Finite Group Databasebeta

← #11805693

Subgroups — #11805693

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic, complemented
2C2×#67⋊Dic3C211yesmaximal, characteristic
3C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C3×#4956C211yesmaximal, characteristic
5C3×#4945C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic
7#10591720C211yesmaximal, characteristic, complemented
8#10591701C211yesmaximal, characteristic, complemented
9#10591369C211yesmaximal, characteristic, complemented
10#10591368C211yesmaximal, characteristic, complemented
11#10591335C211yesmaximal, characteristic, complemented
12#10591334C211yesmaximal, characteristic, complemented
13C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
14#10591247C211yesmaximal, characteristic, complemented
15#10591243C211yesmaximal, characteristic, complemented
16#75834—31nomaximal
17#74673—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29#64086—24no—
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36#67⋊Dic3C418yescomplemented
37C2×#3724C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45D3×Dic3⋊C4—24no—
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×D4×Dic3—31no—
57C22×Dic3⋊C4—31no—
58C2×D3×C4⋊C4—31no—
59C2×#67⋊C4—31no—
60C2×#877—31no—
61C2×#877—31no—
62C2×#877—61no—
63C3×#388—31no—
64C3×#386—31no—
65#5220—31no—
66C4×#217—31no—
67#4978—31no—
68#4956—31no—
69#4956D311yescharacteristic
70#4951—31no—
71#4945D311yescharacteristic, complemented
72#4944—31no—
73#4942—31no—
74#4942—31no—
75#4942—31no—
76Dic3×C22⋊C4—31no—
77C4×(C2×D3)⋊C4—31no—
78C4×Dic3⋊C4—31no—
79#4667—31no—
80#4666—31no—
81#4655—31no—
82#4654—31no—
83#4653—31no—
84#4650—31no—
85#4650—31no—
86#4649—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3—22no—
92C22×C3⋊Dic3—22no—
93C22×C3⋊Dic3C2×C414yescomplemented
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67C2×C414yes—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—41no—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C2×D3×Dic3—22no—
114C2×D3×Dic3—22no—
115C2×D3×Dic3—41no—
116C2×D3×Dic3C2×C414yes—
117C32×C22⋊C4—22no—
118#3757—22no—
119#3750—22no—
120#3750D414yescomplemented
121C4×C3⋊Dic3—22no—
122C4×C3⋊Dic3—22no—
123C3×#217—41no—
124C3×#217—41no—
125C3×#217C2×C414yescomplemented
126C3×(C2×D3)⋊C4—22no—
127C3×Dic3⋊C4—22no—
128C3×C4×Dic3—41no—
129#3724—22no—
130#3724—22no—
131Dic3⋊Dic3—22no—
132Dic3⋊Dic3C2×C414yescomplemented
133(C2×D3)⋊Dic3—22no—
134(C2×D3)⋊Dic3C2×C414yes—
135Dic32—41no—
136Dic32C2×C414yescomplemented
137#2352—91noSylow
138C22×C3×D4—31no—
139C23×C3×C4—31no—
140C22×#67C2×D311yescharacteristic
141C23×Dic3—31no—
142C23×Dic3—31no—
143C23×Dic3—31no—
144C23×Dic3—31no—
145C23×Dic3—61no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3C2×D311yescharacteristic
149C2×C3×C4⋊C4—31no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4C2×D311yescharacteristic
156C2×C3×C22⋊C4C2×D311yescharacteristic
157C2×C3×C42—31no—
158C2×#217—31no—
159C2×#217—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—61no—
163C2×#217C2×D311yescharacteristic
164C2×#217C2×D311yescharacteristic
165C2×#217C2×D311yescharacteristic
166D4×Dic3—38no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4C2×D311yescharacteristic
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—61no—
183C2×Dic3⋊C4—61no—
184C2×Dic3⋊C4—64no—
185C2×Dic3⋊C4C2×D311yescharacteristic
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—61no—
195C2×C4×Dic3—61no—
196C2×C4×Dic3C2×D311yescharacteristic
197D3×C4⋊C4—64no—
198#67⋊C4—38no—
199#877—64no—
200#877—64no—
201#877—68no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95—31no—
205C3×#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C3⋊#95C2×D311yescharacteristic
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32C22×C412yes—
229C23×C32C2411yescharacteristic
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3C22×C412yes—
235C22×C3×D3#4112yes—
236C22×C3×D3#4112yes—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D412yes—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—28no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C22×C412yes—
252C2×C3⋊Dic3C22×C412yes—
253C2×C3⋊Dic3C2×D412yes—
254C2×C3⋊Dic3C2×D412yes—
255C2×C3⋊Dic3#4112yes—
256C3×#67—28no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C22×C412yes—
276C2×C3×Dic3C22×C412yes—
277C2×C3×Dic3C22×C412yes—
278C3×C4×D3—44no—
279D3×Dic3—28no—
280D3×Dic3—44no—
281C2×C4×D4—91no—
282C2×#117—91no—
283C22×C4⋊C4—91no—
284#388—31no—
285#388—91no—
286#387—91no—
287#387—91no—
288#386—31no—
289#386—91no—
290#382—91no—
291#380—91no—
292#380—91no—
293C4×C4⋊C4—91no—
294C4×C22⋊C4—91no—
295C4×C22⋊C4—91no—
296C24×C3—21no—
297C24×C3—31no—
298C24×C3C22×D311yescharacteristic
299C24×C3C22×D311yescharacteristic
300C23×D3C22×D311yescharacteristic
301C2×C3×D4—34no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—62no—
314C22×C3×C4—62no—
315C22×C3×C4—121no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—22no—
321C2×#67—22no—
322C2×#67C4×D314yes—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—34no—
326C22×Dic3—34no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—34no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—64no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—62no—
340C22×Dic3—62no—
341C22×Dic3—62no—
342C22×Dic3—62no—
343C22×Dic3—62no—
344C22×Dic3—62no—
345C22×Dic3—62no—
346C22×Dic3—62no—
347C22×Dic3—64no—
348C22×Dic3—64no—
349C22×Dic3—121no—
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C2×C4×D3—22no—
358C2×C4×D3—22no—
359C2×C4×D3—34no—
360C2×C4×D3—41no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—121no—
366C3×C4⋊C4—62no—
367C3×C22⋊C4—24no—
368C3×C22⋊C4—22no—
369C3×C22⋊C4—22no—
370C3×C22⋊C4—34no—
371C3×C22⋊C4—62no—
372C3×C22⋊C4—121no—
373C3×C22⋊C4—121no—
374C3×C42—121no—
375#217—34no—
376#217—41no—
377#217—41no—
378#217—62no—
379#217—62no—
380#217—62no—
381#217—64no—
382#217C4×D314yescomplemented
383(C2×D3)⋊C4—22no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—62no—
386C4⋊Dic3—34no—
387C4⋊Dic3—62no—
388Dic3⋊C4—22no—
389Dic3⋊C4—34no—
390Dic3⋊C4—34no—
391Dic3⋊C4—34no—
392Dic3⋊C4—64no—
393Dic3⋊C4—62no—
394Dic3⋊C4—62no—
395Dic3⋊C4—62no—
396Dic3⋊C4—62no—
397Dic3⋊C4—62no—
398Dic3⋊C4—62no—
399Dic3⋊C4—62no—
400Dic3⋊C4—64no—
401C4×Dic3—34no—
402C4×Dic3—34no—
403C4×Dic3—41no—
404C4×Dic3—62no—
405C4×Dic3—62no—
406C4×Dic3—64no—
407C4×Dic3—64no—
408C4×Dic3—62no—
409C4×Dic3—62no—
410C4×Dic3—121no—
411C4×Dic3—121no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C23×C411yescharacteristic
420C22×C32C22×D411yescharacteristic
421C22×C32C2×#4111yescharacteristic
422C22×C32C2×#4111yescharacteristic
423C22×C32C2×#4111yescharacteristic
424C22×C32H(5,𝔽2)11yescharacteristic
425C22×C322−1+411yescharacteristic
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3#11714yescomplemented
433C32×C4—22no—
434C32×C4—41no—
435C3⋊Dic3—22no—
436C3⋊Dic3—22no—
437C3⋊Dic3—41no—
438C3⋊Dic3C4×D414yes—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—22no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—31no—
447C23×C4—31no—
448C23×C4—91no—
449C23×C4—91no—
450C23×C4—91no—
451C4×D4—98no—
452#117—184no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—91no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—91no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—91no—
460C2×C4⋊C4—184no—
461C2×C22⋊C4—31no—
462C2×C22⋊C4—31no—
463C2×C22⋊C4—31no—
464C2×C22⋊C4—31no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—91no—
467C2×C22⋊C4—91no—
468C2×C22⋊C4D3211yescharacteristic
469C2×C42—31no—
470C2×C42—91no—
471C2×C42—91no—
472C2×C42—91no—
473C2×C42—91no—
474#95—31no—
475#95—31no—
476#95—31no—
477#95—31no—
478#95—91no—
479#95—91no—
480#95—91no—
481#95—91no—
482#95—91no—
483#95—91no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—22no—
500C23×C3—32no—
501C23×C3—32no—
502C23×C3—32no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—61no—
508C23×C3—61no—
509C23×C3—61no—
510C23×C3—61no—
511C23×C3C2×C4×D312yes—
512C23×C3C2×C4×D312yes—
513C23×C3C23×D311yescharacteristic
514C23×C3C23×D311yescharacteristic
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3C2×C4×D312yes—
520C22×D3#23712yes—
521C22×D3#23712yes—
522C3×D4—68no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—22no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—22no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—124no—
561C2×C3×C4D3×D412yes—
562C2×C3×C4D3×D412yes—
563#67—28no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—32no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—32no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—62no—
593C2×Dic3—62no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—68no—
598C2×Dic3—68no—
599C2×Dic3—68no—
600C2×Dic3—62no—
601C2×Dic3—616no—
602C2×Dic3—62no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—62no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—121no—
619C2×Dic3—121no—
620C2×Dic3—121no—
621C2×Dic3—121no—
622C2×Dic3—124no—
623C2×Dic3C2×C4×D312yes—
624C2×Dic3C2×C4×D312yes—
625C2×Dic3C2×C4×D312yes—
626C4×D3—44no—
627C4×D3—68no—
628C4×D3—124no—
629C2×C32—42no—
630C2×C32C2×#11711yescharacteristic
631C2×C32C2×C4×D411yescharacteristic
632C2×C32#52011yescharacteristic
633C2×C32#54611yescharacteristic
634C2×C32#54811yescharacteristic
635C2×C32#55211yescharacteristic
636C2×C32#55311yescharacteristic
637C3×D3—24no—
638C24—31no—
639C24C2×D3211yescharacteristic
640C2×D4—34no—
641C2×D4—62no—
642C2×D4—62no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—94no—
653C22×C4—91no—
654C22×C4—91no—
655C22×C4—91no—
656C22×C4—94no—
657C22×C4—91no—
658C22×C4—121no—
659C22×C4—182no—
660C22×C4—182no—
661C22×C4—182no—
662C22×C4—182no—
663C22×C4—182no—
664C22×C4—182no—
665C22×C4—361no—
666C22×C4C2×D3211yescharacteristic
667C22×C4C2×D3211yescharacteristic
668C4⋊C4—62no—
669C4⋊C4—94no—
670C4⋊C4—94no—
671C4⋊C4—182no—
672C4⋊C4—182no—
673C4⋊C4—182no—
674C4⋊C4—182no—
675C22⋊C4—22no—
676C22⋊C4—34no—
677C22⋊C4—62no—
678C22⋊C4—94no—
679C22⋊C4—121no—
680C22⋊C4—121no—
681C22⋊C4—182no—
682C22⋊C4—182no—
683C42—94no—
684C42—121no—
685C42—182no—
686C42—182no—
687C42—361no—
688C22×C3—24no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—34no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—62no—
718C22×C3—62no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3C22×C4×D311yescharacteristic
724C22×C3C22×C4×D311yescharacteristic
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C2×D3×D411yescharacteristic
727C22×C3C2×#23711yescharacteristic
728C22×C3C2×#23711yescharacteristic
729C22×C3#100411yescharacteristic
730C22×C3#100411yescharacteristic
731C22×C3D3×#4111yescharacteristic
732C22×C3D3×#4111yescharacteristic
733C22×C3D3×#4111yescharacteristic
734C22×C3D3×#4111yescharacteristic
735C22×C3#101011yescharacteristic
736C22×C3#101011yescharacteristic
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3#87714yescomplemented
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—62no—
751C3×C4—62no—
752C3×C4—62no—
753C3×C4—121no—
754C3×C4—121no—
755C3×C4—121no—
756C3×C4—121no—
757Dic3—22no—
758Dic3—22no—
759Dic3—22no—
760Dic3—34no—
761Dic3—34no—
762Dic3—41no—
763Dic3—41no—
764Dic3—41no—
765Dic3—41no—
766Dic3—64no—
767Dic3—64no—
768Dic3—62no—
769Dic3—62no—
770Dic3—62no—
771Dic3—62no—
772Dic3—122no—
773Dic3—122no—
774Dic3—121no—
775Dic3—121no—
776C32#235211yescharacteristic, complemented, Sylow
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—32no—
784C23—32no—
785C23—32no—
786C23—61no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23C4×D3212yes—
791C23C22×D3211yescharacteristic
792D4—68no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—32no—
799C2×C4—32no—
800C2×C4—32no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—92no—
820C2×C4—92no—
821C2×C4—92no—
822C2×C4—92no—
823C2×C4—92no—
824C2×C4—124no—
825C2×C4—188no—
826C2×C4—188no—
827C2×C4—181no—
828C2×C4—181no—
829C2×C4—181no—
830C2×C4—181no—
831C2×C4—181no—
832C2×C4—181no—
833C2×C4—181no—
834C2×C4—364no—
835C2×C4#381112yes—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—44no—
844C2×C3—42no—
845C2×C3—42no—
846C2×C3—64no—
847C2×C3C2×#87711yescharacteristic
848C2×C3D3×#11711yescharacteristic
849C2×C3C4×D3×D411yescharacteristic
850C2×C3C4×D3×D411yescharacteristic
851C2×C3#554611yescharacteristic
852C2×C3#554611yescharacteristic
853C2×C3#559111yescharacteristic
854C2×C3#559811yescharacteristic
855C2×C3#560111yescharacteristic
856C2×C3#561011yescharacteristic
857C2×C3#565011yescharacteristic
858C2×C3#566111yescharacteristic
859C2×C3#567711yescharacteristic
860C2×C3#570811yescharacteristic
861D3—24no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—34no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—62no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22C2×C4×D3211yescharacteristic
877C22#6430611yescharacteristic
878C22#6430911yescharacteristic
879C22D3×#23711yescharacteristic
880C22D3×#23711yescharacteristic
881C22#6431311yescharacteristic
882C22C2×#381111yescharacteristic
883C4—22no—
884C4—41no—
885C4—62no—
886C4—62no—
887C4—62no—
888C4—94no—
889C4—121no—
890C4—121no—
891C4—121no—
892C4—121no—
893C4—182no—
894C4—182no—
895C4—361no—
896C3—21no—
897C3#7467311yescharacteristic, complemented
898C3#7583411yescharacteristic, complemented
899C2—42no—
900C2—64no—
901C2D3×#87711yescharacteristic
902C2#1059405111yescharacteristic
903C2#1059412011yescharacteristic
904C2#1059421011yescharacteristic
905C2C4×#381111yescharacteristic
906C2#1059516111yescharacteristic
907C2#1059530711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64086C2semidirect
3. C2×D3×Dic3⋊C4C2semidirect
5. C3×#4945C2semidirect
7. #10591720C2semidirect
8. #10591701C2semidirect
9. #10591369C2semidirect
10. #10591368C2semidirect
11. #10591335C2semidirect
12. #10591334C2semidirect
13. C4×(C2×D3)⋊Dic3C2semidirect
14. #10591247C2semidirect
15. #10591243C2semidirect
36. #67⋊Dic3C4semidirect
71. #4945D3semidirect
93. C22×C3⋊Dic3C2×C4semidirect
120. #3750D4semidirect
125. C3×#217C2×C4semidirect
132. Dic3⋊Dic3C2×C4semidirect
136. Dic32C2×C4semidirect
382. #217C4×D3semidirect
432. C2×C3×D3#117semidirect
743. C2×D3#877semidirect
776. C32#2352semidirect
897. C3#74673semidirect
898. C3#75834semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C2×#67⋊Dic32
C2×D3×Dic3⋊C42
C3×#49562
C3×#49452
#105917212
#105917202
#105917012
#105913692
#105913682
#105913352
#105913342
C4×(C2×D3)⋊Dic32
#105912472
#105912432
#758343
#746733