Finite Group Databasebeta

← #11856278

Subgroups — #11856278

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×C3×#894C211yesmaximal, characteristic, complemented
3C2×#63922C211yesmaximal, characteristic
4C2×#63884C211yesmaximal, characteristic, complemented
5#10592688C211yesmaximal, characteristic, complemented
6C3×#4989C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591387C211yesmaximal, characteristic, complemented
9#10591381C211yesmaximal, characteristic, complemented
10#10591374C211yesmaximal, characteristic, complemented
11#10591372C211yesmaximal, characteristic, complemented
12#10591363C211yesmaximal, characteristic, complemented
13#10591362C211yesmaximal, characteristic, complemented
14#10591294C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#82912—31nomaximal
17#74656—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×C32×C4⋊C4C2211yescharacteristic, complemented
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
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×C3×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C3×#894—24no—
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
49#63922—24no—
50#63884—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57#63579C2211yescharacteristic, complemented
58#63579C2211yescharacteristic, complemented
59C23×C4×D3—31no—
60C23×C4×D3—31no—
61C2×C3×#123—31no—
62C2×#937—31no—
63C2×#935—31no—
64C2×#894—31no—
65C2×#894D311yescharacteristic, complemented
66C2×#882—31no—
67C3×#385—31no—
68#5213—31no—
69#5211—31no—
70#4989—31no—
71#4989—31no—
72#4989—31no—
73#4989—31no—
74#4989—31no—
75#4989—61no—
76#4989D311yescharacteristic, complemented
77#4958—31no—
78#4956—31no—
79#4956—31no—
80#4956—31no—
81#4956—31no—
82#4955—31no—
83#4955—31no—
84#4946—31no—
85#4943—31no—
86#4665—31no—
87#4665—31no—
88#4664—31no—
89#4664—31no—
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—
140C32×C4⋊C4—22no—
141#3752—22no—
142#3752—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—
149C3×Dic3⋊C4—22no—
150C3×Dic3⋊C4—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
185C3×#123—64no—
186C2×C3×C4⋊C4—21no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
190C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201#937—64no—
202#935—64no—
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—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—61no—
215C2×(C2×D3)⋊C4—61no—
216C2×(C2×D3)⋊C4C2×D311yescharacteristic
217C2×(C2×D3)⋊C4C2×D311yescharacteristic
218C2×(C2×D3)⋊C4C2×D311yescharacteristic
219C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
220C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—61no—
224C2×Dic3⋊C4C2×D311yescharacteristic, complemented
225C2×Dic3⋊C4C2×D311yescharacteristic, complemented
226#894—24no—
227#894—64no—
228#882—64no—
229C3×#95—31no—
230C3×#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—31no—
241C3⋊#95—31no—
242C3⋊#95—31no—
243C3⋊#95—61no—
244C3⋊#95—61no—
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—31no—
327C2×#123—91no—
328C2×#120—91no—
329#386—91no—
330#386—91no—
331#386—91no—
332#386—91no—
333#385—31no—
334#385—91no—
335#385—91no—
336#385—91no—
337#381—91no—
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×D3#6714yescomplemented
450C3×C4⋊C4—22no—
451C3×C4⋊C4—22no—
452C3×C4⋊C4—42no—
453C3×C4⋊C4—62no—
454C3×C4⋊C4—62no—
455C3×C22⋊C4—62no—
456C3×C22⋊C4—62no—
457C3×C22⋊C4—62no—
458C3×C22⋊C4—62no—
459C3×C22⋊C4—62no—
460#217—62no—
461#217—62no—
462#217—62no—
463#217—62no—
464#217—62no—
465(C2×D3)⋊C4—22no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—22no—
468(C2×D3)⋊C4—22no—
469(C2×D3)⋊C4—22no—
470(C2×D3)⋊C4—62no—
471(C2×D3)⋊C4—62no—
472(C2×D3)⋊C4—62no—
473(C2×D3)⋊C4—62no—
474(C2×D3)⋊C4—62no—
475(C2×D3)⋊C4—62no—
476(C2×D3)⋊C4—62no—
477(C2×D3)⋊C4—64no—
478(C2×D3)⋊C4—62no—
479(C2×D3)⋊C4—62no—
480(C2×D3)⋊C4—62no—
481(C2×D3)⋊C4—62no—
482(C2×D3)⋊C4—122no—
483Dic3⋊C4—22no—
484Dic3⋊C4—22no—
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—64no—
549#123—184no—
550#120—184no—
551C2×C4⋊C4—31no—
552C2×C4⋊C4—31no—
553C2×C4⋊C4—91no—
554C2×C4⋊C4D3211yescharacteristic, complemented
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—91no—
571#95—91no—
572#95—91no—
573#95—91no—
574#95—91no—
575#95—91no—
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×D3#23512yes—
651C22×D3D3×D412yes—
652C22×D3D3×D412yes—
653C22×D3D3×D412yes—
654C22×D3#23912yes—
655C22×D3C2×#6712yes—
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×C4D3×D412yes—
700C2×C3×C4C2×#6712yes—
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×Dic3D3×D412yes—
747C2×Dic3C2×#6712yes—
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—22no—
821C4⋊C4—62no—
822C4⋊C4—62no—
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×C3C2×#23511yescharacteristic
866C22×C3C2×D3×D411yescharacteristic
867C22×C3C2×D3×D411yescharacteristic
868C22×C3C2×D3×D411yescharacteristic
869C22×C3C2×D3×D411yescharacteristic
870C22×C3C2×D3×D411yescharacteristic
871C22×C3C2×#23911yescharacteristic
872C22×C3D3×#4111yescharacteristic
873C22×C3D3×#4111yescharacteristic
874C22×C3D3×#4111yescharacteristic
875C22×C3D3×#4111yescharacteristic
876C22×C3D3×#4111yescharacteristic
877C22×C3D3×#4111yescharacteristic
878C22×C3C22×#6711yescharacteristic
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#89414yescomplemented
922C2×D3#93714yes—
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×#6712yes—
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×#89411yescharacteristic
1041C2×C3#554711yescharacteristic
1042C2×C3#554711yescharacteristic
1043C2×C3D3×#12011yescharacteristic
1044C2×C3#562711yescharacteristic
1045C2×C3#562711yescharacteristic
1046C2×C3D3×#12311yescharacteristic
1047C2×C3D3×#12311yescharacteristic
1048C2×C3D3×#12311yescharacteristic
1049C2×C3#565611yescharacteristic
1050C2×C3#565611yescharacteristic
1051C2×C3C2×#93711yescharacteristic
1052C2×C3#582811yescharacteristic
1053C2×C3#582811yescharacteristic
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—
1089C22D3×#23511yescharacteristic
1090C22#6430611yescharacteristic
1091C22D32×D411yescharacteristic
1092C22D32×D411yescharacteristic
1093C22D3×#23911yescharacteristic
1094C22#6431911yescharacteristic
1095C22C2×D3×#6711yescharacteristic
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#7465611yescharacteristic, complemented
1109C3#8291211yescharacteristic, complemented
1110C2—64no—
1111C2—64no—
1112C2—184no—
1113C2—241no—
1114C2D3×#89411yescharacteristic
1115C2#1059460811yescharacteristic
1116C2#1059461411yescharacteristic
1117C2#1059461511yescharacteristic
1118C2#1059506011yescharacteristic
1119C2D3×#93711yescharacteristic
1120C2#1059542411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63922C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D32C2semidirect
2. C2×C3×#894C2semidirect
4. C2×#63884C2semidirect
5. #10592688C2semidirect
6. C3×#4989C2semidirect
7. #10591399C2semidirect
8. #10591387C2semidirect
9. #10591381C2semidirect
10. #10591374C2semidirect
11. #10591372C2semidirect
12. #10591363C2semidirect
13. #10591362C2semidirect
14. #10591294C2semidirect
15. #10591275C2semidirect
31. C2×C32×C4⋊C4C22semidirect
34. C2×#3750C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
57. #63579C22semidirect
58. #63579C22semidirect
65. C2×#894D3semidirect
76. #4989D3semidirect
123. C2×C3×C4×D3D4semidirect
138. C2×D3×Dic3D4semidirect
189. C2×C3×C4⋊C4C2×D3semidirect
190. C2×C3×C4⋊C4C2×D3semidirect
219. C2×(C2×D3)⋊C4C2×D3semidirect
220. C2×(C2×D3)⋊C4C2×D3semidirect
224. C2×Dic3⋊C4C2×D3semidirect
225. C2×Dic3⋊C4C2×D3semidirect
245. C3⋊#95C2×D3semidirect
246. C3⋊#95C2×D3semidirect
449. C2×C4×D3#67semidirect
501. C2×C3⋊D3#123semidirect
522. C2×C3×D3#123semidirect
554. C2×C4⋊C4D32semidirect
921. C2×D3#894semidirect
951. C32#2849semidirect
1108. C3#74656semidirect
1109. C3#82912semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×C3×#8942
C2×#639222
C2×#638842
#105926882
C3×#49892
#105913992
#105913872
#105913812
#105913742
#105913722
#105913632
#105913622
#105912942
#105912752
#829123
#746563