Finite Group Databasebeta

← C2×#22591353 #32156978

Subgroups — C2×#22591353 #32156978

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×C4×D284C211yesmaximal, characteristic, complemented
3C22×(C22⋊D71)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C22⋊D71)⋊C4C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
6#22591353C2116yesmaximal, direct product factor
7C2×#17985899C211yesmaximal, characteristic, complemented
8C2×#17985896C211yesmaximal, characteristic, complemented
9C2×#17985891C211yesmaximal, characteristic, complemented
10C2×#17985877C211yesmaximal, characteristic, complemented
11C2×#17985875C211yesmaximal, characteristic, complemented
12C2×#17985874C211yesmaximal, characteristic, complemented
13C2×#17985870C211yesmaximal, characteristic, complemented
14C2×C4×Dic71⋊C4C211yesmaximal, characteristic, complemented
15C2×#17985846C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C24×Dic71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C23×C4×D71C2211yescharacteristic
24C23×C4×D71C2211yescharacteristic
25C2×#14556101C4116yescomplemented
26C2×#14556101C2218yes—
27C2×C4×D284—28no—
28C2×C4×D284C2218yescomplemented
29C2×(C22⋊D71)⋊C4—28no—
30C2×(C22⋊D71)⋊C4—28no—
31C2×(C22⋊D71)⋊C4C2218yescomplemented
32C2×(C22⋊D71)⋊C4C2218yescomplemented
33C22×C4⋊Dic71C2211yescharacteristic
34C22×C4⋊Dic71C2211yescharacteristic
35C22×Dic71⋊C4C2211yescharacteristic
36C22×Dic71⋊C4C2211yescharacteristic
37C22×Dic71⋊C4C2211yescharacteristic
38C22×Dic71⋊C4C2211yescharacteristic
39C2×C4⋊C4×D71—28no—
40C2×C4⋊C4×D71C2218yescomplemented
41C22×C22⋊Dic71C2211yescharacteristic
42C22×(C2×D71)⋊C4C2211yescharacteristic
43C22×(C2×D71)⋊C4C2211yescharacteristic
44C22×(C2×D71)⋊C4C2211yescharacteristic
45C22×(C2×D71)⋊C4C2211yescharacteristic
46C22×(C2×D71)⋊C4C2211yescharacteristic
47C22×(C2×D71)⋊C4C2211yescharacteristic
48C22×C4×Dic71C2211yescharacteristic
49C22×C4×Dic71C2211yescharacteristic
50C22×C4×Dic71C2211yescharacteristic
51#17985899C2218yescomplemented
52#17985896C2218yescomplemented
53#17985891C2218yescomplemented
54#17985877C2218yescomplemented
55#17985875C2218yescomplemented
56#17985874C2218yescomplemented
57#17985870C2218yescomplemented
58C4×Dic71⋊C4C2218yescomplemented
59#17985846C2218yescomplemented
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C2×C71⋊#95C2211yescharacteristic
63C2×C71⋊#95C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68C22×C42×C71C2211yescharacteristic
69#388×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×Dic71—24no—
87C23×Dic71—24no—
88C23×Dic71—42no—
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C23×Dic71C2314yes—
92C23×Dic71C2311yescharacteristic
93C23×Dic71C2311yescharacteristic
94C23×Dic71C2311yescharacteristic
95C23×Dic71C2311yescharacteristic
96C22×C4×D71—24no—
97C22×C4×D71—24no—
98C22×C4×D71—24no—
99C22×C4×D71—24no—
100C22×C4×D71—24no—
101C22×C4×D71—24no—
102C22×C4×D71—24no—
103C22×C4×D71—24no—
104C22×C4×D71—42no—
105C22×C4×D71—42no—
106C22×C4×D71—42no—
107C22×C4×D71C2×C418yescomplemented
108C22×C4×D71C2314yes—
109C22×C4×D71C2314yes—
110C22×C4×D71C2314yes—
111C22×C4×D71C2314yes—
112#14556101C2×C4164yescomplemented
113C4×D284—232no—
114(C22⋊D71)⋊C4—232no—
115(C22⋊D71)⋊C4—232no—
116C2×C4⋊Dic71—24no—
117C2×C4⋊Dic71—24no—
118C2×C4⋊Dic71C2314yes—
119C2×C4⋊Dic71C2314yes—
120C2×Dic71⋊C4—24no—
121C2×Dic71⋊C4—24no—
122C2×Dic71⋊C4C2×C418yescomplemented
123C2×Dic71⋊C4D418yescomplemented
124C2×Dic71⋊C4C2314yes—
125C2×Dic71⋊C4C2314yes—
126C2×Dic71⋊C4C2314yes—
127C2×Dic71⋊C4C2314yes—
128C4⋊C4×D71—232no—
129C2×C22⋊Dic71—42no—
130C2×C22⋊Dic71C2314yes—
131C2×(C2×D71)⋊C4—24no—
132C2×(C2×D71)⋊C4—24no—
133C2×(C2×D71)⋊C4—24no—
134C2×(C2×D71)⋊C4—42no—
135C2×(C2×D71)⋊C4C2×C418yescomplemented
136C2×(C2×D71)⋊C4D418yescomplemented
137C2×(C2×D71)⋊C4C2314yes—
138C2×(C2×D71)⋊C4C2314yes—
139C2×(C2×D71)⋊C4C2314yes—
140C2×(C2×D71)⋊C4C2314yes—
141C2×(C2×D71)⋊C4C2314yes—
142C2×(C2×D71)⋊C4C2314yes—
143C2×C4×Dic71—24no—
144C2×C4×Dic71—24no—
145C2×C4×Dic71—24no—
146C2×C4×Dic71C2314yes—
147C2×C4×Dic71C2314yes—
148C2×C4×Dic71C2314yes—
149C71⋊#95C2314yes—
150C71⋊#95C2314yes—
151C71⋊#95C2314yes—
152C71⋊#95C2314yes—
153C25×C71C2311yescharacteristic
154C23×C4×C71C2311yescharacteristic
155C23×C4×C71C2311yescharacteristic
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C2×C4⋊C4×C71—24no—
161C2×C4⋊C4×C71C2314yes—
162C2×C22⋊C4×C71—24no—
163C2×C22⋊C4×C71—24no—
164C2×C22⋊C4×C71C2×C418yescomplemented
165C2×C22⋊C4×C71C2314yes—
166C2×C22⋊C4×C71C2314yes—
167C2×C22⋊C4×C71C2314yes—
168C2×C42×C71—24no—
169C2×C42×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×Dic71—28no—
213C22×Dic71—28no—
214C22×Dic71—44no—
215C22×Dic71—416no—
216C22×Dic71C22×C414yes—
217C22×Dic71C22×C414yes—
218C22×Dic71C2×D414yes—
219C22×Dic71C2×D414yes—
220C22×Dic71C2×D414yes—
221C22×Dic71#4114yes—
222C22×Dic71C2412yes—
223C22×Dic71C2412yes—
224C22×Dic71C2412yes—
225C22×Dic71C2412yes—
226C22×Dic71C2412yes—
227C22×Dic71C2412yes—
228C2×C4×D71—232no—
229C2×C4×D71—28no—
230C2×C4×D71—28no—
231C2×C4×D71—28no—
232C2×C4×D71—28no—
233C2×C4×D71—28no—
234C2×C4×D71—28no—
235C2×C4×D71—28no—
236C2×C4×D71—28no—
237C2×C4×D71—44no—
238C2×C4×D71—44no—
239C2×C4×D71—44no—
240C2×C4×D71—416no—
241C2×C4×D71—416no—
242C2×C4×D71—416no—
243C2×C4×D71C22×C4116yescomplemented
244C4⋊Dic71—28no—
245C4⋊Dic71—28no—
246Dic71⋊C4—28no—
247Dic71⋊C4—28no—
248Dic71⋊C4C22×C4116yescomplemented
249Dic71⋊C4C2×D4116yescomplemented
250C22⋊Dic71—44no—
251(C2×D71)⋊C4—28no—
252(C2×D71)⋊C4—28no—
253(C2×D71)⋊C4—28no—
254(C2×D71)⋊C4—44no—
255(C2×D71)⋊C4C22×C4116yescomplemented
256(C2×D71)⋊C4C2×D4116yescomplemented
257C4×Dic71—28no—
258C4×Dic71—28no—
259C4×Dic71—28no—
260C24×C71—22no—
261C24×C71—22no—
262C24×C71—22no—
263C24×C71—22no—
264C24×C71—22no—
265C24×C71—22no—
266C24×C71C22×C414yes—
267C24×C71C2412yes—
268C24×C71C2411yescharacteristic
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—22no—
281C22×C4×C71—22no—
282C22×C4×C71—22no—
283C22×C4×C71C22×C414yes—
284C22×C4×C71C22×C414yes—
285C22×C4×C71C2×D414yes—
286C22×C4×C71C2×D414yes—
287C22×C4×C71C2412yes—
288C22×C4×C71C2412yes—
289C22×C4×C71C2412yes—
290C22×C4×C71C2412yes—
291C22×C4×C71C2412yes—
292C22×C4×C71C2412yes—
293C4⋊C4×C71—28no—
294C22⋊C4×C71—28no—
295C22⋊C4×C71—28no—
296C22⋊C4×C71C22×C4116yescomplemented
297C42×C71—28no—
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—44no—
367C2×C4×C71—44no—
368C2×C4×C71C23×C414yes—
369C2×C4×C71C23×C414yes—
370C2×C4×C71C22×D414yes—
371C2×C4×C71C22×D414yes—
372C22⋊D71—232no—
373C22⋊D71—232no—
374C2×Dic71—28no—
375C2×Dic71—28no—
376C2×Dic71—28no—
377C2×Dic71—22no—
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—416no—
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×#388D7111yescharacteristic, complemented
476C2×#386—711no—
477C2×#386—711no—
478C2×#385—711no—
479C2×#385—711no—
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×C4—711no—
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—711no—
505C22×C4⋊C4—718no—
506C22×C4⋊C4—1428no—
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⋊C4C2×D7111yescharacteristic
516C22×C22⋊C4C2×D7111yescharacteristic
517C22×C22⋊C4C2×D7111yescharacteristic
518C22×C42—711no—
519C22×C42—711no—
520C22×C42—711no—
521C22×C42C2×D7111yescharacteristic
522#390—718no—
523#389—718no—
524#388—718no—
525#388C2×D7118yescomplemented
526#386—718no—
527#386—718no—
528#385—718no—
529#385—718no—
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—2842no—
554C23×C4—2842no—
555C23×C4—2842no—
556C23×C4—2842no—
557C23×C4—714no—
558C23×C4—714no—
559C23×C4—714no—
560C23×C4—714no—
561C23×C4—711no—
562C23×C4—711no—
563C23×C4—711no—
564C23×C4—711no—
565C23×C4—718no—
566C23×C4—714no—
567C23×C4—711no—
568C23×C4—711no—
569C23×C4—1424no—
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×C4—1424no—
579C23×C4C22×D7111yescharacteristic
580C23×C4C22×D7111yescharacteristic
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—718no—
591C2×C4⋊C4—718no—
592C2×C4⋊C4—714no—
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⋊C4—1424no—
603C2×C4⋊C4C22×D7114yes—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—2842no—
607C2×C22⋊C4—2842no—
608C2×C22⋊C4—714no—
609C2×C22⋊C4—714no—
610C2×C22⋊C4—718no—
611C2×C22⋊C4—718no—
612C2×C22⋊C4—714no—
613C2×C22⋊C4—714no—
614C2×C22⋊C4—714no—
615C2×C22⋊C4—714no—
616C2×C22⋊C4—714no—
617C2×C22⋊C4—1424no—
618C2×C22⋊C4—1424no—
619C2×C22⋊C4—1424no—
620C2×C22⋊C4C4×D7118yescomplemented
621C2×C22⋊C4C22×D7114yes—
622C2×C22⋊C4C22×D7114yes—
623C2×C22⋊C4C22×D7114yes—
624C2×C42—24no—
625C2×C42—714no—
626C2×C42—714no—
627C2×C42—714no—
628C2×C42—1424no—
629C2×C42—1424no—
630C2×C42—1424no—
631C2×C42C22×D7114yes—
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—28416no—
690C22×C4—28416no—
691C22×C4—2844no—
692C22×C4—2844no—
693C22×C4—2844no—
694C22×C4—28416no—
695C22×C4—2844no—
696C22×C4—28416no—
697C22×C4—714no—
698C22×C4—714no—
699C22×C4—714no—
700C22×C4—712no—
701C22×C4—714no—
702C22×C4—714no—
703C22×C4—714no—
704C22×C4—712no—
705C22×C4—712no—
706C22×C4—712no—
707C22×C4—7116no—
708C22×C4—712no—
709C22×C4—712no—
710C22×C4—1428no—
711C22×C4—1428no—
712C22×C4—1428no—
713C22×C4—1428no—
714C22×C4—1428no—
715C22×C4—1428no—
716C22×C4—14232no—
717C22×C4—1428no—
718C22×C4—1428no—
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—7116no—
745C4⋊C4—7116no—
746C4⋊C4—1428no—
747C4⋊C4—1428no—
748C4⋊C4—1428no—
749C4⋊C4—1428no—
750C22⋊C4—28no—
751C22⋊C4—28no—
752C22⋊C4—2844no—
753C22⋊C4—2844no—
754C22⋊C4—7116no—
755C22⋊C4—7116no—
756C22⋊C4—1428no—
757C22⋊C4—1428no—
758C22⋊C4—1428no—
759C22⋊C4C2×C4×D71116yescomplemented
760C42—28no—
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#1455617412yes—
812C23#1455617512yes—
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—44no—
836C2×C4—44no—
837C2×C4—28416no—
838C2×C4—28416no—
839C2×C4—28416no—
840C2×C4—2844no—
841C2×C4—2844no—
842C2×C4—28416no—
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#1798647914yes—
897C22#1798663314yes—
898C22#1798664714yes—
899C22#1798665714yes—
900C22#1798670014yes—
901C22C23×C4×D7111yescharacteristic
902C22C22×D4×D7111yescharacteristic
903C22C22×D4×D7111yescharacteristic
904C22C2×#41×D7111yescharacteristic
905C22C2×#41×D7111yescharacteristic
906C22C2×#1455617411yescharacteristic
907C22C2×#1455617511yescharacteristic
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#2259135318yesdirect product factor
924C2C2×C4×D4×D7111yescharacteristic
925C2C2×C4×D4×D7111yescharacteristic
926C2C2×#1798647911yescharacteristic
927C2C2×#1798663311yescharacteristic
928C2C2×#1798664711yescharacteristic
929C2C2×#1798665711yescharacteristic
930C2C2×#1798670011yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC22×#14556101C2
cosocleC23×C71C25
hypercenterC2×#388D71
hypocenterC71C2×#2361
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×D284C2semidirect
3. C22×(C22⋊D71)⋊C4C2semidirect
4. C22×(C22⋊D71)⋊C4C2semidirect
5. C22×C4⋊C4×D71C2semidirect
6. #22591353C2direct (N × H)
7. C2×#17985899C2semidirect
8. C2×#17985896C2semidirect
9. C2×#17985891C2semidirect
10. C2×#17985877C2semidirect
11. C2×#17985875C2semidirect
12. C2×#17985874C2semidirect
13. C2×#17985870C2semidirect
14. C2×C4×Dic71⋊C4C2semidirect
15. C2×#17985846C2semidirect
16. C2×#388×C71C2semidirect
25. C2×#14556101C4semidirect
28. C2×C4×D284C22semidirect
31. C2×(C22⋊D71)⋊C4C22semidirect
32. C2×(C22⋊D71)⋊C4C22semidirect
40. C2×C4⋊C4×D71C22semidirect
51. #17985899C22semidirect
52. #17985896C22semidirect
53. #17985891C22semidirect
54. #17985877C22semidirect
55. #17985875C22semidirect
56. #17985874C22semidirect
57. #17985870C22semidirect
58. C4×Dic71⋊C4C22semidirect
59. #17985846C22semidirect
69. #388×C71C22semidirect
76. C22×D284C2×C4semidirect
82. C22×C22⋊D71C2×C4semidirect
83. C22×C22⋊D71C2×C4semidirect
107. C22×C4×D71C2×C4semidirect
112. #14556101C2×C4semidirect
122. C2×Dic71⋊C4C2×C4semidirect
123. C2×Dic71⋊C4D4semidirect
135. C2×(C2×D71)⋊C4C2×C4semidirect
136. C2×(C2×D71)⋊C4D4semidirect
164. C2×C22⋊C4×C71C2×C4semidirect
191. C2×D284C22×C4semidirect
198. C2×C22⋊D71C22×C4semidirect
199. C2×C22⋊D71C22×C4semidirect
243. C2×C4×D71C22×C4semidirect
248. Dic71⋊C4C22×C4semidirect
249. Dic71⋊C4C2×D4semidirect
255. (C2×D71)⋊C4C22×C4semidirect
256. (C2×D71)⋊C4C2×D4semidirect
296. 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
475. C2×#388D71semidirect
482. C71C2×#2361semidirect
525. #388C2×D71semidirect
620. C2×C22⋊C4C4×D71semidirect
759. C22⋊C4C2×C4×D71semidirect
923. C2#22591353direct (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×C4×D2842
C22×(C22⋊D71)⋊C42
C22×C4⋊C4×D712
#225913532
C2×#179858992
C2×#179858962
C2×#179858912
C2×#179858772
C2×#179858752
C2×#179858742
C2×#179858702
C2×C4×Dic71⋊C42
C2×#179858462
C2×#388×C712
C2×#236171