Finite Group Databasebeta

← C2×#22593257 #32169219

Subgroups — C2×#22593257 #32169219

Order 18176.

3614 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556106C211yesmaximal, characteristic, complemented
2C22×#14556105C211yesmaximal, characteristic, complemented
3C22×#14556093C211yesmaximal, characteristic, complemented
4C22×(C22⋊D71)⋊C4C211yesmaximal, characteristic
5#22593257C2116yesmaximal, direct product factor
6C2×#17985922C211yesmaximal, characteristic, complemented
7C2×#17985921C211yesmaximal, characteristic, complemented
8C2×#17985921C211yesmaximal, characteristic, complemented
9C2×#17985899C211yesmaximal, characteristic
10C2×#17985899C211yesmaximal, characteristic
11C2×#17985896C211yesmaximal, characteristic, complemented
12C2×#17985894C211yesmaximal, characteristic, complemented
13C2×#17985868C211yesmaximal, characteristic, complemented
14C2×#17985858C211yesmaximal, characteristic, complemented
15C2×#17985857C211yesmaximal, characteristic, complemented
16C2×#396×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556106—28no—
22C2×#14556106C2218yescomplemented
23C2×#14556105—28no—
24C2×#14556105C2218yescomplemented
25C2×#14556093—28no—
26C2×#14556093C2218yescomplemented
27C2×(C22⋊D71)⋊C4—28no—
28C2×(C22⋊D71)⋊C4C2218yes—
29C22×C4⋊Dic71C2211yescharacteristic
30C22×C4⋊Dic71C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×Dic71⋊C4C2211yescharacteristic
35C22×Dic71⋊C4C2211yescharacteristic
36C22×Dic71⋊C4C2211yescharacteristic
37C22×Dic71⋊C4C2211yescharacteristic
38C22×Dic71⋊C4C2211yescharacteristic
39C22×Dic71⋊C4C2211yescharacteristic
40C22×C22⋊Dic71C2211yescharacteristic
41C22×C22⋊Dic71C2211yescharacteristic
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
50#17985922C2218yescomplemented
51#17985921C2218yescomplemented
52#17985921C2218yescomplemented
53#17985899C2218yes—
54#17985899C2218yes—
55#17985896C2218yescomplemented
56#17985894C2218yescomplemented
57#17985868C2218yescomplemented
58#17985858C2218yescomplemented
59#17985857C2218yescomplemented
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C2×C71⋊#95C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C4⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68C22×C22⋊C4×C71C2211yescharacteristic
69#396×C71C2218yescomplemented
70C2×#95×C71C2211yescharacteristic
71C24×D71C2311yescharacteristic
72C22×Dic142—24no—
73C22×Dic142—24no—
74C22×Dic142D418yescomplemented
75C22×Dic142C2314yes—
76C22×C22⋊D71—24no—
77C22×C22⋊D71—24no—
78C22×C22⋊D71Q818yescomplemented
79C22×C22⋊D71C2314yes—
80C23×Dic71—24no—
81C23×Dic71—24no—
82C23×Dic71—24no—
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2314yes—
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C22×C4×D71—24no—
92C22×C4×D71—24no—
93C22×C4×D71—24no—
94C22×C4×D71C2314yes—
95#14556106—232no—
96#14556105—232no—
97#14556093—232no—
98(C22⋊D71)⋊C4—232no—
99C2×C4⋊Dic71—24no—
100C2×C4⋊Dic71—42no—
101C2×C4⋊Dic71C2314yes—
102C2×C4⋊Dic71C2314yes—
103C2×Dic71⋊C4—24no—
104C2×Dic71⋊C4—24no—
105C2×Dic71⋊C4—24no—
106C2×Dic71⋊C4—24no—
107C2×Dic71⋊C4—24no—
108C2×Dic71⋊C4—24no—
109C2×Dic71⋊C4—24no—
110C2×Dic71⋊C4—24no—
111C2×Dic71⋊C4—24no—
112C2×Dic71⋊C4C2314yes—
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C2×Dic71⋊C4C2314yes—
116C2×Dic71⋊C4C2314yes—
117C2×Dic71⋊C4C2314yes—
118C2×Dic71⋊C4C2314yes—
119C2×Dic71⋊C4C2314yes—
120C2×Dic71⋊C4C2314yes—
121C2×C22⋊Dic71—24no—
122C2×C22⋊Dic71—42no—
123C2×C22⋊Dic71C2314yes—
124C2×C22⋊Dic71C2314yes—
125C2×(C2×D71)⋊C4—24no—
126C2×(C2×D71)⋊C4—24no—
127C2×(C2×D71)⋊C4—24no—
128C2×(C2×D71)⋊C4—42no—
129C2×(C2×D71)⋊C4—42no—
130C2×(C2×D71)⋊C4C2314yes—
131C2×(C2×D71)⋊C4C2314yes—
132C2×(C2×D71)⋊C4C2314yes—
133C2×(C2×D71)⋊C4C2314yes—
134C2×(C2×D71)⋊C4C2314yes—
135C2×C4×Dic71—24no—
136C2×C4×Dic71—24no—
137C2×C4×Dic71D418yes—
138C2×C4×Dic71C2314yes—
139C2×C4×Dic71C2314yes—
140C2×C4×Dic71C2314yes—
141C71⋊#95C2314yes—
142C71⋊#95C2314yes—
143C71⋊#95C2314yes—
144C25×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2311yescharacteristic
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C2×C4⋊C4×C71—24no—
152C2×C4⋊C4×C71—24no—
153C2×C4⋊C4×C71—42no—
154C2×C4⋊C4×C71C2314yes—
155C2×C4⋊C4×C71C2314yes—
156C2×C4⋊C4×C71C2314yes—
157C2×C22⋊C4×C71—24no—
158C2×C22⋊C4×C71—24no—
159C2×C22⋊C4×C71—42no—
160C2×C22⋊C4×C71C2314yes—
161C2×C22⋊C4×C71C2314yes—
162C2×C22⋊C4×C71C2314yes—
163#95×C71C2314yes—
164C23×D71—22no—
165C23×D71—22no—
166C23×D71—22no—
167C23×D71—22no—
168C23×D71—22no—
169C23×D71—22no—
170C23×D71C2×Q814yes—
171C23×D71C2412yes—
172C2×Dic142—232no—
173C2×Dic142—28no—
174C2×Dic142—28no—
175C2×Dic142C2×D4116yescomplemented
176C2×C22⋊D71—232no—
177C2×C22⋊D71—28no—
178C2×C22⋊D71—28no—
179C2×C22⋊D71C2×Q8116yescomplemented
180C22×Dic71—22no—
181C22×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71—22no—
184C22×Dic71—22no—
185C22×Dic71—22no—
186C22×Dic71—22no—
187C22×Dic71—22no—
188C22×Dic71—22no—
189C22×Dic71—22no—
190C22×Dic71—22no—
191C22×Dic71—22no—
192C22×Dic71—22no—
193C22×Dic71—22no—
194C22×Dic71—28no—
195C22×Dic71—28no—
196C22×Dic71—28no—
197C22×Dic71—416no—
198C22×Dic71C2×D414yes—
199C22×Dic71C2×D414yes—
200C22×Dic71C2×D414yes—
201C22×Dic71C2×D414yes—
202C22×Dic71C2×Q814yes—
203C22×Dic71#4114yes—
204C22×Dic71#4114yes—
205C22×Dic71C2412yes—
206C22×Dic71C2412yes—
207C22×Dic71C2412yes—
208C22×Dic71C2412yes—
209C22×Dic71C2412yes—
210C22×Dic71C2412yes—
211C22×Dic71C2412yes—
212C2×C4×D71—28no—
213C2×C4×D71—28no—
214C2×C4×D71—28no—
215C2×C4×D71—416no—
216C4⋊Dic71—28no—
217C4⋊Dic71—44no—
218Dic71⋊C4—28no—
219Dic71⋊C4—28no—
220Dic71⋊C4—28no—
221Dic71⋊C4—28no—
222Dic71⋊C4—28no—
223Dic71⋊C4—28no—
224Dic71⋊C4—28no—
225Dic71⋊C4—28no—
226Dic71⋊C4—28no—
227C22⋊Dic71—28no—
228C22⋊Dic71—44no—
229(C2×D71)⋊C4—28no—
230(C2×D71)⋊C4—28no—
231(C2×D71)⋊C4—28no—
232(C2×D71)⋊C4—44no—
233(C2×D71)⋊C4—44no—
234C4×Dic71—28no—
235C4×Dic71—28no—
236C4×Dic71C2×D4116yes—
237C24×C71—22no—
238C24×C71—22no—
239C24×C71—22no—
240C24×C71—22no—
241C24×C71—22no—
242C24×C71—22no—
243C24×C71C2×Q814yes—
244C24×C71C2412yes—
245C24×C71C2411yescharacteristic
246C22×C4×C71—22no—
247C22×C4×C71—22no—
248C22×C4×C71—22no—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—22no—
254C22×C4×C71—22no—
255C22×C4×C71—22no—
256C22×C4×C71—22no—
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—22no—
262C22×C4×C71C2×D414yes—
263C22×C4×C71C2×D414yes—
264C22×C4×C71C2412yes—
265C22×C4×C71C2412yes—
266C22×C4×C71C2412yes—
267C22×C4×C71C2412yes—
268C22×C4×C71C2412yes—
269C22×C4×C71C2412yes—
270C4⋊C4×C71—28no—
271C4⋊C4×C71—28no—
272C4⋊C4×C71—44no—
273C22⋊C4×C71—28no—
274C22⋊C4×C71—28no—
275C22⋊C4×C71—44no—
276C23×C71—28no—
277C23×C71—28no—
278C23×C71—28no—
279C23×C71—22no—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—44no—
286C23×C71—44no—
287C23×C71—44no—
288C23×C71—44no—
289C23×C71C22×D412yes—
290C23×C71C22×D412yes—
291C23×C71C22×Q814yes—
292C23×C71C22×Q812yes—
293C23×C71C2×#4112yes—
294C23×C71C2×#4112yes—
295C23×C71H(5,𝔽2)12yes—
296C23×C712−1+412yes—
297C23×C71C2511yescharacteristic
298C22×D71—28no—
299C22×D71—28no—
300C22×D71—28no—
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—44no—
308C22×D71—44no—
309C22×D71—44no—
310C22×D71—44no—
311C22×D71C22×Q814yes—
312C2×C4×C71—28no—
313C2×C4×C71—28no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—44no—
331C2×C4×C71—44no—
332C2×C4×C71—44no—
333C2×C4×C71—44no—
334C2×C4×C71C22×D414yes—
335C2×C4×C71C22×D414yes—
336C22⋊D71—232no—
337C2×Dic71—28no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—22no—
348C2×Dic71—22no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—22no—
352C2×Dic71—44no—
353C2×Dic71—44no—
354C2×Dic71—44no—
355C2×Dic71—44no—
356C2×Dic71—416no—
357C2×Dic71#121116yes—
358C2×Dic71C22⋊Q8116yescomplemented
359C2×Dic71C22×D414yes—
360C2×Dic71C22×D414yes—
361C2×Dic71C22×D414yes—
362C2×Dic71C22×D414yes—
363C2×Dic71C22×Q814yes—
364C2×Dic71C2×#4114yes—
365C2×Dic71C2×#4114yes—
366C4×D71—416no—
367Dic142—232no—
368C22×C71—24no—
369C22×C71—24no—
370C22×C71—24no—
371C22×C71—42no—
372C22×C71—42no—
373C22×C71—42no—
374C22×C71—42no—
375C22×C71—416no—
376C22×C71C2×#12114yes—
377C22×C71C2×C22⋊Q814yes—
378C22×C71#53714yes—
379C22×C71D4×Q814yes—
380C22×C71#55014yes—
381C22×C71#55414yes—
382C22×C71#55614yes—
383C22×C71C23×D411yescharacteristic
384C22×C71C23×D411yescharacteristic
385C22×C71C23×Q811yescharacteristic
386C22×C71C22×#4111yescharacteristic
387C22×C71C22×#4111yescharacteristic
388C22×C71C2×H(5,𝔽2)11yescharacteristic
389C22×C71C2×2−1+411yescharacteristic
390C2×D71—24no—
391C2×D71—24no—
392C2×D71—24no—
393C2×D71—42no—
394C2×D71—42no—
395C2×D71—42no—
396C2×D71—42no—
397C2×D71—416no—
398C4×C71—24no—
399C4×C71—24no—
400C4×C71—42no—
401C4×C71—42no—
402C4×C71—42no—
403C4×C71—42no—
404Dic71—24no—
405Dic71—42no—
406Dic71—42no—
407Dic71—42no—
408Dic71—42no—
409Dic71C2×#12118yes—
410Dic71C2×C22⋊Q818yescomplemented
411C2×#2538—711nomaximal, Sylow
412C2×C71—44no—
413C2×C71#253818yescomplemented
414C2×C71C22×#12111yescharacteristic
415C2×C71C22×C22⋊Q811yescharacteristic
416C2×C71C2×#53711yescharacteristic
417C2×C71C2×D4×Q811yescharacteristic
418C2×C71C2×#55011yescharacteristic
419C2×C71C2×#55411yescharacteristic
420C2×C71C2×#55611yescharacteristic
421D71—44no—
422C22×C22⋊Q8—711no—
423C22×C22⋊Q8—711no—
424C22×C4×Q8—711no—
425C22×C4×D4—711no—
426#2538—7116no—
427C2×#396—711no—
428C2×#396—711no—
429C2×#396—711no—
430C2×#396D7111yescharacteristic, complemented
431C2×#390—711no—
432C2×#390—711no—
433C2×#389—711no—
434C2×#389—711no—
435C2×#384—711no—
436C2×#380—711no—
437C2×#380—711no—
438C71C2×#253811yescharacteristic, complemented, Sylow
439C23×Q8—711no—
440C23×D4—711no—
441C24×C4—711no—
442C24×C4—711no—
443C2×C22⋊Q8—718no—
444C2×C22⋊Q8—718no—
445C2×C22⋊Q8—1428no—
446C2×C22⋊Q8—1428no—
447C2×C4×Q8—718no—
448C2×C4×Q8—1428no—
449C2×C4×D4—718no—
450C2×C4×D4—1428no—
451C22×C4⋊C4—711no—
452C22×C4⋊C4—711no—
453C22×C4⋊C4—711no—
454C22×C4⋊C4—711no—
455C22×C4⋊C4—711no—
456C22×C4⋊C4—711no—
457C22×C4⋊C4—711no—
458C22×C4⋊C4—711no—
459C22×C4⋊C4—711no—
460C22×C4⋊C4—711no—
461C22×C4⋊C4—711no—
462C22×C4⋊C4C2×D7111yescharacteristic
463C22×C4⋊C4C2×D7111yescharacteristic
464C22×C4⋊C4C2×D7111yescharacteristic
465C22×C22⋊C4—711no—
466C22×C22⋊C4—711no—
467C22×C22⋊C4—711no—
468C22×C22⋊C4—711no—
469C22×C22⋊C4—711no—
470C22×C22⋊C4—711no—
471C22×C22⋊C4—711no—
472C22×C22⋊C4C2×D7111yescharacteristic
473C22×C22⋊C4C2×D7111yescharacteristic
474C22×C22⋊C4C2×D7111yescharacteristic
475C22×C42—711no—
476C22×C42—711no—
477C22×C42—711no—
478#396—718no—
479#396—718no—
480#396—718no—
481#396C2×D7118yescomplemented
482#390—718no—
483#390—718no—
484#389—718no—
485#389—718no—
486#384—718no—
487#380—718no—
488#380—718no—
489C2×#95—711no—
490C2×#95—711no—
491C2×#95—711no—
492C2×#95C2×D7111yescharacteristic
493C25—711no—
494C25C22×D7111yescharacteristic
495C22×Q8—718no—
496C22×Q8—714no—
497C22×Q8—1424no—
498C22×Q8—1424no—
499C22×D4—718no—
500C22×D4—714no—
501C22×D4—1424no—
502C22×D4—1424no—
503C23×C4—711no—
504C23×C4—711no—
505C23×C4—711no—
506C23×C4—714no—
507C23×C4—711no—
508C23×C4—711no—
509C23×C4—711no—
510C23×C4—711no—
511C23×C4—714no—
512C23×C4—1424no—
513C23×C4—1424no—
514C23×C4—1424no—
515C23×C4—1424no—
516C23×C4—1424no—
517C23×C4—1424no—
518C23×C4C22×D7111yescharacteristic
519C23×C4C22×D7111yescharacteristic
520C23×C4C22×D7111yescharacteristic
521C23×C4C22×D7111yescharacteristic
522C23×C4C22×D7111yescharacteristic
523C23×C4C22×D7111yescharacteristic
524C22⋊Q8—14232no—
525C22⋊Q8—14232no—
526C4×Q8—14232no—
527C4×D4—14232no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—42no—
531C2×C4⋊C4—2842no—
532C2×C4⋊C4—714no—
533C2×C4⋊C4—714no—
534C2×C4⋊C4—714no—
535C2×C4⋊C4—714no—
536C2×C4⋊C4—714no—
537C2×C4⋊C4—714no—
538C2×C4⋊C4—714no—
539C2×C4⋊C4—714no—
540C2×C4⋊C4—714no—
541C2×C4⋊C4—714no—
542C2×C4⋊C4—714no—
543C2×C4⋊C4—1424no—
544C2×C4⋊C4—1424no—
545C2×C4⋊C4—1424no—
546C2×C4⋊C4—1424no—
547C2×C4⋊C4—1424no—
548C2×C4⋊C4—1424no—
549C2×C4⋊C4—1424no—
550C2×C4⋊C4—1424no—
551C2×C4⋊C4—1424no—
552C2×C4⋊C4—1424no—
553C2×C4⋊C4C22×D7114yes—
554C2×C4⋊C4C22×D7114yes—
555C2×C4⋊C4C22×D7114yes—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—2842no—
560C2×C22⋊C4—2842no—
561C2×C22⋊C4—2842no—
562C2×C22⋊C4—714no—
563C2×C22⋊C4—714no—
564C2×C22⋊C4—714no—
565C2×C22⋊C4—714no—
566C2×C22⋊C4—714no—
567C2×C22⋊C4—714no—
568C2×C22⋊C4—714no—
569C2×C22⋊C4—1424no—
570C2×C22⋊C4—1424no—
571C2×C22⋊C4—1424no—
572C2×C22⋊C4—1424no—
573C2×C22⋊C4C22×D7114yes—
574C2×C22⋊C4C22×D7114yes—
575C2×C22⋊C4C22×D7114yes—
576C2×C42—718no—
577C2×C42—714no—
578C2×C42—714no—
579C2×C42—714no—
580C2×C42—1424no—
581C2×C42—1424no—
582#95—714no—
583#95—714no—
584#95—714no—
585#95C22×D7114yes—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—714no—
593C24—712no—
594C24—1422no—
595C24—1422no—
596C24—1422no—
597C24—1422no—
598C24—1422no—
599C24—1422no—
600C24Q8×D7114yes—
601C24C23×D7112yes—
602C24C23×D7111yescharacteristic
603C2×Q8—7116no—
604C2×Q8—1428no—
605C2×Q8—1428no—
606C2×Q8—14232no—
607C2×D4—7116no—
608C2×D4—1428no—
609C2×D4—1428no—
610C2×D4—14232no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—28416no—
628C22×C4—28416no—
629C22×C4—714no—
630C22×C4—714no—
631C22×C4—714no—
632C22×C4—714no—
633C22×C4—714no—
634C22×C4—714no—
635C22×C4—712no—
636C22×C4—712no—
637C22×C4—714no—
638C22×C4—712no—
639C22×C4—712no—
640C22×C4—712no—
641C22×C4—712no—
642C22×C4—712no—
643C22×C4—1428no—
644C22×C4—1428no—
645C22×C4—1428no—
646C22×C4—1428no—
647C22×C4—1428no—
648C22×C4—1428no—
649C22×C4—1422no—
650C22×C4—1422no—
651C22×C4—1422no—
652C22×C4—1422no—
653C22×C4—1422no—
654C22×C4—1422no—
655C22×C4—1422no—
656C22×C4—1422no—
657C22×C4—1422no—
658C22×C4—1422no—
659C22×C4—1422no—
660C22×C4—1422no—
661C22×C4—1422no—
662C22×C4—1422no—
663C22×C4D4×D7114yes—
664C22×C4D4×D7114yes—
665C22×C4C23×D7112yes—
666C22×C4C23×D7112yes—
667C22×C4C23×D7112yes—
668C22×C4C23×D7112yes—
669C22×C4C23×D7112yes—
670C22×C4C23×D7112yes—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—44no—
674C4⋊C4—2844no—
675C4⋊C4—1428no—
676C4⋊C4—1428no—
677C4⋊C4—1428no—
678C4⋊C4—1428no—
679C4⋊C4—1428no—
680C4⋊C4—1428no—
681C4⋊C4—1428no—
682C4⋊C4—1428no—
683C4⋊C4—1428no—
684C4⋊C4—1428no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—44no—
688C22⋊C4—2844no—
689C22⋊C4—2844no—
690C22⋊C4—2844no—
691C22⋊C4—1428no—
692C22⋊C4—1428no—
693C22⋊C4—1428no—
694C22⋊C4—1428no—
695C42—7116no—
696C42—1428no—
697C42—1428no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—28no—
705C23—28no—
706C23—28no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—2844no—
712C23—2844no—
713C23—2844no—
714C23—2844no—
715C23—714no—
716C23—1422no—
717C23—1422no—
718C23—1422no—
719C23—1422no—
720C23—1422no—
721C23—1422no—
722C23—1428no—
723C23—1428no—
724C23—1428no—
725C23C2×D4×D7112yes—
726C23C2×D4×D7112yes—
727C23C2×Q8×D7114yes—
728C23C2×Q8×D7112yes—
729C23#41×D7112yes—
730C23#41×D7112yes—
731C23#1455617312yes—
732C23#1455617512yes—
733C23C24×D7111yescharacteristic
734Q8—14232no—
735D4—14232no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—28no—
740C2×C4—22no—
741C2×C4—28no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—28416no—
759C2×C4—2844no—
760C2×C4—2844no—
761C2×C4—2844no—
762C2×C4—2844no—
763C2×C4—28416no—
764C2×C4—714no—
765C2×C4—714no—
766C2×C4—714no—
767C2×C4—714no—
768C2×C4—714no—
769C2×C4—714no—
770C2×C4—7116no—
771C2×C4—7116no—
772C2×C4—714no—
773C2×C4—1422no—
774C2×C4—1422no—
775C2×C4—1422no—
776C2×C4—1422no—
777C2×C4—1422no—
778C2×C4—1422no—
779C2×C4—1422no—
780C2×C4—1422no—
781C2×C4—1422no—
782C2×C4—1422no—
783C2×C4—1422no—
784C2×C4—1422no—
785C2×C4—1422no—
786C2×C4—1422no—
787C2×C4—1428no—
788C2×C4C2×D4×D7114yes—
789C2×C4C2×D4×D7114yes—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—416no—
798C22—2842no—
799C22—2842no—
800C22—2842no—
801C22—2842no—
802C22—28416no—
803C22—1424no—
804C22—1424no—
805C22—1424no—
806C22#121×D7114yes—
807C22C22⋊Q8×D7114yes—
808C22#1798657614yes—
809C22#1798666214yes—
810C22#1798666714yes—
811C22#1798670314yes—
812C22#1798671614yes—
813C22C22×D4×D7111yescharacteristic
814C22C22×D4×D7111yescharacteristic
815C22C22×Q8×D7111yescharacteristic
816C22C2×#41×D7111yescharacteristic
817C22C2×#41×D7111yescharacteristic
818C22C2×#1455617311yescharacteristic
819C22C2×#1455617511yescharacteristic
820C4—24no—
821C4—24no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—2842no—
827C4—2842no—
828C4—2842no—
829C4—2842no—
830C4—718no—
831C4—718no—
832C4—1424no—
833C2—44no—
834C2—2844no—
835C2#2259325718yesdirect product factor
836C2C2×#121×D7111yescharacteristic
837C2C2×C22⋊Q8×D7111yescharacteristic
838C2C2×#1798657611yescharacteristic
839C2C2×#1798666211yescharacteristic
840C2C2×#1798666711yescharacteristic
841C2C2×#1798670311yescharacteristic
842C2C2×#1798671611yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#396×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC2×#396D71
hypocenterC71C2×#2538
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14556106C2semidirect
2. C22×#14556105C2semidirect
3. C22×#14556093C2semidirect
5. #22593257C2direct (N × H)
6. C2×#17985922C2semidirect
7. C2×#17985921C2semidirect
8. C2×#17985921C2semidirect
11. C2×#17985896C2semidirect
12. C2×#17985894C2semidirect
13. C2×#17985868C2semidirect
14. C2×#17985858C2semidirect
15. C2×#17985857C2semidirect
16. C2×#396×C71C2semidirect
22. C2×#14556106C22semidirect
24. C2×#14556105C22semidirect
26. C2×#14556093C22semidirect
50. #17985922C22semidirect
51. #17985921C22semidirect
52. #17985921C22semidirect
55. #17985896C22semidirect
56. #17985894C22semidirect
57. #17985868C22semidirect
58. #17985858C22semidirect
59. #17985857C22semidirect
69. #396×C71C22semidirect
74. C22×Dic142D4semidirect
78. C22×C22⋊D71Q8semidirect
175. C2×Dic142C2×D4semidirect
179. C2×C22⋊D71C2×Q8semidirect
358. C2×Dic71C22⋊Q8semidirect
410. Dic71C2×C22⋊Q8semidirect
413. C2×C71#2538semidirect
430. C2×#396D71semidirect
438. C71C2×#2538semidirect
481. #396C2×D71semidirect
835. C2#22593257direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561062
C22×#145561052
C22×#145560932
C22×(C22⋊D71)⋊C42
#225932572
C2×#179859222
C2×#179859212
C2×#179858992
C2×#179858962
C2×#179858942
C2×#179858682
C2×#179858582
C2×#179858572
C2×#396×C712
C2×#253871