Finite Group Databasebeta

← #11805261

Subgroups — #11805261

Order 1152.

1181 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic3⋊C4C211yesmaximal, characteristic
2#10592675C211yesmaximal, characteristic, complemented
3C3×#4987C211yesmaximal, characteristic
4C3×#4978C211yesmaximal, characteristic, complemented
5#10591369C211yesmaximal, characteristic
6#10591369C211yesmaximal, characteristic
7#10591368C211yesmaximal, characteristic
8Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic
9#10591264C211yesmaximal, characteristic, complemented
10#10591262C211yesmaximal, characteristic, complemented
11#10591257C211yesmaximal, characteristic, complemented
12#10591251C211yesmaximal, characteristic, complemented
13#10591250C211yesmaximal, characteristic, complemented
14#10591243C211yesmaximal, characteristic, complemented
15#10591237C211yesmaximal, characteristic
16#74962—31nomaximal
17#73880—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41D3×Dic3⋊C4C418yescomplemented
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C22×Dic3⋊C4—31no—
55C2×D3×C4⋊C4—31no—
56C3×#387—31no—
57C3×#380—31no—
58C4×#217—31no—
59#4987D311yescharacteristic
60#4980—31no—
61#4978—31no—
62#4978D311yescharacteristic, complemented
63#4976—31no—
64#4976—31no—
65#4976—31no—
66#4976—61no—
67#4942—31no—
68#4942—31no—
69Dic3×C22⋊C4—31no—
70Dic3×C22⋊C4—31no—
71C4×(C2×D3)⋊C4—31no—
72C4×Dic3⋊C4—31no—
73#4667—31no—
74#4667—31no—
75#4666—31no—
76#4666—31no—
77#4654—31no—
78#4653—31no—
79#4652—31no—
80#4652—31no—
81#4649—31no—
82#4649—31no—
83#4649—31no—
84#4647—31no—
85C23×C3×D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×C4×D3—41no—
101C2×C3×C4×D3—41no—
102C2×C3×C4×D3C2×C414yes—
103C2×D3×Dic3—22no—
104C2×D3×Dic3—22no—
105C2×D3×Dic3—41no—
106C2×D3×Dic3—41no—
107C2×D3×Dic3C2×C414yes—
108C2×D3×Dic3C2×C414yes—
109C32×C4⋊C4—41no—
110#3750—22no—
111#3750—41no—
112#3750C2×C414yes—
113C4×C3⋊Dic3—22no—
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×C4⋊Dic3—41no—
117C3×Dic3⋊C4C2×C414yes—
118C3×C4×Dic3—41no—
119#3724—22no—
120#3724—41no—
121#3724C2×C414yes—
122Dic3⋊Dic3C2×C414yes—
123(C2×D3)⋊Dic3—22no—
124(C2×D3)⋊Dic3Q814yes—
125Dic32—22no—
126Dic32—41no—
127Dic32—41no—
128Dic32—41no—
129#2345—91noSylow
130C23×C3×C4—31no—
131C23×Dic3—31no—
132C23×Dic3—31no—
133C22×C4×D3—31no—
134C22×C4×D3—31no—
135C22×C4×D3C2×D311yescharacteristic
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4C2×D311yescharacteristic
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C42—31no—
144C2×#217—31no—
145C2×#217—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4C2×D311yescharacteristic
149C2×(C2×D3)⋊C4C2×D311yescharacteristic
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3C2×D311yescharacteristic
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—38no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—61no—
167C2×Dic3⋊C4—61no—
168C2×Dic3⋊C4—61no—
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—61no—
181C2×C4×Dic3C2×D311yescharacteristic
182D3×C4⋊C4—38no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—61no—
202C3⋊#95—61no—
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C23×C32C2411yescharacteristic
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3—21no—
213C22×C3×D3—21no—
214C22×C3×D3C22×C412yes—
215C22×C3×D3C2×Q812yes—
216C22×C3×D3#4112yes—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4C22×C412yes—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3C22×C412yes—
234C2×C3⋊Dic3C22×C412yes—
235C2×C3⋊Dic3C2×Q812yes—
236C2×C3⋊Dic3#4112yes—
237C2×C3⋊Dic3#4112yes—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C22×C412yes—
256C2×C3×Dic3C22×C412yes—
257C2×C3×Dic3C22×C412yes—
258C2×C3×Dic3C2×Q812yes—
259C3×C4×D3—44no—
260D3×Dic3—28no—
261D3×Dic3—44no—
262C22×C4⋊C4—91no—
263#389—91no—
264#389—91no—
265#387—31no—
266#387—91no—
267#387—91no—
268#387—91no—
269#380—31no—
270#380—91no—
271#380—91no—
272C4×C4⋊C4—91no—
273C4×C4⋊C4—91no—
274C4×C22⋊C4—91no—
275C4×C22⋊C4—91no—
276C4×C22⋊C4—91no—
277C24×C3—31no—
278C23×D3C22×D311yescharacteristic
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—34no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—121no—
291C22×C3×C4—121no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—34no—
305C22×Dic3—34no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—62no—
313C22×Dic3—62no—
314C22×Dic3—121no—
315C22×Dic3—121no—
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C2×C4×D3—34no—
324C2×C4×D3—34no—
325C2×C4×D3—41no—
326C2×C4×D3—41no—
327C2×C4×D3—62no—
328C2×C4×D3—62no—
329C2×C4×D3—121no—
330C2×C4×D3—121no—
331C2×C4×D3C4×D314yes—
332C3×C4⋊C4—34no—
333C3×C4⋊C4—41no—
334C3×C4⋊C4—41no—
335C3×C4⋊C4—42no—
336C3×C4⋊C4—121no—
337C3×C22⋊C4—62no—
338C3×C22⋊C4—62no—
339C3×C42—121no—
340#217—34no—
341#217—62no—
342(C2×D3)⋊C4—22no—
343(C2×D3)⋊C4—22no—
344(C2×D3)⋊C4—34no—
345(C2×D3)⋊C4—62no—
346C4⋊Dic3—34no—
347C4⋊Dic3—41no—
348Dic3⋊C4—34no—
349Dic3⋊C4—34no—
350Dic3⋊C4—34no—
351Dic3⋊C4—34no—
352Dic3⋊C4—34no—
353Dic3⋊C4—64no—
354Dic3⋊C4—62no—
355Dic3⋊C4—62no—
356Dic3⋊C4—62no—
357Dic3⋊C4—62no—
358Dic3⋊C4—122no—
359Dic3⋊C4—121no—
360Dic3⋊C4—121no—
361Dic3⋊C4—121no—
362Dic3⋊C4—121no—
363Dic3⋊C4—122no—
364Dic3⋊C4C4×D314yes—
365C4×Dic3—41no—
366C4×Dic3—62no—
367C4×Dic3—62no—
368C4×Dic3—62no—
369C4×Dic3—62no—
370C4×Dic3—122no—
371C4×Dic3—121no—
372C4×Dic3—121no—
373C4×Dic3—121no—
374C4×Dic3—121no—
375C4×Dic3—121no—
376C4×Dic3—121no—
377C22×C32C23×C411yescharacteristic
378C22×C32C22×Q811yescharacteristic
379C22×C32C2×#4111yescharacteristic
380C22×C32C2×#4111yescharacteristic
381C22×C32C2×#4111yescharacteristic
382C22×C32H(5,𝔽2)11yescharacteristic
383C22×C32H(5,𝔽2)11yescharacteristic
384C2×C3×D3—22no—
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3C4×Q814yes—
391C32×C4—22no—
392C32×C4—41no—
393C32×C4—41no—
394C3⋊Dic3—22no—
395C3⋊Dic3—22no—
396C3⋊Dic3—41no—
397C3⋊Dic3#11714yes—
398C3×Dic3—22no—
399C3×Dic3—22no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C23×C4—31no—
406C23×C4—91no—
407C23×C4—91no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—98no—
411C2×C4⋊C4—91no—
412C2×C4⋊C4—91no—
413C2×C4⋊C4—91no—
414C2×C4⋊C4—91no—
415C2×C4⋊C4—91no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4D3211yescharacteristic
419C2×C22⋊C4—31no—
420C2×C22⋊C4—31no—
421C2×C22⋊C4—91no—
422C2×C22⋊C4—91no—
423C2×C42—31no—
424C2×C42—91no—
425C2×C42—91no—
426C2×C42—91no—
427C2×C42—91no—
428C2×C42—91no—
429#95—31no—
430#95—31no—
431#95—31no—
432#95—31no—
433#95—31no—
434#95—31no—
435#95—91no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95—91no—
441C23×C3—21no—
442C23×C3—32no—
443C23×C3—32no—
444C23×C3—32no—
445C23×C3—61no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3—61no—
449C23×C3C23×D311yescharacteristic
450C23×C3C23×D311yescharacteristic
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3C2×C4×D312yes—
456C22×D3#23712yes—
457C22×D3D3×Q812yes—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—22no—
476C2×C3×C4—32no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—124no—
505C2×C3×C4C2×C4×D312yes—
506C2×C3×C4C2×C4×D312yes—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—32no—
527C2×Dic3—32no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—32no—
533C2×Dic3—32no—
534C2×Dic3—62no—
535C2×Dic3—62no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—68no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—121no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—124no—
562C2×Dic3C2×C4×D312yes—
563C2×Dic3C2×C4×D312yes—
564C2×Dic3C2×C4×D312yes—
565C2×Dic3D3×Q812yes—
566C4×D3—44no—
567C4×D3—68no—
568C4×D3—124no—
569C2×C32C2×#11711yescharacteristic
570C2×C32C2×C4×Q811yescharacteristic
571C2×C32#51811yescharacteristic
572C2×C32#55311yescharacteristic
573C2×C32#55311yescharacteristic
574C2×C32#55411yescharacteristic
575C2×C32#55411yescharacteristic
576C3×D3—24no—
577C24—31no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—34no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—94no—
587C22×C4—94no—
588C22×C4—91no—
589C22×C4—91no—
590C22×C4—91no—
591C22×C4—91no—
592C22×C4—121no—
593C22×C4—121no—
594C22×C4—182no—
595C22×C4—182no—
596C22×C4—361no—
597C22×C4—361no—
598C22×C4C2×D3211yescharacteristic
599C22×C4C2×D3211yescharacteristic
600C22×C4C2×D3211yescharacteristic
601C4⋊C4—34no—
602C4⋊C4—41no—
603C4⋊C4—94no—
604C4⋊C4—94no—
605C4⋊C4—94no—
606C4⋊C4—121no—
607C4⋊C4—182no—
608C4⋊C4—182no—
609C4⋊C4—361no—
610C4⋊C4—361no—
611C22⋊C4—62no—
612C22⋊C4—62no—
613C22⋊C4—94no—
614C22⋊C4—182no—
615C42—121no—
616C42—182no—
617C42—182no—
618C42—361no—
619C42—361no—
620C42—361no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—34no—
629C22×C3—62no—
630C22×C3—62no—
631C22×C3—62no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3C22×C4×D311yescharacteristic
636C22×C3C22×C4×D311yescharacteristic
637C22×C3C2×#23711yescharacteristic
638C22×C3#100411yescharacteristic
639C22×C3#100411yescharacteristic
640C22×C3#100411yescharacteristic
641C22×C3C2×D3×Q811yescharacteristic
642C22×C3C2×D3×Q811yescharacteristic
643C22×C3D3×#4111yescharacteristic
644C22×C3D3×#4111yescharacteristic
645C22×C3D3×#4111yescharacteristic
646C22×C3D3×#4111yescharacteristic
647C22×C3D3×#4111yescharacteristic
648C22×C3#100911yescharacteristic
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—22no—
655C2×D3#88714yes—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—42no—
659C3×C4—42no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—62no—
665C3×C4—62no—
666C3×C4—62no—
667C3×C4—62no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672Dic3—22no—
673Dic3—22no—
674Dic3—22no—
675Dic3—22no—
676Dic3—34no—
677Dic3—34no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3—64no—
682Dic3—62no—
683Dic3—62no—
684Dic3—62no—
685Dic3—62no—
686Dic3—122no—
687Dic3—122no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691C32#234511yescharacteristic, complemented, Sylow
692C23—32no—
693C23—32no—
694C23—32no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23C22×D3211yescharacteristic
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—92no—
730C2×C4—92no—
731C2×C4—92no—
732C2×C4—92no—
733C2×C4—92no—
734C2×C4—124no—
735C2×C4—188no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—364no—
744C2×C4C4×D3212yes—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—64no—
753C2×C3#548611yescharacteristic
754C2×C3C2×#88711yescharacteristic
755C2×C3D3×#11711yescharacteristic
756C2×C3D3×#11711yescharacteristic
757C2×C3#554511yescharacteristic
758C2×C3C4×D3×Q811yescharacteristic
759C2×C3#560111yescharacteristic
760C2×C3#560111yescharacteristic
761C2×C3#563611yescharacteristic
762C2×C3#563611yescharacteristic
763C2×C3#563611yescharacteristic
764C2×C3#566111yescharacteristic
765C2×C3#569011yescharacteristic
766C2×C3#570911yescharacteristic
767D3—24no—
768C22—34no—
769C22—62no—
770C22—62no—
771C22—62no—
772C22—62no—
773C22—62no—
774C22—62no—
775C22C2×C4×D3211yescharacteristic
776C22#6430711yescharacteristic
777C22D3×#23711yescharacteristic
778C22#6431211yescharacteristic
779C22D32×Q811yescharacteristic
780C22#6431911yescharacteristic
781C22#6433011yescharacteristic
782C4—22no—
783C4—41no—
784C4—41no—
785C4—62no—
786C4—62no—
787C4—62no—
788C4—62no—
789C4—94no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—182no—
794C4—182no—
795C4—361no—
796C3—21no—
797C3#7388011yescharacteristic, complemented
798C3#7496211yescharacteristic, complemented
799C2—64no—
800C2D3×#88711yescharacteristic
801C2#1059439511yescharacteristic
802C2#1059443411yescharacteristic
803C2#1059460211yescharacteristic
804C2#1059505611yescharacteristic
805C2#1059518311yescharacteristic
806C2#1059537011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2345
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592675C2semidirect
4. C3×#4978C2semidirect
9. #10591264C2semidirect
10. #10591262C2semidirect
11. #10591257C2semidirect
12. #10591251C2semidirect
13. #10591250C2semidirect
14. #10591243C2semidirect
41. D3×Dic3⋊C4C4semidirect
62. #4978D3semidirect
691. C32#2345semidirect
797. C3#73880semidirect
798. C3#74962semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic3⋊C42
#105926752
C3×#49872
C3×#49782
#105913692
#105913682
Dic3×(C2×D3)⋊C42
#105912642
#105912622
#105912572
#105912512
#105912502
#105912432
#105912372
#749623
#738803