Finite Group Databasebeta

← #11803620

Subgroups — #11803620

Order 1152.

1431 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#884C211yesmaximal, characteristic
2C2×Dic3×#67C211yesmaximal, characteristic, complemented
3C2×#63841C211yesmaximal, characteristic, complemented
4#10592650C211yesmaximal, characteristic, complemented
5C3×#4950C211yesmaximal, characteristic, complemented
6#10591710C211yesmaximal, characteristic, complemented
7#10591707C211yesmaximal, characteristic, complemented
8#10591707C211yesmaximal, characteristic, complemented
9#10591377C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591323C211yesmaximal, characteristic, complemented
12#10591316C211yesmaximal, characteristic, complemented
13#10591295C211yesmaximal, characteristic, complemented
14#10591265C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#82633—31nomaximal
17#74385—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C3×#884C418yescomplemented
35Dic3×#67—24no—
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49#63841—24no—
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×#121—31no—
57C2×D4×Dic3—31no—
58C2×C4×#67—31no—
59C2×#926—31no—
60C2×#892—31no—
61C2×#884D311yescharacteristic
62C3×#385—31no—
63#5221—31no—
64#5221—31no—
65#5221—31no—
66#5220—31no—
67#5220—31no—
68#5213—31no—
69#5212—31no—
70#4989—31no—
71#4988—31no—
72#4984—31no—
73#4976—31no—
74Dic3×C4⋊C4—31no—
75#4957—31no—
76#4957—31no—
77#4951—31no—
78#4951—31no—
79#4951—31no—
80#4951—61no—
81#4950—31no—
82#4950D311yescharacteristic, complemented
83#4670—31no—
84#4667—31no—
85#4665—31no—
86#4649—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C3×#67—22no—
97C2×C3×#67—22no—
98C2×C3×#67—41no—
99C2×C3×#67—41no—
100C2×C3×#67C2×C414yes—
101C2×C3×#67C2×C414yescomplemented
102C22×C3×Dic3—22no—
103C22×C3×Dic3—41no—
104C22×C3×Dic3—41no—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×C3×D12—41no—
112C2×C3×D12—41no—
113C2×C3×D12C2×C414yescomplemented
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3C2×C414yescomplemented
117C2×D3×Dic3—22no—
118C2×D3×Dic3—41no—
119C2×D3×Dic3—41no—
120C32×C22⋊C4C2×C414yescomplemented
121#3757—22no—
122#3757—41no—
123C4⋊(C3⋊Dic3)—22no—
124C4×C3⋊Dic3—41no—
125C3×#217—41no—
126C3×(C2×D3)⋊C4C2×C414yescomplemented
127C3×C4⋊Dic3—22no—
128C3×C4⋊Dic3—41no—
129C3×Dic3⋊C4C2×C414yescomplemented
130Dic3⋊Dic3—22no—
131Dic3⋊Dic3—22no—
132Dic3⋊Dic3—41no—
133(C2×D3)⋊Dic3—22no—
134(C2×D3)⋊Dic3—22no—
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3—41no—
137(C2×D3)⋊Dic3—41no—
138(C2×D3)⋊Dic3—41no—
139(C2×D3)⋊Dic3—41no—
140Dic32—22no—
141Dic32—41no—
142Dic32D414yescomplemented
143#2324—91noSylow
144C22×C3×D4—31no—
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C23×C3×C4—31no—
148C23×C3×C4—31no—
149C22×#67C2×D311yescharacteristic
150C22×#67C2×D311yescharacteristic
151C23×Dic3—31no—
152C23×Dic3C2×D311yescharacteristic
153C22×D12C2×D311yescharacteristic
154C22×C4×D3—31no—
155C22×C4×D3C2×D311yescharacteristic
156C3×#121—38no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4C2×D311yescharacteristic
164C2×C3×C22⋊C4C2×D311yescharacteristic
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—61no—
177C2×#217—61no—
178C2×#217C2×D311yescharacteristic
179D4×Dic3—64no—
180C4×#67—64no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189#926—64no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—61no—
196C2×C4⋊Dic3C2×D311yescharacteristic
197C2×C4⋊Dic3C2×D311yescharacteristic
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4C2×D311yescharacteristic
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—61no—
211#892—64no—
212#884Dic318yescomplemented
213C3×#95—31no—
214C3×#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—61no—
224C3⋊#95—61no—
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C23×C32—21no—
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32C22×C412yes—
234C23×C32C2411yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3C22×C412yes—
248C22×C3×D3C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C22×C412yes—
254C2×C32×C4C22×C412yes—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C2×D412yes—
267C3×#67—28no—
268C3×#67—44no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—44no—
283C2×C3×Dic3C22×C412yes—
284C2×C3×Dic3C22×C412yes—
285C2×C3×Dic3C2×D412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3#4112yes—
288C3×D12—44no—
289C3×C4×D3—28no—
290D3×Dic3—44no—
291C2×#121—31no—
292C2×C4×D4—91no—
293C2×#117—91no—
294#390—91no—
295#390—91no—
296#390—91no—
297#389—91no—
298#388—91no—
299#388—91no—
300#386—91no—
301#386—91no—
302#385—31no—
303#385—91no—
304#380—91no—
305C4×C4⋊C4—91no—
306C24×C3—21no—
307C24×C3—31no—
308C24×C3—31no—
309C24×C3C22×D311yescharacteristic
310C24×C3C22×D311yescharacteristic
311C23×D3C22×D311yescharacteristic
312C23×D3C22×D311yescharacteristic
313C2×C3×D4—34no—
314C2×C3×D4—34no—
315C2×C3×D4—34no—
316C2×C3×D4—62no—
317C2×C3×D4—62no—
318C2×C3×D4—121no—
319C2×C3×D4—121no—
320C2×C3×D4—121no—
321C2×C3×D4—121no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—34no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—121no—
335C22×C3×C4—121no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C2×#67—22no—
341C2×#67—22no—
342C2×#67—41no—
343C2×#67—41no—
344C2×#67C2×Dic314yes—
345C2×#67C2×Dic314yescomplemented
346C22×Dic3—22no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—41no—
356C22×Dic3—41no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—62no—
362C22×Dic3—121no—
363C22×Dic3—121no—
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C2×D12—41no—
371C2×D12—41no—
372C2×D12C2×Dic314yescomplemented
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—62no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3C2×Dic314yescomplemented
379C3×C4⋊C4—34no—
380C3×C4⋊C4—62no—
381C3×C4⋊C4—121no—
382C3×C22⋊C4—24no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—121no—
385C3×C22⋊C4C4×D314yescomplemented
386C3×C22⋊C4C2×Dic314yescomplemented
387#217—41no—
388#217—62no—
389#217—62no—
390#217—62no—
391#217—62no—
392#217—62no—
393#217—122no—
394#217—121no—
395#217—121no—
396#217—121no—
397#217—121no—
398#217—121no—
399#217—121no—
400#217—122no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—121no—
405(C2×D3)⋊C4—121no—
406(C2×D3)⋊C4—121no—
407(C2×D3)⋊C4—121no—
408(C2×D3)⋊C4C2×Dic314yescomplemented
409C4⋊Dic3—22no—
410C4⋊Dic3—41no—
411C4⋊Dic3—62no—
412C4⋊Dic3—62no—
413C4⋊Dic3—62no—
414C4⋊Dic3—62no—
415C4⋊Dic3—122no—
416C4⋊Dic3—121no—
417Dic3⋊C4—62no—
418Dic3⋊C4—62no—
419Dic3⋊C4—121no—
420Dic3⋊C4C2×Dic314yescomplemented
421C4×Dic3—34no—
422C4×Dic3—34no—
423C4×Dic3—62no—
424C4×Dic3—62no—
425C4×Dic3—121no—
426C4×Dic3—121no—
427C4×Dic3—121no—
428C4×Dic3—121no—
429C4×Dic3—122no—
430C22×C32—22no—
431C22×C32—22no—
432C22×C32—22no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32C23×C411yescharacteristic
438C22×C32C22×D411yescharacteristic
439C22×C32C2×#4111yescharacteristic
440C22×C32H(5,𝔽2)11yescharacteristic
441C22×C32H(5,𝔽2)11yescharacteristic
442C22×C32H(5,𝔽2)11yescharacteristic
443C22×C322−1+411yescharacteristic
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—22no—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C32×C4—22no—
459C32×C4—22no—
460C3⋊Dic3—22no—
461C3⋊Dic3—41no—
462C3⋊Dic3—41no—
463C3⋊Dic3—41no—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—41no—
467C3×Dic3—41no—
468C3×Dic3—41no—
469C3×Dic3C4×D414yes—
470C22×D4—31no—
471C22×D4—31no—
472C22×D4—31no—
473C23×C4—31no—
474C23×C4—31no—
475C23×C4—91no—
476#121—38no—
477C4×D4—184no—
478#117—184no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—91no—
483C2×C4⋊C4—91no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4—91no—
486C2×C22⋊C4—31no—
487C2×C22⋊C4—31no—
488C2×C22⋊C4—91no—
489C2×C22⋊C4—91no—
490C2×C22⋊C4—91no—
491C2×C22⋊C4—91no—
492C2×C22⋊C4—91no—
493C2×C22⋊C4—91no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4D3211yescharacteristic
498C2×C42—91no—
499C2×C42—91no—
500C2×C42—91no—
501C2×C42—91no—
502#95—31no—
503#95—31no—
504#95—91no—
505#95—91no—
506#95—91no—
507#95—91no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—22no—
522C23×C3—32no—
523C23×C3—32no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3C2×C4×D312yes—
543C23×C3C22×Dic312yes—
544C23×C3C23×D311yescharacteristic
545C23×C3C23×D311yescharacteristic
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3C22×Dic312yes—
559C22×D3C22×Dic312yes—
560C3×D4—68no—
561C3×D4—124no—
562C3×D4—124no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—68no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—124no—
597C2×C3×C4C2×C4×D312yes—
598C2×C3×C4C2×C4×D312yes—
599C2×C3×C4C22×Dic312yes—
600C2×C3×C4C22×Dic312yes—
601#67—28no—
602#67—44no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—44no—
619C2×Dic3—62no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—62no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3—121no—
653C2×Dic3—124no—
654C2×Dic3D3×D412yes—
655C2×Dic3D3×D412yes—
656C2×Dic3#23712yes—
657C2×Dic3C22×Dic312yes—
658C2×Dic3C22×Dic312yes—
659D12—44no—
660C4×D3—28no—
661C4×D3—124no—
662C2×C32—42no—
663C2×C32C2×C4×D411yescharacteristic
664C2×C32#51811yescharacteristic
665C2×C32#52011yescharacteristic
666C2×C32#53511yescharacteristic
667C2×C32#53711yescharacteristic
668C2×C32#54011yescharacteristic
669C2×C32#54211yescharacteristic
670C3×D3—42no—
671C3×D3—42no—
672C24—31no—
673C24—31no—
674C24C2×D3211yescharacteristic
675C2×D4—34no—
676C2×D4—34no—
677C2×D4—34no—
678C2×D4—62no—
679C2×D4—62no—
680C2×D4—121no—
681C2×D4—121no—
682C2×D4—121no—
683C2×D4—121no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—34no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—91no—
698C22×C4—121no—
699C22×C4—121no—
700C22×C4—182no—
701C22×C4—361no—
702C22×C4—361no—
703C22×C4C2×D3211yescharacteristic
704C22×C4C2×D3211yescharacteristic
705C4⋊C4—34no—
706C4⋊C4—62no—
707C4⋊C4—121no—
708C4⋊C4—182no—
709C4⋊C4—182no—
710C4⋊C4—182no—
711C4⋊C4—361no—
712C22⋊C4—34no—
713C22⋊C4—121no—
714C22⋊C4—182no—
715C22⋊C4—182no—
716C22⋊C4—182no—
717C22⋊C4—182no—
718C22⋊C4—361no—
719C22⋊C4—361no—
720C22⋊C4—361no—
721C22⋊C4—361no—
722C22⋊C4—361no—
723C22⋊C4D3×Dic314yescomplemented
724C42—94no—
725C42—182no—
726C42—361no—
727C42—361no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—62no—
753C22×C3—62no—
754C22×C3—62no—
755C22×C3—62no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—81no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3C22×C4×D311yescharacteristic
771C22×C3C2×D3×D411yescharacteristic
772C22×C3C2×D3×D411yescharacteristic
773C22×C3C2×#23711yescharacteristic
774C22×C3#100411yescharacteristic
775C22×C3#100411yescharacteristic
776C22×C3#100411yescharacteristic
777C22×C3#100411yescharacteristic
778C22×C3#100711yescharacteristic
779C22×C3D3×#4111yescharacteristic
780C22×C3#100911yescharacteristic
781C22×C3#100911yescharacteristic
782C22×C3#101011yescharacteristic
783C22×C3C23×Dic311yescharacteristic
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—41no—
794C2×D3—41no—
795C2×D3—41no—
796C2×D3—41no—
797C2×D3—41no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—34no—
803C3×C4—42no—
804C3×C4—42no—
805C3×C4—62no—
806C3×C4—62no—
807C3×C4—121no—
808C3×C4—121no—
809C3×C4—121no—
810Dic3—22no—
811Dic3—22no—
812Dic3—41no—
813Dic3—41no—
814Dic3—41no—
815Dic3—62no—
816Dic3—62no—
817Dic3—122no—
818Dic3—122no—
819Dic3—121no—
820Dic3—121no—
821Dic3—121no—
822Dic3—121no—
823Dic3—121no—
824Dic3—121no—
825Dic3—241no—
826Dic3—241no—
827Dic3D4×Dic314yes—
828C32#232411yescharacteristic, complemented, Sylow
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—32no—
836C23—32no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23C2×D3×Dic312yes—
850C23C22×D3211yescharacteristic
851D4—68no—
852D4—124no—
853D4—124no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—68no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—92no—
878C2×C4—124no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—364no—
891C2×C4C2×D3×Dic312yes—
892C2×C4C2×D3×Dic312yes—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—42no—
901C2×C3—42no—
902C2×C3—82no—
903C2×C3—122no—
904C2×C3—122no—
905C2×C3#550411yescharacteristic
906C2×C3C4×D3×D411yescharacteristic
907C2×C3#554511yescharacteristic
908C2×C3#559211yescharacteristic
909C2×C3#560311yescharacteristic
910C2×C3#560711yescharacteristic
911C2×C3#560811yescharacteristic
912C2×C3#561911yescharacteristic
913C2×C3#562911yescharacteristic
914C2×C3#564011yescharacteristic
915C2×C3#566311yescharacteristic
916C2×C3C2×D4×Dic311yescharacteristic
917C2×C3#579811yescharacteristic
918C2×C3#582711yescharacteristic
919D3—42no—
920D3—42no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—62no—
932C22—62no—
933C22—62no—
934C22—121no—
935C22—121no—
936C22—121no—
937C22—121no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22#6429711yescharacteristic
943C22#6430711yescharacteristic
944C22D32×D411yescharacteristic
945C22D3×#23711yescharacteristic
946C22#6431311yescharacteristic
947C22#6431411yescharacteristic
948C22C22×D3×Dic311yescharacteristic
949C4—22no—
950C4—22no—
951C4—34no—
952C4—62no—
953C4—62no—
954C4—121no—
955C4—121no—
956C4—121no—
957C4—182no—
958C4—361no—
959C4—361no—
960C4—361no—
961C3—21no—
962C3#7438511yescharacteristic, complemented
963C3#8263311yescharacteristic, complemented
964C2—42no—
965C2—122no—
966C2—122no—
967C2#1059406911yescharacteristic
968C2#1059414911yescharacteristic
969C2#1059422111yescharacteristic
970C2#1059426911yescharacteristic
971C2#1059498611yescharacteristic
972C2D3×D4×Dic311yescharacteristic
973C2#1059521511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#884C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×#67C2semidirect
3. C2×#63841C2semidirect
4. #10592650C2semidirect
5. C3×#4950C2semidirect
6. #10591710C2semidirect
7. #10591707C2semidirect
8. #10591707C2semidirect
9. #10591377C2semidirect
10. #10591376C2semidirect
11. #10591323C2semidirect
12. #10591316C2semidirect
13. #10591295C2semidirect
14. #10591265C2semidirect
15. #10591241C2semidirect
34. C3×#884C4semidirect
82. #4950D3semidirect
101. C2×C3×#67C2×C4semidirect
113. C2×C3×D12C2×C4semidirect
116. C2×C3×C4×D3C2×C4semidirect
120. C32×C22⋊C4C2×C4semidirect
126. C3×(C2×D3)⋊C4C2×C4semidirect
129. C3×Dic3⋊C4C2×C4semidirect
142. Dic32D4semidirect
212. #884Dic3semidirect
345. C2×#67C2×Dic3semidirect
372. C2×D12C2×Dic3semidirect
378. C2×C4×D3C2×Dic3semidirect
385. C3×C22⋊C4C4×D3semidirect
386. C3×C22⋊C4C2×Dic3semidirect
408. (C2×D3)⋊C4C2×Dic3semidirect
420. Dic3⋊C4C2×Dic3semidirect
723. C22⋊C4D3×Dic3semidirect
828. C32#2324semidirect
962. C3#74385semidirect
963. C3#82633semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8842
C2×Dic3×#672
C2×#638412
#105926502
C3×#49502
#105917102
#105917072
#105913772
#105913762
#105913232
#105913162
#105912952
#105912652
#105912412
#826333
#743853