Finite Group Databasebeta

← #26375723

Subgroups — #26375723

Order 12032.

3142 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2#20246362C211yesmaximal, characteristic, complemented
3#20246356C211yesmaximal, characteristic, complemented
4#20246329C211yesmaximal, characteristic, complemented
5#20246328C211yesmaximal, characteristic, complemented
6#20246321C211yesmaximal, characteristic, complemented
7#20246295C211yesmaximal, characteristic, complemented
8#20246292C211yesmaximal, characteristic, complemented
9#20246262C212yesmaximal, complemented
10#20246232C212yesmaximal, complemented
11#20246231C212yesmaximal, complemented
12#20246206C212yesmaximal
13#20245848C212yesmaximal, complemented
14#20245828C212yesmaximal, complemented
15#20245826C212yesmaximal, complemented
16#20245785C211yesmaximal, characteristic, complemented
17#20245770C211yesmaximal, characteristic, complemented
18#20245768C211yesmaximal, characteristic, complemented
19C4×(C22⋊D47)⋊C4C212yesmaximal, complemented
20#20245727C211yesmaximal, characteristic, complemented
21C2×#15688970C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D47C211yesmaximal, characteristic, complemented
23C47×#2353C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28C2×D4×Dic47C2211yescharacteristic
29C2×#13093986C2211yescharacteristic
30C2×C4×C22⋊D47C2212yes—
31C2×C4×C22⋊D47C2211yescharacteristic
32C2×C4×C22⋊D47C2211yescharacteristic
33C2×(C22⋊D47)⋊C4C2212yes—
34C2×(C22⋊D47)⋊C4C2211yescharacteristic
35C2×(C22⋊D47)⋊C4C2211yescharacteristic
36C4×D4×D47C4116yescomplemented
37C2×#13093982C2212yescomplemented
38C2×#13093981C2212yes—
39C2×#13093980C2212yescomplemented
40C2×C4⋊C4×D47C2211yescharacteristic
41C22×(C2×D47)⋊C4C2212yes—
42C2×C22⋊C4×D47C2212yes—
43C2×C22⋊C4×D47C2211yescharacteristic
44C2×C22⋊C4×D47C2211yescharacteristic
45C22×C4×Dic47C2212yescomplemented
46C2×C42×D47C2211yescharacteristic
47C2×C42×D47C2212yescomplemented
48#15689023C2212yes—
49#15689023C2212yes—
50#15689020C2212yescomplemented
51#15689018C2212yescomplemented
52#15689017C2212yescomplemented
53#15689016C2212yescomplemented
54#15689014C2212yescomplemented
55#15689014C2212yescomplemented
56#15689012C2212yescomplemented
57#15689012C2212yescomplemented
58#15689011C2212yescomplemented
59#15689009C2212yescomplemented
60#15689008C2212yescomplemented
61#15689006C2212yescomplemented
62#15689003C2212yes—
63#15689001C2212yes—
64#15689001C2212yes—
65#15688997C2212yescomplemented
66#15688996C2212yescomplemented
67#15688995C2212yescomplemented
68#15688994C2212yescomplemented
69#15688991C2211yescharacteristic, complemented
70#15688987C2211yescharacteristic, complemented
71#15688987C2211yescharacteristic, complemented
72#15688986C2211yescharacteristic, complemented
73#15688985C2212yes—
74#15688985C2211yescharacteristic, complemented
75#15688985C2211yescharacteristic, complemented
76#15688983C2211yescharacteristic, complemented
77#15688982C2212yes—
78#15688982C2212yes—
79#15688982C2211yescharacteristic, complemented
80#15688982C2211yescharacteristic, complemented
81#15688980C2212yes—
82#15688978C2212yes—
83#15688978C2212yes—
84C4×Dic47⋊C4C2212yescomplemented
85#15688974C2211yescharacteristic, complemented
86#15688974C2211yescharacteristic, complemented
87#15688974C2212yescomplemented
88#15688974C2212yescomplemented
89#15688974C2212yescomplemented
90C22⋊C4×Dic47C2212yescomplemented
91C22⋊C4×Dic47C2212yescomplemented
92C22⋊C4×Dic47C2212yescomplemented
93C4×(C2×D47)⋊C4C2212yes—
94C4×(C2×D47)⋊C4C2212yescomplemented
95C4×C22⋊Dic47C2211yescharacteristic, complemented
96#15688970C2211yescharacteristic
97#15688970C2211yescharacteristic
98#15688970C2211yescharacteristic
99#15688970C2212yes—
100#15688970C2211yescharacteristic
101#15688970C2212yes—
102#15688970C2212yescomplemented
103#15688970C2211yescharacteristic, complemented
104#15688970C2212yescomplemented
105#15688970C2211yescharacteristic, complemented
106#15688970C2212yescomplemented
107#15688969C2211yescharacteristic, complemented
108#15688968C2212yescomplemented
109C2×C47⋊#95C2211yescharacteristic, complemented
110#95×D47C2211yescharacteristic, complemented
111#95×D47C2211yescharacteristic, complemented
112C42×Dic47C2212yescomplemented
113C2×C4×D4×C47C2211yescharacteristic
114C47×#388C2212yescomplemented
115C47×#387C2212yescomplemented
116C47×#386C2212yes—
117C47×#383C2211yescharacteristic, complemented
118C47×#381C2211yescharacteristic, complemented
119C47×#380C2211yescharacteristic, complemented
120C4×C22⋊C4×C47C2211yescharacteristic, complemented
121C4×C22⋊C4×C47C2212yescomplemented
122C47×#376C2211yescharacteristic, complemented
123C2×#95×C47C2211yescharacteristic, complemented
124C24×D47C2311yescharacteristic
125C24×D47C2311yescharacteristic
126C22×D188C2311yescharacteristic
127C22×C22⋊D47C2311yescharacteristic
128C22×C22⋊D47C2311yescharacteristic
129C2×D4×D47—24no—
130C2×D4×D47—24no—
131C2×D4×D47C2×C418yes—
132C23×Dic47C2312yes—
133C23×Dic47C2311yescharacteristic
134C23×Dic47C2311yescharacteristic
135C22×C4×D47—44no—
136C22×C4×D47—44no—
137C22×C4×D47C2×C418yescomplemented
138C22×C4×D47C2×C418yescomplemented
139C22×C4×D47C2312yes—
140C22×C4×D47C2312yes—
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C4×D188C2×C418yescomplemented
151D4×Dic47C2×C418yescomplemented
152#13093986C2×C418yescomplemented
153C4×C22⋊D47—28no—
154C4×C22⋊D47C2×C418yes—
155C4×C22⋊D47C2×C418yescomplemented
156(C22⋊D47)⋊C4—28no—
157(C22⋊D47)⋊C4C2×C418yes—
158(C22⋊D47)⋊C4C2×C418yescomplemented
159#13093982—44no—
160#13093981—28no—
161#13093980—44no—
162C2×C4⋊Dic47C2312yes—
163C2×C4⋊Dic47C2311yescharacteristic
164C2×Dic47⋊C4C2312yes—
165C2×Dic47⋊C4C2312yes—
166C2×Dic47⋊C4C2312yes—
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2312yes—
170C2×Dic47⋊C4C2311yescharacteristic
171C2×Dic47⋊C4C2311yescharacteristic
172C4⋊C4×D47C2×C418yescomplemented
173C2×C22⋊Dic47C2312yes—
174C2×C22⋊Dic47C2312yes—
175C2×C22⋊Dic47C2312yes—
176C2×C22⋊Dic47C2311yescharacteristic
177C2×C22⋊Dic47C2311yescharacteristic
178C2×(C2×D47)⋊C4—28no—
179C2×(C2×D47)⋊C4C2312yes—
180C2×(C2×D47)⋊C4C2312yes—
181C2×(C2×D47)⋊C4C2312yes—
182C2×(C2×D47)⋊C4C2312yes—
183C2×(C2×D47)⋊C4C2312yes—
184C2×(C2×D47)⋊C4C2312yes—
185C2×(C2×D47)⋊C4C2312yes—
186C2×(C2×D47)⋊C4C2312yes—
187C2×(C2×D47)⋊C4C2312yes—
188C2×(C2×D47)⋊C4C2311yescharacteristic
189C2×(C2×D47)⋊C4C2311yescharacteristic
190C2×(C2×D47)⋊C4C2311yescharacteristic
191C2×(C2×D47)⋊C4C2311yescharacteristic
192C2×(C2×D47)⋊C4C2312yes—
193C22⋊C4×D47—28no—
194C22⋊C4×D47C2×C418yescomplemented
195C22⋊C4×D47C2×C418yescomplemented
196C2×C4×Dic47—44no—
197C2×C4×Dic47C2312yes—
198C2×C4×Dic47C2312yes—
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2312yes—
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2312yes—
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C2311yescharacteristic
208C2×C4×Dic47C2311yescharacteristic
209C2×C4×Dic47C2311yescharacteristic
210C42×D47—44no—
211C42×D47C2×C418yescomplemented
212C47⋊#95C2311yescharacteristic
213C47⋊#95C2311yescharacteristic
214C47⋊#95C2312yes—
215C47⋊#95C2312yes—
216C47⋊#95C2311yescharacteristic
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2311yescharacteristic
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C22×D4×C47C2311yescharacteristic
228C23×C4×C47C2312yes—
229C23×C4×C47C2311yescharacteristic
230C23×C4×C47C2311yescharacteristic
231C4×D4×C47C2×C418yescomplemented
232C2×C4⋊C4×C47C2312yes—
233C2×C4⋊C4×C47C2311yescharacteristic
234C2×C22⋊C4×C47C2312yes—
235C2×C22⋊C4×C47C2312yes—
236C2×C22⋊C4×C47C2312yes—
237C2×C22⋊C4×C47C2311yescharacteristic
238C2×C22⋊C4×C47C2311yescharacteristic
239C2×C42×C47C2312yes—
240C2×C42×C47C2312yes—
241C2×C42×C47C2311yescharacteristic
242#95×C47C2311yescharacteristic
243#95×C47C2311yescharacteristic
244#95×C47C2312yes—
245#95×C47C2311yescharacteristic
246#95×C47C2312yes—
247#95×C47C2311yescharacteristic
248#95×C47C2312yes—
249#95×C47C2312yes—
250#95×C47C2312yes—
251C24×C47C2411yescharacteristic
252C24×C47C2411yescharacteristic
253C23×D47—22no—
254C23×D47—22no—
255C23×D47—24no—
256C23×D47—24no—
257C23×D47—22no—
258C23×D47—22no—
259C23×D47—42no—
260C23×D47—42no—
261C23×D47C22×C414yes—
262C23×D47C22×C414yes—
263C23×D47C2411yescharacteristic
264C23×D47C2411yescharacteristic
265C23×D47C2411yescharacteristic
266C2×D4×C47—22no—
267C2×D4×C47—22no—
268C2×D4×C47C22×C414yes—
269C22×C4×C47—24no—
270C22×C4×C47—24no—
271C22×C4×C47—42no—
272C22×C4×C47—42no—
273C22×C4×C47—42no—
274C22×C4×C47C22×C414yes—
275C22×C4×C47C22×C414yes—
276C22×C4×C47C2412yes—
277C22×C4×C47C2412yes—
278C22×C4×C47C2412yes—
279C22×C4×C47C2411yescharacteristic
280C22×C4×C47C2411yescharacteristic
281C22×C4×C47C2411yescharacteristic
282C22×C4×C47C2411yescharacteristic
283C22×C4×C47C2411yescharacteristic
284C22×C4×C47C2412yes—
285C2×C22⋊D47—22no—
286C2×C22⋊D47—22no—
287C2×C22⋊D47C22×C414yes—
288C2×C22⋊D47C22×C414yes—
289C2×C22⋊D47#4114yes—
290C2×C22⋊D47#4114yes—
291C22×Dic47—24no—
292C22×Dic47—24no—
293C22×Dic47—24no—
294C22×Dic47—24no—
295C22×Dic47—42no—
296C22×Dic47C22×C414yes—
297C22×Dic47C22×C414yes—
298C22×Dic47C2412yes—
299C22×Dic47C2412yes—
300C22×Dic47C2412yes—
301C22×Dic47C2411yescharacteristic
302C22×Dic47C2411yescharacteristic
303C22×Dic47C2411yescharacteristic
304C22×Dic47C2412yes—
305C22×Dic47C2411yescharacteristic
306C22×Dic47C2411yescharacteristic
307D4×D47—232no—
308C2×D188—22no—
309C2×D188—22no—
310C2×D188C22×C414yes—
311C2×C4×D47—24no—
312C2×C4×D47—22no—
313C2×C4×D47—22no—
314C2×C4×D47—24no—
315C2×C4×D47—24no—
316C2×C4×D47—24no—
317C2×C4×D47—24no—
318C2×C4×D47—24no—
319C2×C4×D47—24no—
320C2×C4×D47—24no—
321C2×C4×D47—416no—
322C2×C4×D47—416no—
323C2×C4×D47—42no—
324C2×C4×D47—42no—
325C2×C4×D47—42no—
326C2×C4×D47—42no—
327C2×C4×D47—42no—
328C2×C4×D47—42no—
329C2×C4×D47C22×C414yes—
330C2×C4×D47C22×C414yes—
331C2×C4×D47C22×C414yes—
332C2×C4×D47C22×C414yes—
333C2×C4×D47C22×C414yes—
334C2×C4×D47C22×C414yes—
335C2×C4×D47C22×C414yes—
336C2×C4×D47C22×C414yes—
337C2×C4×D47C22×C414yes—
338C4⋊C4×C47—42no—
339C4⋊C4×C47C22×C414yes—
340C22⋊C4×C47—24no—
341C22⋊C4×C47—24no—
342C22⋊C4×C47—42no—
343C22⋊C4×C47C22×C414yes—
344C22⋊C4×C47C22×C414yes—
345C42×C47—24no—
346C42×C47—42no—
347C42×C47C22×C414yes—
348C22⋊Dic47—24no—
349C22⋊Dic47—24no—
350C22⋊Dic47—42no—
351C22⋊Dic47C22×C414yes—
352C22⋊Dic47C22×C414yes—
353(C2×D47)⋊C4—24no—
354(C2×D47)⋊C4—24no—
355(C2×D47)⋊C4—24no—
356(C2×D47)⋊C4—24no—
357(C2×D47)⋊C4—24no—
358(C2×D47)⋊C4—24no—
359(C2×D47)⋊C4—24no—
360(C2×D47)⋊C4—42no—
361(C2×D47)⋊C4—42no—
362(C2×D47)⋊C4C22×C414yes—
363(C2×D47)⋊C4C22×C414yes—
364(C2×D47)⋊C4C22×C414yes—
365(C2×D47)⋊C4C22×C414yes—
366(C2×D47)⋊C4#4118yes—
367C4⋊Dic47—42no—
368C4⋊Dic47C22×C414yes—
369Dic47⋊C4—24no—
370Dic47⋊C4—24no—
371Dic47⋊C4—24no—
372Dic47⋊C4—24no—
373Dic47⋊C4—42no—
374Dic47⋊C4—42no—
375Dic47⋊C4C22×C414yes—
376Dic47⋊C4C22×C414yes—
377C4×Dic47—24no—
378C4×Dic47—24no—
379C4×Dic47—24no—
380C4×Dic47—24no—
381C4×Dic47—24no—
382C4×Dic47—24no—
383C4×Dic47—24no—
384C4×Dic47—42no—
385C4×Dic47—42no—
386C4×Dic47—42no—
387C4×Dic47C22×C414yes—
388C4×Dic47C22×C414yes—
389C4×Dic47C22×C414yes—
390C23×C47—22no—
391C23×C47—22no—
392C23×C47—22no—
393C23×C47—21no—
394C23×C47—21no—
395C23×C47—22no—
396C23×C47C23×C412yes—
397C23×C47C23×C412yes—
398C23×C47C2×#4112yes—
399C23×C47C2×#4112yes—
400C23×C47C2511yescharacteristic
401C22×D47—22no—
402C22×D47—21no—
403C22×D47—21no—
404C22×D47—22no—
405C22×D47—22no—
406C22×D47—28no—
407C22×D47—22no—
408C22×D47—21no—
409C22×D47—21no—
410C22×D47—22no—
411C22×D47—28no—
412C22×D47—28no—
413C22×D47—28no—
414C22×D47—44no—
415C22×D47—44no—
416C22×D47—48no—
417C22×D47—48no—
418C22×D47—48no—
419C22×D47—48no—
420C22×D47C23×C412yes—
421C22×D47C23×C412yes—
422C22×D47C23×C412yes—
423C22×D47C2×#4112yes—
424C22×D47C2×#4112yes—
425C22×D47C2×#4114yes—
426D4×C47—28no—
427C2×C4×C47—22no—
428C2×C4×C47—22no—
429C2×C4×C47—21no—
430C2×C4×C47—21no—
431C2×C4×C47—22no—
432C2×C4×C47—22no—
433C2×C4×C47—22no—
434C2×C4×C47—22no—
435C2×C4×C47—22no—
436C2×C4×C47—22no—
437C2×C4×C47—22no—
438C2×C4×C47—22no—
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—22no—
442C2×C4×C47—22no—
443C2×C4×C47—22no—
444C2×C4×C47—44no—
445C2×C4×C47—44no—
446C2×C4×C47—48no—
447C2×C4×C47C23×C412yes—
448C2×C4×C47C23×C412yes—
449C2×C4×C47C23×C412yes—
450C2×C4×C47C23×C412yes—
451C2×C4×C47C23×C412yes—
452C2×C4×C47C2×#4114yes—
453C22⋊D47—28no—
454C22⋊D47#117116yescomplemented
455C2×Dic47—22no—
456C2×Dic47—22no—
457C2×Dic47—22no—
458C2×Dic47—22no—
459C2×Dic47—22no—
460C2×Dic47—28no—
461C2×Dic47—28no—
462C2×Dic47—22no—
463C2×Dic47—22no—
464C2×Dic47—22no—
465C2×Dic47—22no—
466C2×Dic47—22no—
467C2×Dic47—22no—
468C2×Dic47—22no—
469C2×Dic47—22no—
470C2×Dic47—22no—
471C2×Dic47—48no—
472C2×Dic47C23×C412yes—
473C2×Dic47C23×C412yes—
474C2×Dic47C23×C412yes—
475C2×Dic47C23×C412yes—
476C2×Dic47C23×C412yes—
477C2×Dic47C2×#4114yes—
478C2×Dic47C2×#4112yes—
479C2×Dic47C2×#4112yes—
480C2×Dic47H(5,𝔽2)14yes—
481D188—28no—
482C4×D47—28no—
483C4×D47—28no—
484C4×D47—28no—
485C4×D47—28no—
486C4×D47—28no—
487C4×D47—44no—
488C4×D47—44no—
489C4×D47—44no—
490C4×D47—44no—
491C4×D47—48no—
492C4×D47—48no—
493#34126—471nomaximal, Sylow
494C22×C47—22no—
495C22×C47—22no—
496C22×C47—24no—
497C22×C47—24no—
498C22×C47—22no—
499C22×C47—22no—
500C22×C47—22no—
501C22×C47—42no—
502C22×C47—42no—
503C22×C47C2×#11714yes—
504C22×C47C24×C411yescharacteristic
505C22×C47C22×#4111yescharacteristic
506C22×C47C22×#4111yescharacteristic
507C22×C47C22×#4112yes—
508C22×C47C2×H(5,𝔽2)12yes—
509C2×D47—22no—
510C2×D47—22no—
511C2×D47—22no—
512C2×D47—22no—
513C2×D47—24no—
514C2×D47—24no—
515C2×D47—24no—
516C2×D47—24no—
517C2×D47—22no—
518C2×D47—22no—
519C2×D47—22no—
520C2×D47—416no—
521C2×D47—416no—
522C2×D47—42no—
523C2×D47—42no—
524C2×D47C2×#11714yes—
525C2×D47C4×#4114yes—
526C4×C47—22no—
527C4×C47—22no—
528C4×C47—22no—
529C4×C47—22no—
530C4×C47—22no—
531C4×C47—24no—
532C4×C47—42no—
533C4×C47—42no—
534C4×C47—42no—
535Dic47—22no—
536Dic47—22no—
537Dic47—22no—
538Dic47—24no—
539Dic47—42no—
540Dic47—42no—
541Dic47—42no—
542Dic47C2×#11714yes—
543Dic47#51814yes—
544C22×C4×D4—471no—
545#2357—471no—
546#2357—471no—
547#2353—471no—
548#2353—471no—
549#2353—471no—
550#2353D4711yescharacteristic, complemented
551#2349—471no—
552#2349—471no—
553#2345—472no—
554#2342—472no—
555#2342—472no—
556D4×C22⋊C4—472no—
557#2293—472no—
558#2290—472no—
559#2290—472no—
560#2283—471no—
561#2280—471no—
562#2280—471no—
563C42×D4—472no—
564C4×#117—471no—
565C2×C4×C22⋊C4—471no—
566C2×C4×C22⋊C4—471no—
567C2×C47—24no—
568C2×C47—42no—
569C2×C47C22×#11711yescharacteristic
570C2×C47C2×C4×#4111yescharacteristic
571C2×C47C2×#51811yescharacteristic
572C2×C47#348112yes—
573C2×C47#348112yes—
574D47—24no—
575D47—24no—
576D47—42no—
577C23×D4—471no—
578C24×C4—471no—
579C24×C4—471no—
580C2×C4×D4—471no—
581C2×C4×D4—471no—
582C2×C4×D4—471no—
583C2×C4×D4—4716no—
584C2×C4×D4—472no—
585C2×C4×D4—471no—
586C2×C4×D4—471no—
587C2×C4×D4—471no—
588C2×C4×D4—472no—
589C2×C4×D4—471no—
590C2×C4×D4C2×D4711yescharacteristic
591C2×#117—472no—
592C2×#117—472no—
593C2×#117—472no—
594C22×C4⋊C4—471no—
595C22×C22⋊C4—471no—
596C22×C22⋊C4—471no—
597C22×C22⋊C4—472no—
598C22×C22⋊C4—472no—
599C22×C42—471no—
600C22×C42—472no—
601C22×C42—472no—
602#390—472no—
603#390—472no—
604#389—472no—
605#389—472no—
606#388—472no—
607#388—472no—
608#388—472no—
609#388—472no—
610#388—472no—
611#388—472no—
612#388—472no—
613#388C2×D4712yescomplemented
614#387—472no—
615#387—472no—
616#387—472no—
617#387C2×D4712yescomplemented
618#386—472no—
619#386—472no—
620#386—472no—
621#386C2×D4712yes—
622#385—472no—
623#385—472no—
624#385—472no—
625#385—472no—
626#383—471no—
627#383C2×D4711yescharacteristic, complemented
628#382—471no—
629#382—471no—
630#381—471no—
631#381—472no—
632#381—471no—
633#381—471no—
634#381C2×D4711yescharacteristic, complemented
635#380—471no—
636#380—472no—
637#380—472no—
638#380—472no—
639#380—471no—
640#380—471no—
641#380C2×D4711yescharacteristic, complemented
642#379—472no—
643#379—472no—
644C4×C4⋊C4—472no—
645C4×C4⋊C4—472no—
646C4×C4⋊C4—471no—
647C4×C4⋊C4—471no—
648C4×C4⋊C4—472no—
649C4×C4⋊C4—472no—
650C4×C22⋊C4—471no—
651C4×C22⋊C4—472no—
652C4×C22⋊C4—472no—
653C4×C22⋊C4—472no—
654C4×C22⋊C4—472no—
655C4×C22⋊C4—472no—
656C4×C22⋊C4—472no—
657C4×C22⋊C4—472no—
658C4×C22⋊C4—471no—
659C4×C22⋊C4—471no—
660C4×C22⋊C4—471no—
661C4×C22⋊C4—471no—
662C4×C22⋊C4—472no—
663C4×C22⋊C4—471no—
664C4×C22⋊C4—471no—
665C4×C22⋊C4—472no—
666C4×C22⋊C4—472no—
667C4×C22⋊C4C2×D4712yescomplemented
668C4×C22⋊C4C2×D4711yescharacteristic, complemented
669#376—471no—
670#376—472no—
671#376C2×D4711yescharacteristic, complemented
672C2×#95—471no—
673C2×#95—471no—
674C2×#95—471no—
675C2×#95C2×D4711yescharacteristic, complemented
676C43—472no—
677C47#3412611yescharacteristic, complemented, Sylow
678C25—471no—
679C25—471no—
680C22×D4—471no—
681C22×D4—471no—
682C22×D4—478no—
683C22×D4—471no—
684C22×D4—944no—
685C22×D4—944no—
686C22×D4C22×D4711yescharacteristic
687C23×C4—471no—
688C23×C4—471no—
689C23×C4—471no—
690C23×C4—471no—
691C23×C4—471no—
692C23×C4—471no—
693C23×C4—471no—
694C23×C4—478no—
695C23×C4—478no—
696C23×C4—471no—
697C23×C4—471no—
698C23×C4—471no—
699C23×C4—471no—
700C23×C4—472no—
701C23×C4—472no—
702C23×C4—472no—
703C23×C4—1884no—
704C23×C4—1884no—
705C23×C4C22×D4712yes—
706C23×C4C22×D4711yescharacteristic
707C23×C4C22×D4711yescharacteristic
708C4×D4—478no—
709C4×D4—478no—
710C4×D4—478no—
711C4×D4—478no—
712C4×D4—478no—
713C4×D4—478no—
714C4×D4—478no—
715C4×D4—948no—
716C4×D4—948no—
717C4×D4C4×D4718yescomplemented
718#117—948no—
719#117—1884no—
720#117—1884no—
721C2×C4⋊C4—471no—
722C2×C4⋊C4—471no—
723C2×C4⋊C4—471no—
724C2×C4⋊C4—478no—
725C2×C4⋊C4—472no—
726C2×C4⋊C4—472no—
727C2×C4⋊C4—472no—
728C2×C4⋊C4—472no—
729C2×C4⋊C4—472no—
730C2×C4⋊C4—472no—
731C2×C4⋊C4—472no—
732C2×C4⋊C4C22×D4712yes—
733C2×C4⋊C4C22×D4711yescharacteristic
734C2×C22⋊C4—471no—
735C2×C22⋊C4—471no—
736C2×C22⋊C4—472no—
737C2×C22⋊C4—471no—
738C2×C22⋊C4—471no—
739C2×C22⋊C4—471no—
740C2×C22⋊C4—471no—
741C2×C22⋊C4—478no—
742C2×C22⋊C4—478no—
743C2×C22⋊C4—472no—
744C2×C22⋊C4—472no—
745C2×C22⋊C4—472no—
746C2×C22⋊C4—472no—
747C2×C22⋊C4—472no—
748C2×C22⋊C4—472no—
749C2×C22⋊C4—472no—
750C2×C22⋊C4—472no—
751C2×C22⋊C4—472no—
752C2×C22⋊C4—472no—
753C2×C22⋊C4—472no—
754C2×C22⋊C4—472no—
755C2×C22⋊C4—948no—
756C2×C22⋊C4—948no—
757C2×C22⋊C4C22×D4712yes—
758C2×C22⋊C4C22×D4712yes—
759C2×C22⋊C4C22×D4712yes—
760C2×C22⋊C4C22×D4711yescharacteristic
761C2×C22⋊C4C22×D4711yescharacteristic
762C2×C42—471no—
763C2×C42—471no—
764C2×C42—471no—
765C2×C42—478no—
766C2×C42—472no—
767C2×C42—472no—
768C2×C42—472no—
769C2×C42—472no—
770C2×C42—472no—
771C2×C42—472no—
772C2×C42—472no—
773C2×C42—472no—
774C2×C42—472no—
775C2×C42—472no—
776C2×C42—1884no—
777C2×C42—1884no—
778C2×C42C22×D4712yes—
779C2×C42C22×D4712yes—
780C2×C42C22×D4711yescharacteristic
781#95—471no—
782#95—471no—
783#95—471no—
784#95—472no—
785#95—472no—
786#95—472no—
787#95—471no—
788#95—472no—
789#95—472no—
790#95—472no—
791#95—472no—
792#95—472no—
793#95—472no—
794#95—472no—
795#95—472no—
796#95C22×D4711yescharacteristic
797#95C22×D4711yescharacteristic
798#95C22×D4711yescharacteristic
799#95C22×D4712yes—
800#95C22×D4712yes—
801#95C22×D4711yescharacteristic
802#95C22×D4712yes—
803#95C22×D4712yes—
804#95C22×D4712yes—
805C24—471no—
806C24—471no—
807C24—471no—
808C24—474no—
809C24—474no—
810C24—944no—
811C24—944no—
812C24—942no—
813C24—942no—
814C24—942no—
815C24—942no—
816C24—1882no—
817C24—1882no—
818C24C23×D4711yescharacteristic
819C24C23×D4711yescharacteristic
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—474no—
823C2×D4—474no—
824C2×D4—474no—
825C2×D4—474no—
826C2×D4—474no—
827C2×D4—942no—
828C2×D4—942no—
829C2×D4—942no—
830C2×D4—942no—
831C2×D4—9432no—
832C2×D4C2×C4×D4714yes—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—471no—
839C22×C4—471no—
840C22×C4—474no—
841C22×C4—474no—
842C22×C4—472no—
843C22×C4—471no—
844C22×C4—471no—
845C22×C4—471no—
846C22×C4—474no—
847C22×C4—474no—
848C22×C4—474no—
849C22×C4—474no—
850C22×C4—474no—
851C22×C4—474no—
852C22×C4—474no—
853C22×C4—474no—
854C22×C4—474no—
855C22×C4—472no—
856C22×C4—472no—
857C22×C4—472no—
858C22×C4—944no—
859C22×C4—944no—
860C22×C4—944no—
861C22×C4—942no—
862C22×C4—942no—
863C22×C4—944no—
864C22×C4—944no—
865C22×C4—944no—
866C22×C4—944no—
867C22×C4—944no—
868C22×C4—944no—
869C22×C4—944no—
870C22×C4—944no—
871C22×C4—944no—
872C22×C4—1882no—
873C22×C4—1882no—
874C22×C4—1882no—
875C22×C4—1882no—
876C22×C4—1882no—
877C22×C4—1882no—
878C22×C4—18816no—
879C22×C4—18816no—
880C22×C4—1882no—
881C22×C4C2×C4×D4714yes—
882C22×C4C2×C4×D4714yes—
883C22×C4C23×D4712yes—
884C22×C4C23×D4712yes—
885C22×C4C23×D4712yes—
886C22×C4C23×D4711yescharacteristic
887C22×C4C23×D4711yescharacteristic
888C22×C4C23×D4711yescharacteristic
889C22×C4C23×D4711yescharacteristic
890C22×C4C23×D4711yescharacteristic
891C22×C4C23×D4712yes—
892C4⋊C4—42no—
893C4⋊C4—474no—
894C4⋊C4—474no—
895C4⋊C4—474no—
896C4⋊C4—944no—
897C4⋊C4—944no—
898C4⋊C4—944no—
899C4⋊C4—944no—
900C4⋊C4—1882no—
901C4⋊C4—1882no—
902C4⋊C4—1882no—
903C4⋊C4C2×C4×D4714yes—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—42no—
907C22⋊C4—474no—
908C22⋊C4—474no—
909C22⋊C4—474no—
910C22⋊C4—474no—
911C22⋊C4—474no—
912C22⋊C4—474no—
913C22⋊C4—478no—
914C22⋊C4—944no—
915C22⋊C4—944no—
916C22⋊C4—944no—
917C22⋊C4—944no—
918C22⋊C4—944no—
919C22⋊C4—944no—
920C22⋊C4—944no—
921C22⋊C4—944no—
922C22⋊C4—944no—
923C22⋊C4—1882no—
924C22⋊C4—1882no—
925C22⋊C4—1882no—
926C22⋊C4C2×C4×D4714yes—
927C22⋊C4C2×C4×D4714yes—
928C42—24no—
929C42—42no—
930C42—474no—
931C42—474no—
932C42—474no—
933C42—944no—
934C42—944no—
935C42—944no—
936C42—944no—
937C42—944no—
938C42—944no—
939C42—944no—
940C42—1882no—
941C42—1882no—
942C42—1882no—
943C42C2×C4×D4714yes—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—21no—
948C23—21no—
949C23—22no—
950C23—472no—
951C23—472no—
952C23—474no—
953C23—472no—
954C23—472no—
955C23—472no—
956C23—948no—
957C23—948no—
958C23—948no—
959C23—942no—
960C23—941no—
961C23—941no—
962C23—942no—
963C23—942no—
964C23—948no—
965C23—942no—
966C23—941no—
967C23—941no—
968C23—942no—
969C23—1884no—
970C23—1884no—
971C23—1888no—
972C23—1888no—
973C23—1888no—
974C23—1888no—
975C23C22×C4×D4712yes—
976C23C22×C4×D4712yes—
977C23#41×D4712yes—
978C23#41×D4712yes—
979C23C24×D4711yescharacteristic
980D4—28no—
981D4—4716no—
982D4—948no—
983D4—948no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—48no—
1004C2×C4—472no—
1005C2×C4—472no—
1006C2×C4—472no—
1007C2×C4—472no—
1008C2×C4—474no—
1009C2×C4—472no—
1010C2×C4—472no—
1011C2×C4—472no—
1012C2×C4—474no—
1013C2×C4—948no—
1014C2×C4—948no—
1015C2×C4—948no—
1016C2×C4—948no—
1017C2×C4—948no—
1018C2×C4—948no—
1019C2×C4—948no—
1020C2×C4—942no—
1021C2×C4—942no—
1022C2×C4—942no—
1023C2×C4—942no—
1024C2×C4—942no—
1025C2×C4—942no—
1026C2×C4—942no—
1027C2×C4—942no—
1028C2×C4—942no—
1029C2×C4—942no—
1030C2×C4—942no—
1031C2×C4—942no—
1032C2×C4—942no—
1033C2×C4—942no—
1034C2×C4—1884no—
1035C2×C4—1884no—
1036C2×C4—1884no—
1037C2×C4—1884no—
1038C2×C4—1888no—
1039C2×C4—1888no—
1040C2×C4—1888no—
1041C2×C4C22×C4×D4712yes—
1042C2×C4C22×C4×D4712yes—
1043C2×C4C22×C4×D4712yes—
1044C2×C4C22×C4×D4712yes—
1045C2×C4C22×C4×D4712yes—
1046C2×C4#41×D4714yes—
1047C22—22no—
1048C22—22no—
1049C22—24no—
1050C22—24no—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—42no—
1055C22—42no—
1056C22—474no—
1057C22—474no—
1058C22—942no—
1059C22—942no—
1060C22—942no—
1061C22—942no—
1062C22—944no—
1063C22—944no—
1064C22—944no—
1065C22—944no—
1066C22—942no—
1067C22—942no—
1068C22—942no—
1069C22—18816no—
1070C22—18816no—
1071C22—1882no—
1072C22—1882no—
1073C22#117×D4714yes—
1074C22C23×C4×D4711yescharacteristic
1075C22C2×#41×D4711yescharacteristic
1076C22C2×#41×D4711yescharacteristic
1077C22C2×#41×D4712yes—
1078C22H(5,𝔽2)×D4712yes—
1079C4—22no—
1080C4—22no—
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—24no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—474no—
1089C4—474no—
1090C4—942no—
1091C4—942no—
1092C4—942no—
1093C4—944no—
1094C4—1882no—
1095C4—1882no—
1096C4—1882no—
1097C2—24no—
1098C2—42no—
1099C2—944no—
1100C2—944no—
1101C2—1882no—
1102C2C2×#117×D4711yescharacteristic
1103C2C4×#41×D4711yescharacteristic
1104C2#518×D4711yescharacteristic
1105C2#2025699112yes—
1106C2#2025699512yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2353C2
socle, cosocleC23×C47C25
prime radicalC22×D4×D47C22
hypercenter#2353D47
hypocenterC47#34126
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2353

Complements

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

NH ≅ G/Ntype
2. #20246362C2semidirect
3. #20246356C2semidirect
4. #20246329C2semidirect
5. #20246328C2semidirect
6. #20246321C2semidirect
7. #20246295C2semidirect
8. #20246292C2semidirect
9. #20246262C2semidirect
10. #20246232C2semidirect
11. #20246231C2semidirect
13. #20245848C2semidirect
14. #20245828C2semidirect
15. #20245826C2semidirect
16. #20245785C2semidirect
17. #20245770C2semidirect
18. #20245768C2semidirect
19. C4×(C22⋊D47)⋊C4C2semidirect
20. #20245727C2semidirect
21. C2×#15688970C2semidirect
22. C4×C22⋊C4×D47C2semidirect
23. C47×#2353C2semidirect
36. C4×D4×D47C4semidirect
37. C2×#13093982C22semidirect
39. C2×#13093980C22semidirect
45. C22×C4×Dic47C22semidirect
47. C2×C42×D47C22semidirect
50. #15689020C22semidirect
51. #15689018C22semidirect
52. #15689017C22semidirect
53. #15689016C22semidirect
54. #15689014C22semidirect
55. #15689014C22semidirect
56. #15689012C22semidirect
57. #15689012C22semidirect
58. #15689011C22semidirect
59. #15689009C22semidirect
60. #15689008C22semidirect
61. #15689006C22semidirect
65. #15688997C22semidirect
66. #15688996C22semidirect
67. #15688995C22semidirect
68. #15688994C22semidirect
69. #15688991C22semidirect
70. #15688987C22semidirect
71. #15688987C22semidirect
72. #15688986C22semidirect
74. #15688985C22semidirect
75. #15688985C22semidirect
76. #15688983C22semidirect
79. #15688982C22semidirect
80. #15688982C22semidirect
84. C4×Dic47⋊C4C22semidirect
85. #15688974C22semidirect
86. #15688974C22semidirect
87. #15688974C22semidirect
88. #15688974C22semidirect
89. #15688974C22semidirect
90. C22⋊C4×Dic47C22semidirect
91. C22⋊C4×Dic47C22semidirect
92. C22⋊C4×Dic47C22semidirect
94. C4×(C2×D47)⋊C4C22semidirect
95. C4×C22⋊Dic47C22semidirect
102. #15688970C22semidirect
103. #15688970C22semidirect
104. #15688970C22semidirect
105. #15688970C22semidirect
106. #15688970C22semidirect
107. #15688969C22semidirect
108. #15688968C22semidirect
109. C2×C47⋊#95C22semidirect
110. #95×D47C22semidirect
111. #95×D47C22semidirect
112. C42×Dic47C22semidirect
114. C47×#388C22semidirect
115. C47×#387C22semidirect
117. C47×#383C22semidirect
118. C47×#381C22semidirect
119. C47×#380C22semidirect
120. C4×C22⋊C4×C47C22semidirect
121. C4×C22⋊C4×C47C22semidirect
122. C47×#376C22semidirect
123. C2×#95×C47C22semidirect
137. C22×C4×D47C2×C4semidirect
138. C22×C4×D47C2×C4semidirect
150. C4×D188C2×C4semidirect
151. D4×Dic47C2×C4semidirect
152. #13093986C2×C4semidirect
155. C4×C22⋊D47C2×C4semidirect
158. (C22⋊D47)⋊C4C2×C4semidirect
172. C4⋊C4×D47C2×C4semidirect
194. C22⋊C4×D47C2×C4semidirect
195. C22⋊C4×D47C2×C4semidirect
211. C42×D47C2×C4semidirect
231. C4×D4×C47C2×C4semidirect
454. C22⋊D47#117semidirect
550. #2353D47semidirect
613. #388C2×D47semidirect
617. #387C2×D47semidirect
627. #383C2×D47semidirect
634. #381C2×D47semidirect
641. #380C2×D47semidirect
667. C4×C22⋊C4C2×D47semidirect
668. C4×C22⋊C4C2×D47semidirect
671. #376C2×D47semidirect
675. C2×#95C2×D47semidirect
677. C47#34126semidirect
717. C4×D4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D472
#202463622
#202463562
#202463292
#202463282
#202463212
#202462952
#202462922
#202462622
#202462322
#202462312
#202462062
#202458482
#202458282
#202458262
#202457852
#202457702
#202457682
C4×(C22⋊D47)⋊C42
#202457272
C2×#156889702
C4×C22⋊C4×D472
C47×#23532
#3412647