C71—24no—
437C22×C71—24no—
438C22×C71—24no—
439C22×C71—24no—
440C22×C71—24no—
441C22×C71—24no—
442C22×C71—24no—
443C22×C71—24no—
444C22×C71—464no—
445C22×C71—42no—
446C22×C71—42no—
447C22×C71—416no—
448C22×C71—416no—
449C22×C71—42no—
450C22×C71—42no—
451C22×C71—42no—
452C22×C71—42no—
453C22×C71—42no—
454C22×C71—42no—
455C22×C71C2×#12314yes—
456C22×C71C2×#12318yescomplemented
457C22×C71#52514yes—
458C22×C71#53814yes—
459C22×C71D4214yes—
460C22×C71#54614yes—
461C22×C71#54614yes—
462C22×C71#55114yes—
463C22×C71C23×D411yescharacteristic
464C22×C71C23×D411yescharacteristic
465C22×C71C22×#4111yescharacteristic
466C22×C71C22×#4111yescharacteristic
467C22×C71C22×#4111yescharacteristic
468C22×C71C2×H(5,𝔽2)11yescharacteristic
469C22×C71C2×H(5,𝔽2)11yescharacteristic
470C2×D71—24no—
471C2×D71—24no—
472C2×D71—24no—
473C2×D71—42no—
474C2×D71—416no—
475C2×D71—42no—
476C2×D71—42no—
477C2×D71—42no—
478C4×C71—24no—
479C4×C71—24no—
480C4×C71—42no—
481C4×C71—42no—
482Dic71—24no—
483Dic71—42no—
484Dic71—42no—
485Dic71—42no—
486Dic71—42no—
487Dic71—42no—
488Dic71—42no—
489C2×#2418—711nomaximal, Sylow
490C2×C71—28no—
491C2×C71—44no—
492C2×C71—44no—
493C2×C71#241818yescomplemented
494C2×C71C22×#12311yescharacteristic
495C2×C71C2×#52511yescharacteristic
496C2×C71C2×#53811yescharacteristic
497C2×C71C2×D4211yescharacteristic
498C2×C71C2×#54611yescharacteristic
499C2×C71C2×#54611yescharacteristic
500C2×C71C2×#55111yescharacteristic
501D71—44no—
502C22×#123—711no—
503C22×#120—711no—
504C22×C4×D4—711no—
505C23×C22⋊C4D7111yescharacteristic, complemented
506#2418—7116no—
507C2×#399—711no—
508C2×#397—711no—
509C2×#394—711no—
510C2×#394—711no—
511C2×#388—711no—
512C2×#388—711no—
513C2×#386—711no—
514C2×#386—711no—
515C2×#385—711no—
516C2×#380—711no—
517C2×#379—711no—
518C71C2×#241811yescharacteristic, complemented, Sylow
519C26C2×D7111yescharacteristic
520C23×D4—711no—
521C23×D4—711no—
522C23×D4—711no—
523C24×C4—711no—
524C24×C4C2×D7111yescharacteristic
525C24×C4C2×D7111yescharacteristic
526C2×#123—718no—
527C2×#123—1428no—
528C2×#120—718no—
529C2×#120—1428no—
530C2×C4×D4—718no—
531C2×C4×D4—1428no—
532C22×C4⋊C4—711no—
533C22×C4⋊C4—711no—
534C22×C4⋊C4—711no—
535C22×C4⋊C4—711no—
536C22×C4⋊C4—711no—
537C22×C22⋊C4—28no—
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—711no—
548C22×C22⋊C4—711no—
549C22×C22⋊C4—711no—
550C22×C22⋊C4C2×D7111yescharacteristic
551C22×C22⋊C4C2×D7111yescharacteristic
552C22×C22⋊C4C2×D7111yescharacteristic
553C22×C22⋊C4C2×D7111yescharacteristic
554C22×C22⋊C4C2×D7118yescomplemented
555C22×C42—711no—
556#399—718no—
557#397—718no—
558#394—718no—
559#394—718no—
560#388—718no—
561#388—718no—
562#386—718no—
563#386—718no—
564#385—718no—
565#380—718no—
566#379—718no—
567C2×#95—711no—
568C2×#95—711no—
569C2×#95—711no—
570C2×#95—711no—
571C2×#95—711no—
572C2×#95—711no—
573C25—24no—
574C25—24no—
575C25—24no—
576C25—24no—
577C25—24no—
578C25—42no—
579C25—42no—
580C25—711no—
581C25C22×D7111yescharacteristic
582C25C22×D7111yescharacteristic
583C25C22×D7114yes—
584C25C22×D7111yescharacteristic
585C22×D4—2842no—
586C22×D4—2842no—
587C22×D4—714no—
588C22×D4—714no—
589C22×D4—718no—
590C22×D4—714no—
591C22×D4—1424no—
592C22×D4—1424no—
593C22×D4—1424no—
594C22×D4—1424no—
595C22×D4—1424no—
596C22×D4—1424no—
597C23×C4—24no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—24no—
601C23×C4—42no—
602C23×C4—42no—
603C23×C4—2842no—
604C23×C4—714no—
605C23×C4—711no—
606C23×C4—711no—
607C23×C4—711no—
608C23×C4—711no—
609C23×C4—711no—
610C23×C4—711no—
611C23×C4—711no—
612C23×C4—1424no—
613C23×C4—1424no—
614C23×C4C22×D7111yescharacteristic
615C23×C4C22×D7111yescharacteristic
616C23×C4C22×D7114yes—
617C23×C4C22×D7114yes—
618C23×C4C22×D7111yescharacteristic
619C23×C4C22×D7111yescharacteristic
620#123—14232no—
621#120—14232no—
622C4×D4—14232no—
623C2×C4⋊C4—2842no—
624C2×C4⋊C4—2842no—
625C2×C4⋊C4—714no—
626C2×C4⋊C4—714no—
627C2×C4⋊C4—714no—
628C2×C4⋊C4—714no—
629C2×C4⋊C4—714no—
630C2×C4⋊C4—1424no—
631C2×C4⋊C4—1424no—
632C2×C4⋊C4—1424no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—232no—
637C2×C22⋊C4—2842no—
638C2×C22⋊C4—2842no—
639C2×C22⋊C4—2842no—
640C2×C22⋊C4—714no—
641C2×C22⋊C4—714no—
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—1424no—
653C2×C22⋊C4—1424no—
654C2×C22⋊C4—1424no—
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⋊C4C22⋊D7118yescomplemented
662C2×C22⋊C4C22×D7114yes—
663C2×C22⋊C4C22×D7114yes—
664C2×C22⋊C4C22×D7114yes—
665C2×C22⋊C4C22×D7114yes—
666C2×C42—714no—
667C2×C42—1424no—
668#95—714no—
669#95—714no—
670#95—714no—
671#95—714no—
672#95—714no—
673#95—714no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—232no—
679C24—22no—
680C24—22no—
681C24—28no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—28no—
686C24—28no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—28no—
695C24—28no—
696C24—44no—
697C24—44no—
698C24—416no—
699C24—416no—
700C24—416no—
701C24—416no—
702C24—416no—
703C24—416no—
704C24—714no—
705C24—712no—
706C24—1422no—
707C24—1422no—
708C24—1422no—
709C24—1422no—
710C24—1422no—
711C24—1422no—
712C24D4×D7114yes—
713C24C2×C22⋊D7114yes—
714C24#1176586414yes—
715C24#1176586514yes—
716C24#1176586514yes—
717C24C23×D7112yes—
718C24C23×D7112yes—
719C24C23×D7112yes—
720C24C23×D7111yescharacteristic
721C2×D4—28416no—
722C2×D4—28416no—
723C2×D4—2844no—
724C2×D4—2844no—
725C2×D4—7116no—
726C2×D4—1428no—
727C2×D4—1428no—
728C2×D4—1428no—
729C2×D4—1428no—
730C2×D4—1428no—
731C2×D4—1428no—
732C2×D4—14232no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—28no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—28no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—416no—
750C22×C4—416no—
751C22×C4—28416no—
752C22×C4—2844no—
753C22×C4—714no—
754C22×C4—712no—
755C22×C4—712no—
756C22×C4—712no—
757C22×C4—712no—
758C22×C4—712no—
759C22×C4—712no—
760C22×C4—712no—
761C22×C4—1428no—
762C22×C4—1422no—
763C22×C4—1422no—
764C22×C4—1422no—
765C22×C4—1422no—
766C22×C4—1422no—
767C22×C4—1422no—
768C22×C4—1422no—
769C22×C4—1422no—
770C22×C4—1422no—
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—1428no—
781C22×C4—1422no—
782C22×C4—1422no—
783C22×C4C2×C22⋊D7114yes—
784C22×C4C2×C22⋊D7114yes—
785C22×C4C23×D7112yes—
786C22×C4C23×D7112yes—
787C22×C4C23×D7112yes—
788C22×C4C23×D7112yes—
789C4⋊C4—2844no—
790C4⋊C4—2844no—
791C4⋊C4—1428no—
792C4⋊C4—1428no—
793C4⋊C4—1428no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—2844no—
798C22⋊C4—2844no—
799C22⋊C4—2844no—
800C22⋊C4—1428no—
801C22⋊C4—1428no—
802C22⋊C4—1428no—
803C22⋊C4—1428no—
804C22⋊C4—1428no—
805C22⋊C4—1428no—
806C22⋊C4—1428no—
807C22⋊C4—1428no—
808C22⋊C4—1428no—
809C22⋊C4C2×C22⋊D71116yescomplemented
810C42—1428no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—28no—
816C23—28no—
817C23—28no—
818C23—28no—
819C23—28no—
820C23—28no—
821C23—232no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—28no—
835C23—28no—
836C23—28no—
837C23—28no—
838C23—28no—
839C23—28no—
840C23—416no—
841C23—416no—
842C23—416no—
843C23—416no—
844C23—4128no—
845C23—416no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—44no—
850C23—44no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—416no—
855C23—2844no—
856C23—2844no—
857C23—2844no—
858C23—2844no—
859C23—714no—
860C23—1422no—
861C23—1422no—
862C23—1422no—
863C23—1422no—
864C23—1422no—
865C23—1422no—
866C23—1428no—
867C23—1428no—
868C23—1428no—
869C23#14556110116yescomplemented
870C23C2×D4×D7114yes—
871C23C2×D4×D7112yes—
872C23C22×C22⋊D7114yes—
873C23C22×C22⋊D7112yes—
874C23C2×#1176586414yes—
875C23C2×#1176586412yes—
876C23C2×#1176586514yes—
877C23C2×#1176586514yes—
878C23C2×#1176586512yes—
879C23C2×#1176586512yes—
880C23#1455617312yes—
881C23#1455617312yes—
882C23C24×D7111yescharacteristic
883D4—28416no—
884D4—28416no—
885D4—14232no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—416no—
899C2×C4—416no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—28416no—
903C2×C4—2844no—
904C2×C4—2844no—
905C2×C4—2844no—
906C2×C4—2844no—
907C2×C4—2844no—
908C2×C4—2844no—
909C2×C4—714no—
910C2×C4—1422no—
911C2×C4—1422no—
912C2×C4—1422no—
913C2×C4—1422no—
914C2×C4—1422no—
915C2×C4—1422no—
916C2×C4—1422no—
917C2×C4—1422no—
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—1428no—
931C2×C4C22×C22⋊D7114yes—
932C2×C4C22×C22⋊D7114yes—
933C22—24no—
934C22—24no—
935C22—232no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—464no—
947C22—42no—
948C22—42no—
949C22—416no—
950C22—416no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—28416no—
958C22—2842no—
959C22—2842no—
960C22—2842no—
961C22—2842no—
962C22—1424no—
963C22—1424no—
964C22—1424no—
965C22C2×#1455611014yes—
966C22C2×#1455611018yescomplemented
967C22#1798651014yes—
968C22#1798658714yes—
969C22D4×C22⋊D7114yes—
970C22#1798663914yes—
971C22#1798664314yes—
972C22#1798667514yes—
973C22C22×D4×D7111yescharacteristic
974C22C23×C22⋊D7111yescharacteristic
975C22C22×#1176586411yescharacteristic
976C22C22×#1176586511yescharacteristic
977C22C22×#1176586511yescharacteristic
978C22C2×#1455617311yescharacteristic
979C22C2×#1455617311yescharacteristic
980C4—24no—
981C4—24no—
982C4—42no—
983C4—42no—
984C4—2842no—
985C4—2842no—
986C4—2842no—
987C4—2842no—
988C4—2842no—
989C4—2842no—
990C4—1424no—
991C2—28no—
992C2—44no—
993C2—44no—
994C2—2844no—
995C2#2259180218yesdirect product factor
996C2C22×#1455611011yescharacteristic
997C2C2×#1798651011yescharacteristic
998C2C2×#1798658711yescharacteristic
999C2C2×D4×C22⋊D7111yescharacteristic
1000C2C2×#1798663911yescharacteristic
1001C2C2×#1798664311yescharacteristic
1002C2C2×#1798667511yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC23×C22⋊C4×C71C2
socleC24×C71C24
prime radicalC22×#14556097C2
hypercenterC23×C22⋊C4D71
hypocenterC71C2×#2418
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14556110C2semidirect
3. C22×C4×C22⋊D71C2semidirect
4. #22591802C2direct (N × H)
5. C2×#17985935C2semidirect
6. C2×#17985927C2semidirect
7. C2×#17985915C2semidirect
8. C2×#17985914C2semidirect
9. C2×#17985893C2semidirect
10. C2×#17985892C2semidirect
11. C2×#17985878C2semidirect
12. C2×#17985875C2semidirect
13. C2×#17985872C2semidirect
14. C2×#17985859C2semidirect
15. C2×#17985855C2semidirect
16. C23×C22⋊C4×C71C2semidirect
20. C23×C4×D71C22semidirect
22. C2×#14556110C22semidirect
26. C2×C4×C22⋊D71C22semidirect
27. C22×C4⋊Dic71C22semidirect
28. C22×C4⋊Dic71C22semidirect
29. C22×Dic71⋊C4C22semidirect
30. C22×Dic71⋊C4C22semidirect
31. C22×Dic71⋊C4C22semidirect
41. C22×(C2×D71)⋊C4C22semidirect
42. C22×(C2×D71)⋊C4C22semidirect
43. C22×(C2×D71)⋊C4C22semidirect
44. C22×C4×Dic71C22semidirect
45. #17985935C22semidirect
46. #17985927C22semidirect
47. #17985915C22semidirect
48. #17985914C22semidirect
49. #17985893C22semidirect
50. #17985892C22semidirect
51. #17985878C22semidirect
52. #17985875C22semidirect
53. #17985872C22semidirect
54. #17985859C22semidirect
55. #17985855C22semidirect
56. C2×C71⋊#95C22semidirect
57. C2×C71⋊#95C22semidirect
58. C2×C71⋊#95C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
61. C2×C71⋊#95C22semidirect
70. C22×C22⋊C4×C71C22semidirect
94. C22×C4×D71C23semidirect
100. C2×C4⋊Dic71C23semidirect
101. C2×C4⋊Dic71C23semidirect
105. C2×Dic71⋊C4C23semidirect
106. C2×Dic71⋊C4C23semidirect
107. C2×Dic71⋊C4C23semidirect
129. C2×(C2×D71)⋊C4C23semidirect
130. C2×(C2×D71)⋊C4C23semidirect
131. C2×(C2×D71)⋊C4C23semidirect
133. C2×C4×Dic71C23semidirect
134. C71⋊#95C23semidirect
135. C71⋊#95C23semidirect
136. C71⋊#95C23semidirect
137. C71⋊#95C23semidirect
138. C71⋊#95C23semidirect
139. C71⋊#95C23semidirect
167. C2×C22⋊C4×C71D4semidirect
308. C22⋊C4×C71C2×D4semidirect
353. C23×C71#123semidirect
456. C22×C71C2×#123semidirect
493. C2×C71#2418semidirect
505. C23×C22⋊C4D71semidirect
518. C71C2×#2418semidirect
554. C22×C22⋊C4C2×D71semidirect
661. C2×C22⋊C4C22⋊D71semidirect
809. C22⋊C4C2×C22⋊D71semidirect
869. C23#14556110semidirect
966. C22C2×#14556110semidirect
995. C2#22591802direct (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×#145560972
C22×C4×C22⋊D712
#225918022
C2×#179859352
C2×#179859272
C2×#179859152
C2×#179859142
C2×#179858932
C2×#179858922
C2×#179858782
C2×#179858752
C2×#179858722
C2×#179858592
C2×#179858552
C23×C22⋊C4×C712
C2×#241871