Finite Group Databasebeta

← #25257315

Subgroups — #25257315

Order 11008.

2826 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×#14583412C211yesmaximal, characteristic
2#19137611C211yesmaximal, characteristic, complemented
3#19137609C211yesmaximal, characteristic, complemented
4#19137604C211yesmaximal, characteristic, complemented
5#19137577C212yesmaximal, complemented
6#19137571C212yesmaximal, complemented
7#19137534C212yesmaximal, complemented
8#19137504C212yesmaximal, complemented
9#19137484C211yesmaximal, characteristic, complemented
10#19137479C211yesmaximal, characteristic, complemented
11#19137433C211yesmaximal, characteristic, complemented
12#19137424C211yesmaximal, characteristic, complemented
13#19137388C212yesmaximal, complemented
14#19137384C212yesmaximal, complemented
15#19137223C212yesmaximal, complemented
16#19137133C211yesmaximal, characteristic, complemented
17C4×#13063301C211yesmaximal, characteristic, complemented
18C4×#13063300C211yesmaximal, characteristic, complemented
19#19137103C211yesmaximal, characteristic, complemented
20C2×#14582756C211yesmaximal, characteristic, complemented
21#19136954C212yesmaximal, complemented
22C4×C22⋊C4×D43C211yesmaximal, characteristic, complemented
23C43×#2360C211yesmaximal, characteristic, complemented
24C22×#10621902C2211yescharacteristic
25C23×C4×D43C2211yescharacteristic
26#14583412C4116yescomplemented
27C2×#13063310C2212yes—
28C2×#13063301C2211yescharacteristic
29C2×#13063300C2211yescharacteristic
30C2×#13063299C2211yescharacteristic
31C2×#13063295C2212yes—
32C2×Q8×Dic43C2211yescharacteristic, complemented
33C2×C4×D172C2212yes—
34C2×C4×D172C2211yescharacteristic, complemented
35C2×#13063287C2212yes—
36C2×#13063287C2212yes—
37C2×#13063287C2211yescharacteristic, complemented
38C2×C4×C22⋊D43C2212yes—
39C2×(C22⋊D43)⋊C4C2212yes—
40C2×(C22⋊D43)⋊C4C2212yes—
41C2×#13063283C2211yescharacteristic
42C22×C4⋊Dic43C2211yescharacteristic
43C22×(C2×D43)⋊C4C2212yes—
44C2×C22⋊C4×D43C2211yescharacteristic
45C2×C22⋊C4×D43C2211yescharacteristic
46C2×C42×D43C2211yescharacteristic
47C2×C42×D43C2211yescharacteristic
48#14582806C2211yescharacteristic, complemented
49#14582801C2212yes—
50#14582801C2211yescharacteristic, complemented
51#14582800C2212yes—
52#14582800C2211yescharacteristic, complemented
53#14582798C2211yescharacteristic, complemented
54#14582798C2212yescomplemented
55#14582797C2211yescharacteristic, complemented
56#14582795C2211yescharacteristic, complemented
57#14582791C2212yes—
58#14582791C2212yescomplemented
59#14582791C2212yescomplemented
60#14582790C2212yes—
61#14582789C2212yes—
62#14582789C2212yescomplemented
63#14582789C2212yescomplemented
64#14582788C2212yes—
65#14582786C2212yescomplemented
66#14582785C2212yescomplemented
67#14582780C2212yescomplemented
68#14582778C2212yes—
69#14582777C2212yes—
70#14582777C2212yes—
71#14582777C2212yes—
72#14582777C2212yes—
73#14582776C2212yes—
74#14582774C2212yes—
75#14582773C2212yes—
76#14582773C2212yescomplemented
77#14582770C2212yes—
78#14582770C2212yescomplemented
79#14582766C2212yescomplemented
80#14582764C2212yescomplemented
81#14582761C2212yescomplemented
82#14582756C2211yescharacteristic
83#14582756C2211yescharacteristic
84#14582756C2212yes—
85#14582756C2211yescharacteristic
86#14582756C2211yescharacteristic
87#14582756C2212yes—
88#14582756C2212yescomplemented
89C4⋊C4×Dic43C2211yescharacteristic, complemented
90C4⋊C4×Dic43C2211yescharacteristic, complemented
91C4×Dic43⋊C4C2212yescomplemented
92C4×Dic43⋊C4C2212yescomplemented
93C4×C4⋊Dic43C2211yescharacteristic, complemented
94#14582750C2212yescomplemented
95C22⋊C4×Dic43C2212yes—
96C22⋊C4×Dic43C2211yescharacteristic
97C22⋊C4×Dic43C2211yescharacteristic
98C4×(C2×D43)⋊C4C2212yes—
99C4×(C2×D43)⋊C4C2211yescharacteristic
100C4×(C2×D43)⋊C4C2211yescharacteristic
101C4×(C2×D43)⋊C4C2212yescomplemented
102C4×(C2×D43)⋊C4C2212yescomplemented
103C4×C22⋊Dic43C2211yescharacteristic
104#14582746C2212yes—
105#14582746C2211yescharacteristic
106#14582746C2211yescharacteristic
107#14582746C2212yescomplemented
108#14582744C2212yescomplemented
109C2×C43⋊#95C2212yes—
110#95×D43C2211yescharacteristic
111#95×D43C2211yescharacteristic
112#95×D43C2212yescomplemented
113C2×C22⋊Q8×C43C2211yescharacteristic
114C2×C4×Q8×C43C2211yescharacteristic, complemented
115C22×C4⋊C4×C43C2211yescharacteristic
116C43×#391C2211yescharacteristic, complemented
117C43×#389C2211yescharacteristic, complemented
118C43×#389C2212yescomplemented
119C43×#387C2212yescomplemented
120C43×#385C2212yes—
121C4×C4⋊C4×C43C2211yescharacteristic, complemented
122C4×C22⋊C4×C43C2212yes—
123C4×C22⋊C4×C43C2211yescharacteristic
124C24×D43C2311yescharacteristic
125C2×#10621902—42no—
126C2×#10621902—42no—
127C2×#10621902C2×C418yescomplemented
128C22×D172C2311yescharacteristic
129C22×D172C2312yes—
130C22×D172C2312yes—
131C22×C22⋊D43C2312yes—
132C23×Dic43C2312yes—
133C23×Dic43C2311yescharacteristic
134C22×C4×D43—42no—
135C22×C4×D43—42no—
136C22×C4×D43C2×C418yescomplemented
137C22×C4×D43C2311yescharacteristic
138C22×C4×D43C2311yescharacteristic
139C22×C4×D43C2311yescharacteristic
140C22×C4×D43C2311yescharacteristic
141C22×C4×D43C2311yescharacteristic
142C22×C4×D43C2311yescharacteristic
143C22×C4×D43C2312yes—
144C22×C4×D43C2312yes—
145C22×C4×D43C2312yes—
146C22×C4×D43C2311yescharacteristic
147C22×C4×D43C2311yescharacteristic
148#13063310C2×C4116yescomplemented
149#13063301C2×C418yescomplemented
150#13063300C2×C418yescomplemented
151#13063299C2×C418yescomplemented
152#13063295C2×C4116yescomplemented
153Q8×Dic43—42no—
154C4×D172—42no—
155C4×D172—44no—
156#13063287—42no—
157#13063287—44no—
158#13063287C2×C4116yescomplemented
159C4×C22⋊D43—28no—
160(C22⋊D43)⋊C4—28no—
161(C22⋊D43)⋊C4C2×C4116yescomplemented
162#13063283C2×C418yescomplemented
163C2×C4⋊Dic43—42no—
164C2×C4⋊Dic43C2311yescharacteristic
165C2×C4⋊Dic43C2311yescharacteristic
166C2×C4⋊Dic43C2312yes—
167C2×C4⋊Dic43C2312yes—
168C2×C4⋊Dic43C2312yes—
169C2×C4⋊Dic43C2311yescharacteristic
170C2×Dic43⋊C4C2312yes—
171C2×Dic43⋊C4C2312yes—
172C2×Dic43⋊C4C2312yes—
173C2×C22⋊Dic43C2311yescharacteristic
174C2×C22⋊Dic43C2311yescharacteristic
175C2×(C2×D43)⋊C4—44no—
176C2×(C2×D43)⋊C4C2311yescharacteristic
177C2×(C2×D43)⋊C4C2311yescharacteristic
178C2×(C2×D43)⋊C4C2312yes—
179C2×(C2×D43)⋊C4C2311yescharacteristic
180C2×(C2×D43)⋊C4C2311yescharacteristic
181C2×(C2×D43)⋊C4C2312yes—
182C2×(C2×D43)⋊C4C2312yes—
183C2×(C2×D43)⋊C4C2312yes—
184C2×(C2×D43)⋊C4C2312yes—
185C2×(C2×D43)⋊C4C2312yes—
186C2×(C2×D43)⋊C4C2312yes—
187C2×(C2×D43)⋊C4C2312yes—
188C2×(C2×D43)⋊C4C2312yes—
189C2×(C2×D43)⋊C4C2312yes—
190C2×(C2×D43)⋊C4C2312yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2312yes—
193C2×(C2×D43)⋊C4C2312yes—
194C22⋊C4×D43—24no—
195C22⋊C4×D43—24no—
196C2×C4×Dic43C2312yes—
197C2×C4×Dic43C2312yes—
198C2×C4×Dic43C2311yescharacteristic
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2312yes—
201C2×C4×Dic43C2311yescharacteristic
202C2×C4×Dic43C2312yes—
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2311yescharacteristic
206C2×C4×Dic43C2312yes—
207C42×D43—42no—
208C42×D43—42no—
209C43⋊#95C2311yescharacteristic
210C43⋊#95C2312yes—
211C43⋊#95C2312yes—
212C43⋊#95C2312yes—
213C43⋊#95C2312yes—
214C43⋊#95C2312yes—
215C43⋊#95C2312yes—
216C43⋊#95C2312yes—
217C43⋊#95C2312yes—
218C43⋊#95C2312yes—
219C43⋊#95C2311yescharacteristic
220C43⋊#95C2312yes—
221C43⋊#95C2311yescharacteristic
222C43⋊#95C2311yescharacteristic
223C43⋊#95C2311yescharacteristic
224C43⋊#95C2311yescharacteristic
225C43⋊#95C2312yes—
226C43⋊#95C2312yes—
227C22×Q8×C43C2311yescharacteristic
228C23×C4×C43C2311yescharacteristic
229C23×C4×C43C2312yes—
230C22⋊Q8×C43C2×C418yescomplemented
231C4×Q8×C43—42no—
232C2×C4⋊C4×C43—42no—
233C2×C4⋊C4×C43C2311yescharacteristic
234C2×C4⋊C4×C43C2311yescharacteristic
235C2×C4⋊C4×C43C2312yes—
236C2×C4⋊C4×C43C2312yes—
237C2×C4⋊C4×C43C2312yes—
238C2×C4⋊C4×C43C2312yes—
239C2×C4⋊C4×C43C2311yescharacteristic
240C2×C22⋊C4×C43C2311yescharacteristic
241C2×C22⋊C4×C43C2312yes—
242C2×C22⋊C4×C43C2311yescharacteristic
243C2×C42×C43C2311yescharacteristic
244C2×C42×C43C2311yescharacteristic
245C2×C42×C43C2312yes—
246C2×C42×C43C2312yes—
247#95×C43C2312yes—
248#95×C43C2312yes—
249#95×C43C2312yes—
250#95×C43C2311yescharacteristic
251#95×C43C2311yescharacteristic
252#95×C43C2312yes—
253C24×C43C2411yescharacteristic
254C23×D43—22no—
255C23×D43—22no—
256C23×D43—22no—
257C23×D43—22no—
258C23×D43—41no—
259C23×D43—41no—
260C23×D43C22×C414yes—
261C23×D43C2411yescharacteristic
262C23×D43C2412yes—
263C23×D43C2411yescharacteristic
264C2×Q8×C43—22no—
265C2×Q8×C43—22no—
266C2×Q8×C43C22×C414yes—
267C22×C4×C43—22no—
268C22×C4×C43—22no—
269C22×C4×C43—24no—
270C22×C4×C43—42no—
271C22×C4×C43—42no—
272C22×C4×C43C22×C414yes—
273C22×C4×C43C2411yescharacteristic
274C22×C4×C43C2412yes—
275C22×C4×C43C2412yes—
276C22×C4×C43C2411yescharacteristic
277C22×C4×C43C2412yes—
278C22×C4×C43C2412yes—
279C22×C4×C43C2411yescharacteristic
280C22×C4×C43C2411yescharacteristic
281C22×C4×C43C2411yescharacteristic
282C22×C4×C43C2411yescharacteristic
283C2×C22⋊D43—24no—
284C2×C22⋊D43—24no—
285C2×C22⋊D43C22×C418yes—
286C22×Dic43—24no—
287C22×Dic43—41no—
288C22×Dic43—41no—
289C22×Dic43—42no—
290C22×Dic43—42no—
291C22×Dic43C22×C414yes—
292C22×Dic43C2411yescharacteristic
293C22×Dic43C2412yes—
294C22×Dic43C2412yes—
295C22×Dic43C2411yescharacteristic
296C22×Dic43C2411yescharacteristic
297C22×Dic43C2411yescharacteristic
298C22×Dic43C2412yes—
299C22×Dic43C2411yescharacteristic
300C22×Dic43C2411yescharacteristic
301#10621902—416no—
302C2×D172—22no—
303C2×D172—22no—
304C2×D172—24no—
305C2×D172—24no—
306C2×D172—42no—
307C2×D172—42no—
308C2×D172C22×C418yes—
309C2×D172C22×C414yes—
310C2×D172C22×C418yes—
311C2×C4×D43—22no—
312C2×C4×D43—22no—
313C2×C4×D43—22no—
314C2×C4×D43—22no—
315C2×C4×D43—22no—
316C2×C4×D43—22no—
317C2×C4×D43—22no—
318C2×C4×D43—22no—
319C2×C4×D43—24no—
320C2×C4×D43—24no—
321C2×C4×D43—22no—
322C2×C4×D43—22no—
323C2×C4×D43—22no—
324C2×C4×D43—22no—
325C2×C4×D43—41no—
326C2×C4×D43—41no—
327C2×C4×D43—41no—
328C2×C4×D43—41no—
329C2×C4×D43—41no—
330C2×C4×D43—41no—
331C2×C4×D43—41no—
332C2×C4×D43—41no—
333C2×C4×D43—42no—
334C2×C4×D43—42no—
335C2×C4×D43—42no—
336C2×C4×D43—42no—
337C2×C4×D43—42no—
338C2×C4×D43—42no—
339C2×C4×D43—416no—
340C2×C4×D43C22×C414yes—
341C2×C4×D43C22×C414yes—
342C2×C4×D43C22×C418yes—
343C2×C4×D43C22×C414yes—
344C2×C4×D43C22×C414yes—
345C4⋊C4×C43—22no—
346C4⋊C4×C43—22no—
347C4⋊C4×C43—42no—
348C4⋊C4×C43—42no—
349C4⋊C4×C43—42no—
350C4⋊C4×C43C22×C414yes—
351C4⋊C4×C43C22×C418yes—
352C22⋊C4×C43—22no—
353C22⋊C4×C43C22×C418yes—
354C22⋊C4×C43#4114yescomplemented
355C42×C43—22no—
356C42×C43—22no—
357C42×C43—42no—
358C42×C43—42no—
359C22⋊Dic43—22no—
360C22⋊Dic43#4114yescomplemented
361(C2×D43)⋊C4—22no—
362(C2×D43)⋊C4—22no—
363(C2×D43)⋊C4—24no—
364(C2×D43)⋊C4—22no—
365(C2×D43)⋊C4—22no—
366(C2×D43)⋊C4—24no—
367(C2×D43)⋊C4—24no—
368(C2×D43)⋊C4—24no—
369(C2×D43)⋊C4—42no—
370(C2×D43)⋊C4—42no—
371(C2×D43)⋊C4—42no—
372(C2×D43)⋊C4—42no—
373(C2×D43)⋊C4—42no—
374(C2×D43)⋊C4—42no—
375(C2×D43)⋊C4C22×C418yes—
376(C2×D43)⋊C4C22×C418yes—
377(C2×D43)⋊C4C22×C418yes—
378(C2×D43)⋊C4C22×C418yes—
379C4⋊Dic43—22no—
380C4⋊Dic43—22no—
381C4⋊Dic43—42no—
382C4⋊Dic43—42no—
383C4⋊Dic43—42no—
384C4⋊Dic43C22×C414yes—
385Dic43⋊C4—24no—
386Dic43⋊C4—24no—
387Dic43⋊C4C22×C418yes—
388C4×Dic43—24no—
389C4×Dic43—22no—
390C4×Dic43—22no—
391C4×Dic43—24no—
392C4×Dic43—41no—
393C4×Dic43—41no—
394C4×Dic43—41no—
395C4×Dic43—41no—
396C4×Dic43—42no—
397C4×Dic43—42no—
398C4×Dic43C22×C418yes—
399C23×C43—21no—
400C23×C43—21no—
401C23×C43—21no—
402C23×C43—21no—
403C23×C43C23×C412yes—
404C23×C43C2×#4112yes—
405C23×C43C2×#4112yes—
406C23×C43C2511yescharacteristic
407C22×D43—21no—
408C22×D43—21no—
409C22×D43—21no—
410C22×D43—21no—
411C22×D43—28no—
412C22×D43—21no—
413C22×D43—21no—
414C22×D43—22no—
415C22×D43—22no—
416C22×D43—21no—
417C22×D43—22no—
418C22×D43—22no—
419C22×D43—22no—
420C22×D43—21no—
421C22×D43—21no—
422C22×D43—22no—
423C22×D43—21no—
424C22×D43—28no—
425C22×D43—44no—
426C22×D43—44no—
427C22×D43—44no—
428C22×D43—44no—
429C22×D43—44no—
430C22×D43C23×C412yes—
431C22×D43C23×C414yes—
432C22×D43C23×C412yes—
433C22×D43H(5,𝔽2)12yes—
434C22×D432−1+412yes—
435Q8×C43—28no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—21no—
439C2×C4×C43—21no—
440C2×C4×C43—21no—
441C2×C4×C43—21no—
442C2×C4×C43—22no—
443C2×C4×C43—21no—
444C2×C4×C43—21no—
445C2×C4×C43—22no—
446C2×C4×C43—28no—
447C2×C4×C43—22no—
448C2×C4×C43—22no—
449C2×C4×C43—21no—
450C2×C4×C43—21no—
451C2×C4×C43—21no—
452C2×C4×C43—21no—
453C2×C4×C43—22no—
454C2×C4×C43—22no—
455C2×C4×C43—21no—
456C2×C4×C43—22no—
457C2×C4×C43—22no—
458C2×C4×C43—21no—
459C2×C4×C43—84no—
460C2×C4×C43C23×C414yes—
461C2×C4×C43C23×C414yes—
462C2×C4×C43C23×C412yes—
463C2×C4×C43C23×C412yes—
464C2×C4×C43C2×#4112yes—
465C2×C4×C43C2×#4112yes—
466C2×C4×C43H(5,𝔽2)12yes—
467C2×C4×C43H(5,𝔽2)12yes—
468C22⋊D43—216no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—21no—
472C2×Dic43—21no—
473C2×Dic43—21no—
474C2×Dic43—21no—
475C2×Dic43—21no—
476C2×Dic43—21no—
477C2×Dic43—21no—
478C2×Dic43—21no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—21no—
482C2×Dic43—21no—
483C2×Dic43—21no—
484C2×Dic43—21no—
485C2×Dic43—22no—
486C2×Dic43—22no—
487C2×Dic43—22no—
488C2×Dic43—21no—
489C2×Dic43—22no—
490C2×Dic43—21no—
491C2×Dic43—44no—
492C2×Dic43—84no—
493C2×Dic43C23×C412yes—
494C2×Dic43C23×C414yes—
495C2×Dic43C23×C412yes—
496C2×Dic43C2×#4112yes—
497C2×Dic43C2×#4112yes—
498D172—216no—
499D172—28no—
500D172—48no—
501C4×D43—28no—
502C4×D43—28no—
503C4×D43—44no—
504C4×D43—44no—
505C4×D43—48no—
506C4×D43—44no—
507C4×D43—44no—
508C4×D43—44no—
509C4×D43—44no—
510C4×D43—84no—
511C4×D43—84no—
512#34233—431nomaximal, Sylow
513C22×C43—22no—
514C22×C43—22no—
515C22×C43—22no—
516C22×C43—22no—
517C22×C43—22no—
518C22×C43—22no—
519C22×C43C4×#4114yes—
520C22×C43C24×C411yescharacteristic
521C22×C43C22×#4111yescharacteristic
522C22×C43C22×#4111yescharacteristic
523C22×C43C2×H(5,𝔽2)11yescharacteristic
524C22×C43C2×H(5,𝔽2)11yescharacteristic
525C22×C43C2×H(5,𝔽2)11yescharacteristic
526C22×C43C2×2−1+411yescharacteristic
527C2×D43—22no—
528C2×D43—22no—
529C2×D43—22no—
530C2×D43—22no—
531C2×D43—22no—
532C2×D43—22no—
533C2×D43—22no—
534C2×D43—24no—
535C2×D43—22no—
536C2×D43—24no—
537C2×D43—22no—
538C2×D43—24no—
539C2×D43—416no—
540C2×D43—41no—
541C2×D43—41no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—41no—
547C2×D43—41no—
548C2×D43#52014yes—
549C4×C43—22no—
550C4×C43—24no—
551C4×C43—24no—
552C4×C43—22no—
553C4×C43—22no—
554C4×C43—41no—
555C4×C43—42no—
556C4×C43—42no—
557C4×C43—41no—
558C4×C43#51814yes—
559Dic43—24no—
560Dic43—22no—
561Dic43—22no—
562Dic43—22no—
563Dic43—22no—
564Dic43—41no—
565Dic43—42no—
566Dic43—42no—
567Dic43—41no—
568C2×#525—431no—
569#2361—431no—
570#2361—431no—
571#2360—431no—
572#2360D4311yescharacteristic, complemented
573#2358—432no—
574#2358—432no—
575#2353—432no—
576#2349—432no—
577#2347—431no—
578#2346—431no—
579#2341—431no—
580#2339—431no—
581#2335—432no—
582#2335—432no—
583#2318—432no—
584C4×C22⋊Q8—431no—
585C4×C22⋊Q8—431no—
586C4×#121—431no—
587C4×#121—431no—
588C2×#380—431no—
589#2275—432no—
590C2×C4×C22⋊C4—431no—
591C2×C43—24no—
592C2×C43C2×C4×#4111yescharacteristic
593C2×C43C2×#51811yescharacteristic
594C2×C43C2×#52011yescharacteristic
595C2×C43#351911yescharacteristic
596C2×C43#351911yescharacteristic
597C2×C43#352011yescharacteristic
598C2×C43#352011yescharacteristic
599D43—24no—
600D43—44no—
601D43—42no—
602C22×#41—431no—
603C24×C4—431no—
604#525—4316no—
605C2×#123—432no—
606C2×C22⋊Q8—431no—
607C2×C22⋊Q8C2×D4311yescharacteristic
608C2×#121—431no—
609C2×#121—431no—
610C2×#120—432no—
611C2×C4×Q8—431no—
612C2×C4×Q8C2×D4311yescharacteristic, complemented
613C2×C4×D4—432no—
614C2×C4×D4—432no—
615C2×C4×D4—431no—
616C2×C4×D4—432no—
617C2×C4×D4—432no—
618C2×C4×D4—432no—
619C2×C4×D4—431no—
620C2×C4×D4—432no—
621C2×#117—431no—
622C22×C4⋊C4—431no—
623C22×C4⋊C4C2×D4311yescharacteristic
624C22×C22⋊C4—432no—
625C22×C22⋊C4—431no—
626C22×C22⋊C4—431no—
627C22×C42—431no—
628C22×C42—431no—
629#391—431no—
630#391C2×D4311yescharacteristic, complemented
631#390—432no—
632#390—431no—
633#390—432no—
634#390—431no—
635#389—431no—
636#389—432no—
637#389—431no—
638#389—431no—
639#389C2×D4312yescomplemented
640#389C2×D4311yescharacteristic, complemented
641#388—432no—
642#388—432no—
643#388—432no—
644#388—432no—
645#388—432no—
646#388—432no—
647#388—432no—
648#388—432no—
649#387—432no—
650#387—432no—
651#387—432no—
652#387C2×D4312yescomplemented
653#386—432no—
654#386—432no—
655#386—432no—
656#386—432no—
657#386—432no—
658#386—432no—
659#385—432no—
660#385—432no—
661#385—432no—
662#385—432no—
663#385—432no—
664#385C2×D4312yes—
665#383—432no—
666#382—432no—
667#381—432no—
668#380—432no—
669#380—432no—
670#380—431no—
671#380—431no—
672#380—432no—
673#380—431no—
674#380—431no—
675C4×C4⋊C4—431no—
676C4×C4⋊C4—431no—
677C4×C4⋊C4—432no—
678C4×C4⋊C4—431no—
679C4×C4⋊C4—432no—
680C4×C4⋊C4—432no—
681C4×C4⋊C4C2×D4311yescharacteristic, complemented
682C4×C22⋊C4—431no—
683C4×C22⋊C4—431no—
684C4×C22⋊C4—432no—
685C4×C22⋊C4—431no—
686C4×C22⋊C4—432no—
687C4×C22⋊C4—431no—
688C4×C22⋊C4—431no—
689C4×C22⋊C4—432no—
690C4×C22⋊C4—432no—
691C4×C22⋊C4—431no—
692C4×C22⋊C4—431no—
693C4×C22⋊C4—432no—
694C4×C22⋊C4—432no—
695C4×C22⋊C4C2×D4312yes—
696C4×C22⋊C4C2×D4311yescharacteristic
697#376—432no—
698C2×#95—432no—
699C2×#95—432no—
700C2×#95—431no—
701C2×#95—431no—
702C43#3423311yescharacteristic, complemented, Sylow
703C25—431no—
704C2×#41—438no—
705C2×#41—1722no—
706C2×#41—1722no—
707C22×Q8C22×D4311yescharacteristic
708C22×D4—432no—
709C22×D4—432no—
710C22×D4—431no—
711C22×D4—432no—
712C23×C4—431no—
713C23×C4—431no—
714C23×C4—431no—
715C23×C4—438no—
716C23×C4—431no—
717C23×C4—432no—
718C23×C4—431no—
719C23×C4—432no—
720C23×C4—431no—
721C23×C4—431no—
722C23×C4—431no—
723C23×C4—431no—
724C23×C4—432no—
725C23×C4—432no—
726C23×C4—1722no—
727C23×C4—1722no—
728C23×C4C22×D4311yescharacteristic
729C23×C4C22×D4312yes—
730#123—4316no—
731C22⋊Q8—438no—
732C22⋊Q8C4×D4318yescomplemented
733#121—438no—
734#121—438no—
735#120—4316no—
736C4×Q8—42no—
737C4×Q8—1722no—
738C4×D4—4316no—
739C4×D4—4316no—
740C4×D4—868no—
741C4×D4—868no—
742C4×D4—1722no—
743C4×D4—1724no—
744C4×D4—1722no—
745C4×D4—1724no—
746#117—438no—
747C2×C4⋊C4—42no—
748C2×C4⋊C4—431no—
749C2×C4⋊C4—432no—
750C2×C4⋊C4—431no—
751C2×C4⋊C4—431no—
752C2×C4⋊C4—432no—
753C2×C4⋊C4—432no—
754C2×C4⋊C4—432no—
755C2×C4⋊C4—432no—
756C2×C4⋊C4—432no—
757C2×C4⋊C4—1722no—
758C2×C4⋊C4C22×D4311yescharacteristic
759C2×C4⋊C4C22×D4311yescharacteristic
760C2×C4⋊C4C22×D4312yes—
761C2×C4⋊C4C22×D4312yes—
762C2×C4⋊C4C22×D4312yes—
763C2×C4⋊C4C22×D4311yescharacteristic
764C2×C4⋊C4C22×D4312yes—
765C2×C22⋊C4—431no—
766C2×C22⋊C4—432no—
767C2×C22⋊C4—432no—
768C2×C22⋊C4—432no—
769C2×C22⋊C4—432no—
770C2×C22⋊C4—431no—
771C2×C22⋊C4—432no—
772C2×C22⋊C4—432no—
773C2×C22⋊C4—431no—
774C2×C22⋊C4—431no—
775C2×C22⋊C4—431no—
776C2×C22⋊C4—431no—
777C2×C22⋊C4—432no—
778C2×C22⋊C4—432no—
779C2×C22⋊C4—432no—
780C2×C22⋊C4—432no—
781C2×C22⋊C4—432no—
782C2×C22⋊C4—432no—
783C2×C22⋊C4—432no—
784C2×C22⋊C4—432no—
785C2×C22⋊C4—864no—
786C2×C22⋊C4—864no—
787C2×C22⋊C4—1724no—
788C2×C22⋊C4C22×D4311yescharacteristic
789C2×C22⋊C4C22×D4312yes—
790C2×C22⋊C4C22×D4311yescharacteristic
791C2×C42—432no—
792C2×C42—432no—
793C2×C42—432no—
794C2×C42—431no—
795C2×C42—431no—
796C2×C42—432no—
797C2×C42—432no—
798C2×C42—431no—
799C2×C42—431no—
800C2×C42—431no—
801C2×C42—431no—
802C2×C42—1722no—
803C2×C42—1722no—
804C2×C42C22×D4311yescharacteristic
805C2×C42C22×D4311yescharacteristic
806C2×C42C22×D4312yes—
807C2×C42C22×D4312yes—
808#95—431no—
809#95—432no—
810#95—431no—
811#95—431no—
812#95—431no—
813#95—431no—
814#95—431no—
815#95—432no—
816#95—432no—
817#95—432no—
818#95—432no—
819#95—432no—
820#95—432no—
821#95—432no—
822#95—432no—
823#95—432no—
824#95—432no—
825#95—432no—
826#95C22×D4311yescharacteristic
827#95C22×D4311yescharacteristic
828#95C22×D4312yes—
829#95C22×D4312yes—
830#95C22×D4312yes—
831#95C22×D4312yes—
832C24—431no—
833C24—431no—
834C24—432no—
835C24—434no—
836C24—862no—
837C24—862no—
838C24—862no—
839C24—862no—
840C24—1721no—
841C24—1721no—
842C24C23×D4311yescharacteristic
843#41—17216no—
844C2×Q8—22no—
845C2×Q8—22no—
846C2×Q8C2×C4×D4314yes—
847C2×D4—438no—
848C2×D4—438no—
849C2×D4—434no—
850C2×D4—438no—
851C2×D4—864no—
852C2×D4—864no—
853C2×D4—864no—
854C2×D4—864no—
855C2×D4—862no—
856C2×D4—862no—
857C2×D4—1722no—
858C2×D4—1722no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—24no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—431no—
865C22×C4—431no—
866C22×C4—431no—
867C22×C4—431no—
868C22×C4—432no—
869C22×C4—434no—
870C22×C4—434no—
871C22×C4—434no—
872C22×C4—434no—
873C22×C4—438no—
874C22×C4—434no—
875C22×C4—431no—
876C22×C4—432no—
877C22×C4—431no—
878C22×C4—432no—
879C22×C4—864no—
880C22×C4—862no—
881C22×C4—862no—
882C22×C4—862no—
883C22×C4—862no—
884C22×C4—862no—
885C22×C4—862no—
886C22×C4—862no—
887C22×C4—862no—
888C22×C4—862no—
889C22×C4—862no—
890C22×C4—864no—
891C22×C4—864no—
892C22×C4—862no—
893C22×C4—862no—
894C22×C4—17216no—
895C22×C4—1722no—
896C22×C4—1722no—
897C22×C4—1722no—
898C22×C4—1722no—
899C22×C4—1721no—
900C22×C4—1721no—
901C22×C4—1721no—
902C22×C4—1721no—
903C22×C4—1721no—
904C22×C4—1721no—
905C22×C4—1721no—
906C22×C4—1721no—
907C22×C4—1722no—
908C22×C4—1722no—
909C22×C4—1722no—
910C22×C4—1722no—
911C22×C4—1721no—
912C22×C4—1721no—
913C22×C4C2×C4×D4314yes—
914C22×C4C23×D4311yescharacteristic
915C22×C4C23×D4312yes—
916C22×C4C23×D4311yescharacteristic
917C22×C4C23×D4312yes—
918C22×C4C23×D4312yes—
919C22×C4C23×D4312yes—
920C22×C4C23×D4311yescharacteristic
921C22×C4C23×D4311yescharacteristic
922C22×C4C23×D4311yescharacteristic
923C22×C4C23×D4311yescharacteristic
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—434no—
930C4⋊C4—438no—
931C4⋊C4—864no—
932C4⋊C4—864no—
933C4⋊C4—862no—
934C4⋊C4—862no—
935C4⋊C4—1722no—
936C4⋊C4—1722no—
937C4⋊C4—1722no—
938C4⋊C4C2×C4×D4314yes—
939C4⋊C4C2×C4×D4318yes—
940C22⋊C4—22no—
941C22⋊C4—434no—
942C22⋊C4—438no—
943C22⋊C4—438no—
944C22⋊C4—438no—
945C22⋊C4—438no—
946C22⋊C4—862no—
947C22⋊C4—862no—
948C22⋊C4—864no—
949C22⋊C4—864no—
950C22⋊C4—864no—
951C22⋊C4—862no—
952C22⋊C4—862no—
953C22⋊C4—862no—
954C22⋊C4—864no—
955C22⋊C4—1722no—
956C22⋊C4—1722no—
957C22⋊C4—1722no—
958C22⋊C4—1722no—
959C22⋊C4—1722no—
960C22⋊C4—1722no—
961C22⋊C4C2×C4×D4318yes—
962C22⋊C4#1062190214yescomplemented
963C42—22no—
964C42—22no—
965C42—42no—
966C42—42no—
967C42—438no—
968C42—864no—
969C42—864no—
970C42—862no—
971C42—862no—
972C42—1721no—
973C42—1721no—
974C42—1721no—
975C42—1721no—
976C42—1722no—
977C42—1722no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—432no—
983C23—432no—
984C23—432no—
985C23—432no—
986C23—434no—
987C23—868no—
988C23—861no—
989C23—861no—
990C23—861no—
991C23—861no—
992C23—868no—
993C23—861no—
994C23—862no—
995C23—861no—
996C23—862no—
997C23—861no—
998C23—862no—
999C23—862no—
1000C23—861no—
1001C23—862no—
1002C23—861no—
1003C23—862no—
1004C23—861no—
1005C23—1724no—
1006C23—1724no—
1007C23—1724no—
1008C23—1724no—
1009C23—1724no—
1010C23C22×C4×D4312yes—
1011C23#41×D4312yes—
1012C23C2×#1062190212yes—
1013C23C24×D4311yescharacteristic
1014Q8—28no—
1015D4—8616no—
1016D4—8616no—
1017D4—868no—
1018D4—1728no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—28no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—84no—
1043C2×C4—432no—
1044C2×C4—434no—
1045C2×C4—432no—
1046C2×C4—432no—
1047C2×C4—432no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—861no—
1051C2×C4—861no—
1052C2×C4—861no—
1053C2×C4—861no—
1054C2×C4—861no—
1055C2×C4—861no—
1056C2×C4—861no—
1057C2×C4—861no—
1058C2×C4—868no—
1059C2×C4—868no—
1060C2×C4—862no—
1061C2×C4—861no—
1062C2×C4—861no—
1063C2×C4—862no—
1064C2×C4—862no—
1065C2×C4—862no—
1066C2×C4—861no—
1067C2×C4—861no—
1068C2×C4—861no—
1069C2×C4—862no—
1070C2×C4—862no—
1071C2×C4—861no—
1072C2×C4—3444no—
1073C2×C4—3444no—
1074C2×C4—3444no—
1075C2×C4—1724no—
1076C2×C4—1724no—
1077C2×C4—1728no—
1078C2×C4—1724no—
1079C2×C4—1724no—
1080C2×C4—1724no—
1081C2×C4—1724no—
1082C2×C4—1724no—
1083C2×C4C22×C4×D4314yes—
1084C2×C4C22×C4×D4312yes—
1085C2×C4C22×C4×D4314yes—
1086C2×C4C22×C4×D4312yes—
1087C2×C4C2×#1062190212yes—
1088C2×C4C2×#1062190212yes—
1089C2×C4#1306337012yes—
1090C2×C4#1306337112yes—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—434no—
1098C22—862no—
1099C22—862no—
1100C22—862no—
1101C22—862no—
1102C22—862no—
1103C22—862no—
1104C22—864no—
1105C22—862no—
1106C22—862no—
1107C22—864no—
1108C22—864no—
1109C22—862no—
1110C22—17216no—
1111C22—1722no—
1112C22—1721no—
1113C22—1722no—
1114C22—1721no—
1115C22—1721no—
1116C22—1722no—
1117C22—1721no—
1118C22—1722no—
1119C22C4×#1062190214yes—
1120C22C23×C4×D4311yescharacteristic
1121C22C2×#41×D4311yescharacteristic
1122C22C22×#1062190211yescharacteristic
1123C22H(5,𝔽2)×D4311yescharacteristic
1124C22C2×#1306337011yescharacteristic
1125C22C2×#1306337111yescharacteristic
1126C222−1+4×D4311yescharacteristic
1127C4—22no—
1128C4—24no—
1129C4—24no—
1130C4—22no—
1131C4—22no—
1132C4—42no—
1133C4—42no—
1134C4—41no—
1135C4—41no—
1136C4—864no—
1137C4—862no—
1138C4—862no—
1139C4—862no—
1140C4—862no—
1141C4—1722no—
1142C4—1722no—
1143C4—1721no—
1144C4—1721no—
1145C4#1458337114yes—
1146C2—24no—
1147C2—864no—
1148C2—1722no—
1149C2—1724no—
1150C2C2×C4×#1062190211yescharacteristic
1151C2C2×#1458337111yescharacteristic
1152C2#520×D4311yescharacteristic
1153C2#1914862411yescharacteristic
1154C2#1914862811yescharacteristic
1155C2#1914864111yescharacteristic
1156C2#1914864511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2360C2
socle, cosocleC23×C43C25
prime radicalC2×#14583412C2
hypercenter#2360D43
hypocenterC43#34233
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. #19137611C2semidirect
3. #19137609C2semidirect
4. #19137604C2semidirect
5. #19137577C2semidirect
6. #19137571C2semidirect
7. #19137534C2semidirect
8. #19137504C2semidirect
9. #19137484C2semidirect
10. #19137479C2semidirect
11. #19137433C2semidirect
12. #19137424C2semidirect
13. #19137388C2semidirect
14. #19137384C2semidirect
15. #19137223C2semidirect
16. #19137133C2semidirect
17. C4×#13063301C2semidirect
18. C4×#13063300C2semidirect
19. #19137103C2semidirect
20. C2×#14582756C2semidirect
21. #19136954C2semidirect
22. C4×C22⋊C4×D43C2semidirect
23. C43×#2360C2semidirect
26. #14583412C4semidirect
32. C2×Q8×Dic43C22semidirect
34. C2×C4×D172C22semidirect
37. C2×#13063287C22semidirect
48. #14582806C22semidirect
50. #14582801C22semidirect
52. #14582800C22semidirect
53. #14582798C22semidirect
54. #14582798C22semidirect
55. #14582797C22semidirect
56. #14582795C22semidirect
58. #14582791C22semidirect
59. #14582791C22semidirect
62. #14582789C22semidirect
63. #14582789C22semidirect
65. #14582786C22semidirect
66. #14582785C22semidirect
67. #14582780C22semidirect
76. #14582773C22semidirect
78. #14582770C22semidirect
79. #14582766C22semidirect
80. #14582764C22semidirect
81. #14582761C22semidirect
88. #14582756C22semidirect
89. C4⋊C4×Dic43C22semidirect
90. C4⋊C4×Dic43C22semidirect
91. C4×Dic43⋊C4C22semidirect
92. C4×Dic43⋊C4C22semidirect
93. C4×C4⋊Dic43C22semidirect
94. #14582750C22semidirect
101. C4×(C2×D43)⋊C4C22semidirect
102. C4×(C2×D43)⋊C4C22semidirect
107. #14582746C22semidirect
108. #14582744C22semidirect
112. #95×D43C22semidirect
114. C2×C4×Q8×C43C22semidirect
116. C43×#391C22semidirect
117. C43×#389C22semidirect
118. C43×#389C22semidirect
119. C43×#387C22semidirect
121. C4×C4⋊C4×C43C22semidirect
127. C2×#10621902C2×C4semidirect
136. C22×C4×D43C2×C4semidirect
148. #13063310C2×C4semidirect
149. #13063301C2×C4semidirect
150. #13063300C2×C4semidirect
151. #13063299C2×C4semidirect
152. #13063295C2×C4semidirect
158. #13063287C2×C4semidirect
161. (C22⋊D43)⋊C4C2×C4semidirect
162. #13063283C2×C4semidirect
230. C22⋊Q8×C43C2×C4semidirect
354. C22⋊C4×C43#41semidirect
360. C22⋊Dic43#41semidirect
572. #2360D43semidirect
612. C2×C4×Q8C2×D43semidirect
630. #391C2×D43semidirect
639. #389C2×D43semidirect
640. #389C2×D43semidirect
652. #387C2×D43semidirect
681. C4×C4⋊C4C2×D43semidirect
702. C43#34233semidirect
732. C22⋊Q8C4×D43semidirect
962. C22⋊C4#10621902semidirect

Maximal subgroups

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

subgroupindex
C2×#145834122
#191376112
#191376092
#191376042
#191375772
#191375712
#191375342
#191375042
#191374842
#191374792
#191374332
#191374242
#191373882
#191373842
#191372232
#191371332
C4×#130633012
C4×#130633002
#191371032
C2×#145827562
#191369542
C4×C22⋊C4×D432
C43×#23602
#3423343