Finite Group Databasebeta

← #11805694

Subgroups — #11805694

Order 1152.

1463 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#877C211yesmaximal, characteristic, complemented
2C2×#63952C211yesmaximal, characteristic
3C2×#63883C211yesmaximal, characteristic, complemented
4#10592655C211yesmaximal, characteristic
5C3×#4945C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic
7#10591716C211yesmaximal, characteristic, complemented
8#10591702C211yesmaximal, characteristic, complemented
9#10591367C211yesmaximal, characteristic, complemented
10#10591333C211yesmaximal, characteristic, complemented
11C4×#3722C211yesmaximal, characteristic, complemented
12#10591245C211yesmaximal, characteristic, complemented
13Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591193C211yesmaximal, characteristic, complemented
16#82272—31nomaximal
17#75834—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C3×#877—24no—
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63952C418yescomplemented
45#63883—24no—
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×#117—31no—
57C2×C4×#67—31no—
58C2×D3×C4⋊C4—31no—
59C2×D3×C4⋊C4—31no—
60C2×#67⋊C4—31no—
61C2×#877D311yescharacteristic, complemented
62C3×#388—31no—
63#5212—31no—
64#4987—31no—
65#4978—31no—
66#4977—31no—
67Dic3×C4⋊C4—31no—
68#4956—31no—
69#4956—31no—
70#4956—31no—
71#4956—31no—
72#4956—61no—
73#4951—31no—
74#4945—31no—
75#4945D311yescharacteristic, complemented
76#4942—31no—
77C4×(C2×D3)⋊C4—31no—
78C4×(C2×D3)⋊C4—31no—
79C4×(C2×D3)⋊C4—31no—
80#4933—31no—
81#4933—31no—
82C4×Dic3⋊C4—31no—
83#4667—31no—
84#4666—31no—
85#4655—31no—
86#4650—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C2×#638—22no—
92C2×#638—22no—
93C2×#638C2×C414yes—
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—41no—
100C22×C3×Dic3—22no—
101C22×C3×Dic3—22no—
102C22×C3×Dic3C2×C414yescomplemented
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×#624—22no—
112C2×#624—22no—
113C2×#624—22no—
114C2×#624—22no—
115C2×#624—41no—
116C2×#624C2×C414yes—
117C32×C22⋊C4—22no—
118#3757—41no—
119#3752—22no—
120C3×#217—22no—
121C3×#217—41no—
122C3×#217C2×C414yescomplemented
123C3×Dic3⋊C4—22no—
124C3×Dic3⋊C4—22no—
125C3×Dic3⋊C4D414yescomplemented
126C3×C4×Dic3—22no—
127C3×C4×Dic3—22no—
128C3×C4×Dic3—41no—
129#3724C2×C414yescomplemented
130Dic3⋊Dic3—22no—
131Dic3⋊Dic3—22no—
132Dic3⋊Dic3—22no—
133#3722—22no—
134#3722C2×C414yes—
135Dic32—41no—
136Dic32C2×C414yescomplemented
137#2352—91noSylow
138C23×C3×C4—31no—
139C22×#67—31no—
140C22×#67—31no—
141C22×#67—61no—
142C23×Dic3C2×D311yescharacteristic
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—61no—
150C3×#117—64no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4C2×D311yescharacteristic
159C2×C3×C22⋊C4C2×D311yescharacteristic
160C2×C3×C42—31no—
161C2×C3×C42—31no—
162C2×C3×C42—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—61no—
166C2×#217C2×D311yescharacteristic
167C2×#217C2×D311yescharacteristic
168C2×#217C2×D311yescharacteristic
169C4×#67—38no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—61no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4C2×D311yescharacteristic
186C2×Dic3⋊C4C2×D311yescharacteristic
187C2×Dic3⋊C4C2×D311yescharacteristic
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3C2×D311yescharacteristic
193C2×C4×Dic3C2×D311yescharacteristic
194C2×C4×Dic3C2×D311yescharacteristic
195D3×C4⋊C4—64no—
196D3×C4⋊C4—64no—
197#67⋊C4—38no—
198#877—24no—
199C3×#95—31no—
200C3×#95—31no—
201C3⋊#95—31no—
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—61no—
218C3⋊#95—61no—
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32C22×C412yes—
228C23×C32C2411yescharacteristic
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3C22×C412yes—
234C22×C3⋊D3#4112yes—
235C22×C3⋊D3#4112yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2×D412yes—
242#638—28no—
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⋊Dic3C22×C412yes—
252C4×C3⋊D3—44no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—28no—
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×Dic3C22×C412yes—
272C2×C3×Dic3C22×C412yes—
273C2×C3×Dic3C22×C412yes—
274C2×C3×Dic3C22×C412yes—
275C2×C3×Dic3C2×D412yes—
276C2×C3×Dic3C2×D412yes—
277C2×C3×Dic3#4112yes—
278#624—28no—
279#624—44no—
280C2×C4×D4—91no—
281C2×#117—31no—
282C22×C4⋊C4—91no—
283#388—31no—
284#388—91no—
285#387—91no—
286#387—91no—
287#386—91no—
288#386—91no—
289#382—91no—
290#380—91no—
291#380—91no—
292C4×C4⋊C4—91no—
293C4×C22⋊C4—91no—
294C4×C22⋊C4—91no—
295C24×C3—21no—
296C24×C3C22×D311yescharacteristic
297C24×C3C22×D311yescharacteristic
298C23×D3—31no—
299C23×D3—31no—
300C23×D3—61no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—34no—
305C22×C3×C4—31no—
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—62no—
313C22×C3×C4—62no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—34no—
319C2×#67—34no—
320C2×#67—64no—
321C2×#67—62no—
322C2×#67—62no—
323C2×#67—62no—
324C2×#67—62no—
325C2×#67—122no—
326C2×#67—122no—
327C22×Dic3—22no—
328C22×Dic3—22no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3C4×D314yescomplemented
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C2×C4×D3—34no—
348C2×C4×D3—34no—
349C2×C4×D3—62no—
350C2×C4×D3—62no—
351C2×C4×D3—62no—
352C2×C4×D3—62no—
353C2×C4×D3—62no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—122no—
362C2×C4×D3—122no—
363C2×C4×D3—121no—
364C2×C4×D3—121no—
365C2×C4×D3—121no—
366C2×C4×D3—121no—
367C2×C4×D3—122no—
368C3×C4⋊C4—34no—
369C3×C4⋊C4—62no—
370C3×C4⋊C4—62no—
371C3×C22⋊C4—22no—
372C3×C22⋊C4—22no—
373C3×C22⋊C4—34no—
374C3×C22⋊C4—42no—
375C3×C22⋊C4—62no—
376C3×C22⋊C4—121no—
377C3×C42—62no—
378C3×C42—62no—
379C3×C42—121no—
380#217—22no—
381#217—41no—
382#217—121no—
383#217—121no—
384#217—122no—
385#217C4×D314yescomplemented
386(C2×D3)⋊C4—34no—
387(C2×D3)⋊C4—34no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—122no—
393C4⋊Dic3—62no—
394C4⋊Dic3—62no—
395C4⋊Dic3—62no—
396Dic3⋊C4—22no—
397Dic3⋊C4—22no—
398Dic3⋊C4—34no—
399Dic3⋊C4—34no—
400Dic3⋊C4—62no—
401Dic3⋊C4—62no—
402Dic3⋊C4—62no—
403Dic3⋊C4#6714yescomplemented
404C4×Dic3—22no—
405C4×Dic3—22no—
406C4×Dic3—34no—
407C4×Dic3—34no—
408C4×Dic3—41no—
409C4×Dic3—121no—
410C4×Dic3—121no—
411C22×C32—22no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C23×C411yescharacteristic
419C22×C32C22×D411yescharacteristic
420C22×C32C2×#4111yescharacteristic
421C22×C32C2×#4111yescharacteristic
422C22×C32C2×#4111yescharacteristic
423C22×C32H(5,𝔽2)11yescharacteristic
424C22×C322−1+411yescharacteristic
425C2×C3⋊D3—22no—
426C2×C3⋊D3—22no—
427C2×C3⋊D3—22no—
428C2×C3⋊D3—22no—
429C2×C3⋊D3—22no—
430C2×C3⋊D3—22no—
431C2×C3⋊D3#11714yescomplemented
432C32×C4—22no—
433C32×C4—41no—
434C3⋊Dic3—22no—
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3C4×D414yes—
445C22×D4—91no—
446C23×C4—31no—
447C23×C4—91no—
448C23×C4—91no—
449C23×C4—91no—
450C4×D4—98no—
451#117—64no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—91no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—184no—
460C2×C22⋊C4—31no—
461C2×C22⋊C4—31no—
462C2×C22⋊C4—31no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—91no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—91no—
467C2×C22⋊C4D3211yescharacteristic
468C2×C42—31no—
469C2×C42—31no—
470C2×C42—31no—
471C2×C42—91no—
472C2×C42—91no—
473#95—31no—
474#95—31no—
475#95—91no—
476#95—91no—
477#95—91no—
478#95—91no—
479#95—91no—
480#95—91no—
481#95—91no—
482#95—91no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
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—22no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3C2×C4×D312yes—
504C23×C3C2×C4×D312yes—
505C23×C3C23×D311yescharacteristic
506C23×C3C23×D311yescharacteristic
507C22×D3—32no—
508C22×D3—32no—
509C22×D3—32no—
510C22×D3—32no—
511C22×D3—32no—
512C22×D3—32no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—62no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—121no—
525C22×D3—121no—
526C22×D3—121no—
527C22×D3—121no—
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—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—22no—
539C2×C3×C4—32no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—32no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—68no—
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—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4D3×D412yes—
570C2×C3×C4C2×#6712yes—
571#67—68no—
572#67—68no—
573#67—128no—
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—28no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—62no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—62no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
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—61no—
612C2×Dic3—121no—
613C2×Dic3—121no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—121no—
617C2×Dic3—121no—
618C2×Dic3—121no—
619C2×Dic3C2×C4×D312yes—
620C2×Dic3C2×C4×D312yes—
621C2×Dic3C2×C4×D312yes—
622C2×Dic3C2×C4×D312yes—
623C2×Dic3#23512yes—
624C2×Dic3C2×#6712yes—
625C2×Dic3C2×#6712yes—
626C4×D3—68no—
627C4×D3—68no—
628C4×D3—124no—
629C4×D3—124no—
630C4×D3—124no—
631C4×D3—124no—
632C4×D3—128no—
633C2×C32—42no—
634C2×C32C2×#11711yescharacteristic
635C2×C32C2×C4×D411yescharacteristic
636C2×C32#52011yescharacteristic
637C2×C32#54611yescharacteristic
638C2×C32#54811yescharacteristic
639C2×C32#55211yescharacteristic
640C2×C32#55311yescharacteristic
641C3⋊D3—24no—
642C24—91no—
643C24C2×D3211yescharacteristic
644C2×D4—94no—
645C2×D4—182no—
646C2×D4—182no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—34no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—31no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—94no—
659C22×C4—91no—
660C22×C4—91no—
661C22×C4—91no—
662C22×C4—182no—
663C22×C4—182no—
664C22×C4—182no—
665C22×C4—182no—
666C22×C4—182no—
667C22×C4—182no—
668C22×C4—361no—
669C22×C4—361no—
670C22×C4C2×D3211yescharacteristic
671C22×C4C2×D3211yescharacteristic
672C4⋊C4—34no—
673C4⋊C4—62no—
674C4⋊C4—62no—
675C4⋊C4—94no—
676C4⋊C4—182no—
677C4⋊C4—182no—
678C4⋊C4—182no—
679C22⋊C4—22no—
680C22⋊C4—34no—
681C22⋊C4—62no—
682C22⋊C4—94no—
683C22⋊C4—121no—
684C22⋊C4—182no—
685C22⋊C4—182no—
686C22⋊C4—361no—
687C42—62no—
688C42—62no—
689C42—94no—
690C42—121no—
691C42—361no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—81no—
720C22×C3C22×C4×D311yescharacteristic
721C22×C3C22×C4×D311yescharacteristic
722C22×C3C2×#23511yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C22×C3#100411yescharacteristic
725C22×C3D3×#4111yescharacteristic
726C22×C3D3×#4111yescharacteristic
727C22×C3D3×#4111yescharacteristic
728C22×C3D3×#4111yescharacteristic
729C22×C3D3×#4111yescharacteristic
730C22×C3#100911yescharacteristic
731C22×C3#101011yescharacteristic
732C22×C3#101011yescharacteristic
733C22×C3C22×#6711yescharacteristic
734C2×D3—34no—
735C2×D3—34no—
736C2×D3—64no—
737C2×D3—62no—
738C2×D3—62no—
739C2×D3—62no—
740C2×D3—62no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—122no—
750C2×D3—122no—
751C2×D3—122no—
752C2×D3—122no—
753C2×D3—122no—
754C2×D3—122no—
755C3×C4—22no—
756C3×C4—22no—
757C3×C4—34no—
758C3×C4—42no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—62no—
762C3×C4—62no—
763C3×C4—62no—
764C3×C4—62no—
765C3×C4—81no—
766C3×C4—121no—
767C3×C4—121no—
768C3×C4—121no—
769Dic3—22no—
770Dic3—22no—
771Dic3—22no—
772Dic3—22no—
773Dic3—41no—
774Dic3—41no—
775Dic3—41no—
776Dic3—62no—
777Dic3—62no—
778Dic3—122no—
779Dic3—122no—
780Dic3—121no—
781Dic3—121no—
782Dic3—121no—
783Dic3—121no—
784Dic3—241no—
785Dic3C4×#6714yes—
786C32#235211yescharacteristic, complemented, Sylow
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—92no—
794C23—92no—
795C23—92no—
796C23—181no—
797C23—181no—
798C23—181no—
799C23—181no—
800C23C4×D3212yes—
801C23C22×D3211yescharacteristic
802D4—188no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—68no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—92no—
834C2×C4—188no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—181no—
843C2×C4—364no—
844C2×C4—364no—
845C2×C4D3×#6712yes—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—42no—
854C2×C3—42no—
855C2×C3—82no—
856C2×C3D3×#11711yescharacteristic
857C2×C3D3×#11711yescharacteristic
858C2×C3#552311yescharacteristic
859C2×C3#552911yescharacteristic
860C2×C3#553011yescharacteristic
861C2×C3C4×D3×D411yescharacteristic
862C2×C3#554611yescharacteristic
863C2×C3#561011yescharacteristic
864C2×C3#566111yescharacteristic
865C2×C3#567711yescharacteristic
866C2×C3#570811yescharacteristic
867C2×C3C2×C4×#6711yescharacteristic
868C2×C3#582911yescharacteristic
869C2×C3#583111yescharacteristic
870D3—64no—
871D3—64no—
872D3—124no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—94no—
881C22—182no—
882C22—182no—
883C22—182no—
884C22—182no—
885C22—182no—
886C22—182no—
887C22C2×C4×D3211yescharacteristic
888C22D3×#23511yescharacteristic
889C22#6430911yescharacteristic
890C22#6431211yescharacteristic
891C22#6431211yescharacteristic
892C22#6431411yescharacteristic
893C22C2×D3×#6711yescharacteristic
894C4—22no—
895C4—34no—
896C4—41no—
897C4—62no—
898C4—62no—
899C4—62no—
900C4—62no—
901C4—121no—
902C4—121no—
903C4—121no—
904C4—182no—
905C4—361no—
906C4—361no—
907C3—21no—
908C3#7583411yescharacteristic, complemented
909C3#8227211yescharacteristic, complemented
910C2—42no—
911C2—184no—
912C2#1059402411yescharacteristic
913C2#1059404911yescharacteristic
914C2#1059405211yescharacteristic
915C2#1059420411yescharacteristic
916C2C4×D3×#6711yescharacteristic
917C2#1059523711yescharacteristic
918C2#1059530511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
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×C3×#877C2semidirect
3. C2×#63883C2semidirect
5. C3×#4945C2semidirect
7. #10591716C2semidirect
8. #10591702C2semidirect
9. #10591367C2semidirect
10. #10591333C2semidirect
11. C4×#3722C2semidirect
12. #10591245C2semidirect
13. Dic3×Dic3⋊C4C2semidirect
14. #10591233C2semidirect
15. #10591193C2semidirect
44. #63952C4semidirect
61. C2×#877D3semidirect
75. #4945D3semidirect
102. C22×C3×Dic3C2×C4semidirect
122. C3×#217C2×C4semidirect
125. C3×Dic3⋊C4D4semidirect
129. #3724C2×C4semidirect
136. Dic32C2×C4semidirect
338. C22×Dic3C4×D3semidirect
385. #217C4×D3semidirect
403. Dic3⋊C4#67semidirect
431. C2×C3⋊D3#117semidirect
786. C32#2352semidirect
908. C3#75834semidirect
909. C3#82272semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8772
C2×#639522
C2×#638832
#105926552
C3×#49452
#105917222
#105917162
#105917022
#105913672
#105913332
C4×#37222
#105912452
Dic3×Dic3⋊C42
#105912332
#105911932
#822723
#758343