Finite Group Databasebeta

← #11805601

Subgroups — #11805601

Order 1152.

1253 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic
4C3×C4×Dic3⋊C4C211yesmaximal, characteristic
5C3×#4928C211yesmaximal, characteristic
6#10591352C211yesmaximal, characteristic
7#10591337C212yesmaximal
8#10591256C212yesmaximal
9#10591247C212yesmaximal
10#10591241C212yesmaximal
11#10591224C211yesmaximal, characteristic
12#75982—31nomaximal
13#73637—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2212yes—
18C2×C4×C3⋊Dic3C2212yes—
19C4×#634—24no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×#3724C2212yes—
28C2×#3724C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32#63844—24no—
33#63844C418yescomplemented
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×#887—31no—
41C2×#887—31no—
42C2×C4×Dic6—31no—
43C2×C4×Dic6—31no—
44C2×C4×Dic6—31no—
45C2×C4×Dic6—31no—
46C2×C4×Dic6—61no—
47C3×#389—31no—
48C3×C4×C4⋊C4—31no—
49#4984—31no—
50#4977—31no—
51#4976—32no—
52#4976—32no—
53#4976—32no—
54Dic3×C4⋊C4—32no—
55#4936—31no—
56C4×Dic3⋊C4D311yescharacteristic
57#4928—31no—
58#4928D311yescharacteristic
59#4650—32no—
60#4650—32no—
61#4649—32no—
62#4647—32no—
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C2×#634C2×C414yes—
69C2×#634D414yes—
70C2×#634Q814yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C32×C42—22no—
78C4⋊(C3⋊Dic3)—22no—
79#3750—24no—
80C4×C3⋊Dic3—24no—
81C3×C4⋊Dic3—22no—
82C3×C4⋊Dic3C2×C414yes—
83C3×Dic3⋊C4—22no—
84C3×Dic3⋊C4—24no—
85C3×Dic3⋊C4—22no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3C2×C414yes—
88#3724—24no—
89#3724C2×C418yes—
90Dic3⋊Dic3—24no—
91Dic32—24no—
92Dic32C2×C418yes—
93#2351—91noSylow
94C22×Dic6—31no—
95C22×Dic6—31no—
96C22×Dic6—61no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C42—21no—
103C2×C3×C42—31no—
104C2×C3×C42—31no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—32no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—62no—
121C2×Dic3⋊C4C2×D311yescharacteristic
122C2×Dic3⋊C4C2×D312yes—
123C2×Dic3⋊C4C2×D311yescharacteristic
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—62no—
131C2×C4×Dic3C2×D311yescharacteristic
132C2×C4×Dic3C2×D311yescharacteristic
133#887—38no—
134#887—64no—
135C4×Dic6—38no—
136C4×Dic6—64no—
137C4×Dic6—64no—
138C4×Dic6—64no—
139C4×Dic6—68no—
140C3×#95—32no—
141C3×#95—31no—
142C3×#95—31no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95C2×D311yescharacteristic
150C3⋊#95C2×D312yes—
151C3⋊#95C2×D311yescharacteristic
152C23×C32C2411yescharacteristic
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4C22×C412yes—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×Q812yes—
161C2×C32×C4#4112yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3C22×C414yes—
166C2×C3⋊Dic3C2×D414yes—
167C2×C3⋊Dic3C2×Q814yes—
168#634C4⋊C4116yescomplemented
169C2×C3×Dic3—21no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3C22×C412yes—
184C2×C3×Dic3C22×C414yes—
185C2×C3×Dic3C22×C412yes—
186C2×C3×Dic3#4112yes—
187C2×C4×Q8—91no—
188C2×C4×Q8—91no—
189C2×C4×Q8—91no—
190#389—31no—
191#389—92no—
192#389—91no—
193#389—92no—
194#382—92no—
195#382—91no—
196C4×C4⋊C4—31no—
197C4×C4⋊C4—92no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—32no—
204C22×C3×C4—31no—
205C22×C3×C4—32no—
206C22×C3×C4—31no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D311yescharacteristic
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D311yescharacteristic
225C2×Dic6—34no—
226C2×Dic6—34no—
227C2×Dic6—34no—
228C2×Dic6—34no—
229C2×Dic6—34no—
230C2×Dic6—34no—
231C2×Dic6—64no—
232C2×Dic6—64no—
233C2×Dic6—64no—
234C3×C4⋊C4—34no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—64no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—62no—
239C3×C42—24no—
240C3×C42—22no—
241C3×C42—22no—
242C3×C42—34no—
243C3×C42—62no—
244C4⋊Dic3—22no—
245C4⋊Dic3—64no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3—64no—
249C4⋊Dic3C4×D314yes—
250Dic3⋊C4—22no—
251Dic3⋊C4—24no—
252Dic3⋊C4—22no—
253Dic3⋊C4—38no—
254Dic3⋊C4—38no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260Dic3⋊C4—68no—
261C4×Dic3—22no—
262C4×Dic3—38no—
263C4×Dic3—38no—
264C4×Dic3—64no—
265C4×Dic3—64no—
266C4×Dic3—64no—
267C4×Dic3—64no—
268C4×Dic3—68no—
269C4×Dic3C4×D314yes—
270C22×C32C23×C411yescharacteristic
271C22×C32C22×D411yescharacteristic
272C22×C32C22×Q811yescharacteristic
273C22×C32C2×#4111yescharacteristic
274C22×C32C2×#4111yescharacteristic
275C22×C322−1+411yescharacteristic
276C22×C322−1+411yescharacteristic
277C32×C4—22no—
278C32×C4—41no—
279C32×C4C2×C4⋊C414yes—
280C3⋊Dic3—42no—
281C3⋊Dic3C2×C4⋊C418yes—
282C3×Dic3—22no—
283C3×Dic3—24no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—41no—
287C3×Dic3—42no—
288C22×Q8—91no—
289C4×Q8—98no—
290C4×Q8—184no—
291C4×Q8—184no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—31no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—32no—
297C2×C4⋊C4—92no—
298C2×C4⋊C4—92no—
299C2×C4⋊C4—92no—
300C2×C4⋊C4—92no—
301C2×C4⋊C4—91no—
302C2×C42—31no—
303C2×C42—31no—
304C2×C42—92no—
305C2×C42—92no—
306C2×C42—92no—
307C2×C42D3211yescharacteristic
308#95—31no—
309#95—31no—
310#95—32no—
311#95—92no—
312#95—92no—
313#95—92no—
314C23×C3—21no—
315C23×C3C23×D311yescharacteristic
316C23×C3C23×D311yescharacteristic
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—32no—
335C2×C3×C4—34no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4—61no—
354C2×C3×C4C2×C4×D312yes—
355C2×C3×C4C2×C4×D312yes—
356C2×C3×C4#23512yes—
357C2×C3×C4D3×D412yes—
358C2×C3×C4D3×D412yes—
359C2×C3×C4#23712yes—
360C2×C3×C4D3×Q812yes—
361C2×C3×C4D3×Q812yes—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—21no—
375C2×Dic3—22no—
376C2×Dic3—34no—
377C2×Dic3—34no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—34no—
382C2×Dic3—64no—
383C2×Dic3—64no—
384C2×Dic3—64no—
385C2×Dic3—64no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3C2×C4×D312yes—
395C2×Dic3C2×C4×D314yes—
396C2×Dic3C2×C4×D312yes—
397C2×Dic3#23512yes—
398Dic6—316no—
399Dic6—316no—
400Dic6—616no—
401C2×C32C22×C4⋊C411yescharacteristic
402C2×C32C4×#4111yescharacteristic
403C2×C32#51911yescharacteristic
404C2×C32#54811yescharacteristic
405C2×C32#54811yescharacteristic
406C2×C32#55711yescharacteristic
407C2×C32#55711yescharacteristic
408C2×Q8—94no—
409C2×Q8—94no—
410C2×Q8—94no—
411C22×C4—31no—
412C22×C4—32no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—32no—
417C22×C4—92no—
418C22×C4—92no—
419C22×C4C2×D3211yescharacteristic
420C22×C4C2×D3211yescharacteristic
421C22×C4C2×D3211yescharacteristic
422C4⋊C4—34no—
423C4⋊C4—62no—
424C4⋊C4—62no—
425C4⋊C4—64no—
426C4⋊C4—62no—
427C4⋊C4—98no—
428C4⋊C4—184no—
429C4⋊C4—184no—
430C4⋊C4—184no—
431C4⋊C4—182no—
432C42—22no—
433C42—34no—
434C42—62no—
435C42—98no—
436C42—184no—
437C42—184no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3C22×C4×D311yescharacteristic
446C22×C3C22×C4×D311yescharacteristic
447C22×C3C2×#23511yescharacteristic
448C22×C3C2×#23511yescharacteristic
449C22×C3C2×D3×D411yescharacteristic
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C2×#23711yescharacteristic
452C22×C3C2×D3×Q811yescharacteristic
453C22×C3C2×D3×Q811yescharacteristic
454C22×C3#100711yescharacteristic
455C22×C3D3×#4111yescharacteristic
456C22×C3#101011yescharacteristic
457C22×C3#101011yescharacteristic
458C22×C3#101011yescharacteristic
459C3×C4—24no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—24no—
463C3×C4—42no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—62no—
467C3×C4—64no—
468C3×C4—62no—
469C3×C4—62no—
470C3×C4—122no—
471C3×C4—121no—
472C3×C4D3×C4⋊C414yes—
473C3×C4D3×C4⋊C414yes—
474Dic3—22no—
475Dic3—22no—
476Dic3—24no—
477Dic3—22no—
478Dic3—38no—
479Dic3—38no—
480Dic3—41no—
481Dic3—42no—
482Dic3—68no—
483Dic3—124no—
484Dic3—122no—
485Dic3—122no—
486C32#235111yescharacteristic, complemented, Sylow
487C23C22×D3211yescharacteristic
488Q8—916no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—34no—
497C2×C4—32no—
498C2×C4—62no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—62no—
508C2×C4—61no—
509C2×C4—62no—
510C2×C4—61no—
511C2×C4—62no—
512C2×C4—94no—
513C2×C4—94no—
514C2×C4—94no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4#379512yes—
519C2×C4#379712yes—
520C2×C4C4×D3212yes—
521C2×C4#381112yes—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3C4×#23511yescharacteristic
530C2×C3C2×D3×C4⋊C411yescharacteristic
531C2×C3C2×D3×C4⋊C411yescharacteristic
532C2×C3#551611yescharacteristic
533C2×C3C4×#23711yescharacteristic
534C2×C3#555211yescharacteristic
535C2×C3#555211yescharacteristic
536C2×C3#556711yescharacteristic
537C2×C3#556711yescharacteristic
538C2×C3#557211yescharacteristic
539C2×C3#559811yescharacteristic
540C2×C3#563311yescharacteristic
541C2×C3#568511yescharacteristic
542C2×C3#572111yescharacteristic
543C22C2×#379511yescharacteristic
544C22#6429711yescharacteristic
545C22#6429811yescharacteristic
546C22C2×#379711yescharacteristic
547C22C2×C4×D3211yescharacteristic
548C22D3×#23511yescharacteristic
549C22C2×#381111yescharacteristic
550C4—22no—
551C4—41no—
552C4—62no—
553C4—62no—
554C4—64no—
555C4—62no—
556C4—98no—
557C4—121no—
558C4—122no—
559C4—362no—
560C4#6388314yes—
561C3—21no—
562C3#7363711yescharacteristic, complemented
563C3#7598211yescharacteristic, complemented
564C2#1059385211yescharacteristic
565C2#1059386411yescharacteristic
566C2#1059388511yescharacteristic
567C2C4×#379511yescharacteristic
568C2C2×#6388311yescharacteristic
569C2#1059491611yescharacteristic
570C2#1059491811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2351
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
33. #63844C4semidirect
168. #634C4⋊C4semidirect
486. C32#2351semidirect
562. C3#73637semidirect
563. C3#75982semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×#638442
C3×C4×Dic3⋊C42
C3×#49282
#105913522
#105913372
#105912562
#105912472
#105912412
#105912242
#759823
#736373