Finite Group Databasebeta

← #11805463

Subgroups — #11805463

Order 1152.

1765 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×#63894C211yesmaximal, characteristic
3C2×#63894C211yesmaximal, characteristic
4C2×#63883C212yesmaximal, complemented
5C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C3×#4928C211yesmaximal, characteristic, complemented
7#10591375C212yesmaximal, complemented
8#10591367C212yesmaximal, complemented
9#10591352C211yesmaximal, characteristic, complemented
10#10591349C211yesmaximal, characteristic, complemented
11#10591290C212yesmaximal, complemented
12#76202—31nomaximal
13C4⋊C4×D12—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2212yes—
16C22×#624C2212yes—
17C22×#624C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C4×C4⋊(C3⋊D3)—24no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34#63894—24no—
35#63894C418yescomplemented
36#63883—28no—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40#63579C2212yes—
41C2×#893—31no—
42C2×#893—31no—
43C2×D3×C4⋊C4—32no—
44C2×D3×C4⋊C4—32no—
45C2×C4×D12—31no—
46C2×C4×D12—31no—
47C2×C4×D12—31no—
48C2×C4×D12—31no—
49C2×C4×D12—61no—
50C3×#389—31no—
51C3×C4×C4⋊C4—31no—
52#4989—32no—
53#4987—32no—
54#4984—31no—
55#4975—31no—
56#4935—31no—
57C4×Dic3⋊C4D311yescharacteristic, complemented
58#4928—31no—
59#4928D311yescharacteristic, complemented
60#4668—32no—
61#4668—32no—
62#4668—32no—
63#4667—32no—
64C23×C3⋊D3C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C2×C4⋊(C3⋊D3)C2×C414yes—
70C2×C4⋊(C3⋊D3)D414yes—
71C2×C4⋊(C3⋊D3)Q814yes—
72C2×C4×C3⋊D3—24no—
73C2×C4×C3⋊D3—24no—
74C2×C4×C3⋊D3—42no—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C2×#624—24no—
82C2×#624—24no—
83C2×#624—24no—
84C2×#624—24no—
85C2×#624—42no—
86C2×#624C2×C418yescomplemented
87C32×C42—22no—
88#3752—24no—
89C4⋊(C3⋊Dic3)—22no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3C2×C414yescomplemented
92C3×Dic3⋊C4—24no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D414yescomplemented
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2×C414yescomplemented
97Dic3⋊Dic3—24no—
98Dic3⋊Dic3—24no—
99Dic3⋊Dic3—42no—
100#3722—24no—
101#3722C2×C418yescomplemented
102D4×C4⋊C4—91noSylow
103C22×D12—31no—
104C22×D12—31no—
105C22×D12—61no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3—32no—
109C22×C4×D3—32no—
110C22×C4×D3—32no—
111C22×C4×D3—32no—
112C22×C4×D3—62no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C42—21no—
119C2×C3×C42—31no—
120C2×C3×C42—31no—
121C2×C3×C42C2×D311yescharacteristic
122C2×C3×C42C2×D311yescharacteristic
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—62no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—32no—
133C2×C4⋊Dic3—32no—
134C2×C4⋊Dic3—32no—
135C2×C4⋊Dic3—61no—
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4C2×D311yescharacteristic
142C2×Dic3⋊C4C2×D312yes—
143C2×Dic3⋊C4C2×D311yescharacteristic
144C2×C4×Dic3C2×D311yescharacteristic
145C2×C4×Dic3C2×D311yescharacteristic
146#893—38no—
147#893—64no—
148D3×C4⋊C4—68no—
149D3×C4⋊C4—68no—
150C4×D12—38no—
151C4×D12—64no—
152C4×D12—64no—
153C4×D12—64no—
154C4×D12—68no—
155C3×#95—32no—
156C3×#95—31no—
157C3×#95—31no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95C2×D311yescharacteristic
161C3⋊#95C2×D312yes—
162C3⋊#95C2×D311yescharacteristic
163C23×C32C2411yescharacteristic
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3C22×C414yes—
169C22×C3⋊D3C2×D414yes—
170C22×C3⋊D3C2×Q814yes—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×Q812yes—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—22no—
183C4⋊(C3⋊D3)C4⋊C4116yescomplemented
184C4×C3⋊D3—48no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3C22×C412yes—
198C2×C3×Dic3C22×C414yes—
199C2×C3×Dic3C22×C412yes—
200C2×C3×Dic3C2×D412yes—
201C2×C3×Dic3C2×D412yes—
202C2×C3×Dic3#4112yes—
203#624—216no—
204#624—48no—
205C2×C4×D4—91no—
206C2×C4×D4—91no—
207C2×C4×D4—91no—
208C22×C4⋊C4—92no—
209#389—31no—
210#389—91no—
211#385—92no—
212#385—92no—
213#384—91no—
214#380—92no—
215C4×C4⋊C4—31no—
216C23×D3—32no—
217C23×D3—32no—
218C23×D3—62no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—32no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—62no—
237C22×Dic3C22×D311yescharacteristic
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D311yescharacteristic
241C22×Dic3C22×D311yescharacteristic
242C22×Dic3C22×D311yescharacteristic
243C2×D12—34no—
244C2×D12—34no—
245C2×D12—34no—
246C2×D12—34no—
247C2×D12—34no—
248C2×D12—34no—
249C2×D12—64no—
250C2×D12—64no—
251C2×D12—64no—
252C2×C4×D3—38no—
253C2×C4×D3—38no—
254C2×C4×D3—64no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C2×C4×D3—68no—
264C2×C4×D3—64no—
265C2×C4×D3—64no—
266C2×C4×D3—64no—
267C2×C4×D3—124no—
268C2×C4×D3—122no—
269C2×C4×D3—122no—
270C2×C4×D3—122no—
271C2×C4×D3—122no—
272C2×C4×D3—124no—
273C3×C4⋊C4—34no—
274C3×C4⋊C4—34no—
275C3×C4⋊C4—62no—
276C3×C4⋊C4—64no—
277C3×C4⋊C4—62no—
278C3×C42—24no—
279C3×C42—22no—
280C3×C42—22no—
281C3×C42—34no—
282C3×C42—62no—
283(C2×D3)⋊C4—38no—
284(C2×D3)⋊C4—38no—
285(C2×D3)⋊C4—64no—
286(C2×D3)⋊C4—64no—
287(C2×D3)⋊C4—64no—
288(C2×D3)⋊C4—64no—
289(C2×D3)⋊C4—68no—
290C4⋊Dic3—22no—
291C4⋊Dic3—64no—
292C4⋊Dic3—64no—
293C4⋊Dic3—62no—
294C4⋊Dic3—62no—
295C4⋊Dic3—64no—
296C4⋊Dic3—122no—
297C4⋊Dic3C4×D314yescomplemented
298Dic3⋊C4—24no—
299Dic3⋊C4—22no—
300Dic3⋊C4—64no—
301Dic3⋊C4—64no—
302Dic3⋊C4—122no—
303Dic3⋊C4D1214yescomplemented
304C4×Dic3—22no—
305C4×Dic3C4×D314yescomplemented
306C22×C32C23×C411yescharacteristic
307C22×C32C22×D411yescharacteristic
308C22×C32C22×D411yescharacteristic
309C22×C32C22×Q811yescharacteristic
310C22×C32C2×#4111yescharacteristic
311C22×C32H(5,𝔽2)11yescharacteristic
312C22×C322−1+411yescharacteristic
313C2×C3⋊D3—24no—
314C2×C3⋊D3—24no—
315C2×C3⋊D3—24no—
316C2×C3⋊D3—24no—
317C2×C3⋊D3—24no—
318C2×C3⋊D3—24no—
319C2×C3⋊D3C2×C4⋊C418yescomplemented
320C32×C4—22no—
321C32×C4—41no—
322C32×C4C2×C4⋊C414yescomplemented
323C3⋊Dic3—42no—
324C3×Dic3—24no—
325C3×Dic3—22no—
326C3×Dic3—22no—
327C3×Dic3—42no—
328C3×Dic3—41no—
329C3×Dic3C4×D414yescomplemented
330C22×D4—91no—
331C23×C4—92no—
332C23×C4—92no—
333C23×C4—92no—
334C4×D4—98no—
335C4×D4—184no—
336C4×D4—184no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—32no—
340C2×C4⋊C4—31no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—92no—
343C2×C4⋊C4—92no—
344C2×C4⋊C4—91no—
345C2×C4⋊C4—92no—
346C2×C4⋊C4—188no—
347C2×C22⋊C4—92no—
348C2×C22⋊C4—92no—
349C2×C22⋊C4—92no—
350C2×C42—31no—
351C2×C42—31no—
352C2×C42D3211yescharacteristic
353#95—31no—
354#95—31no—
355#95—32no—
356#95—92no—
357C23×C3—21no—
358C23×C3C23×D311yescharacteristic
359C23×C3C23×D311yescharacteristic
360C22×D3—34no—
361C22×D3—34no—
362C22×D3—34no—
363C22×D3—34no—
364C22×D3—34no—
365C22×D3—34no—
366C22×D3—64no—
367C22×D3—64no—
368C22×D3—64no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—122no—
378C22×D3—122no—
379C22×D3—122no—
380C22×D3—122no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—32no—
399C2×C3×C4—32no—
400C2×C3×C4—32no—
401C2×C3×C4—32no—
402C2×C3×C4—34no—
403C2×C3×C4—32no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4—61no—
414C2×C3×C4—62no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—62no—
418C2×C3×C4C2×C4×D312yes—
419C2×C3×C4C2×C4×D312yes—
420C2×C3×C4C2×D1212yes—
421C2×C3×C4D3×D412yes—
422C2×C3×C4D3×D412yes—
423C2×C3×C4D3×D412yes—
424C2×C3×C4D3×Q812yes—
425C2×C3×C4D3×Q812yes—
426C2×Dic3—21no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—21no—
438C2×Dic3—64no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—122no—
446C2×Dic3—122no—
447C2×Dic3C2×C4×D312yes—
448C2×Dic3C2×C4×D314yes—
449C2×Dic3C2×C4×D312yes—
450C2×Dic3C2×D1212yes—
451C2×Dic3C2×D1212yes—
452C2×Dic3#23512yes—
453D12—316no—
454D12—316no—
455D12—616no—
456C4×D3—616no—
457C4×D3—616no—
458C4×D3—128no—
459C4×D3—128no—
460C4×D3—128no—
461C4×D3—128no—
462C4×D3—1216no—
463C2×C32C22×C4⋊C411yescharacteristic
464C2×C32C2×C4×D411yescharacteristic
465C2×C32#52011yescharacteristic
466C2×C32D4211yescharacteristic
467C2×C32#54711yescharacteristic
468C2×C32D4×Q811yescharacteristic
469C2×C32#55411yescharacteristic
470C3⋊D3—28no—
471C24—92no—
472C2×D4—94no—
473C2×D4—94no—
474C2×D4—94no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—32no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—32no—
481C22×C4—98no—
482C22×C4—92no—
483C22×C4—184no—
484C22×C4—184no—
485C22×C4—184no—
486C22×C4—184no—
487C22×C4—184no—
488C22×C4—184no—
489C22×C4—362no—
490C22×C4—362no—
491C22×C4C2×D3211yescharacteristic
492C22×C4C2×D3211yescharacteristic
493C22×C4C2×D3211yescharacteristic
494C4⋊C4—34no—
495C4⋊C4—34no—
496C4⋊C4—62no—
497C4⋊C4—64no—
498C4⋊C4—62no—
499C4⋊C4—184no—
500C4⋊C4—184no—
501C4⋊C4—182no—
502C4⋊C4—362no—
503C22⋊C4—98no—
504C22⋊C4—184no—
505C22⋊C4—184no—
506C42—22no—
507C42—34no—
508C42—62no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3C22×C4×D311yescharacteristic
517C22×C3C22×C4×D311yescharacteristic
518C22×C3C22×D1211yescharacteristic
519C22×C3C2×#23511yescharacteristic
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C2×D3×D411yescharacteristic
522C22×C3C2×D3×D411yescharacteristic
523C22×C3C2×D3×Q811yescharacteristic
524C22×C3C2×D3×Q811yescharacteristic
525C22×C3#100711yescharacteristic
526C22×C3D3×#4111yescharacteristic
527C22×C3#100911yescharacteristic
528C22×C3#100911yescharacteristic
529C22×C3#101011yescharacteristic
530C2×D3—38no—
531C2×D3—38no—
532C2×D3—68no—
533C2×D3—64no—
534C2×D3—64no—
535C2×D3—64no—
536C2×D3—64no—
537C2×D3—64no—
538C2×D3—64no—
539C2×D3—64no—
540C2×D3—64no—
541C2×D3—64no—
542C2×D3—64no—
543C2×D3—64no—
544C2×D3—64no—
545C2×D3—124no—
546C2×D3—124no—
547C2×D3—124no—
548C2×D3—124no—
549C2×D3—124no—
550C2×D3—124no—
551C3×C4—24no—
552C3×C4—22no—
553C3×C4—22no—
554C3×C4—24no—
555C3×C4—34no—
556C3×C4—42no—
557C3×C4—41no—
558C3×C4—41no—
559C3×C4—64no—
560C3×C4—62no—
561C3×C4—62no—
562C3×C4—122no—
563C3×C4—121no—
564C3×C4D3×C4⋊C414yescomplemented
565C3×C4D3×C4⋊C414yescomplemented
566Dic3—22no—
567Dic3—24no—
568Dic3—22no—
569Dic3—41no—
570Dic3—42no—
571Dic3—124no—
572Dic3—122no—
573Dic3—122no—
574Dic3C4×D1214yescomplemented
575C32D4×C4⋊C411yescharacteristic, complemented, Sylow
576C23—94no—
577C23—94no—
578C23—94no—
579C23—182no—
580C23—182no—
581C23—182no—
582C23—182no—
583C23C22×D3211yescharacteristic
584D4—916no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—32no—
591C2×C4—32no—
592C2×C4—32no—
593C2×C4—32no—
594C2×C4—34no—
595C2×C4—32no—
596C2×C4—61no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—62no—
604C2×C4—61no—
605C2×C4—62no—
606C2×C4—61no—
607C2×C4—62no—
608C2×C4—1816no—
609C2×C4—182no—
610C2×C4—182no—
611C2×C4—182no—
612C2×C4—368no—
613C2×C4—368no—
614C2×C4#379712yes—
615C2×C4C4×D3212yes—
616C2×C4D3×D1212yes—
617C2×C4#381112yes—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3C2×C4×D1211yescharacteristic
626C2×C3C2×D3×C4⋊C411yescharacteristic
627C2×C3C2×D3×C4⋊C411yescharacteristic
628C2×C3#552311yescharacteristic
629C2×C3C4×D3×D411yescharacteristic
630C2×C3D4×D1211yescharacteristic
631C2×C3#555111yescharacteristic
632C2×C3#557411yescharacteristic
633C2×C3Q8×D1211yescharacteristic
634C2×C3#557911yescharacteristic
635C2×C3#560911yescharacteristic
636C2×C3#563111yescharacteristic
637C2×C3#569011yescharacteristic
638C2×C3#572711yescharacteristic
639D3—68no—
640D3—68no—
641D3—128no—
642C22—98no—
643C22—184no—
644C22—184no—
645C22—184no—
646C22—184no—
647C22—184no—
648C22—184no—
649C22#6429711yescharacteristic
650C22C2×#379711yescharacteristic
651C22C2×C4×D3211yescharacteristic
652C22C2×D3×D1211yescharacteristic
653C22D3×#23511yescharacteristic
654C22#6430811yescharacteristic
655C22C2×#381111yescharacteristic
656C4—22no—
657C4—34no—
658C4—41no—
659C4—62no—
660C4—62no—
661C4—64no—
662C4—122no—
663C4—121no—
664C4—362no—
665C4#6388314yescomplemented
666C3—21no—
667C3C4⋊C4×D1211yescharacteristic, complemented
668C3#7620211yescharacteristic, complemented
669C2—188no—
670C2#1059389011yescharacteristic
671C2#1059390311yescharacteristic
672C2#1059393811yescharacteristic
673C2C4×D3×D1211yescharacteristic
674C2#1059483411yescharacteristic
675C2C2×#6388311yescharacteristic
676C2#1059507411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C2×#63883C2semidirect
5. C3×C4×Dic3⋊C4C2semidirect
6. C3×#4928C2semidirect
7. #10591375C2semidirect
8. #10591367C2semidirect
9. #10591352C2semidirect
10. #10591349C2semidirect
11. #10591290C2semidirect
35. #63894C4semidirect
57. C4×Dic3⋊C4D3semidirect
59. #4928D3semidirect
86. C2×#624C2×C4semidirect
91. C3×C4⋊Dic3C2×C4semidirect
94. C3×Dic3⋊C4D4semidirect
96. C3×C4×Dic3C2×C4semidirect
101. #3722C2×C4semidirect
183. C4⋊(C3⋊D3)C4⋊C4semidirect
297. C4⋊Dic3C4×D3semidirect
303. Dic3⋊C4D12semidirect
305. C4×Dic3C4×D3semidirect
319. C2×C3⋊D3C2×C4⋊C4semidirect
322. C32×C4C2×C4⋊C4semidirect
329. C3×Dic3C4×D4semidirect
564. C3×C4D3×C4⋊C4semidirect
565. C3×C4D3×C4⋊C4semidirect
574. Dic3C4×D12semidirect
575. C32D4×C4⋊C4semidirect
665. C4#63883semidirect
667. C3C4⋊C4×D12semidirect
668. C3#76202semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×#638942
C2×#638832
C3×C4×Dic3⋊C42
C3×#49282
#105913752
#105913672
#105913522
#105913492
#105912902
#762023
C4⋊C4×D123