Finite Group Databasebeta

← C2×#22591359 #32156984

Subgroups — C2×#22591359 #32156984

Order 18176.

4782 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556101C211yesmaximal, characteristic
2C22×#14556090C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
6#22591359C2116yesmaximal, direct product factor
7C2×#17985899C211yesmaximal, characteristic, complemented
8C2×#17985894C211yesmaximal, characteristic, complemented
9C2×#17985892C211yesmaximal, characteristic, complemented
10C2×#17985889C211yesmaximal, characteristic, complemented
11C2×#17985877C211yesmaximal, characteristic, complemented
12C2×#17985875C211yesmaximal, characteristic, complemented
13C2×#17985873C211yesmaximal, characteristic, complemented
14C2×#17985850C211yesmaximal, characteristic, complemented
15C2×#17985846C211yesmaximal, characteristic, complemented
16C2×#385×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C23×C4×D71C2211yescharacteristic
24C2×#14556101C4116yescomplemented
25C2×#14556101C2218yes—
26C2×#14556090—28no—
27C2×#14556090C2218yescomplemented
28C2×C4×C22⋊D71—28no—
29C2×C4×C22⋊D71—28no—
30C2×C4×C22⋊D71C2218yescomplemented
31C2×C4×C22⋊D71C2218yescomplemented
32C22×C4⋊Dic71C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×Dic71⋊C4C2211yescharacteristic
35C22×Dic71⋊C4C2211yescharacteristic
36C22×Dic71⋊C4C2211yescharacteristic
37C2×C4⋊C4×D71—28no—
38C2×C4⋊C4×D71C2218yescomplemented
39C22×C22⋊Dic71C2211yescharacteristic
40C22×C22⋊Dic71C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×(C2×D71)⋊C4C2211yescharacteristic
43C22×(C2×D71)⋊C4C2211yescharacteristic
44C22×(C2×D71)⋊C4C2211yescharacteristic
45C22×(C2×D71)⋊C4C2211yescharacteristic
46C22×(C2×D71)⋊C4C2211yescharacteristic
47C22×C4×Dic71C2211yescharacteristic
48C22×C4×Dic71C2211yescharacteristic
49C22×C4×Dic71C2211yescharacteristic
50C22×C4×Dic71C2211yescharacteristic
51#17985899C2218yescomplemented
52#17985894C2218yescomplemented
53#17985892C2218yescomplemented
54#17985889C2218yescomplemented
55#17985877C2218yescomplemented
56#17985875C2218yescomplemented
57#17985873C2218yescomplemented
58#17985850C2218yescomplemented
59#17985846C2218yescomplemented
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C2×C71⋊#95C2211yescharacteristic
63C2×C71⋊#95C2211yescharacteristic
64C24×C4×C71C2211yescharacteristic
65C22×C4⋊C4×C71C2211yescharacteristic
66C22×C4⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68C22×C22⋊C4×C71C2211yescharacteristic
69#385×C71C2218yescomplemented
70C2×#95×C71C2211yescharacteristic
71C2×#95×C71C2211yescharacteristic
72C24×D71C2311yescharacteristic
73C24×D71C2311yescharacteristic
74C22×D284—24no—
75C22×D284—24no—
76C22×D284C2×C418yescomplemented
77C22×D284C2314yes—
78C22×C22⋊D71—24no—
79C22×C22⋊D71—24no—
80C22×C22⋊D71—24no—
81C22×C22⋊D71—24no—
82C22×C22⋊D71C2×C418yescomplemented
83C22×C22⋊D71C2×C418yescomplemented
84C22×C22⋊D71C2314yes—
85C22×C22⋊D71C2314yes—
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C23×Dic71C2311yescharacteristic
92C22×C4×D71—24no—
93C22×C4×D71—24no—
94C22×C4×D71—24no—
95C22×C4×D71—24no—
96C22×C4×D71—24no—
97C22×C4×D71—24no—
98C22×C4×D71—24no—
99C22×C4×D71—24no—
100C22×C4×D71—42no—
101C22×C4×D71—42no—
102C22×C4×D71—42no—
103C22×C4×D71C2×C418yescomplemented
104C22×C4×D71C2314yes—
105C22×C4×D71C2314yes—
106C22×C4×D71C2314yes—
107C22×C4×D71C2314yes—
108#14556101C2×C4164yescomplemented
109#14556090—232no—
110C4×C22⋊D71—232no—
111C4×C22⋊D71—232no—
112C2×C4⋊Dic71—24no—
113C2×C4⋊Dic71C2314yes—
114C2×Dic71⋊C4—24no—
115C2×Dic71⋊C4—24no—
116C2×Dic71⋊C4C2×C418yescomplemented
117C2×Dic71⋊C4D418yescomplemented
118C2×Dic71⋊C4C2314yes—
119C2×Dic71⋊C4C2314yes—
120C2×Dic71⋊C4C2314yes—
121C2×Dic71⋊C4C2314yes—
122C4⋊C4×D71—232no—
123C2×C22⋊Dic71—24no—
124C2×C22⋊Dic71—24no—
125C2×C22⋊Dic71C2314yes—
126C2×C22⋊Dic71C2314yes—
127C2×(C2×D71)⋊C4—24no—
128C2×(C2×D71)⋊C4—24no—
129C2×(C2×D71)⋊C4—24no—
130C2×(C2×D71)⋊C4—42no—
131C2×(C2×D71)⋊C4C2×C418yescomplemented
132C2×(C2×D71)⋊C4D418yescomplemented
133C2×(C2×D71)⋊C4C2314yes—
134C2×(C2×D71)⋊C4C2314yes—
135C2×(C2×D71)⋊C4C2314yes—
136C2×(C2×D71)⋊C4C2314yes—
137C2×(C2×D71)⋊C4C2314yes—
138C2×(C2×D71)⋊C4C2314yes—
139C2×C4×Dic71—24no—
140C2×C4×Dic71—24no—
141C2×C4×Dic71—24no—
142C2×C4×Dic71—24no—
143C2×C4×Dic71C2314yes—
144C2×C4×Dic71C2314yes—
145C2×C4×Dic71C2314yes—
146C2×C4×Dic71C2314yes—
147C71⋊#95C2314yes—
148C71⋊#95C2314yes—
149C71⋊#95C2314yes—
150C71⋊#95C2314yes—
151C25×C71C2311yescharacteristic
152C23×C4×C71—24no—
153C23×C4×C71—24no—
154C23×C4×C71—42no—
155C23×C4×C71C2311yescharacteristic
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2314yes—
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C23×C4×C71C2311yescharacteristic
162C2×C4⋊C4×C71—24no—
163C2×C4⋊C4×C71—24no—
164C2×C4⋊C4×C71C2314yes—
165C2×C4⋊C4×C71C2314yes—
166C2×C22⋊C4×C71—42no—
167C2×C22⋊C4×C71C2×C418yescomplemented
168C2×C22⋊C4×C71C2314yes—
169C2×C22⋊C4×C71C2314yes—
170#95×C71C2314yes—
171#95×C71C2314yes—
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—22no—
181C23×D71—22no—
182C23×D71C22×C414yes—
183C23×D71C22×C414yes—
184C23×D71C2×D414yes—
185C23×D71#4114yes—
186C23×D71C2412yes—
187C23×D71C2412yes—
188C2×D284—232no—
189C2×D284—28no—
190C2×D284—28no—
191C2×D284C22×C4116yescomplemented
192C2×C22⋊D71—232no—
193C2×C22⋊D71—28no—
194C2×C22⋊D71—28no—
195C2×C22⋊D71—232no—
196C2×C22⋊D71—28no—
197C2×C22⋊D71—28no—
198C2×C22⋊D71C22×C4116yescomplemented
199C2×C22⋊D71C22×C4116yescomplemented
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×Dic71C22×C414yes—
213C22×Dic71C22×C414yes—
214C22×Dic71C2×D414yes—
215C22×Dic71C2×D414yes—
216C22×Dic71C2×D414yes—
217C22×Dic71#4114yes—
218C22×Dic71C2412yes—
219C22×Dic71C2412yes—
220C22×Dic71C2412yes—
221C22×Dic71C2412yes—
222C22×Dic71C2412yes—
223C22×Dic71C2412yes—
224C2×C4×D71—232no—
225C2×C4×D71—28no—
226C2×C4×D71—28no—
227C2×C4×D71—28no—
228C2×C4×D71—28no—
229C2×C4×D71—28no—
230C2×C4×D71—28no—
231C2×C4×D71—28no—
232C2×C4×D71—28no—
233C2×C4×D71—44no—
234C2×C4×D71—44no—
235C2×C4×D71—44no—
236C2×C4×D71—416no—
237C2×C4×D71—416no—
238C2×C4×D71—416no—
239C2×C4×D71C22×C4116yescomplemented
240C4⋊Dic71—28no—
241Dic71⋊C4—28no—
242Dic71⋊C4—28no—
243Dic71⋊C4C22×C4116yescomplemented
244Dic71⋊C4C2×D4116yescomplemented
245C22⋊Dic71—28no—
246C22⋊Dic71—28no—
247(C2×D71)⋊C4—28no—
248(C2×D71)⋊C4—28no—
249(C2×D71)⋊C4—28no—
250(C2×D71)⋊C4—44no—
251(C2×D71)⋊C4C22×C4116yescomplemented
252(C2×D71)⋊C4C2×D4116yescomplemented
253C4×Dic71—28no—
254C4×Dic71—28no—
255C4×Dic71—28no—
256C4×Dic71—28no—
257C24×C71—22no—
258C24×C71—22no—
259C24×C71—22no—
260C24×C71—22no—
261C24×C71—22no—
262C24×C71—22no—
263C24×C71C22×C414yes—
264C24×C71C2412yes—
265C24×C71C2411yescharacteristic
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×C71—28no—
281C22×C4×C71—28no—
282C22×C4×C71—44no—
283C22×C4×C71—416no—
284C22×C4×C71C22×C414yes—
285C22×C4×C71C22×C414yes—
286C22×C4×C71C2×D414yes—
287C22×C4×C71C2×D414yes—
288C22×C4×C71C2412yes—
289C22×C4×C71C2412yes—
290C22×C4×C71C2412yes—
291C22×C4×C71C2412yes—
292C22×C4×C71C2412yes—
293C22×C4×C71C2412yes—
294C4⋊C4×C71—28no—
295C4⋊C4×C71—28no—
296C22⋊C4×C71—44no—
297C22⋊C4×C71C22×C4116yescomplemented
298C23×C71—28no—
299C23×C71—28no—
300C23×C71—28no—
301C23×C71—22no—
302C23×C71—22no—
303C23×C71—22no—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71—22no—
307C23×C71—44no—
308C23×C71—44no—
309C23×C71—44no—
310C23×C71—44no—
311C23×C71C23×C414yes—
312C23×C71C23×C412yes—
313C23×C71C22×D412yes—
314C23×C71C22×D412yes—
315C23×C71C2×#4112yes—
316C23×C71C2×#4112yes—
317C23×C71H(5,𝔽2)12yes—
318C23×C712−1+412yes—
319C23×C71C2511yescharacteristic
320C22×D71—28no—
321C22×D71—28no—
322C22×D71—28no—
323C22×D71—28no—
324C22×D71—28no—
325C22×D71—28no—
326C22×D71—22no—
327C22×D71—22no—
328C22×D71—22no—
329C22×D71—22no—
330C22×D71—28no—
331C22×D71—28no—
332C22×D71—28no—
333C22×D71—22no—
334C22×D71—22no—
335C22×D71—22no—
336C22×D71—22no—
337C22×D71—22no—
338C22×D71—22no—
339C22×D71—44no—
340C22×D71—44no—
341C22×D71—44no—
342C22×D71—44no—
343C22×D71C4×D4116yescomplemented
344C22×D71C23×C414yes—
345C22×D71C23×C414yes—
346C22×D71C22×D414yes—
347C22×D71C2×#4114yes—
348C2×C4×C71—28no—
349C2×C4×C71—28no—
350C2×C4×C71—28no—
351C2×C4×C71—28no—
352C2×C4×C71—22no—
353C2×C4×C71—22no—
354C2×C4×C71—22no—
355C2×C4×C71—22no—
356C2×C4×C71—22no—
357C2×C4×C71—22no—
358C2×C4×C71—22no—
359C2×C4×C71—22no—
360C2×C4×C71—22no—
361C2×C4×C71—22no—
362C2×C4×C71—22no—
363C2×C4×C71—22no—
364C2×C4×C71—22no—
365C2×C4×C71—22no—
366C2×C4×C71—416no—
367C2×C4×C71—44no—
368C2×C4×C71—44no—
369C2×C4×C71C23×C414yes—
370C2×C4×C71C23×C414yes—
371C2×C4×C71C22×D414yes—
372C2×C4×C71C22×D414yes—
373C22⋊D71—232no—
374C22⋊D71—232no—
375C2×Dic71—28no—
376C2×Dic71—28no—
377C2×Dic71—28no—
378C2×Dic71—22no—
379C2×Dic71—22no—
380C2×Dic71—22no—
381C2×Dic71—22no—
382C2×Dic71—22no—
383C2×Dic71—22no—
384C2×Dic71—22no—
385C2×Dic71—22no—
386C2×Dic71—22no—
387C2×Dic71—22no—
388C2×Dic71—22no—
389C2×Dic71—22no—
390C2×Dic71—44no—
391C2×Dic71—44no—
392C2×Dic71C4×D4116yescomplemented
393C2×Dic71C23×C414yes—
394C2×Dic71C23×C414yes—
395C2×Dic71C22×D414yes—
396C2×Dic71C22×D414yes—
397C2×Dic71C22×D414yes—
398C2×Dic71C2×#4114yes—
399D284—232no—
400C4×D71—232no—
401C4×D71—416no—
402C4×D71—416no—
403C4×D71—416no—
404C22×C71—24no—
405C22×C71—24no—
406C22×C71—24no—
407C22×C71—416no—
408C22×C71—42no—
409C22×C71—42no—
410C22×C71—42no—
411C22×C71—42no—
412C22×C71C2×C4×D414yes—
413C22×C71C2×C4×D414yes—
414C22×C71#52014yes—
415C22×C71D4214yes—
416C22×C71#54714yes—
417C22×C71#54814yes—
418C22×C71#55314yes—
419C22×C71C24×C411yescharacteristic
420C22×C71C23×D411yescharacteristic
421C22×C71C23×D411yescharacteristic
422C22×C71C22×#4111yescharacteristic
423C22×C71C22×#4111yescharacteristic
424C22×C71C2×H(5,𝔽2)11yescharacteristic
425C22×C71C2×2−1+411yescharacteristic
426C2×D71—232no—
427C2×D71—24no—
428C2×D71—24no—
429C2×D71—24no—
430C2×D71—24no—
431C2×D71—24no—
432C2×D71—24no—
433C2×D71—24no—
434C2×D71—24no—
435C2×D71—24no—
436C2×D71—416no—
437C2×D71—42no—
438C2×D71—42no—
439C2×D71—42no—
440C2×D71—42no—
441C2×D71C2×C4×D418yescomplemented
442C4×C71—24no—
443C4×C71—24no—
444C4×C71—24no—
445C4×C71—24no—
446C4×C71—42no—
447C4×C71—42no—
448Dic71—24no—
449Dic71—24no—
450Dic71—24no—
451Dic71—42no—
452Dic71—42no—
453Dic71C2×C4×D418yescomplemented
454C2×#2361—711nomaximal, Sylow
455C2×C71—44no—
456C2×C71#236118yescomplemented
457C2×C71C22×C4×D411yescharacteristic
458C2×C71C22×C4×D411yescharacteristic
459C2×C71C2×#52011yescharacteristic
460C2×C71C2×D4211yescharacteristic
461C2×C71C2×#54711yescharacteristic
462C2×C71C2×#54811yescharacteristic
463C2×C71C2×#55311yescharacteristic
464D71—28no—
465D71—44no—
466C22×#121—711no—
467C22×C4×D4—711no—
468C22×C4×D4—711no—
469C22×C4×D4—711no—
470C23×C4⋊C4—711no—
471#2361—7116no—
472C2×#390—711no—
473C2×#389—711no—
474C2×#388—711no—
475C2×#388—711no—
476C2×#386—711no—
477C2×#386—711no—
478C2×#385—711no—
479C2×#385D7111yescharacteristic, complemented
480C2×C4×C4⋊C4—711no—
481C2×C4×C22⋊C4—711no—
482C71C2×#236111yescharacteristic, complemented, Sylow
483C23×D4—711no—
484C23×D4—711no—
485C23×D4—711no—
486C24×C4—711no—
487C24×C4—711no—
488C24×C4—711no—
489C24×C4—711no—
490C24×C4C2×D7111yescharacteristic
491C2×#121—7116no—
492C2×#121—718no—
493C2×C4×D4—718no—
494C2×C4×D4—718no—
495C2×C4×D4—718no—
496C2×C4×D4—1428no—
497C2×C4×D4—1428no—
498C2×C4×D4—1428no—
499C22×C4⋊C4—711no—
500C22×C4⋊C4—711no—
501C22×C4⋊C4—711no—
502C22×C4⋊C4—711no—
503C22×C4⋊C4—711no—
504C22×C4⋊C4—718no—
505C22×C4⋊C4—1428no—
506C22×C4⋊C4C2×D7111yescharacteristic
507C22×C4⋊C4C2×D7111yescharacteristic
508C22×C22⋊C4—711no—
509C22×C22⋊C4—711no—
510C22×C22⋊C4—711no—
511C22×C22⋊C4—711no—
512C22×C22⋊C4—711no—
513C22×C22⋊C4—711no—
514C22×C22⋊C4—711no—
515C22×C22⋊C4—711no—
516C22×C22⋊C4C2×D7111yescharacteristic
517C22×C22⋊C4C2×D7111yescharacteristic
518C22×C42—711no—
519C22×C42—711no—
520C22×C42—711no—
521C22×C42—711no—
522#390—718no—
523#389—718no—
524#388—718no—
525#388—718no—
526#386—718no—
527#386—718no—
528#385—718no—
529#385C2×D7118yescomplemented
530C4×C4⋊C4—718no—
531C4×C22⋊C4—718no—
532C2×#95—711no—
533C2×#95—711no—
534C2×#95—711no—
535C2×#95—711no—
536C2×#95C2×D7111yescharacteristic
537C2×#95C2×D7111yescharacteristic
538C25—711no—
539C25—711no—
540C25C22×D7111yescharacteristic
541C22×D4—718no—
542C22×D4—718no—
543C22×D4—714no—
544C22×D4—714no—
545C22×D4—718no—
546C22×D4—714no—
547C22×D4—1424no—
548C22×D4—1424no—
549C22×D4—1424no—
550C22×D4—1424no—
551C22×D4—1424no—
552C22×D4—1424no—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—42no—
556C23×C4—2842no—
557C23×C4—2842no—
558C23×C4—2842no—
559C23×C4—714no—
560C23×C4—714no—
561C23×C4—714no—
562C23×C4—711no—
563C23×C4—711no—
564C23×C4—711no—
565C23×C4—711no—
566C23×C4—718no—
567C23×C4—714no—
568C23×C4—711no—
569C23×C4—711no—
570C23×C4—1424no—
571C23×C4—1424no—
572C23×C4—1424no—
573C23×C4—1424no—
574C23×C4—1424no—
575C23×C4—1424no—
576C23×C4—1424no—
577C23×C4—1424no—
578C23×C4C22×D7111yescharacteristic
579C23×C4C22×D7111yescharacteristic
580C23×C4C22×D7114yes—
581C23×C4C22×D7111yescharacteristic
582C23×C4C22×D7111yescharacteristic
583C23×C4C22×D7111yescharacteristic
584C23×C4C22×D7111yescharacteristic
585#121—7164no—
586C4×D4—14232no—
587C4×D4—14232no—
588C4×D4—14232no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—718no—
592C2×C4⋊C4—718no—
593C2×C4⋊C4—714no—
594C2×C4⋊C4—714no—
595C2×C4⋊C4—714no—
596C2×C4⋊C4—714no—
597C2×C4⋊C4—714no—
598C2×C4⋊C4—14232no—
599C2×C4⋊C4—1424no—
600C2×C4⋊C4—1424no—
601C2×C4⋊C4—1424no—
602C2×C4⋊C4C22×D7114yes—
603C2×C4⋊C4C22×D7114yes—
604C2×C22⋊C4—42no—
605C2×C22⋊C4—2842no—
606C2×C22⋊C4—714no—
607C2×C22⋊C4—718no—
608C2×C22⋊C4—718no—
609C2×C22⋊C4—714no—
610C2×C22⋊C4—714no—
611C2×C22⋊C4—714no—
612C2×C22⋊C4—714no—
613C2×C22⋊C4—714no—
614C2×C22⋊C4—714no—
615C2×C22⋊C4—714no—
616C2×C22⋊C4—1424no—
617C2×C22⋊C4—1424no—
618C2×C22⋊C4—1424no—
619C2×C22⋊C4—1424no—
620C2×C22⋊C4—1424no—
621C2×C22⋊C4C4×D7118yescomplemented
622C2×C22⋊C4C22×D7114yes—
623C2×C22⋊C4C22×D7114yes—
624C2×C42—714no—
625C2×C42—714no—
626C2×C42—714no—
627C2×C42—714no—
628C2×C42—1424no—
629C2×C42—1424no—
630C2×C42—1424no—
631C2×C42—1424no—
632#95—714no—
633#95—714no—
634#95—714no—
635#95—714no—
636#95C22×D7114yes—
637#95C22×D7114yes—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—714no—
645C24—714no—
646C24—714no—
647C24—712no—
648C24—714no—
649C24—712no—
650C24—1422no—
651C24—1422no—
652C24—1422no—
653C24—1422no—
654C24—1422no—
655C24—1422no—
656C24—1422no—
657C24—1422no—
658C24—1422no—
659C24—1422no—
660C24C2×C4×D7114yes—
661C24C23×D7112yes—
662C24C23×D7111yescharacteristic
663C2×D4—7116no—
664C2×D4—7116no—
665C2×D4—7116no—
666C2×D4—1428no—
667C2×D4—1428no—
668C2×D4—14232no—
669C2×D4—1428no—
670C2×D4—1428no—
671C2×D4—14232no—
672C2×D4—1428no—
673C2×D4—1428no—
674C2×D4—14232no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—44no—
692C22×C4—416no—
693C22×C4—28416no—
694C22×C4—28416no—
695C22×C4—2844no—
696C22×C4—2844no—
697C22×C4—2844no—
698C22×C4—28416no—
699C22×C4—714no—
700C22×C4—714no—
701C22×C4—714no—
702C22×C4—712no—
703C22×C4—714no—
704C22×C4—714no—
705C22×C4—714no—
706C22×C4—712no—
707C22×C4—712no—
708C22×C4—712no—
709C22×C4—7116no—
710C22×C4—712no—
711C22×C4—712no—
712C22×C4—1428no—
713C22×C4—1428no—
714C22×C4—1428no—
715C22×C4—1428no—
716C22×C4—1428no—
717C22×C4—1428no—
718C22×C4—14232no—
719C22×C4—1422no—
720C22×C4—1422no—
721C22×C4—1422no—
722C22×C4—1422no—
723C22×C4—1422no—
724C22×C4—1422no—
725C22×C4—1428no—
726C22×C4—1428no—
727C22×C4—1422no—
728C22×C4—1422no—
729C22×C4—1422no—
730C22×C4—1422no—
731C22×C4—1422no—
732C22×C4—1422no—
733C22×C4C2×C4×D7114yes—
734C22×C4C2×C4×D7114yes—
735C22×C4D4×D7114yes—
736C22×C4D4×D7114yes—
737C22×C4C23×D7112yes—
738C22×C4C23×D7112yes—
739C22×C4C23×D7112yes—
740C22×C4C23×D7112yes—
741C22×C4C23×D7112yes—
742C22×C4C23×D7112yes—
743C4⋊C4—28no—
744C4⋊C4—28no—
745C4⋊C4—7116no—
746C4⋊C4—7116no—
747C4⋊C4—1428no—
748C4⋊C4—1428no—
749C4⋊C4—1428no—
750C22⋊C4—44no—
751C22⋊C4—2844no—
752C22⋊C4—7116no—
753C22⋊C4—7116no—
754C22⋊C4—1428no—
755C22⋊C4—1428no—
756C22⋊C4—1428no—
757C22⋊C4—1428no—
758C22⋊C4—1428no—
759C22⋊C4C2×C4×D71116yescomplemented
760C42—1428no—
761C42—1428no—
762C42—1428no—
763C42—1428no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—28no—
771C23—28no—
772C23—28no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—2844no—
778C23—2844no—
779C23—2844no—
780C23—2844no—
781C23—714no—
782C23—714no—
783C23—714no—
784C23—7116no—
785C23—714no—
786C23—1422no—
787C23—1422no—
788C23—1422no—
789C23—1422no—
790C23—1422no—
791C23—1422no—
792C23—1428no—
793C23—1428no—
794C23—1428no—
795C23—1422no—
796C23—1422no—
797C23—1422no—
798C23—1422no—
799C23—1428no—
800C23—1428no—
801C23—1428no—
802C23—1428no—
803C23—1428no—
804C23—1428no—
805C23C22×C4×D7114yes—
806C23C22×C4×D7112yes—
807C23C2×D4×D7112yes—
808C23C2×D4×D7112yes—
809C23#41×D7112yes—
810C23#41×D7112yes—
811C23#1455617312yes—
812C23#1455617612yes—
813C23C24×D7111yescharacteristic
814D4—14232no—
815D4—14232no—
816D4—14232no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—28no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—416no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—28416no—
839C2×C4—28416no—
840C2×C4—28416no—
841C2×C4—2844no—
842C2×C4—2844no—
843C2×C4—714no—
844C2×C4—714no—
845C2×C4—714no—
846C2×C4—7116no—
847C2×C4—714no—
848C2×C4—714no—
849C2×C4—714no—
850C2×C4—14232no—
851C2×C4—1422no—
852C2×C4—1422no—
853C2×C4—1422no—
854C2×C4—1422no—
855C2×C4—1422no—
856C2×C4—1422no—
857C2×C4—1422no—
858C2×C4—1422no—
859C2×C4—1422no—
860C2×C4—1422no—
861C2×C4—1422no—
862C2×C4—1422no—
863C2×C4—1428no—
864C2×C4—1428no—
865C2×C4—1428no—
866C2×C4C22×C4×D7114yes—
867C2×C4C22×C4×D7114yes—
868C2×C4C2×D4×D7114yes—
869C2×C4C2×D4×D7114yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—416no—
877C22—42no—
878C22—2842no—
879C22—2842no—
880C22—2842no—
881C22—28416no—
882C22—2842no—
883C22—718no—
884C22—1424no—
885C22—1424no—
886C22—1424no—
887C22—1424no—
888C22—1424no—
889C22—1424no—
890C22—1424no—
891C22—1424no—
892C22—14232no—
893C22—1424no—
894C22C4×D4×D7114yes—
895C22C4×D4×D7114yes—
896C22#1798648014yes—
897C22#1798663114yes—
898C22#1798665114yes—
899C22#1798665914yes—
900C22#1798669414yes—
901C22C23×C4×D7111yescharacteristic
902C22C22×D4×D7111yescharacteristic
903C22C22×D4×D7111yescharacteristic
904C22C2×#41×D7111yescharacteristic
905C22C2×#41×D7111yescharacteristic
906C22C2×#1455617311yescharacteristic
907C22C2×#1455617611yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—42no—
914C4—2842no—
915C4—2842no—
916C4—718no—
917C4—1424no—
918C4—1424no—
919C4—1424no—
920C2—44no—
921C2—2844no—
922C2—1428no—
923C2#2259135918yesdirect product factor
924C2C2×C4×D4×D7111yescharacteristic
925C2C2×C4×D4×D7111yescharacteristic
926C2C2×#1798648011yescharacteristic
927C2C2×#1798663111yescharacteristic
928C2C2×#1798665111yescharacteristic
929C2C2×#1798665911yescharacteristic
930C2C2×#1798669411yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#385×C71C2
socleC24×C71C24
prime radicalC22×#14556101C2
cosocleC23×C71C25
hypercenterC2×#385D71
hypocenterC71C2×#2361
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#14556090C2semidirect
3. C22×C4×C22⋊D71C2semidirect
4. C22×C4×C22⋊D71C2semidirect
5. C22×C4⋊C4×D71C2semidirect
6. #22591359C2direct (N × H)
7. C2×#17985899C2semidirect
8. C2×#17985894C2semidirect
9. C2×#17985892C2semidirect
10. C2×#17985889C2semidirect
11. C2×#17985877C2semidirect
12. C2×#17985875C2semidirect
13. C2×#17985873C2semidirect
14. C2×#17985850C2semidirect
15. C2×#17985846C2semidirect
16. C2×#385×C71C2semidirect
24. C2×#14556101C4semidirect
27. C2×#14556090C22semidirect
30. C2×C4×C22⋊D71C22semidirect
31. C2×C4×C22⋊D71C22semidirect
38. C2×C4⋊C4×D71C22semidirect
51. #17985899C22semidirect
52. #17985894C22semidirect
53. #17985892C22semidirect
54. #17985889C22semidirect
55. #17985877C22semidirect
56. #17985875C22semidirect
57. #17985873C22semidirect
58. #17985850C22semidirect
59. #17985846C22semidirect
69. #385×C71C22semidirect
76. C22×D284C2×C4semidirect
82. C22×C22⋊D71C2×C4semidirect
83. C22×C22⋊D71C2×C4semidirect
103. C22×C4×D71C2×C4semidirect
108. #14556101C2×C4semidirect
116. C2×Dic71⋊C4C2×C4semidirect
117. C2×Dic71⋊C4D4semidirect
131. C2×(C2×D71)⋊C4C2×C4semidirect
132. C2×(C2×D71)⋊C4D4semidirect
167. C2×C22⋊C4×C71C2×C4semidirect
191. C2×D284C22×C4semidirect
198. C2×C22⋊D71C22×C4semidirect
199. C2×C22⋊D71C22×C4semidirect
239. C2×C4×D71C22×C4semidirect
243. Dic71⋊C4C22×C4semidirect
244. Dic71⋊C4C2×D4semidirect
251. (C2×D71)⋊C4C22×C4semidirect
252. (C2×D71)⋊C4C2×D4semidirect
297. C22⋊C4×C71C22×C4semidirect
343. C22×D71C4×D4semidirect
392. C2×Dic71C4×D4semidirect
441. C2×D71C2×C4×D4semidirect
453. Dic71C2×C4×D4semidirect
456. C2×C71#2361semidirect
479. C2×#385D71semidirect
482. C71C2×#2361semidirect
529. #385C2×D71semidirect
621. C2×C22⋊C4C4×D71semidirect
759. C22⋊C4C2×C4×D71semidirect
923. C2#22591359direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561012
C22×#145560902
C22×C4×C22⋊D712
C22×C4⋊C4×D712
#225913592
C2×#179858992
C2×#179858942
C2×#179858922
C2×#179858892
C2×#179858772
C2×#179858752
C2×#179858732
C2×#179858502
C2×#179858462
C2×#385×C712
C2×#236171