Finite Group Databasebeta

← C2×#22591799 #32164885

Subgroups — C2×#22591799 #32164885

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×#14556096C211yesmaximal, characteristic
2C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
3C22×C22⋊C4×D71C211yesmaximal, characteristic, complemented
4#22591799C2116yesmaximal, direct product factor
5C2×#17985934C211yesmaximal, characteristic, complemented
6C2×#17985927C211yesmaximal, characteristic, complemented
7C2×#17985915C211yesmaximal, characteristic, complemented
8C2×#17985913C211yesmaximal, characteristic, complemented
9C2×#17985892C211yesmaximal, characteristic, complemented
10C2×#17985889C211yesmaximal, characteristic, complemented
11C2×#17985878C211yesmaximal, characteristic, complemented
12C2×#17985875C211yesmaximal, characteristic, complemented
13C2×#17985870C211yesmaximal, characteristic, complemented
14C2×#17985856C211yesmaximal, characteristic, complemented
15C2×#17985854C211yesmaximal, characteristic, complemented
16C22×#123×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C2×#14556096—28no—
23C2×#14556096C2218yes—
24C2×C4×C22⋊D71—28no—
25C2×C4×C22⋊D71C2218yescomplemented
26C22×C4⋊Dic71C2211yescharacteristic, complemented
27C22×Dic71⋊C4C2211yescharacteristic, complemented
28C22×Dic71⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic71C2211yescharacteristic
30C22×C22⋊Dic71C2211yescharacteristic
31C22×C22⋊Dic71C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic, complemented
33C22×C22⋊Dic71C2211yescharacteristic, complemented
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C2×C22⋊C4×D71—28no—
43C2×C22⋊C4×D71C2218yescomplemented
44C22×C4×Dic71C2211yescharacteristic, complemented
45#17985934C2218yescomplemented
46#17985927C2218yescomplemented
47#17985915C2218yescomplemented
48#17985913C2218yescomplemented
49#17985892C2218yescomplemented
50#17985889C2218yescomplemented
51#17985878C2218yescomplemented
52#17985875C2218yescomplemented
53#17985870C2218yescomplemented
54#17985856C2218yescomplemented
55#17985854C2218yescomplemented
56C2×C71⋊#95C2211yescharacteristic, complemented
57C2×C71⋊#95C2211yescharacteristic, complemented
58C2×C71⋊#95C2211yescharacteristic, complemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C2×C71⋊#95C2211yescharacteristic, complemented
62C23×D4×C71C2211yescharacteristic
63C24×C4×C71C2211yescharacteristic, complemented
64C2×#123×C71—28no—
65C2×#123×C71C2218yescomplemented
66C22×C4⋊C4×C71C2211yescharacteristic, complemented
67C22×C4⋊C4×C71C2211yescharacteristic, complemented
68C22×C22⋊C4×C71C2211yescharacteristic
69C22×C22⋊C4×C71C2211yescharacteristic
70C22×C22⋊C4×C71C2211yescharacteristic, complemented
71C24×D71—24no—
72C24×D71—24no—
73C24×D71—24no—
74C24×D71—24no—
75C24×D71—24no—
76C24×D71—42no—
77C24×D71—42no—
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⋊D71D418yes—
87C22×C22⋊D71C2314yes—
88C22×C22⋊D71C2314yes—
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C23×Dic71C2311yescharacteristic
92C23×Dic71C2311yescharacteristic
93C23×Dic71C2311yescharacteristic
94C23×Dic71C2311yescharacteristic
95C22×C4×D71—24no—
96C22×C4×D71—24no—
97C22×C4×D71—24no—
98C22×C4×D71—24no—
99C22×C4×D71—42no—
100C22×C4×D71—42no—
101C22×C4×D71C2314yes—
102C22×C4×D71C2314yes—
103#14556096—232no—
104C4×C22⋊D71—232no—
105C2×C4⋊Dic71—42no—
106C2×C4⋊Dic71C2314yescomplemented
107C2×Dic71⋊C4—24no—
108C2×Dic71⋊C4—42no—
109C2×Dic71⋊C4C2314yescomplemented
110C2×Dic71⋊C4C2314yescomplemented
111C2×C22⋊Dic71—24no—
112C2×C22⋊Dic71—24no—
113C2×C22⋊Dic71—24no—
114C2×C22⋊Dic71—42no—
115C2×C22⋊Dic71—42no—
116C2×C22⋊Dic71C2314yes—
117C2×C22⋊Dic71C2314yes—
118C2×C22⋊Dic71C2314yes—
119C2×C22⋊Dic71C2314yescomplemented
120C2×C22⋊Dic71C2314yescomplemented
121C2×(C2×D71)⋊C4—24no—
122C2×(C2×D71)⋊C4—24no—
123C2×(C2×D71)⋊C4—24no—
124C2×(C2×D71)⋊C4—24no—
125C2×(C2×D71)⋊C4—24no—
126C2×(C2×D71)⋊C4—24no—
127C2×(C2×D71)⋊C4—24no—
128C2×(C2×D71)⋊C4—42no—
129C2×(C2×D71)⋊C4C2314yes—
130C2×(C2×D71)⋊C4C2314yes—
131C2×(C2×D71)⋊C4C2314yes—
132C2×(C2×D71)⋊C4C2314yes—
133C2×(C2×D71)⋊C4C2314yes—
134C2×(C2×D71)⋊C4C2314yes—
135C2×(C2×D71)⋊C4C2314yes—
136C2×(C2×D71)⋊C4C2314yes—
137C22⋊C4×D71—232no—
138C2×C4×Dic71—24no—
139C2×C4×Dic71C2314yescomplemented
140C71⋊#95C2314yescomplemented
141C71⋊#95C2314yescomplemented
142C71⋊#95C2314yescomplemented
143C71⋊#95C2314yescomplemented
144C71⋊#95C2314yescomplemented
145C71⋊#95C2314yescomplemented
146C25×C71C2311yescharacteristic
147C25×C71C2311yescharacteristic
148C22×D4×C71—24no—
149C22×D4×C71—24no—
150C22×D4×C71—42no—
151C22×D4×C71C2314yes—
152C23×C4×C71—24no—
153C23×C4×C71—24no—
154C23×C4×C71—42no—
155C23×C4×C71C2311yescharacteristic
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2314yescomplemented
161#123×C71—232no—
162C2×C4⋊C4×C71—24no—
163C2×C4⋊C4×C71—24no—
164C2×C4⋊C4×C71C2314yescomplemented
165C2×C4⋊C4×C71C2314yescomplemented
166C2×C22⋊C4×C71—24no—
167C2×C22⋊C4×C71—24no—
168C2×C22⋊C4×C71D418yescomplemented
169C2×C22⋊C4×C71C2314yes—
170C2×C22⋊C4×C71C2314yes—
171C2×C22⋊C4×C71C2314yescomplemented
172C23×D71—22no—
173C23×D71—22no—
174C23×D71—22no—
175C23×D71—22no—
176C23×D71—232no—
177C23×D71—22no—
178C23×D71—28no—
179C23×D71—22no—
180C23×D71—22no—
181C23×D71—22no—
182C23×D71—22no—
183C23×D71—22no—
184C23×D71—28no—
185C23×D71—28no—
186C23×D71—28no—
187C23×D71—28no—
188C23×D71—44no—
189C23×D71—44no—
190C23×D71—416no—
191C23×D71—416no—
192C23×D71—416no—
193C23×D71—416no—
194C23×D71—416no—
195C23×D71—416no—
196C23×D71C2×D414yes—
197C23×D71#4114yes—
198C23×D71#4114yes—
199C23×D71#4114yes—
200C23×D71C2412yes—
201C23×D71C2412yes—
202C2×C22⋊D71—232no—
203C2×C22⋊D71—28no—
204C2×C22⋊D71—28no—
205C2×C22⋊D71—28no—
206C2×C22⋊D71—28no—
207C2×C22⋊D71—44no—
208C2×C22⋊D71—416no—
209C2×C22⋊D71C2×D4116yes—
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—22no—
221C22×Dic71—22no—
222C22×Dic71—22no—
223C22×Dic71—22no—
224C22×Dic71—22no—
225C22×Dic71—22no—
226C22×Dic71—22no—
227C22×Dic71C2×D414yes—
228C22×Dic71C2412yes—
229C22×Dic71C2412yes—
230C22×Dic71C2412yes—
231C22×Dic71C2412yes—
232C22×Dic71C2412yes—
233C22×Dic71C2412yes—
234C2×C4×D71—28no—
235C2×C4×D71—28no—
236C2×C4×D71—28no—
237C2×C4×D71—28no—
238C2×C4×D71—44no—
239C2×C4×D71—44no—
240C2×C4×D71—416no—
241C2×C4×D71—416no—
242C4⋊Dic71—44no—
243Dic71⋊C4—28no—
244Dic71⋊C4—44no—
245C22⋊Dic71—28no—
246C22⋊Dic71—28no—
247C22⋊Dic71—28no—
248C22⋊Dic71—44no—
249C22⋊Dic71—44no—
250(C2×D71)⋊C4—28no—
251(C2×D71)⋊C4—28no—
252(C2×D71)⋊C4—28no—
253(C2×D71)⋊C4—28no—
254(C2×D71)⋊C4—28no—
255(C2×D71)⋊C4—28no—
256(C2×D71)⋊C4—28no—
257(C2×D71)⋊C4—44no—
258C4×Dic71—28no—
259C24×C71—22no—
260C24×C71—22no—
261C24×C71—22no—
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×C71C2×D414yes—
272C24×C71C2×D414yes—
273C24×C71C2412yes—
274C24×C71C2412yes—
275C24×C71C2411yescharacteristic
276C2×D4×C71—28no—
277C2×D4×C71—28no—
278C2×D4×C71—44no—
279C2×D4×C71—416no—
280C22×C4×C71—22no—
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—22no—
290C22×C4×C71—22no—
291C22×C4×C71—22no—
292C22×C4×C71—22no—
293C22×C4×C71—22no—
294C22×C4×C71—28no—
295C22×C4×C71—44no—
296C22×C4×C71—416no—
297C22×C4×C71C2×D414yes—
298C22×C4×C71C2×D414yes—
299C22×C4×C71C2412yes—
300C22×C4×C71C2412yes—
301C22×C4×C71C2412yes—
302C22×C4×C71C2412yes—
303C22×C4×C71C2412yes—
304C4⋊C4×C71—28no—
305C4⋊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—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—44no—
335C23×C71C22×D414yes—
336C23×C71C22×D412yes—
337C23×C71C22×D414yes—
338C23×C71C22×D412yes—
339C23×C71C2×#4112yes—
340C23×C71C2×#4112yes—
341C23×C71C2×#4112yes—
342C23×C71H(5,𝔽2)12yes—
343C23×C71H(5,𝔽2)12yes—
344C23×C71C2511yescharacteristic
345C22×D71—28no—
346C22×D71—28no—
347C22×D71—28no—
348C22×D71—28no—
349C22×D71—28no—
350C22×D71—28no—
351C22×D71—22no—
352C22×D71—22no—
353C22×D71—22no—
354C22×D71—22no—
355C22×D71—232no—
356C22×D71—28no—
357C22×D71—28no—
358C22×D71—28no—
359C22×D71—22no—
360C22×D71—22no—
361C22×D71—22no—
362C22×D71—22no—
363C22×D71—22no—
364C22×D71—22no—
365C22×D71—416no—
366C22×D71—416no—
367C22×D71—416no—
368C22×D71—416no—
369C22×D71—4128no—
370C22×D71—416no—
371C22×D71—44no—
372C22×D71—44no—
373C22×D71—44no—
374C22×D71—44no—
375C22×D71—416no—
376C22×D71#123116yescomplemented
377C22×D71C22×D414yes—
378C22×D71C2×#4114yes—
379C22×D71C2×#4114yes—
380C22×D71C2×#4114yes—
381D4×C71—416no—
382C2×C4×C71—28no—
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—416no—
398C2×C4×C71—44no—
399C2×C4×C71—44no—
400C2×C4×C71—44no—
401C2×C4×C71C22×D414yes—
402C2×C4×C71C22×D414yes—
403C22⋊D71—232no—
404C22⋊D71—416no—
405C2×Dic71—28no—
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×Dic71C22×D414yes—
429C4×D71—416no—
430C4×D71—416no—
431C22×C71—24no—
432C22×C71—24no—
433C22×C71—24no—
434C22×C71—24no—
435C22×C71—24no—
436C22×C71—24no—
437C22×C71—42no—
438C22×C71—42no—
439C22×C71—416no—
440C22×C71—416no—
441C22×C71—42no—
442C22×C71—42no—
443C22×C71—42no—
444C22×C71—42no—
445C22×C71—42no—
446C22×C71—42no—
447C22×C71C2×#12314yes—
448C22×C71#52514yes—
449C22×C71#53814yes—
450C22×C71D4214yes—
451C22×C71#54614yes—
452C22×C71#54614yes—
453C22×C71#55114yes—
454C22×C71C23×D411yescharacteristic
455C22×C71C23×D411yescharacteristic
456C22×C71C22×#4111yescharacteristic
457C22×C71C22×#4111yescharacteristic
458C22×C71C22×#4111yescharacteristic
459C22×C71C2×H(5,𝔽2)11yescharacteristic
460C22×C71C2×H(5,𝔽2)11yescharacteristic
461C2×D71—24no—
462C2×D71—232no—
463C2×D71—24no—
464C2×D71—24no—
465C2×D71—24no—
466C2×D71—24no—
467C2×D71—24no—
468C2×D71—24no—
469C2×D71—24no—
470C2×D71—24no—
471C2×D71—464no—
472C2×D71—42no—
473C2×D71—416no—
474C2×D71—42no—
475C2×D71—42no—
476C2×D71—42no—
477C2×D71C2×#12318yescomplemented
478C4×C71—24no—
479C4×C71—24no—
480C4×C71—42no—
481C4×C71—42no—
482C4×C71—42no—
483Dic71—24no—
484Dic71—42no—
485Dic71—42no—
486Dic71—42no—
487Dic71—42no—
488Dic71—42no—
489C2×#2418—711nomaximal, Sylow
490C2×C71—44no—
491C2×C71—44no—
492C2×C71#241818yescomplemented
493C2×C71C22×#12311yescharacteristic
494C2×C71C2×#52511yescharacteristic
495C2×C71C2×#53811yescharacteristic
496C2×C71C2×D4211yescharacteristic
497C2×C71C2×#54611yescharacteristic
498C2×C71C2×#54611yescharacteristic
499C2×C71C2×#55111yescharacteristic
500D71—28no—
501D71—44no—
502C22×#123D7111yescharacteristic, complemented
503C22×#120—711no—
504C22×C4×D4—711no—
505C23×C22⋊C4—711no—
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
519C26—711no—
520C23×D4—711no—
521C23×D4—711no—
522C23×D4C2×D7111yescharacteristic
523C24×C4—711no—
524C24×C4—711no—
525C24×C4C2×D7111yescharacteristic, complemented
526C2×#123—28no—
527C2×#123C2×D7118yescomplemented
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⋊C4C2×D7111yescharacteristic, complemented
536C22×C4⋊C4C2×D7111yescharacteristic, complemented
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—711no—
548C22×C22⋊C4—711no—
549C22×C22⋊C4—711no—
550C22×C22⋊C4—718no—
551C22×C22⋊C4—1428no—
552C22×C22⋊C4C2×D7111yescharacteristic
553C22×C22⋊C4C2×D7111yescharacteristic
554C22×C22⋊C4C2×D7111yescharacteristic, complemented
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—2842no—
574C25—2842no—
575C25—714no—
576C25—711no—
577C25—711no—
578C25—1424no—
579C25—1424no—
580C25—1424no—
581C25—1424no—
582C25—1424no—
583C25C22×D7111yescharacteristic
584C25C22×D7111yescharacteristic
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—2842no—
589C22×D4—714no—
590C22×D4—718no—
591C22×D4—714no—
592C22×D4—1424no—
593C22×D4—1424no—
594C22×D4—1424no—
595C22×D4—1424no—
596C22×D4C22×D7114yes—
597C23×C4—24no—
598C23×C4—24no—
599C23×C4—42no—
600C23×C4—2842no—
601C23×C4—2842no—
602C23×C4—714no—
603C23×C4—714no—
604C23×C4—711no—
605C23×C4—711no—
606C23×C4—711no—
607C23×C4—711no—
608C23×C4—711no—
609C23×C4—711no—
610C23×C4—1424no—
611C23×C4—1424no—
612C23×C4—1424no—
613C23×C4—1424no—
614C23×C4C22×D7111yescharacteristic
615C23×C4C22×D7111yescharacteristic
616C23×C4C22×D7111yescharacteristic
617C23×C4C22×D7111yescharacteristic
618C23×C4C22×D7111yescharacteristic
619C23×C4C22×D7114yescomplemented
620#123—232no—
621#120—14232no—
622C4×D4—14232no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—2842no—
626C2×C4⋊C4—2842no—
627C2×C4⋊C4—714no—
628C2×C4⋊C4—714no—
629C2×C4⋊C4—714no—
630C2×C4⋊C4—1424no—
631C2×C4⋊C4C22×D7114yescomplemented
632C2×C4⋊C4C22×D7114yescomplemented
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—2842no—
636C2×C22⋊C4—2842no—
637C2×C22⋊C4—2842no—
638C2×C22⋊C4—714no—
639C2×C22⋊C4—714no—
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—1424no—
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⋊C4—14232no—
662C2×C22⋊C4C22⋊D7118yescomplemented
663C2×C22⋊C4C22×D7114yes—
664C2×C22⋊C4C22×D7114yes—
665C2×C22⋊C4C22×D7114yescomplemented
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—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—28416no—
687C24—28416no—
688C24—2844no—
689C24—2844no—
690C24—28416no—
691C24—28416no—
692C24—28416no—
693C24—28416no—
694C24—714no—
695C24—714no—
696C24—714no—
697C24—712no—
698C24—714no—
699C24—712no—
700C24—1428no—
701C24—1428no—
702C24—1428no—
703C24—1428no—
704C24—14232no—
705C24—1422no—
706C24—1428no—
707C24—1422no—
708C24—1422no—
709C24—1422no—
710C24—1422no—
711C24—1422no—
712C24—1422no—
713C24—1422no—
714C24—1422no—
715C24—1422no—
716C24D4×D7114yes—
717C24C2×C22⋊D7114yes—
718C24C23×D7112yes—
719C24C23×D7112yes—
720C24C23×D7111yescharacteristic
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—44no—
724C2×D4—416no—
725C2×D4—28416no—
726C2×D4—2844no—
727C2×D4—7116no—
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—22no—
739C22×C4—28no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—28no—
748C22×C4—44no—
749C22×C4—416no—
750C22×C4—28416no—
751C22×C4—28416no—
752C22×C4—2844no—
753C22×C4—2844no—
754C22×C4—714no—
755C22×C4—712no—
756C22×C4—712no—
757C22×C4—712no—
758C22×C4—712no—
759C22×C4—712no—
760C22×C4—712no—
761C22×C4—1428no—
762C22×C4—1428no—
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—1428no—
779C22×C4—1428no—
780C22×C4—1422no—
781C22×C4—1422no—
782C22×C4C2×C22⋊D7114yes—
783C22×C4C2×C22⋊D7114yes—
784C22×C4C23×D7112yes—
785C22×C4C23×D7112yes—
786C22×C4C23×D7112yes—
787C22×C4C23×D7112yes—
788C22×C4C23×D7112yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—2844no—
792C4⋊C4—2844no—
793C4⋊C4—1428no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—2844no—
797C22⋊C4—2844no—
798C22⋊C4—2844no—
799C22⋊C4—1428no—
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—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—28no—
824C23—28no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—28no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—28416no—
838C23—28416no—
839C23—28416no—
840C23—284128no—
841C23—28416no—
842C23—28416no—
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—1428no—
863C23—1422no—
864C23—1422no—
865C23—1422no—
866C23—1422no—
867C23—1428no—
868C23—1428no—
869C23—1428no—
870C23—1428no—
871C23—1428no—
872C23—1428no—
873C23C2×D4×D7114yes—
874C23C2×D4×D7112yes—
875C23C22×C22⋊D7114yes—
876C23C22×C22⋊D7112yes—
877C23#41×D7112yes—
878C23#41×D7112yes—
879C23#41×D7112yes—
880C23#1455617312yes—
881C23#1455617412yes—
882C23C24×D7111yescharacteristic
883D4—416no—
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—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—416no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—28416no—
906C2×C4—28416no—
907C2×C4—2844no—
908C2×C4—2844no—
909C2×C4—2844no—
910C2×C4—2844no—
911C2×C4—2844no—
912C2×C4—714no—
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—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—416no—
940C22—416no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—28464no—
950C22—2842no—
951C22—28416no—
952C22—2842no—
953C22—2842no—
954C22—2842no—
955C22—718no—
956C22—1424no—
957C22—1424no—
958C22—1424no—
959C22—1424no—
960C22—14232no—
961C22—1424no—
962C22—1424no—
963C22—1424no—
964C22—1424no—
965C22—1424no—
966C22#123×D7114yes—
967C22#1798650614yes—
968C22#1798658514yes—
969C22D4×C22⋊D7114yes—
970C22#1798663714yes—
971C22#1798664114yes—
972C22#1798667714yes—
973C22C22×D4×D7111yescharacteristic
974C22C23×C22⋊D7111yescharacteristic
975C22C2×#41×D7111yescharacteristic
976C22C2×#41×D7111yescharacteristic
977C22C2×#41×D7111yescharacteristic
978C22C2×#1455617311yescharacteristic
979C22C2×#1455617411yescharacteristic
980C4—24no—
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—2842no—
986C4—2842no—
987C4—2842no—
988C4—2842no—
989C4—2842no—
990C4—1424no—
991C2—44no—
992C2—44no—
993C2—2844no—
994C2—1428no—
995C2#2259179918yesdirect product factor
996C2C2×#123×D7111yescharacteristic
997C2C2×#1798650611yescharacteristic
998C2C2×#1798658511yescharacteristic
999C2C2×D4×C22⋊D7111yescharacteristic
1000C2C2×#1798663711yescharacteristic
1001C2C2×#1798664111yescharacteristic
1002C2C2×#1798667711yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×#123×C71C2
socleC24×C71C24
prime radicalC22×#14556096C2
hypercenterC22×#123D71
hypocenterC71C2×#2418
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D71C2semidirect
3. C22×C22⋊C4×D71C2semidirect
4. #22591799C2direct (N × H)
5. C2×#17985934C2semidirect
6. C2×#17985927C2semidirect
7. C2×#17985915C2semidirect
8. C2×#17985913C2semidirect
9. C2×#17985892C2semidirect
10. C2×#17985889C2semidirect
11. C2×#17985878C2semidirect
12. C2×#17985875C2semidirect
13. C2×#17985870C2semidirect
14. C2×#17985856C2semidirect
15. C2×#17985854C2semidirect
16. C22×#123×C71C2semidirect
25. C2×C4×C22⋊D71C22semidirect
26. C22×C4⋊Dic71C22semidirect
27. C22×Dic71⋊C4C22semidirect
28. C22×Dic71⋊C4C22semidirect
32. C22×C22⋊Dic71C22semidirect
33. C22×C22⋊Dic71C22semidirect
43. C2×C22⋊C4×D71C22semidirect
44. C22×C4×Dic71C22semidirect
45. #17985934C22semidirect
46. #17985927C22semidirect
47. #17985915C22semidirect
48. #17985913C22semidirect
49. #17985892C22semidirect
50. #17985889C22semidirect
51. #17985878C22semidirect
52. #17985875C22semidirect
53. #17985870C22semidirect
54. #17985856C22semidirect
55. #17985854C22semidirect
56. C2×C71⋊#95C22semidirect
57. C2×C71⋊#95C22semidirect
58. C2×C71⋊#95C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
61. C2×C71⋊#95C22semidirect
63. C24×C4×C71C22semidirect
65. C2×#123×C71C22semidirect
66. C22×C4⋊C4×C71C22semidirect
67. C22×C4⋊C4×C71C22semidirect
70. C22×C22⋊C4×C71C22semidirect
106. C2×C4⋊Dic71C23semidirect
109. C2×Dic71⋊C4C23semidirect
110. C2×Dic71⋊C4C23semidirect
119. C2×C22⋊Dic71C23semidirect
120. C2×C22⋊Dic71C23semidirect
139. C2×C4×Dic71C23semidirect
140. C71⋊#95C23semidirect
141. C71⋊#95C23semidirect
142. C71⋊#95C23semidirect
143. C71⋊#95C23semidirect
144. C71⋊#95C23semidirect
145. C71⋊#95C23semidirect
160. C23×C4×C71C23semidirect
164. C2×C4⋊C4×C71C23semidirect
165. C2×C4⋊C4×C71C23semidirect
168. C2×C22⋊C4×C71D4semidirect
171. C2×C22⋊C4×C71C23semidirect
308. C22⋊C4×C71C2×D4semidirect
376. C22×D71#123semidirect
477. C2×D71C2×#123semidirect
492. C2×C71#2418semidirect
502. C22×#123D71semidirect
518. C71C2×#2418semidirect
525. C24×C4C2×D71semidirect
527. C2×#123C2×D71semidirect
535. C22×C4⋊C4C2×D71semidirect
536. C22×C4⋊C4C2×D71semidirect
554. C22×C22⋊C4C2×D71semidirect
619. C23×C4C22×D71semidirect
631. C2×C4⋊C4C22×D71semidirect
632. C2×C4⋊C4C22×D71semidirect
662. C2×C22⋊C4C22⋊D71semidirect
665. C2×C22⋊C4C22×D71semidirect
809. C22⋊C4C2×C22⋊D71semidirect
995. C2#22591799direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145560962
C22×C4×C22⋊D712
C22×C22⋊C4×D712
#225917992
C2×#179859342
C2×#179859272
C2×#179859152
C2×#179859132
C2×#179858922
C2×#179858892
C2×#179858782
C2×#179858752
C2×#179858702
C2×#179858562
C2×#179858542
C22×#123×C712
C2×#241871