Finite Group Databasebeta

← #11803313

Subgroups — #11803313

Order 1152.

1733 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63922C211yesmaximal, characteristic
2C2×#63921C211yesmaximal, characteristic, complemented
3C2×#63904C211yesmaximal, characteristic, complemented
4#10592367C211yesmaximal, characteristic, complemented
5C3×#4669C211yesmaximal, characteristic, complemented
6C3×#4665C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591387C211yesmaximal, characteristic, complemented
9#10591386C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591318C211yesmaximal, characteristic, complemented
12#10591316C211yesmaximal, characteristic, complemented
13#10591285C211yesmaximal, characteristic, complemented
14#10591281C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16#75826—31nomaximal
17#74876—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic, complemented
22C22×#626C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
28C2×#3750C2211yescharacteristic, complemented
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37C2×#3722C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
45C2×Dic32C2211yescharacteristic, complemented
46C2×Dic32C2211yescharacteristic, complemented
47#63922C418yescomplemented
48#63921—24no—
49#63904—24no—
50C32×#95C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×#937—31no—
57C2×C4×#67—31no—
58C2×#893—31no—
59C2×#882—31no—
60C2×D3×C22⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C3×#388—31no—
63C3×#386—31no—
64#5221—31no—
65#5213—31no—
66#4990—31no—
67#4957—31no—
68#4957—31no—
69#4956—31no—
70#4956—31no—
71#4955—31no—
72#4955—31no—
73#4951—31no—
74#4944—31no—
75#4944—31no—
76#4939—31no—
77C4×(C2×D3)⋊C4—31no—
78#4670—31no—
79#4669—31no—
80#4669D311yescharacteristic, complemented
81#4668—31no—
82#4668—31no—
83#4668—61no—
84#4666—31no—
85#4665—31no—
86#4665D311yescharacteristic, complemented
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
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3—41no—
106C2×C4×C3⋊D3—41no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×D12—41no—
113C2×C3×D12—41no—
114C2×C3×D12C2×C414yescomplemented
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3—41no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626C2×C414yes—
121C2×#625—41no—
122C2×#625—41no—
123C2×#625C2×C414yescomplemented
124C2×#624—41no—
125C2×#624—41no—
126C2×#624D414yescomplemented
127#3752—22no—
128#3752C2×C414yescomplemented
129C4⋊(C3⋊Dic3)—41no—
130#3750—41no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—41no—
134C3×(C2×D3)⋊C4—41no—
135C3×(C2×D3)⋊C4—41no—
136C3×(C2×D3)⋊C4C2×C414yescomplemented
137C3×Dic3⋊C4—22no—
138C3×C4×Dic3—41no—
139#3722—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—41no—
144(C2×D3)⋊Dic3—41no—
145(C2×D3)⋊Dic3—41no—
146(C2×D3)⋊Dic3C2×C414yescomplemented
147Dic32—22no—
148Dic32—41no—
149#2321—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C22×C3×D4—31no—
153C23×C3×C4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×D12—31no—
158C22×D12C2×D311yescharacteristic
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—61no—
164C22×C4×D3C2×D311yescharacteristic, complemented
165C2×C3×C4⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C42—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180#937—38no—
181C4×#67—64no—
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—61no—
196C2×(C2×D3)⋊C4—61no—
197C2×(C2×D3)⋊C4C2×D311yescharacteristic
198C2×(C2×D3)⋊C4C2×D311yescharacteristic
199C2×(C2×D3)⋊C4C2×D311yescharacteristic
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
203C2×C4⋊Dic3—31no—
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—61no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—61no—
209C2×Dic3⋊C4C2×D311yescharacteristic, complemented
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3C2×D311yescharacteristic, complemented
215#893—64no—
216#882—38no—
217D3×C22⋊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⋊D3C22×C412yes—
239C22×C3⋊D3C2×D412yes—
240C22×C3⋊D3#4112yes—
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×D3—21no—
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×D3—21no—
259C22×C3×D3C22×C412yes—
260C22×C3×D3C22×C412yes—
261C22×C3×D3C22×C412yes—
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⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3C22×C412yes—
287C4×C3⋊D3—44no—
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×Dic3C22×C412yes—
301C2×C3×Dic3C2×D412yes—
302C2×C3×Dic3C2×D412yes—
303C3×D12—44no—
304C3×C4×D3—44no—
305#626—28no—
306#625—44no—
307#624—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—31no—
318#386—91no—
319#386—91no—
320#385—91no—
321#379—91no—
322C4×C22⋊C4—91no—
323C24×C3—31no—
324C24×C3—31no—
325C24×C3—31no—
326C23×D3—31no—
327C23×D3—31no—
328C23×D3—34no—
329C23×D3—34no—
330C23×D3—61no—
331C23×D3—62no—
332C23×D3—62no—
333C23×D3—62no—
334C23×D3—62no—
335C23×D3—121no—
336C23×D3—121no—
337C23×D3—121no—
338C23×D3—121no—
339C23×D3—121no—
340C23×D3—121no—
341C23×D3—121no—
342C23×D3—121no—
343C23×D3C22×D311yescharacteristic
344C23×D3C22×D311yescharacteristic
345C23×D3C22×D311yescharacteristic
346C2×C3×D4—34no—
347C2×C3×D4—121no—
348C2×C3×D4—121no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—62no—
358C22×C3×C4—121no—
359C22×C3×C4—121no—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C2×#67—34no—
367C2×#67—34no—
368C2×#67—34no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—121no—
372C2×#67—121no—
373C2×#67—121no—
374C2×#67—121no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C2×D12—34no—
390C2×D12—41no—
391C2×D12—41no—
392C2×D12—62no—
393C2×D12—62no—
394C2×D12C4×D314yescomplemented
395C2×C4×D3—22no—
396C2×C4×D3—34no—
397C2×C4×D3—34no—
398C2×C4×D3—41no—
399C2×C4×D3—41no—
400C2×C4×D3—62no—
401C2×C4×D3—62no—
402C2×C4×D3—122no—
403C2×C4×D3—121no—
404C2×C4×D3—121no—
405C2×C4×D3—121no—
406C2×C4×D3—121no—
407C2×C4×D3—121no—
408C2×C4×D3—121no—
409C2×C4×D3—121no—
410C2×C4×D3—121no—
411C2×C4×D3—122no—
412C2×C4×D3—122no—
413C3×C4⋊C4—62no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—62no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—121no—
418C3×C22⋊C4—121no—
419C3×C22⋊C4—121no—
420C3×C42—121no—
421#217—34no—
422#217—62no—
423#217—62no—
424#217—62no—
425#217—121no—
426#217—121no—
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—34no—
433(C2×D3)⋊C4—41no—
434(C2×D3)⋊C4—41no—
435(C2×D3)⋊C4—41no—
436(C2×D3)⋊C4—64no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—122no—
445(C2×D3)⋊C4—121no—
446(C2×D3)⋊C4—121no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4C4×D314yescomplemented
449C4⋊Dic3—121no—
450C4⋊Dic3—121no—
451C4⋊Dic3—122no—
452Dic3⋊C4—22no—
453Dic3⋊C4—121no—
454Dic3⋊C4—121no—
455Dic3⋊C4—122no—
456C4×Dic3—41no—
457C4×Dic3—62no—
458C4×Dic3—62no—
459C4×Dic3—121no—
460C4×Dic3—121no—
461C22×C32C23×C411yescharacteristic
462C22×C32C22×D411yescharacteristic
463C22×C32C2×#4111yescharacteristic
464C22×C32H(5,𝔽2)11yescharacteristic
465C22×C32H(5,𝔽2)11yescharacteristic
466C22×C32H(5,𝔽2)11yescharacteristic
467C22×C32H(5,𝔽2)11yescharacteristic
468C2×C3⋊D3—22no—
469C2×C3⋊D3—22no—
470C2×C3⋊D3—22no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3C4×D414yes—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496D32—416no—
497C32×C4—22no—
498C32×C4—41no—
499C32×C4—41no—
500C3⋊Dic3—22no—
501C3⋊Dic3—41no—
502C3⋊Dic3—41no—
503C3×Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C25—91no—
509C22×D4—31no—
510C22×D4—91no—
511C22×D4—91no—
512C23×C4—31no—
513C23×C4—91no—
514C23×C4—91no—
515#120—98no—
516C4×D4—184no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—91no—
519C2×C4⋊C4—91no—
520C2×C22⋊C4—31no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—91no—
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—184no—
537C2×C42—31no—
538C2×C42—91no—
539C2×C42—91no—
540#95—31no—
541#95—31no—
542#95—91no—
543#95—91no—
544#95—91no—
545#95D3211yescharacteristic, complemented
546C23×C3—21no—
547C23×C3—32no—
548C23×C3—32no—
549C23×C3—32no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
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×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3C23×D311yescharacteristic
569C23×C3C23×D311yescharacteristic
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—32no—
589C22×D3—32no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—32no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—68no—
598C22×D3—68no—
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—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—124no—
612C22×D3—124no—
613C22×D3—124no—
614C22×D3—124no—
615C22×D3—124no—
616C22×D3—124no—
617C22×D3—124no—
618C22×D3—124no—
619C22×D3—124no—
620C22×D3—124no—
621C22×D3—124no—
622C22×D3—124no—
623C22×D3C2×C4×D312yes—
624C22×D3C2×C4×D312yes—
625C22×D3C2×C4×D312yes—
626C3×D4—124no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—22no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—22no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—124no—
668C2×C3×C4C2×C4×D312yes—
669C2×C3×C4C2×C4×D312yes—
670#67—68no—
671#67—124no—
672#67—124no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—62no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—62no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—121no—
706C2×Dic3—121no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3C2×C4×D312yes—
713C2×Dic3D3×D412yes—
714C2×Dic3D3×D412yes—
715D12—44no—
716D12—68no—
717C4×D3—44no—
718C4×D3—124no—
719C4×D3—124no—
720C4×D3—124no—
721C4×D3—124no—
722C4×D3—128no—
723C2×C32C2×C4×D411yescharacteristic
724C2×C32#51811yescharacteristic
725C2×C32#51811yescharacteristic
726C2×C32#53411yescharacteristic
727C2×C32#53511yescharacteristic
728C2×C32#53811yescharacteristic
729C2×C32#53811yescharacteristic
730C3⋊D3—24no—
731C3×D3—42no—
732C3×D3—42no—
733C3×D3—42no—
734C24—31no—
735C24—31no—
736C24—31no—
737C24—94no—
738C24—91no—
739C24—182no—
740C24—182no—
741C24—361no—
742C24—361no—
743C24—361no—
744C24—361no—
745C2×D4—34no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—121no—
749C2×D4—121no—
750C2×D4—182no—
751C2×D4—182no—
752C2×D4—361no—
753C2×D4—361no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—62no—
760C22×C4—94no—
761C22×C4—91no—
762C22×C4—91no—
763C22×C4—91no—
764C22×C4—121no—
765C22×C4—121no—
766C22×C4—182no—
767C22×C4—361no—
768C22×C4—361no—
769C22×C4—361no—
770C22×C4—361no—
771C22×C4C2×D3211yescharacteristic
772C22×C4C2×D3211yescharacteristic
773C22×C4C2×D3211yescharacteristic
774C4⋊C4—62no—
775C4⋊C4—361no—
776C4⋊C4—361no—
777C22⋊C4—34no—
778C22⋊C4—62no—
779C22⋊C4—62no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—121no—
783C22⋊C4—121no—
784C22⋊C4—121no—
785C22⋊C4—182no—
786C22⋊C4—182no—
787C22⋊C4—182no—
788C22⋊C4—182no—
789C22⋊C4—182no—
790C22⋊C4—361no—
791C22⋊C4—361no—
792C22⋊C4—361no—
793C42—121no—
794C42—182no—
795C42—361no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3—121no—
816C22×C3—121no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
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×C3#100411yescharacteristic
832C22×C3D3×#4111yescharacteristic
833C22×C3D3×#4111yescharacteristic
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—34no—
848C2×D3—34no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—64no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—122no—
875C2×D3—122no—
876C2×D3—122no—
877C2×D3—122no—
878C2×D3—122no—
879C2×D3—122no—
880C2×D3—1216no—
881C2×D3—1216no—
882C3×C4—22no—
883C3×C4—22no—
884C3×C4—42no—
885C3×C4—42no—
886C3×C4—41no—
887C3×C4—41no—
888C3×C4—41no—
889C3×C4—41no—
890C3×C4—62no—
891C3×C4—62no—
892C3×C4—62no—
893C3×C4—81no—
894C3×C4—121no—
895C3×C4—121no—
896Dic3—22no—
897Dic3—22no—
898Dic3—22no—
899Dic3—41no—
900Dic3—41no—
901Dic3—62no—
902Dic3—62no—
903Dic3—122no—
904Dic3—122no—
905Dic3—121no—
906Dic3—121no—
907Dic3—121no—
908Dic3—121no—
909Dic3—241no—
910C32#232111yescharacteristic, complemented, Sylow
911C23—32no—
912C23—32no—
913C23—32no—
914C23—61no—
915C23—61no—
916C23—61no—
917C23—61no—
918C23—61no—
919C23—61no—
920C23—61no—
921C23—61no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—92no—
933C23—92no—
934C23—92no—
935C23—188no—
936C23—181no—
937C23—181no—
938C23—181no—
939C23—181no—
940C23—364no—
941C23—364no—
942C23—364no—
943C23—364no—
944C23—364no—
945C23—364no—
946C23C22×D3211yescharacteristic
947D4—124no—
948D4—188no—
949D4—364no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—92no—
974C2×C4—124no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—181no—
982C2×C4—181no—
983C2×C4—364no—
984C2×C4—364no—
985C2×C4C4×D3212yes—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—122no—
994C2×C3—122no—
995C2×C3—122no—
996C2×C3#548611yescharacteristic
997C2×C3#552111yescharacteristic
998C2×C3C4×D3×D411yescharacteristic
999C2×C3C4×D3×D411yescharacteristic
1000C2×C3#554511yescharacteristic
1001C2×C3#554511yescharacteristic
1002C2×C3#558911yescharacteristic
1003C2×C3#560511yescharacteristic
1004C2×C3#560711yescharacteristic
1005C2×C3#561311yescharacteristic
1006C2×C3#565711yescharacteristic
1007C2×C3#565711yescharacteristic
1008C2×C3#567411yescharacteristic
1009C2×C3#570411yescharacteristic
1010D3—42no—
1011D3—42no—
1012D3—42no—
1013D3—64no—
1014D3—64no—
1015D3—124no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—94no—
1026C22—121no—
1027C22—121no—
1028C22—121no—
1029C22—121no—
1030C22—121no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—121no—
1036C22—121no—
1037C22—121no—
1038C22—182no—
1039C22—182no—
1040C22—182no—
1041C22—182no—
1042C22—182no—
1043C22—182no—
1044C22—3616no—
1045C22C2×C4×D3211yescharacteristic
1046C22#6430711yescharacteristic
1047C22#6430811yescharacteristic
1048C22D32×D411yescharacteristic
1049C22#6431311yescharacteristic
1050C22#6431411yescharacteristic
1051C22#6431911yescharacteristic
1052C4—22no—
1053C4—41no—
1054C4—41no—
1055C4—62no—
1056C4—62no—
1057C4—62no—
1058C4—121no—
1059C4—121no—
1060C4—182no—
1061C4—361no—
1062C4—361no—
1063C3—21no—
1064C3#7487611yescharacteristic, complemented
1065C3#7582611yescharacteristic, complemented
1066C2—122no—
1067C2—122no—
1068C2—122no—
1069C2—184no—
1070C2#1059399411yescharacteristic
1071C2#1059425411yescharacteristic
1072C2#1059426311yescharacteristic
1073C2#1059428711yescharacteristic
1074C2#1059460511yescharacteristic
1075C2#1059465911yescharacteristic
1076C2#1059466011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63922C2
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×#63921C2semidirect
3. C2×#63904C2semidirect
4. #10592367C2semidirect
5. C3×#4669C2semidirect
6. C3×#4665C2semidirect
7. #10591399C2semidirect
8. #10591387C2semidirect
9. #10591386C2semidirect
10. #10591381C2semidirect
11. #10591318C2semidirect
12. #10591316C2semidirect
13. #10591285C2semidirect
14. #10591281C2semidirect
15. #10591233C2semidirect
21. C22×C3×C4×D3C22semidirect
27. C2×C4⋊(C3⋊Dic3)C22semidirect
28. C2×#3750C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×C4×Dic3C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×Dic32C22semidirect
46. C2×Dic32C22semidirect
47. #63922C4semidirect
50. C32×#95C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
80. #4669D3semidirect
86. #4665D3semidirect
97. C22×D32C2×C4semidirect
114. C2×C3×D12C2×C4semidirect
123. C2×#625C2×C4semidirect
126. C2×#624D4semidirect
128. #3752C2×C4semidirect
136. C3×(C2×D3)⋊C4C2×C4semidirect
146. (C2×D3)⋊Dic3C2×C4semidirect
164. C22×C4×D3C2×D3semidirect
202. C2×(C2×D3)⋊C4C2×D3semidirect
209. C2×Dic3⋊C4C2×D3semidirect
214. C2×C4×Dic3C2×D3semidirect
222. C3×#95C2×D3semidirect
223. C3×#95C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
394. C2×D12C4×D3semidirect
448. (C2×D3)⋊C4C4×D3semidirect
545. #95D32semidirect
910. C32#2321semidirect
1064. C3#74876semidirect
1065. C3#75826semidirect

Maximal subgroups

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

subgroupindex
C2×#639222
C2×#639212
C2×#639042
#105923672
C3×#46692
C3×#46652
#105913992
#105913872
#105913862
#105913812
#105913182
#105913162
#105912852
#105912812
#105912332
#758263
#748763