Finite Group Databasebeta

← #11803269

Subgroups — #11803269

Order 1152.

1745 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×#63881C211yesmaximal, characteristic, complemented
4C4×#3752C211yesmaximal, characteristic, complemented
5C3×#4940C211yesmaximal, characteristic, complemented
6C3×#4939C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591385C211yesmaximal, characteristic, complemented
9#10591378C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591363C211yesmaximal, characteristic, complemented
12#10591307C211yesmaximal, characteristic, complemented
13#10591283C211yesmaximal, characteristic, complemented
14#10591282C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#76429—31nomaximal
17#75826—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×C32×C42C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic, 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×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×#3724C2211yescharacteristic, complemented
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
46C2×Dic32C2211yescharacteristic, complemented
47#63922C418yescomplemented
48#63921—24no—
49#63881—24no—
50#63658C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×#937—31no—
57C2×#893—31no—
58C2×#882—31no—
59C2×#67⋊C4—31no—
60C2×D3×C22⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C3×#390—31no—
63C3×#388—31no—
64#5220—31no—
65#4990—31no—
66#4990—31no—
67#4989—31no—
68#4958—31no—
69#4957—31no—
70#4957—31no—
71#4956—31no—
72#4956—31no—
73#4955—31no—
74#4955—31no—
75#4951—31no—
76#4945—31no—
77#4945—31no—
78#4940D311yescharacteristic, complemented
79#4939D311yescharacteristic, complemented
80C4×(C2×D3)⋊C4—31no—
81C4×(C2×D3)⋊C4—31no—
82C4×(C2×D3)⋊C4—61no—
83#4669—31no—
84#4668—31no—
85#4665—31no—
86#4665—31no—
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—41no—
105C2×C4×C3⋊D3—41no—
106C2×C4×C3⋊D3D414yescomplemented
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×#626—22no—
116C2×#626—22no—
117C2×#626C2×C414yes—
118C2×#625—41no—
119C2×#625—41no—
120C2×#625C2×C414yescomplemented
121C2×#624—22no—
122C2×#624—41no—
123C2×#624—41no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3—41no—
127C32×C42—41no—
128#3752—22no—
129#3752C2×C414yescomplemented
130C4×C3⋊Dic3—41no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—41no—
135C3×(C2×D3)⋊C4—41no—
136C3×(C2×D3)⋊C4—41no—
137C3×(C2×D3)⋊C4C2×C414yescomplemented
138C3×C4⋊Dic3—41no—
139C3×Dic3⋊C4—22no—
140#3724—41no—
141#3722—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—41no—
145(C2×D3)⋊Dic3—41no—
146(C2×D3)⋊Dic3—41no—
147(C2×D3)⋊Dic3C2×C414yescomplemented
148Dic32—22no—
149#2321—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C22×C3×D4—31no—
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—31no—
156C23×Dic3—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—31no—
164C22×C4×D3—61no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊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×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C42—21no—
175C2×C3×C42C2×D311yescharacteristic, complemented
176C2×C3×C42C2×D311yescharacteristic, complemented
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183#937—38no—
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—61no—
197C2×(C2×D3)⋊C4—61no—
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
203C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
204C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
205C2×C4⋊Dic3C2×D311yescharacteristic, complemented
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4C2×D311yescharacteristic, complemented
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—61no—
214#893—64no—
215#882—38no—
216#67⋊C4—64no—
217D3×C22⋊C4—64no—
218D3×C22⋊C4—64no—
219C3×#95—31no—
220C3×#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—61no—
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×C4C22×C412yes—
277C2×C32×C4C2×D412yes—
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⋊Dic3C22×C412yes—
286C2×C3⋊Dic3C2×D412yes—
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×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3C22×C412yes—
303C3×D12—44no—
304#626—28no—
305#625—44no—
306#624—44no—
307D3×Dic3—44no—
308C2×#120—91no—
309C2×C4×D4—91no—
310C22×C22⋊C4—91no—
311#390—31no—
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—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×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C2×#67—34no—
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—121no—
369C2×#67—121no—
370C2×#67—121no—
371C2×#67—121no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—62no—
382C22×Dic3—121no—
383C22×Dic3—121no—
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—34no—
396C2×C4×D3—34no—
397C2×C4×D3—64no—
398C2×C4×D3—62no—
399C2×C4×D3—62no—
400C2×C4×D3—62no—
401C2×C4×D3—121no—
402C2×C4×D3—121no—
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×C4⋊C4—121no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—121no—
420C3×C22⋊C4—121no—
421C3×C22⋊C4—121no—
422C3×C42—41no—
423C3×C42—41no—
424C3×C42—42no—
425#217—34no—
426#217—62no—
427#217—62no—
428#217—121no—
429#217—121no—
430#217—121no—
431(C2×D3)⋊C4—22no—
432(C2×D3)⋊C4—22no—
433(C2×D3)⋊C4—22no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—41no—
438(C2×D3)⋊C4—41no—
439(C2×D3)⋊C4—41no—
440(C2×D3)⋊C4—64no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—64no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4C4×D314yescomplemented
452C4⋊Dic3—41no—
453Dic3⋊C4—22no—
454Dic3⋊C4—121no—
455Dic3⋊C4—121no—
456C4×Dic3—62no—
457C4×Dic3—62no—
458C4×Dic3—121no—
459C4×Dic3—121no—
460C4×Dic3—122no—
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—22no—
499C32×C4—41no—
500C3⋊Dic3—22no—
501C3⋊Dic3—22no—
502C3⋊Dic3—41no—
503C3×Dic3—22no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C25—91no—
509C22×D4—31no—
510C22×D4—91no—
511C22×D4—91no—
512C23×C4—91no—
513C23×C4—91no—
514C23×C4—91no—
515#120—98no—
516C4×D4—184no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
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—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—184no—
537C2×C42—91no—
538C2×C42—91no—
539C2×C42D3211yescharacteristic, complemented
540#95—31no—
541#95—31no—
542#95—91no—
543#95—91no—
544#95—91no—
545#95—91no—
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—22no—
628C2×C3×C4—22no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—22no—
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—22no—
646C2×C3×C4—32no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
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×C4C2×C4×D312yes—
666C2×C3×C4C2×C4×D312yes—
667C2×C3×C4D3×D412yes—
668C2×C3×C4D3×D412yes—
669#67—68no—
670#67—124no—
671#67—124no—
672C2×Dic3—21no—
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—21no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—32no—
689C2×Dic3—32no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—62no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—124no—
714C2×Dic3C2×C4×D312yes—
715D12—44no—
716D12—68no—
717C4×D3—124no—
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—91no—
760C22×C4—91no—
761C22×C4—94no—
762C22×C4—91no—
763C22×C4—182no—
764C22×C4—182no—
765C22×C4—361no—
766C22×C4—361no—
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—121no—
776C4⋊C4—361no—
777C22⋊C4—34no—
778C22⋊C4—62no—
779C22⋊C4—62no—
780C22⋊C4—62no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4—121no—
784C22⋊C4—121no—
785C22⋊C4—121no—
786C22⋊C4—182no—
787C22⋊C4—182no—
788C22⋊C4—182no—
789C22⋊C4—182no—
790C22⋊C4—361no—
791C22⋊C4—361no—
792C22⋊C4—361no—
793C42—41no—
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—24no—
883C3×C4—22no—
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—22no—
887C3×C4—42no—
888C3×C4—42no—
889C3×C4—41no—
890C3×C4—41no—
891C3×C4—62no—
892C3×C4—121no—
893C3×C4—121no—
894C3×C4—121no—
895C3×C4—121no—
896Dic3—22no—
897Dic3—41no—
898Dic3—41no—
899Dic3—41no—
900Dic3—41no—
901Dic3—62no—
902Dic3—62no—
903Dic3—62no—
904Dic3—62no—
905Dic3—122no—
906Dic3—122no—
907Dic3—122no—
908Dic3—121no—
909Dic3—121no—
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—32no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
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—92no—
973C2×C4—92no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—364no—
982C2×C4—364no—
983C2×C4—364no—
984C2×C4C4×D3212yes—
985C2×C4#380212yes—
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#560511yescharacteristic
1003C2×C3#560511yescharacteristic
1004C2×C3#561311yescharacteristic
1005C2×C3#565711yescharacteristic
1006C2×C3#567411yescharacteristic
1007C2×C3#567811yescharacteristic
1008C2×C3#570411yescharacteristic
1009C2×C3#571511yescharacteristic
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
1046C22C2×#380211yescharacteristic
1047C22#6430611yescharacteristic
1048C22#6430711yescharacteristic
1049C22#6430711yescharacteristic
1050C22#6430811yescharacteristic
1051C22#6433011yescharacteristic
1052C4—22no—
1053C4—22no—
1054C4—41no—
1055C4—62no—
1056C4—121no—
1057C4—121no—
1058C4—121no—
1059C4—121no—
1060C4—182no—
1061C4—182no—
1062C4—361no—
1063C3—21no—
1064C3#7582611yescharacteristic, complemented
1065C3#7642911yescharacteristic, complemented
1066C2—122no—
1067C2—122no—
1068C2—122no—
1069C2—184no—
1070C2#1059399411yescharacteristic
1071C2C4×#380211yescharacteristic
1072C2#1059401011yescharacteristic
1073C2#1059401911yescharacteristic
1074C2#1059505611yescharacteristic
1075C2#1059508411yescharacteristic
1076C2#1059508911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#63922C2
hypercenterC2×C42D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63921C2semidirect
3. C2×#63881C2semidirect
4. C4×#3752C2semidirect
5. C3×#4940C2semidirect
6. C3×#4939C2semidirect
7. #10591399C2semidirect
8. #10591385C2semidirect
9. #10591378C2semidirect
10. #10591376C2semidirect
11. #10591363C2semidirect
12. #10591307C2semidirect
13. #10591283C2semidirect
14. #10591282C2semidirect
15. #10591275C2semidirect
24. C22×D3×Dic3C22semidirect
25. C2×C32×C42C22semidirect
28. C2×C4×C3⋊Dic3C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×#3724C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×Dic32C22semidirect
47. #63922C4semidirect
50. #63658C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
78. #4940D3semidirect
79. #4939D3semidirect
97. C22×D32C2×C4semidirect
106. C2×C4×C3⋊D3D4semidirect
114. C2×C3×D12C2×C4semidirect
120. C2×#625C2×C4semidirect
129. #3752C2×C4semidirect
137. C3×(C2×D3)⋊C4C2×C4semidirect
147. (C2×D3)⋊Dic3C2×C4semidirect
175. C2×C3×C42C2×D3semidirect
176. C2×C3×C42C2×D3semidirect
203. C2×(C2×D3)⋊C4C2×D3semidirect
204. C2×(C2×D3)⋊C4C2×D3semidirect
205. C2×C4⋊Dic3C2×D3semidirect
208. C2×Dic3⋊C4C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
394. C2×D12C4×D3semidirect
451. (C2×D3)⋊C4C4×D3semidirect
539. C2×C42D32semidirect
910. C32#2321semidirect
1064. C3#75826semidirect
1065. C3#76429semidirect

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×#638812
C4×#37522
C3×#49402
C3×#49392
#105913992
#105913852
#105913782
#105913762
#105913632
#105913072
#105912832
#105912822
#105912752
#764293
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