Finite Group Databasebeta

← #11803595

Subgroups — #11803595

Order 1152.

1453 conjugacy classes of subgroups.

The subgroup lattice has 717 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63916C211yesmaximal, characteristic
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3C2×#63874C211yesmaximal, characteristic, complemented
4#10592686C211yesmaximal, characteristic, complemented
5C3×#4988C211yesmaximal, characteristic, complemented
6C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
7#10591383C212yesmaximal, complemented
8#10591373C212yesmaximal, complemented
9#10591364C212yesmaximal, complemented
10#10591352C211yesmaximal, characteristic, complemented
11#10591279C212yesmaximal, complemented
12#76430—31nomaximal
13#73763—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×#626C2212yes—
17C22×D3×Dic3C2212yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×#3724C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30C2×#3722C2211yescharacteristic
31C2×#3722C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34#63916C418yescomplemented
35Dic3×D12—24no—
36#63874—24no—
37#63658C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×#938—31no—
41C2×D4×Dic3—31no—
42C2×#895—31no—
43C2×C4×D12—31no—
44C2×#872—31no—
45C2×#872—31no—
46C3×#390—31no—
47C3×C4×C4⋊C4—31no—
48#4988D311yescharacteristic, complemented
49#4987—31no—
50#4987—31no—
51#4987—61no—
52#4984—31no—
53Dic3×C4⋊C4D311yescharacteristic, complemented
54#4958—32no—
55#4957—32no—
56#4946—32no—
57#4944—32no—
58#4940—32no—
59#4939—32no—
60#4928—31no—
61#4668—32no—
62#4665—32no—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3C2×C414yescomplemented
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×D12—22no—
78C2×C3×D12—22no—
79C2×C3×D12C2×C414yes—
80C2×#626—42no—
81C2×#626—42no—
82C2×#626C2×C418yescomplemented
83C2×D3×Dic3—24no—
84C2×D3×Dic3—42no—
85C2×D3×Dic3—42no—
86C32×C4⋊C4—22no—
87#3752—42no—
88C4⋊(C3⋊Dic3)—22no—
89C3×(C2×D3)⋊C4—42no—
90C3×(C2×D3)⋊C4—42no—
91C3×C4⋊Dic3C2×C414yescomplemented
92C3×C4×Dic3—22no—
93C3×C4×Dic3—42no—
94C3×C4×Dic3D414yescomplemented
95#3724—22no—
96#3724—22no—
97Dic3⋊Dic3—42no—
98#3722—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—24no—
101(C2×D3)⋊Dic3C2×C418yescomplemented
102#2324—91noSylow
103C22×C3×D4—31no—
104C22×#67—32no—
105C23×Dic3—32no—
106C22×D12—32no—
107C22×D12C2×D311yescharacteristic
108C22×C4×D3—31no—
109C22×C4×D3—31no—
110C22×C4×D3—32no—
111C22×C4×D3—61no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C4⋊C4C2×D311yescharacteristic
116C2×C3×C22⋊C4—32no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C42—31no—
119C2×C3×C42—31no—
120C2×C3×C42—32no—
121C2×#217—32no—
122C2×#217—32no—
123#938—38no—
124D4×Dic3—64no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—62no—
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×(C2×D3)⋊C4C2×D312yes—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—32no—
139C2×C4⋊Dic3—61no—
140C2×C4⋊Dic3C2×D311yescharacteristic
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—32no—
146C2×C4×Dic3C2×D311yescharacteristic
147C2×C4×Dic3C2×D312yes—
148C2×C4×Dic3C2×D311yescharacteristic
149#895—38no—
150C4×D12—64no—
151#872—64no—
152#872—64no—
153C3×#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—62no—
159C3⋊#95C2×D312yes—
160C23×C32C2411yescharacteristic
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3C22×C412yes—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3C22×C414yes—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C2×D412yes—
180C2×C32×C4#4112yes—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3C22×C412yes—
187C4×C3⋊D3—28no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3C22×C414yes—
201C2×C3×Dic3C2×D412yes—
202C2×C3×Dic3C2×D412yes—
203C3×D12—28no—
204#626—48no—
205D3×Dic3—48no—
206C2×#121—91no—
207C2×C4×D4—91no—
208C2×#117—91no—
209#390—31no—
210#390—92no—
211#389—91no—
212#388—92no—
213#386—92no—
214#385—92no—
215#380—91no—
216C4×C4⋊C4—31no—
217C24×C3—32no—
218C23×D3—31no—
219C23×D3—31no—
220C23×D3—61no—
221C23×D3C22×D312yes—
222C2×C3×D4—34no—
223C2×C3×D4—62no—
224C2×C3×D4—62no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—32no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—38no—
237C2×#67—122no—
238C2×#67—122no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—32no—
242C22×Dic3—32no—
243C22×Dic3—61no—
244C22×Dic3—62no—
245C22×Dic3—64no—
246C22×Dic3—122no—
247C22×Dic3—122no—
248C22×Dic3C22×D311yescharacteristic
249C22×Dic3C22×D311yescharacteristic
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D311yescharacteristic
252C22×Dic3C22×D311yescharacteristic
253C2×D12—22no—
254C2×D12—22no—
255C2×D12—38no—
256C2×D12—122no—
257C2×D12—122no—
258C2×D12C4×D314yes—
259C2×C4×D3—34no—
260C2×C4×D3—34no—
261C2×C4×D3—64no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×C4×D3—64no—
267C2×C4×D3—122no—
268C2×C4×D3—122no—
269C2×C4×D3—122no—
270C2×C4×D3—122no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—34no—
274C3×C4⋊C4—42no—
275C3×C22⋊C4—122no—
276C3×C22⋊C4—122no—
277C3×C42—34no—
278C3×C42—62no—
279C3×C42—122no—
280#217—38no—
281#217—64no—
282(C2×D3)⋊C4—38no—
283(C2×D3)⋊C4—42no—
284(C2×D3)⋊C4—42no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—64no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—122no—
291(C2×D3)⋊C4—122no—
292(C2×D3)⋊C4—124no—
293C4⋊Dic3—62no—
294C4⋊Dic3—62no—
295C4⋊Dic3—122no—
296C4⋊Dic3—122no—
297C4⋊Dic3C4×D314yescomplemented
298Dic3⋊C4—62no—
299Dic3⋊C4—62no—
300Dic3⋊C4—62no—
301Dic3⋊C4—62no—
302Dic3⋊C4—122no—
303C4×Dic3—22no—
304C4×Dic3—42no—
305C4×Dic3D1214yescomplemented
306C22×C32C23×C411yescharacteristic
307C22×C32C22×D411yescharacteristic
308C22×C32C2×#4111yescharacteristic
309C22×C32H(5,𝔽2)11yescharacteristic
310C22×C32H(5,𝔽2)11yescharacteristic
311C22×C32H(5,𝔽2)11yescharacteristic
312C22×C322−1+411yescharacteristic
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—22no—
316C2×C3⋊D3—41no—
317C2×C3⋊D3—41no—
318C2×C3⋊D3—41no—
319C2×C3⋊D3—41no—
320C2×C3×D3—24no—
321C2×C3×D3—24no—
322C2×C3×D3—24no—
323C2×C3×D3—42no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C2×C3×D3—42no—
327C32×C4—42no—
328C32×C4C4×D414yes—
329C3⋊Dic3—22no—
330C3⋊Dic3—42no—
331C3×Dic3—24no—
332C3×Dic3—22no—
333C3×Dic3—22no—
334C3×Dic3—41no—
335C3×Dic3—41no—
336C22×D4—31no—
337C22×D4—92no—
338C23×C4—92no—
339C23×C4—91no—
340#121—98no—
341C4×D4—184no—
342#117—184no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—91no—
345C2×C4⋊C4—91no—
346C2×C4⋊C4—91no—
347C2×C4⋊C4—92no—
348C2×C4⋊C4D3211yescharacteristic
349C2×C22⋊C4—32no—
350C2×C22⋊C4—32no—
351C2×C22⋊C4—92no—
352C2×C22⋊C4—91no—
353C2×C22⋊C4—91no—
354C2×C22⋊C4—92no—
355C2×C22⋊C4—92no—
356C2×C42—31no—
357C2×C42—31no—
358C2×C42—32no—
359#95—32no—
360#95—92no—
361#95—92no—
362C23×C3—21no—
363C23×C3—34no—
364C23×C3—62no—
365C23×C3—62no—
366C23×C3—62no—
367C23×C3—62no—
368C23×C3—62no—
369C23×C3—62no—
370C23×C3C23×D311yescharacteristic
371C23×C3C23×D311yescharacteristic
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—32no—
379C22×D3—32no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—62no—
383C22×D3—61no—
384C22×D3—61no—
385C22×D3—61no—
386C22×D3—61no—
387C22×D3—61no—
388C22×D3—61no—
389C22×D3—61no—
390C22×D3—61no—
391C22×D3—61no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—121no—
396C22×D3—121no—
397C22×D3—121no—
398C22×D3—121no—
399C22×D3C2×C4×D314yes—
400C3×D4—68no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—34no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—61no—
417C2×C3×C4—62no—
418C2×C3×C4—61no—
419C2×C3×C4—62no—
420C2×C3×C4—61no—
421C2×C3×C4—61no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4C2×C4×D312yes—
429C2×C3×C4C2×C4×D312yes—
430C2×C3×C4C2×D1212yes—
431C2×C3×C4#23512yes—
432C2×C3×C4D3×D412yes—
433C2×C3×C4#23712yes—
434#67—128no—
435C2×Dic3—21no—
436C2×Dic3—22no—
437C2×Dic3—21no—
438C2×Dic3—22no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—32no—
448C2×Dic3—32no—
449C2×Dic3—62no—
450C2×Dic3—61no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—121no—
461C2×Dic3—121no—
462C2×Dic3—122no—
463C2×Dic3—122no—
464C2×Dic3—122no—
465C2×Dic3—128no—
466C2×Dic3C2×C4×D314yes—
467C2×Dic3C2×D1212yes—
468C2×Dic3C2×D1212yes—
469D12—28no—
470D12—128no—
471C4×D3—68no—
472C4×D3—68no—
473C4×D3—128no—
474C4×D3—128no—
475C2×C32C2×C4×D411yescharacteristic
476C2×C32#51811yescharacteristic
477C2×C32#52011yescharacteristic
478C2×C32#53511yescharacteristic
479C2×C32#53711yescharacteristic
480C2×C32#54011yescharacteristic
481C2×C32#54211yescharacteristic
482C3⋊D3—42no—
483C3×D3—44no—
484C24—32no—
485C24—91no—
486C2×D4—34no—
487C2×D4—62no—
488C2×D4—62no—
489C2×D4—98no—
490C2×D4—362no—
491C2×D4—362no—
492C22×C4—31no—
493C22×C4—32no—
494C22×C4—31no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—91no—
498C22×C4—94no—
499C22×C4—92no—
500C22×C4—184no—
501C22×C4—182no—
502C22×C4—182no—
503C22×C4—362no—
504C22×C4—362no—
505C22×C4C2×D3212yes—
506C22×C4C2×D3211yescharacteristic
507C4⋊C4—22no—
508C4⋊C4—34no—
509C4⋊C4—182no—
510C4⋊C4—182no—
511C4⋊C4—182no—
512C4⋊C4—362no—
513C22⋊C4—98no—
514C22⋊C4—122no—
515C22⋊C4—122no—
516C22⋊C4—182no—
517C22⋊C4—182no—
518C22⋊C4—184no—
519C22⋊C4—362no—
520C42—34no—
521C42—62no—
522C42—122no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—64no—
531C22×C3—64no—
532C22×C3—64no—
533C22×C3—122no—
534C22×C3—122no—
535C22×C3—122no—
536C22×C3—122no—
537C22×C3C22×C4×D311yescharacteristic
538C22×C3C22×C4×D311yescharacteristic
539C22×C3C22×D1211yescharacteristic
540C22×C3C2×#23511yescharacteristic
541C22×C3C2×D3×D411yescharacteristic
542C22×C3C2×#23711yescharacteristic
543C22×C3#100411yescharacteristic
544C22×C3#100411yescharacteristic
545C22×C3#100411yescharacteristic
546C22×C3#100711yescharacteristic
547C22×C3#100911yescharacteristic
548C22×C3#100911yescharacteristic
549C22×C3#100911yescharacteristic
550C22×C3#101011yescharacteristic
551C2×D3—24no—
552C2×D3—24no—
553C2×D3—24no—
554C2×D3—42no—
555C2×D3—42no—
556C2×D3—42no—
557C2×D3—42no—
558C2×D3—64no—
559C2×D3—62no—
560C2×D3—62no—
561C2×D3—62no—
562C2×D3—62no—
563C2×D3—62no—
564C2×D3—62no—
565C2×D3—122no—
566C2×D3—122no—
567C2×D3—122no—
568C2×D3—122no—
569C2×D3—122no—
570C2×D3—122no—
571C2×D3—121no—
572C2×D3—121no—
573C2×D3—121no—
574C2×D3—121no—
575C2×D3—121no—
576C2×D3—121no—
577C2×D3—121no—
578C2×D3—121no—
579C3×C4—24no—
580C3×C4—42no—
581C3×C4—42no—
582C3×C4—64no—
583C3×C4—62no—
584C3×C4—62no—
585C3×C4—82no—
586C3×C4—121no—
587C3×C4—121no—
588C3×C4C4×D1214yes—
589C3×C4#67⋊C414yes—
590Dic3—22no—
591Dic3—22no—
592Dic3—24no—
593Dic3—41no—
594Dic3—41no—
595Dic3—62no—
596Dic3—62no—
597Dic3—122no—
598Dic3—122no—
599Dic3—122no—
600Dic3—242no—
601C32#232411yescharacteristic, complemented, Sylow
602C23—34no—
603C23—62no—
604C23—62no—
605C23—62no—
606C23—62no—
607C23—62no—
608C23—62no—
609C23—92no—
610C23—181no—
611C23—181no—
612C23—181no—
613C23—181no—
614C23—181no—
615C23—181no—
616C23C22×D3211yescharacteristic
617D4—68no—
618D4—368no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—34no—
623C2×C4—32no—
624C2×C4—32no—
625C2×C4—61no—
626C2×C4—62no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—62no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—92no—
638C2×C4—181no—
639C2×C4—181no—
640C2×C4—188no—
641C2×C4—182no—
642C2×C4—182no—
643C2×C4—182no—
644C2×C4—368no—
645C2×C4C4×D3212yes—
646C2×C4D3×D1212yes—
647C2×C4#380412yes—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—124no—
656C2×C3C2×C4×D1211yescharacteristic
657C2×C3C2×#67⋊C411yescharacteristic
658C2×C3#551011yescharacteristic
659C2×C3#552511yescharacteristic
660C2×C3#554511yescharacteristic
661C2×C3#554511yescharacteristic
662C2×C3#554611yescharacteristic
663C2×C3#556211yescharacteristic
664C2×C3#557411yescharacteristic
665C2×C3#558211yescharacteristic
666C2×C3#560711yescharacteristic
667C2×C3#560811yescharacteristic
668C2×C3#568211yescharacteristic
669C2×C3#571911yescharacteristic
670D3—44no—
671D3—124no—
672D3—122no—
673D3—122no—
674C22—64no—
675C22—64no—
676C22—64no—
677C22—122no—
678C22—122no—
679C22—122no—
680C22—122no—
681C22—182no—
682C22—182no—
683C22—182no—
684C22—361no—
685C22—361no—
686C22—361no—
687C22—361no—
688C22C2×C4×D3211yescharacteristic
689C22C2×D3×D1211yescharacteristic
690C22#6431311yescharacteristic
691C22#6431411yescharacteristic
692C22#6431511yescharacteristic
693C22#6432011yescharacteristic
694C22C2×#380411yescharacteristic
695C4—42no—
696C4—64no—
697C4—62no—
698C4—62no—
699C4—121no—
700C4—121no—
701C4—182no—
702C4—362no—
703C4#6388014yes—
704C3—21no—
705C3#7376311yescharacteristic, complemented
706C3#7643011yescharacteristic, complemented
707C2—124no—
708C2—362no—
709C2#1059436111yescharacteristic
710C2#1059452211yescharacteristic
711C2#1059460611yescharacteristic
712C2#1059462811yescharacteristic
713C2C2×#6388011yescharacteristic
714C2#1059521811yescharacteristic
715C2#1059539511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63916C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×D12C2semidirect
3. C2×#63874C2semidirect
4. #10592686C2semidirect
5. C3×#4988C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
7. #10591383C2semidirect
8. #10591373C2semidirect
9. #10591364C2semidirect
10. #10591352C2semidirect
11. #10591279C2semidirect
34. #63916C4semidirect
48. #4988D3semidirect
53. Dic3×C4⋊C4D3semidirect
71. C2×C4×C3⋊D3C2×C4semidirect
82. C2×#626C2×C4semidirect
91. C3×C4⋊Dic3C2×C4semidirect
94. C3×C4×Dic3D4semidirect
101. (C2×D3)⋊Dic3C2×C4semidirect
297. C4⋊Dic3C4×D3semidirect
305. C4×Dic3D12semidirect
601. C32#2324semidirect
705. C3#73763semidirect
706. C3#76430semidirect

Maximal subgroups

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

subgroupindex
C2×#639162
C2×Dic3×D122
C2×#638742
#105926862
C3×#49882
C3×Dic3×C4⋊C42
#105913832
#105913732
#105913642
#105913522
#105912792
#764303
#737633