Finite Group Databasebeta

← #11856281

Subgroups — #11856281

Order 1152.

2321 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic, complemented
2C2×#63922C211yesmaximal, characteristic
3C2×#63905C211yesmaximal, characteristic, complemented
4C2×#63891C211yesmaximal, characteristic, complemented
5#10592367C211yesmaximal, characteristic, complemented
6C3×#4665C211yesmaximal, characteristic, complemented
7C3×#4664C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591379C211yesmaximal, characteristic, complemented
11#10591376C211yesmaximal, characteristic, complemented
12#10591375C211yesmaximal, characteristic, complemented
13#10591362C211yesmaximal, characteristic, complemented
14#10591278C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#74936—31nomaximal
17#74146—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C4×D32—24no—
29C2×C4×D32—24no—
30C2×C4×D32—24no—
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×Dic3⋊Dic3C2211yescharacteristic, complemented
42C2×#3722C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48#63922—24no—
49#63905—24no—
50#63891—24no—
51C32×#95C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57#63579C2211yescharacteristic, complemented
58#63579C2211yescharacteristic, complemented
59C23×C4×D3—31no—
60C23×C4×D3—31no—
61C2×#937—31no—
62C2×#929—31no—
63C2×#886—31no—
64C2×#883—31no—
65C2×#883—31no—
66C2×#882—31no—
67C3×#386—31no—
68C3×#381—31no—
69#5220—31no—
70#5210—31no—
71#4956—31no—
72#4956—31no—
73#4955—31no—
74#4955—31no—
75#4950—31no—
76#4943—31no—
77#4668—31no—
78#4668—31no—
79#4668—31no—
80#4668—31no—
81#4668—31no—
82#4668—31no—
83#4668—61no—
84#4665—31no—
85#4665—31no—
86#4665—31no—
87#4665D311yescharacteristic, complemented
88#4664—31no—
89#4664D311yescharacteristic, complemented
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C23×C3×D3C2311yescharacteristic
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—22no—
97C22×D32—22no—
98C22×D32—22no—
99C22×D32—22no—
100C22×D32D414yes—
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C2×C4×C3⋊D3—22no—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—22no—
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×D12—22no—
116C2×C3×D12—22no—
117C2×C3×D12—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—22no—
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3D414yescomplemented
124C2×#626—22no—
125C2×#626—22no—
126C2×#626—22no—
127C2×#625—22no—
128C2×#625—22no—
129C2×#625—22no—
130C2×#624—22no—
131C2×#624—22no—
132C2×#624—22no—
133C2×D3×Dic3—22no—
134C2×D3×Dic3—22no—
135C2×D3×Dic3—22no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3—22no—
138C2×D3×Dic3D414yescomplemented
139C4×D32—232no—
140#3752—22no—
141#3752—22no—
142C4⋊(C3⋊Dic3)—22no—
143#3750—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—22no—
147C3×(C2×D3)⋊C4—22no—
148C3×(C2×D3)⋊C4—22no—
149Dic3⋊Dic3—22no—
150Dic3⋊Dic3—22no—
151#3722—22no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—22no—
155(C2×D3)⋊Dic3—22no—
156(C2×D3)⋊Dic3—22no—
157#2849—91noSylow
158C24×D3—31no—
159C24×D3—31no—
160C22×C3×D4—31no—
161C23×C3×C4—31no—
162C23×C3×C4—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C23×Dic3—31no—
167C23×Dic3—31no—
168C22×D12—31no—
169C22×D12C2×D311yescharacteristic
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—61no—
177C22×C4×D3—64no—
178C22×C4×D3—64no—
179C22×C4×D3—64no—
180C22×C4×D3—64no—
181C22×C4×D3—64no—
182C22×C4×D3—64no—
183C22×C4×D3C2×D311yescharacteristic
184C22×C4×D3C2×D311yescharacteristic
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193C2×#217—31no—
194C2×#217—31no—
195#937—64no—
196#929—64no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—61no—
209C2×(C2×D3)⋊C4—61no—
210C2×(C2×D3)⋊C4C2×D311yescharacteristic
211C2×(C2×D3)⋊C4C2×D311yescharacteristic
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
214C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—61no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—61no—
225#886—64no—
226#883—64no—
227#883—64no—
228#882—64no—
229C3×#95—21no—
230C3×#95—31no—
231C3×#95—31no—
232C3×#95—31no—
233C3×#95—31no—
234C3×#95C2×D311yescharacteristic, complemented
235C3×#95C2×D311yescharacteristic, complemented
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—31no—
241C3⋊#95—31no—
242C3⋊#95—61no—
243C3⋊#95C2×D311yescharacteristic, complemented
244C3⋊#95C2×D311yescharacteristic, complemented
245C3⋊#95C2×D311yescharacteristic, complemented
246C3⋊#95C2×D311yescharacteristic, complemented
247C23×C32C2411yescharacteristic
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3C2×D412yes—
253C22×C3⋊D3#4112yes—
254C22×C3⋊D3#4112yes—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3C2×D412yes—
271C22×C3×D3C2×D412yes—
272C22×C3×D3C2×D412yes—
273C22×C3×D3C2×D412yes—
274C22×C3×D3#4112yes—
275C22×C3×D3#4112yes—
276C2×D32—28no—
277C2×D32—28no—
278C2×D32—28no—
279C2×D32—28no—
280C2×D32—28no—
281C2×D32—28no—
282C2×D32—28no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4C2×D412yes—
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⋊Dic3C2×D412yes—
301C4×C3⋊D3—28no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3—21no—
315C2×C3×Dic3C2×D412yes—
316C2×C3×Dic3C2×D412yes—
317C3×D12—44no—
318C3×C4×D3—28no—
319C3×C4×D3—28no—
320#626—44no—
321#625—44no—
322#624—28no—
323D3×Dic3—28no—
324D3×Dic3—28no—
325C24×C4—91no—
326C2×#123—91no—
327C2×#123—91no—
328C2×#120—91no—
329#386—31no—
330#386—91no—
331#386—91no—
332#386—91no—
333#385—91no—
334#385—91no—
335#385—91no—
336#385—91no—
337#381—31no—
338#381—91no—
339#379—91no—
340C24×C3—31no—
341C24×C3—31no—
342C24×C3—31no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—34no—
346C23×D3—34no—
347C23×D3—61no—
348C23×D3—62no—
349C23×D3—62no—
350C23×D3—62no—
351C23×D3—62no—
352C23×D3—62no—
353C23×D3—62no—
354C23×D3—62no—
355C23×D3—62no—
356C23×D3—62no—
357C23×D3—62no—
358C23×D3—62no—
359C23×D3—62no—
360C23×D3C22×D311yescharacteristic
361C23×D3C22×D311yescharacteristic
362C23×D3C22×D311yescharacteristic
363C2×C3×D4—62no—
364C2×C3×D4—62no—
365C2×C3×D4—62no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—34no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—62no—
376C22×C3×C4—62no—
377C22×C3×C4—62no—
378C22×C3×C4—62no—
379C22×C3×C4—62no—
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67—62no—
391C2×#67—62no—
392C2×#67—62no—
393C2×#67—62no—
394C2×#67—62no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—34no—
398C22×Dic3—31no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—61no—
405C22×Dic3—62no—
406C22×Dic3—62no—
407C22×Dic3—62no—
408C22×Dic3—62no—
409C22×Dic3—62no—
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C2×D12—22no—
416C2×D12—22no—
417C2×D12—22no—
418C2×D12—62no—
419C2×D12—62no—
420C2×D12—62no—
421C2×C4×D3—22no—
422C2×C4×D3—22no—
423C2×C4×D3—22no—
424C2×C4×D3—22no—
425C2×C4×D3—22no—
426C2×C4×D3—34no—
427C2×C4×D3—632no—
428C2×C4×D3—632no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—62no—
432C2×C4×D3—62no—
433C2×C4×D3—62no—
434C2×C4×D3—62no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C2×C4×D3—62no—
438C2×C4×D3—62no—
439C2×C4×D3—62no—
440C2×C4×D3—62no—
441C2×C4×D3—62no—
442C2×C4×D3—62no—
443C2×C4×D3—62no—
444C2×C4×D3—62no—
445C2×C4×D3—62no—
446C2×C4×D3—122no—
447C2×C4×D3—122no—
448C2×C4×D3—122no—
449C2×C4×D3D1214yescomplemented
450C3×C22⋊C4—62no—
451C3×C22⋊C4—62no—
452C3×C22⋊C4—62no—
453C3×C22⋊C4—62no—
454C3×C22⋊C4—62no—
455#217—62no—
456#217—62no—
457#217—62no—
458#217—62no—
459#217—62no—
460(C2×D3)⋊C4—22no—
461(C2×D3)⋊C4—22no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—62no—
466(C2×D3)⋊C4—62no—
467(C2×D3)⋊C4—62no—
468(C2×D3)⋊C4—62no—
469(C2×D3)⋊C4—62no—
470(C2×D3)⋊C4—62no—
471(C2×D3)⋊C4—62no—
472(C2×D3)⋊C4—64no—
473(C2×D3)⋊C4—62no—
474(C2×D3)⋊C4—62no—
475(C2×D3)⋊C4—62no—
476(C2×D3)⋊C4—62no—
477(C2×D3)⋊C4—122no—
478C4⋊Dic3—62no—
479C4⋊Dic3—62no—
480C4⋊Dic3—62no—
481C4⋊Dic3—62no—
482C4⋊Dic3—122no—
483Dic3⋊C4—62no—
484Dic3⋊C4—62no—
485Dic3⋊C4—62no—
486Dic3⋊C4—62no—
487Dic3⋊C4—122no—
488C22×C32C22×D411yescharacteristic
489C22×C32C22×D411yescharacteristic
490C22×C32C22×D411yescharacteristic
491C22×C32C2×#4111yescharacteristic
492C22×C32C2×#4111yescharacteristic
493C22×C32C2×#4111yescharacteristic
494C22×C32C2×#4111yescharacteristic
495C2×C3⋊D3—22no—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3#12314yescomplemented
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—41no—
515C2×C3×D3—41no—
516C2×C3×D3—41no—
517C2×C3×D3—41no—
518C2×C3×D3—41no—
519C2×C3×D3—41no—
520C2×C3×D3—41no—
521C2×C3×D3#12014yes—
522C2×C3×D3#12314yescomplemented
523D32—232no—
524C32×C4—22no—
525C32×C4—41no—
526C32×C4—41no—
527C3⋊Dic3—22no—
528C3⋊Dic3—41no—
529C3⋊Dic3—41no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C3×Dic3—41no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C25—91no—
536C22×D4—31no—
537C22×D4—91no—
538C22×D4—91no—
539C23×C4—31no—
540C23×C4—31no—
541C23×C4—91no—
542C23×C4—91no—
543C23×C4—91no—
544C23×C4—91no—
545C23×C4—184no—
546C23×C4—184no—
547C23×C4—184no—
548#123—184no—
549#123—184no—
550#120—184no—
551C2×C4⋊C4—91no—
552C2×C4⋊C4—91no—
553C2×C4⋊C4—91no—
554C2×C4⋊C4—91no—
555C2×C22⋊C4—31no—
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—31no—
559C2×C22⋊C4—31no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4—91no—
562C2×C22⋊C4—91no—
563C2×C22⋊C4—91no—
564C2×C22⋊C4—91no—
565C2×C22⋊C4—91no—
566C2×C22⋊C4—91no—
567C2×C22⋊C4—91no—
568#95—31no—
569#95—31no—
570#95—31no—
571#95—31no—
572#95—91no—
573#95—91no—
574#95—91no—
575#95D3211yescharacteristic, complemented
576C23×C3—21no—
577C23×C3—32no—
578C23×C3—32no—
579C23×C3—32no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—32no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3C23×D311yescharacteristic
599C23×C3C23×D311yescharacteristic
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—32no—
616C22×D3—32no—
617C22×D3—32no—
618C22×D3—32no—
619C22×D3—32no—
620C22×D3—32no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—68no—
625C22×D3—68no—
626C22×D3—68no—
627C22×D3—68no—
628C22×D3—68no—
629C22×D3—68no—
630C22×D3—68no—
631C22×D3—68no—
632C22×D3—68no—
633C22×D3—68no—
634C22×D3—68no—
635C22×D3—68no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—61no—
640C22×D3—61no—
641C22×D3—61no—
642C22×D3—61no—
643C22×D3—61no—
644C22×D3—68no—
645C22×D3—68no—
646C22×D3—121no—
647C22×D3—121no—
648C22×D3—121no—
649C22×D3—121no—
650C22×D3C2×D1212yes—
651C22×D3#23512yes—
652C22×D3D3×D412yes—
653C22×D3D3×D412yes—
654C22×D3D3×D412yes—
655C22×D3#23712yes—
656C3×D4—124no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—22no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—22no—
675C2×C3×C4—32no—
676C2×C3×C4—32no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—68no—
685C2×C3×C4—68no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4C2×D1212yes—
700C2×C3×C4D3×D412yes—
701#67—124no—
702#67—124no—
703#67—124no—
704C2×Dic3—21no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
708C2×Dic3—21no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—32no—
718C2×Dic3—32no—
719C2×Dic3—62no—
720C2×Dic3—68no—
721C2×Dic3—68no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—62no—
727C2×Dic3—61no—
728C2×Dic3—61no—
729C2×Dic3—61no—
730C2×Dic3—61no—
731C2×Dic3—61no—
732C2×Dic3—61no—
733C2×Dic3—61no—
734C2×Dic3—61no—
735C2×Dic3—61no—
736C2×Dic3—61no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—121no—
740C2×Dic3—121no—
741C2×Dic3—121no—
742C2×Dic3—121no—
743C2×Dic3—121no—
744C2×Dic3—121no—
745C2×Dic3—121no—
746C2×Dic3C2×D1212yes—
747C2×Dic3D3×D412yes—
748D12—44no—
749D12—124no—
750C4×D3—28no—
751C4×D3—28no—
752C4×D3—68no—
753C4×D3—68no—
754C4×D3—68no—
755C4×D3—68no—
756C4×D3—68no—
757C4×D3—68no—
758C4×D3—128no—
759C2×C32C2×#12011yescharacteristic
760C2×C32C2×#12311yescharacteristic
761C2×C32C2×#12311yescharacteristic
762C2×C32#52511yescharacteristic
763C2×C32#52511yescharacteristic
764C2×C32#52511yescharacteristic
765C2×C32#52511yescharacteristic
766C3⋊D3—24no—
767C3×D3—24no—
768C3×D3—24no—
769C3×D3—81no—
770C24—31no—
771C24—31no—
772C24—31no—
773C24—94no—
774C24—91no—
775C24—182no—
776C24—182no—
777C24—182no—
778C24—182no—
779C24—182no—
780C24—182no—
781C2×D4—62no—
782C2×D4—62no—
783C2×D4—62no—
784C2×D4—182no—
785C2×D4—182no—
786C2×D4—182no—
787C2×D4—182no—
788C2×D4—182no—
789C2×D4—182no—
790C22×C4—31no—
791C22×C4—31no—
792C22×C4—34no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—62no—
797C22×C4—62no—
798C22×C4—62no—
799C22×C4—62no—
800C22×C4—62no—
801C22×C4—94no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—91no—
805C22×C4—182no—
806C22×C4—182no—
807C22×C4—182no—
808C22×C4—182no—
809C22×C4—182no—
810C22×C4—182no—
811C22×C4—1832no—
812C22×C4—182no—
813C22×C4—182no—
814C22×C4—182no—
815C22×C4—182no—
816C22×C4—182no—
817C22×C4C2×D3211yescharacteristic
818C22×C4C2×D3211yescharacteristic
819C22×C4C2×D3211yescharacteristic
820C4⋊C4—182no—
821C4⋊C4—182no—
822C4⋊C4—182no—
823C4⋊C4—182no—
824C22⋊C4—62no—
825C22⋊C4—62no—
826C22⋊C4—62no—
827C22⋊C4—62no—
828C22⋊C4—62no—
829C22⋊C4—182no—
830C22⋊C4—182no—
831C22⋊C4—182no—
832C22⋊C4—182no—
833C22⋊C4—182no—
834C22⋊C4—182no—
835C22⋊C4—182no—
836C22⋊C4—182no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—34no—
845C22×C3—34no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—121no—
859C22×C3—121no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3C22×D1211yescharacteristic
866C22×C3C2×#23511yescharacteristic
867C22×C3C2×D3×D411yescharacteristic
868C22×C3C2×D3×D411yescharacteristic
869C22×C3C2×D3×D411yescharacteristic
870C22×C3C2×D3×D411yescharacteristic
871C22×C3C2×D3×D411yescharacteristic
872C22×C3C2×#23711yescharacteristic
873C22×C3D3×#4111yescharacteristic
874C22×C3D3×#4111yescharacteristic
875C22×C3D3×#4111yescharacteristic
876C22×C3D3×#4111yescharacteristic
877C22×C3D3×#4111yescharacteristic
878C22×C3D3×#4111yescharacteristic
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—34no—
892C2×D3—34no—
893C2×D3—41no—
894C2×D3—41no—
895C2×D3—41no—
896C2×D3—41no—
897C2×D3—41no—
898C2×D3—41no—
899C2×D3—41no—
900C2×D3—64no—
901C2×D3—632no—
902C2×D3—632no—
903C2×D3—62no—
904C2×D3—62no—
905C2×D3—62no—
906C2×D3—62no—
907C2×D3—62no—
908C2×D3—62no—
909C2×D3—62no—
910C2×D3—62no—
911C2×D3—62no—
912C2×D3—62no—
913C2×D3—62no—
914C2×D3—62no—
915C2×D3—122no—
916C2×D3—122no—
917C2×D3—122no—
918C2×D3—122no—
919C2×D3—122no—
920C2×D3—122no—
921C2×D3#88214yes—
922C2×D3#88314yescomplemented
923C3×C4—22no—
924C3×C4—22no—
925C3×C4—42no—
926C3×C4—42no—
927C3×C4—41no—
928C3×C4—41no—
929C3×C4—41no—
930C3×C4—41no—
931C3×C4—62no—
932C3×C4—62no—
933C3×C4—81no—
934C3×C4—121no—
935C3×C4—121no—
936C3×C4—121no—
937Dic3—22no—
938Dic3—22no—
939Dic3—41no—
940Dic3—41no—
941Dic3—41no—
942Dic3—62no—
943Dic3—62no—
944Dic3—122no—
945Dic3—122no—
946Dic3—121no—
947Dic3—121no—
948Dic3—121no—
949Dic3—121no—
950Dic3—241no—
951C32#284911yescharacteristic, complemented, Sylow
952C23—32no—
953C23—32no—
954C23—32no—
955C23—32no—
956C23—32no—
957C23—32no—
958C23—61no—
959C23—61no—
960C23—61no—
961C23—61no—
962C23—61no—
963C23—61no—
964C23—61no—
965C23—61no—
966C23—61no—
967C23—61no—
968C23—61no—
969C23—61no—
970C23—61no—
971C23—61no—
972C23—61no—
973C23—92no—
974C23—92no—
975C23—92no—
976C23—188no—
977C23—188no—
978C23—188no—
979C23—188no—
980C23—188no—
981C23—188no—
982C23—188no—
983C23—181no—
984C23—181no—
985C23—181no—
986C23—181no—
987C23C22×D3211yescharacteristic
988D4—124no—
989D4—364no—
990D4—364no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—32no—
1000C2×C4—32no—
1001C2×C4—68no—
1002C2×C4—68no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—61no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—61no—
1012C2×C4—61no—
1013C2×C4—61no—
1014C2×C4—61no—
1015C2×C4—61no—
1016C2×C4—92no—
1017C2×C4—188no—
1018C2×C4—188no—
1019C2×C4—188no—
1020C2×C4—188no—
1021C2×C4—181no—
1022C2×C4—181no—
1023C2×C4—181no—
1024C2×C4—181no—
1025C2×C4—181no—
1026C2×C4—181no—
1027C2×C4—181no—
1028C2×C4—181no—
1029C2×C4D3×D1212yes—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—64no—
1038C2×C3—64no—
1039C2×C3—241no—
1040C2×C3C2×#88211yescharacteristic
1041C2×C3C2×#88311yescharacteristic
1042C2×C3#552411yescharacteristic
1043C2×C3#552411yescharacteristic
1044C2×C3#554711yescharacteristic
1045C2×C3#554711yescharacteristic
1046C2×C3D3×#12011yescharacteristic
1047C2×C3#560611yescharacteristic
1048C2×C3#560611yescharacteristic
1049C2×C3D3×#12311yescharacteristic
1050C2×C3D3×#12311yescharacteristic
1051C2×C3D3×#12311yescharacteristic
1052C2×C3#565611yescharacteristic
1053C2×C3#565611yescharacteristic
1054D3—24no—
1055D3—24no—
1056D3—64no—
1057D3—64no—
1058D3—81no—
1059D3—124no—
1060C22—34no—
1061C22—34no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—62no—
1068C22—62no—
1069C22—62no—
1070C22—62no—
1071C22—62no—
1072C22—62no—
1073C22—62no—
1074C22—94no—
1075C22—121no—
1076C22—121no—
1077C22—121no—
1078C22—121no—
1079C22—121no—
1080C22—121no—
1081C22—121no—
1082C22—1832no—
1083C22—182no—
1084C22—182no—
1085C22—182no—
1086C22—182no—
1087C22—182no—
1088C22—182no—
1089C22C2×D3×D1211yescharacteristic
1090C22D3×#23511yescharacteristic
1091C22#6430611yescharacteristic
1092C22D32×D411yescharacteristic
1093C22D32×D411yescharacteristic
1094C22D3×#23711yescharacteristic
1095C22#6431911yescharacteristic
1096C4—22no—
1097C4—41no—
1098C4—41no—
1099C4—62no—
1100C4—62no—
1101C4—121no—
1102C4—121no—
1103C4—121no—
1104C4—182no—
1105C4—361no—
1106C4—361no—
1107C3—21no—
1108C3#7414611yescharacteristic, complemented
1109C3#7493611yescharacteristic, complemented
1110C2—64no—
1111C2—64no—
1112C2—184no—
1113C2—241no—
1114C2#1059399711yescharacteristic
1115C2D3×#88211yescharacteristic
1116C2D3×#88311yescharacteristic
1117C2#1059426711yescharacteristic
1118C2#1059460811yescharacteristic
1119C2#1059461411yescharacteristic
1120C2#1059462611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC2×#63922C2
hypercenter#95D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C22×C4×D32C2semidirect
3. C2×#63905C2semidirect
4. C2×#63891C2semidirect
5. #10592367C2semidirect
6. C3×#4665C2semidirect
7. C3×#4664C2semidirect
8. #10591399C2semidirect
9. #10591387C2semidirect
10. #10591379C2semidirect
11. #10591376C2semidirect
12. #10591375C2semidirect
13. #10591362C2semidirect
14. #10591278C2semidirect
15. #10591275C2semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. C2×#3750C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
51. C32×#95C22semidirect
52. #63658C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
57. #63579C22semidirect
58. #63579C22semidirect
87. #4665D3semidirect
89. #4664D3semidirect
123. C2×C3×C4×D3D4semidirect
138. C2×D3×Dic3D4semidirect
213. C2×(C2×D3)⋊C4C2×D3semidirect
214. C2×(C2×D3)⋊C4C2×D3semidirect
234. C3×#95C2×D3semidirect
235. C3×#95C2×D3semidirect
243. C3⋊#95C2×D3semidirect
244. C3⋊#95C2×D3semidirect
245. C3⋊#95C2×D3semidirect
246. C3⋊#95C2×D3semidirect
449. C2×C4×D3D12semidirect
501. C2×C3⋊D3#123semidirect
522. C2×C3×D3#123semidirect
575. #95D32semidirect
922. C2×D3#883semidirect
951. C32#2849semidirect
1108. C3#74146semidirect
1109. C3#74936semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×#639222
C2×#639052
C2×#638912
#105923672
C3×#46652
C3×#46642
#105913992
#105913872
#105913792
#105913762
#105913752
#105913622
#105912782
#105912752
#749363
#741463