Finite Group Databasebeta

← #26375288

Subgroups — #26375288

Order 12032.

3770 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×#15689681C211yesmaximal, characteristic
2C2×C4×D4×D47C212yesmaximal, complemented
3#20246091C211yesmaximal, characteristic, complemented
4#20246086C212yesmaximal, complemented
5#20246061C212yesmaximal, complemented
6#20246055C212yesmaximal, complemented
7#20246050C212yesmaximal, complemented
8#20246044C212yesmaximal, complemented
9#20246001C211yesmaximal, characteristic, complemented
10#20245962C212yesmaximal, complemented
11#20245915C212yesmaximal, complemented
12#20245909C212yesmaximal, complemented
13#121×Dic47C211yesmaximal, characteristic, complemented
14#20245898C212yesmaximal, complemented
15#20245894C211yesmaximal, characteristic, complemented
16#20245893C212yesmaximal, complemented
17#20245889C212yesmaximal, complemented
18C2×#15688970C211yesmaximal, characteristic, complemented
19C47×#2325C211yesmaximal, characteristic, complemented
20C22×D4×D47C2212yes—
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2212yescomplemented
23#15689681C4116yescomplemented
24C2×#13094009C2212yes—
25C2×#13094006C2212yes—
26C2×#13093998C2211yescharacteristic
27C2×#13093996C2212yes—
28C2×#13093994C2212yes—
29C2×#13093992C2212yes—
30C2×C4×D188C2212yes—
31C2×D4×Dic47C2212yescomplemented
32C2×D4×Dic47C2211yescharacteristic, complemented
33C2×#13093986C2212yes—
34C2×#13093986C2211yescharacteristic, complemented
35C2×C4×C22⋊D47C2212yes—
36C2×C4×C22⋊D47C2212yescomplemented
37C2×(C22⋊D47)⋊C4C2212yes—
38C2×(C22⋊D47)⋊C4C2212yescomplemented
39C2×(C22⋊D47)⋊C4C2212yescomplemented
40C4×D4×D47—216no—
41C2×C4⋊C4×D47C2212yescomplemented
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C2×C22⋊C4×D47C2212yes—
45C2×C22⋊C4×D47C2212yescomplemented
46C22×C4×Dic47C2211yescharacteristic, complemented
47C22×C4×Dic47C2211yescharacteristic, complemented
48C2×C42×D47C2212yescomplemented
49#15689026C2211yescharacteristic, complemented
50#15689024C2211yescharacteristic, complemented
51#15689023C2212yescomplemented
52#15689022C2211yescharacteristic, complemented
53#15689020C2212yescomplemented
54#15689019C2211yescharacteristic, complemented
55#15689016C2212yescomplemented
56#15689015C2212yescomplemented
57#15689015C2212yescomplemented
58#15689014C2212yescomplemented
59#15689012C2212yescomplemented
60#15689011C2212yescomplemented
61#15689011C2212yescomplemented
62#15689008C2212yescomplemented
63#15689007C2212yescomplemented
64#15689004C2212yescomplemented
65#15689003C2212yescomplemented
66#15689002C2212yescomplemented
67#15689002C2212yescomplemented
68#15689001C2212yes—
69#15689001C2212yes—
70#15689001C2212yescomplemented
71#15689000C2212yescomplemented
72#15688999C2212yes—
73#15688999C2212yes—
74#15688999C2212yescomplemented
75#15688997C2212yescomplemented
76#15688997C2212yescomplemented
77#15688997C2212yescomplemented
78#15688996C2212yescomplemented
79#15688994C2212yescomplemented
80#15688994C2212yescomplemented
81#15688994C2212yescomplemented
82#15688985C2212yescomplemented
83#15688985C2212yescomplemented
84#15688983C2211yescharacteristic, complemented
85#15688981C2212yescomplemented
86#15688978C2212yescomplemented
87#15688978C2212yescomplemented
88C4⋊C4×Dic47C2211yescharacteristic, complemented
89C4⋊C4×Dic47C2211yescharacteristic, complemented
90#15688974C2212yescomplemented
91C22⋊C4×Dic47C2212yescomplemented
92C22⋊C4×Dic47C2212yescomplemented
93#15688970C2212yescomplemented
94#15688970C2212yescomplemented
95#15688970C2212yescomplemented
96#15688970C2212yescomplemented
97#15688970C2212yescomplemented
98#15688970C2212yescomplemented
99C2×C47⋊#95C2211yescharacteristic, complemented
100C2×#121×C47C2211yescharacteristic
101C2×C4×D4×C47C2212yescomplemented
102C47×#388C2212yescomplemented
103C47×#387C2212yescomplemented
104C47×#386C2212yescomplemented
105C47×#386C2212yescomplemented
106C47×#385C2212yescomplemented
107C47×#380C2211yescharacteristic, complemented
108C2×#95×C47C2211yescharacteristic, complemented
109C24×D47C2312yes—
110C24×D47C2311yescharacteristic
111C22×D188C2312yes—
112C22×D188C2311yescharacteristic
113C22×C22⋊D47C2312yes—
114C22×C22⋊D47C2312yes—
115C22×C22⋊D47C2312yes—
116C2×D4×D47—28no—
117C2×D4×D47—28no—
118C2×D4×D47C2×C4116yescomplemented
119C23×Dic47C2312yes—
120C23×Dic47C2311yescharacteristic
121C23×Dic47C2311yescharacteristic
122C23×Dic47C2311yescharacteristic
123C22×C4×D47—28no—
124C22×C4×D47—42no—
125C22×C4×D47—42no—
126C22×C4×D47—44no—
127C22×C4×D47—44no—
128C22×C4×D47D418yescomplemented
129C22×C4×D47C2312yes—
130C22×C4×D47C2312yes—
131C22×C4×D47C2312yes—
132C22×C4×D47C2312yes—
133C22×C4×D47C2312yes—
134C22×C4×D47C2312yes—
135C22×C4×D47C2312yes—
136#13094009C2×C4116yescomplemented
137#13094006C2×C4116yescomplemented
138#13093998C2×C418yescomplemented
139#13093996C2×C4116yescomplemented
140#13093994C2×C4116yescomplemented
141#13093992C2×C4116yescomplemented
142C4×D188—28no—
143D4×Dic47—28no—
144D4×Dic47—42no—
145#13093986—28no—
146#13093986—42no—
147C4×C22⋊D47—28no—
148C4×C22⋊D47—28no—
149(C22⋊D47)⋊C4—28no—
150(C22⋊D47)⋊C4—28no—
151(C22⋊D47)⋊C4—44no—
152C2×C4⋊Dic47C2312yes—
153C2×C4⋊Dic47C2311yescharacteristic
154C2×C4⋊Dic47C2311yescharacteristic
155C2×C4⋊Dic47C2311yescharacteristic
156C2×Dic47⋊C4C2312yes—
157C2×Dic47⋊C4C2312yes—
158C2×Dic47⋊C4C2312yes—
159C2×Dic47⋊C4C2312yes—
160C2×Dic47⋊C4C2312yes—
161C4⋊C4×D47—28no—
162C2×C22⋊Dic47C2312yes—
163C2×C22⋊Dic47C2312yes—
164C2×C22⋊Dic47C2312yes—
165C2×C22⋊Dic47C2312yes—
166C2×C22⋊Dic47C2312yes—
167C2×(C2×D47)⋊C4—24no—
168C2×(C2×D47)⋊C4C2×C418yescomplemented
169C2×(C2×D47)⋊C4C2312yes—
170C2×(C2×D47)⋊C4C2312yes—
171C2×(C2×D47)⋊C4C2312yes—
172C2×(C2×D47)⋊C4C2312yes—
173C2×(C2×D47)⋊C4C2312yes—
174C2×(C2×D47)⋊C4C2312yes—
175C2×(C2×D47)⋊C4C2312yes—
176C2×(C2×D47)⋊C4C2312yes—
177C2×(C2×D47)⋊C4C2312yes—
178C2×(C2×D47)⋊C4C2312yes—
179C2×(C2×D47)⋊C4C2312yes—
180C2×(C2×D47)⋊C4C2312yes—
181C2×(C2×D47)⋊C4C2312yes—
182C2×(C2×D47)⋊C4C2312yes—
183C22⋊C4×D47—28no—
184C22⋊C4×D47—28no—
185C2×C4×Dic47—42no—
186C2×C4×Dic47—42no—
187C2×C4×Dic47C2311yescharacteristic
188C2×C4×Dic47C2312yes—
189C2×C4×Dic47C2311yescharacteristic
190C2×C4×Dic47C2312yes—
191C2×C4×Dic47C2312yes—
192C2×C4×Dic47C2312yes—
193C2×C4×Dic47C2312yes—
194C2×C4×Dic47C2311yescharacteristic
195C2×C4×Dic47C2311yescharacteristic
196C42×D47—28no—
197C47⋊#95C2312yes—
198C47⋊#95C2312yes—
199C47⋊#95C2312yes—
200C47⋊#95C2312yes—
201C47⋊#95C2312yes—
202C47⋊#95C2312yes—
203C47⋊#95C2312yes—
204C47⋊#95C2312yes—
205C47⋊#95C2312yes—
206C47⋊#95C2312yes—
207C47⋊#95C2312yes—
208C22×D4×C47C2312yes—
209C22×D4×C47C2311yescharacteristic
210C23×C4×C47C2312yes—
211C23×C4×C47C2311yescharacteristic
212C23×C4×C47C2311yescharacteristic
213C23×C4×C47C2311yescharacteristic
214#121×C47C2×C418yescomplemented
215C4×D4×C47—28no—
216C2×C4⋊C4×C47C2312yes—
217C2×C4⋊C4×C47C2311yescharacteristic
218C2×C4⋊C4×C47C2311yescharacteristic
219C2×C4⋊C4×C47C2311yescharacteristic
220C2×C22⋊C4×C47C2312yes—
221C2×C22⋊C4×C47C2312yes—
222C2×C22⋊C4×C47C2312yes—
223C2×C22⋊C4×C47C2312yes—
224C2×C22⋊C4×C47C2312yes—
225C2×C42×C47C2312yes—
226#95×C47C2312yes—
227#95×C47C2312yes—
228#95×C47C2312yes—
229#95×C47C2312yes—
230#95×C47C2312yes—
231C24×C47C2412yes—
232C24×C47C2411yescharacteristic
233C23×D47—24no—
234C23×D47—24no—
235C23×D47—41no—
236C23×D47—41no—
237C23×D47—42no—
238C23×D47—42no—
239C23×D47—41no—
240C23×D47—41no—
241C23×D47—42no—
242C23×D47—42no—
243C23×D47C22×C414yes—
244C23×D47C22×C418yescomplemented
245C23×D47C2×D414yes—
246C23×D47#4114yes—
247C23×D47C2412yes—
248C23×D47C2412yes—
249C2×D4×C47—24no—
250C2×D4×C47—24no—
251C2×D4×C47—41no—
252C2×D4×C47—41no—
253C2×D4×C47C22×C418yescomplemented
254C2×D4×C47C22×C414yescomplemented
255C22×C4×C47—22no—
256C22×C4×C47—24no—
257C22×C4×C47—41no—
258C22×C4×C47—41no—
259C22×C4×C47—41no—
260C22×C4×C47—41no—
261C22×C4×C47—41no—
262C22×C4×C47—41no—
263C22×C4×C47—42no—
264C22×C4×C47—42no—
265C22×C4×C47C22×C414yescomplemented
266C22×C4×C47C2×D414yes—
267C22×C4×C47C2412yes—
268C22×C4×C47C2412yes—
269C22×C4×C47C2412yes—
270C22×C4×C47C2412yes—
271C22×C4×C47C2411yescharacteristic
272C22×C4×C47C2411yescharacteristic
273C22×C4×C47C2412yes—
274C2×C22⋊D47—24no—
275C2×C22⋊D47—24no—
276C2×C22⋊D47—24no—
277C2×C22⋊D47—24no—
278C2×C22⋊D47—42no—
279C2×C22⋊D47—42no—
280C2×C22⋊D47C22×C418yes—
281C2×C22⋊D47C22×C418yescomplemented
282C2×C22⋊D47C22×C418yescomplemented
283C22×Dic47—22no—
284C22×Dic47—22no—
285C22×Dic47—22no—
286C22×Dic47—24no—
287C22×Dic47—24no—
288C22×Dic47—24no—
289C22×Dic47—41no—
290C22×Dic47—41no—
291C22×Dic47—41no—
292C22×Dic47—41no—
293C22×Dic47C22×C414yescomplemented
294C22×Dic47C2×D414yes—
295C22×Dic47C2411yescharacteristic
296C22×Dic47C2411yescharacteristic
297C22×Dic47C2412yes—
298C22×Dic47C2412yes—
299C22×Dic47C2412yes—
300C22×Dic47C2412yes—
301C22×Dic47C2411yescharacteristic
302C22×Dic47C2411yescharacteristic
303D4×D47—264no—
304C2×D188—24no—
305C2×D188—24no—
306C2×D188—41no—
307C2×D188—41no—
308C2×D188C22×C418yes—
309C2×D188C22×C414yescomplemented
310C2×C4×D47—24no—
311C2×C4×D47—24no—
312C2×C4×D47—24no—
313C2×C4×D47—24no—
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—416no—
321C2×C4×D47—432no—
322C2×C4×D47—42no—
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×D47—42no—
330C2×C4×D47C22×C418yescomplemented
331C2×C4×D47C2×D418yes—
332C2×C4×D47C2×D418yes—
333C4⋊C4×C47—24no—
334C4⋊C4×C47—41no—
335C4⋊C4×C47—41no—
336C4⋊C4×C47C22×C414yescomplemented
337C22⋊C4×C47—24no—
338C22⋊C4×C47—24no—
339C22⋊C4×C47—42no—
340C22⋊C4×C47—42no—
341C22⋊C4×C47C22×C418yescomplemented
342C42×C47—24no—
343C22⋊Dic47—24no—
344C22⋊Dic47—24no—
345C22⋊Dic47—42no—
346C22⋊Dic47—42no—
347C22⋊Dic47C22×C418yescomplemented
348(C2×D47)⋊C4—24no—
349(C2×D47)⋊C4—24no—
350(C2×D47)⋊C4—24no—
351(C2×D47)⋊C4—24no—
352(C2×D47)⋊C4—24no—
353(C2×D47)⋊C4—24no—
354(C2×D47)⋊C4—42no—
355(C2×D47)⋊C4—42no—
356(C2×D47)⋊C4—42no—
357(C2×D47)⋊C4—42no—
358(C2×D47)⋊C4C22×C418yescomplemented
359(C2×D47)⋊C4C22×C418yescomplemented
360(C2×D47)⋊C4C22×C418yescomplemented
361(C2×D47)⋊C4C22×C418yescomplemented
362C4⋊Dic47—24no—
363C4⋊Dic47—41no—
364C4⋊Dic47—41no—
365C4⋊Dic47C22×C414yescomplemented
366Dic47⋊C4—24no—
367Dic47⋊C4—24no—
368Dic47⋊C4—42no—
369Dic47⋊C4—42no—
370Dic47⋊C4C22×C418yescomplemented
371C4×Dic47—24no—
372C4×Dic47—24no—
373C4×Dic47—24no—
374C4×Dic47—24no—
375C4×Dic47—22no—
376C4×Dic47—22no—
377C4×Dic47—42no—
378C4×Dic47—41no—
379C4×Dic47—41no—
380C23×C47—21no—
381C23×C47—21no—
382C23×C47—21no—
383C23×C47—21no—
384C23×C47—22no—
385C23×C47—22no—
386C23×C47—22no—
387C23×C47—22no—
388C23×C47—22no—
389C23×C47—22no—
390C23×C47C23×C414yes—
391C23×C47C23×C412yes—
392C23×C47C22×D412yes—
393C23×C47C2×#4112yes—
394C23×C47C2511yescharacteristic
395C22×D47—22no—
396C22×D47—22no—
397C22×D47—22no—
398C22×D47—22no—
399C22×D47—22no—
400C22×D47—22no—
401C22×D47—22no—
402C22×D47—22no—
403C22×D47—22no—
404C22×D47—22no—
405C22×D47—216no—
406C22×D47—44no—
407C22×D47—44no—
408C22×D47—44no—
409C22×D47—48no—
410C22×D47—48no—
411C22×D47—44no—
412C22×D47—44no—
413C22×D47—44no—
414C22×D47—48no—
415C22×D47—48no—
416C22×D47—48no—
417C22×D47—48no—
418C22×D47C4×D4116yescomplemented
419C22×D47C23×C414yes—
420C22×D47C23×C414yes—
421C22×D47C22×D414yes—
422C22×D47C2×#4114yes—
423D4×C47—216no—
424D4×C47—44no—
425C2×C4×C47—22no—
426C2×C4×C47—22no—
427C2×C4×C47—21no—
428C2×C4×C47—21no—
429C2×C4×C47—22no—
430C2×C4×C47—22no—
431C2×C4×C47—21no—
432C2×C4×C47—21no—
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—44no—
443C2×C4×C47—44no—
444C2×C4×C47—48no—
445C2×C4×C47—44no—
446C2×C4×C47C23×C414yes—
447C2×C4×C47C23×C412yes—
448C2×C4×C47C23×C412yes—
449C2×C4×C47C22×D414yes—
450C22⋊D47—216no—
451C22⋊D47—216no—
452C22⋊D47—48no—
453C2×Dic47—22no—
454C2×Dic47—22no—
455C2×Dic47—22no—
456C2×Dic47—21no—
457C2×Dic47—21no—
458C2×Dic47—22no—
459C2×Dic47—28no—
460C2×Dic47—22no—
461C2×Dic47—22no—
462C2×Dic47—21no—
463C2×Dic47—21no—
464C2×Dic47—21no—
465C2×Dic47—21no—
466C2×Dic47—22no—
467C2×Dic47—22no—
468C2×Dic47—22no—
469C2×Dic47—22no—
470C2×Dic47—21no—
471C2×Dic47—21no—
472C2×Dic47—44no—
473C2×Dic47—44no—
474C2×Dic47—48no—
475C2×Dic47C23×C414yes—
476C2×Dic47C23×C414yes—
477C2×Dic47C22×D412yes—
478C2×Dic47C22×D412yes—
479C2×Dic47H(5,𝔽2)12yes—
480C2×Dic47H(5,𝔽2)12yes—
481D188—216no—
482D188—44no—
483C4×D47—216no—
484C4×D47—216no—
485C4×D47—48no—
486C4×D47—48no—
487C4×D47—48no—
488C4×D47—48no—
489C4×D47—48no—
490C4×#534—471nomaximal, Sylow
491C22×C47—22no—
492C22×C47—22no—
493C22×C47—22no—
494C22×C47—22no—
495C22×C47—22no—
496C22×C47—22no—
497C22×C47—24no—
498C22×C47—24no—
499C22×C47—24no—
500C22×C47—42no—
501C22×C47—42no—
502C22×C47—42no—
503C22×C47—42no—
504C22×C47C2×C4×D414yes—
505C22×C47C24×C411yescharacteristic
506C22×C47C23×D411yescharacteristic
507C22×C47C22×#4111yescharacteristic
508C22×C47C2×H(5,𝔽2)11yescharacteristic
509C22×C47C2×H(5,𝔽2)11yescharacteristic
510C22×C47#58511yescharacteristic
511C22×C47#58511yescharacteristic
512C2×D47—24no—
513C2×D47—24no—
514C2×D47—24no—
515C2×D47—24no—
516C2×D47—24no—
517C2×D47—24no—
518C2×D47—24no—
519C2×D47—24no—
520C2×D47—24no—
521C2×D47—416no—
522C2×D47—432no—
523C2×D47—42no—
524C2×D47—42no—
525C2×D47—42no—
526C2×D47—42no—
527C2×D47C2×C4×D418yes—
528C4×C47—24no—
529C4×C47—22no—
530C4×C47—22no—
531C4×C47—24no—
532C4×C47—42no—
533C4×C47—42no—
534C4×C47—42no—
535Dic47—24no—
536Dic47—24no—
537Dic47—22no—
538Dic47—42no—
539Dic47—42no—
540Dic47—41no—
541Dic47—41no—
542Dic47#53414yescomplemented
543C2×#534—471no—
544C22×C4×D4—472no—
545#2325—471no—
546#2325—472no—
547#2325D4711yescharacteristic, complemented
548#2322—472no—
549#2322—472no—
550#2321—472no—
551#2321—472no—
552#2315—471no—
553#2308—472no—
554C4×#123—472no—
555C4×#123—472no—
556C4×#121—472no—
557C4×#121—471no—
558C4×#121—471no—
559C4×#120—472no—
560C4×#120—472no—
561C2×C4×C22⋊C4—471no—
562C2×C47—24no—
563C2×C47—44no—
564C2×C47C22×C4×D411yescharacteristic
565C2×C47C4×H(5,𝔽2)11yescharacteristic
566C2×C47C4×H(5,𝔽2)11yescharacteristic
567C2×C47C2×#53411yescharacteristic
568C2×C47#344911yescharacteristic
569C2×C47#345911yescharacteristic
570C2×C47#345911yescharacteristic
571D47—28no—
572D47—44no—
573C23×D4—472no—
574C24×C4—471no—
575C24×C4—472no—
576#534—4716no—
577C2×#123—472no—
578C2×#123—472no—
579C2×#121—472no—
580C2×#121—471no—
581C2×#121C2×D4711yescharacteristic
582C2×#120—472no—
583C2×#120—472no—
584C2×C4×D4—472no—
585C2×C4×D4—472no—
586C2×C4×D4—472no—
587C2×C4×D4—471no—
588C2×C4×D4—472no—
589C2×C4×D4—471no—
590C2×C4×D4—472no—
591C2×C4×D4—472no—
592C2×C4×D4—472no—
593C2×C4×D4—472no—
594C2×C4×D4—9416no—
595C2×C4×D4C2×D4712yescomplemented
596C22×C4⋊C4—472no—
597C22×C22⋊C4—471no—
598C22×C22⋊C4—471no—
599C22×C22⋊C4—472no—
600C22×C22⋊C4—472no—
601C22×C42—471no—
602C22×C42—471no—
603C22×C42—472no—
604#390—471no—
605#390—471no—
606#390—472no—
607#389—471no—
608#389—471no—
609#389—472no—
610#388—472no—
611#388—472no—
612#388—472no—
613#388—472no—
614#388—472no—
615#388—472no—
616#388—472no—
617#388C2×D4712yescomplemented
618#387—472no—
619#387—472no—
620#387—472no—
621#387C2×D4712yescomplemented
622#386—472no—
623#386—472no—
624#386—472no—
625#386—472no—
626#386—472no—
627#386—472no—
628#386—472no—
629#386—472no—
630#386—472no—
631#386—472no—
632#386C2×D4712yescomplemented
633#386C2×D4712yescomplemented
634#385—472no—
635#385—472no—
636#385—472no—
637#385—472no—
638#385—472no—
639#385—472no—
640#385—472no—
641#385C2×D4712yescomplemented
642#381—472no—
643#381—472no—
644#380—471no—
645#380—472no—
646#380C2×D4711yescharacteristic, complemented
647#379—472no—
648#379—472no—
649C4×C4⋊C4—471no—
650C4×C4⋊C4—471no—
651C4×C4⋊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—472no—
659C4×C22⋊C4—472no—
660C2×#95—471no—
661C2×#95C2×D4711yescharacteristic, complemented
662C47C4×#53411yescharacteristic, complemented, Sylow
663C25—471no—
664C25—472no—
665C22×D4—472no—
666C22×D4—472no—
667C22×D4—472no—
668C22×D4—4716no—
669C22×D4—472no—
670C22×D4—471no—
671C22×D4—948no—
672C22×D4—948no—
673C22×D4C22×D4712yes—
674C22×D4C22×D4711yescharacteristic
675C23×C4—471no—
676C23×C4—471no—
677C23×C4—472no—
678C23×C4—472no—
679C23×C4—478no—
680C23×C4—472no—
681C23×C4—472no—
682C23×C4—471no—
683C23×C4—472no—
684C23×C4—472no—
685C23×C4—472no—
686C23×C4—472no—
687C23×C4—948no—
688C23×C4—1882no—
689C23×C4—1882no—
690C23×C4—1884no—
691C23×C4—1884no—
692C23×C4C22×D4711yescharacteristic
693C23×C4C22×D4712yes—
694C23×C4C22×D4711yescharacteristic
695C23×C4C22×D4711yescharacteristic
696#123—4716no—
697#123—4716no—
698#121—4716no—
699#121—478no—
700#121C4×D4718yescomplemented
701#120—4716no—
702#120—4716no—
703C4×D4—28no—
704C4×D4—948no—
705C4×D4—948no—
706C4×D4—948no—
707C4×D4—948no—
708C4×D4—948no—
709C4×D4—948no—
710C4×D4—948no—
711C4×D4—1884no—
712C4×D4—1882no—
713C4×D4—1882no—
714C2×C4⋊C4—472no—
715C2×C4⋊C4—471no—
716C2×C4⋊C4—472no—
717C2×C4⋊C4—472no—
718C2×C4⋊C4—472no—
719C2×C4⋊C4—472no—
720C2×C4⋊C4—471no—
721C2×C4⋊C4—472no—
722C2×C4⋊C4—471no—
723C2×C4⋊C4—948no—
724C2×C4⋊C4C22×D4712yes—
725C2×C4⋊C4C22×D4711yescharacteristic
726C2×C4⋊C4C22×D4711yescharacteristic
727C2×C4⋊C4C22×D4711yescharacteristic
728C2×C22⋊C4—472no—
729C2×C22⋊C4—478no—
730C2×C22⋊C4—472no—
731C2×C22⋊C4—472no—
732C2×C22⋊C4—472no—
733C2×C22⋊C4—472no—
734C2×C22⋊C4—472no—
735C2×C22⋊C4—472no—
736C2×C22⋊C4—472no—
737C2×C22⋊C4—472no—
738C2×C22⋊C4—472no—
739C2×C22⋊C4—472no—
740C2×C22⋊C4—472no—
741C2×C22⋊C4—472no—
742C2×C22⋊C4—472no—
743C2×C22⋊C4—472no—
744C2×C22⋊C4—472no—
745C2×C22⋊C4—472no—
746C2×C22⋊C4—472no—
747C2×C22⋊C4—472no—
748C2×C22⋊C4—948no—
749C2×C22⋊C4—948no—
750C2×C22⋊C4—944no—
751C2×C22⋊C4C22×D4712yes—
752C2×C22⋊C4C22×D4712yes—
753C2×C22⋊C4C22×D4712yes—
754C2×C22⋊C4C22×D4712yes—
755C2×C22⋊C4C22×D4712yes—
756C2×C42—472no—
757C2×C42—472no—
758C2×C42—472no—
759C2×C42—472no—
760C2×C42—471no—
761C2×C42—471no—
762C2×C42—472no—
763C2×C42—471no—
764C2×C42—471no—
765C2×C42—948no—
766C2×C42—1882no—
767C2×C42—1882no—
768C2×C42C22×D4712yes—
769#95—472no—
770#95—472no—
771#95—472no—
772#95—472no—
773#95—472no—
774#95—472no—
775#95—472no—
776#95—472no—
777#95—472no—
778#95—472no—
779#95—472no—
780#95C22×D4712yes—
781#95C22×D4712yes—
782#95C22×D4712yes—
783#95C22×D4712yes—
784#95C22×D4712yes—
785C24—472no—
786C24—474no—
787C24—474no—
788C24—474no—
789C24—472no—
790C24—478no—
791C24—944no—
792C24—944no—
793C24—1881no—
794C24—1881no—
795C24—1882no—
796C24—1882no—
797C24—1881no—
798C24—1881no—
799C24—1882no—
800C24—1882no—
801C24C23×D4712yes—
802C24C23×D4711yescharacteristic
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—41no—
806C2×D4—41no—
807C2×D4—478no—
808C2×D4—478no—
809C2×D4—478no—
810C2×D4—478no—
811C2×D4—474no—
812C2×D4—944no—
813C2×D4—944no—
814C2×D4—9464no—
815C2×D4—944no—
816C2×D4—944no—
817C2×D4—944no—
818C2×D4—944no—
819C2×D4—1881no—
820C2×D4—1881no—
821C2×D4—1882no—
822C2×D4—1882no—
823C2×D4C2×C4×D4718yescomplemented
824C2×D4C2×C4×D4714yescomplemented
825C22×C4—22no—
826C22×C4—24no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—471no—
836C22×C4—474no—
837C22×C4—472no—
838C22×C4—472no—
839C22×C4—471no—
840C22×C4—474no—
841C22×C4—478no—
842C22×C4—478no—
843C22×C4—478no—
844C22×C4—471no—
845C22×C4—471no—
846C22×C4—472no—
847C22×C4—472no—
848C22×C4—944no—
849C22×C4—944no—
850C22×C4—944no—
851C22×C4—944no—
852C22×C4—944no—
853C22×C4—944no—
854C22×C4—944no—
855C22×C4—944no—
856C22×C4—944no—
857C22×C4—942no—
858C22×C4—942no—
859C22×C4—944no—
860C22×C4—944no—
861C22×C4—944no—
862C22×C4—942no—
863C22×C4—944no—
864C22×C4—1882no—
865C22×C4—1882no—
866C22×C4—1882no—
867C22×C4—1882no—
868C22×C4—1882no—
869C22×C4—1882no—
870C22×C4—1882no—
871C22×C4—1882no—
872C22×C4—18816no—
873C22×C4—18832no—
874C22×C4—1881no—
875C22×C4—1881no—
876C22×C4—1881no—
877C22×C4—1881no—
878C22×C4C2×C4×D4714yescomplemented
879C22×C4D4×D4714yes—
880C22×C4C23×D4712yes—
881C22×C4C23×D4712yes—
882C22×C4C23×D4712yes—
883C22×C4C23×D4711yescharacteristic
884C22×C4C23×D4712yes—
885C22×C4C23×D4711yescharacteristic
886C22×C4C23×D4712yes—
887C4⋊C4—24no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—478no—
891C4⋊C4—474no—
892C4⋊C4—944no—
893C4⋊C4—944no—
894C4⋊C4—944no—
895C4⋊C4—1882no—
896C4⋊C4—1882no—
897C4⋊C4—1881no—
898C4⋊C4—1881no—
899C4⋊C4C2×C4×D4714yescomplemented
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—478no—
905C22⋊C4—478no—
906C22⋊C4—478no—
907C22⋊C4—478no—
908C22⋊C4—478no—
909C22⋊C4—944no—
910C22⋊C4—944no—
911C22⋊C4—944no—
912C22⋊C4—944no—
913C22⋊C4—944no—
914C22⋊C4—944no—
915C22⋊C4—944no—
916C22⋊C4—944no—
917C22⋊C4—1882no—
918C22⋊C4—1882no—
919C22⋊C4—1882no—
920C22⋊C4—1882no—
921C22⋊C4—1882no—
922C22⋊C4—1882no—
923C22⋊C4C2×C4×D4718yescomplemented
924C42—24no—
925C42—944no—
926C42—944no—
927C42—942no—
928C42—942no—
929C42—944no—
930C42—944no—
931C42—1881no—
932C42—1881no—
933C42—1882no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—474no—
945C23—474no—
946C23—474no—
947C23—4716no—
948C23—474no—
949C23—9416no—
950C23—942no—
951C23—942no—
952C23—942no—
953C23—942no—
954C23—942no—
955C23—942no—
956C23—942no—
957C23—942no—
958C23—942no—
959C23—942no—
960C23—1884no—
961C23—1884no—
962C23—1884no—
963C23—1884no—
964C23—1884no—
965C23—1884no—
966C23—1888no—
967C23—1888no—
968C23—1888no—
969C23—1888no—
970C23—1888no—
971C23—1888no—
972C23C22×C4×D4714yes—
973C23C22×C4×D4712yes—
974C23C2×D4×D4712yes—
975C23#41×D4712yes—
976C23C24×D4711yescharacteristic
977D4—216no—
978D4—44no—
979D4—9416no—
980D4—9416no—
981D4—9416no—
982D4—1884no—
983D4—1888no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
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—44no—
1005C2×C4—472no—
1006C2×C4—472no—
1007C2×C4—472no—
1008C2×C4—474no—
1009C2×C4—474no—
1010C2×C4—472no—
1011C2×C4—9416no—
1012C2×C4—9416no—
1013C2×C4—948no—
1014C2×C4—942no—
1015C2×C4—942no—
1016C2×C4—942no—
1017C2×C4—941no—
1018C2×C4—941no—
1019C2×C4—942no—
1020C2×C4—942no—
1021C2×C4—942no—
1022C2×C4—941no—
1023C2×C4—941no—
1024C2×C4—941no—
1025C2×C4—941no—
1026C2×C4—942no—
1027C2×C4—942no—
1028C2×C4—942no—
1029C2×C4—941no—
1030C2×C4—941no—
1031C2×C4—942no—
1032C2×C4—1888no—
1033C2×C4—1888no—
1034C2×C4—1888no—
1035C2×C4—1888no—
1036C2×C4—1888no—
1037C2×C4—1888no—
1038C2×C4—1884no—
1039C2×C4—1884no—
1040C2×C4C22×C4×D4712yes—
1041C2×C4C22×C4×D4712yes—
1042C2×C4C22×C4×D4714yes—
1043C2×C4C2×D4×D4714yes—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—22no—
1050C22—24no—
1051C22—24no—
1052C22—24no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—478no—
1058C22—944no—
1059C22—944no—
1060C22—944no—
1061C22—944no—
1062C22—944no—
1063C22—944no—
1064C22—944no—
1065C22—944no—
1066C22—944no—
1067C22—18816no—
1068C22—18832no—
1069C22—1882no—
1070C22—1882no—
1071C22—1882no—
1072C22—1882no—
1073C22C4×D4×D4714yes—
1074C22C23×C4×D4711yescharacteristic
1075C22C22×D4×D4711yescharacteristic
1076C22C2×#41×D4711yescharacteristic
1077C22H(5,𝔽2)×D4711yescharacteristic
1078C22H(5,𝔽2)×D4711yescharacteristic
1079C22#1568995811yescharacteristic
1080C22#1568996011yescharacteristic
1081C4—24no—
1082C4—22no—
1083C4—22no—
1084C4—24no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—474no—
1089C4—944no—
1090C4—944no—
1091C4—942no—
1092C4—1881no—
1093C4—1881no—
1094C4—1882no—
1095C4—1882no—
1096C2—24no—
1097C2—44no—
1098C2—948no—
1099C2—1884no—
1100C2C2×C4×D4×D4711yescharacteristic
1101C2#2025659211yescharacteristic
1102C2#2025659411yescharacteristic
1103C2#534×D4711yescharacteristic
1104C2#2025671611yescharacteristic
1105C2#2025679611yescharacteristic
1106C2#2025679911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2325C2
socle, cosocleC23×C47C25
prime radicalC2×#15689681C2
hypercenter#2325D47
hypocenterC47C4×#534
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2325

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×D47C2semidirect
3. #20246091C2semidirect
4. #20246086C2semidirect
5. #20246061C2semidirect
6. #20246055C2semidirect
7. #20246050C2semidirect
8. #20246044C2semidirect
9. #20246001C2semidirect
10. #20245962C2semidirect
11. #20245915C2semidirect
12. #20245909C2semidirect
13. #121×Dic47C2semidirect
14. #20245898C2semidirect
15. #20245894C2semidirect
16. #20245893C2semidirect
17. #20245889C2semidirect
18. C2×#15688970C2semidirect
19. C47×#2325C2semidirect
22. C23×C4×D47C22semidirect
23. #15689681C4semidirect
31. C2×D4×Dic47C22semidirect
32. C2×D4×Dic47C22semidirect
34. C2×#13093986C22semidirect
36. C2×C4×C22⋊D47C22semidirect
38. C2×(C22⋊D47)⋊C4C22semidirect
39. C2×(C22⋊D47)⋊C4C22semidirect
41. C2×C4⋊C4×D47C22semidirect
45. C2×C22⋊C4×D47C22semidirect
46. C22×C4×Dic47C22semidirect
47. C22×C4×Dic47C22semidirect
48. C2×C42×D47C22semidirect
49. #15689026C22semidirect
50. #15689024C22semidirect
51. #15689023C22semidirect
52. #15689022C22semidirect
53. #15689020C22semidirect
54. #15689019C22semidirect
55. #15689016C22semidirect
56. #15689015C22semidirect
57. #15689015C22semidirect
58. #15689014C22semidirect
59. #15689012C22semidirect
60. #15689011C22semidirect
61. #15689011C22semidirect
62. #15689008C22semidirect
63. #15689007C22semidirect
64. #15689004C22semidirect
65. #15689003C22semidirect
66. #15689002C22semidirect
67. #15689002C22semidirect
70. #15689001C22semidirect
71. #15689000C22semidirect
74. #15688999C22semidirect
75. #15688997C22semidirect
76. #15688997C22semidirect
77. #15688997C22semidirect
78. #15688996C22semidirect
79. #15688994C22semidirect
80. #15688994C22semidirect
81. #15688994C22semidirect
82. #15688985C22semidirect
83. #15688985C22semidirect
84. #15688983C22semidirect
85. #15688981C22semidirect
86. #15688978C22semidirect
87. #15688978C22semidirect
88. C4⋊C4×Dic47C22semidirect
89. C4⋊C4×Dic47C22semidirect
90. #15688974C22semidirect
91. C22⋊C4×Dic47C22semidirect
92. C22⋊C4×Dic47C22semidirect
93. #15688970C22semidirect
94. #15688970C22semidirect
95. #15688970C22semidirect
96. #15688970C22semidirect
97. #15688970C22semidirect
98. #15688970C22semidirect
99. C2×C47⋊#95C22semidirect
101. C2×C4×D4×C47C22semidirect
102. C47×#388C22semidirect
103. C47×#387C22semidirect
104. C47×#386C22semidirect
105. C47×#386C22semidirect
106. C47×#385C22semidirect
107. C47×#380C22semidirect
108. C2×#95×C47C22semidirect
118. C2×D4×D47C2×C4semidirect
128. C22×C4×D47D4semidirect
136. #13094009C2×C4semidirect
137. #13094006C2×C4semidirect
138. #13093998C2×C4semidirect
139. #13093996C2×C4semidirect
140. #13093994C2×C4semidirect
141. #13093992C2×C4semidirect
168. C2×(C2×D47)⋊C4C2×C4semidirect
214. #121×C47C2×C4semidirect
244. C23×D47C22×C4semidirect
253. C2×D4×C47C22×C4semidirect
254. C2×D4×C47C22×C4semidirect
265. C22×C4×C47C22×C4semidirect
281. C2×C22⋊D47C22×C4semidirect
282. C2×C22⋊D47C22×C4semidirect
293. C22×Dic47C22×C4semidirect
309. C2×D188C22×C4semidirect
330. C2×C4×D47C22×C4semidirect
336. C4⋊C4×C47C22×C4semidirect
341. C22⋊C4×C47C22×C4semidirect
347. C22⋊Dic47C22×C4semidirect
358. (C2×D47)⋊C4C22×C4semidirect
359. (C2×D47)⋊C4C22×C4semidirect
360. (C2×D47)⋊C4C22×C4semidirect
361. (C2×D47)⋊C4C22×C4semidirect
365. C4⋊Dic47C22×C4semidirect
370. Dic47⋊C4C22×C4semidirect
418. C22×D47C4×D4semidirect
542. Dic47#534semidirect
547. #2325D47semidirect
595. C2×C4×D4C2×D47semidirect
617. #388C2×D47semidirect
621. #387C2×D47semidirect
632. #386C2×D47semidirect
633. #386C2×D47semidirect
641. #385C2×D47semidirect
646. #380C2×D47semidirect
661. C2×#95C2×D47semidirect
662. C47C4×#534semidirect
700. #121C4×D47semidirect
823. C2×D4C2×C4×D47semidirect
824. C2×D4C2×C4×D47semidirect
878. C22×C4C2×C4×D47semidirect
899. C4⋊C4C2×C4×D47semidirect
923. 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×#156896812
C2×C4×D4×D472
#202460912
#202460862
#202460612
#202460552
#202460502
#202460442
#202460012
#202459622
#202459152
#202459092
#121×Dic472
#202458982
#202458942
#202458932
#202458892
C2×#156889702
C47×#23252
C4×#53447