Finite Group Databasebeta

← #11805502

Subgroups — #11805502

Order 1152.

1573 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C2×#67⋊Dic3C211yesmaximal, characteristic
3C2×#67⋊Dic3C211yesmaximal, characteristic
4C2×#63658C211yesmaximal, characteristic, complemented
5C3×#5210C211yesmaximal, characteristic, complemented
6#10591720C211yesmaximal, characteristic, complemented
7#10591719C211yesmaximal, characteristic, complemented
8#10591373C211yesmaximal, characteristic, complemented
9#10591366C211yesmaximal, characteristic, complemented
10D3×C3⋊#95C211yesmaximal, characteristic, complemented
11#10591327C211yesmaximal, characteristic, complemented
12#10591277C211yesmaximal, characteristic, complemented
13#10591246C211yesmaximal, characteristic, complemented
14#10591245C211yesmaximal, characteristic, complemented
15Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#82334—31nomaximal
17#74394—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C3×C4×#67—24no—
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34#67⋊Dic3—24no—
35#67⋊Dic3C418yescomplemented
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×C4×D4—31no—
57C2×D4×Dic3—31no—
58C2×D4×Dic3—31no—
59C2×C4×#67D311yescharacteristic
60C2×#67⋊C4—31no—
61C2×#67⋊C4—31no—
62C3×#385—31no—
63#5210—31no—
64#5210D311yescharacteristic, complemented
65C2×C3⋊#95—31no—
66C2×C3⋊#95—31no—
67C2×C3⋊#95—31no—
68C2×C3⋊#95—61no—
69#4989—31no—
70#4987—31no—
71#4977—31no—
72#4976—31no—
73Dic3×C4⋊C4—31no—
74#4972—31no—
75#4950—31no—
76#4946—31no—
77#4946—31no—
78#4942—31no—
79#4942—31no—
80#4942—31no—
81C4×Dic3⋊C4—31no—
82#4928—31no—
83#4668—31no—
84D3×#95—31no—
85#4650—31no—
86#4647—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4—22no—
90C22×C32×C4—22no—
91C22×C32×C4—41no—
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—22no—
95C22×C3⋊Dic3—22no—
96C22×C3⋊Dic3—41no—
97C22×C3⋊Dic3—41no—
98C22×C3⋊Dic3—41no—
99C22×C3⋊Dic3C2×C414yescomplemented
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C3×#67C2×C414yes—
105C2×C3×#67D414yes—
106C2×C3×#67Q814yes—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—41no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3—41no—
121C2×D3×Dic3—41no—
122C2×D3×Dic3C2×C414yescomplemented
123C3×#217—22no—
124C3×#217—22no—
125C3×#217C2×C414yescomplemented
126C3×(C2×D3)⋊C4—22no—
127C3×Dic3⋊C4—22no—
128C3×Dic3⋊C4—22no—
129C3×Dic3⋊C4—41no—
130C3×C4×Dic3—22no—
131#3724—41no—
132#3724—41no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—41no—
136Dic3⋊Dic3C2×C414yescomplemented
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3C2×C414yescomplemented
139Dic32—22no—
140Dic32C2×C414yescomplemented
141#2349—91noSylow
142C22×C3×D4—31no—
143C23×C3×C4—21no—
144C23×C3×C4—31no—
145C23×C3×C4C2×D311yescharacteristic
146C23×C3×C4C2×D311yescharacteristic
147C22×#67C2×D311yescharacteristic
148C23×Dic3—31no—
149C23×Dic3—31no—
150C23×Dic3—31no—
151C23×Dic3—31no—
152C23×Dic3—31no—
153C23×Dic3—31no—
154C23×Dic3—61no—
155C23×Dic3—61no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3C2×D311yescharacteristic
159C3×C4×D4—64no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C42—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217C2×D311yescharacteristic
171C2×#217C2×D311yescharacteristic
172C2×#217C2×D311yescharacteristic
173D4×Dic3—38no—
174D4×Dic3—64no—
175C4×#67—24no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4C2×D311yescharacteristic
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4C2×D311yescharacteristic
192C2×Dic3⋊C4C2×D311yescharacteristic
193C2×Dic3⋊C4C2×D311yescharacteristic
194C2×C4×Dic3—31no—
195C2×C4×Dic3—31no—
196C2×C4×Dic3—31no—
197C2×C4×Dic3—31no—
198C2×C4×Dic3C2×D311yescharacteristic
199#67⋊C4—38no—
200#67⋊C4—64no—
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—31no—
218C3⋊#95—31no—
219C3⋊#95—61no—
220C3⋊#95—61no—
221C3⋊#95—61no—
222C3⋊#95—61no—
223C3⋊#95C2×D311yescharacteristic
224C3⋊#95C2×D311yescharacteristic
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32C22×C412yes—
230C23×C32C2×D412yes—
231C23×C32C2×Q812yes—
232C23×C32C2411yescharacteristic
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C22×C412yes—
238C22×C3×D3C2×D412yes—
239C22×C3×D3C2×Q812yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—44no—
246C2×C32×C4#4112yes—
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⋊Dic3—21no—
256C2×C3⋊Dic3—44no—
257C2×C3⋊Dic3—44no—
258C2×C3⋊Dic3C22×C412yes—
259C2×C3⋊Dic3C22×C412yes—
260C2×C3⋊Dic3#4112yes—
261C3×#67C4⋊C4116yescomplemented
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×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C22×C412yes—
279C2×C3×Dic3C22×C412yes—
280C2×C3×Dic3C22×C412yes—
281C2×C3×Dic3C2×D412yes—
282C2×C3×Dic3C2×Q812yes—
283C3×C4×D3—44no—
284D3×Dic3—44no—
285D3×Dic3—44no—
286C2×C4×D4—31no—
287C2×C4×D4—91no—
288C2×C4×D4—91no—
289#389—91no—
290#389—91no—
291#385—31no—
292#385—91no—
293#385—91no—
294#385—91no—
295#382—91no—
296#380—91no—
297#380—91no—
298C4×C4⋊C4—91no—
299C2×#95—91no—
300C2×#95—91no—
301C24×C3—21no—
302C24×C3—31no—
303C24×C3C22×D311yescharacteristic
304C24×C3C22×D311yescharacteristic
305C23×D3C22×D311yescharacteristic
306C2×C3×D4—34no—
307C2×C3×D4—34no—
308C2×C3×D4—34no—
309C22×C3×C4—24no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—42no—
324C22×C3×C4—41no—
325C22×C3×C4—41no—
326C22×C3×C4—42no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—121no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C2×#67Dic614yes—
335C2×#67C4×D314yes—
336C2×#67#6714yes—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—34no—
344C22×Dic3—34no—
345C22×Dic3—34no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—64no—
353C22×Dic3—62no—
354C22×Dic3—62no—
355C22×Dic3—62no—
356C22×Dic3—62no—
357C22×Dic3—64no—
358C22×Dic3—62no—
359C22×Dic3—62no—
360C22×Dic3—122no—
361C22×Dic3—121no—
362C22×Dic3—121no—
363C22×Dic3—121no—
364C22×Dic3—121no—
365C22×Dic3—121no—
366C22×Dic3—121no—
367C22×Dic3—121no—
368C22×Dic3—121no—
369C22×Dic3—121no—
370C22×Dic3—122no—
371C22×Dic3—122no—
372C22×Dic3—122no—
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C2×C4×D3—22no—
381C2×C4×D3—22no—
382C2×C4×D3—34no—
383C2×C4×D3—41no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—121no—
387C2×C4×D3—121no—
388C2×C4×D3—121no—
389C3×C4⋊C4—62no—
390C3×C4⋊C4—62no—
391C3×C4⋊C4—121no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—62no—
396C3×C42—62no—
397#217—22no—
398#217—22no—
399#217—34no—
400#217—62no—
401#217C4×D314yescomplemented
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—62no—
405C4⋊Dic3—34no—
406C4⋊Dic3—62no—
407C4⋊Dic3—62no—
408C4⋊Dic3—121no—
409Dic3⋊C4—22no—
410Dic3⋊C4—22no—
411Dic3⋊C4—34no—
412Dic3⋊C4—41no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415Dic3⋊C4—121no—
416Dic3⋊C4—121no—
417Dic3⋊C4—121no—
418Dic3⋊C4—121no—
419Dic3⋊C4—121no—
420C4×Dic3—22no—
421C4×Dic3—34no—
422C4×Dic3—34no—
423C4×Dic3—62no—
424C4×Dic3—62no—
425C22×C32—22no—
426C22×C32—22no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—22no—
430C22×C32—22no—
431C22×C32C2×C4⋊C414yes—
432C22×C32C23×C411yescharacteristic
433C22×C32C22×D411yescharacteristic
434C22×C32C22×Q811yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32H(5,𝔽2)11yescharacteristic
438C22×C32H(5,𝔽2)11yescharacteristic
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3C2×C4⋊C414yes—
446C32×C4—22no—
447C32×C4—41no—
448C3⋊Dic3—22no—
449C3⋊Dic3—22no—
450C3⋊Dic3—22no—
451C3⋊Dic3—41no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3C2×C4⋊C414yes—
459C22×D4—31no—
460C23×C4—31no—
461C23×C4—91no—
462C23×C4—91no—
463C23×C4—91no—
464C23×C4—91no—
465C23×C4D3211yescharacteristic
466C4×D4—64no—
467C4×D4—98no—
468C4×D4—184no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—31no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—91no—
473C2×C4⋊C4—91no—
474C2×C4⋊C4—91no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C22⋊C4—31no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—31no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—91no—
483C2×C22⋊C4—91no—
484C2×C42—31no—
485C2×C42—91no—
486C2×C42—91no—
487#95—31no—
488#95—31no—
489#95—91no—
490#95—91no—
491#95—91no—
492#95—91no—
493#95—91no—
494#95—91no—
495#95—91no—
496#95—91no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—32no—
514C23×C3—32no—
515C23×C3—32no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3C2×Dic612yes—
521C23×C3C2×C4×D312yes—
522C23×C3C2×C4×D312yes—
523C23×C3D3×D412yes—
524C23×C3D3×Q812yes—
525C23×C3C2×#6712yes—
526C23×C3C23×D311yescharacteristic
527C23×C3C23×D311yescharacteristic
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3C2×Dic612yes—
533C22×D3C2×C4×D312yes—
534C22×D3C2×#6712yes—
535C3×D4—316no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—22no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—22no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—32no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—44no—
558C2×C3×C4—44no—
559C2×C3×C4—48no—
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×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—124no—
577C2×C3×C4#23712yes—
578C2×C3×C4#23712yes—
579#67Dic3⋊C4116yescomplemented
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
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—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—32no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—62no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—121no—
627C2×Dic3—121no—
628C2×Dic3—121no—
629C2×Dic3—121no—
630C2×Dic3—121no—
631C2×Dic3—121no—
632C2×Dic3—124no—
633C2×Dic3—124no—
634C2×Dic3—124no—
635C2×Dic3—124no—
636C2×Dic3—124no—
637C2×Dic3—124no—
638C2×Dic3—128no—
639C2×Dic3—128no—
640C2×Dic3C2×Dic612yes—
641C2×Dic3C2×C4×D312yes—
642C2×Dic3C2×C4×D312yes—
643C2×Dic3C2×C4×D312yes—
644C2×Dic3C2×#6712yes—
645C4×D3—44no—
646C4×D3—124no—
647C4×D3—124no—
648C2×C32—24no—
649C2×C32C22×C4⋊C411yescharacteristic
650C2×C32C4×#4111yescharacteristic
651C2×C32#51811yescharacteristic
652C2×C32#54611yescharacteristic
653C2×C32#54611yescharacteristic
654C2×C32#55411yescharacteristic
655C2×C32#55411yescharacteristic
656C3×D3—24no—
657C24—31no—
658C24C2×D3211yescharacteristic
659C2×D4—34no—
660C2×D4—34no—
661C2×D4—34no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—41no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—94no—
675C22×C4—91no—
676C22×C4—91no—
677C22×C4—91no—
678C22×C4—94no—
679C22×C4—91no—
680C22×C4—121no—
681C22×C4—182no—
682C22×C4—182no—
683C22×C4—182no—
684C22×C4—182no—
685C22×C4—361no—
686C22×C4—361no—
687C22×C4—361no—
688C22×C4—361no—
689C22×C4—361no—
690C22×C4—361no—
691C22×C4C2×D3211yescharacteristic
692C22×C4C2×D3211yescharacteristic
693C4⋊C4—62no—
694C4⋊C4—62no—
695C4⋊C4—94no—
696C4⋊C4—121no—
697C4⋊C4—182no—
698C4⋊C4—182no—
699C4⋊C4—361no—
700C4⋊C4—361no—
701C4⋊C4—361no—
702C22⋊C4—34no—
703C22⋊C4—62no—
704C22⋊C4—62no—
705C22⋊C4—62no—
706C22⋊C4—94no—
707C22⋊C4—182no—
708C42—62no—
709C42—94no—
710C42—182no—
711C22×C3—24no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—24no—
737C22×C3—34no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3D3×C4⋊C414yes—
745C22×C3C2×Dic3⋊C414yes—
746C22×C3C22×Dic611yescharacteristic
747C22×C3C22×C4×D311yescharacteristic
748C22×C3C22×C4×D311yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C22×C3C2×#23711yescharacteristic
751C22×C3C2×#23711yescharacteristic
752C22×C3#100411yescharacteristic
753C22×C3#100411yescharacteristic
754C22×C3C2×D3×Q811yescharacteristic
755C22×C3D3×#4111yescharacteristic
756C22×C3D3×#4111yescharacteristic
757C22×C3#100911yescharacteristic
758C22×C3#100911yescharacteristic
759C22×C3C22×#6711yescharacteristic
760C2×D3—22no—
761C2×D3—22no—
762C2×D3—22no—
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3C2×Dic3⋊C414yes—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—34no—
770C3×C4—42no—
771C3×C4—42no—
772C3×C4—41no—
773C3×C4—41no—
774C3×C4—62no—
775C3×C4—62no—
776C3×C4—121no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4—121no—
780Dic3—22no—
781Dic3—22no—
782Dic3—41no—
783Dic3—41no—
784Dic3—41no—
785Dic3—41no—
786Dic3—62no—
787Dic3—62no—
788Dic3—62no—
789Dic3—62no—
790Dic3—62no—
791Dic3—62no—
792Dic3—122no—
793Dic3—122no—
794Dic3—122no—
795Dic3—122no—
796Dic3—121no—
797Dic3—121no—
798Dic3C2×Dic3⋊C414yes—
799C32#234911yescharacteristic, complemented, Sylow
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—32no—
805C23—32no—
806C23—32no—
807C23—61no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23D3×Dic612yes—
812C23C4×D3212yes—
813C23D3×#6712yes—
814C23C22×D3211yescharacteristic
815D4—316no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—44no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—92no—
844C2×C4—92no—
845C2×C4—92no—
846C2×C4—124no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—181no—
853C2×C4—181no—
854C2×C4—181no—
855C2×C4—181no—
856C2×C4—364no—
857C2×C4—364no—
858C2×C4—364no—
859C2×C4—364no—
860C2×C4#380512yes—
861C2×C3—28no—
862C2×C3—24no—
863C2×C3—24no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—64no—
872C2×C3C2×D3×C4⋊C411yescharacteristic
873C2×C3C4×#23711yescharacteristic
874C2×C3C4×#23711yescharacteristic
875C2×C3#553911yescharacteristic
876C2×C3#554311yescharacteristic
877C2×C3#554511yescharacteristic
878C2×C3#554511yescharacteristic
879C2×C3#559111yescharacteristic
880C2×C3#563511yescharacteristic
881C2×C3#563611yescharacteristic
882C2×C3#565411yescharacteristic
883C2×C3C22×Dic3⋊C411yescharacteristic
884C2×C3#580611yescharacteristic
885C2×C3#582911yescharacteristic
886D3—24no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—34no—
894C22—62no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22D3×Dic3⋊C414yes—
901C22C2×D3×Dic611yescharacteristic
902C22C2×C4×D3211yescharacteristic
903C22#6430611yescharacteristic
904C22#6430811yescharacteristic
905C22C2×#380511yescharacteristic
906C22C2×D3×#6711yescharacteristic
907C22#6433011yescharacteristic
908C4—22no—
909C4—34no—
910C4—41no—
911C4—62no—
912C4—62no—
913C4—121no—
914C4—121no—
915C4—121no—
916C4—121no—
917C4—182no—
918C4—182no—
919C4—182no—
920C4—361no—
921C3—21no—
922C3#7439411yescharacteristic, complemented
923C3#8233411yescharacteristic, complemented
924C2—24no—
925C2—64no—
926C2C2×D3×Dic3⋊C411yescharacteristic
927C2C4×#380511yescharacteristic
928C2#1059495911yescharacteristic
929C2#1059499311yescharacteristic
930C2#1059505811yescharacteristic
931C2#1059506811yescharacteristic
932C2#1059549411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63658C2semidirect
5. C3×#5210C2semidirect
6. #10591720C2semidirect
7. #10591719C2semidirect
8. #10591373C2semidirect
9. #10591366C2semidirect
10. D3×C3⋊#95C2semidirect
11. #10591327C2semidirect
12. #10591277C2semidirect
13. #10591246C2semidirect
14. #10591245C2semidirect
15. Dic3×Dic3⋊C4C2semidirect
35. #67⋊Dic3C4semidirect
64. #5210D3semidirect
99. C22×C3⋊Dic3C2×C4semidirect
122. C2×D3×Dic3C2×C4semidirect
125. C3×#217C2×C4semidirect
136. Dic3⋊Dic3C2×C4semidirect
138. (C2×D3)⋊Dic3C2×C4semidirect
140. Dic32C2×C4semidirect
261. C3×#67C4⋊C4semidirect
401. #217C4×D3semidirect
579. #67Dic3⋊C4semidirect
799. C32#2349semidirect
922. C3#74394semidirect
923. C3#82334semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×#67⋊Dic32
C2×#636582
C3×#52102
#105917202
#105917192
#105913732
#105913662
D3×C3⋊#952
#105913272
#105912772
#105912462
#105912452
Dic3×Dic3⋊C42
#823343
#743943