Finite Group Databasebeta

← #26388564

Subgroups — #26388564

Order 12032.

3114 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689651C211yesmaximal, characteristic, complemented
2C2×C4×D4×D47C211yesmaximal, characteristic, complemented
3#20249018C211yesmaximal, characteristic, complemented
4#20249016C211yesmaximal, characteristic, complemented
5#20249010C211yesmaximal, characteristic, complemented
6#20249008C211yesmaximal, characteristic, complemented
7#20248583C212yesmaximal, complemented
8#20248354C212yesmaximal, complemented
9#20247875C211yesmaximal, characteristic, complemented
10#20247861C211yesmaximal, characteristic, complemented
11#20247034C211yesmaximal, characteristic, complemented
12#20247020C211yesmaximal, characteristic
13#20246768C212yesmaximal, complemented
14#20246766C212yesmaximal, complemented
15#20246628C211yesmaximal, characteristic, complemented
16#20246626C211yesmaximal, characteristic, complemented
17#20246624C211yesmaximal, characteristic, complemented
18C4×#13094020C212yesmaximal, complemented
19C4×#13094010C212yesmaximal, complemented
20C4×#13093994C212yesmaximal, complemented
21C4×#13093992C212yesmaximal, complemented
22C4×#13093982C211yesmaximal, characteristic, complemented
23C47×#2392C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C23×C4×D47C2212yes—
26C2×#13094020C2212yes—
27#15689651—28no—
28C2×#13094019C2211yescharacteristic, complemented
29C2×#13094017C2211yescharacteristic, complemented
30C2×#13094014C2211yescharacteristic, complemented
31C2×#13094010C2212yes—
32C2×#13094010C2211yescharacteristic, complemented
33C2×#13094009C2211yescharacteristic
34C2×#13094006C2211yescharacteristic
35C2×#13094002C2211yescharacteristic
36C2×#13093997C2211yescharacteristic
37C2×#13093994C2212yes—
38C2×#13093992C2212yes—
39C2×C4×Dic94C2211yescharacteristic, complemented
40C2×C4×D188C2211yescharacteristic
41C2×C4×D188C2211yescharacteristic
42C2×C4×D188C2212yescomplemented
43C2×D4×Dic47C2211yescharacteristic
44C2×#13093986C2211yescharacteristic
45C2×C4×C22⋊D47C2212yes—
46C2×C4×C22⋊D47C2211yescharacteristic
47C2×C4×C22⋊D47C2211yescharacteristic, complemented
48C2×C4×C22⋊D47C2212yescomplemented
49C2×C4×C22⋊D47C2212yescomplemented
50C2×(C22⋊D47)⋊C4C2212yes—
51C4×D4×D47—28no—
52C2×#13093982C2212yes—
53C2×#13093981C2211yescharacteristic, complemented
54C2×C4⋊C4×D47C2211yescharacteristic
55C2×C22⋊C4×D47C2212yes—
56C2×C42×D47C2211yescharacteristic
57#15689055C2211yescharacteristic, complemented
58#15689054C2211yescharacteristic, complemented
59#15689053C2211yescharacteristic, complemented
60#15689050C2211yescharacteristic, complemented
61#15689049C2211yescharacteristic, complemented
62#15689048C2211yescharacteristic, complemented
63#15689046C2212yescomplemented
64#15689045C2212yescomplemented
65#15689045C2212yescomplemented
66#15689041C2211yescharacteristic
67#15689040C2211yescharacteristic
68#15689040C2212yescomplemented
69#15689039C2212yescomplemented
70#15689039C2212yescomplemented
71#15689037C2211yescharacteristic
72#15689033C2211yescharacteristic
73#15689032C2211yescharacteristic
74#15689031C2211yescharacteristic
75#15689027C2212yescomplemented
76#15689026C2212yescomplemented
77#15689024C2212yescomplemented
78#15689023C2212yes—
79#15689023C2212yes—
80#15689023C2212yescomplemented
81#15689023C2212yescomplemented
82#15689023C2212yescomplemented
83#15689016C2212yescomplemented
84#15689015C2212yescomplemented
85#15689012C2212yescomplemented
86#15689011C2212yescomplemented
87#15689003C2212yescomplemented
88#15689001C2212yes—
89#15689001C2212yescomplemented
90#15689000C2212yescomplemented
91#15688999C2212yes—
92#15688999C2212yescomplemented
93#15688998C2212yescomplemented
94#15688997C2212yes—
95#15688997C2212yescomplemented
96#15688995C2212yescomplemented
97#15688994C2212yes—
98#15688994C2212yescomplemented
99#15688992C2212yescomplemented
100#15688987C2212yescomplemented
101#15688978C2212yes—
102#15688978C2212yes—
103C4⋊C4×Dic47C2212yescomplemented
104C4×C4⋊Dic47C2211yescharacteristic, complemented
105C4×(C2×D47)⋊C4C2212yes—
106C4×(C2×D47)⋊C4C2212yescomplemented
107C4×(C2×D47)⋊C4C2212yescomplemented
108C4×C22⋊Dic47C2212yescomplemented
109#15688970C2211yescharacteristic
110#15688970C2211yescharacteristic
111#15688968C2211yescharacteristic, complemented
112#15688968C2211yescharacteristic, complemented
113C42×Dic47C2212yescomplemented
114C2×C4×D4×C47C2211yescharacteristic
115C2×C4×D4×C47C2212yescomplemented
116C2×#117×C47C2211yescharacteristic, complemented
117C47×#398C2211yescharacteristic, complemented
118C47×#397C2211yescharacteristic, complemented
119C47×#396C2212yescomplemented
120C47×#394C2211yescharacteristic
121C47×#394C2212yescomplemented
122C47×#392C2211yescharacteristic
123C4×C4⋊C4×C47C2211yescharacteristic, complemented
124C4×C22⋊C4×C47C2212yescomplemented
125C24×D47C2312yes—
126C22×Dic94C2311yescharacteristic
127C22×D188C2311yescharacteristic
128C22×D188C2311yescharacteristic
129C22×D188C2312yes—
130C22×C22⋊D47C2311yescharacteristic
131C22×C22⋊D47C2311yescharacteristic
132C22×C22⋊D47C2312yes—
133C22×C22⋊D47C2312yes—
134C22×C22⋊D47C2312yes—
135C2×D4×D47—28no—
136C2×D4×D47—24no—
137C23×Dic47C2312yes—
138C22×C4×D47—28no—
139C22×C4×D47—44no—
140C22×C4×D47—44no—
141C22×C4×D47C2312yes—
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2312yes—
147C22×C4×D47C2312yes—
148#13094020—28no—
149#13094019—24no—
150#13094017—24no—
151#13094014—24no—
152#13094010—28no—
153#13094010—24no—
154#13094009—24no—
155#13094006—24no—
156#13094002—24no—
157#13093997—24no—
158#13093994—28no—
159#13093992—28no—
160C4×Dic94—24no—
161C4×D188—24no—
162C4×D188—24no—
163C4×D188—44no—
164D4×Dic47—24no—
165#13093986—24no—
166C4×C22⋊D47—24no—
167C4×C22⋊D47—28no—
168C4×C22⋊D47—24no—
169C4×C22⋊D47—44no—
170C4×C22⋊D47—44no—
171(C22⋊D47)⋊C4—28no—
172#13093982—28no—
173#13093981—24no—
174C2×C4⋊Dic47C2312yes—
175C2×C4⋊Dic47C2311yescharacteristic
176C2×C4⋊Dic47C2311yescharacteristic
177C2×C4⋊Dic47C2311yescharacteristic
178C2×C4⋊Dic47C2312yes—
179C2×Dic47⋊C4C2311yescharacteristic
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2311yescharacteristic
182C2×Dic47⋊C4C2311yescharacteristic
183C2×Dic47⋊C4C2311yescharacteristic
184C2×Dic47⋊C4C2311yescharacteristic
185C2×Dic47⋊C4C2311yescharacteristic
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C4⋊C4×D47—24no—
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2311yescharacteristic
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2311yescharacteristic
194C2×C22⋊Dic47C2312yes—
195C2×C22⋊Dic47C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2311yescharacteristic
202C2×(C2×D47)⋊C4C2311yescharacteristic
203C2×(C2×D47)⋊C4C2311yescharacteristic
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2311yescharacteristic
206C2×(C2×D47)⋊C4C2311yescharacteristic
207C2×(C2×D47)⋊C4C2311yescharacteristic
208C2×(C2×D47)⋊C4C2312yes—
209C2×(C2×D47)⋊C4C2312yes—
210C2×(C2×D47)⋊C4C2312yes—
211C2×(C2×D47)⋊C4C2312yes—
212C2×(C2×D47)⋊C4C2312yes—
213C2×(C2×D47)⋊C4C2312yes—
214C22⋊C4×D47—28no—
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2312yes—
217C2×C4×Dic47C2312yes—
218C2×C4×Dic47C2312yes—
219C2×C4×Dic47C2312yes—
220C2×C4×Dic47C2311yescharacteristic
221C2×C4×Dic47C2311yescharacteristic
222C2×C4×Dic47C2311yescharacteristic
223C2×C4×Dic47C2311yescharacteristic
224C42×D47D418yescomplemented
225C47⋊#95C2311yescharacteristic
226C47⋊#95C2311yescharacteristic
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C22×D4×C47C2311yescharacteristic
236C22×D4×C47C2312yes—
237C23×C4×C47C2312yes—
238C23×C4×C47C2311yescharacteristic
239C4×D4×C47—24no—
240C4×D4×C47—44no—
241#117×C47—24no—
242C2×C4⋊C4×C47C2312yes—
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2311yescharacteristic
246C2×C4⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2311yescharacteristic
250C2×C22⋊C4×C47C2311yescharacteristic
251C2×C22⋊C4×C47C2312yes—
252C2×C22⋊C4×C47C2312yes—
253C2×C22⋊C4×C47C2312yes—
254C2×C42×C47C2312yes—
255C2×C42×C47C2311yescharacteristic
256C2×C42×C47C2311yescharacteristic
257#95×C47C2311yescharacteristic
258#95×C47C2311yescharacteristic
259#95×C47C2312yes—
260#95×C47C2312yes—
261C24×C47C2411yescharacteristic
262C24×C47C2412yes—
263C23×D47—24no—
264C23×D47—24no—
265C23×D47—24no—
266C23×D47—24no—
267C23×D47—24no—
268C23×D47—42no—
269C23×D47—42no—
270C23×D47C2411yescharacteristic
271C23×D47C2412yes—
272C23×D47C2411yescharacteristic
273C2×D4×C47—24no—
274C2×D4×C47—24no—
275C2×D4×C47—22no—
276C2×D4×C47—24no—
277C2×D4×C47—42no—
278C22×C4×C47—22no—
279C22×C4×C47—24no—
280C22×C4×C47—22no—
281C22×C4×C47—24no—
282C22×C4×C47—22no—
283C22×C4×C47—24no—
284C22×C4×C47C2412yes—
285C22×C4×C47C2411yescharacteristic
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2412yes—
289C22×C4×C47C2411yescharacteristic
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2412yes—
292C22×C4×C47C2411yescharacteristic
293C2×C22⋊D47—24no—
294C2×C22⋊D47—22no—
295C2×C22⋊D47—24no—
296C2×C22⋊D47—24no—
297C2×C22⋊D47—24no—
298C2×C22⋊D47—22no—
299C2×C22⋊D47—24no—
300C2×C22⋊D47—24no—
301C2×C22⋊D47—24no—
302C2×C22⋊D47—24no—
303C2×C22⋊D47—42no—
304C2×C22⋊D47—42no—
305C2×C22⋊D47#4118yes—
306C22×Dic47—24no—
307C22×Dic47—42no—
308C22×Dic47—42no—
309C22×Dic47C2412yes—
310C22×Dic47C2411yescharacteristic
311C22×Dic47C2411yescharacteristic
312C22×Dic47C2412yes—
313C22×Dic47C2411yescharacteristic
314C22×Dic47C2411yescharacteristic
315C22×Dic47C2411yescharacteristic
316C22×Dic47C2412yes—
317C22×Dic47C2411yescharacteristic
318D4×D47—232no—
319C2×D188—24no—
320C2×D188—22no—
321C2×D188—22no—
322C2×D188—24no—
323C2×D188—24no—
324C2×D188—24no—
325C2×D188—42no—
326C2×C4×D47—24no—
327C2×C4×D47—22no—
328C2×C4×D47—22no—
329C2×C4×D47—24no—
330C2×C4×D47—24no—
331C2×C4×D47—22no—
332C2×C4×D47—24no—
333C2×C4×D47—22no—
334C2×C4×D47—24no—
335C2×C4×D47—22no—
336C2×C4×D47—24no—
337C2×C4×D47—24no—
338C2×C4×D47—432no—
339C2×C4×D47—42no—
340C2×C4×D47—42no—
341C2×C4×D47—42no—
342C2×C4×D47—42no—
343C2×C4×D47C2×D414yes—
344C2×C4×D47C2×D414yes—
345C2×C4×D47C2×D414yes—
346C2×Dic94—22no—
347C2×Dic94—24no—
348C4⋊C4×C47—22no—
349C4⋊C4×C47—22no—
350C4⋊C4×C47—22no—
351C4⋊C4×C47—24no—
352C4⋊C4×C47—42no—
353C22⋊C4×C47—24no—
354C22⋊C4×C47—22no—
355C22⋊C4×C47—22no—
356C22⋊C4×C47—24no—
357C22⋊C4×C47—24no—
358C22⋊C4×C47—42no—
359C22⋊C4×C47—42no—
360C42×C47—22no—
361C42×C47—24no—
362C42×C47C2×D414yes—
363C22⋊Dic47—24no—
364C22⋊Dic47—24no—
365C22⋊Dic47—22no—
366C22⋊Dic47—22no—
367C22⋊Dic47—24no—
368C22⋊Dic47—42no—
369C22⋊Dic47—42no—
370(C2×D47)⋊C4—22no—
371(C2×D47)⋊C4—22no—
372(C2×D47)⋊C4—24no—
373(C2×D47)⋊C4—24no—
374(C2×D47)⋊C4—24no—
375(C2×D47)⋊C4—24no—
376(C2×D47)⋊C4—22no—
377(C2×D47)⋊C4—22no—
378(C2×D47)⋊C4—24no—
379(C2×D47)⋊C4—24no—
380(C2×D47)⋊C4—22no—
381(C2×D47)⋊C4—22no—
382(C2×D47)⋊C4—24no—
383(C2×D47)⋊C4—42no—
384(C2×D47)⋊C4—42no—
385(C2×D47)⋊C4—42no—
386(C2×D47)⋊C4—42no—
387(C2×D47)⋊C4#4118yes—
388C4⋊Dic47—22no—
389C4⋊Dic47—22no—
390C4⋊Dic47—22no—
391C4⋊Dic47—24no—
392C4⋊Dic47—42no—
393Dic47⋊C4—22no—
394Dic47⋊C4—22no—
395Dic47⋊C4—24no—
396Dic47⋊C4—22no—
397Dic47⋊C4—22no—
398Dic47⋊C4—22no—
399Dic47⋊C4—22no—
400Dic47⋊C4—42no—
401Dic47⋊C4—42no—
402C4×Dic47—22no—
403C4×Dic47—24no—
404C4×Dic47—24no—
405C4×Dic47—24no—
406C4×Dic47—24no—
407C4×Dic47—24no—
408C4×Dic47C2×D414yes—
409C4×Dic47C2×D414yes—
410C4×Dic47C2×D414yes—
411C23×C47—22no—
412C23×C47—22no—
413C23×C47—22no—
414C23×C47—22no—
415C23×C47—22no—
416C23×C47—22no—
417C23×C47—21no—
418C23×C47—22no—
419C23×C47—22no—
420C23×C47—21no—
421C23×C47—21no—
422C23×C47C2×#4114yes—
423C23×C47C2511yescharacteristic
424C22×D47—22no—
425C22×D47—21no—
426C22×D47—21no—
427C22×D47—216no—
428C22×D47—22no—
429C22×D47—22no—
430C22×D47—22no—
431C22×D47—22no—
432C22×D47—22no—
433C22×D47—22no—
434C22×D47—21no—
435C22×D47—22no—
436C22×D47—22no—
437C22×D47—21no—
438C22×D47—21no—
439C22×D47—48no—
440C22×D47—48no—
441C22×D47—48no—
442C22×D47—48no—
443C22×D47—48no—
444C22×D47—48no—
445C22×D47C22×D412yes—
446C22×D47C2×#4114yes—
447C22×D47C2×#4114yes—
448D4×C47—28no—
449D4×C47—48no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—22no—
453C2×C4×C47—22no—
454C2×C4×C47—21no—
455C2×C4×C47—21no—
456C2×C4×C47—22no—
457C2×C4×C47—21no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—21no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—21no—
466C2×C4×C47—22no—
467C2×C4×C47—48no—
468C2×C4×C47—44no—
469C2×C4×C47C22×D412yes—
470C2×C4×C47C22×D412yes—
471C2×C4×C47C22×D412yes—
472C2×C4×C47C2×#4114yes—
473C2×C4×C47H(5,𝔽2)12yes—
474C2×C4×C47H(5,𝔽2)12yes—
475C22⋊D47—216no—
476C22⋊D47—48no—
477C22⋊D47—48no—
478C22⋊D47—44no—
479C22⋊D47—44no—
480C2×Dic47—22no—
481C2×Dic47—22no—
482C2×Dic47—22no—
483C2×Dic47—21no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—21no—
487C2×Dic47—21no—
488C2×Dic47—22no—
489C2×Dic47—22no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—21no—
495C2×Dic47—22no—
496C2×Dic47—21no—
497C2×Dic47—22no—
498C2×Dic47—48no—
499C2×Dic47C22×D412yes—
500C2×Dic47C22×D412yes—
501C2×Dic47C22×D412yes—
502C2×Dic47C2×#4114yes—
503C2×Dic47C2×#4114yes—
504D188—28no—
505D188—48no—
506D188—44no—
507C4×D47—28no—
508C4×D47—28no—
509C4×D47—28no—
510C4×D47—48no—
511C4×D47—48no—
512C4×D47—44no—
513C4×D47—48no—
514Dic94—44no—
515#34965—471nomaximal, Sylow
516C22×C47—24no—
517C22×C47—24no—
518C22×C47—24no—
519C22×C47—42no—
520C22×C47—42no—
521C22×C47—42no—
522C22×C47—42no—
523C22×C47—41no—
524C22×C47—41no—
525C22×C47—41no—
526C22×C47—42no—
527C22×C47—42no—
528C22×C47C23×D411yescharacteristic
529C22×C47C22×#4112yes—
530C22×C47C22×#4112yes—
531C22×C47C2×H(5,𝔽2)11yescharacteristic
532C22×C47C2×H(5,𝔽2)11yescharacteristic
533C2×D47—22no—
534C2×D47—22no—
535C2×D47—24no—
536C2×D47—24no—
537C2×D47—24no—
538C2×D47—24no—
539C2×D47—24no—
540C2×D47—432no—
541C2×D47—42no—
542C2×D47—42no—
543C2×D47—42no—
544C2×D47—42no—
545C2×D47—41no—
546C2×D47—41no—
547C2×D47—41no—
548C2×D47—42no—
549C2×D47—42no—
550C2×D47#53214yes—
551C4×C47—22no—
552C4×C47—22no—
553C4×C47—24no—
554C4×C47—41no—
555C4×C47—41no—
556C4×C47—42no—
557C4×C47—41no—
558C4×C47—42no—
559C4×C47#53514yes—
560Dic47—22no—
561Dic47—22no—
562Dic47—24no—
563Dic47—41no—
564Dic47—41no—
565Dic47—42no—
566Dic47—41no—
567Dic47—42no—
568Dic47#52514yes—
569C2×#529—471no—
570C22×C4×D4—471no—
571#2603—471no—
572#2603—471no—
573#2603—471no—
574#2603—471no—
575#2566—472no—
576#2544—472no—
577#2504—471no—
578#2502—471no—
579#2435—471no—
580#2433—471no—
581#2411—472no—
582#2411—472no—
583#2392—471no—
584#2392—471no—
585#2392—471no—
586#2392D4711yescharacteristic, complemented
587C4×#127—472no—
588C4×#124—472no—
589C4×#120—472no—
590C4×#120—472no—
591C4×#117—471no—
592C2×C47—44no—
593C2×C47—81no—
594C2×C47C2×#52511yescharacteristic
595C2×C47C2×#53211yescharacteristic
596C2×C47C2×#53511yescharacteristic
597C2×C47#348112yes—
598C2×C47#348112yes—
599D47—24no—
600D47—44no—
601D47—81no—
602C23×D4—471no—
603C24×C4—472no—
604C2×#127—472no—
605#529—948no—
606C2×#126—471no—
607C2×#126—471no—
608C2×#125—471no—
609C2×#124—471no—
610C2×#124—472no—
611C2×#123—471no—
612C2×#123—471no—
613C2×C22⋊Q8—471no—
614C2×#121—471no—
615C2×#120—472no—
616C2×#120—472no—
617C2×C4×Q8—471no—
618C2×C4×D4—471no—
619C2×C4×D4—471no—
620C2×C4×D4—472no—
621C2×C4×D4—471no—
622C2×C4×D4—472no—
623C2×C4×D4—472no—
624C2×C4×D4—471no—
625C2×C4×D4—472no—
626C2×C4×D4—471no—
627C2×C4×D4—471no—
628C2×C4×D4—472no—
629C2×C4×D4—948no—
630C2×C4×D4C2×D4711yescharacteristic
631C2×C4×D4C2×D4712yescomplemented
632C2×#117—472no—
633C2×#117—471no—
634C2×#117C2×D4711yescharacteristic, complemented
635C22×C4⋊C4—471no—
636C22×C22⋊C4—472no—
637C22×C42—471no—
638#398—471no—
639#398—471no—
640#398—471no—
641#398C2×D4711yescharacteristic, complemented
642#397—471no—
643#397—471no—
644#397—471no—
645#397C2×D4711yescharacteristic, complemented
646#396—472no—
647#396—472no—
648#396—472no—
649#396C2×D4712yescomplemented
650#394—471no—
651#394—471no—
652#394—472no—
653#394—472no—
654#394—472no—
655#394—471no—
656#394C2×D4711yescharacteristic
657#394C2×D4712yescomplemented
658#392—471no—
659#392—471no—
660#392—471no—
661#392C2×D4711yescharacteristic
662#391—472no—
663#390—472no—
664#390—472no—
665#390—472no—
666#390—472no—
667#390—472no—
668#390—472no—
669#390—472no—
670#388—472no—
671#388—472no—
672#388—472no—
673#388—472no—
674#386—472no—
675#386—472no—
676#386—472no—
677#386—472no—
678#386—472no—
679#386—472no—
680#385—472no—
681#385—472no—
682#385—472no—
683#385—472no—
684#385—472no—
685#385—472no—
686#384—472no—
687#382—472no—
688#379—472no—
689#379—472no—
690C4×C4⋊C4—472no—
691C4×C4⋊C4—471no—
692C4×C4⋊C4C2×D4711yescharacteristic, complemented
693C4×C22⋊C4—472no—
694C4×C22⋊C4—472no—
695C4×C22⋊C4—472no—
696C4×C22⋊C4—472no—
697C4×C22⋊C4—471no—
698C4×C22⋊C4—471no—
699C4×C22⋊C4C2×D4712yescomplemented
700#376—471no—
701#376—471no—
702C43—472no—
703C47#3496511yescharacteristic, complemented, Sylow
704C25—472no—
705C22×Q8—471no—
706C22×D4—472no—
707C22×D4—471no—
708C22×D4—471no—
709C22×D4—472no—
710C22×D4—472no—
711C22×D4—471no—
712C22×D4—471no—
713C22×D4—472no—
714C22×D4—944no—
715C22×D4—948no—
716C22×D4C22×D4711yescharacteristic
717C22×D4C22×D4712yes—
718C23×C4—471no—
719C23×C4—471no—
720C23×C4—471no—
721C23×C4—472no—
722C23×C4—471no—
723C23×C4—472no—
724C23×C4—472no—
725C23×C4—472no—
726C23×C4—948no—
727C23×C4—1884no—
728C23×C4—1884no—
729C23×C4C22×D4711yescharacteristic
730C23×C4C22×D4712yes—
731#127—948no—
732#126—944no—
733#126—944no—
734#125—944no—
735#124—944no—
736#124—948no—
737#123—944no—
738#123—944no—
739C22⋊Q8—944no—
740#121—944no—
741#120—948no—
742#120—948no—
743C4×Q8—944no—
744C4×D4—24no—
745C4×D4—44no—
746C4×D4—944no—
747C4×D4—948no—
748C4×D4—944no—
749C4×D4—948no—
750C4×D4—944no—
751C4×D4—944no—
752C4×D4—944no—
753C4×D4—944no—
754C4×D4—1884no—
755C4×D4—1884no—
756C4×D4—1884no—
757#117—24no—
758#117—948no—
759#117—944no—
760C2×C4⋊C4—472no—
761C2×C4⋊C4—471no—
762C2×C4⋊C4—471no—
763C2×C4⋊C4—471no—
764C2×C4⋊C4—472no—
765C2×C4⋊C4—471no—
766C2×C4⋊C4—471no—
767C2×C4⋊C4—471no—
768C2×C4⋊C4—471no—
769C2×C4⋊C4—471no—
770C2×C4⋊C4—471no—
771C2×C4⋊C4—472no—
772C2×C4⋊C4—472no—
773C2×C4⋊C4—472no—
774C2×C4⋊C4—944no—
775C2×C4⋊C4C22×D4711yescharacteristic
776C2×C4⋊C4C22×D4712yes—
777C2×C4⋊C4C22×D4711yescharacteristic
778C2×C4⋊C4C22×D4711yescharacteristic
779C2×C4⋊C4C22×D4712yes—
780C2×C22⋊C4—472no—
781C2×C22⋊C4—472no—
782C2×C22⋊C4—471no—
783C2×C22⋊C4—471no—
784C2×C22⋊C4—472no—
785C2×C22⋊C4—472no—
786C2×C22⋊C4—472no—
787C2×C22⋊C4—472no—
788C2×C22⋊C4—471no—
789C2×C22⋊C4—471no—
790C2×C22⋊C4—472no—
791C2×C22⋊C4—471no—
792C2×C22⋊C4—471no—
793C2×C22⋊C4—471no—
794C2×C22⋊C4—471no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—472no—
797C2×C22⋊C4—472no—
798C2×C22⋊C4—472no—
799C2×C22⋊C4—472no—
800C2×C22⋊C4—472no—
801C2×C22⋊C4—472no—
802C2×C22⋊C4—472no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—472no—
805C2×C22⋊C4—948no—
806C2×C22⋊C4C22×D4712yes—
807C2×C22⋊C4C22×D4711yescharacteristic
808C2×C22⋊C4C22×D4711yescharacteristic
809C2×C22⋊C4C22×D4712yes—
810C2×C22⋊C4C22×D4712yes—
811C2×C22⋊C4C22×D4712yes—
812C2×C22⋊C4C22×D4712yes—
813C2×C42—471no—
814C2×C42—471no—
815C2×C42—471no—
816C2×C42—478no—
817C2×C42—472no—
818C2×C42—472no—
819C2×C42—472no—
820C2×C42—472no—
821C2×C42—471no—
822C2×C42—472no—
823C2×C42C22×D4711yescharacteristic
824C2×C42C22×D4712yes—
825C2×C42C22×D4711yescharacteristic
826#95—472no—
827#95—472no—
828#95—471no—
829#95—471no—
830#95—472no—
831#95—472no—
832#95—472no—
833#95—472no—
834#95—472no—
835#95—472no—
836#95C22×D4711yescharacteristic
837#95C22×D4711yescharacteristic
838#95C22×D4712yes—
839#95C22×D4712yes—
840C24—471no—
841C24—472no—
842C24—471no—
843C24—944no—
844C24—944no—
845C24—944no—
846C24—944no—
847C24—944no—
848C24—1882no—
849C24—1882no—
850C24C23×D4711yescharacteristic
851C24C23×D4712yes—
852C2×Q8—942no—
853C2×Q8—944no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—22no—
857C2×D4—24no—
858C2×D4—42no—
859C2×D4—478no—
860C2×D4—944no—
861C2×D4—942no—
862C2×D4—944no—
863C2×D4—944no—
864C2×D4—944no—
865C2×D4—944no—
866C2×D4—942no—
867C2×D4—944no—
868C2×D4—944no—
869C2×D4—944no—
870C2×D4—9432no—
871C2×D4—942no—
872C2×D4—944no—
873C2×D4—944no—
874C2×D4—944no—
875C2×D4—942no—
876C2×D4—944no—
877C2×D4—1882no—
878C2×D4—1882no—
879C2×D4—1882no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—22no—
883C22×C4—24no—
884C22×C4—22no—
885C22×C4—24no—
886C22×C4—471no—
887C22×C4—472no—
888C22×C4—471no—
889C22×C4—471no—
890C22×C4—474no—
891C22×C4—474no—
892C22×C4—474no—
893C22×C4—472no—
894C22×C4—471no—
895C22×C4—471no—
896C22×C4—472no—
897C22×C4—471no—
898C22×C4—944no—
899C22×C4—944no—
900C22×C4—944no—
901C22×C4—944no—
902C22×C4—944no—
903C22×C4—942no—
904C22×C4—942no—
905C22×C4—942no—
906C22×C4—944no—
907C22×C4—942no—
908C22×C4—944no—
909C22×C4—942no—
910C22×C4—944no—
911C22×C4—1882no—
912C22×C4—1882no—
913C22×C4—1882no—
914C22×C4—1882no—
915C22×C4—18832no—
916C22×C4—1882no—
917C22×C4—1882no—
918C22×C4C23×D4712yes—
919C22×C4C23×D4711yescharacteristic
920C22×C4C23×D4711yescharacteristic
921C22×C4C23×D4712yes—
922C22×C4C23×D4711yescharacteristic
923C22×C4C23×D4711yescharacteristic
924C22×C4C23×D4711yescharacteristic
925C22×C4C23×D4712yes—
926C22×C4C23×D4711yescharacteristic
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—24no—
931C4⋊C4—42no—
932C4⋊C4—944no—
933C4⋊C4—942no—
934C4⋊C4—942no—
935C4⋊C4—942no—
936C4⋊C4—942no—
937C4⋊C4—944no—
938C4⋊C4—942no—
939C4⋊C4—942no—
940C4⋊C4—942no—
941C4⋊C4—942no—
942C4⋊C4—942no—
943C4⋊C4—1882no—
944C4⋊C4—1882no—
945C4⋊C4—1882no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—24no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—478no—
954C22⋊C4—944no—
955C22⋊C4—942no—
956C22⋊C4—942no—
957C22⋊C4—944no—
958C22⋊C4—944no—
959C22⋊C4—942no—
960C22⋊C4—942no—
961C22⋊C4—944no—
962C22⋊C4—944no—
963C22⋊C4—944no—
964C22⋊C4—942no—
965C22⋊C4—942no—
966C22⋊C4—944no—
967C22⋊C4—944no—
968C22⋊C4—944no—
969C22⋊C4—942no—
970C22⋊C4—942no—
971C22⋊C4—944no—
972C22⋊C4—1882no—
973C22⋊C4—1882no—
974C22⋊C4—1882no—
975C22⋊C4—1882no—
976C22⋊C4—1882no—
977C22⋊C4—1882no—
978C42—22no—
979C42—24no—
980C42—474no—
981C42—474no—
982C42—474no—
983C42—944no—
984C42—944no—
985C42—944no—
986C42—942no—
987C42—944no—
988C42—944no—
989C42D4×D4714yes—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—21no—
1000C23—21no—
1001C23—472no—
1002C23—474no—
1003C23—474no—
1004C23—9416no—
1005C23—942no—
1006C23—941no—
1007C23—941no—
1008C23—942no—
1009C23—942no—
1010C23—942no—
1011C23—942no—
1012C23—942no—
1013C23—942no—
1014C23—941no—
1015C23—942no—
1016C23—942no—
1017C23—941no—
1018C23—941no—
1019C23—1888no—
1020C23—1888no—
1021C23—1888no—
1022C23—1888no—
1023C23—1888no—
1024C23—1888no—
1025C23#41×D4714yes—
1026C23C24×D4711yescharacteristic
1027Q8—1884no—
1028D4—28no—
1029D4—48no—
1030D4—948no—
1031D4—9416no—
1032D4—1888no—
1033D4—1884no—
1034D4—1884no—
1035D4—1888no—
1036D4—1888no—
1037D4—1884no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—44no—
1056C2×C4—48no—
1057C2×C4—472no—
1058C2×C4—474no—
1059C2×C4—472no—
1060C2×C4—472no—
1061C2×C4—474no—
1062C2×C4—948no—
1063C2×C4—948no—
1064C2×C4—942no—
1065C2×C4—942no—
1066C2×C4—941no—
1067C2×C4—942no—
1068C2×C4—941no—
1069C2×C4—948no—
1070C2×C4—941no—
1071C2×C4—941no—
1072C2×C4—941no—
1073C2×C4—942no—
1074C2×C4—942no—
1075C2×C4—942no—
1076C2×C4—942no—
1077C2×C4—942no—
1078C2×C4—941no—
1079C2×C4—942no—
1080C2×C4—942no—
1081C2×C4—941no—
1082C2×C4—942no—
1083C2×C4—1888no—
1084C2×C4—1888no—
1085C2×C4—1888no—
1086C2×C4—1884no—
1087C2×C4—1888no—
1088C2×C4C2×D4×D4712yes—
1089C2×C4C2×D4×D4712yes—
1090C2×C4C2×D4×D4712yes—
1091C2×C4#41×D4714yes—
1092C2×C4#1309406912yes—
1093C2×C4#1309407012yes—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—42no—
1105C22—42no—
1106C22—474no—
1107C22—942no—
1108C22—942no—
1109C22—944no—
1110C22—944no—
1111C22—944no—
1112C22—944no—
1113C22—944no—
1114C22—18832no—
1115C22—1881no—
1116C22—1881no—
1117C22—1881no—
1118C22—1882no—
1119C22—1882no—
1120C22—1882no—
1121C22—1882no—
1122C22—1882no—
1123C22—1882no—
1124C22C22×D4×D4711yescharacteristic
1125C22C2×#41×D4712yes—
1126C22C2×#41×D4712yes—
1127C22C2×#1309406911yescharacteristic
1128C22C2×#1309407011yescharacteristic
1129C4—22no—
1130C4—22no—
1131C4—24no—
1132C4—41no—
1133C4—41no—
1134C4—42no—
1135C4—41no—
1136C4—42no—
1137C4—474no—
1138C4—942no—
1139C4—942no—
1140C4—944no—
1141C4—1881no—
1142C4—1881no—
1143C4—1882no—
1144C4—1881no—
1145C4—1882no—
1146C4#1568968914yes—
1147C2—44no—
1148C2—81no—
1149C2—944no—
1150C2—3761no—
1151C2—1884no—
1152C2#525×D4711yescharacteristic
1153C2#532×D4711yescharacteristic
1154C2C2×#1568968911yescharacteristic
1155C2#2025699012yes—
1156C2#2025699412yes—
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC47×#2392C2
prime radical#20247020C2
hypercenter#2392D47
hypocenterC47#34965
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. C2×#15689651C2semidirect
2. C2×C4×D4×D47C2semidirect
3. #20249018C2semidirect
4. #20249016C2semidirect
5. #20249010C2semidirect
6. #20249008C2semidirect
7. #20248583C2semidirect
8. #20248354C2semidirect
9. #20247875C2semidirect
10. #20247861C2semidirect
11. #20247034C2semidirect
13. #20246768C2semidirect
14. #20246766C2semidirect
15. #20246628C2semidirect
16. #20246626C2semidirect
17. #20246624C2semidirect
18. C4×#13094020C2semidirect
19. C4×#13094010C2semidirect
20. C4×#13093994C2semidirect
21. C4×#13093992C2semidirect
22. C4×#13093982C2semidirect
23. C47×#2392C2semidirect
28. C2×#13094019C22semidirect
29. C2×#13094017C22semidirect
30. C2×#13094014C22semidirect
32. C2×#13094010C22semidirect
39. C2×C4×Dic94C22semidirect
42. C2×C4×D188C22semidirect
47. C2×C4×C22⋊D47C22semidirect
48. C2×C4×C22⋊D47C22semidirect
49. C2×C4×C22⋊D47C22semidirect
53. C2×#13093981C22semidirect
57. #15689055C22semidirect
58. #15689054C22semidirect
59. #15689053C22semidirect
60. #15689050C22semidirect
61. #15689049C22semidirect
62. #15689048C22semidirect
63. #15689046C22semidirect
64. #15689045C22semidirect
65. #15689045C22semidirect
68. #15689040C22semidirect
69. #15689039C22semidirect
70. #15689039C22semidirect
75. #15689027C22semidirect
76. #15689026C22semidirect
77. #15689024C22semidirect
80. #15689023C22semidirect
81. #15689023C22semidirect
82. #15689023C22semidirect
83. #15689016C22semidirect
84. #15689015C22semidirect
85. #15689012C22semidirect
86. #15689011C22semidirect
87. #15689003C22semidirect
89. #15689001C22semidirect
90. #15689000C22semidirect
92. #15688999C22semidirect
93. #15688998C22semidirect
95. #15688997C22semidirect
96. #15688995C22semidirect
98. #15688994C22semidirect
99. #15688992C22semidirect
100. #15688987C22semidirect
103. C4⋊C4×Dic47C22semidirect
104. C4×C4⋊Dic47C22semidirect
106. C4×(C2×D47)⋊C4C22semidirect
107. C4×(C2×D47)⋊C4C22semidirect
108. C4×C22⋊Dic47C22semidirect
111. #15688968C22semidirect
112. #15688968C22semidirect
113. C42×Dic47C22semidirect
115. C2×C4×D4×C47C22semidirect
116. C2×#117×C47C22semidirect
117. C47×#398C22semidirect
118. C47×#397C22semidirect
119. C47×#396C22semidirect
121. C47×#394C22semidirect
123. C4×C4⋊C4×C47C22semidirect
124. C4×C22⋊C4×C47C22semidirect
224. C42×D47D4semidirect
586. #2392D47semidirect
631. C2×C4×D4C2×D47semidirect
634. C2×#117C2×D47semidirect
641. #398C2×D47semidirect
645. #397C2×D47semidirect
649. #396C2×D47semidirect
657. #394C2×D47semidirect
692. C4×C4⋊C4C2×D47semidirect
699. C4×C22⋊C4C2×D47semidirect
703. C47#34965semidirect

Maximal subgroups

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

subgroupindex
C2×#156896512
C2×C4×D4×D472
#202490182
#202490162
#202490102
#202490082
#202485832
#202483542
#202478752
#202478612
#202470342
#202470202
#202467682
#202467662
#202466282
#202466262
#202466242
C4×#130940202
C4×#130940102
C4×#130939942
C4×#130939922
C4×#130939822
C47×#23922
#3496547