Finite Group Databasebeta

← #11805441

Subgroups — #11805441

Order 1152.

1761 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×#67⋊Dic3C212yesmaximal
4C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#5212C211yesmaximal, characteristic, complemented
6#10591719C212yesmaximal, complemented
7#10591379C212yesmaximal, complemented
8#10591349C211yesmaximal, characteristic, complemented
9#10591313C211yesmaximal, characteristic, complemented
10#10591268C212yesmaximal, complemented
11Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12D4×C4⋊Dic3—31nomaximal
13#74010—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3⋊Dic3C2212yes—
16C22×C3×#67C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×C4⋊(C3⋊Dic3)—24no—
20C2×C4⋊(C3⋊Dic3)C2212yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×C3×#217C2211yescharacteristic
25C3×C4×#67C418yescomplemented
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31#67⋊Dic3—28no—
32C2×Dic3⋊Dic3C2212yes—
33C2×Dic3⋊Dic3C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×Dic32C2212yes—
37D3×C4⋊Dic3—24no—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40#63579C2212yes—
41C2×C3×C4×D4—31no—
42C2×D4×Dic3—32no—
43C2×C4×#67D311yescharacteristic
44C22×C4⋊Dic3—31no—
45C22×C4⋊Dic3—31no—
46C22×C4⋊Dic3—31no—
47C22×C4⋊Dic3—61no—
48C2×D3×C4⋊C4—31no—
49C2×#67⋊C4—32no—
50C3×#380—31no—
51#5212—31no—
52#5212D311yescharacteristic, complemented
53#4987—31no—
54#4984—32no—
55#4975—31no—
56Dic3×C4⋊C4—31no—
57#4950—32no—
58#4950—32no—
59#4946—32no—
60#4935—31no—
61C4×C4⋊Dic3—31no—
62#4668—32no—
63#4647—32no—
64C24×C32C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4—22no—
67C22×C32×C4—22no—
68C22×C32×C4C2×C414yescomplemented
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3—24no—
73C22×C3⋊Dic3—42no—
74C22×C3⋊Dic3C2312yes—
75C22×C3⋊Dic3C2312yes—
76C2×C3×#67C2×C414yes—
77C2×C3×#67D414yes—
78C2×C3×#67Q814yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3C2×C414yescomplemented
87C2×D3×Dic3—24no—
88C2×D3×Dic3—24no—
89C2×D3×Dic3—42no—
90C4⋊(C3⋊Dic3)—22no—
91C4⋊(C3⋊Dic3)—24no—
92C4⋊(C3⋊Dic3)D414yescomplemented
93C3×#217—24no—
94C3×#217C2×C414yescomplemented
95C3×(C2×D3)⋊C4C2×C414yescomplemented
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3—22no—
98C3×Dic3⋊C4C2×C414yescomplemented
99C3×C4×Dic3C2×C414yescomplemented
100Dic3⋊Dic3—24no—
101Dic3⋊Dic3—24no—
102Dic3⋊Dic3—42no—
103(C2×D3)⋊Dic3—24no—
104Dic32—24no—
105D4×C4⋊C4—91noSylow
106C22×C3×D4—31no—
107C23×C3×C4—21no—
108C23×C3×C4—31no—
109C23×C3×C4C2×D311yescharacteristic
110C23×C3×C4C2×D311yescharacteristic
111C22×#67C2×D311yescharacteristic
112C23×Dic3—32no—
113C23×Dic3—32no—
114C23×Dic3—32no—
115C23×Dic3—62no—
116C22×C4×D3—32no—
117C22×C4×D3C2×D311yescharacteristic
118C3×C4×D4—38no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C22⋊C4—31no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C42—31no—
126C2×#217—32no—
127C2×#217C2×D312yes—
128C2×#217C2×D311yescharacteristic
129D4×Dic3—68no—
130C4×#67Dic318yescomplemented
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4C2×D311yescharacteristic
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—32no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—32no—
140C2×C4⋊Dic3—32no—
141C2×C4⋊Dic3—32no—
142C2×C4⋊Dic3—61no—
143C2×C4⋊Dic3—61no—
144C2×C4⋊Dic3—62no—
145C2×C4⋊Dic3—64no—
146C2×C4⋊Dic3—64no—
147C2×C4⋊Dic3—64no—
148C2×C4⋊Dic3—68no—
149C2×C4⋊Dic3C2×D311yescharacteristic
150C2×C4⋊Dic3C2×D311yescharacteristic
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4C2×D311yescharacteristic
155C2×C4×Dic3—32no—
156C2×C4×Dic3—32no—
157C2×C4×Dic3C2×D311yescharacteristic
158D3×C4⋊C4—64no—
159#67⋊C4—68no—
160C3×#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—32no—
164C3⋊#95—32no—
165C3⋊#95C2×D312yes—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32C22×C412yes—
171C23×C32C2×D412yes—
172C23×C32C2×Q812yes—
173C23×C32C2411yescharacteristic
174C22×C3×D3—21no—
175C22×C3×D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3—21no—
178C22×C3×D3C22×C412yes—
179C22×C3×D3C2×D412yes—
180C22×C3×D3C2×Q812yes—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—28no—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C22×C412yes—
186C2×C32×C4C2×D412yes—
187C2×C32×C4#4112yes—
188C2×C3⋊Dic3—22no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—48no—
194C2×C3⋊Dic3C2×D414yes—
195C3×#67C4⋊C4116yescomplemented
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3C22×C412yes—
207C2×C3×Dic3C22×C412yes—
208C2×C3×Dic3C22×C412yes—
209C2×C3×Dic3C2×D412yes—
210C2×C3×Dic3C2×Q812yes—
211C3×C4×D3—28no—
212D3×Dic3—48no—
213C2×C4×D4—31no—
214C2×C4×D4—92no—
215C22×C4⋊C4—91no—
216C22×C4⋊C4—91no—
217#389—92no—
218#385—92no—
219#385—92no—
220#384—91no—
221#380—31no—
222#380—91no—
223C4×C4⋊C4—91no—
224C24×C3—21no—
225C24×C3—31no—
226C24×C3C22×D311yescharacteristic
227C24×C3C22×D311yescharacteristic
228C23×D3C22×D311yescharacteristic
229C2×C3×D4—34no—
230C2×C3×D4—34no—
231C2×C3×D4—34no—
232C22×C3×C4—24no—
233C22×C3×C4—24no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—24no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—34no—
245C22×C3×C4—32no—
246C22×C3×C4—32no—
247C22×C3×C4—62no—
248C22×C3×C4—62no—
249C22×C3×C4C4×D314yescomplemented
250C22×C3×C4C2×Dic314yescomplemented
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C2×#67Dic614yes—
256C2×#67D1214yes—
257C2×#67C2×Dic314yes—
258C22×Dic3—32no—
259C22×Dic3—32no—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—62no—
263C22×Dic3—62no—
264C22×Dic3—64no—
265C22×Dic3—64no—
266C22×Dic3—64no—
267C22×Dic3—64no—
268C22×Dic3—68no—
269C22×Dic3—64no—
270C22×Dic3—64no—
271C22×Dic3—124no—
272C22×Dic3—122no—
273C22×Dic3—122no—
274C22×Dic3—122no—
275C22×Dic3—124no—
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D312yes—
278C22×Dic3C22×D311yescharacteristic
279C22×Dic3C22×D311yescharacteristic
280C22×Dic3C22×D311yescharacteristic
281C2×C4×D3—22no—
282C2×C4×D3—22no—
283C2×C4×D3—64no—
284C2×C4×D3—64no—
285C2×C4×D3—122no—
286C2×C4×D3C2×Dic314yescomplemented
287C3×C4⋊C4—34no—
288C3×C4⋊C4—62no—
289C3×C4⋊C4—62no—
290C3×C22⋊C4—34no—
291C3×C22⋊C4—34no—
292C3×C22⋊C4—64no—
293C3×C42—34no—
294#217—24no—
295#217—64no—
296#217C2×Dic314yescomplemented
297(C2×D3)⋊C4—64no—
298(C2×D3)⋊C4C2×Dic314yescomplemented
299C4⋊Dic3—22no—
300C4⋊Dic3—22no—
301C4⋊Dic3—34no—
302C4⋊Dic3—34no—
303C4⋊Dic3—64no—
304C4⋊Dic3—64no—
305C4⋊Dic3—64no—
306C4⋊Dic3—64no—
307C4⋊Dic3—64no—
308C4⋊Dic3—68no—
309C4⋊Dic3—64no—
310C4⋊Dic3—62no—
311C4⋊Dic3—62no—
312C4⋊Dic3—122no—
313Dic3⋊C4—64no—
314Dic3⋊C4—64no—
315Dic3⋊C4—122no—
316Dic3⋊C4C2×Dic314yescomplemented
317C4×Dic3—64no—
318C4×Dic3—64no—
319C4×Dic3C2×Dic314yescomplemented
320C22×C32—22no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32C2×C4⋊C414yescomplemented
327C22×C32C23×C411yescharacteristic
328C22×C32C22×D411yescharacteristic
329C22×C32C22×D411yescharacteristic
330C22×C32C22×Q811yescharacteristic
331C22×C32C2×#4111yescharacteristic
332C22×C32H(5,𝔽2)11yescharacteristic
333C22×C322−1+411yescharacteristic
334C2×C3×D3—22no—
335C2×C3×D3—22no—
336C2×C3×D3—22no—
337C2×C3×D3—22no—
338C2×C3×D3—22no—
339C2×C3×D3—22no—
340C2×C3×D3C2×C4⋊C414yescomplemented
341C32×C4—22no—
342C32×C4C4×D414yescomplemented
343C3⋊Dic3—24no—
344C3⋊Dic3—42no—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C3×Dic3—42no—
348C3×Dic3—42no—
349C3×Dic3C2×C4⋊C414yescomplemented
350C22×D4—31no—
351C23×C4—31no—
352C23×C4—92no—
353C23×C4—92no—
354C23×C4D3211yescharacteristic
355C4×D4—38no—
356C4×D4—188no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—91no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4—184no—
367C2×C4⋊C4—184no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—31no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—92no—
372C2×C42—31no—
373C2×C42—92no—
374#95—32no—
375#95—92no—
376#95—92no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—32no—
394C23×C3—32no—
395C23×C3—32no—
396C23×C3—61no—
397C23×C3—61no—
398C23×C3—61no—
399C23×C3—61no—
400C23×C3C2×Dic612yes—
401C23×C3C2×C4×D312yes—
402C23×C3C2×D1212yes—
403C23×C3D3×D412yes—
404C23×C3D3×Q812yes—
405C23×C3C22×Dic312yes—
406C23×C3C23×D311yescharacteristic
407C23×C3C23×D311yescharacteristic
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3C2×Dic612yes—
413C22×D3C2×D1212yes—
414C22×D3C22×Dic312yes—
415C3×D4—316no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—216no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—28no—
424C2×C3×C4—28no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—32no—
430C2×C3×C4—32no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4—61no—
438C2×C3×C4—68no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4—62no—
444C2×C3×C4—62no—
445C2×C3×C4C2×C4×D312yes—
446C2×C3×C4C2×C4×D312yes—
447C2×C3×C4D3×D412yes—
448C2×C3×C4D3×D412yes—
449C2×C3×C4#23712yes—
450C2×C3×C4#23712yes—
451C2×C3×C4C22×Dic312yes—
452C2×C3×C4C22×Dic312yes—
453#67C4⋊Dic3116yescomplemented
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—34no—
465C2×Dic3—34no—
466C2×Dic3—64no—
467C2×Dic3—62no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—64no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—62no—
475C2×Dic3—62no—
476C2×Dic3—62no—
477C2×Dic3—62no—
478C2×Dic3—122no—
479C2×Dic3—122no—
480C2×Dic3—122no—
481C2×Dic3—122no—
482C2×Dic3—128no—
483C2×Dic3—128no—
484C2×Dic3—128no—
485C2×Dic3—1216no—
486C2×Dic3C2×Dic612yes—
487C2×Dic3C2×D1212yes—
488C2×Dic3C22×Dic312yes—
489C2×Dic3C22×Dic312yes—
490C2×Dic3C22×Dic312yes—
491C4×D3—28no—
492C4×D3—128no—
493C2×C32—24no—
494C2×C32C22×C4⋊C411yescharacteristic
495C2×C32C2×C4×D411yescharacteristic
496C2×C32#52011yescharacteristic
497C2×C32D4211yescharacteristic
498C2×C32#54711yescharacteristic
499C2×C32D4×Q811yescharacteristic
500C2×C32#55411yescharacteristic
501C3×D3—24no—
502C24—31no—
503C24C2×D3211yescharacteristic
504C2×D4—34no—
505C2×D4—34no—
506C2×D4—34no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—31no—
510C22×C4—31no—
511C22×C4—31no—
512C22×C4—34no—
513C22×C4—32no—
514C22×C4—32no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—92no—
518C22×C4—92no—
519C22×C4—184no—
520C22×C4—184no—
521C22×C4—184no—
522C22×C4—184no—
523C22×C4—362no—
524C22×C4—362no—
525C22×C4D3×Dic314yescomplemented
526C22×C4C2×D3211yescharacteristic
527C22×C4C2×D3211yescharacteristic
528C4⋊C4—34no—
529C4⋊C4—62no—
530C4⋊C4—62no—
531C4⋊C4—94no—
532C4⋊C4—184no—
533C4⋊C4—184no—
534C4⋊C4—184no—
535C4⋊C4—182no—
536C4⋊C4—362no—
537C22⋊C4—34no—
538C22⋊C4—34no—
539C22⋊C4—64no—
540C22⋊C4—184no—
541C42—34no—
542C42—184no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—24no—
546C22×C3—24no—
547C22×C3—24no—
548C22×C3—24no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—22no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—24no—
569C22×C3—34no—
570C22×C3—62no—
571C22×C3—62no—
572C22×C3—62no—
573C22×C3—62no—
574C22×C3—62no—
575C22×C3—62no—
576C22×C3D3×C4⋊C414yescomplemented
577C22×C3C2×C4⋊Dic314yescomplemented
578C22×C3C22×Dic611yescharacteristic
579C22×C3C22×C4×D311yescharacteristic
580C22×C3C22×D1211yescharacteristic
581C22×C3C2×D3×D411yescharacteristic
582C22×C3C2×D3×D411yescharacteristic
583C22×C3C2×D3×D411yescharacteristic
584C22×C3C2×#23711yescharacteristic
585C22×C3C2×#23711yescharacteristic
586C22×C3C2×D3×Q811yescharacteristic
587C22×C3#100911yescharacteristic
588C22×C3#100911yescharacteristic
589C22×C3#101011yescharacteristic
590C22×C3#101011yescharacteristic
591C22×C3C23×Dic311yescharacteristic
592C2×D3—22no—
593C2×D3—22no—
594C2×D3—22no—
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3C2×C4⋊Dic314yescomplemented
599C3×C4—24no—
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—24no—
603C3×C4—34no—
604C3×C4—62no—
605C3×C4—62no—
606C3×C4—122no—
607C3×C4—122no—
608C3×C4#67⋊C414yescomplemented
609C3×C4D4×Dic314yescomplemented
610Dic3—22no—
611Dic3—22no—
612Dic3—42no—
613Dic3—42no—
614Dic3—64no—
615Dic3—64no—
616Dic3—124no—
617Dic3—124no—
618Dic3—122no—
619Dic3—122no—
620Dic3C2×C4⋊Dic314yescomplemented
621C32D4×C4⋊C411yescharacteristic, complemented, Sylow
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—32no—
627C23—32no—
628C23—32no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23—61no—
633C23D3×Dic612yes—
634C23D3×D1212yes—
635C23C2×D3×Dic312yes—
636C23C22×D3211yescharacteristic
637D4—316no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—28no—
641C2×C4—32no—
642C2×C4—32no—
643C2×C4—32no—
644C2×C4—32no—
645C2×C4—32no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—68no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—94no—
658C2×C4—182no—
659C2×C4—182no—
660C2×C4—182no—
661C2×C4—182no—
662C2×C4—182no—
663C2×C4—368no—
664C2×C4—368no—
665C2×C4C2×D3×Dic312yes—
666C2×C4C2×D3×Dic312yes—
667C2×C4#380512yes—
668C2×C4#381112yes—
669C2×C3—28no—
670C2×C3—24no—
671C2×C3—24no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—64no—
680C2×C3C2×#67⋊C411yescharacteristic
681C2×C3C2×D3×C4⋊C411yescharacteristic
682C2×C3#552311yescharacteristic
683C2×C3D4×Dic611yescharacteristic
684C2×C3#554311yescharacteristic
685C2×C3D4×D1211yescharacteristic
686C2×C3#555511yescharacteristic
687C2×C3#560911yescharacteristic
688C2×C3#561111yescharacteristic
689C2×C3#563211yescharacteristic
690C2×C3#563511yescharacteristic
691C2×C3C22×C4⋊Dic311yescharacteristic
692C2×C3C2×D4×Dic311yescharacteristic
693C2×C3#582711yescharacteristic
694D3—24no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—34no—
702C22—62no—
703C22—62no—
704C22—62no—
705C22—62no—
706C22—62no—
707C22—62no—
708C22D3×C4⋊Dic314yescomplemented
709C22C2×D3×Dic611yescharacteristic
710C22#6429811yescharacteristic
711C22C2×D3×D1211yescharacteristic
712C22#6430811yescharacteristic
713C22C22×D3×Dic311yescharacteristic
714C22C2×#380511yescharacteristic
715C22C2×#381111yescharacteristic
716C4—22no—
717C4—34no—
718C4—62no—
719C4—62no—
720C4—122no—
721C4—122no—
722C4—184no—
723C4—362no—
724C4#67⋊Dic314yescomplemented
725C3—21no—
726C3#7401011yescharacteristic, complemented
727C3D4×C4⋊Dic311yescharacteristic, complemented
728C2—24no—
729C2—64no—
730C2C2×D3×C4⋊Dic311yescharacteristic
731C2#1059490711yescharacteristic
732C2#1059491511yescharacteristic
733C2#1059499211yescharacteristic
734C2#1059499311yescharacteristic
735C2#1059507411yescharacteristic
736C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊(C3⋊Dic3)C2semidirect
4. C2×D3×C4⋊Dic3C2semidirect
5. C3×#5212C2semidirect
6. #10591719C2semidirect
7. #10591379C2semidirect
8. #10591349C2semidirect
9. #10591313C2semidirect
10. #10591268C2semidirect
11. Dic3×C4⋊Dic3C2semidirect
25. C3×C4×#67C4semidirect
52. #5212D3semidirect
68. C22×C32×C4C2×C4semidirect
86. C2×C3×C4×D3C2×C4semidirect
92. C4⋊(C3⋊Dic3)D4semidirect
94. C3×#217C2×C4semidirect
95. C3×(C2×D3)⋊C4C2×C4semidirect
98. C3×Dic3⋊C4C2×C4semidirect
99. C3×C4×Dic3C2×C4semidirect
130. C4×#67Dic3semidirect
195. C3×#67C4⋊C4semidirect
249. C22×C3×C4C4×D3semidirect
250. C22×C3×C4C2×Dic3semidirect
286. C2×C4×D3C2×Dic3semidirect
296. #217C2×Dic3semidirect
298. (C2×D3)⋊C4C2×Dic3semidirect
316. Dic3⋊C4C2×Dic3semidirect
319. C4×Dic3C2×Dic3semidirect
326. C22×C32C2×C4⋊C4semidirect
340. C2×C3×D3C2×C4⋊C4semidirect
342. C32×C4C4×D4semidirect
349. C3×Dic3C2×C4⋊C4semidirect
453. #67C4⋊Dic3semidirect
525. C22×C4D3×Dic3semidirect
576. C22×C3D3×C4⋊C4semidirect
577. C22×C3C2×C4⋊Dic3semidirect
598. C2×D3C2×C4⋊Dic3semidirect
608. C3×C4#67⋊C4semidirect
609. C3×C4D4×Dic3semidirect
620. Dic3C2×C4⋊Dic3semidirect
621. C32D4×C4⋊C4semidirect
708. C22D3×C4⋊Dic3semidirect
724. C4#67⋊Dic3semidirect
726. C3#74010semidirect
727. C3D4×C4⋊Dic3semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C2×C3×C4×#672
C2×#67⋊Dic32
C2×D3×C4⋊Dic32
C3×#52122
#105917192
#105913792
#105913492
#105913132
#105912682
Dic3×C4⋊Dic32
D4×C4⋊Dic33
#740103