Finite Group Databasebeta

← #11803275

Subgroups — #11803275

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×#63977C211yesmaximal, characteristic
2C2×D3×#217C211yesmaximal, characteristic, complemented
3C2×#63881C211yesmaximal, characteristic, complemented
4#10592655C211yesmaximal, characteristic, complemented
5C3×#4955C211yesmaximal, characteristic, complemented
6C3×#4944C211yesmaximal, characteristic, complemented
7#10591704C211yesmaximal, characteristic, complemented
8#10591702C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591383C211yesmaximal, characteristic, complemented
11#10591373C211yesmaximal, characteristic, complemented
12Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#10591364C211yesmaximal, characteristic, complemented
14#10591285C211yesmaximal, characteristic, complemented
15#10591282C211yesmaximal, characteristic, complemented
16#75826—31nomaximal
17#73821—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic, complemented
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic, complemented
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37#63977C418yescomplemented
38D3×#217—24no—
39C2×#3724C2211yescharacteristic, complemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic, complemented
42C2×#3722C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×Dic32C2211yescharacteristic, complemented
48C2×Dic32C2211yescharacteristic, complemented
49#63881—24no—
50#63658C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×#953—31no—
57C22×#217—31no—
58C2×#893—31no—
59C2×#882—31no—
60C2×#67⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C3×#388—31no—
63C3×#379—31no—
64#4990—31no—
65#4958—31no—
66#4957—31no—
67#4957—31no—
68#4957—31no—
69#4956—31no—
70#4956—31no—
71#4956—31no—
72#4956—61no—
73#4955D311yescharacteristic, complemented
74#4951—31no—
75#4946—31no—
76#4945—31no—
77#4945—31no—
78#4944—31no—
79#4944D311yescharacteristic, complemented
80Dic3×C22⋊C4—31no—
81#4939—31no—
82C4×(C2×D3)⋊C4—31no—
83#4669—31no—
84#4668—31no—
85#4665—31no—
86#4665—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—41no—
92C23×C3×D3—41no—
93C23×C3×D3—41no—
94C23×C3×D3—41no—
95C23×C3×D3C2×C414yescomplemented
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#638—41no—
101C2×#638—41no—
102C2×#638C2×C414yescomplemented
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
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×#626—22no—
116C2×#626—22no—
117C2×#626—41no—
118C2×#626—41no—
119C2×#626C2×C414yes—
120C2×#626C2×C414yescomplemented
121C2×D3×Dic3—22no—
122C2×D3×Dic3—41no—
123C2×D3×Dic3—41no—
124C2×D3×Dic3—41no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3D414yescomplemented
127C32×C22⋊C4—41no—
128#3757—22no—
129#3752—41no—
130C3×#217—22no—
131C3×#217—41no—
132C3×#217C2×C414yescomplemented
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—41no—
136C3×(C2×D3)⋊C4—41no—
137C3×Dic3⋊C4—22no—
138C3×C4×Dic3—41no—
139#3724—41no—
140Dic3⋊Dic3—41no—
141#3722—22no—
142#3722—41no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3C2×C414yescomplemented
146(C2×D3)⋊Dic3C2×C414yescomplemented
147Dic32—22no—
148Dic32—41no—
149#2321—91noSylow
150C25×C3—31no—
151C24×D3C2×D311yescharacteristic
152C22×#67—31no—
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—61no—
157C23×Dic3—31no—
158C23×Dic3—31no—
159C22×D12—31no—
160C22×D12—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—61no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—21no—
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×C22⋊C4—31no—
175C2×C3×C22⋊C4C2×D311yescharacteristic
176C2×C3×C22⋊C4C2×D311yescharacteristic
177C2×C3×C42—31no—
178#953—38no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—61no—
186C2×#217—64no—
187C2×#217C2×D311yescharacteristic
188C2×#217C2×D311yescharacteristic
189C2×#217C2×D311yescharacteristic
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—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—61no—
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×C4⋊Dic3—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
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—
217#67⋊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×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32C22×C412yes—
240C23×C32C2411yescharacteristic
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×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—28no—
259C22×C3×D3—44no—
260C22×C3×D3—44no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3C22×C412yes—
266C22×C3×D3C22×C412yes—
267C22×C3×D3C2×D412yes—
268C22×C3×D3#4112yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275#638—44no—
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—21no—
283C2×C3⋊Dic3C22×C412yes—
284C2×C3⋊Dic3C2×D412yes—
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—
304#626—28no—
305#626—44no—
306D3×Dic3—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—91no—
321#379—31no—
322C4×C22⋊C4—91no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3—31no—
326C24×C3—34no—
327C24×C3—62no—
328C24×C3—62no—
329C24×C3—121no—
330C24×C3—121no—
331C24×C3—121no—
332C24×C3—121no—
333C24×C3C22×D311yescharacteristic
334C24×C3C22×D311yescharacteristic
335C23×D3—22no—
336C23×D3—22no—
337C23×D3—31no—
338C23×D3—31no—
339C23×D3—41no—
340C23×D3—41no—
341C23×D3—41no—
342C23×D3—41no—
343C23×D3—61no—
344C23×D3C4×D314yescomplemented
345C23×D3C22×D311yescharacteristic
346C23×D3C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—34no—
363C2×#67—64no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67—121no—
367C2×#67—121no—
368C2×#67—121no—
369C2×#67—121no—
370C2×#67—121no—
371C2×#67—121no—
372C2×#67—122no—
373C2×#67—122no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—34no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—62no—
385C22×Dic3—121no—
386C22×Dic3—121no—
387C22×Dic3—121no—
388C22×Dic3—121no—
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C2×D12—34no—
396C2×D12—34no—
397C2×D12—62no—
398C2×D12—62no—
399C2×D12—121no—
400C2×D12—121no—
401C2×C4×D3—34no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×C4×D3—62no—
405C2×C4×D3—122no—
406C2×C4×D3—121no—
407C2×C4×D3—121no—
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×C22⋊C4—34no—
418C3×C22⋊C4—41no—
419C3×C22⋊C4—41no—
420C3×C22⋊C4—42no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—121no—
425C3×C22⋊C4—121no—
426C3×C22⋊C4—121no—
427C3×C42—121no—
428#217—22no—
429#217—34no—
430#217—34no—
431#217—41no—
432#217—62no—
433#217—62no—
434#217—62no—
435#217—62no—
436#217—122no—
437#217C4×D314yescomplemented
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—22no—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—34no—
442(C2×D3)⋊C4—41no—
443(C2×D3)⋊C4—41no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4—121no—
452(C2×D3)⋊C4—122no—
453C4⋊Dic3—121no—
454Dic3⋊C4—22no—
455Dic3⋊C4—121no—
456Dic3⋊C4—121no—
457Dic3⋊C4—121no—
458C4×Dic3—41no—
459C4×Dic3—62no—
460C4×Dic3—62no—
461C4×Dic3—121no—
462C4×Dic3—121no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32C23×C411yescharacteristic
471C22×C32C22×D411yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32H(5,𝔽2)11yescharacteristic
474C22×C32H(5,𝔽2)11yescharacteristic
475C22×C32H(5,𝔽2)11yescharacteristic
476C22×C32H(5,𝔽2)11yescharacteristic
477C2×C3⋊D3—22no—
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
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—416no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3C4×D414yes—
499C32×C4—41no—
500C32×C4—41no—
501C3⋊Dic3—22no—
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—31no—
511C22×D4—91no—
512C22×D4—91no—
513C22×D4—91no—
514C23×C4—91no—
515C23×C4—91no—
516C23×C4—91no—
517#120—98no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
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—184no—
538C2×C22⋊C4D3211yescharacteristic
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#95—91no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—22no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—68no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—124no—
584C23×C3—124no—
585C23×C3—124no—
586C23×C3—124no—
587C23×C3—124no—
588C23×C3—124no—
589C23×C3C2×C4×D312yes—
590C23×C3C2×C4×D312yes—
591C23×C3C23×D311yescharacteristic
592C23×C3C23×D311yescharacteristic
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—28no—
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—44no—
607C22×D3—44no—
608C22×D3—44no—
609C22×D3—44no—
610C22×D3—44no—
611C22×D3—44no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3C2×C4×D312yes—
632C22×D3C2×C4×D312yes—
633C22×D3D3×D412yes—
634C22×D3#23712yes—
635C2×C3×C4—22no—
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—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
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—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671#67—68no—
672#67—124no—
673#67—124no—
674#67—124no—
675#67—128no—
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—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—32no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—62no—
696C2×Dic3—62no—
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—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—121no—
717C2×Dic3—121no—
718C2×Dic3—124no—
719C2×Dic3—124no—
720C2×Dic3C2×C4×D312yes—
721C2×Dic3C2×C4×D312yes—
722C2×Dic3D3×D412yes—
723D12—68no—
724D12—124no—
725C4×D3—124no—
726C4×D3—124no—
727C4×D3—124no—
728C4×D3—128no—
729C4×D3—124no—
730C2×C32—42no—
731C2×C32C2×C4×D411yescharacteristic
732C2×C32#51811yescharacteristic
733C2×C32#51811yescharacteristic
734C2×C32#53411yescharacteristic
735C2×C32#53511yescharacteristic
736C2×C32#53811yescharacteristic
737C2×C32#53811yescharacteristic
738C3⋊D3—42no—
739C3×D3—24no—
740C3×D3—42no—
741C24—31no—
742C24—31no—
743C24—34no—
744C24—62no—
745C24—62no—
746C24—91no—
747C24—121no—
748C24—121no—
749C24—121no—
750C24—121no—
751C24C2×D3211yescharacteristic
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—94no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—182no—
772C22×C4—182no—
773C22×C4—361no—
774C22×C4—361no—
775C22×C4—361no—
776C22×C4—361no—
777C22×C4—361no—
778C22×C4—361no—
779C22×C4C2×D3211yescharacteristic
780C22×C4C2×D3211yescharacteristic
781C4⋊C4—62no—
782C4⋊C4—361no—
783C4⋊C4—361no—
784C22⋊C4—34no—
785C22⋊C4—41no—
786C22⋊C4—62no—
787C22⋊C4—62no—
788C22⋊C4—62no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—121no—
792C22⋊C4—121no—
793C22⋊C4—121no—
794C22⋊C4—182no—
795C22⋊C4—182no—
796C22⋊C4—182no—
797C22⋊C4—182no—
798C22⋊C4—361no—
799C22⋊C4—361no—
800C42—121no—
801C42—182no—
802C42—361no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—34no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3—1216no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3C22×C4×D311yescharacteristic
847C22×C3C22×C4×D311yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C22×C3C2×D3×D411yescharacteristic
850C22×C3C2×#23711yescharacteristic
851C22×C3#100411yescharacteristic
852C22×C3#100411yescharacteristic
853C22×C3#100411yescharacteristic
854C22×C3#100411yescharacteristic
855C22×C3#100411yescharacteristic
856C22×C3D3×#4111yescharacteristic
857C22×C3#100911yescharacteristic
858C22×C3#100911yescharacteristic
859C22×C3#100911yescharacteristic
860C2×D3—22no—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—416no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—64no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—122no—
882C2×D3—122no—
883C2×D3—122no—
884C2×D3—122no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—121no—
894C2×D3—121no—
895C2×D3#67⋊C414yes—
896C3×C4—42no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—62no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—81no—
905C3×C4—121no—
906C3×C4—121no—
907C3×C4—121no—
908Dic3—22no—
909Dic3—22no—
910Dic3—22no—
911Dic3—41no—
912Dic3—41no—
913Dic3—41no—
914Dic3—62no—
915Dic3—62no—
916Dic3—62no—
917Dic3—62no—
918Dic3—122no—
919Dic3—122no—
920Dic3—121no—
921Dic3—121no—
922Dic3—241no—
923C32#232111yescharacteristic, complemented, Sylow
924C23—21no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—32no—
931C23—32no—
932C23—32no—
933C23—32no—
934C23—68no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—92no—
946C23—124no—
947C23—124no—
948C23—124no—
949C23—124no—
950C23—124no—
951C23—124no—
952C23—181no—
953C23—181no—
954C23—181no—
955C23—181no—
956C23—181no—
957C23—181no—
958C23C4×D3212yes—
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—32no—
970C2×C4—32no—
971C2×C4—32no—
972C2×C4—61no—
973C2×C4—61no—
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—92no—
988C2×C4—92no—
989C2×C4—181no—
990C2×C4—181no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—364no—
997C2×C4—364no—
998C2×C4—364no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—42no—
1007C2×C3—42no—
1008C2×C3—64no—
1009C2×C3—82no—
1010C2×C3—122no—
1011C2×C3C2×#67⋊C411yescharacteristic
1012C2×C3#548611yescharacteristic
1013C2×C3#548611yescharacteristic
1014C2×C3#552111yescharacteristic
1015C2×C3C4×D3×D411yescharacteristic
1016C2×C3#554511yescharacteristic
1017C2×C3#558911yescharacteristic
1018C2×C3#559211yescharacteristic
1019C2×C3#559311yescharacteristic
1020C2×C3#559311yescharacteristic
1021C2×C3#560511yescharacteristic
1022C2×C3#565711yescharacteristic
1023C2×C3#567411yescharacteristic
1024C2×C3#570411yescharacteristic
1025D3—24no—
1026D3—42no—
1027D3—124no—
1028D3—122no—
1029D3—122no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—34no—
1034C22—41no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—62no—
1039C22—62no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—1216no—
1048C22—121no—
1049C22—121no—
1050C22—121no—
1051C22—121no—
1052C22—182no—
1053C22—182no—
1054C22—182no—
1055C22—361no—
1056C22—361no—
1057C22—361no—
1058C22—361no—
1059C22C2×C4×D3211yescharacteristic
1060C22#6430711yescharacteristic
1061C22D32×D411yescharacteristic
1062C22D3×#23711yescharacteristic
1063C22#6431411yescharacteristic
1064C22#6431411yescharacteristic
1065C22#6433011yescharacteristic
1066C4—41no—
1067C4—41no—
1068C4—62no—
1069C4—62no—
1070C4—62no—
1071C4—121no—
1072C4—121no—
1073C4—121no—
1074C4—182no—
1075C4—182no—
1076C4—361no—
1077C3—21no—
1078C3#7382111yescharacteristic, complemented
1079C3#7582611yescharacteristic, complemented
1080C2—42no—
1081C2—64no—
1082C2—122no—
1083C2—362no—
1084C2#1059412711yescharacteristic
1085C2#1059418211yescharacteristic
1086C2D3×#67⋊C411yescharacteristic
1087C2#1059427011yescharacteristic
1088C2#1059505611yescharacteristic
1089C2#1059518511yescharacteristic
1090C2#1059528111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63977C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2321
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×D3×#217C2semidirect
3. C2×#63881C2semidirect
4. #10592655C2semidirect
5. C3×#4955C2semidirect
6. C3×#4944C2semidirect
7. #10591704C2semidirect
8. #10591702C2semidirect
9. #10591387C2semidirect
10. #10591383C2semidirect
11. #10591373C2semidirect
12. Dic3×(C2×D3)⋊C4C2semidirect
13. #10591364C2semidirect
14. #10591285C2semidirect
15. #10591282C2semidirect
20. C22×C4×C3⋊D3C22semidirect
27. C2×#3752C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×C4×Dic3C22semidirect
37. #63977C4semidirect
39. C2×#3724C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×#3722C22semidirect
42. C2×#3722C22semidirect
47. C2×Dic32C22semidirect
48. C2×Dic32C22semidirect
50. #63658C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
73. #4955D3semidirect
79. #4944D3semidirect
95. C23×C3×D3C2×C4semidirect
102. C2×#638C2×C4semidirect
120. C2×#626C2×C4semidirect
126. C2×D3×Dic3D4semidirect
132. C3×#217C2×C4semidirect
145. (C2×D3)⋊Dic3C2×C4semidirect
146. (C2×D3)⋊Dic3C2×C4semidirect
209. C2×Dic3⋊C4C2×D3semidirect
214. C2×C4×Dic3C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
344. C23×D3C4×D3semidirect
437. #217C4×D3semidirect
923. C32#2321semidirect
1078. C3#73821semidirect
1079. C3#75826semidirect

Maximal subgroups

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

subgroupindex
C2×#639772
C2×D3×#2172
C2×#638812
#105926552
C3×#49552
C3×#49442
#105917042
#105917022
#105913872
#105913832
#105913732
Dic3×(C2×D3)⋊C42
#105913642
#105912852
#105912822
#758263
#738213