Finite Group Databasebeta

← C4×#14583444 #25255121

Subgroups — C4×#14583444 #25255121

Order 11008.

3526 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583444C211yesmaximal, characteristic
2C2×C4×#10621900C212yesmaximal, complemented
3#19137166C211yesmaximal, characteristic, complemented
4C4×#13063324C211yesmaximal, characteristic, complemented
5#19137159C211yesmaximal, characteristic, complemented
6C4×#13063321C211yesmaximal, characteristic, complemented
7#19137136C212yesmaximal, complemented
8C4×#13063311C212yesmaximal, complemented
9#121×Dic43C211yesmaximal, characteristic, complemented
10C4×#13063299C211yesmaximal, characteristic, complemented
11#19137105C212yesmaximal, complemented
12C4×#13063297C212yesmaximal, complemented
13#19137101C211yesmaximal, characteristic, complemented
14#19137080C212yesmaximal, complemented
15#19137057C211yesmaximal, characteristic, complemented
16#19137055C212yesmaximal, complemented
17#19137053C211yesmaximal, characteristic, complemented
18#19136997C211yesmaximal, characteristic, complemented
19C4×D4×Dic43C211yesmaximal, characteristic, complemented
20C4×#13063287C211yesmaximal, characteristic, complemented
21C4×(C22⋊D43)⋊C4C212yesmaximal, complemented
22C2×C42×Dic43C211yesmaximal, characteristic, complemented
23C4×#121×C43C211yesmaximal, characteristic, complemented
24C22×#10621900C2212yes—
25#14583444C4116yesdirect product factor
26C2×#13063324C2211yescharacteristic
27C2×#13063321C2211yescharacteristic
28C2×#13063311C2212yes—
29C2×#13063299C2211yescharacteristic
30C2×#13063297C2212yes—
31C4×#10621900—216no—
32C2×C4×Dic86C2212yes—
33C2×#13063290C2212yes—
34C2×C4×D172C2211yescharacteristic
35C2×D4×Dic43C2212yes—
36C2×D4×Dic43C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×#13063287C2211yescharacteristic
40C2×C4×C22⋊D43C2212yes—
41C2×C4×C22⋊D43C2212yes—
42C2×C4×C22⋊D43C2212yes—
43C2×(C22⋊D43)⋊C4C2212yes—
44C2×(C22⋊D43)⋊C4C2212yes—
45C2×(C22⋊D43)⋊C4C2212yes—
46C2×(C22⋊D43)⋊C4C2212yes—
47C2×#13063283C2212yes—
48C2×#13063281C2212yes—
49C2×#13063281C2212yes—
50C22×C4×Dic43C2211yescharacteristic
51C22×C4×Dic43C2211yescharacteristic
52C22×C4×Dic43C2211yescharacteristic
53C22×C4×Dic43C2211yescharacteristic
54C22×C4×Dic43C2212yes—
55C22×C4×Dic43C2211yescharacteristic
56C22×C4×Dic43C2211yescharacteristic
57C2×C42×D43C2212yes—
58#14582803C2212yes—
59#14582803C2212yes—
60#14582802C2211yescharacteristic
61#14582801C2211yescharacteristic
62#14582800C2211yescharacteristic
63#14582799C2212yes—
64#14582799C2212yes—
65#14582799C2212yes—
66#14582799C2212yes—
67#14582798C2211yescharacteristic
68#14582797C2211yescharacteristic
69#14582796C2212yes—
70#14582795C2211yescharacteristic
71#14582794C2212yes—
72#14582793C2212yes—
73#14582792C2212yes—
74#14582791C2212yes—
75#14582790C2212yes—
76#14582789C2212yes—
77#14582788C2212yes—
78#14582787C2212yes—
79#14582779C2212yes—
80#14582778C2212yes—
81#14582776C2212yes—
82#14582768C2211yescharacteristic
83#14582768C2211yescharacteristic
84#14582763C2212yes—
85#14582759C2211yescharacteristic
86#14582757C2212yes—
87C4⋊C4×Dic43C2211yescharacteristic
88C4⋊C4×Dic43C2211yescharacteristic
89C4⋊C4×Dic43C2211yescharacteristic
90C4⋊C4×Dic43C2211yescharacteristic
91C4×Dic43⋊C4C2212yes—
92C4×C4⋊Dic43C2211yescharacteristic
93#14582750C2212yes—
94#14582750C2212yes—
95C22⋊C4×Dic43C2212yes—
96C22⋊C4×Dic43C2212yes—
97C22⋊C4×Dic43C2212yes—
98C22⋊C4×Dic43C2212yes—
99C4×(C2×D43)⋊C4C2212yes—
100C4×(C2×D43)⋊C4C2212yes—
101C4×C22⋊Dic43C2212yes—
102#14582746C2212yes—
103#14582746C2212yes—
104#14582746C2212yes—
105#14582746C2212yes—
106C42×Dic43C2211yescharacteristic
107C42×Dic43C2211yescharacteristic
108C42×Dic43C2211yescharacteristic
109C42×Dic43C2211yescharacteristic
110C42×Dic43C2211yescharacteristic
111C42×Dic43C2211yescharacteristic
112C42×Dic43C2211yescharacteristic
113C42×Dic43C2211yescharacteristic
114C2×#121×C43C2211yescharacteristic
115C2×C4×D4×C43C2212yes—
116C2×C4×D4×C43C2211yescharacteristic
117C22×C42×C43C2211yescharacteristic
118C43×#390C2211yescharacteristic
119C43×#389C2211yescharacteristic
120C43×#388C2212yes—
121C43×#386C2212yes—
122C43×#380C2211yescharacteristic
123C4×C4⋊C4×C43C2211yescharacteristic
124C4×C22⋊C4×C43C2212yes—
125C2×#10621900—28no—
126C2×#10621900—28no—
127C2×#10621900C2×C4116yescomplemented
128C22×Dic86C2312yes—
129C22×D172C2311yescharacteristic
130C22×C22⋊D43C2312yes—
131C22×C22⋊D43C2312yes—
132C22×C22⋊D43C2312yes—
133C23×Dic43C2311yescharacteristic
134C23×Dic43C2312yes—
135C23×Dic43C2311yescharacteristic
136C23×Dic43C2312yes—
137C23×Dic43C2311yescharacteristic
138C23×Dic43C2311yescharacteristic
139C22×C4×D43C2312yes—
140C22×C4×D43C2312yes—
141C22×C4×D43C2312yes—
142#13063324C2×C418yescomplemented
143#13063321C2×C418yescomplemented
144#13063311C2×C4116yescomplemented
145#13063299C2×C418yescomplemented
146#13063297C2×C4116yescomplemented
147C4×Dic86—28no—
148#13063290—28no—
149C4×D172—24no—
150D4×Dic43—28no—
151D4×Dic43—24no—
152D4×Dic43C2×C418yescomplemented
153#13063287—24no—
154#13063287C2×C418yescomplemented
155C4×C22⋊D43—28no—
156C4×C22⋊D43—28no—
157C4×C22⋊D43—28no—
158(C22⋊D43)⋊C4—28no—
159(C22⋊D43)⋊C4—28no—
160(C22⋊D43)⋊C4—28no—
161(C22⋊D43)⋊C4C2×C4116yescomplemented
162#13063283—28no—
163#13063281—28no—
164#13063281—28no—
165C2×C4⋊Dic43C2312yes—
166C2×C4⋊Dic43C2311yescharacteristic
167C2×C4⋊Dic43C2311yescharacteristic
168C2×C4⋊Dic43C2311yescharacteristic
169C2×Dic43⋊C4C2312yes—
170C2×Dic43⋊C4C2312yes—
171C2×Dic43⋊C4C2312yes—
172C2×Dic43⋊C4C2312yes—
173C2×Dic43⋊C4C2312yes—
174C2×Dic43⋊C4C2312yes—
175C2×Dic43⋊C4C2312yes—
176C2×C22⋊Dic43C2312yes—
177C2×C22⋊Dic43C2312yes—
178C2×C22⋊Dic43C2312yes—
179C2×C22⋊Dic43C2312yes—
180C2×C22⋊Dic43C2312yes—
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×C4×Dic43—24no—
190C2×C4×Dic43—28no—
191C2×C4×Dic43—24no—
192C2×C4×Dic43—24no—
193C2×C4×Dic43—24no—
194C2×C4×Dic43C2×C418yescomplemented
195C2×C4×Dic43D418yescomplemented
196C2×C4×Dic43C2311yescharacteristic
197C2×C4×Dic43C2311yescharacteristic
198C2×C4×Dic43C2311yescharacteristic
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C2×C4×Dic43C2311yescharacteristic
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2312yes—
205C2×C4×Dic43C2312yes—
206C2×C4×Dic43C2312yes—
207C2×C4×Dic43C2312yes—
208C2×C4×Dic43C2312yes—
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2311yescharacteristic
211C2×C4×Dic43C2311yescharacteristic
212C2×C4×Dic43C2311yescharacteristic
213C2×C4×Dic43C2311yescharacteristic
214C2×C4×Dic43C2311yescharacteristic
215C2×C4×Dic43C2311yescharacteristic
216C2×C4×Dic43C2311yescharacteristic
217C2×C4×Dic43C2311yescharacteristic
218C2×C4×Dic43C2311yescharacteristic
219C2×C4×Dic43C2311yescharacteristic
220C2×C4×Dic43C2311yescharacteristic
221C2×C4×Dic43C2311yescharacteristic
222C2×C4×Dic43C2311yescharacteristic
223C2×C4×Dic43C2311yescharacteristic
224C2×C4×Dic43C2311yescharacteristic
225C42×D43—28no—
226C43⋊#95C2312yes—
227C43⋊#95C2312yes—
228C43⋊#95C2312yes—
229C43⋊#95C2312yes—
230C43⋊#95C2312yes—
231C43⋊#95C2312yes—
232C43⋊#95C2312yes—
233C43⋊#95C2312yes—
234C43⋊#95C2312yes—
235C22×D4×C43C2311yescharacteristic
236C22×D4×C43C2312yes—
237C23×C4×C43C2311yescharacteristic
238C23×C4×C43C2312yes—
239C23×C4×C43C2311yescharacteristic
240C23×C4×C43C2311yescharacteristic
241#121×C43C2×C418yescomplemented
242C4×D4×C43—28no—
243C4×D4×C43—24no—
244C2×C4⋊C4×C43C2312yes—
245C2×C4⋊C4×C43C2311yescharacteristic
246C2×C4⋊C4×C43C2311yescharacteristic
247C2×C4⋊C4×C43C2311yescharacteristic
248C2×C22⋊C4×C43C2312yes—
249C2×C22⋊C4×C43C2312yes—
250C2×C22⋊C4×C43C2312yes—
251C2×C22⋊C4×C43C2312yes—
252C2×C22⋊C4×C43C2312yes—
253C2×C42×C43—24no—
254C2×C42×C43C2311yescharacteristic
255C2×C42×C43C2311yescharacteristic
256C2×C42×C43C2311yescharacteristic
257C2×C42×C43C2312yes—
258C2×C42×C43C2311yescharacteristic
259#95×C43C2312yes—
260#95×C43C2312yes—
261#95×C43C2312yes—
262C24×C43C2412yes—
263C24×C43C2411yescharacteristic
264C23×D43C2412yes—
265C2×D4×C43—22no—
266C2×D4×C43—22no—
267C2×D4×C43—24no—
268C2×D4×C43—24no—
269C2×D4×C43C22×C414yes—
270C2×D4×C43C22×C418yes—
271C22×C4×C43—22no—
272C22×C4×C43—22no—
273C22×C4×C43—22no—
274C22×C4×C43—22no—
275C22×C4×C43—22no—
276C22×C4×C43—22no—
277C22×C4×C43—24no—
278C22×C4×C43—24no—
279C22×C4×C43—24no—
280C22×C4×C43—22no—
281C22×C4×C43C22×C414yes—
282C22×C4×C43C2×D414yes—
283C22×C4×C43C2412yes—
284C22×C4×C43C2412yes—
285C22×C4×C43C2411yescharacteristic
286C22×C4×C43C2412yes—
287C22×C4×C43C2411yescharacteristic
288C22×C4×C43C2411yescharacteristic
289C22×C4×C43C2411yescharacteristic
290C22×C4×C43C2411yescharacteristic
291C22×C4×C43C2411yescharacteristic
292C2×C22⋊D43—24no—
293C2×C22⋊D43—24no—
294C2×C22⋊D43—24no—
295C2×C22⋊D43—24no—
296C2×C22⋊D43—24no—
297C2×C22⋊D43—24no—
298C2×C22⋊D43C22×C418yes—
299C2×C22⋊D43C22×C418yes—
300C2×C22⋊D43C22×C418yes—
301C22×Dic43—24no—
302C22×Dic43—22no—
303C22×Dic43—22no—
304C22×Dic43—22no—
305C22×Dic43—22no—
306C22×Dic43—22no—
307C22×Dic43—22no—
308C22×Dic43—24no—
309C22×Dic43—24no—
310C22×Dic43—24no—
311C22×Dic43—24no—
312C22×Dic43—22no—
313C22×Dic43C22×C414yes—
314C22×Dic43C22×C418yes—
315C22×Dic43C22×C414yes—
316C22×Dic43C2×D414yes—
317C22×Dic43C2×D414yes—
318C22×Dic43#4114yes—
319C22×Dic43C2412yes—
320C22×Dic43C2412yes—
321C22×Dic43C2411yescharacteristic
322C22×Dic43C2412yes—
323C22×Dic43C2411yescharacteristic
324C22×Dic43C2411yescharacteristic
325C22×Dic43C2411yescharacteristic
326C22×Dic43C2411yescharacteristic
327C22×Dic43C2411yescharacteristic
328C22×Dic43C2411yescharacteristic
329C22×Dic43C2411yescharacteristic
330#10621900—264no—
331C2×D172—22no—
332C2×D172—22no—
333C2×D172C22×C414yes—
334C2×C4×D43—24no—
335C2×C4×D43—24no—
336C2×C4×D43—24no—
337C2×C4×D43—24no—
338C2×C4×D43—24no—
339C2×C4×D43—24no—
340C2×C4×D43—24no—
341C2×C4×D43—24no—
342C2×C4×D43C22×C418yes—
343C2×Dic86—24no—
344C2×Dic86—24no—
345C2×Dic86C22×C418yes—
346C4⋊C4×C43—24no—
347C4⋊C4×C43—22no—
348C4⋊C4×C43—22no—
349C4⋊C4×C43C22×C414yes—
350C22⋊C4×C43—24no—
351C22⋊C4×C43—24no—
352C22⋊C4×C43—24no—
353C22⋊C4×C43—24no—
354C22⋊C4×C43C22×C418yes—
355C42×C43—24no—
356C42×C43—22no—
357C42×C43—22no—
358C42×C43—22no—
359C42×C43#4114yescomplemented
360C22⋊Dic43—24no—
361C22⋊Dic43—24no—
362C22⋊Dic43—24no—
363C22⋊Dic43—24no—
364C22⋊Dic43C22×C418yes—
365(C2×D43)⋊C4—24no—
366(C2×D43)⋊C4—24no—
367(C2×D43)⋊C4—24no—
368(C2×D43)⋊C4—24no—
369(C2×D43)⋊C4—24no—
370(C2×D43)⋊C4—24no—
371(C2×D43)⋊C4C22×C418yes—
372(C2×D43)⋊C4C22×C418yes—
373C4⋊Dic43—22no—
374C4⋊Dic43—22no—
375C4⋊Dic43—24no—
376C4⋊Dic43C22×C414yes—
377Dic43⋊C4—24no—
378Dic43⋊C4—24no—
379Dic43⋊C4—24no—
380Dic43⋊C4—24no—
381Dic43⋊C4—24no—
382Dic43⋊C4—24no—
383Dic43⋊C4C22×C418yes—
384C4×Dic43—24no—
385C4×Dic43—22no—
386C4×Dic43—22no—
387C4×Dic43—22no—
388C4×Dic43—24no—
389C4×Dic43—24no—
390C4×Dic43—24no—
391C4×Dic43—24no—
392C4×Dic43—22no—
393C4×Dic43—22no—
394C4×Dic43—22no—
395C4×Dic43—22no—
396C4×Dic43—22no—
397C4×Dic43—22no—
398C4×Dic43—22no—
399C4×Dic43—22no—
400C4×Dic43—22no—
401C4×Dic43—22no—
402C4×Dic43C22×C414yes—
403C4×Dic43C22×C414yes—
404C4×Dic43C22×C414yes—
405C4×Dic43C22×C414yes—
406C4×Dic43C2×D414yes—
407C4×Dic43C2×D414yes—
408C4×Dic43C2×D414yes—
409C4×Dic43C2×D414yes—
410C4×Dic43#4114yescomplemented
411C4×Dic43#4114yescomplemented
412C4×Dic43#4114yescomplemented
413C23×C43—21no—
414C23×C43—21no—
415C23×C43—21no—
416C23×C43—21no—
417C23×C43—22no—
418C23×C43—22no—
419C23×C43—22no—
420C23×C43—22no—
421C23×C43—22no—
422C23×C43—22no—
423C23×C43C23×C414yes—
424C23×C43C23×C412yes—
425C23×C43C22×D412yes—
426C23×C43C2×#4112yes—
427C23×C43C2511yescharacteristic
428C22×D43—22no—
429C22×D43—22no—
430C22×D43—22no—
431C22×D43—22no—
432C22×D43—22no—
433C22×D43—22no—
434C22×D43C23×C414yes—
435D4×C43—216no—
436D4×C43—28no—
437C2×C4×C43—28no—
438C2×C4×C43—22no—
439C2×C4×C43—21no—
440C2×C4×C43—21no—
441C2×C4×C43—21no—
442C2×C4×C43—21no—
443C2×C4×C43—21no—
444C2×C4×C43—21no—
445C2×C4×C43—21no—
446C2×C4×C43—21no—
447C2×C4×C43—22no—
448C2×C4×C43—28no—
449C2×C4×C43—28no—
450C2×C4×C43—22no—
451C2×C4×C43—22no—
452C2×C4×C43—22no—
453C2×C4×C43—22no—
454C2×C4×C43—22no—
455C2×C4×C43—22no—
456C2×C4×C43—48no—
457C2×C4×C43C23×C412yes—
458C2×C4×C43C23×C414yes—
459C2×C4×C43C23×C412yes—
460C2×C4×C43C22×D412yes—
461C2×C4×C43C22×D412yes—
462C2×C4×C43C2×#4112yes—
463C2×C4×C43C2×#4112yes—
464C2×C4×C43C2×#4112yes—
465C2×C4×C43C2×#4112yes—
466C2×C4×C43C2×#4112yes—
467C2×C4×C43C2×#4112yes—
468C22⋊D43—216no—
469C22⋊D43—216no—
470C22⋊D43—216no—
471C2×Dic43—28no—
472C2×Dic43—22no—
473C2×Dic43—21no—
474C2×Dic43—21no—
475C2×Dic43—21no—
476C2×Dic43—21no—
477C2×Dic43—21no—
478C2×Dic43—21no—
479C2×Dic43—21no—
480C2×Dic43—21no—
481C2×Dic43—22no—
482C2×Dic43—216no—
483C2×Dic43—28no—
484C2×Dic43—28no—
485C2×Dic43—22no—
486C2×Dic43—22no—
487C2×Dic43—22no—
488C2×Dic43—22no—
489C2×Dic43—22no—
490C2×Dic43—22no—
491C2×Dic43—48no—
492C2×Dic43C4×D4116yescomplemented
493C2×Dic43C23×C412yes—
494C2×Dic43C23×C414yes—
495C2×Dic43C23×C412yes—
496C2×Dic43C23×C412yes—
497C2×Dic43C23×C412yes—
498C2×Dic43C22×D412yes—
499C2×Dic43C22×D412yes—
500C2×Dic43C22×D412yes—
501C2×Dic43C22×D412yes—
502C2×Dic43C2×#4112yes—
503C2×Dic43C2×#4112yes—
504C2×Dic43C2×#4112yes—
505C2×Dic43C2×#4112yes—
506C2×Dic43C2×#4112yes—
507C2×Dic43C2×#4112yes—
508C2×Dic43C2×#4112yes—
509C2×Dic43C2×#4112yes—
510D172—28no—
511C4×D43—216no—
512C4×D43—48no—
513C4×D43—48no—
514Dic86—216no—
515C4×#532—431nomaximal, Sylow
516C22×C43—22no—
517C22×C43—22no—
518C22×C43—22no—
519C22×C43—22no—
520C22×C43—22no—
521C22×C43—22no—
522C22×C43—24no—
523C22×C43—24no—
524C22×C43—24no—
525C22×C43—42no—
526C22×C43—42no—
527C22×C43—42no—
528C22×C43—42no—
529C22×C43C2×C4×D414yes—
530C22×C43C24×C411yescharacteristic
531C22×C43C23×D411yescharacteristic
532C22×C43C22×#4111yescharacteristic
533C22×C43C22×#4111yescharacteristic
534C22×C43C22×#4111yescharacteristic
535C22×C43C22×#4111yescharacteristic
536C22×C43C22×#4111yescharacteristic
537C2×D43—24no—
538C2×D43—24no—
539C2×D43—24no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C4×C43—24no—
545C4×C43—22no—
546C4×C43—22no—
547C4×C43—22no—
548C4×C43—22no—
549C4×C43—42no—
550C4×C43—42no—
551C4×C43C4×#4114yescomplemented
552C4×C43#53214yescomplemented
553Dic43—24no—
554Dic43—22no—
555Dic43—22no—
556Dic43—22no—
557Dic43—22no—
558Dic43—42no—
559Dic43—42no—
560Dic43C2×C4×D414yes—
561Dic43C2×C4×D414yes—
562Dic43C4×#4114yescomplemented
563Dic43#53214yescomplemented
564C2×#532—431no—
565C2×C4×#41—432no—
566C4×C4⋊Q8—431no—
567C4×C4⋊Q8—431no—
568C4×#127—431no—
569C4×#127—431no—
570C4×#124—432no—
571C4×#124—432no—
572C4×#121—431no—
573C4×#121—432no—
574C4×#121—431no—
575C4×#121—431no—
576C4×#121—432no—
577C4×#121D4311yescharacteristic, complemented
578#2297—432no—
579#2293—431no—
580#2293—431no—
581#2293—432no—
582#2285—431no—
583C42×D4—431no—
584C42×D4—432no—
585C42×D4—431no—
586C2×C43—431no—
587C2×C43—24no—
588C2×C43—44no—
589C2×C43C22×C4×D411yescharacteristic
590C2×C43C2×C4×#4111yescharacteristic
591C2×C43C2×C4×#4111yescharacteristic
592C2×C43C2×#53211yescharacteristic
593C2×C43C2×#53211yescharacteristic
594C2×C43#344411yescharacteristic
595C2×C43#344411yescharacteristic
596D43—44no—
597C22×#41—432no—
598#532—4316no—
599C2×C4⋊Q8—431no—
600C2×#127—431no—
601C2×#124—432no—
602C2×#121—432no—
603C2×#121—431no—
604C2×#121C2×D4311yescharacteristic
605C4×#41—8616no—
606C2×C4×Q8—432no—
607C2×C4×Q8—432no—
608C2×C4×D4—431no—
609C2×C4×D4—431no—
610C2×C4×D4—432no—
611C2×C4×D4—432no—
612C2×C4×D4—432no—
613C2×C4×D4—432no—
614C2×C4×D4—431no—
615C2×C4×D4—431no—
616C2×C4×D4—432no—
617C2×C4×D4—432no—
618C2×C4×D4—432no—
619C2×C4×D4—432no—
620C2×C4×D4—431no—
621C2×C4×D4C2×D4311yescharacteristic
622C2×C4×D4C2×D4312yes—
623C2×#117—432no—
624C2×#117—432no—
625C2×#117—432no—
626C22×C42—431no—
627C22×C42—431no—
628C22×C42—432no—
629C22×C42—431no—
630C22×C42—431no—
631C22×C42—431no—
632C22×C42—431no—
633C22×C42—432no—
634C22×C42C2×D4311yescharacteristic
635#391—432no—
636#391—432no—
637#390—431no—
638#390—431no—
639#390—432no—
640#390—432no—
641#390—432no—
642#390—432no—
643#390—431no—
644#390C2×D4311yescharacteristic
645#389—432no—
646#389—431no—
647#389—431no—
648#389—431no—
649#389—432no—
650#389C2×D4311yescharacteristic
651#388—432no—
652#388—432no—
653#388—432no—
654#388—432no—
655#388—432no—
656#388—432no—
657#388—432no—
658#388C2×D4312yes—
659#386—432no—
660#386—432no—
661#386—432no—
662#386C2×D4312yes—
663#384—431no—
664#384—431no—
665#382—432no—
666#380—431no—
667#380—432no—
668#380C2×D4311yescharacteristic
669C4×C4⋊C4—431no—
670C4×C4⋊C4—431no—
671C4×C4⋊C4—431no—
672C4×C4⋊C4—431no—
673C4×C4⋊C4—431no—
674C4×C4⋊C4—432no—
675C4×C4⋊C4—432no—
676C4×C4⋊C4—432no—
677C4×C4⋊C4C2×D4311yescharacteristic
678C4×C22⋊C4—432no—
679C4×C22⋊C4—432no—
680C4×C22⋊C4—432no—
681C4×C22⋊C4—432no—
682C4×C22⋊C4—432no—
683C4×C22⋊C4—432no—
684C4×C22⋊C4—432no—
685C4×C22⋊C4—432no—
686C4×C22⋊C4—432no—
687C4×C22⋊C4—432no—
688C4×C22⋊C4—432no—
689C4×C22⋊C4C2×D4312yes—
690C43—431no—
691C43—431no—
692C43—431no—
693C43—431no—
694C43—431no—
695C43—431no—
696C43—431no—
697C43—431no—
698C43C4×#53211yescharacteristic, complemented, Sylow
699C2×#41—4316no—
700C2×#41—868no—
701C2×#41—868no—
702C22×Q8—432no—
703C22×D4—432no—
704C22×D4—432no—
705C22×D4—432no—
706C22×D4—431no—
707C22×D4C22×D4311yescharacteristic
708C22×D4C22×D4312yes—
709C23×C4—431no—
710C23×C4—432no—
711C23×C4—431no—
712C23×C4—431no—
713C23×C4—432no—
714C23×C4—432no—
715C23×C4—431no—
716C23×C4—432no—
717C23×C4—432no—
718C23×C4C22×D4311yescharacteristic
719C23×C4C22×D4312yes—
720C23×C4C22×D4311yescharacteristic
721C23×C4C22×D4311yescharacteristic
722C4⋊Q8—438no—
723#127—438no—
724#124—4316no—
725#121—4316no—
726#121—438no—
727#121C4×D4318yescomplemented
728C4×Q8—868no—
729C4×Q8—868no—
730C4×D4—28no—
731C4×D4—24no—
732C4×D4—438no—
733C4×D4—438no—
734C4×D4—4316no—
735C4×D4—868no—
736C4×D4—868no—
737C4×D4—864no—
738C4×D4—868no—
739C4×D4—868no—
740C4×D4—864no—
741C4×D4—868no—
742C4×D4—868no—
743C4×D4—868no—
744C4×D4—864no—
745#117—868no—
746#117—868no—
747#117—868no—
748C2×C4⋊C4—432no—
749C2×C4⋊C4—431no—
750C2×C4⋊C4—432no—
751C2×C4⋊C4—432no—
752C2×C4⋊C4—432no—
753C2×C4⋊C4—432no—
754C2×C4⋊C4—432no—
755C2×C4⋊C4—432no—
756C2×C4⋊C4—432no—
757C2×C4⋊C4—431no—
758C2×C4⋊C4—431no—
759C2×C4⋊C4C22×D4312yes—
760C2×C4⋊C4C22×D4311yescharacteristic
761C2×C4⋊C4C22×D4311yescharacteristic
762C2×C4⋊C4C22×D4311yescharacteristic
763C2×C22⋊C4—432no—
764C2×C22⋊C4—432no—
765C2×C22⋊C4—432no—
766C2×C22⋊C4—432no—
767C2×C22⋊C4—432no—
768C2×C22⋊C4—432no—
769C2×C22⋊C4—432no—
770C2×C22⋊C4—432no—
771C2×C22⋊C4—432no—
772C2×C22⋊C4—432no—
773C2×C22⋊C4—432no—
774C2×C22⋊C4—432no—
775C2×C22⋊C4—432no—
776C2×C22⋊C4C22×D4312yes—
777C2×C22⋊C4C22×D4312yes—
778C2×C22⋊C4C22×D4312yes—
779C2×C22⋊C4C22×D4312yes—
780C2×C22⋊C4C22×D4312yes—
781C2×C42—24no—
782C2×C42—438no—
783C2×C42—438no—
784C2×C42—431no—
785C2×C42—431no—
786C2×C42—431no—
787C2×C42—431no—
788C2×C42—431no—
789C2×C42—431no—
790C2×C42—431no—
791C2×C42—431no—
792C2×C42—431no—
793C2×C42—431no—
794C2×C42—431no—
795C2×C42—432no—
796C2×C42—432no—
797C2×C42—432no—
798C2×C42—432no—
799C2×C42—431no—
800C2×C42—431no—
801C2×C42—431no—
802C2×C42—431no—
803C2×C42—431no—
804C2×C42—431no—
805C2×C42—431no—
806C2×C42—431no—
807C2×C42—431no—
808C2×C42—431no—
809C2×C42—431no—
810C2×C42—431no—
811C2×C42—432no—
812C2×C42—431no—
813C2×C42—868no—
814C2×C42—868no—
815C2×C42—864no—
816C2×C42—864no—
817C2×C42—864no—
818C2×C42—864no—
819C2×C42C22×D4311yescharacteristic
820C2×C42C22×D4311yescharacteristic
821C2×C42C22×D4312yes—
822C2×C42C22×D4311yescharacteristic
823C2×C42C22×D4311yescharacteristic
824#95—432no—
825#95—432no—
826#95—432no—
827#95—432no—
828#95—432no—
829#95—432no—
830#95—432no—
831#95—432no—
832#95—432no—
833#95C22×D4312yes—
834#95C22×D4312yes—
835#95C22×D4312yes—
836C24—432no—
837C24C23×D4312yes—
838C24C23×D4311yescharacteristic
839#41—8664no—
840C2×Q8—438no—
841C2×Q8—864no—
842C2×Q8—864no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—438no—
848C2×D4—438no—
849C2×D4—438no—
850C2×D4—434no—
851C2×D4—864no—
852C2×D4—864no—
853C2×D4—864no—
854C2×D4—864no—
855C2×D4—864no—
856C2×D4—864no—
857C2×D4—862no—
858C2×D4—862no—
859C2×D4C2×C4×D4314yes—
860C2×D4C2×C4×D4318yes—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—434no—
872C22×C4—434no—
873C22×C4—434no—
874C22×C4—431no—
875C22×C4—431no—
876C22×C4—431no—
877C22×C4—431no—
878C22×C4—434no—
879C22×C4—438no—
880C22×C4—434no—
881C22×C4—431no—
882C22×C4—431no—
883C22×C4—431no—
884C22×C4—432no—
885C22×C4—431no—
886C22×C4—438no—
887C22×C4—432no—
888C22×C4—432no—
889C22×C4—864no—
890C22×C4—864no—
891C22×C4—864no—
892C22×C4—864no—
893C22×C4—864no—
894C22×C4—864no—
895C22×C4—862no—
896C22×C4—862no—
897C22×C4—862no—
898C22×C4—862no—
899C22×C4—862no—
900C22×C4—862no—
901C22×C4—864no—
902C22×C4—864no—
903C22×C4—864no—
904C22×C4—864no—
905C22×C4—862no—
906C22×C4—864no—
907C22×C4—864no—
908C22×C4—864no—
909C22×C4C2×C4×D4314yes—
910C22×C4D4×D4314yes—
911C22×C4C23×D4312yes—
912C22×C4C23×D4312yes—
913C22×C4C23×D4311yescharacteristic
914C22×C4C23×D4312yes—
915C22×C4C23×D4311yescharacteristic
916C22×C4C23×D4311yescharacteristic
917C22×C4C23×D4311yescharacteristic
918C22×C4C23×D4311yescharacteristic
919C22×C4C23×D4311yescharacteristic
920C4⋊C4—24no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—438no—
924C4⋊C4—434no—
925C4⋊C4—864no—
926C4⋊C4—864no—
927C4⋊C4—864no—
928C4⋊C4—864no—
929C4⋊C4—864no—
930C4⋊C4—864no—
931C4⋊C4—864no—
932C4⋊C4—862no—
933C4⋊C4—862no—
934C4⋊C4C2×C4×D4314yes—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—438no—
940C22⋊C4—438no—
941C22⋊C4—438no—
942C22⋊C4—864no—
943C22⋊C4—864no—
944C22⋊C4—864no—
945C22⋊C4—864no—
946C22⋊C4—864no—
947C22⋊C4—864no—
948C22⋊C4—864no—
949C22⋊C4—864no—
950C22⋊C4—864no—
951C22⋊C4—864no—
952C22⋊C4C2×C4×D4318yes—
953C42—24no—
954C42—22no—
955C42—22no—
956C42—22no—
957C42—434no—
958C42—434no—
959C42—434no—
960C42—434no—
961C42—434no—
962C42—434no—
963C42—434no—
964C42—434no—
965C42—434no—
966C42—434no—
967C42—434no—
968C42—864no—
969C42—864no—
970C42—864no—
971C42—864no—
972C42—862no—
973C42—862no—
974C42—862no—
975C42—862no—
976C42—862no—
977C42—862no—
978C42—862no—
979C42—862no—
980C42—862no—
981C42—862no—
982C42—864no—
983C42—862no—
984C42—862no—
985C42—862no—
986C42#1062190014yescomplemented
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—434no—
998C23—862no—
999C23—862no—
1000C23—862no—
1001C23—862no—
1002C23—862no—
1003C23—862no—
1004C23C22×C4×D4314yes—
1005C23C22×C4×D4312yes—
1006C23C2×D4×D4312yes—
1007C23#41×D4312yes—
1008C23C24×D4311yescharacteristic
1009Q8—8616no—
1010D4—216no—
1011D4—28no—
1012D4—8616no—
1013D4—8616no—
1014D4—8616no—
1015D4—868no—
1016C2×C4—28no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—48no—
1036C2×C4—4316no—
1037C2×C4—432no—
1038C2×C4—432no—
1039C2×C4—432no—
1040C2×C4—432no—
1041C2×C4—432no—
1042C2×C4—432no—
1043C2×C4—432no—
1044C2×C4—432no—
1045C2×C4—432no—
1046C2×C4—432no—
1047C2×C4—432no—
1048C2×C4—432no—
1049C2×C4—432no—
1050C2×C4—434no—
1051C2×C4—432no—
1052C2×C4—432no—
1053C2×C4—432no—
1054C2×C4—8616no—
1055C2×C4—8616no—
1056C2×C4—868no—
1057C2×C4—868no—
1058C2×C4—868no—
1059C2×C4—862no—
1060C2×C4—861no—
1061C2×C4—861no—
1062C2×C4—861no—
1063C2×C4—861no—
1064C2×C4—861no—
1065C2×C4—861no—
1066C2×C4—861no—
1067C2×C4—861no—
1068C2×C4—862no—
1069C2×C4—862no—
1070C2×C4—862no—
1071C2×C4—862no—
1072C2×C4—862no—
1073C2×C4—862no—
1074C2×C4—862no—
1075C2×C4—1728no—
1076C2×C4—1728no—
1077C2×C4—1728no—
1078C2×C4C22×C4×D4312yes—
1079C2×C4C22×C4×D4314yes—
1080C2×C4C22×C4×D4312yes—
1081C2×C4C2×D4×D4312yes—
1082C2×C4C2×D4×D4312yes—
1083C2×C4#41×D4312yes—
1084C2×C4#41×D4312yes—
1085C2×C4#41×D4312yes—
1086C2×C4C2×#1062190012yes—
1087C2×C4C2×#1062190012yes—
1088C2×C4C2×#1062190012yes—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—24no—
1096C22—24no—
1097C22—24no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—864no—
1103C22—864no—
1104C22—864no—
1105C22—1722no—
1106C22—1722no—
1107C22—1722no—
1108C22—1722no—
1109C22C4×D4×D4314yes—
1110C22C23×C4×D4311yescharacteristic
1111C22C22×D4×D4311yescharacteristic
1112C22C2×#41×D4311yescharacteristic
1113C22C2×#41×D4311yescharacteristic
1114C22C2×#41×D4311yescharacteristic
1115C22C2×#41×D4311yescharacteristic
1116C22C22×#1062190011yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—24no—
1121C4—22no—
1122C4—42no—
1123C4—42no—
1124C4—434no—
1125C4—434no—
1126C4—434no—
1127C4—434no—
1128C4—862no—
1129C4—862no—
1130C4—862no—
1131C4—864no—
1132C4—862no—
1133C4—1722no—
1134C4—1722no—
1135C4C4×#1062190014yescomplemented
1136C4#1458344414yesdirect product factor
1137C2—24no—
1138C2—44no—
1139C2—1724no—
1140C2C2×C4×D4×D4311yescharacteristic
1141C2C4×#41×D4311yescharacteristic
1142C2C2×C4×#1062190011yescharacteristic
1143C2#532×D4311yescharacteristic
1144C2C2×#1458344411yescharacteristic
1145C2#1914788711yescharacteristic
1146C2#1914788911yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC4×#121×C43C2
socle, cosocleC23×C43C25
prime radicalC2×#14583444C2
hypercenterC4×#121D43
hypocenterC43C4×#532
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621900C2semidirect
3. #19137166C2semidirect
4. C4×#13063324C2semidirect
5. #19137159C2semidirect
6. C4×#13063321C2semidirect
7. #19137136C2semidirect
8. C4×#13063311C2semidirect
9. #121×Dic43C2semidirect
10. C4×#13063299C2semidirect
11. #19137105C2semidirect
12. C4×#13063297C2semidirect
13. #19137101C2semidirect
14. #19137080C2semidirect
15. #19137057C2semidirect
16. #19137055C2semidirect
17. #19137053C2semidirect
18. #19136997C2semidirect
19. C4×D4×Dic43C2semidirect
20. C4×#13063287C2semidirect
21. C4×(C22⋊D43)⋊C4C2semidirect
22. C2×C42×Dic43C2semidirect
23. C4×#121×C43C2semidirect
25. #14583444C4direct (N × H)
127. C2×#10621900C2×C4semidirect
142. #13063324C2×C4semidirect
143. #13063321C2×C4semidirect
144. #13063311C2×C4semidirect
145. #13063299C2×C4semidirect
146. #13063297C2×C4semidirect
152. D4×Dic43C2×C4semidirect
154. #13063287C2×C4semidirect
161. (C22⋊D43)⋊C4C2×C4semidirect
194. C2×C4×Dic43C2×C4semidirect
195. C2×C4×Dic43D4semidirect
241. #121×C43C2×C4semidirect
359. C42×C43#41semidirect
410. C4×Dic43#41semidirect
411. C4×Dic43#41semidirect
412. C4×Dic43#41semidirect
492. C2×Dic43C4×D4semidirect
551. C4×C43C4×#41semidirect
552. C4×C43#532semidirect
562. Dic43C4×#41semidirect
563. Dic43#532semidirect
577. C4×#121D43semidirect
698. C43C4×#532semidirect
727. #121C4×D43semidirect
986. C42#10621900semidirect
1135. C4C4×#10621900semidirect
1136. C4#14583444direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834442
C2×C4×#106219002
#191371662
C4×#130633242
#191371592
C4×#130633212
#191371362
C4×#130633112
#121×Dic432
C4×#130632992
#191371052
C4×#130632972
#191371012
#191370802
#191370572
#191370552
#191370532
#191369972
C4×D4×Dic432
C4×#130632872
C4×(C22⋊D43)⋊C42
C2×C42×Dic432
C4×#121×C432
C4×#53243