Finite Group Databasebeta

← #26376556

Subgroups — #26376556

Order 12032.

3534 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689631C211yesmaximal, characteristic
2C2×#15689602C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#20246407C212yesmaximal, complemented
5#20246401C212yesmaximal, complemented
6#20246396C212yesmaximal, complemented
7#20246390C212yesmaximal, complemented
8#20246316C212yesmaximal, complemented
9#20246312C212yesmaximal, complemented
10#20246289C212yesmaximal, complemented
11#20246286C212yesmaximal, complemented
12#20246060C211yesmaximal, characteristic, complemented
13#20246057C211yesmaximal, characteristic, complemented
14#20246054C211yesmaximal, characteristic, complemented
15#20246007C211yesmaximal, characteristic, complemented
16#20245975C211yesmaximal, characteristic, complemented
17#20245893C211yesmaximal, characteristic, complemented
18C4×#13093994C211yesmaximal, characteristic, complemented
19#20245889C211yesmaximal, characteristic, complemented
20C4×#13093992C211yesmaximal, characteristic, complemented
21#20245768C211yesmaximal, characteristic, complemented
22#20245743C211yesmaximal, characteristic, complemented
23C47×#2322C211yesmaximal, characteristic, complemented
24C22×#10625352C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27C23×C4×D47C2211yescharacteristic
28#15689631C4116yescomplemented
29C2×#13094007C2211yescharacteristic
30C2×#13094002C2212yes—
31C2×#13093997C2212yes—
32C2×#13093994C2211yescharacteristic
33C2×#13093992C2211yescharacteristic
34#15689602—28no—
35C2×C4×Dic94C2211yescharacteristic, complemented
36C2×#13093989C2211yescharacteristic, complemented
37C2×C4×D188C2212yes—
38C2×D4×Dic47C2211yescharacteristic
39C2×#13093986C2212yes—
40C2×#13093986C2212yes—
41C2×C4×C22⋊D47C2211yescharacteristic
42C2×C4×C22⋊D47C2212yes—
43C2×C4×C22⋊D47C2211yescharacteristic, complemented
44C2×(C22⋊D47)⋊C4C2211yescharacteristic
45C2×(C22⋊D47)⋊C4C2212yes—
46C2×(C22⋊D47)⋊C4C2212yes—
47C2×(C22⋊D47)⋊C4C2211yescharacteristic, complemented
48C2×#13093981C2211yescharacteristic, complemented
49C2×#13093980C2211yescharacteristic
50C2×#13093980C2211yescharacteristic
51C2×#13093980C2211yescharacteristic
52C2×#13093980C2211yescharacteristic, complemented
53C22×C4⋊Dic47C2211yescharacteristic
54C22×Dic47⋊C4C2211yescharacteristic
55C22×Dic47⋊C4C2211yescharacteristic
56C22×Dic47⋊C4C2211yescharacteristic, complemented
57C2×C4⋊C4×D47—28no—
58C2×C4⋊C4×D47C2212yes—
59C2×C4⋊C4×D47C2212yes—
60C2×C4⋊C4×D47C2212yes—
61C2×C4⋊C4×D47C2212yes—
62C2×C4⋊C4×D47C2211yescharacteristic, complemented
63#15689027C2212yescomplemented
64#15689023C2212yescomplemented
65#15689022C2212yescomplemented
66#15689020C2212yescomplemented
67#15689020C2212yescomplemented
68#15689018C2212yescomplemented
69#15689018C2212yescomplemented
70#15689016C2212yescomplemented
71#15689015C2212yescomplemented
72#15689013C2212yescomplemented
73#15689010C2212yescomplemented
74#15689009C2212yescomplemented
75#15689004C2212yescomplemented
76#15689003C2211yescharacteristic
77#15689002C2211yescharacteristic
78#15689001C2212yes—
79#15689001C2212yes—
80#15689000C2211yescharacteristic
81#15688999C2212yes—
82#15688999C2212yes—
83#15688998C2211yescharacteristic
84#15688998C2212yescomplemented
85#15688997C2212yes—
86#15688997C2212yes—
87#15688997C2212yescomplemented
88#15688996C2211yescharacteristic
89#15688995C2211yescharacteristic
90#15688994C2212yes—
91#15688994C2212yes—
92#15688994C2212yescomplemented
93#15688992C2212yescomplemented
94#15688987C2212yescomplemented
95#15688986C2211yescharacteristic
96#15688982C2212yes—
97#15688982C2212yes—
98#15688982C2212yescomplemented
99#15688981C2212yescomplemented
100#15688978C2211yescharacteristic
101#15688978C2211yescharacteristic
102C4×Dic47⋊C4C2212yescomplemented
103C4×Dic47⋊C4C2212yescomplemented
104#15688974C2212yescomplemented
105#15688974C2212yescomplemented
106C22⋊C4×Dic47C2211yescharacteristic
107C22⋊C4×Dic47C2211yescharacteristic
108C4×(C2×D47)⋊C4C2212yes—
109C4×(C2×D47)⋊C4C2212yes—
110C4×C22⋊Dic47C2211yescharacteristic
111#15688970C2212yes—
112#15688970C2212yes—
113#15688970C2212yes—
114#15688970C2212yes—
115C2×#123×C47C2211yescharacteristic
116C2×C4×D4×C47C2211yescharacteristic
117C22×C4⋊C4×C47C2211yescharacteristic
118C47×#389C2212yescomplemented
119C47×#388C2212yescomplemented
120C47×#387C2212yescomplemented
121C47×#386C2211yescharacteristic
122C47×#385C2211yescharacteristic
123C47×#385C2212yescomplemented
124C47×#381C2211yescharacteristic
125C4×C22⋊C4×C47C2211yescharacteristic
126C24×D47C2311yescharacteristic
127C2×#10625352—24no—
128C2×#10625352—24no—
129C2×#10625352C2×C418yescomplemented
130C22×Dic94C2311yescharacteristic
131C22×D188C2312yes—
132C22×C22⋊D47C2312yes—
133C22×C22⋊D47C2311yescharacteristic
134C22×C22⋊D47C2311yescharacteristic
135C23×Dic47C2311yescharacteristic
136C23×Dic47C2311yescharacteristic
137C23×Dic47C2311yescharacteristic
138C23×Dic47C2311yescharacteristic
139C23×Dic47C2311yescharacteristic
140C22×C4×D47—24no—
141C22×C4×D47—24no—
142C22×C4×D47—24no—
143C22×C4×D47—24no—
144C22×C4×D47—44no—
145C22×C4×D47—44no—
146C22×C4×D47C2×C418yescomplemented
147C22×C4×D47C2312yes—
148C22×C4×D47C2312yes—
149C22×C4×D47C2312yes—
150C22×C4×D47C2312yes—
151C22×C4×D47C2312yes—
152C22×C4×D47C2312yes—
153C22×C4×D47C2311yescharacteristic
154C22×C4×D47C2311yescharacteristic
155C22×C4×D47C2311yescharacteristic
156#13094007C2×C418yescomplemented
157#13094002C2×C4116yescomplemented
158#13093997C2×C4116yescomplemented
159#13093994C2×C418yescomplemented
160#13093992C2×C418yescomplemented
161C4×Dic94—24no—
162#13093989—24no—
163C4×D188—44no—
164D4×Dic47—24no—
165#13093986—44no—
166#13093986C2×C4116yescomplemented
167C4×C22⋊D47—24no—
168C4×C22⋊D47—24no—
169C4×C22⋊D47—44no—
170(C22⋊D47)⋊C4—24no—
171(C22⋊D47)⋊C4—24no—
172(C22⋊D47)⋊C4—44no—
173(C22⋊D47)⋊C4C2×C4116yescomplemented
174#13093981—24no—
175#13093980—24no—
176#13093980—24no—
177#13093980—24no—
178#13093980C2×C418yescomplemented
179C2×C4⋊Dic47—24no—
180C2×C4⋊Dic47C2311yescharacteristic
181C2×C4⋊Dic47C2312yes—
182C2×C4⋊Dic47C2312yes—
183C2×C4⋊Dic47C2312yes—
184C2×Dic47⋊C4—24no—
185C2×Dic47⋊C4—24no—
186C2×Dic47⋊C4D418yescomplemented
187C2×Dic47⋊C4C2312yes—
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2311yescharacteristic
190C2×Dic47⋊C4C2311yescharacteristic
191C2×Dic47⋊C4C2311yescharacteristic
192C2×Dic47⋊C4C2311yescharacteristic
193C2×Dic47⋊C4C2312yes—
194C2×Dic47⋊C4C2312yes—
195C2×Dic47⋊C4C2312yes—
196C2×Dic47⋊C4C2312yes—
197C2×Dic47⋊C4C2312yes—
198C2×Dic47⋊C4C2311yescharacteristic
199C2×Dic47⋊C4C2311yescharacteristic
200C2×Dic47⋊C4C2311yescharacteristic
201C2×Dic47⋊C4C2311yescharacteristic
202C4⋊C4×D47—28no—
203C4⋊C4×D47—28no—
204C4⋊C4×D47—28no—
205C4⋊C4×D47—28no—
206C4⋊C4×D47—24no—
207C2×C22⋊Dic47C2311yescharacteristic
208C2×C22⋊Dic47C2311yescharacteristic
209C2×C22⋊Dic47C2311yescharacteristic
210C2×C22⋊Dic47C2312yes—
211C2×C22⋊Dic47C2311yescharacteristic
212C2×(C2×D47)⋊C4C2312yes—
213C2×(C2×D47)⋊C4C2312yes—
214C2×(C2×D47)⋊C4C2312yes—
215C2×(C2×D47)⋊C4C2312yes—
216C2×(C2×D47)⋊C4C2311yescharacteristic
217C2×(C2×D47)⋊C4C2311yescharacteristic
218C2×(C2×D47)⋊C4C2312yes—
219C2×(C2×D47)⋊C4C2312yes—
220C2×(C2×D47)⋊C4C2312yes—
221C2×(C2×D47)⋊C4C2312yes—
222C2×(C2×D47)⋊C4C2312yes—
223C2×C4×Dic47C2312yes—
224C2×C4×Dic47C2311yescharacteristic
225C2×C4×Dic47C2311yescharacteristic
226C2×C4×Dic47C2311yescharacteristic
227C2×C4×Dic47C2311yescharacteristic
228C2×C4×Dic47C2311yescharacteristic
229C2×C4×Dic47C2312yes—
230C2×C4×Dic47C2312yes—
231C2×C4×Dic47C2312yes—
232C2×C4×Dic47C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C47⋊#95C2312yes—
237C47⋊#95C2312yes—
238C47⋊#95C2312yes—
239C47⋊#95C2312yes—
240C47⋊#95C2312yes—
241C47⋊#95C2312yes—
242C47⋊#95C2312yes—
243C47⋊#95C2312yes—
244C22×D4×C47C2311yescharacteristic
245C23×C4×C47C2311yescharacteristic
246C23×C4×C47C2311yescharacteristic
247C23×C4×C47C2311yescharacteristic
248C23×C4×C47C2311yescharacteristic
249#123×C47C2×C418yescomplemented
250C4×D4×C47—24no—
251C2×C4⋊C4×C47—24no—
252C2×C4⋊C4×C47C2311yescharacteristic
253C2×C4⋊C4×C47C2312yes—
254C2×C4⋊C4×C47C2312yes—
255C2×C4⋊C4×C47C2312yes—
256C2×C4⋊C4×C47C2312yes—
257C2×C22⋊C4×C47C2311yescharacteristic
258C2×C22⋊C4×C47C2311yescharacteristic
259C2×C22⋊C4×C47C2311yescharacteristic
260C2×C22⋊C4×C47C2312yes—
261C2×C22⋊C4×C47C2311yescharacteristic
262C2×C22⋊C4×C47C2312yes—
263C2×C42×C47C2311yescharacteristic
264C2×C42×C47C2312yes—
265#95×C47C2312yes—
266#95×C47C2312yes—
267#95×C47C2312yes—
268#95×C47C2312yes—
269#95×C47C2312yes—
270C24×C47C2411yescharacteristic
271C24×C47C2411yescharacteristic
272C23×D47—22no—
273C23×D47—22no—
274C23×D47—24no—
275C23×D47—24no—
276C23×D47C22×C414yes—
277C23×D47C2411yescharacteristic
278C23×D47C2412yes—
279C2×D4×C47—22no—
280C2×D4×C47—22no—
281C2×D4×C47C22×C414yes—
282C22×C4×C47—22no—
283C22×C4×C47—22no—
284C22×C4×C47—22no—
285C22×C4×C47—22no—
286C22×C4×C47—42no—
287C22×C4×C47—42no—
288C22×C4×C47—42no—
289C22×C4×C47C22×C414yes—
290C22×C4×C47C2×D414yes—
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2412yes—
293C22×C4×C47C2412yes—
294C22×C4×C47C2411yescharacteristic
295C22×C4×C47C2412yes—
296C22×C4×C47C2411yescharacteristic
297C22×C4×C47C2412yes—
298C22×C4×C47C2411yescharacteristic
299C22×C4×C47C2411yescharacteristic
300C2×C22⋊D47—22no—
301C2×C22⋊D47—22no—
302C2×C22⋊D47—24no—
303C2×C22⋊D47—24no—
304C2×C22⋊D47—22no—
305C2×C22⋊D47—22no—
306C2×C22⋊D47C22×C418yes—
307C2×C22⋊D47C22×C414yes—
308C2×C22⋊D47C22×C414yescomplemented
309C22×Dic47—22no—
310C22×Dic47—22no—
311C22×Dic47—22no—
312C22×Dic47—22no—
313C22×Dic47—42no—
314C22×Dic47—42no—
315C22×Dic47—42no—
316C22×Dic47C22×C414yes—
317C22×Dic47C22×C414yescomplemented
318C22×Dic47C2×D414yes—
319C22×Dic47C2×D414yes—
320C22×Dic47#4114yes—
321C22×Dic47C2411yescharacteristic
322C22×Dic47C2412yes—
323C22×Dic47C2412yes—
324C22×Dic47C2411yescharacteristic
325C22×Dic47C2412yes—
326C22×Dic47C2411yescharacteristic
327C22×Dic47C2411yescharacteristic
328C22×Dic47C2411yescharacteristic
329C22×Dic47C2411yescharacteristic
330C22×Dic47C2411yescharacteristic
331#10625352—232no—
332C2×D188—24no—
333C2×D188—24no—
334C2×D188C22×C418yes—
335C2×C4×D47—232no—
336C2×C4×D47—24no—
337C2×C4×D47—24no—
338C2×C4×D47—22no—
339C2×C4×D47—24no—
340C2×C4×D47—24no—
341C2×C4×D47—22no—
342C2×C4×D47—24no—
343C2×C4×D47—24no—
344C2×C4×D47—24no—
345C2×C4×D47—24no—
346C2×C4×D47—24no—
347C2×C4×D47—24no—
348C2×C4×D47—24no—
349C2×C4×D47—24no—
350C2×C4×D47—22no—
351C2×C4×D47—22no—
352C2×C4×D47—42no—
353C2×C4×D47—42no—
354C2×C4×D47—42no—
355C2×C4×D47—42no—
356C2×C4×D47—416no—
357C2×C4×D47—416no—
358C2×C4×D47—42no—
359C2×C4×D47—42no—
360C2×C4×D47C22×C418yes—
361C2×C4×D47C22×C418yes—
362C2×C4×D47C22×C414yescomplemented
363C2×Dic94—22no—
364C2×Dic94—22no—
365C2×Dic94C22×C414yescomplemented
366C4⋊C4×C47—24no—
367C4⋊C4×C47—24no—
368C4⋊C4×C47—22no—
369C4⋊C4×C47—42no—
370C4⋊C4×C47C22×C418yescomplemented
371C22⋊C4×C47—22no—
372C22⋊C4×C47—22no—
373C22⋊C4×C47—22no—
374C22⋊C4×C47—42no—
375C22⋊C4×C47C22×C414yes—
376C22⋊C4×C47C22×C418yescomplemented
377C42×C47—22no—
378C42×C47—42no—
379C22⋊Dic47—22no—
380C22⋊Dic47—22no—
381C22⋊Dic47—22no—
382C22⋊Dic47—42no—
383C22⋊Dic47C22×C414yes—
384(C2×D47)⋊C4—24no—
385(C2×D47)⋊C4—24no—
386(C2×D47)⋊C4—24no—
387(C2×D47)⋊C4—24no—
388(C2×D47)⋊C4—22no—
389(C2×D47)⋊C4—22no—
390(C2×D47)⋊C4—42no—
391(C2×D47)⋊C4—42no—
392(C2×D47)⋊C4C22×C418yes—
393(C2×D47)⋊C4C22×C418yes—
394(C2×D47)⋊C4C22×C418yescomplemented
395C4⋊Dic47—24no—
396C4⋊Dic47—24no—
397C4⋊Dic47—22no—
398C4⋊Dic47—42no—
399Dic47⋊C4—22no—
400Dic47⋊C4—24no—
401Dic47⋊C4—24no—
402Dic47⋊C4—22no—
403Dic47⋊C4—22no—
404Dic47⋊C4—22no—
405Dic47⋊C4—24no—
406Dic47⋊C4—42no—
407Dic47⋊C4—42no—
408Dic47⋊C4C22×C418yescomplemented
409Dic47⋊C4C22×C418yescomplemented
410Dic47⋊C4C2×D414yes—
411Dic47⋊C4C2×D414yes—
412Dic47⋊C4C2×D414yes—
413Dic47⋊C4C2×D414yes—
414C4×Dic47—22no—
415C4×Dic47—22no—
416C4×Dic47—22no—
417C4×Dic47—22no—
418C4×Dic47—22no—
419C4×Dic47—24no—
420C4×Dic47—42no—
421C4×Dic47—42no—
422C4×Dic47—42no—
423C4×Dic47C22×C418yescomplemented
424C23×C47—22no—
425C23×C47—22no—
426C23×C47—21no—
427C23×C47—21no—
428C23×C47—22no—
429C23×C47—22no—
430C23×C47C23×C412yes—
431C23×C47C23×C412yes—
432C23×C47C22×D412yes—
433C23×C47C2×#4112yes—
434C23×C47C2511yescharacteristic
435C22×D47—28no—
436C22×D47—28no—
437C22×D47—216no—
438C22×D47—28no—
439C22×D47—22no—
440C22×D47—22no—
441C22×D47—22no—
442C22×D47—22no—
443C22×D47—216no—
444C22×D47—21no—
445C22×D47—21no—
446C22×D47—22no—
447C22×D47—22no—
448C22×D47C23×C412yes—
449C22×D47C23×C414yes—
450C22×D47H(5,𝔽2)14yes—
451C22×D472−1+414yes—
452D4×C47—28no—
453C2×C4×C47—28no—
454C2×C4×C47—21no—
455C2×C4×C47—22no—
456C2×C4×C47—21no—
457C2×C4×C47—22no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—21no—
463C2×C4×C47—21no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—44no—
473C2×C4×C47—44no—
474C2×C4×C47—82no—
475C2×C4×C47C23×C414yes—
476C2×C4×C47C23×C414yes—
477C2×C4×C47C23×C412yes—
478C2×C4×C47C22×D412yes—
479C2×C4×C47C22×D412yes—
480C22⋊D47—28no—
481C22⋊D47—216no—
482C22⋊D47—28no—
483C2×Dic47—21no—
484C2×Dic47—21no—
485C2×Dic47—22no—
486C2×Dic47—22no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—28no—
490C2×Dic47—21no—
491C2×Dic47—21no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—22no—
500C2×Dic47—44no—
501C2×Dic47—44no—
502C2×Dic47—82no—
503C2×Dic47C4×D4116yescomplemented
504C2×Dic47C23×C414yes—
505C2×Dic47C23×C412yes—
506C2×Dic47C23×C412yes—
507C2×Dic47C23×C412yes—
508C2×Dic47C22×D412yes—
509C2×Dic47C22×D412yes—
510C2×Dic47C22×D412yes—
511C2×Dic47C22×D412yes—
512C2×Dic47C2×#4112yes—
513C2×Dic47C2×#4112yes—
514D188—216no—
515C4×D47—216no—
516C4×D47—216no—
517C4×D47—28no—
518C4×D47—48no—
519C4×D47—48no—
520C4×D47—48no—
521C4×D47—48no—
522C4×D47—82no—
523C4×D47—82no—
524Dic94—28no—
525#34200—471nomaximal, Sylow
526C22×C47—24no—
527C22×C47—22no—
528C22×C47—22no—
529C22×C47—24no—
530C22×C47—22no—
531C22×C47—24no—
532C22×C47—41no—
533C22×C47—41no—
534C22×C47—42no—
535C22×C47C2×C4×D414yes—
536C22×C47C24×C411yescharacteristic
537C22×C47C23×D411yescharacteristic
538C22×C47C22×#4111yescharacteristic
539C22×C47C2×H(5,𝔽2)12yes—
540C22×C47C2×2−1+412yes—
541C2×D47—232no—
542C2×D47—24no—
543C2×D47—24no—
544C2×D47—24no—
545C2×D47—24no—
546C2×D47—24no—
547C2×D47—24no—
548C2×D47—22no—
549C2×D47—24no—
550C2×D47—41no—
551C2×D47—41no—
552C2×D47—42no—
553C2×D47#52018yescomplemented
554C4×C47—22no—
555C4×C47—24no—
556C4×C47—24no—
557C4×C47—22no—
558C4×C47—22no—
559C4×C47—42no—
560C4×C47—41no—
561C4×C47—41no—
562C4×C47—42no—
563Dic47—22no—
564Dic47—24no—
565Dic47—22no—
566Dic47—22no—
567Dic47—42no—
568Dic47—41no—
569Dic47—41no—
570Dic47—42no—
571Dic47C2×C4×D414yes—
572Dic47C2×C4×D414yes—
573C2×#525—471no—
574C2×#520—471no—
575C23×C4⋊C4—471no—
576#2361—472no—
577#2361—472no—
578#2360—472no—
579#2360—472no—
580#2352—472no—
581#2352—472no—
582D4×C4⋊C4—472no—
583D4×C4⋊C4—472no—
584#2322—471no—
585#2322—471no—
586#2322—471no—
587#2322D4711yescharacteristic, complemented
588#2317—471no—
589#2311—471no—
590C4×#120—471no—
591C4×#120—471no—
592C4×#120—471no—
593C4×#120—471no—
594#2280—471no—
595#2274—471no—
596C2×C47—24no—
597C2×C47—42no—
598C2×C47C22×C4×D411yescharacteristic
599C2×C47C2×#52012yes—
600C2×C47#348411yescharacteristic
601C2×C47#348611yescharacteristic
602C2×C47#349212yes—
603D47—28no—
604D47—42no—
605C22×#41—471no—
606C24×C4—471no—
607C24×C4—471no—
608C24×C4—471no—
609#525—4716no—
610C2×#123—471no—
611C2×#123C2×D4711yescharacteristic
612C2×C22⋊Q8—472no—
613C2×#121—472no—
614C2×#120—471no—
615C2×#120—471no—
616#520—948no—
617C2×C4×Q8—471no—
618C2×C4×Q8—471no—
619C2×C4×D4—471no—
620C2×C4×D4—471no—
621C2×C4×D4—471no—
622C2×C4×D4—472no—
623C2×C4×D4—472no—
624C2×C4×D4—472no—
625C2×C4×D4—472no—
626C2×C4×D4—471no—
627C2×C4×D4—471no—
628C2×C4×D4—472no—
629C2×C4×D4—472no—
630C2×C4×D4C2×D4711yescharacteristic
631C2×#117—471no—
632C2×#117—471no—
633C2×#117—471no—
634C2×#117—471no—
635C2×#117—471no—
636C22×C4⋊C4—471no—
637C22×C4⋊C4—471no—
638C22×C4⋊C4—471no—
639C22×C4⋊C4—471no—
640C22×C4⋊C4—471no—
641C22×C4⋊C4—472no—
642C22×C4⋊C4—472no—
643C22×C4⋊C4—472no—
644C22×C4⋊C4—472no—
645C22×C4⋊C4—948no—
646C22×C4⋊C4C2×D4711yescharacteristic
647#391—472no—
648#390—472no—
649#389—472no—
650#389—472no—
651#389—472no—
652#389—472no—
653#389—472no—
654#389C2×D4712yescomplemented
655#388—472no—
656#388—472no—
657#388—472no—
658#388C2×D4712yescomplemented
659#387—472no—
660#387—472no—
661#387—472no—
662#387C2×D4712yescomplemented
663#386—471no—
664#386—471no—
665#386—471no—
666#386—472no—
667#386—472no—
668#386—472no—
669#386—472no—
670#386C2×D4711yescharacteristic
671#385—471no—
672#385—472no—
673#385—472no—
674#385—472no—
675#385—471no—
676#385—471no—
677#385—472no—
678#385—472no—
679#385—472no—
680#385—472no—
681#385C2×D4711yescharacteristic
682#385C2×D4712yescomplemented
683#384—472no—
684#382—472no—
685#381—471no—
686#381C2×D4711yescharacteristic
687#380—472no—
688#380—472no—
689#380—472no—
690#380—472no—
691#379—471no—
692#379—471no—
693C4×C4⋊C4—472no—
694C4×C4⋊C4—472no—
695C4×C4⋊C4—472no—
696C4×C4⋊C4—472no—
697C4×C22⋊C4—471no—
698C4×C22⋊C4—471no—
699C4×C22⋊C4—471no—
700C4×C22⋊C4—472no—
701C4×C22⋊C4—472no—
702C4×C22⋊C4—472no—
703C4×C22⋊C4—472no—
704C4×C22⋊C4—472no—
705C4×C22⋊C4—472no—
706C4×C22⋊C4C2×D4711yescharacteristic
707C47#3420011yescharacteristic, complemented, Sylow
708C25—471no—
709C2×#41—478no—
710C2×#41—944no—
711C2×#41—944no—
712C22×Q8—471no—
713C22×D4—472no—
714C22×D4—471no—
715C22×D4—471no—
716C22×D4—472no—
717C22×D4C22×D4711yescharacteristic
718C23×C4—471no—
719C23×C4—471no—
720C23×C4—471no—
721C23×C4—478no—
722C23×C4—472no—
723C23×C4—472no—
724C23×C4—471no—
725C23×C4—471no—
726C23×C4—471no—
727C23×C4—472no—
728C23×C4—472no—
729C23×C4—472no—
730C23×C4—472no—
731C23×C4—471no—
732C23×C4—471no—
733C23×C4—944no—
734C23×C4—944no—
735C23×C4—944no—
736C23×C4—944no—
737C23×C4—1884no—
738C23×C4—1884no—
739C23×C4C22×D4711yescharacteristic
740C23×C4C22×D4711yescharacteristic
741C23×C4C22×D4711yescharacteristic
742C23×C4C22×D4711yescharacteristic
743#123—478no—
744#123C4×D4718yescomplemented
745C22⋊Q8—4716no—
746#121—4716no—
747#120—478no—
748#120—478no—
749C4×Q8—944no—
750C4×Q8—944no—
751C4×D4—24no—
752C4×D4—4716no—
753C4×D4—4716no—
754C4×D4—944no—
755C4×D4—944no—
756C4×D4—944no—
757C4×D4—944no—
758C4×D4—944no—
759C4×D4—1884no—
760C4×D4—1884no—
761C4×D4—1884no—
762C4×D4—1884no—
763#117—478no—
764#117—944no—
765#117—944no—
766#117—944no—
767#117—944no—
768C2×C4⋊C4—24no—
769C2×C4⋊C4—478no—
770C2×C4⋊C4—471no—
771C2×C4⋊C4—471no—
772C2×C4⋊C4—471no—
773C2×C4⋊C4—471no—
774C2×C4⋊C4—472no—
775C2×C4⋊C4—472no—
776C2×C4⋊C4—472no—
777C2×C4⋊C4—472no—
778C2×C4⋊C4—472no—
779C2×C4⋊C4—472no—
780C2×C4⋊C4—471no—
781C2×C4⋊C4—471no—
782C2×C4⋊C4—471no—
783C2×C4⋊C4—471no—
784C2×C4⋊C4—471no—
785C2×C4⋊C4—472no—
786C2×C4⋊C4—472no—
787C2×C4⋊C4—472no—
788C2×C4⋊C4—472no—
789C2×C4⋊C4—948no—
790C2×C4⋊C4—948no—
791C2×C4⋊C4—948no—
792C2×C4⋊C4—948no—
793C2×C4⋊C4—944no—
794C2×C4⋊C4—944no—
795C2×C4⋊C4—944no—
796C2×C4⋊C4—944no—
797C2×C4⋊C4C22×D4712yes—
798C2×C4⋊C4C22×D4712yes—
799C2×C4⋊C4C22×D4711yescharacteristic
800C2×C4⋊C4C22×D4712yes—
801C2×C4⋊C4C22×D4712yes—
802C2×C22⋊C4—471no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—472no—
805C2×C22⋊C4—472no—
806C2×C22⋊C4—471no—
807C2×C22⋊C4—471no—
808C2×C22⋊C4—471no—
809C2×C22⋊C4—471no—
810C2×C22⋊C4—471no—
811C2×C22⋊C4—472no—
812C2×C22⋊C4—472no—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—472no—
815C2×C22⋊C4—472no—
816C2×C22⋊C4—472no—
817C2×C22⋊C4—472no—
818C2×C22⋊C4C22×D4711yescharacteristic
819C2×C22⋊C4C22×D4711yescharacteristic
820C2×C22⋊C4C22×D4711yescharacteristic
821C2×C22⋊C4C22×D4712yes—
822C2×C22⋊C4C22×D4711yescharacteristic
823C2×C22⋊C4C22×D4712yes—
824C2×C42—472no—
825C2×C42—471no—
826C2×C42—471no—
827C2×C42—471no—
828C2×C42—471no—
829C2×C42—471no—
830C2×C42—472no—
831C2×C42—472no—
832C2×C42—472no—
833C2×C42—472no—
834C2×C42C22×D4711yescharacteristic
835C2×C42C22×D4712yes—
836#95—472no—
837#95—472no—
838#95—472no—
839#95—472no—
840#95—472no—
841#95—472no—
842#95—472no—
843#95—472no—
844#95—472no—
845#95—472no—
846#95—472no—
847#95C22×D4712yes—
848#95C22×D4712yes—
849#95C22×D4712yes—
850#95C22×D4712yes—
851#95C22×D4712yes—
852C24—472no—
853C24—474no—
854C24—471no—
855C24—944no—
856C24—944no—
857C24—942no—
858C24—942no—
859C24C23×D4711yescharacteristic
860C24C23×D4711yescharacteristic
861#41—9432no—
862C2×Q8—474no—
863C2×Q8—942no—
864C2×Q8—942no—
865C2×D4—22no—
866C2×D4—22no—
867C2×D4—478no—
868C2×D4—474no—
869C2×D4—474no—
870C2×D4—478no—
871C2×D4—944no—
872C2×D4—944no—
873C2×D4—942no—
874C2×D4—942no—
875C2×D4—944no—
876C2×D4—944no—
877C2×D4—942no—
878C2×D4—942no—
879C2×D4C2×C4×D4714yes—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—474no—
888C22×C4—474no—
889C22×C4—474no—
890C22×C4—471no—
891C22×C4—471no—
892C22×C4—474no—
893C22×C4—472no—
894C22×C4—471no—
895C22×C4—471no—
896C22×C4—471no—
897C22×C4—474no—
898C22×C4—478no—
899C22×C4—478no—
900C22×C4—474no—
901C22×C4—471no—
902C22×C4—472no—
903C22×C4—472no—
904C22×C4—471no—
905C22×C4—944no—
906C22×C4—944no—
907C22×C4—942no—
908C22×C4—9432no—
909C22×C4—944no—
910C22×C4—944no—
911C22×C4—942no—
912C22×C4—942no—
913C22×C4—944no—
914C22×C4—944no—
915C22×C4—944no—
916C22×C4—944no—
917C22×C4—944no—
918C22×C4—944no—
919C22×C4—942no—
920C22×C4—942no—
921C22×C4—942no—
922C22×C4—942no—
923C22×C4—942no—
924C22×C4—944no—
925C22×C4—944no—
926C22×C4—1882no—
927C22×C4—1882no—
928C22×C4—1882no—
929C22×C4—1882no—
930C22×C4—1882no—
931C22×C4—1882no—
932C22×C4—18816no—
933C22×C4—18816no—
934C22×C4—1882no—
935C22×C4—1882no—
936C22×C4—1882no—
937C22×C4C2×C4×D4714yes—
938C22×C4D4×D4714yes—
939C22×C4C23×D4711yescharacteristic
940C22×C4C23×D4712yes—
941C22×C4C23×D4712yes—
942C22×C4C23×D4711yescharacteristic
943C22×C4C23×D4712yes—
944C22×C4C23×D4711yescharacteristic
945C22×C4C23×D4712yes—
946C22×C4C23×D4711yescharacteristic
947C22×C4C23×D4711yescharacteristic
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—42no—
952C4⋊C4—478no—
953C4⋊C4—478no—
954C4⋊C4—474no—
955C4⋊C4—474no—
956C4⋊C4—474no—
957C4⋊C4—474no—
958C4⋊C4—944no—
959C4⋊C4—944no—
960C4⋊C4—942no—
961C4⋊C4—942no—
962C4⋊C4—944no—
963C4⋊C4—942no—
964C4⋊C4—944no—
965C4⋊C4—944no—
966C4⋊C4—942no—
967C4⋊C4—942no—
968C4⋊C4—1882no—
969C4⋊C4—1882no—
970C4⋊C4—1882no—
971C4⋊C4C2×C4×D4718yescomplemented
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—42no—
976C22⋊C4—474no—
977C22⋊C4—478no—
978C22⋊C4—478no—
979C22⋊C4—478no—
980C22⋊C4—942no—
981C22⋊C4—944no—
982C22⋊C4—944no—
983C22⋊C4—944no—
984C22⋊C4—944no—
985C22⋊C4—942no—
986C22⋊C4—942no—
987C22⋊C4—942no—
988C22⋊C4—942no—
989C22⋊C4—1882no—
990C22⋊C4—1882no—
991C22⋊C4—1882no—
992C22⋊C4C2×C4×D4714yes—
993C22⋊C4C2×C4×D4718yescomplemented
994C42—22no—
995C42—42no—
996C42—478no—
997C42—944no—
998C42—942no—
999C42—942no—
1000C42—942no—
1001C42—942no—
1002C42—942no—
1003C42—1882no—
1004C42—1882no—
1005C42—1882no—
1006C23—22no—
1007C23—22no—
1008C23—21no—
1009C23—21no—
1010C23—22no—
1011C23—22no—
1012C23—474no—
1013C23—474no—
1014C23—474no—
1015C23—472no—
1016C23—9416no—
1017C23—948no—
1018C23—948no—
1019C23—9416no—
1020C23—948no—
1021C23—942no—
1022C23—942no—
1023C23—942no—
1024C23—942no—
1025C23—941no—
1026C23—941no—
1027C23—942no—
1028C23—942no—
1029C23C22×C4×D4712yes—
1030C23C22×C4×D4712yes—
1031C23C2×D4×D4712yes—
1032C23#41×D4712yes—
1033C23C24×D4711yescharacteristic
1034Q8—948no—
1035D4—28no—
1036D4—9416no—
1037D4—948no—
1038D4—9416no—
1039D4—948no—
1040C2×C4—28no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—82no—
1062C2×C4—4716no—
1063C2×C4—472no—
1064C2×C4—472no—
1065C2×C4—472no—
1066C2×C4—472no—
1067C2×C4—472no—
1068C2×C4—472no—
1069C2×C4—474no—
1070C2×C4—472no—
1071C2×C4—472no—
1072C2×C4—472no—
1073C2×C4—9416no—
1074C2×C4—9416no—
1075C2×C4—948no—
1076C2×C4—948no—
1077C2×C4—941no—
1078C2×C4—941no—
1079C2×C4—942no—
1080C2×C4—942no—
1081C2×C4—942no—
1082C2×C4—942no—
1083C2×C4—941no—
1084C2×C4—941no—
1085C2×C4—942no—
1086C2×C4—942no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—942no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—942no—
1093C2×C4—3762no—
1094C2×C4—3762no—
1095C2×C4—3762no—
1096C2×C4—1888no—
1097C2×C4—1888no—
1098C2×C4—1888no—
1099C2×C4—1888no—
1100C2×C4—1884no—
1101C2×C4—1884no—
1102C2×C4C22×C4×D4714yes—
1103C2×C4C22×C4×D4712yes—
1104C2×C4C22×C4×D4714yes—
1105C2×C4C2×D4×D4712yes—
1106C2×C4C2×D4×D4712yes—
1107C22—22no—
1108C22—24no—
1109C22—24no—
1110C22—22no—
1111C22—22no—
1112C22—24no—
1113C22—41no—
1114C22—42no—
1115C22—41no—
1116C22—478no—
1117C22—9432no—
1118C22—944no—
1119C22—944no—
1120C22—944no—
1121C22—944no—
1122C22—944no—
1123C22—944no—
1124C22—942no—
1125C22—944no—
1126C22—1881no—
1127C22—1882no—
1128C22—1881no—
1129C22C4×D4×D4714yes—
1130C22C23×C4×D4711yescharacteristic
1131C22C22×D4×D4711yescharacteristic
1132C22C2×#41×D4711yescharacteristic
1133C22H(5,𝔽2)×D4712yes—
1134C222−1+4×D4712yes—
1135C4—24no—
1136C4—22no—
1137C4—24no—
1138C4—22no—
1139C4—22no—
1140C4—41no—
1141C4—42no—
1142C4—42no—
1143C4—41no—
1144C4—474no—
1145C4—474no—
1146C4—942no—
1147C4—944no—
1148C4—942no—
1149C4—942no—
1150C4—1881no—
1151C4—1882no—
1152C4—1881no—
1153C4—1882no—
1154C2—24no—
1155C2—42no—
1156C2—948no—
1157C2—1882no—
1158C2C2×C4×D4×D4711yescharacteristic
1159C2#520×D4712yes—
1160C2#2025702011yescharacteristic
1161C2#2025703711yescharacteristic
1162C2#2025709312yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2322C2
socle, cosocleC23×C47C25
prime radicalC2×#15689631C2
hypercenter#2322D47
hypocenterC47#34200
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2322

Complements

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

NH ≅ G/Ntype
2. C2×#15689602C2semidirect
3. C22×C4⋊C4×D47C2semidirect
4. #20246407C2semidirect
5. #20246401C2semidirect
6. #20246396C2semidirect
7. #20246390C2semidirect
8. #20246316C2semidirect
9. #20246312C2semidirect
10. #20246289C2semidirect
11. #20246286C2semidirect
12. #20246060C2semidirect
13. #20246057C2semidirect
14. #20246054C2semidirect
15. #20246007C2semidirect
16. #20245975C2semidirect
17. #20245893C2semidirect
18. C4×#13093994C2semidirect
19. #20245889C2semidirect
20. C4×#13093992C2semidirect
21. #20245768C2semidirect
22. #20245743C2semidirect
23. C47×#2322C2semidirect
28. #15689631C4semidirect
35. C2×C4×Dic94C22semidirect
36. C2×#13093989C22semidirect
43. C2×C4×C22⋊D47C22semidirect
47. C2×(C22⋊D47)⋊C4C22semidirect
48. C2×#13093981C22semidirect
52. C2×#13093980C22semidirect
56. C22×Dic47⋊C4C22semidirect
62. C2×C4⋊C4×D47C22semidirect
63. #15689027C22semidirect
64. #15689023C22semidirect
65. #15689022C22semidirect
66. #15689020C22semidirect
67. #15689020C22semidirect
68. #15689018C22semidirect
69. #15689018C22semidirect
70. #15689016C22semidirect
71. #15689015C22semidirect
72. #15689013C22semidirect
73. #15689010C22semidirect
74. #15689009C22semidirect
75. #15689004C22semidirect
84. #15688998C22semidirect
87. #15688997C22semidirect
92. #15688994C22semidirect
93. #15688992C22semidirect
94. #15688987C22semidirect
98. #15688982C22semidirect
99. #15688981C22semidirect
102. C4×Dic47⋊C4C22semidirect
103. C4×Dic47⋊C4C22semidirect
104. #15688974C22semidirect
105. #15688974C22semidirect
118. C47×#389C22semidirect
119. C47×#388C22semidirect
120. C47×#387C22semidirect
123. C47×#385C22semidirect
129. C2×#10625352C2×C4semidirect
146. C22×C4×D47C2×C4semidirect
156. #13094007C2×C4semidirect
157. #13094002C2×C4semidirect
158. #13093997C2×C4semidirect
159. #13093994C2×C4semidirect
160. #13093992C2×C4semidirect
166. #13093986C2×C4semidirect
173. (C22⋊D47)⋊C4C2×C4semidirect
178. #13093980C2×C4semidirect
186. C2×Dic47⋊C4D4semidirect
249. #123×C47C2×C4semidirect
308. C2×C22⋊D47C22×C4semidirect
317. C22×Dic47C22×C4semidirect
362. C2×C4×D47C22×C4semidirect
365. C2×Dic94C22×C4semidirect
370. C4⋊C4×C47C22×C4semidirect
376. C22⋊C4×C47C22×C4semidirect
394. (C2×D47)⋊C4C22×C4semidirect
408. Dic47⋊C4C22×C4semidirect
409. Dic47⋊C4C22×C4semidirect
423. C4×Dic47C22×C4semidirect
503. C2×Dic47C4×D4semidirect
553. C2×D47#520semidirect
587. #2322D47semidirect
654. #389C2×D47semidirect
658. #388C2×D47semidirect
662. #387C2×D47semidirect
682. #385C2×D47semidirect
707. C47#34200semidirect
744. #123C4×D47semidirect
971. C4⋊C4C2×C4×D47semidirect
993. C22⋊C4C2×C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896312
C2×#156896022
C22×C4⋊C4×D472
#202464072
#202464012
#202463962
#202463902
#202463162
#202463122
#202462892
#202462862
#202460602
#202460572
#202460542
#202460072
#202459752
#202458932
C4×#130939942
#202458892
C4×#130939922
#202457682
#202457432
C47×#23222
#3420047