Finite Group Databasebeta

← #11803314

Subgroups — #11803314

Order 1152.

1759 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63923C211yesmaximal, characteristic
2C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#63881C211yesmaximal, characteristic, complemented
4#10592364C211yesmaximal, characteristic, complemented
5C3×#4669C211yesmaximal, characteristic, complemented
6C3×#4668C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591387C211yesmaximal, characteristic, complemented
9#10591384C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#10591320C211yesmaximal, characteristic, complemented
13#10591307C211yesmaximal, characteristic, complemented
14#10591258C211yesmaximal, characteristic, complemented
15#10591258C211yesmaximal, characteristic, complemented
16#75826—31nomaximal
17#74592—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic, complemented
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic, complemented
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic, complemented
46C2×Dic32C2211yescharacteristic, complemented
47#63923C418yescomplemented
48D3×(C2×D3)⋊C4—24no—
49#63881—24no—
50C32×#95C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C22×(C2×D3)⋊C4—31no—
57C2×#893—31no—
58C2×#882—31no—
59C2×#882—31no—
60C2×#67⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C3×#388—31no—
63C3×#385—31no—
64#5213—31no—
65#4990—31no—
66#4990—31no—
67#4990—31no—
68#4988—31no—
69#4988—31no—
70#4957—31no—
71#4956—31no—
72#4955—31no—
73#4955—31no—
74#4951—31no—
75Dic3×C22⋊C4—31no—
76#4939—31no—
77C4×(C2×D3)⋊C4—31no—
78#4669—31no—
79#4669—31no—
80#4669D311yescharacteristic, complemented
81#4668D311yescharacteristic, complemented
82#4665—31no—
83#4665—31no—
84#4665—31no—
85#4665—31no—
86#4665—61no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×D32—22no—
92C22×D32—22no—
93C22×D32—41no—
94C22×D32—41no—
95C22×D32—41no—
96C22×D32—41no—
97C22×D32C2×C414yescomplemented
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C2×C4⋊(C3⋊D3)—41no—
104C2×C4⋊(C3⋊D3)—41no—
105C2×C4⋊(C3⋊D3)C2×C414yescomplemented
106C2×C4×C3⋊D3—22no—
107C2×C4×C3⋊D3—41no—
108C2×C4×C3⋊D3—41no—
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3—41no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—41no—
121C2×#626—41no—
122C2×#626C2×C414yes—
123C2×#626C2×C414yescomplemented
124C2×D3×Dic3—41no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3D414yescomplemented
127#3752—22no—
128#3752—41no—
129#3752—41no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—41no—
133C3×(C2×D3)⋊C4C2×C414yescomplemented
134C3×(C2×D3)⋊C4C2×C414yescomplemented
135C3×C4⋊Dic3—41no—
136C3×Dic3⋊C4—22no—
137C3×Dic3⋊C4—41no—
138C3×C4×Dic3—41no—
139#3722—22no—
140#3722—22no—
141#3722—41no—
142#3722—41no—
143#3722C2×C414yescomplemented
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—41no—
147Dic32—22no—
148Dic32—41no—
149#2321—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C23×C3×C4—31no—
153C22×#67—31no—
154C22×#67—31no—
155C23×Dic3—31no—
156C22×D12—31no—
157C22×D12—31no—
158C22×D12—31no—
159C22×D12—31no—
160C22×D12—61no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—61no—
165C22×C4×D3C2×D311yescharacteristic
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C42—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
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)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—61no—
198C2×(C2×D3)⋊C4—61no—
199C2×(C2×D3)⋊C4—61no—
200C2×(C2×D3)⋊C4—64no—
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×C4⋊Dic3C2×D311yescharacteristic, complemented
207C2×Dic3⋊C4C2×D311yescharacteristic, complemented
208C2×Dic3⋊C4C2×D311yescharacteristic, complemented
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3C2×D311yescharacteristic, complemented
214#893—64no—
215#882—38no—
216#882—38no—
217#67⋊C4—64no—
218D3×C22⋊C4—64no—
219C3×#95—21no—
220C3×#95—31no—
221C3×#95—31no—
222C3×#95C2×D311yescharacteristic, complemented
223C3×#95C2×D311yescharacteristic, complemented
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—61no—
231C3⋊#95C2×D311yescharacteristic, complemented
232C3⋊#95C2×D311yescharacteristic, complemented
233C23×C32C2411yescharacteristic
234C22×C3⋊D3—21no—
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⋊D3C22×C412yes—
247C22×C3⋊D3C22×C412yes—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C22×C412yes—
259C22×C3×D3C22×C412yes—
260C22×C3×D3C2×D412yes—
261C22×C3×D3#4112yes—
262C2×D32—28no—
263C2×D32—44no—
264C2×D32—44no—
265C2×D32—44no—
266C2×D32—44no—
267C2×D32—44no—
268C2×D32—44no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C22×C412yes—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3C2×D412yes—
284C4⋊(C3⋊D3)—44no—
285C4×C3⋊D3—44no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3C22×C412yes—
302C2×C3×Dic3C22×C412yes—
303C2×C3×Dic3C2×D412yes—
304C3×C4×D3—44no—
305#626—28no—
306#626—44no—
307D3×Dic3—44no—
308C2×#120—91no—
309C2×C4×D4—91no—
310C22×C22⋊C4—91no—
311#390—91no—
312#390—91no—
313#388—31no—
314#388—91no—
315#388—91no—
316#388—91no—
317#386—91no—
318#386—91no—
319#386—91no—
320#385—31no—
321#379—91no—
322C4×C22⋊C4—91no—
323C24×C3—31no—
324C24×C3—31no—
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—31no—
328C23×D3—31no—
329C23×D3—34no—
330C23×D3—34no—
331C23×D3—61no—
332C23×D3—61no—
333C23×D3—62no—
334C23×D3—62no—
335C23×D3—62no—
336C23×D3—62no—
337C23×D3—121no—
338C23×D3—121no—
339C23×D3—121no—
340C23×D3—121no—
341C23×D3—121no—
342C23×D3—121no—
343C23×D3—121no—
344C23×D3—121no—
345C23×D3C22×D311yescharacteristic
346C23×D3C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—62no—
357C22×C3×C4—121no—
358C22×C3×C4—121no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—121no—
370C2×#67—121no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—34no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—121no—
379C22×Dic3—121no—
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C2×D12—34no—
387C2×D12—34no—
388C2×D12—34no—
389C2×D12—34no—
390C2×D12—64no—
391C2×D12—62no—
392C2×D12—62no—
393C2×D12—121no—
394C2×D12—121no—
395C2×D12—121no—
396C2×D12—121no—
397C2×D12—122no—
398C2×D12—122no—
399C2×D12—121no—
400C2×D12—121no—
401C2×C4×D3—22no—
402C2×C4×D3—34no—
403C2×C4×D3—41no—
404C2×C4×D3—41no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—122no—
408C2×C4×D3—121no—
409C2×C4×D3—121no—
410C2×C4×D3—121no—
411C2×C4×D3—121no—
412C2×C4×D3—121no—
413C2×C4×D3—121no—
414C2×C4×D3—122no—
415C2×C4×D3—122no—
416C3×C4⋊C4—62no—
417C3×C4⋊C4—121no—
418C3×C4⋊C4—121no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—34no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—121no—
424C3×C42—121no—
425#217—62no—
426#217—62no—
427#217—121no—
428(C2×D3)⋊C4—22no—
429(C2×D3)⋊C4—22no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—41no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—122no—
442(C2×D3)⋊C4—121no—
443(C2×D3)⋊C4—121no—
444(C2×D3)⋊C4—121no—
445(C2×D3)⋊C4—121no—
446(C2×D3)⋊C4—121no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4—122no—
452(C2×D3)⋊C4—122no—
453(C2×D3)⋊C4C4×D314yescomplemented
454(C2×D3)⋊C4C4×D314yescomplemented
455C4⋊Dic3—41no—
456Dic3⋊C4—22no—
457Dic3⋊C4—41no—
458C4×Dic3—41no—
459C4×Dic3—62no—
460C4×Dic3—62no—
461C4×Dic3—121no—
462C4×Dic3—121no—
463C22×C32C23×C411yescharacteristic
464C22×C32C22×D411yescharacteristic
465C22×C32C2×#4111yescharacteristic
466C22×C32H(5,𝔽2)11yescharacteristic
467C22×C32H(5,𝔽2)11yescharacteristic
468C22×C32H(5,𝔽2)11yescharacteristic
469C22×C32H(5,𝔽2)11yescharacteristic
470C2×C3⋊D3—22no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—41no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3C4×D414yes—
498D32—416no—
499C32×C4—22no—
500C32×C4—41no—
501C32×C4—41no—
502C3⋊Dic3—22no—
503C3⋊Dic3—41no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C25—91no—
511C22×D4—91no—
512C22×D4—91no—
513C22×D4—91no—
514C23×C4—31no—
515C23×C4—91no—
516C23×C4—91no—
517#120—98no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—184no—
539C2×C42—31no—
540C2×C42—91no—
541C2×C42—91no—
542#95—31no—
543#95—31no—
544#95—91no—
545#95—91no—
546#95—91no—
547#95D3211yescharacteristic, complemented
548C23×C3—21no—
549C23×C3—32no—
550C23×C3—32no—
551C23×C3—32no—
552C23×C3—32no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3C23×D311yescharacteristic
564C23×C3C23×D311yescharacteristic
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—32no—
576C22×D3—32no—
577C22×D3—32no—
578C22×D3—32no—
579C22×D3—62no—
580C22×D3—62no—
581C22×D3—68no—
582C22×D3—62no—
583C22×D3—62no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—68no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3—121no—
616C22×D3—121no—
617C22×D3—121no—
618C22×D3—121no—
619C22×D3—124no—
620C22×D3—124no—
621C22×D3—124no—
622C22×D3—124no—
623C22×D3—124no—
624C22×D3—124no—
625C22×D3—124no—
626C22×D3—124no—
627C22×D3—124no—
628C22×D3—124no—
629C22×D3—124no—
630C22×D3—124no—
631C22×D3C2×C4×D312yes—
632C22×D3C2×C4×D312yes—
633C22×D3D3×D412yes—
634C22×D3#23912yes—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—22no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—22no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—124no—
679C2×C3×C4C2×C4×D312yes—
680C2×C3×C4C2×C4×D312yes—
681#67—68no—
682#67—124no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—62no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—124no—
717C2×Dic3C2×C4×D312yes—
718C2×Dic3C2×C4×D312yes—
719C2×Dic3D3×D412yes—
720D12—68no—
721D12—124no—
722D12—124no—
723D12—128no—
724D12—124no—
725C4×D3—44no—
726C4×D3—124no—
727C4×D3—124no—
728C4×D3—124no—
729C4×D3—128no—
730C2×C32C2×C4×D411yescharacteristic
731C2×C32#51811yescharacteristic
732C2×C32#51811yescharacteristic
733C2×C32#53411yescharacteristic
734C2×C32#53511yescharacteristic
735C2×C32#53811yescharacteristic
736C2×C32#53811yescharacteristic
737C3⋊D3—42no—
738C3⋊D3—42no—
739C3×D3—24no—
740C3×D3—42no—
741C24—31no—
742C24—31no—
743C24—94no—
744C24—91no—
745C24—91no—
746C24—182no—
747C24—182no—
748C24—361no—
749C24—361no—
750C24—361no—
751C24—361no—
752C2×D4—94no—
753C2×D4—94no—
754C2×D4—94no—
755C2×D4—182no—
756C2×D4—182no—
757C2×D4—361no—
758C2×D4—361no—
759C2×D4—361no—
760C2×D4—361no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—62no—
768C22×C4—94no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—121no—
772C22×C4—121no—
773C22×C4—182no—
774C22×C4—361no—
775C22×C4—361no—
776C22×C4—361no—
777C22×C4—361no—
778C22×C4C2×D3211yescharacteristic
779C22×C4C2×D3211yescharacteristic
780C22×C4C2×D3211yescharacteristic
781C4⋊C4—62no—
782C4⋊C4—121no—
783C4⋊C4—121no—
784C22⋊C4—34no—
785C22⋊C4—34no—
786C22⋊C4—62no—
787C22⋊C4—62no—
788C22⋊C4—94no—
789C22⋊C4—121no—
790C22⋊C4—182no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—182no—
795C22⋊C4—361no—
796C22⋊C4—361no—
797C22⋊C4—361no—
798C22⋊C4—361no—
799C22⋊C4—361no—
800C42—121no—
801C42—182no—
802C42—361no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—34no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3C22×C4×D311yescharacteristic
825C22×C3C22×C4×D311yescharacteristic
826C22×C3C2×D3×D411yescharacteristic
827C22×C3C2×D3×D411yescharacteristic
828C22×C3#100411yescharacteristic
829C22×C3#100411yescharacteristic
830C22×C3#100411yescharacteristic
831C22×C3C2×#23911yescharacteristic
832C22×C3D3×#4111yescharacteristic
833C22×C3#100911yescharacteristic
834C22×C3#100911yescharacteristic
835C22×C3#100911yescharacteristic
836C22×C3#100911yescharacteristic
837C22×C3#100911yescharacteristic
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—41no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—64no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—122no—
865C2×D3—122no—
866C2×D3—122no—
867C2×D3—122no—
868C2×D3—122no—
869C2×D3—1216no—
870C2×D3—1216no—
871C2×D3—122no—
872C2×D3—122no—
873C2×D3—122no—
874C2×D3—122no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—241no—
892C2×D3—241no—
893C2×D3—241no—
894C2×D3—241no—
895C2×D3#89314yes—
896C3×C4—22no—
897C3×C4—22no—
898C3×C4—42no—
899C3×C4—42no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—62no—
905C3×C4—62no—
906C3×C4—62no—
907C3×C4—81no—
908C3×C4—121no—
909C3×C4—121no—
910C3×C4—121no—
911Dic3—22no—
912Dic3—22no—
913Dic3—22no—
914Dic3—41no—
915Dic3—41no—
916Dic3—41no—
917Dic3—62no—
918Dic3—62no—
919Dic3—122no—
920Dic3—121no—
921Dic3—121no—
922Dic3—241no—
923C32#232111yescharacteristic, complemented, Sylow
924C23—32no—
925C23—32no—
926C23—32no—
927C23—32no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—92no—
939C23—92no—
940C23—188no—
941C23—181no—
942C23—181no—
943C23—181no—
944C23—181no—
945C23—181no—
946C23—181no—
947C23—181no—
948C23—181no—
949C23—181no—
950C23—181no—
951C23—181no—
952C23—181no—
953C23—364no—
954C23—364no—
955C23—364no—
956C23—364no—
957C23—364no—
958C23—364no—
959C23C22×D3211yescharacteristic
960D4—188no—
961D4—364no—
962D4—364no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—32no—
972C2×C4—32no—
973C2×C4—32no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—92no—
990C2×C4—124no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—364no—
997C2×C4—364no—
998C2×C4C4×D3212yes—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—64no—
1007C2×C3—122no—
1008C2×C3C2×#89311yescharacteristic
1009C2×C3#552111yescharacteristic
1010C2×C3C4×D3×D411yescharacteristic
1011C2×C3#554511yescharacteristic
1012C2×C3#554511yescharacteristic
1013C2×C3#554511yescharacteristic
1014C2×C3#559211yescharacteristic
1015C2×C3#560511yescharacteristic
1016C2×C3#564411yescharacteristic
1017C2×C3#564411yescharacteristic
1018C2×C3#565311yescharacteristic
1019C2×C3#565711yescharacteristic
1020C2×C3#567411yescharacteristic
1021C2×C3#570411yescharacteristic
1022D3—24no—
1023D3—42no—
1024D3—124no—
1025D3—122no—
1026D3—122no—
1027D3—122no—
1028D3—122no—
1029D3—242no—
1030C22—34no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—62no—
1036C22—62no—
1037C22—62no—
1038C22—62no—
1039C22—62no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22—182no—
1045C22—182no—
1046C22—182no—
1047C22—182no—
1048C22—182no—
1049C22—182no—
1050C22—3616no—
1051C22—361no—
1052C22—361no—
1053C22—361no—
1054C22—361no—
1055C22—361no—
1056C22—361no—
1057C22—361no—
1058C22—361no—
1059C22C2×C4×D3211yescharacteristic
1060C22#6430711yescharacteristic
1061C22#6430811yescharacteristic
1062C22D32×D411yescharacteristic
1063C22#6431411yescharacteristic
1064C22#6431411yescharacteristic
1065C22D3×#23911yescharacteristic
1066C4—22no—
1067C4—41no—
1068C4—41no—
1069C4—62no—
1070C4—62no—
1071C4—62no—
1072C4—121no—
1073C4—121no—
1074C4—121no—
1075C4—182no—
1076C4—361no—
1077C3—21no—
1078C3#7459211yescharacteristic, complemented
1079C3#7582611yescharacteristic, complemented
1080C2—64no—
1081C2—122no—
1082C2—362no—
1083C2—362no—
1084C2#1059399411yescharacteristic
1085C2#1059425611yescharacteristic
1086C2#1059426411yescharacteristic
1087C2#1059427011yescharacteristic
1088C2D3×#89311yescharacteristic
1089C2#1059465011yescharacteristic
1090C2#1059465211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63923C2
hypercenter#95D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×D3×(C2×D3)⋊C4C2semidirect
3. C2×#63881C2semidirect
4. #10592364C2semidirect
5. C3×#4669C2semidirect
6. C3×#4668C2semidirect
7. #10591399C2semidirect
8. #10591387C2semidirect
9. #10591384C2semidirect
10. #10591382C2semidirect
11. Dic3×(C2×D3)⋊C4C2semidirect
12. #10591320C2semidirect
13. #10591307C2semidirect
14. #10591258C2semidirect
15. #10591258C2semidirect
20. C22×C4×C3⋊D3C22semidirect
27. C2×#3752C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×Dic3⋊C4C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×C4×Dic3C22semidirect
40. C2×#3722C22semidirect
41. C2×#3722C22semidirect
45. C2×Dic32C22semidirect
46. C2×Dic32C22semidirect
47. #63923C4semidirect
50. C32×#95C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
80. #4669D3semidirect
81. #4668D3semidirect
97. C22×D32C2×C4semidirect
105. C2×C4⋊(C3⋊D3)C2×C4semidirect
123. C2×#626C2×C4semidirect
126. C2×D3×Dic3D4semidirect
133. C3×(C2×D3)⋊C4C2×C4semidirect
134. C3×(C2×D3)⋊C4C2×C4semidirect
143. #3722C2×C4semidirect
206. C2×C4⋊Dic3C2×D3semidirect
207. C2×Dic3⋊C4C2×D3semidirect
208. C2×Dic3⋊C4C2×D3semidirect
213. C2×C4×Dic3C2×D3semidirect
222. C3×#95C2×D3semidirect
223. C3×#95C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
453. (C2×D3)⋊C4C4×D3semidirect
454. (C2×D3)⋊C4C4×D3semidirect
547. #95D32semidirect
923. C32#2321semidirect
1078. C3#74592semidirect
1079. C3#75826semidirect

Maximal subgroups

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

subgroupindex
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#638812
#105923642
C3×#46692
C3×#46682
#105913992
#105913872
#105913842
#105913822
Dic3×(C2×D3)⋊C42
#105913202
#105913072
#105912582
#758263
#745923