Finite Group Databasebeta

← D47×#2318 #26374908

Subgroups — D47×#2318 #26374908

Order 12032.

3262 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#20246024C211yesmaximal, characteristic, complemented
3#20246023C211yesmaximal, characteristic, complemented
4#20246022C211yesmaximal, characteristic, complemented
5#20246021C211yesmaximal, characteristic, complemented
6#20246020C212yesmaximal, complemented
7#20246019C211yesmaximal, characteristic, complemented
8#20246018C212yesmaximal, complemented
9#20246017C211yesmaximal, characteristic, complemented
10#20246016C212yesmaximal, complemented
11#20246015C211yesmaximal, characteristic, complemented
12#20246014C212yesmaximal, complemented
13#388×D47C212yesmaximal, complemented
14#387×D47C212yesmaximal, complemented
15#386×D47C212yesmaximal
16#385×D47C212yesmaximal, complemented
17#383×D47C211yesmaximal, characteristic, complemented
18#382×D47C211yesmaximal, characteristic, complemented
19#381×D47C211yesmaximal, characteristic, complemented
20#380×D47C211yesmaximal, characteristic, complemented
21C4×C22⋊C4×D47C211yesmaximal, characteristic, complemented
22C2×#95×D47C211yesmaximal, characteristic, complemented
23C47×#2318C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C23×C4×D47C2212yes—
26C23×C4×D47C2211yescharacteristic
27C23×C4×D47C2211yescharacteristic
28C2×C4×D188C2211yescharacteristic
29C2×D4×Dic47C2211yescharacteristic
30C2×#13093986C2211yescharacteristic
31C2×C4×C22⋊D47C2211yescharacteristic
32C2×C4×C22⋊D47C2211yescharacteristic
33C2×(C22⋊D47)⋊C4C2211yescharacteristic
34C2×(C22⋊D47)⋊C4C2211yescharacteristic
35C4×D4×D47C4116yescomplemented
36C2×C4⋊C4×D47C2212yes—
37C2×C4⋊C4×D47C2212yes—
38C2×C4⋊C4×D47C2211yescharacteristic
39C2×C22⋊C4×D47C2212yes—
40C2×C22⋊C4×D47C2212yes—
41C2×C22⋊C4×D47C2212yes—
42C2×C22⋊C4×D47C2211yescharacteristic
43C2×C22⋊C4×D47C2211yescharacteristic
44C2×C42×D47C2212yes—
45C2×C42×D47C2211yescharacteristic
46#15689017C2212yescomplemented
47#15689016C2212yescomplemented
48#15689015C2212yescomplemented
49#15689014C2212yescomplemented
50#15689013C2212yescomplemented
51#15689012C2212yescomplemented
52#15689011C2212yescomplemented
53#15689010C2212yescomplemented
54#15689009C2212yescomplemented
55#15689008C2212yescomplemented
56#15689007C2212yescomplemented
57#15689006C2212yescomplemented
58#15689005C2212yescomplemented
59#15689004C2212yescomplemented
60#15689003C2212yes—
61#15689002C2212yes—
62#15689001C2212yes—
63#15689001C2212yes—
64#15689000C2212yes—
65#15688999C2212yes—
66#15688999C2212yes—
67#15688998C2212yescomplemented
68#15688997C2212yescomplemented
69#15688997C2212yescomplemented
70#15688996C2212yescomplemented
71#15688995C2212yescomplemented
72#15688994C2212yescomplemented
73#15688994C2212yescomplemented
74#15688991C2211yescharacteristic, complemented
75#15688990C2212yescomplemented
76#15688990C2211yescharacteristic, complemented
77#15688990C2212yescomplemented
78#15688990C2211yescharacteristic, complemented
79#15688989C2211yescharacteristic, complemented
80#15688988C2212yescomplemented
81#15688987C2211yescharacteristic, complemented
82#15688987C2212yescomplemented
83#15688987C2211yescharacteristic, complemented
84#15688986C2211yescharacteristic, complemented
85#15688985C2212yescomplemented
86#15688985C2211yescharacteristic, complemented
87#15688985C2211yescharacteristic, complemented
88#15688984C2212yescomplemented
89#15688983C2211yescharacteristic, complemented
90#15688982C2211yescharacteristic, complemented
91#15688982C2211yescharacteristic, complemented
92#15688981C2212yescomplemented
93#15688980C2212yescomplemented
94C22⋊C4×Dic47C2212yescomplemented
95C4×(C2×D47)⋊C4C2212yescomplemented
96C4×C22⋊Dic47C2211yescharacteristic, complemented
97#15688970C2211yescharacteristic, complemented
98#15688970C2211yescharacteristic, complemented
99C2×C47⋊#95C2212yescomplemented
100C2×C47⋊#95C2211yescharacteristic, complemented
101#95×D47C2211yescharacteristic
102#95×D47C2211yescharacteristic
103#95×D47C2212yes—
104#95×D47C2212yes—
105#95×D47C2211yescharacteristic
106#95×D47C2212yes—
107#95×D47C2212yes—
108#95×D47C2211yescharacteristic
109#95×D47C2212yes—
110#95×D47C2211yescharacteristic, complemented
111#95×D47C2212yescomplemented
112#95×D47C2211yescharacteristic, complemented
113C2×C4×D4×C47C2211yescharacteristic
114C47×#388C2212yescomplemented
115C47×#387C2212yescomplemented
116C47×#386C2212yes—
117C47×#385C2212yescomplemented
118C47×#383C2211yescharacteristic, complemented
119C47×#382C2211yescharacteristic, complemented
120C47×#381C2211yescharacteristic, complemented
121C47×#380C2211yescharacteristic, complemented
122C4×C22⋊C4×C47C2211yescharacteristic, complemented
123C2×#95×C47C2211yescharacteristic, complemented
124C24×D47C2311yescharacteristic
125C24×D47C2311yescharacteristic
126C22×D188C2311yescharacteristic
127C22×C22⋊D47C2311yescharacteristic
128C22×C22⋊D47C2311yescharacteristic
129C2×D4×D47—28no—
130C2×D4×D47C2×C418yes—
131C23×Dic47C2312yes—
132C23×Dic47C2311yescharacteristic
133C23×Dic47C2311yescharacteristic
134C22×C4×D47—28no—
135C22×C4×D47—44no—
136C22×C4×D47—44no—
137C22×C4×D47—44no—
138C22×C4×D47—44no—
139C22×C4×D47C2×C418yes—
140C22×C4×D47C2×C418yescomplemented
141C22×C4×D47C2312yes—
142C22×C4×D47C2312yes—
143C22×C4×D47C2312yes—
144C22×C4×D47C2312yes—
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2312yes—
151C22×C4×D47C2312yes—
152C22×C4×D47C2311yescharacteristic
153C22×C4×D47C2311yescharacteristic
154C22×C4×D47C2311yescharacteristic
155C22×C4×D47C2311yescharacteristic
156C4×D188C2×C418yescomplemented
157D4×Dic47C2×C418yescomplemented
158#13093986C2×C418yescomplemented
159C4×C22⋊D47C2×C418yescomplemented
160C4×C22⋊D47C2×C418yescomplemented
161(C22⋊D47)⋊C4C2×C418yescomplemented
162(C22⋊D47)⋊C4C2×C418yescomplemented
163C2×C4⋊Dic47C2312yes—
164C2×C4⋊Dic47C2312yes—
165C2×C4⋊Dic47C2311yescharacteristic
166C2×Dic47⋊C4C2312yes—
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2312yes—
170C2×Dic47⋊C4C2311yescharacteristic
171C2×Dic47⋊C4C2311yescharacteristic
172C4⋊C4×D47—44no—
173C4⋊C4×D47—44no—
174C4⋊C4×D47C2×C418yescomplemented
175C2×C22⋊Dic47C2312yes—
176C2×C22⋊Dic47C2312yes—
177C2×C22⋊Dic47C2312yes—
178C2×C22⋊Dic47C2311yescharacteristic
179C2×C22⋊Dic47C2311yescharacteristic
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)⋊C4C2311yescharacteristic
187C2×(C2×D47)⋊C4C2311yescharacteristic
188C2×(C2×D47)⋊C4C2311yescharacteristic
189C2×(C2×D47)⋊C4C2311yescharacteristic
190C22⋊C4×D47—28no—
191C22⋊C4×D47—44no—
192C22⋊C4×D47—44no—
193C22⋊C4×D47C2×C418yes—
194C22⋊C4×D47C2×C418yescomplemented
195C2×C4×Dic47C2312yes—
196C2×C4×Dic47C2312yes—
197C2×C4×Dic47C2312yes—
198C2×C4×Dic47C2311yescharacteristic
199C2×C4×Dic47C2311yescharacteristic
200C2×C4×Dic47C2311yescharacteristic
201C42×D47—44no—
202C42×D47C2×C418yescomplemented
203C47⋊#95C2312yes—
204C47⋊#95C2311yescharacteristic
205C47⋊#95C2312yes—
206C47⋊#95C2311yescharacteristic
207C47⋊#95C2312yes—
208C47⋊#95C2312yes—
209C47⋊#95C2312yes—
210C47⋊#95C2311yescharacteristic
211C47⋊#95C2311yescharacteristic
212C47⋊#95C2312yes—
213C47⋊#95C2312yes—
214C47⋊#95C2312yes—
215C47⋊#95C2312yes—
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C22×D4×C47C2311yescharacteristic
227C23×C4×C47C2312yes—
228C23×C4×C47C2311yescharacteristic
229C23×C4×C47C2311yescharacteristic
230C4×D4×C47C2×C418yescomplemented
231C2×C4⋊C4×C47C2312yes—
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×C47C2311yescharacteristic
241#95×C47C2311yescharacteristic
242#95×C47C2311yescharacteristic
243#95×C47C2312yes—
244#95×C47C2311yescharacteristic
245#95×C47C2311yescharacteristic
246#95×C47C2312yes—
247#95×C47C2312yes—
248#95×C47C2312yes—
249#95×C47C2312yes—
250C24×C47C2411yescharacteristic
251C24×C47C2411yescharacteristic
252C23×D47—24no—
253C23×D47—22no—
254C23×D47—22no—
255C23×D47—24no—
256C23×D47—22no—
257C23×D47—24no—
258C23×D47—22no—
259C23×D47C22×C414yes—
260C23×D47C22×C414yes—
261C23×D47#4118yes—
262C23×D47C2411yescharacteristic
263C23×D47C2411yescharacteristic
264C23×D47C2411yescharacteristic
265C2×D4×C47—24no—
266C2×D4×C47C22×C414yes—
267C22×C4×C47—24no—
268C22×C4×C47—42no—
269C22×C4×C47—42no—
270C22×C4×C47—42no—
271C22×C4×C47—42no—
272C22×C4×C47C22×C414yes—
273C22×C4×C47C22×C414yescomplemented
274C22×C4×C47C2412yes—
275C22×C4×C47C2412yes—
276C22×C4×C47C2412yes—
277C22×C4×C47C2412yes—
278C22×C4×C47C2411yescharacteristic
279C22×C4×C47C2411yescharacteristic
280C22×C4×C47C2411yescharacteristic
281C22×C4×C47C2411yescharacteristic
282C22×C4×C47C2411yescharacteristic
283C2×C22⋊D47—24no—
284C2×C22⋊D47—24no—
285C2×C22⋊D47C22×C414yes—
286C2×C22⋊D47C22×C414yes—
287C22×Dic47—24no—
288C22×Dic47—42no—
289C22×Dic47—42no—
290C22×Dic47—42no—
291C22×Dic47—42no—
292C22×Dic47C22×C414yes—
293C22×Dic47C22×C414yescomplemented
294C22×Dic47C2412yes—
295C22×Dic47C2412yes—
296C22×Dic47C2412yes—
297C22×Dic47C2412yes—
298C22×Dic47C2411yescharacteristic
299C22×Dic47C2411yescharacteristic
300C22×Dic47C2411yescharacteristic
301C22×Dic47C2411yescharacteristic
302C22×Dic47C2411yescharacteristic
303D4×D47—232no—
304C2×D188—24no—
305C2×D188C22×C414yes—
306C2×C4×D47—24no—
307C2×C4×D47—24no—
308C2×C4×D47—22no—
309C2×C4×D47—24no—
310C2×C4×D47—24no—
311C2×C4×D47—22no—
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—24no—
321C2×C4×D47—24no—
322C2×C4×D47—24no—
323C2×C4×D47—24no—
324C2×C4×D47—24no—
325C2×C4×D47—24no—
326C2×C4×D47—416no—
327C2×C4×D47—416no—
328C2×C4×D47—42no—
329C2×C4×D47—42no—
330C2×C4×D47—42no—
331C2×C4×D47—42no—
332C2×C4×D47—42no—
333C2×C4×D47—42no—
334C2×C4×D47—42no—
335C2×C4×D47—42no—
336C2×C4×D47—432no—
337C2×C4×D47C22×C414yes—
338C2×C4×D47C22×C414yes—
339C2×C4×D47C22×C414yes—
340C2×C4×D47C22×C414yes—
341C2×C4×D47C22×C414yes—
342C2×C4×D47C22×C414yes—
343C2×C4×D47C22×C414yes—
344C2×C4×D47C22×C414yescomplemented
345C2×C4×D47C22×C414yescomplemented
346C4⋊C4×C47—42no—
347C4⋊C4×C47—42no—
348C4⋊C4×C47C22×C414yescomplemented
349C22⋊C4×C47—24no—
350C22⋊C4×C47—42no—
351C22⋊C4×C47—42no—
352C22⋊C4×C47C22×C414yes—
353C22⋊C4×C47C22×C414yescomplemented
354C42×C47—42no—
355C42×C47C22×C414yescomplemented
356C22⋊Dic47—24no—
357C22⋊Dic47—42no—
358C22⋊Dic47—42no—
359C22⋊Dic47C22×C414yes—
360C22⋊Dic47C22×C414yescomplemented
361(C2×D47)⋊C4—24no—
362(C2×D47)⋊C4—24no—
363(C2×D47)⋊C4—42no—
364(C2×D47)⋊C4—42no—
365(C2×D47)⋊C4—42no—
366(C2×D47)⋊C4—42no—
367(C2×D47)⋊C4C22×C414yes—
368(C2×D47)⋊C4C22×C414yes—
369(C2×D47)⋊C4C22×C414yescomplemented
370(C2×D47)⋊C4C22×C414yescomplemented
371C4⋊Dic47—42no—
372C4⋊Dic47—42no—
373C4⋊Dic47C22×C414yescomplemented
374Dic47⋊C4—42no—
375Dic47⋊C4—42no—
376Dic47⋊C4—42no—
377Dic47⋊C4—42no—
378Dic47⋊C4C22×C414yescomplemented
379Dic47⋊C4C22×C414yescomplemented
380C4×Dic47—42no—
381C4×Dic47—42no—
382C4×Dic47—42no—
383C4×Dic47C22×C414yescomplemented
384C4×Dic47C22×C414yescomplemented
385C4×Dic47C22×C414yescomplemented
386C23×C47—22no—
387C23×C47—21no—
388C23×C47—21no—
389C23×C47—22no—
390C23×C47—21no—
391C23×C47—22no—
392C23×C47—21no—
393C23×C47C23×C412yes—
394C23×C47C23×C412yes—
395C23×C47C2×#4114yes—
396C23×C47C2511yescharacteristic
397C22×D47—22no—
398C22×D47—21no—
399C22×D47—21no—
400C22×D47—28no—
401C22×D47—28no—
402C22×D47—216no—
403C22×D47—216no—
404C22×D47—22no—
405C22×D47—21no—
406C22×D47—22no—
407C22×D47—21no—
408C22×D47—28no—
409C22×D47—28no—
410C22×D47—28no—
411C22×D47—48no—
412C22×D47—48no—
413C22×D47#117116yes—
414C22×D47C23×C412yes—
415C22×D47C23×C412yes—
416C22×D47C23×C412yes—
417C22×D47C2×#4114yes—
418C22×D47C2×#4114yes—
419C22×D47H(5,𝔽2)14yes—
420C22×D47H(5,𝔽2)12yes—
421C22×D472−1+412yes—
422D4×C47—28no—
423C2×C4×C47—22no—
424C2×C4×C47—22no—
425C2×C4×C47—21no—
426C2×C4×C47—22no—
427C2×C4×C47—22no—
428C2×C4×C47—21no—
429C2×C4×C47—22no—
430C2×C4×C47—22no—
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—44no—
442C2×C4×C47—44no—
443C2×C4×C47—48no—
444C2×C4×C47C23×C412yes—
445C2×C4×C47C23×C412yes—
446C2×C4×C47C23×C412yes—
447C2×C4×C47C23×C412yes—
448C2×C4×C47C23×C412yes—
449C22⋊D47—28no—
450C22⋊D47—28no—
451C2×Dic47—22no—
452C2×Dic47—22no—
453C2×Dic47—21no—
454C2×Dic47—22no—
455C2×Dic47—22no—
456C2×Dic47—21no—
457C2×Dic47—22no—
458C2×Dic47—22no—
459C2×Dic47—22no—
460C2×Dic47—22no—
461C2×Dic47—22no—
462C2×Dic47—22no—
463C2×Dic47—22no—
464C2×Dic47—22no—
465C2×Dic47—22no—
466C2×Dic47—22no—
467C2×Dic47—22no—
468C2×Dic47—22no—
469C2×Dic47—44no—
470C2×Dic47—44no—
471C2×Dic47—48no—
472C2×Dic47C23×C412yes—
473C2×Dic47C23×C412yes—
474C2×Dic47C23×C412yes—
475C2×Dic47C23×C412yes—
476C2×Dic47C23×C412yes—
477D188—28no—
478C4×D47—28no—
479C4×D47—28no—
480C4×D47—28no—
481C4×D47—28no—
482C4×D47—28no—
483C4×D47—44no—
484C4×D47—44no—
485C4×D47—44no—
486C4×D47—44no—
487C4×D47—48no—
488C4×D47—48no—
489C4×D47—48no—
490C4×D47—48no—
491C4×D47—48no—
492C4×D47—48no—
493C2×#2318—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×#4112yes—
506C22×C47C2×H(5,𝔽2)12yes—
507C22×C47C2×H(5,𝔽2)11yescharacteristic
508C22×C47C2×2−1+411yescharacteristic
509C2×D47—22no—
510C2×D47—22no—
511C2×D47—24no—
512C2×D47—24no—
513C2×D47—232no—
514C2×D47—22no—
515C2×D47—22no—
516C2×D47—22no—
517C2×D47—42no—
518C2×D47—42no—
519C2×D47—416no—
520C2×D47C2×#11714yes—
521C2×D47C2×#11714yes—
522C2×D47#51814yes—
523C2×D47#52014yes—
524C2×D47#53818yes—
525C2×D47#53918yes—
526C4×C47—22no—
527C4×C47—22no—
528C4×C47—22no—
529C4×C47—22no—
530C4×C47—22no—
531C4×C47—42no—
532C4×C47—42no—
533C4×C47—42no—
534C4×C47—42no—
535Dic47—22no—
536Dic47—22no—
537Dic47—22no—
538Dic47—22no—
539Dic47—22no—
540Dic47—42no—
541Dic47—42no—
542Dic47—42no—
543Dic47—42no—
544C22×C4×D4—471no—
545#2318—472no—
546#2318—472no—
547#2318—472no—
548#2318—472no—
549#2318—471no—
550#2318—471no—
551#2318—471no—
552#2318—471no—
553#2318—471no—
554#2318—471no—
555#2318—471no—
556#2318D4711yescharacteristic, direct product factor
557C2×#388—472no—
558C2×#387—472no—
559C2×#386—472no—
560C2×#385—472no—
561C2×#383—471no—
562C2×#382—471no—
563C2×#381—471no—
564C2×#380—471no—
565C2×C4×C22⋊C4—471no—
566C22×#95—471no—
567C2×C47—24no—
568C2×C47—42no—
569C2×C47C22×#11711yescharacteristic
570C2×C47C2×#51811yescharacteristic
571C2×C47C2×#52011yescharacteristic
572C2×C47C2×#53812yes—
573C2×C47C2×#53912yes—
574D47—24no—
575D47—42no—
576D47#231818yesdirect product factor
577C23×D4—471no—
578C24×C4—471no—
579C24×C4—471no—
580C24×C4—472no—
581C2×C4×D4—471no—
582C2×C4×D4—471no—
583C2×C4×D4—471no—
584C2×C4×D4—4716no—
585C2×C4×D4—471no—
586C2×C4×D4—471no—
587C2×C4×D4—471no—
588C2×C4×D4—471no—
589C2×C4×D4C2×D4711yescharacteristic
590C22×C4⋊C4—471no—
591C22×C4⋊C4—472no—
592C22×C4⋊C4—472no—
593C22×C22⋊C4—471no—
594C22×C22⋊C4—471no—
595C22×C22⋊C4—472no—
596C22×C22⋊C4—472no—
597C22×C22⋊C4—472no—
598C22×C42—471no—
599C22×C42—472no—
600#388—472no—
601#388—472no—
602#388—472no—
603#388—472no—
604#388—472no—
605#388—472no—
606#388—472no—
607#388C2×D4712yescomplemented
608#387—472no—
609#387—472no—
610#387—472no—
611#387—472no—
612#387—472no—
613#387—472no—
614#387—472no—
615#387C2×D4712yescomplemented
616#386—472no—
617#386—472no—
618#386—472no—
619#386—472no—
620#386—472no—
621#386—472no—
622#386—472no—
623#386C2×D4712yes—
624#385—472no—
625#385—472no—
626#385—472no—
627#385—472no—
628#385—472no—
629#385—472no—
630#385—472no—
631#385C2×D4712yescomplemented
632#383—471no—
633#383—472no—
634#383—472no—
635#383—471no—
636#383—471no—
637#383C2×D4711yescharacteristic, complemented
638#382—472no—
639#382—471no—
640#382—472no—
641#382—471no—
642#382—471no—
643#382C2×D4711yescharacteristic, complemented
644#381—471no—
645#381—472no—
646#381—472no—
647#381—471no—
648#381—471no—
649#381C2×D4711yescharacteristic, complemented
650#380—471no—
651#380—472no—
652#380—472no—
653#380—471no—
654#380—471no—
655#380C2×D4711yescharacteristic, complemented
656C4×C22⋊C4—471no—
657C4×C22⋊C4—472no—
658C4×C22⋊C4—472no—
659C4×C22⋊C4—471no—
660C4×C22⋊C4—471no—
661C4×C22⋊C4C2×D4711yescharacteristic, complemented
662C2×#95—472no—
663C2×#95—471no—
664C2×#95—471no—
665C2×#95—471no—
666C2×#95—472no—
667C2×#95—471no—
668C2×#95—471no—
669C2×#95—472no—
670C2×#95—472no—
671C2×#95—472no—
672C2×#95—472no—
673C2×#95—472no—
674C2×#95—471no—
675C2×#95—471no—
676C2×#95C2×D4711yescharacteristic, complemented
677C47C2×#231811yescharacteristic, complemented, Sylow
678C25—471no—
679C25—471no—
680C22×D4—471no—
681C22×D4—471no—
682C22×D4—478no—
683C22×D4—471no—
684C22×D4—948no—
685C22×D4C22×D4711yescharacteristic
686C23×C4—471no—
687C23×C4—471no—
688C23×C4—471no—
689C23×C4—471no—
690C23×C4—471no—
691C23×C4—471no—
692C23×C4—471no—
693C23×C4—478no—
694C23×C4—478no—
695C23×C4—471no—
696C23×C4—471no—
697C23×C4—471no—
698C23×C4—471no—
699C23×C4—472no—
700C23×C4—472no—
701C23×C4—472no—
702C23×C4—472no—
703C23×C4—472no—
704C23×C4—472no—
705C23×C4—472no—
706C23×C4—948no—
707C23×C4—1884no—
708C23×C4—1884no—
709C23×C4—1884no—
710C23×C4—1884no—
711C23×C4C22×D4712yes—
712C23×C4C22×D4711yescharacteristic
713C23×C4C22×D4711yescharacteristic
714C4×D4—478no—
715C4×D4—478no—
716C4×D4—478no—
717C4×D4—478no—
718C4×D4—478no—
719C4×D4—478no—
720C4×D4—478no—
721C4×D4C4×D4718yescomplemented
722C2×C4⋊C4—471no—
723C2×C4⋊C4—471no—
724C2×C4⋊C4—471no—
725C2×C4⋊C4—478no—
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⋊C4—1884no—
733C2×C4⋊C4—1884no—
734C2×C4⋊C4C22×D4712yes—
735C2×C4⋊C4C22×D4712yes—
736C2×C4⋊C4C22×D4711yescharacteristic
737C2×C22⋊C4—471no—
738C2×C22⋊C4—471no—
739C2×C22⋊C4—471no—
740C2×C22⋊C4—471no—
741C2×C22⋊C4—471no—
742C2×C22⋊C4—471no—
743C2×C22⋊C4—478no—
744C2×C22⋊C4—478no—
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—948no—
755C2×C22⋊C4—1884no—
756C2×C22⋊C4—1884no—
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—1884no—
770C2×C42C22×D4712yes—
771C2×C42C22×D4711yescharacteristic
772#95—472no—
773#95—471no—
774#95—472no—
775#95—471no—
776#95—472no—
777#95—472no—
778#95—472no—
779#95—472no—
780#95—471no—
781#95—472no—
782#95—471no—
783#95—472no—
784#95—472no—
785#95—472no—
786#95—472no—
787#95—472no—
788#95—472no—
789#95—472no—
790#95—472no—
791#95—472no—
792#95—472no—
793#95—472no—
794#95—472no—
795#95C22×D4711yescharacteristic
796#95C22×D4711yescharacteristic
797#95C22×D4712yes—
798#95C22×D4711yescharacteristic
799#95C22×D4711yescharacteristic
800#95C22×D4712yes—
801#95C22×D4712yes—
802#95C22×D4712yes—
803#95C22×D4712yes—
804C24—471no—
805C24—474no—
806C24—478no—
807C24—471no—
808C24—474no—
809C24—471no—
810C24—944no—
811C24—942no—
812C24—942no—
813C24—942no—
814C24—944no—
815C24—944no—
816C24—942no—
817C24C23×D4711yescharacteristic
818C24C23×D4711yescharacteristic
819C2×D4—24no—
820C2×D4—474no—
821C2×D4—474no—
822C2×D4—474no—
823C2×D4—944no—
824C2×D4—9432no—
825C2×D4—944no—
826C2×D4—944no—
827C2×D4C2×C4×D4714yes—
828C22×C4—24no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—471no—
834C22×C4—471no—
835C22×C4—471no—
836C22×C4—471no—
837C22×C4—471no—
838C22×C4—474no—
839C22×C4—474no—
840C22×C4—474no—
841C22×C4—474no—
842C22×C4—474no—
843C22×C4—474no—
844C22×C4—474no—
845C22×C4—474no—
846C22×C4—474no—
847C22×C4—474no—
848C22×C4—474no—
849C22×C4—472no—
850C22×C4—472no—
851C22×C4—472no—
852C22×C4—472no—
853C22×C4—944no—
854C22×C4—942no—
855C22×C4—944no—
856C22×C4—942no—
857C22×C4—944no—
858C22×C4—944no—
859C22×C4—944no—
860C22×C4—944no—
861C22×C4—944no—
862C22×C4—944no—
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—944no—
873C22×C4—944no—
874C22×C4—1882no—
875C22×C4—1882no—
876C22×C4—1882no—
877C22×C4—1882no—
878C22×C4—1882no—
879C22×C4—1882no—
880C22×C4—1882no—
881C22×C4—1882no—
882C22×C4—18816no—
883C22×C4—18816no—
884C22×C4—18832no—
885C22×C4—1882no—
886C22×C4—1882no—
887C22×C4—1882no—
888C22×C4—1882no—
889C22×C4C2×C4×D4714yes—
890C22×C4C2×C4×D4714yescomplemented
891C22×C4C23×D4712yes—
892C22×C4C23×D4712yes—
893C22×C4C23×D4712yes—
894C22×C4C23×D4712yes—
895C22×C4C23×D4711yescharacteristic
896C22×C4C23×D4711yescharacteristic
897C22×C4C23×D4711yescharacteristic
898C22×C4C23×D4711yescharacteristic
899C22×C4C23×D4711yescharacteristic
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—474no—
903C4⋊C4—474no—
904C4⋊C4—474no—
905C4⋊C4—1882no—
906C4⋊C4—1882no—
907C4⋊C4—1882no—
908C4⋊C4—1882no—
909C4⋊C4—1882no—
910C4⋊C4—1882no—
911C4⋊C4C2×C4×D4714yescomplemented
912C22⋊C4—24no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—474no—
916C22⋊C4—474no—
917C22⋊C4—474no—
918C22⋊C4—474no—
919C22⋊C4—474no—
920C22⋊C4—474no—
921C22⋊C4—944no—
922C22⋊C4—944no—
923C22⋊C4—944no—
924C22⋊C4—1882no—
925C22⋊C4—1882no—
926C22⋊C4—1882no—
927C22⋊C4—1882no—
928C22⋊C4—1882no—
929C22⋊C4—1882no—
930C22⋊C4C2×C4×D4714yes—
931C22⋊C4C2×C4×D4714yescomplemented
932C42—42no—
933C42—474no—
934C42—474no—
935C42—474no—
936C42—1882no—
937C42—1882no—
938C42—1882no—
939C42C2×C4×D4714yescomplemented
940C23—22no—
941C23—21no—
942C23—21no—
943C23—22no—
944C23—21no—
945C23—22no—
946C23—21no—
947C23—472no—
948C23—474no—
949C23—474no—
950C23—472no—
951C23—472no—
952C23—4716no—
953C23—472no—
954C23—474no—
955C23—472no—
956C23—948no—
957C23—9416no—
958C23—948no—
959C23—9416no—
960C23—948no—
961C23—948no—
962C23—948no—
963C23—942no—
964C23—941no—
965C23—941no—
966C23—942no—
967C23—941no—
968C23—942no—
969C23—941no—
970C23—1888no—
971C23—1888no—
972C23C22×C4×D4712yes—
973C23C22×C4×D4712yes—
974C23#41×D4714yes—
975C23C24×D4711yescharacteristic
976D4—28no—
977D4—948no—
978D4—948no—
979D4—948no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
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—44no—
999C2×C4—44no—
1000C2×C4—48no—
1001C2×C4—472no—
1002C2×C4—472no—
1003C2×C4—472no—
1004C2×C4—472no—
1005C2×C4—472no—
1006C2×C4—948no—
1007C2×C4—948no—
1008C2×C4—948no—
1009C2×C4—948no—
1010C2×C4—948no—
1011C2×C4—942no—
1012C2×C4—942no—
1013C2×C4—941no—
1014C2×C4—942no—
1015C2×C4—942no—
1016C2×C4—941no—
1017C2×C4—942no—
1018C2×C4—942no—
1019C2×C4—942no—
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—1884no—
1030C2×C4—1884no—
1031C2×C4—1884no—
1032C2×C4—1884no—
1033C2×C4—1888no—
1034C2×C4—1888no—
1035C2×C4—1888no—
1036C2×C4—1888no—
1037C2×C4—1888no—
1038C2×C4—1888no—
1039C2×C4—1884no—
1040C2×C4—1884no—
1041C2×C4—1888no—
1042C2×C4C22×C4×D4712yes—
1043C2×C4C22×C4×D4712yes—
1044C2×C4C22×C4×D4712yes—
1045C2×C4C22×C4×D4712yes—
1046C2×C4C22×C4×D4712yes—
1047C22—22no—
1048C22—22no—
1049C22—24no—
1050C22—24no—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—42no—
1055C22—42no—
1056C22—474no—
1057C22—474no—
1058C22—474no—
1059C22—478no—
1060C22—478no—
1061C22—474no—
1062C22—9432no—
1063C22—942no—
1064C22—942no—
1065C22—944no—
1066C22—944no—
1067C22—942no—
1068C22—942no—
1069C22—942no—
1070C22—18816no—
1071C22—1882no—
1072C22—1882no—
1073C22#117×D4714yes—
1074C22C23×C4×D4711yescharacteristic
1075C22C2×#41×D4712yes—
1076C22H(5,𝔽2)×D4712yes—
1077C22H(5,𝔽2)×D4711yescharacteristic
1078C222−1+4×D4711yescharacteristic
1079C4—22no—
1080C4—22no—
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—942no—
1089C4—942no—
1090C4—942no—
1091C4—942no—
1092C4—942no—
1093C4—1882no—
1094C4—1882no—
1095C4—1882no—
1096C4—1882no—
1097C2—24no—
1098C2—42no—
1099C2—478no—
1100C2—944no—
1101C2—1882no—
1102C2C2×#117×D4711yescharacteristic
1103C2#518×D4711yescharacteristic
1104C2#520×D4711yescharacteristic
1105C2#538×D4712yes—
1106C2#539×D4712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2318C2
socle, cosocleC23×C47C25
prime radicalC22×D4×D47C22
hypercenter#2318D47
hypocenterC47C2×#2318
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #20246024C2semidirect
3. #20246023C2semidirect
4. #20246022C2semidirect
5. #20246021C2semidirect
6. #20246020C2semidirect
7. #20246019C2semidirect
8. #20246018C2semidirect
9. #20246017C2semidirect
10. #20246016C2semidirect
11. #20246015C2semidirect
12. #20246014C2semidirect
13. #388×D47C2semidirect
14. #387×D47C2semidirect
16. #385×D47C2semidirect
17. #383×D47C2semidirect
18. #382×D47C2semidirect
19. #381×D47C2semidirect
20. #380×D47C2semidirect
21. C4×C22⋊C4×D47C2semidirect
22. C2×#95×D47C2semidirect
23. C47×#2318C2semidirect
35. C4×D4×D47C4semidirect
46. #15689017C22semidirect
47. #15689016C22semidirect
48. #15689015C22semidirect
49. #15689014C22semidirect
50. #15689013C22semidirect
51. #15689012C22semidirect
52. #15689011C22semidirect
53. #15689010C22semidirect
54. #15689009C22semidirect
55. #15689008C22semidirect
56. #15689007C22semidirect
57. #15689006C22semidirect
58. #15689005C22semidirect
59. #15689004C22semidirect
67. #15688998C22semidirect
68. #15688997C22semidirect
69. #15688997C22semidirect
70. #15688996C22semidirect
71. #15688995C22semidirect
72. #15688994C22semidirect
73. #15688994C22semidirect
74. #15688991C22semidirect
75. #15688990C22semidirect
76. #15688990C22semidirect
77. #15688990C22semidirect
78. #15688990C22semidirect
79. #15688989C22semidirect
80. #15688988C22semidirect
81. #15688987C22semidirect
82. #15688987C22semidirect
83. #15688987C22semidirect
84. #15688986C22semidirect
85. #15688985C22semidirect
86. #15688985C22semidirect
87. #15688985C22semidirect
88. #15688984C22semidirect
89. #15688983C22semidirect
90. #15688982C22semidirect
91. #15688982C22semidirect
92. #15688981C22semidirect
93. #15688980C22semidirect
94. C22⋊C4×Dic47C22semidirect
95. C4×(C2×D47)⋊C4C22semidirect
96. C4×C22⋊Dic47C22semidirect
97. #15688970C22semidirect
98. #15688970C22semidirect
99. C2×C47⋊#95C22semidirect
100. C2×C47⋊#95C22semidirect
110. #95×D47C22semidirect
111. #95×D47C22semidirect
112. #95×D47C22semidirect
114. C47×#388C22semidirect
115. C47×#387C22semidirect
117. C47×#385C22semidirect
118. C47×#383C22semidirect
119. C47×#382C22semidirect
120. C47×#381C22semidirect
121. C47×#380C22semidirect
122. C4×C22⋊C4×C47C22semidirect
123. C2×#95×C47C22semidirect
140. C22×C4×D47C2×C4semidirect
156. C4×D188C2×C4semidirect
157. D4×Dic47C2×C4semidirect
158. #13093986C2×C4semidirect
159. C4×C22⋊D47C2×C4semidirect
160. C4×C22⋊D47C2×C4semidirect
161. (C22⋊D47)⋊C4C2×C4semidirect
162. (C22⋊D47)⋊C4C2×C4semidirect
174. C4⋊C4×D47C2×C4semidirect
194. C22⋊C4×D47C2×C4semidirect
202. C42×D47C2×C4semidirect
230. C4×D4×C47C2×C4semidirect
273. C22×C4×C47C22×C4semidirect
293. C22×Dic47C22×C4semidirect
344. C2×C4×D47C22×C4semidirect
345. C2×C4×D47C22×C4semidirect
348. C4⋊C4×C47C22×C4semidirect
353. C22⋊C4×C47C22×C4semidirect
355. C42×C47C22×C4semidirect
360. C22⋊Dic47C22×C4semidirect
369. (C2×D47)⋊C4C22×C4semidirect
370. (C2×D47)⋊C4C22×C4semidirect
373. C4⋊Dic47C22×C4semidirect
378. Dic47⋊C4C22×C4semidirect
379. Dic47⋊C4C22×C4semidirect
383. C4×Dic47C22×C4semidirect
384. C4×Dic47C22×C4semidirect
385. C4×Dic47C22×C4semidirect
556. #2318D47direct (N × H)
576. D47#2318direct (N × H)
607. #388C2×D47semidirect
615. #387C2×D47semidirect
631. #385C2×D47semidirect
637. #383C2×D47semidirect
643. #382C2×D47semidirect
649. #381C2×D47semidirect
655. #380C2×D47semidirect
661. C4×C22⋊C4C2×D47semidirect
676. C2×#95C2×D47semidirect
677. C47C2×#2318semidirect
721. C4×D4C4×D47semidirect
890. C22×C4C2×C4×D47semidirect
911. C4⋊C4C2×C4×D47semidirect
931. C22⋊C4C2×C4×D47semidirect
939. C42C2×C4×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
#202460242
#202460232
#202460222
#202460212
#202460202
#202460192
#202460182
#202460172
#202460162
#202460152
#202460142
#388×D472
#387×D472
#386×D472
#385×D472
#383×D472
#382×D472
#381×D472
#380×D472
C4×C22⋊C4×D472
C2×#95×D472
C47×#23182
C2×#231847