Finite Group Databasebeta

← #11817710

Subgroups — #11817710

Order 1152.

1554 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic, complemented
2C2×#64107C211yesmaximal, characteristic, complemented
3C32×#385C211yesmaximal, characteristic, complemented
4#10592912C211yesmaximal, characteristic
5#10592689C211yesmaximal, characteristic, complemented
6#10592680C211yesmaximal, characteristic, complemented
7C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#10592658C211yesmaximal, characteristic
9#10592656C211yesmaximal, characteristic
10#10592650C211yesmaximal, characteristic, complemented
11#10592648C211yesmaximal, characteristic, complemented
12#10592376C211yesmaximal, characteristic, complemented
13#10592368C211yesmaximal, characteristic, complemented
14#10592353C211yesmaximal, characteristic, complemented
15#10592346C211yesmaximal, characteristic, complemented
16#74451—34nomaximal
17C23×C32×C4C2211yescharacteristic
18C22×#638C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32#64135—24no—
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
37C2×#3750C2211yescharacteristic
38C2×#3750C2211yescharacteristic
39C2×#3750C2211yescharacteristic
40C2×#3750C2211yescharacteristic
41C2×C4×C3⋊Dic3C2211yescharacteristic
42C2×C4×C3⋊Dic3C2211yescharacteristic
43C2×C4×C3⋊Dic3C2211yescharacteristic
44C2×C4×C3⋊Dic3C2211yescharacteristic
45#64107—24no—
46C32×#95C2211yescharacteristic
47C32×#95C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54C2×#926—34no—
55C2×#898—34no—
56C3×#385D314yescomplemented
57#5213—34no—
58#4990—34no—
59#4981—34no—
60Dic3×C4⋊C4—34no—
61#4959—34no—
62#4957—34no—
63#4951—34no—
64#4949—34no—
65#4677—34no—
66#4669—34no—
67#4654—34no—
68#4647—34no—
69C24×C32C2311yescharacteristic
70C23×C3⋊D3C2311yescharacteristic
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4—22no—
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C2×#638—22no—
81C2×#638—22no—
82C2×#638—41no—
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C32×C4⋊C4—22no—
91C32×C4⋊C4—22no—
92C32×C22⋊C4—22no—
93C32×C22⋊C4—22no—
94#3757—22no—
95#3757—22no—
96#3757—41no—
97#3752—22no—
98#3752—22no—
99#3752—22no—
100#3752—22no—
101#3752—22no—
102#3752—41no—
103C4⋊(C3⋊Dic3)—22no—
104C4⋊(C3⋊Dic3)—22no—
105C4⋊(C3⋊Dic3)—41no—
106C4⋊(C3⋊Dic3)D414yescomplemented
107#3750—22no—
108#3750—22no—
109#3750—41no—
110#3750—41no—
111C4×C3⋊Dic3—22no—
112C4×C3⋊Dic3—22no—
113C4×C3⋊Dic3—22no—
114C4×C3⋊Dic3—22no—
115#2479—91noSylow
116C23×C3×C4C2×D314yes—
117C22×#67—34no—
118C2×C3×C4⋊C4C2×D314yes—
119C2×C3×C4⋊C4C2×D314yes—
120C2×C3×C22⋊C4C2×D314yes—
121C2×C3×C22⋊C4C2×D314yes—
122C2×#217—34no—
123C2×#217—34no—
124C2×#217—34no—
125C2×(C2×D3)⋊C4—34no—
126C2×(C2×D3)⋊C4—34no—
127C2×(C2×D3)⋊C4—34no—
128C2×(C2×D3)⋊C4—34no—
129C2×(C2×D3)⋊C4—34no—
130C2×(C2×D3)⋊C4—34no—
131#926—616no—
132C2×C4⋊Dic3—34no—
133C2×C4⋊Dic3—34no—
134C2×C4⋊Dic3—34no—
135C2×C4⋊Dic3—34no—
136C2×Dic3⋊C4—34no—
137C2×Dic3⋊C4—34no—
138C2×Dic3⋊C4—34no—
139C2×Dic3⋊C4—34no—
140C2×C4×Dic3—34no—
141C2×C4×Dic3—34no—
142C2×C4×Dic3—34no—
143C2×C4×Dic3—34no—
144#898—616no—
145C3×#95C2×D314yes—
146C3×#95C2×D314yes—
147C3⋊#95—34no—
148C3⋊#95—34no—
149C3⋊#95—34no—
150C3⋊#95—34no—
151C3⋊#95—34no—
152C3⋊#95—34no—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32—21no—
156C23×C32—21no—
157C23×C32—21no—
158C23×C32—21no—
159C23×C32#4112yes—
160C23×C32C2411yescharacteristic
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C2×C32×C4—28no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D412yes—
185C2×C32×C4#4112yes—
186C2×C32×C4#4112yes—
187#638—44no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3C2×D412yes—
207C2×C3⋊Dic3C2×D412yes—
208C2×C3⋊Dic3#4112yes—
209C2×#126—91no—
210C2×#117—91no—
211#399—91no—
212#399—91no—
213#398—91no—
214#394—91no—
215#390—91no—
216#389—91no—
217#388—91no—
218#388—91no—
219#388—91no—
220#387—91no—
221#386—91no—
222#385C3⋊D311yescharacteristic, complemented
223C4×C4⋊C4—91no—
224C24×C3C22×D314yes—
225C23×D3—34no—
226C22×C3×C4—28no—
227C22×C3×C4—28no—
228C22×C3×C4—28no—
229C22×C3×C4C22×D314yes—
230C22×C3×C4C22×D314yes—
231C22×C3×C4C22×D314yes—
232C22×C3×C4C22×D314yes—
233C22×C3×C4C22×D314yes—
234C22×C3×C4C22×D314yes—
235C2×#67—68no—
236C2×#67—68no—
237C2×#67—124no—
238C22×Dic3—34no—
239C22×Dic3—34no—
240C22×Dic3—34no—
241C22×Dic3—34no—
242C22×Dic3—34no—
243C22×Dic3—34no—
244C22×Dic3—34no—
245C3×C4⋊C4—28no—
246C3×C4⋊C4—28no—
247C3×C22⋊C4—28no—
248C3×C22⋊C4—28no—
249#217—68no—
250#217—68no—
251#217—124no—
252(C2×D3)⋊C4—68no—
253(C2×D3)⋊C4—68no—
254(C2×D3)⋊C4—68no—
255(C2×D3)⋊C4—68no—
256(C2×D3)⋊C4—68no—
257(C2×D3)⋊C4—124no—
258C4⋊Dic3—316no—
259C4⋊Dic3—68no—
260C4⋊Dic3—68no—
261C4⋊Dic3—124no—
262Dic3⋊C4—68no—
263Dic3⋊C4—68no—
264Dic3⋊C4—124no—
265Dic3⋊C4—124no—
266C4×Dic3—68no—
267C4×Dic3—68no—
268C4×Dic3—68no—
269C4×Dic3—68no—
270C22×C32—22no—
271C22×C32—22no—
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32C22×D411yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32C2×#4111yescharacteristic
282C22×C32H(5,𝔽2)11yescharacteristic
283C22×C322−1+411yescharacteristic
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—41no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C32×C4—22no—
292C32×C4—22no—
293C32×C4—22no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4—41no—
297C3⋊Dic3—22no—
298C3⋊Dic3—22no—
299C3⋊Dic3—22no—
300C3⋊Dic3—41no—
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C22×D4—91no—
305C23×C4C2×C3⋊D311yescharacteristic
306#126—184no—
307#117—184no—
308C2×C4⋊C4—91no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4—91no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—91no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4C2×C3⋊D311yescharacteristic
317C2×C4⋊C4C2×C3⋊D311yescharacteristic
318C2×C22⋊C4—91no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—91no—
322C2×C22⋊C4—91no—
323C2×C22⋊C4—91no—
324C2×C22⋊C4—91no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4—91no—
327C2×C22⋊C4C2×C3⋊D311yescharacteristic
328C2×C22⋊C4C2×C3⋊D311yescharacteristic
329C2×C42—91no—
330C2×C42—91no—
331C2×C42—91no—
332C2×C42—91no—
333#95—91no—
334#95—91no—
335#95—91no—
336#95—91no—
337#95—91no—
338#95—91no—
339#95C2×C3⋊D311yescharacteristic
340#95C2×C3⋊D311yescharacteristic
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3#23718yes—
348C23×C3C23×D314yes—
349C22×D3—64no—
350C22×D3—64no—
351C22×D3—64no—
352C22×D3—64no—
353C22×D3—64no—
354C22×D3—64no—
355C22×D3—64no—
356C2×C3×C4—232no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4#23518yes—
373C2×C3×C4D3×D418yes—
374C2×C3×C4#23718yes—
375#67—1216no—
376C2×Dic3—38no—
377C2×Dic3—38no—
378C2×Dic3—38no—
379C2×Dic3—64no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—64no—
383C2×Dic3—64no—
384C2×Dic3—64no—
385C2×Dic3—64no—
386C2×Dic3—64no—
387C2×Dic3—64no—
388C2×Dic3—64no—
389C2×Dic3—64no—
390C2×Dic3—64no—
391C2×Dic3—64no—
392C2×Dic3—64no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395C2×Dic3—64no—
396C2×Dic3—64no—
397C2×C32—42no—
398C2×C32#52511yescharacteristic
399C2×C32#52911yescharacteristic
400C2×C32#54211yescharacteristic
401C2×C32#54711yescharacteristic
402C2×C32#55011yescharacteristic
403C2×C32#55111yescharacteristic
404C2×C32#55211yescharacteristic
405C3⋊D3—81no—
406C24—91no—
407C24C22×C3⋊D311yescharacteristic
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—361no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—91no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4C22×C3⋊D311yescharacteristic
422C22×C4C22×C3⋊D311yescharacteristic
423C22×C4C22×C3⋊D311yescharacteristic
424C22×C4C22×C3⋊D311yescharacteristic
425C22×C4C22×C3⋊D311yescharacteristic
426C22×C4C22×C3⋊D311yescharacteristic
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—94no—
430C4⋊C4—182no—
431C4⋊C4—182no—
432C4⋊C4—182no—
433C4⋊C4—182no—
434C4⋊C4—361no—
435C4⋊C4—361no—
436C4⋊C4—361no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—182no—
440C22⋊C4—182no—
441C22⋊C4—182no—
442C22⋊C4—182no—
443C22⋊C4—182no—
444C22⋊C4—182no—
445C22⋊C4—182no—
446C22⋊C4—361no—
447C22⋊C4—361no—
448C42—182no—
449C42—182no—
450C42—182no—
451C42—182no—
452C22×C3—28no—
453C22×C3—28no—
454C22×C3—28no—
455C22×C3—44no—
456C22×C3—44no—
457C22×C3—44no—
458C22×C3—44no—
459C22×C3C2×#23514yes—
460C22×C3C2×D3×D414yes—
461C22×C3C2×#23714yes—
462C22×C3C2×#23714yes—
463C22×C3#100714yes—
464C22×C3D3×#4114yes—
465C22×C3#100914yes—
466C2×D3—124no—
467C2×D3—124no—
468C2×D3—124no—
469C2×D3—124no—
470C2×D3—124no—
471C2×D3—124no—
472C2×D3—124no—
473C3×C4—28no—
474C3×C4—28no—
475C3×C4—28no—
476C3×C4—44no—
477C3×C4—44no—
478C3×C4—44no—
479Dic3—68no—
480Dic3—68no—
481Dic3—68no—
482Dic3—124no—
483Dic3—124no—
484Dic3—124no—
485Dic3—124no—
486C32#247911yescharacteristic, complemented, Sylow
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—181no—
494C23—181no—
495C23—181no—
496C23—181no—
497C23—181no—
498C23—181no—
499C23—181no—
500C23#383012yes—
501C23C23×C3⋊D311yescharacteristic
502D4—364no—
503C2×C4—28no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—92no—
520C2×C4—92no—
521C2×C4—92no—
522C2×C4—181no—
523C2×C4—181no—
524C2×C4—181no—
525C2×C4—181no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4#382812yes—
541C2×C4D4×C3⋊D312yes—
542C2×C4#383012yes—
543C2×C3—48no—
544C2×C3#551314yes—
545C2×C3#553814yes—
546C2×C3#555314yes—
547C2×C3#558614yes—
548C2×C3#563114yes—
549C2×C3#564314yes—
550C2×C3#565814yes—
551D3—244no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—361no—
560C22—361no—
561C22—361no—
562C22—361no—
563C22—361no—
564C22—361no—
565C22—361no—
566C22C2×#382811yescharacteristic
567C22C2×D4×C3⋊D311yescharacteristic
568C22C2×#383011yescharacteristic
569C22C2×#383011yescharacteristic
570C22#6436411yescharacteristic
571C22#41×C3⋊D311yescharacteristic
572C22#6436611yescharacteristic
573C4—22no—
574C4—22no—
575C4—22no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—182no—
580C4—182no—
581C4—182no—
582C4—361no—
583C4—361no—
584C4—361no—
585C4—361no—
586C3#7445114yescomplemented
587C2—42no—
588C2—721no—
589C2#1059598411yescharacteristic
590C2#1059600911yescharacteristic
591C2#1059602411yescharacteristic
592C2#1059605711yescharacteristic
593C2#1059610211yescharacteristic
594C2#1059611411yescharacteristic
595C2#1059612911yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#385C2
prime radicalC22×#638C22
hypercenter#385C3⋊D3
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#64135C2semidirect
2. C2×#64107C2semidirect
3. C32×#385C2semidirect
5. #10592689C2semidirect
6. #10592680C2semidirect
7. C4⋊C4×C3⋊Dic3C2semidirect
10. #10592650C2semidirect
11. #10592648C2semidirect
12. #10592376C2semidirect
13. #10592368C2semidirect
14. #10592353C2semidirect
15. #10592346C2semidirect
56. C3×#385D3semidirect
106. C4⋊(C3⋊Dic3)D4semidirect
222. #385C3⋊D3semidirect
486. C32#2479semidirect
586. C3#74451semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C2×#641072
C32×#3852
#105929122
#105926892
#105926802
C4⋊C4×C3⋊Dic32
#105926582
#105926562
#105926502
#105926482
#105923762
#105923682
#105923532
#105923462
#744513