Finite Group Databasebeta

← #32158396

Subgroups — #32158396

Order 18176.

3106 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986480C211yesmaximal, characteristic
2C2×#17986479C211yesmaximal, characteristic
3C2×#17986467C211yesmaximal, characteristic
4#22591259C212yesmaximal, complemented
5#22591254C212yesmaximal, complemented
6#22591249C212yesmaximal, complemented
7#22591244C214yesmaximal, complemented
8#22591241C212yesmaximal, complemented
9#22591236C214yesmaximal, complemented
10#22590962C212yesmaximal, complemented
11#22590960C211yesmaximal, characteristic, complemented
12#22590955C212yesmaximal, complemented
13#22590822C211yesmaximal, characteristic, complemented
14#22590821C212yesmaximal, complemented
15C2×#17985898C211yesmaximal, characteristic, complemented
16#389×D71C212yesmaximal, complemented
17C71×#2316C211yesmaximal, characteristic, complemented
18C22×#11765865C2211yescharacteristic
19#17986480C4116yescomplemented
20#17986479—28no—
21#17986467—28no—
22C2×C4×Dic142C2212yes—
23C2×#14556093C2211yescharacteristic
24C2×#14556093C2211yescharacteristic
25C2×#14556093C2212yes—
26C2×C4×D284C2212yes—
27C2×#14556090C2211yescharacteristic
28C2×#14556090C2211yescharacteristic
29C2×#14556090C2212yes—
30C2×C4×C22⋊D71C2214yes—
31C2×(C22⋊D71)⋊C4C2212yes—
32C2×(C22⋊D71)⋊C4C2214yes—
33C2×(C22⋊D71)⋊C4C2212yes—
34C2×#14556087C2211yescharacteristic
35C2×#14556086C2212yes—
36C2×#14556086C2212yes—
37C2×#14556085C2212yes—
38C22×C4⋊Dic71C2211yescharacteristic
39C22×C4⋊Dic71C2212yes—
40C2×C4⋊C4×D71C2212yes—
41C2×C4⋊C4×D71C2214yes—
42C2×C4⋊C4×D71C2212yes—
43C22×C4×Dic71C2211yescharacteristic
44C2×C42×D71C2212yes—
45#17985898C2212yes—
46#17985898C2212yes—
47#17985898C2212yes—
48#17985898C2212yes—
49#17985897C2212yes—
50#17985897C2212yes—
51#17985896C2214yes—
52#17985896C2214yes—
53#17985895C2211yescharacteristic
54#17985895C2211yescharacteristic
55#17985895C2211yescharacteristic
56#17985895C2211yescharacteristic
57#17985894C2214yes—
58#17985894C2214yes—
59#17985873C2214yes—
60#17985873C2214yes—
61#17985871C2212yes—
62#17985871C2214yes—
63#17985871C2212yes—
64#17985870C2214yes—
65#17985870C2214yes—
66#17985868C2214yes—
67#17985868C2212yes—
68#17985864C2212yes—
69#17985863C2214yes—
70#17985858C2214yes—
71#17985856C2214yes—
72C4⋊C4×Dic71C2214yes—
73C4×Dic71⋊C4C2212yes—
74C4×Dic71⋊C4C2212yes—
75#17985850C2214yes—
76C2×C71⋊#95C2212yes—
77#95×D71C2214yes—
78C2×#117×C71C2211yescharacteristic
79C2×#117×C71C2211yescharacteristic
80C22×C4⋊C4×C71C2211yescharacteristic
81#389×C71C2212yes—
82#389×C71C2212yes—
83#389×C71C2212yes—
84#389×C71C2212yes—
85#380×C71C2214yes—
86C2×#11765865C2×C418yes—
87C2×#11765865D418yes—
88C2×#11765865Q818yes—
89C22×Dic142C2311yescharacteristic
90C22×D284C2311yescharacteristic
91C22×C22⋊D71C2312yes—
92C23×Dic71C2311yescharacteristic
93C23×Dic71C2311yescharacteristic
94C23×Dic71C2312yes—
95C22×C4×D71C2312yes—
96C22×C4×D71C2312yes—
97C22×C4×D71C2314yes—
98C22×C4×D71C2314yes—
99C22×C4×D71C2312yes—
100C4×Dic142—28no—
101#14556093—24no—
102#14556093—24no—
103#14556093C2×C4116yescomplemented
104C4×D284—28no—
105#14556090—24no—
106#14556090—24no—
107#14556090C2×C4116yescomplemented
108C4×C22⋊D71C2×C4132yescomplemented
109(C22⋊D71)⋊C4—28no—
110(C22⋊D71)⋊C4—28no—
111(C22⋊D71)⋊C4—216no—
112#14556087C2×C418yescomplemented
113#14556086—28no—
114#14556086C2×C4116yescomplemented
115#14556085—28no—
116C2×C4⋊Dic71—24no—
117C2×C4⋊Dic71—44no—
118C2×C4⋊Dic71C2314yes—
119C2×C4⋊Dic71C2312yes—
120C2×C4⋊Dic71C2312yes—
121C2×C4⋊Dic71C2314yes—
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×Dic71⋊C4C2312yes—
125C2×Dic71⋊C4C2312yes—
126C2×Dic71⋊C4C2312yes—
127C2×Dic71⋊C4C2314yes—
128C2×Dic71⋊C4C2312yes—
129C2×Dic71⋊C4C2314yes—
130C2×Dic71⋊C4C2312yes—
131C2×Dic71⋊C4C2312yes—
132C2×Dic71⋊C4C2314yes—
133C2×Dic71⋊C4C2314yes—
134C4⋊C4×D71—28no—
135C4⋊C4×D71—48no—
136C4⋊C4×D71C2×C4116yescomplemented
137C2×C22⋊Dic71C2312yes—
138C2×(C2×D71)⋊C4C2312yes—
139C2×(C2×D71)⋊C4C2314yes—
140C2×(C2×D71)⋊C4C2312yes—
141C2×(C2×D71)⋊C4C2314yes—
142C2×C4×Dic71—24no—
143C2×C4×Dic71C2312yes—
144C2×C4×Dic71C2314yes—
145C2×C4×Dic71C2311yescharacteristic
146C2×C4×Dic71C2311yescharacteristic
147C2×C4×Dic71C2312yes—
148C2×C4×Dic71C2311yescharacteristic
149C2×C4×Dic71C2311yescharacteristic
150C2×C4×Dic71C2314yes—
151C2×C4×Dic71C2312yes—
152C42×D71—28no—
153C71⋊#95C2312yes—
154C71⋊#95C2314yes—
155C71⋊#95C2314yes—
156C71⋊#95C2314yes—
157C71⋊#95C2312yes—
158C71⋊#95C2312yes—
159C71⋊#95C2312yes—
160C71⋊#95C2314yes—
161C23×C4×C71C2312yes—
162C23×C4×C71C2311yescharacteristic
163#117×C71—24no—
164#117×C71—24no—
165C2×C4⋊C4×C71C2×C418yescomplemented
166C2×C4⋊C4×C71C2311yescharacteristic
167C2×C4⋊C4×C71C2311yescharacteristic
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2314yes—
171C2×C4⋊C4×C71C2314yes—
172C2×C4⋊C4×C71C2312yes—
173C2×C4⋊C4×C71C2312yes—
174C2×C22⋊C4×C71C2312yes—
175C2×C22⋊C4×C71C2312yes—
176C2×C42×C71C2312yes—
177C2×C42×C71C2312yes—
178#95×C71C2314yes—
179#95×C71C2314yes—
180C23×D71C2412yes—
181#11765865C4⋊C4164yescomplemented
182C2×Dic142C22×C414yes—
183C2×Dic142C2×D414yes—
184C2×Dic142C2×Q814yes—
185C2×D284C22×C414yes—
186C2×D284C2×D414yes—
187C2×D284C2×Q814yes—
188C2×C22⋊D71C22×C418yes—
189C2×C22⋊D71C2×D418yes—
190C2×C22⋊D71C2×Q818yes—
191C22×Dic71—22no—
192C22×Dic71—22no—
193C22×Dic71—24no—
194C22×Dic71—22no—
195C22×Dic71—22no—
196C22×Dic71—41no—
197C22×Dic71—41no—
198C22×Dic71—42no—
199C22×Dic71—42no—
200C22×Dic71C2414yes—
201C22×Dic71C2411yescharacteristic
202C22×Dic71C2411yescharacteristic
203C22×Dic71C2412yes—
204C22×Dic71C2412yes—
205C22×Dic71C2411yescharacteristic
206C22×Dic71C2411yescharacteristic
207C22×Dic71C2412yes—
208C2×C4×D71—24no—
209C2×C4×D71—24no—
210C2×C4×D71—24no—
211C2×C4×D71—24no—
212C2×C4×D71—28no—
213C2×C4×D71—44no—
214C2×C4×D71—42no—
215C2×C4×D71—42no—
216C2×C4×D71—44no—
217C2×C4×D71—44no—
218C2×C4×D71—44no—
219C2×C4×D71C22×C4116yes—
220C2×C4×D71C22×C418yes—
221C2×C4×D71C2×D418yes—
222C2×C4×D71C2×Q818yes—
223C4⋊Dic71—24no—
224C4⋊Dic71—24no—
225C4⋊Dic71—28no—
226C4⋊Dic71—44no—
227C4⋊Dic71C22×C414yes—
228C4⋊Dic71C22×C414yes—
229Dic71⋊C4—28no—
230Dic71⋊C4—24no—
231Dic71⋊C4—24no—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234Dic71⋊C4—44no—
235Dic71⋊C4—42no—
236Dic71⋊C4—44no—
237Dic71⋊C4—42no—
238Dic71⋊C4C22×C4116yes—
239C22⋊Dic71C22×C418yes—
240(C2×D71)⋊C4—24no—
241(C2×D71)⋊C4—24no—
242(C2×D71)⋊C4—28no—
243(C2×D71)⋊C4C22×C4116yes—
244C4×Dic71—22no—
245C4×Dic71—22no—
246C4×Dic71—22no—
247C4×Dic71—22no—
248C4×Dic71—24no—
249C4×Dic71—24no—
250C4×Dic71—28no—
251C4×Dic71C22×C4116yes—
252C4×Dic71C22×C418yes—
253C24×C71C2411yescharacteristic
254C22×C4×C71—42no—
255C22×C4×C71—42no—
256C22×C4×C71C22×C418yes—
257C22×C4×C71C22×C414yes—
258C22×C4×C71C2×D414yes—
259C22×C4×C71C2×Q814yes—
260C22×C4×C71C2412yes—
261C22×C4×C71C2412yes—
262C22×C4×C71C2412yes—
263C22×C4×C71C2412yes—
264C22×C4×C71C2414yes—
265C22×C4×C71C2411yescharacteristic
266C22×C4×C71C2411yescharacteristic
267C4⋊C4×C71—22no—
268C4⋊C4×C71—22no—
269C4⋊C4×C71—22no—
270C4⋊C4×C71—22no—
271C4⋊C4×C71—44no—
272C4⋊C4×C71—44no—
273C4⋊C4×C71C22×C418yes—
274C4⋊C4×C71C22×C418yes—
275C22⋊C4×C71—24no—
276C22⋊C4×C71—24no—
277C42×C71—24no—
278C42×C71—24no—
279C23×C71—21no—
280C23×C71—21no—
281C23×C71—21no—
282C23×C71—21no—
283C23×C71C23×C412yes—
284C23×C71C22×D412yes—
285C23×C71C22×Q812yes—
286C23×C71C2511yescharacteristic
287C22×D71—22no—
288C22×D71—22no—
289C22×D71—22no—
290C22×D71—22no—
291C22×D71C23×C414yes—
292C22×D71C22×D414yes—
293C22×D71C22×Q814yes—
294C2×C4×C71—24no—
295C2×C4×C71—24no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—48no—
309C2×C4×C71C2×C4⋊C4116yescomplemented
310C2×C4×C71C23×C418yes—
311C2×C4×C71C23×C412yes—
312C2×C4×C71C23×C412yes—
313C2×C4×C71C22×D412yes—
314C2×C4×C71C22×D412yes—
315C2×C4×C71C22×Q812yes—
316C2×C4×C71C22×Q812yes—
317C22⋊D71C2×C4⋊C4132yescomplemented
318C2×Dic71—21no—
319C2×Dic71—21no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—21no—
325C2×Dic71—21no—
326C2×Dic71—21no—
327C2×Dic71—21no—
328C2×Dic71—24no—
329C2×Dic71—24no—
330C2×Dic71—21no—
331C2×Dic71—21no—
332C2×Dic71—21no—
333C2×Dic71—21no—
334C2×Dic71—24no—
335C2×Dic71—44no—
336C2×Dic71—44no—
337C2×Dic71—84no—
338C2×Dic71C23×C414yes—
339C2×Dic71C23×C414yes—
340C2×Dic71C23×C414yes—
341C2×Dic71C22×D414yes—
342C2×Dic71C22×Q814yes—
343C2×Dic71H(5,𝔽2)12yes—
344C2×Dic712−1+412yes—
345D284C2×C4⋊C4116yescomplemented
346C4×D71—416no—
347C4×D71—48no—
348C4×D71—48no—
349C4×D71—88no—
350C4×D71C2×C4⋊C4132yescomplemented
351Dic142C2×C4⋊C4116yescomplemented
352C22×C71—22no—
353C22×C71—22no—
354C22×C71—22no—
355C22×C71—22no—
356C22×C71—22no—
357C22×C71—22no—
358C22×C71C22×C4⋊C414yes—
359C22×C71C24×C411yescharacteristic
360C22×C71C23×D411yescharacteristic
361C22×C71C23×Q811yescharacteristic
362C22×C71C2×H(5,𝔽2)11yescharacteristic
363C22×C71C2×2−1+411yescharacteristic
364C22×C71#58511yescharacteristic
365C22×C71#58511yescharacteristic
366C2×D71—24no—
367C2×D71—24no—
368C2×D71—24no—
369C2×D71—24no—
370C2×D71—24no—
371C2×D71—24no—
372C2×D71C22×C4⋊C418yes—
373C4×C71—28no—
374C4×C71—42no—
375C4×C71—42no—
376C4×C71—42no—
377C4×C71—42no—
378C4×C71C22×C4⋊C414yes—
379C4×C71C22×C4⋊C414yes—
380Dic71—24no—
381Dic71—24no—
382Dic71—22no—
383Dic71—22no—
384Dic71—44no—
385Dic71—41no—
386Dic71—41no—
387Dic71C22×C4⋊C418yes—
388#34250—711nomaximal, Sylow
389C2×C71—24no—
390C2×C71C23×C4⋊C411yescharacteristic
391C2×C71C4×H(5,𝔽2)11yescharacteristic
392C2×C71C4×2−1+411yescharacteristic
393C2×C71#348811yescharacteristic
394C2×C71#348911yescharacteristic
395C2×C71#350311yescharacteristic
396C2×C71#350411yescharacteristic
397D71—28no—
398C2×#520—711no—
399C2×#520—711no—
400C2×C4×#41—711no—
401#2351—712no—
402Q8×C4⋊C4—712no—
403#2349—712no—
404#2349—714no—
405D4×C4⋊C4—712no—
406D4×C4⋊C4—714no—
407#2317—712no—
408#2317—711no—
409#2316—712no—
410#2316D7111yescharacteristic, complemented
411#2296—712no—
412#2296—711no—
413C2×#389—712no—
414C2×#389—711no—
415C71#3425011yescharacteristic, complemented, Sylow
416C22×#41—711no—
417#520—7116no—
418#520—1428no—
419C4×#41—1428no—
420C2×C4×Q8—712no—
421C2×C4×Q8—711no—
422C2×C4×Q8—711no—
423C2×C4×Q8—712no—
424C2×C4×D4—714no—
425C2×C4×D4—712no—
426C2×C4×D4—711no—
427C2×C4×D4—711no—
428C2×C4×D4—712no—
429C2×C4×D4—714no—
430C2×C4×D4—712no—
431C2×C4×D4—712no—
432C2×#117—711no—
433C2×#117—712no—
434C2×#117—712no—
435C2×#117—712no—
436C2×#117C2×D7111yescharacteristic
437C2×#117C2×D7111yescharacteristic
438C22×C4⋊C4—712no—
439C22×C4⋊C4—714no—
440C22×C4⋊C4—712no—
441C22×C4⋊C4—711no—
442C22×C4⋊C4—712no—
443C22×C4⋊C4C2×D7111yescharacteristic
444C22×C42—711no—
445C22×C42—712no—
446#389—711no—
447#389—712no—
448#389—714no—
449#389—711no—
450#389—712no—
451#389—714no—
452#389—712no—
453#389—711no—
454#389—711no—
455#389—712no—
456#389—712no—
457#389—712no—
458#389—714no—
459#389—714no—
460#389C2×D7112yes—
461#389C2×D7112yes—
462#389C2×D7112yes—
463#389C2×D7112yes—
464#385—714no—
465#385—714no—
466#385—714no—
467#385—712no—
468#385—712no—
469#385—714no—
470#385—714no—
471#384—712no—
472#384—714no—
473#382—712no—
474#382—714no—
475#380—714no—
476#380—714no—
477#380C2×D7114yes—
478C4×C4⋊C4—714no—
479C4×C4⋊C4—712no—
480C4×C4⋊C4—712no—
481C4×C4⋊C4—714no—
482C2×#95—712no—
483C2×#95—714no—
484C2×#41—718no—
485C2×#41—718no—
486C2×#41—718no—
487C22×Q8—711no—
488C22×D4—712no—
489C22×D4—711no—
490C23×C4—714no—
491C23×C4—712no—
492C23×C4—714no—
493C23×C4—711no—
494C23×C4—711no—
495C23×C4—712no—
496C23×C4—712no—
497C23×C4—712no—
498C23×C4C22×D7112yes—
499C23×C4C22×D7111yescharacteristic
500C4×Q8—7116no—
501C4×Q8—1428no—
502C4×Q8—1424no—
503C4×Q8—1424no—
504C4×D4—7132no—
505C4×D4—7116no—
506C4×D4—1428no—
507C4×D4—1428no—
508C4×D4—1428no—
509C4×D4—14216no—
510C4×D4—1424no—
511C4×D4—1424no—
512#117—24no—
513#117—24no—
514#117—718no—
515#117—7116no—
516#117—1428no—
517#117—1428no—
518C2×C4⋊C4—2848no—
519C2×C4⋊C4—2844no—
520C2×C4⋊C4—714no—
521C2×C4⋊C4—714no—
522C2×C4⋊C4—712no—
523C2×C4⋊C4—714no—
524C2×C4⋊C4—712no—
525C2×C4⋊C4—711no—
526C2×C4⋊C4—714no—
527C2×C4⋊C4—711no—
528C2×C4⋊C4—7116no—
529C2×C4⋊C4—712no—
530C2×C4⋊C4—712no—
531C2×C4⋊C4—714no—
532C2×C4⋊C4—714no—
533C2×C4⋊C4—712no—
534C2×C4⋊C4—712no—
535C2×C4⋊C4—712no—
536C2×C4⋊C4—712no—
537C2×C4⋊C4—1428no—
538C2×C4⋊C4—1424no—
539C2×C4⋊C4C4×D7118yescomplemented
540C2×C4⋊C4C22×D7111yescharacteristic
541C2×C4⋊C4C22×D7111yescharacteristic
542C2×C4⋊C4C22×D7111yescharacteristic
543C2×C4⋊C4C22×D7111yescharacteristic
544C2×C4⋊C4C22×D7114yes—
545C2×C4⋊C4C22×D7114yes—
546C2×C4⋊C4C22×D7112yes—
547C2×C4⋊C4C22×D7112yes—
548C2×C22⋊C4—712no—
549C2×C22⋊C4—714no—
550C2×C22⋊C4—712no—
551C2×C22⋊C4—714no—
552C2×C22⋊C4—712no—
553C2×C22⋊C4C22×D7112yes—
554C2×C22⋊C4C22×D7112yes—
555C2×C42—714no—
556C2×C42—712no—
557C2×C42—711no—
558C2×C42—714no—
559C2×C42—712no—
560C2×C42—712no—
561C2×C42—711no—
562C2×C42—711no—
563C2×C42—711no—
564C2×C42—1428no—
565C2×C42—1424no—
566C2×C42C22×D7112yes—
567C2×C42C22×D7112yes—
568#95—712no—
569#95—714no—
570#95—714no—
571#95—714no—
572#95—712no—
573#95—712no—
574#95—712no—
575#95—714no—
576#95C22×D7114yes—
577#95C22×D7114yes—
578C24—712no—
579C24C23×D7111yescharacteristic
580#41—7164no—
581C2×Q8—714no—
582C2×Q8—714no—
583C2×Q8—714no—
584C2×D4—718no—
585C2×D4—718no—
586C2×D4—718no—
587C2×D4—714no—
588C2×D4—714no—
589C2×D4—714no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—2844no—
593C22×C4—2844no—
594C22×C4—2842no—
595C22×C4—2842no—
596C22×C4—2844no—
597C22×C4—2844no—
598C22×C4—2841no—
599C22×C4—2841no—
600C22×C4—2842no—
601C22×C4—2842no—
602C22×C4—7116no—
603C22×C4—712no—
604C22×C4—718no—
605C22×C4—718no—
606C22×C4—718no—
607C22×C4—711no—
608C22×C4—712no—
609C22×C4—712no—
610C22×C4—711no—
611C22×C4—711no—
612C22×C4—714no—
613C22×C4—711no—
614C22×C4—1424no—
615C22×C4—1424no—
616C22×C4—1424no—
617C22×C4—1424no—
618C22×C4—1428no—
619C22×C4—1422no—
620C22×C4—1422no—
621C22×C4—1422no—
622C22×C4—1422no—
623C22×C4—1424no—
624C22×C4C2×C4×D7118yes—
625C22×C4C2×C4×D7114yes—
626C22×C4D4×D7114yes—
627C22×C4Q8×D7114yes—
628C22×C4C23×D7112yes—
629C22×C4C23×D7112yes—
630C22×C4C23×D7112yes—
631C22×C4C23×D7112yes—
632C22×C4C23×D7114yes—
633C22×C4C23×D7111yescharacteristic
634C22×C4C23×D7111yescharacteristic
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—2844no—
642C4⋊C4—2842no—
643C4⋊C4—2844no—
644C4⋊C4—2842no—
645C4⋊C4—2844no—
646C4⋊C4—7116no—
647C4⋊C4—714no—
648C4⋊C4—714no—
649C4⋊C4—1424no—
650C4⋊C4—1424no—
651C4⋊C4—1428no—
652C4⋊C4—1424no—
653C4⋊C4—1424no—
654C4⋊C4—1428no—
655C4⋊C4—1424no—
656C4⋊C4—1424no—
657C4⋊C4C2×C4×D7118yes—
658C4⋊C4C2×C4×D7118yes—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—718no—
662C22⋊C4—7116no—
663C22⋊C4—1428no—
664C22⋊C4—1424no—
665C22⋊C4—1424no—
666C42—24no—
667C42—24no—
668C42—7116no—
669C42—718no—
670C42—1424no—
671C42—1424no—
672C42—1428no—
673C42—1422no—
674C42—1422no—
675C42—1422no—
676C42—1422no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—714no—
682C23—714no—
683C23—714no—
684C23—1422no—
685C23—1422no—
686C23—1422no—
687C23—1422no—
688C23C22×C4×D7112yes—
689C23C2×D4×D7112yes—
690C23C2×Q8×D7112yes—
691C23C24×D7111yescharacteristic
692Q8—7116no—
693D4—7132no—
694D4—7116no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—48no—
710C2×C4—28416no—
711C2×C4—2848no—
712C2×C4—2848no—
713C2×C4—2844no—
714C2×C4—2844no—
715C2×C4—5688no—
716C2×C4—5684no—
717C2×C4—714no—
718C2×C4—714no—
719C2×C4—714no—
720C2×C4—7132no—
721C2×C4—714no—
722C2×C4—714no—
723C2×C4—712no—
724C2×C4—712no—
725C2×C4—1421no—
726C2×C4—1421no—
727C2×C4—1424no—
728C2×C4—1421no—
729C2×C4—1424no—
730C2×C4—1421no—
731C2×C4—1421no—
732C2×C4—1421no—
733C2×C4—1424no—
734C2×C4—1421no—
735C2×C4—1421no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1421no—
740C2×C4—1422no—
741C2×C4—1421no—
742C2×C4C4⋊C4×D71116yescomplemented
743C2×C4C22×C4×D7118yes—
744C2×C4C22×C4×D7112yes—
745C2×C4C22×C4×D7112yes—
746C2×C4C2×D4×D7112yes—
747C2×C4C2×D4×D7112yes—
748C2×C4C2×Q8×D7112yes—
749C2×C4C2×Q8×D7112yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—718no—
757C22—1424no—
758C22—1424no—
759C22—1424no—
760C22—1424no—
761C22—1424no—
762C22—1424no—
763C22C2×C4⋊C4×D7114yes—
764C22C23×C4×D7111yescharacteristic
765C22C22×D4×D7111yescharacteristic
766C22C22×Q8×D7111yescharacteristic
767C22H(5,𝔽2)×D7111yescharacteristic
768C222−1+4×D7111yescharacteristic
769C22#1798683411yescharacteristic
770C22#1798683611yescharacteristic
771C4—28no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—2841no—
777C4—2844no—
778C4—2841no—
779C4—718no—
780C4—1422no—
781C4—1422no—
782C4—1424no—
783C4—1424no—
784C4C2×C4⋊C4×D7114yes—
785C4C2×C4⋊C4×D7114yes—
786C2—24no—
787C2—1428no—
788C2C22×C4⋊C4×D7111yescharacteristic
789C2#2260154411yescharacteristic
790C2#2260154911yescharacteristic
791C2#2260200411yescharacteristic
792C2#2260201511yescharacteristic
793C2#2260215511yescharacteristic
794C2#2260216311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2316C2
socle, cosocleC23×C71C25
prime radicalC22×#11765865C22
hypercenter#2316D71
hypocenterC71#34250
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2316

Complements

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

NH ≅ G/Ntype
4. #22591259C2semidirect
5. #22591254C2semidirect
6. #22591249C2semidirect
7. #22591244C2semidirect
8. #22591241C2semidirect
9. #22591236C2semidirect
10. #22590962C2semidirect
11. #22590960C2semidirect
12. #22590955C2semidirect
13. #22590822C2semidirect
14. #22590821C2semidirect
15. C2×#17985898C2semidirect
16. #389×D71C2semidirect
17. C71×#2316C2semidirect
19. #17986480C4semidirect
103. #14556093C2×C4semidirect
107. #14556090C2×C4semidirect
108. C4×C22⋊D71C2×C4semidirect
112. #14556087C2×C4semidirect
114. #14556086C2×C4semidirect
136. C4⋊C4×D71C2×C4semidirect
165. C2×C4⋊C4×C71C2×C4semidirect
181. #11765865C4⋊C4semidirect
309. C2×C4×C71C2×C4⋊C4semidirect
317. C22⋊D71C2×C4⋊C4semidirect
345. D284C2×C4⋊C4semidirect
350. C4×D71C2×C4⋊C4semidirect
351. Dic142C2×C4⋊C4semidirect
410. #2316D71semidirect
415. C71#34250semidirect
539. C2×C4⋊C4C4×D71semidirect
742. C2×C4C4⋊C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179864802
C2×#179864792
C2×#179864672
#225912592
#225912542
#225912492
#225912442
#225912412
#225912362
#225909622
#225909602
#225909552
#225908222
#225908212
C2×#179858982
#389×D712
C71×#23162
#3425071