Finite Group Databasebeta

← #25257530

Subgroups — #25257530

Order 11008.

2858 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583375C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic
3C2×C4×Q8×D43C211yesmaximal, characteristic
4#19137514C213yesmaximal, complemented
5#19137513C211yesmaximal, characteristic, complemented
6#19137512C213yesmaximal, complemented
7Q8×C4⋊Dic43C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic86C213yesmaximal, complemented
9#19137509C213yesmaximal, complemented
10Q8×Dic43⋊C4C211yesmaximal, characteristic, complemented
11#19137220C213yesmaximal
12#19137217C213yesmaximal
13#19137076C213yesmaximal
14#19137075C213yesmaximal
15C43×#2351C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17#14583375—28no—
18#14583375C4116yescomplemented
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×C4×Dic86C2213yes—
23C2×C4×Dic86C2213yes—
24C2×C4×Dic86C2213yes—
25C2×#13063290C2213yes—
26C2×#13063290C2213yes—
27C2×#13063290C2213yes—
28C4×Q8×D43—28no—
29C2×#13063283C2213yes—
30C2×#13063283C2213yes—
31C2×#13063282C2213yes—
32C2×#13063282C2213yes—
33C2×C4⋊C4×D43C2213yes—
34C2×C42×D43C2213yes—
35#14582798C2213yes—
36#14582798C2213yes—
37#14582797C2213yes—
38#14582797C2213yes—
39#14582796C2213yes—
40#14582796C2213yes—
41#14582796C2216yes—
42#14582796C2216yes—
43#14582795C2213yes—
44#14582795C2213yes—
45#14582794C2213yes—
46#14582794C2213yes—
47#14582773C2211yescharacteristic
48#14582773C2213yes—
49#14582773C2216yes—
50#14582770C2213yes—
51#14582770C2213yes—
52#14582769C2213yes—
53#14582768C2216yes—
54#14582768C2213yes—
55#14582764C2213yes—
56#14582763C2216yes—
57C4⋊C4×Dic43C2216yes—
58C4×Dic43⋊C4C2213yes—
59C4×Dic43⋊C4C2213yes—
60C4×C4⋊Dic43C2213yes—
61#14582750C2216yes—
62C2×C4×Q8×C43C2211yescharacteristic
63C2×C4×Q8×C43C2211yescharacteristic
64C2×C4×Q8×C43C2211yescharacteristic
65C43×#389C2213yes—
66C43×#389C2213yes—
67C43×#382C2213yes—
68C4×C4⋊C4×C43C2213yes—
69C22×Dic86C2313yes—
70C2×Q8×D43C2×C418yes—
71C2×Q8×D43D418yes—
72C2×Q8×D43Q818yes—
73C22×C4×D43C2311yescharacteristic
74C22×C4×D43C2313yes—
75C22×C4×D43C2313yes—
76Q8×Dic43—24no—
77Q8×Dic43—24no—
78Q8×Dic43C2×C418yescomplemented
79C4×Dic86—212no—
80C4×Dic86—212no—
81C4×Dic86C2×C4124yescomplemented
82#13063290—212no—
83#13063290—212no—
84#13063290C2×C4124yescomplemented
85#13063283—212no—
86#13063283C2×C4124yes—
87#13063282—212no—
88#13063282C2×C4124yes—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2313yes—
91C2×C4⋊Dic43C2313yes—
92C2×C4⋊Dic43C2313yes—
93C2×C4⋊Dic43C2316yes—
94C2×C4⋊Dic43C2313yes—
95C2×Dic43⋊C4C2311yescharacteristic
96C2×Dic43⋊C4C2313yes—
97C2×Dic43⋊C4C2313yes—
98C2×Dic43⋊C4C2313yes—
99C2×Dic43⋊C4C2316yes—
100C2×Dic43⋊C4C2313yes—
101C2×Dic43⋊C4C2316yes—
102C2×Dic43⋊C4C2313yes—
103C2×Dic43⋊C4C2313yes—
104C2×Dic43⋊C4C2313yes—
105C4⋊C4×D43—212no—
106C2×(C2×D43)⋊C4C2311yescharacteristic
107C2×(C2×D43)⋊C4C2313yes—
108C2×(C2×D43)⋊C4C2311yescharacteristic
109C2×(C2×D43)⋊C4C2313yes—
110C2×C4×Dic43C2313yes—
111C2×C4×Dic43C2313yes—
112C2×C4×Dic43C2313yes—
113C2×C4×Dic43C2313yes—
114C2×C4×Dic43C2316yes—
115C2×C4×Dic43C2313yes—
116C2×C4×Dic43C2316yes—
117C42×D43—212no—
118C43⋊#95C2311yescharacteristic
119C43⋊#95C2313yes—
120C43⋊#95C2313yes—
121C43⋊#95C2313yes—
122C43⋊#95C2313yes—
123C43⋊#95C2316yes—
124C43⋊#95C2313yes—
125C22×Q8×C43C2311yescharacteristic
126C4×Q8×C43—24no—
127C4×Q8×C43—24no—
128C4×Q8×C43C2×C418yescomplemented
129C2×C4⋊C4×C43C2313yes—
130C2×C4⋊C4×C43C2313yes—
131C2×C4⋊C4×C43C2313yes—
132C2×C4⋊C4×C43C2313yes—
133C2×C4⋊C4×C43C2313yes—
134C2×C42×C43C2313yes—
135C2×C42×C43C2313yes—
136C2×C42×C43C2313yes—
137#95×C43C2311yescharacteristic
138#95×C43C2313yes—
139#95×C43C2316yes—
140C23×D43C2411yescharacteristic
141C2×Q8×C43C22×C414yes—
142C2×Q8×C43C2×D414yes—
143C2×Q8×C43C2×Q814yes—
144C22×C4×C43C2413yes—
145C22×C4×C43C2413yes—
146C22×C4×C43C2411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×C4×C43C2413yes—
149C22×C4×C43C2411yescharacteristic
150C22×C4×C43C2413yes—
151C22×Dic43C2411yescharacteristic
152C22×Dic43C2413yes—
153C22×Dic43C2413yes—
154C22×Dic43C2411yescharacteristic
155C22×Dic43C2413yes—
156C22×Dic43C2411yescharacteristic
157C22×Dic43C2413yes—
158Q8×D43C4⋊C4164yescomplemented
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—26no—
163C2×C4×D43—43no—
164C2×C4×D43—43no—
165C2×C4×D43C22×C4112yes—
166C2×C4×D43C2×D4112yes—
167C2×C4×D43C2×Q8112yes—
168C2×Dic86C22×C4112yes—
169C2×Dic86C2×D4112yes—
170C2×Dic86C2×Q8112yes—
171C4⋊C4×C43—26no—
172C4⋊C4×C43—26no—
173C4⋊C4×C43—26no—
174C4⋊C4×C43—43no—
175C4⋊C4×C43C22×C4112yes—
176C42×C43—26no—
177C42×C43—26no—
178C42×C43C22×C4112yes—
179(C2×D43)⋊C4—22no—
180(C2×D43)⋊C4—26no—
181(C2×D43)⋊C4C22×C414yes—
182(C2×D43)⋊C4C22×C4112yes—
183C4⋊Dic43—26no—
184C4⋊Dic43—26no—
185C4⋊Dic43—22no—
186C4⋊Dic43—43no—
187C4⋊Dic43—46no—
188C4⋊Dic43C22×C4112yes—
189Dic43⋊C4—22no—
190Dic43⋊C4—212no—
191Dic43⋊C4—26no—
192Dic43⋊C4—26no—
193Dic43⋊C4—26no—
194Dic43⋊C4—46no—
195Dic43⋊C4—43no—
196Dic43⋊C4—43no—
197Dic43⋊C4C22×C4112yes—
198Dic43⋊C4C22×C4112yes—
199C4×Dic43—26no—
200C4×Dic43—26no—
201C4×Dic43—26no—
202C4×Dic43—26no—
203C4×Dic43—212no—
204C4×Dic43C22×C4112yes—
205C4×Dic43C22×C4124yes—
206C23×C43C2511yescharacteristic
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43C23×C412yes—
212C22×D43C22×D412yes—
213C22×D43C22×Q812yes—
214Q8×C43C2×C4⋊C4116yes—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—23no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—23no—
221C2×C4×C43—23no—
222C2×C4×C43—23no—
223C2×C4×C43—21no—
224C2×C4×C43—23no—
225C2×C4×C43—23no—
226C2×C4×C43—21no—
227C2×C4×C43—23no—
228C2×C4×C43—23no—
229C2×C4×C43—21no—
230C2×C4×C43C23×C416yes—
231C2×C4×C43C23×C412yes—
232C2×C4×C43C23×C416yes—
233C2×C4×C43C22×D416yes—
234C2×C4×C43C22×Q816yes—
235C2×C4×C432−1+412yes—
236C2×Dic43—21no—
237C2×Dic43—23no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—23no—
242C2×Dic43—21no—
243C2×Dic43—23no—
244C2×Dic43—23no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—23no—
248C2×Dic43—23no—
249C2×Dic43—23no—
250C2×Dic43—23no—
251C2×Dic43C23×C412yes—
252C2×Dic43C23×C416yes—
253C2×Dic43C23×C416yes—
254C2×Dic43C22×D416yes—
255C2×Dic43C22×Q816yes—
256C2×Dic432−1+412yes—
257C4×D43—28no—
258C4×D43—412no—
259C4×D43C2×C4⋊C4148yes—
260Dic86C2×C4⋊C4148yes—
261#34249—431nomaximal, Sylow
262C22×C43C24×C411yescharacteristic
263C22×C43C23×D411yescharacteristic
264C22×C43C23×Q811yescharacteristic
265C22×C43C2×2−1+411yescharacteristic
266C22×C43C2×2−1+411yescharacteristic
267C22×C43#58511yescharacteristic
268C22×C43#58511yescharacteristic
269C2×D43—22no—
270C2×D43—22no—
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43C22×C4⋊C414yes—
276C4×C43—22no—
277C4×C43—26no—
278C4×C43—22no—
279C4×C43—43no—
280C4×C43—43no—
281C4×C43—41no—
282C4×C43C22×C4⋊C4112yes—
283Dic43—26no—
284Dic43—22no—
285Dic43—22no—
286Dic43—41no—
287Dic43—43no—
288Dic43—43no—
289Dic43C22×C4⋊C4112yes—
290C2×#519—431no—
291C2×#519—431no—
292C22×C4×Q8—431no—
293#2351—433no—
294#2351—433no—
295#2351—431no—
296#2351D4311yescharacteristic, complemented
297Q8×C4⋊C4—433no—
298Q8×C4⋊C4—433no—
299Q8×C4⋊C4—431no—
300Q8×C4⋊C4—431no—
301#2317—433no—
302#2317—433no—
303#2296—433no—
304#2296—433no—
305C2×C43C23×C4⋊C411yescharacteristic
306C2×C43C4×2−1+411yescharacteristic
307C2×C43C4×2−1+411yescharacteristic
308C2×C43#348611yescharacteristic
309C2×C43#348711yescharacteristic
310C2×C43#350211yescharacteristic
311C2×C43#350211yescharacteristic
312D43—24no—
313C23×Q8—431no—
314#519—4316no—
315#519—868no—
316C2×C4×Q8—431no—
317C2×C4×Q8—431no—
318C2×C4×Q8—431no—
319C2×C4×Q8—433no—
320C2×C4×Q8—433no—
321C2×C4×Q8—433no—
322C2×C4×Q8—433no—
323C2×C4×Q8—433no—
324C2×C4×Q8—433no—
325C2×C4×Q8—868no—
326C2×C4×Q8C2×D4311yescharacteristic
327C2×C4×Q8C2×D4311yescharacteristic
328C2×C4×Q8C2×D4311yescharacteristic
329C2×#117—433no—
330C2×#117—433no—
331C2×#117—433no—
332C2×#117—433no—
333C22×C4⋊C4—433no—
334C22×C42—433no—
335#389—433no—
336#389—433no—
337#389—433no—
338#389—433no—
339#389—433no—
340#389—433no—
341#389—433no—
342#389—433no—
343#389—436no—
344#389—436no—
345#389—433no—
346#389—433no—
347#389C2×D4313yes—
348#389C2×D4313yes—
349#385—433no—
350#385—433no—
351#385—436no—
352#385—433no—
353#385—431no—
354#384—436no—
355#384—433no—
356#384—433no—
357#382—433no—
358#382—436no—
359#382C2×D4313yes—
360C4×C4⋊C4—436no—
361C4×C4⋊C4—433no—
362C4×C4⋊C4—433no—
363C4×C4⋊C4—433no—
364C4×C4⋊C4—436no—
365C4×C4⋊C4C2×D4313yes—
366C43#3424911yescharacteristic, complemented, Sylow
367C22×Q8—438no—
368C22×Q8—438no—
369C22×Q8—438no—
370C22×Q8—433no—
371C22×Q8C22×D4311yescharacteristic
372C23×C4—433no—
373C23×C4—431no—
374C23×C4—433no—
375C4×Q8—24no—
376C4×Q8—24no—
377C4×Q8—438no—
378C4×Q8—4324no—
379C4×Q8—4324no—
380C4×Q8—8612no—
381C4×Q8—8612no—
382C4×Q8—8612no—
383C4×Q8—8612no—
384C4×Q8—864no—
385C4×Q8—864no—
386C4×Q8C4×D4318yescomplemented
387#117—4324no—
388#117—4324no—
389#117—8612no—
390#117—8612no—
391C2×C4⋊C4—433no—
392C2×C4⋊C4—433no—
393C2×C4⋊C4—433no—
394C2×C4⋊C4—436no—
395C2×C4⋊C4—433no—
396C2×C4⋊C4—433no—
397C2×C4⋊C4—433no—
398C2×C4⋊C4—433no—
399C2×C4⋊C4—433no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—433no—
403C2×C4⋊C4—433no—
404C2×C4⋊C4—436no—
405C2×C4⋊C4—436no—
406C2×C4⋊C4—433no—
407C2×C4⋊C4—8612no—
408C2×C4⋊C4C22×D4313yes—
409C2×C4⋊C4C22×D4313yes—
410C2×C4⋊C4C22×D4313yes—
411C2×C4⋊C4C22×D4313yes—
412C2×C4⋊C4C22×D4313yes—
413C2×C22⋊C4—433no—
414C2×C22⋊C4—431no—
415C2×C22⋊C4—431no—
416C2×C22⋊C4—433no—
417C2×C42—436no—
418C2×C42—433no—
419C2×C42—436no—
420C2×C42—433no—
421C2×C42—433no—
422C2×C42—433no—
423C2×C42—433no—
424C2×C42—8612no—
425C2×C42C22×D4313yes—
426C2×C42C22×D4313yes—
427C2×C42C22×D4313yes—
428#95—431no—
429#95—433no—
430#95—433no—
431#95—433no—
432#95—433no—
433#95—436no—
434#95—433no—
435#95C22×D4316yes—
436#95C22×D4311yescharacteristic
437#95C22×D4313yes—
438C24—431no—
439C2×Q8—4364no—
440C2×Q8—4312no—
441C2×Q8—4312no—
442C2×Q8—4312no—
443C2×Q8C2×C4×D4314yes—
444C2×Q8D4×D4314yes—
445C2×Q8Q8×D4314yes—
446C22×C4—433no—
447C22×C4—4312no—
448C22×C4—4312no—
449C22×C4—4312no—
450C22×C4—431no—
451C22×C4—433no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—433no—
455C22×C4—433no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—866no—
459C22×C4—862no—
460C22×C4—1723no—
461C22×C4—1723no—
462C22×C4C23×D4313yes—
463C22×C4C23×D4313yes—
464C22×C4C23×D4311yescharacteristic
465C22×C4C23×D4313yes—
466C22×C4C23×D4311yescharacteristic
467C22×C4C23×D4311yescharacteristic
468C22×C4C23×D4313yes—
469C4⋊C4—26no—
470C4⋊C4—26no—
471C4⋊C4—26no—
472C4⋊C4—43no—
473C4⋊C4—4312no—
474C4⋊C4—4312no—
475C4⋊C4—4312no—
476C4⋊C4—8612no—
477C4⋊C4—866no—
478C4⋊C4—866no—
479C4⋊C4—866no—
480C4⋊C4—862no—
481C4⋊C4—866no—
482C4⋊C4—866no—
483C4⋊C4—862no—
484C4⋊C4—1723no—
485C4⋊C4—1723no—
486C4⋊C4—1726no—
487C4⋊C4—1726no—
488C4⋊C4—1723no—
489C4⋊C4C2×C4×D43112yes—
490C22⋊C4—4312no—
491C22⋊C4—434no—
492C22⋊C4—862no—
493C22⋊C4—866no—
494C42—26no—
495C42—26no—
496C42—4324no—
497C42—4312no—
498C42—866no—
499C42—866no—
500C42—8612no—
501C42—866no—
502C42—866no—
503C42C2×C4×D43112yes—
504C23—432no—
505C23—432no—
506C23—432no—
507C23—861no—
508C23—861no—
509C23—861no—
510C23—861no—
511C23C24×D4311yescharacteristic
512Q8—4348no—
513Q8C4⋊C4×D43116yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—23no—
518C2×C4—23no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—23no—
522C2×C4—23no—
523C2×C4—23no—
524C2×C4—23no—
525C2×C4—21no—
526C2×C4—23no—
527C2×C4—21no—
528C2×C4—23no—
529C2×C4—436no—
530C2×C4—436no—
531C2×C4—436no—
532C2×C4—4348no—
533C2×C4—436no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—868no—
537C2×C4—861no—
538C2×C4—863no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—863no—
543C2×C4—861no—
544C2×C4—863no—
545C2×C4—863no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—863no—
549C2×C4—863no—
550C2×C4—863no—
551C2×C4—863no—
552C2×C4—17212no—
553C2×C4C22×C4×D4316yes—
554C2×C4C22×C4×D4312yes—
555C2×C4C22×C4×D4316yes—
556C2×C4C2×D4×D4316yes—
557C2×C4C2×Q8×D4316yes—
558C2×C4#1306337212yes—
559C22—434no—
560C22—862no—
561C22—862no—
562C22—862no—
563C22—862no—
564C22—862no—
565C22—862no—
566C22C23×C4×D4311yescharacteristic
567C22C22×D4×D4311yescharacteristic
568C22C22×Q8×D4311yescharacteristic
569C222−1+4×D4311yescharacteristic
570C22C2×#1306337211yescharacteristic
571C22#1458373511yescharacteristic
572C22#1458373611yescharacteristic
573C4—22no—
574C4—26no—
575C4—22no—
576C4—43no—
577C4—43no—
578C4—41no—
579C4—4312no—
580C4—866no—
581C4—862no—
582C4—862no—
583C4—1721no—
584C4—1723no—
585C4—1723no—
586C4C2×C4⋊C4×D43112yes—
587C2—864no—
588C2C22×C4⋊C4×D4311yescharacteristic
589C2#1914780411yescharacteristic
590C2C4×#1306337211yescharacteristic
591C2#1914824111yescharacteristic
592C2#1914825211yescharacteristic
593C2#1914839911yescharacteristic
594C2#1914840211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2351C2
socle, cosocleC23×C43C25
prime radicalC23×D43C24
hypercenter#2351D43
hypocenterC43#34249
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2351

Complements

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

NH ≅ G/Ntype
4. #19137514C2semidirect
5. #19137513C2semidirect
6. #19137512C2semidirect
7. Q8×C4⋊Dic43C2semidirect
8. C4⋊C4×Dic86C2semidirect
9. #19137509C2semidirect
10. Q8×Dic43⋊C4C2semidirect
15. C43×#2351C2semidirect
18. #14583375C4semidirect
78. Q8×Dic43C2×C4semidirect
81. C4×Dic86C2×C4semidirect
84. #13063290C2×C4semidirect
128. C4×Q8×C43C2×C4semidirect
158. Q8×D43C4⋊C4semidirect
296. #2351D43semidirect
366. C43#34249semidirect
386. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833752
C2×C4×Q8×D432
#191375142
#191375132
#191375122
Q8×C4⋊Dic432
C4⋊C4×Dic862
#191375092
Q8×Dic43⋊C42
#191372202
#191372172
#191370762
#191370752
C43×#23512
#3424943