Finite Group Databasebeta

← #11805659

Subgroups — #11805659

Order 1152.

1437 conjugacy classes of subgroups.

The subgroup lattice has 709 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×#626C211yesmaximal, characteristic
3C2×#63849C211yesmaximal, characteristic, complemented
4#10592686C211yesmaximal, characteristic, complemented
5C3×#4977C211yesmaximal, characteristic, complemented
6#10591382C212yesmaximal
7#10591313C211yesmaximal, characteristic, complemented
8Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9#10591258C212yesmaximal, complemented
10#10591254C212yesmaximal, complemented
11#10591237C212yesmaximal, complemented
12#82161—31nomaximal
13#74229—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×C4×D3C2211yescharacteristic
17C22×#626C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C3×D3×C4⋊C4—24no—
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×#3722C2212yes—
28C2×#3722C2211yescharacteristic
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2211yescharacteristic
31C2×Dic32C2212yes—
32C2×Dic32C2212yes—
33C4×#626C418yescomplemented
34#63849—24no—
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C22×C3×C4⋊C4—31no—
41C2×C4×#67—31no—
42C2×#892—31no—
43C2×#892—31no—
44C2×D3×C4⋊C4D311yescharacteristic, complemented
45C2×C4×D12—31no—
46C3×#382—31no—
47#5213—32no—
48#5212—31no—
49C4×#217—32no—
50#4990—32no—
51#4987—31no—
52#4987—31no—
53#4987—31no—
54#4987—61no—
55#4978—32no—
56#4977D311yescharacteristic, complemented
57Dic3×C4⋊C4—31no—
58C4×C4⋊Dic3—31no—
59#4669—32no—
60#4666—32no—
61#4665—32no—
62#4654—32no—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
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×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—24no—
80C2×C3×C4×D3—24no—
81C2×C3×C4×D3—42no—
82C2×C3×C4×D3C2×C414yes—
83C2×#626—22no—
84C2×#626—22no—
85C2×#626C2×C414yes—
86C32×C4⋊C4—22no—
87#3752—42no—
88C4⋊(C3⋊Dic3)—22no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3D414yescomplemented
91C3×Dic3⋊C4—24no—
92C3×C4×Dic3C2×C414yescomplemented
93Dic3⋊Dic3C2×C414yescomplemented
94#3722—24no—
95#3722C2×C414yescomplemented
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3C2×C414yes—
98Dic32—24no—
99Dic32—42no—
100#2352—91noSylow
101C23×C3×C4—31no—
102C23×C3×C4—32no—
103C22×#67—31no—
104C22×D12—31no—
105C22×C4×D3—31no—
106C22×C4×D3—31no—
107C22×C4×D3—61no—
108C22×C4×D3C2×D312yes—
109C22×C4×D3C2×D311yescharacteristic
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—64no—
115C2×C3×C4⋊C4C2×D311yescharacteristic
116C2×C3×C4⋊C4C2×D311yescharacteristic
117C2×C3×C42—31no—
118C2×#217—31no—
119C2×#217—32no—
120C4×#67—38no—
121C2×(C2×D3)⋊C4—31no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—31no—
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—31no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4C2×D312yes—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3C2×D311yescharacteristic
143#892—64no—
144#892—64no—
145D3×C4⋊C4—24no—
146C4×D12—38no—
147C3×#95—32no—
148C3×#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—62no—
156C3⋊#95C2×D312yes—
157C3⋊#95C2×D312yes—
158C23×C32C2411yescharacteristic
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3C22×C412yes—
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3C22×C412yes—
171C22×C3×D3#4112yes—
172C22×C3×D3#4112yes—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4#4112yes—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3C22×C412yes—
185C4×C3⋊D3—28no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3C22×C412yes—
198C2×C3×Dic3C22×C412yes—
199C2×C3×Dic3C22×C412yes—
200C2×C3×Dic3C2×D414yes—
201C3×C4×D3—28no—
202C3×C4×D3—48no—
203#626—28no—
204C2×C4×D4—91no—
205C2×#117—91no—
206C22×C4⋊C4—31no—
207#388—92no—
208#387—92no—
209#386—92no—
210#382—31no—
211#380—91no—
212#380—91no—
213C4×C4⋊C4—91no—
214C4×C22⋊C4—92no—
215C24×C3—31no—
216C23×D3—31no—
217C23×D3—31no—
218C23×D3—61no—
219C23×D3C22×D311yescharacteristic
220C22×C3×C4—21no—
221C22×C3×C4—22no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—32no—
225C22×C3×C4—31no—
226C22×C3×C4—34no—
227C22×C3×C4—32no—
228C22×C3×C4—64no—
229C22×C3×C4—64no—
230C22×C3×C4—62no—
231C22×C3×C4—62no—
232C22×C3×C4—122no—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C22×D312yes—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C2×#67—34no—
238C2×#67—62no—
239C2×#67—62no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—32no—
243C22×Dic3—32no—
244C22×Dic3—61no—
245C22×Dic3—62no—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D311yescharacteristic
248C22×Dic3C22×D311yescharacteristic
249C22×Dic3C22×D311yescharacteristic
250C22×Dic3C22×D312yes—
251C2×D12—34no—
252C2×D12—62no—
253C2×D12—62no—
254C2×C4×D3—22no—
255C2×C4×D3—22no—
256C2×C4×D3—24no—
257C2×C4×D3—24no—
258C2×C4×D3—34no—
259C2×C4×D3—34no—
260C2×C4×D3—42no—
261C2×C4×D3—64no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×C4×D3—122no—
267C2×C4×D3—122no—
268C2×C4×D3C4×D314yes—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—34no—
272C3×C4⋊C4—42no—
273C3×C4⋊C4—64no—
274C3×C4⋊C4—62no—
275C3×C42—34no—
276#217—34no—
277#217—64no—
278(C2×D3)⋊C4—34no—
279(C2×D3)⋊C4—34no—
280(C2×D3)⋊C4—34no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—122no—
285(C2×D3)⋊C4—122no—
286(C2×D3)⋊C4—124no—
287C4⋊Dic3—22no—
288C4⋊Dic3—34no—
289C4⋊Dic3—62no—
290C4⋊Dic3—62no—
291C4⋊Dic3—122no—
292C4⋊Dic3#6714yescomplemented
293Dic3⋊C4—24no—
294Dic3⋊C4—34no—
295C4×Dic3—64no—
296C4×Dic3—64no—
297C4×Dic3—122no—
298C4×Dic3—122no—
299C4×Dic3C4×D314yescomplemented
300C22×C32C23×C411yescharacteristic
301C22×C32C22×D411yescharacteristic
302C22×C32C2×#4111yescharacteristic
303C22×C32C2×#4111yescharacteristic
304C22×C32C2×#4111yescharacteristic
305C22×C32H(5,𝔽2)11yescharacteristic
306C22×C322−1+411yescharacteristic
307C2×C3⋊D3—22no—
308C2×C3⋊D3—22no—
309C2×C3⋊D3—22no—
310C2×C3⋊D3—41no—
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3×D3—22no—
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—22no—
319C2×C3×D3—22no—
320C2×C3×D3#11714yescomplemented
321C32×C4—42no—
322C32×C4C4×D414yes—
323C3⋊Dic3—22no—
324C3⋊Dic3—42no—
325C3×Dic3—22no—
326C3×Dic3—22no—
327C3×Dic3—22no—
328C3×Dic3—24no—
329C3×Dic3—42no—
330C22×D4—91no—
331C23×C4—31no—
332C23×C4—32no—
333C23×C4—91no—
334C4×D4—98no—
335#117—184no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—32no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—64no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4D3211yescharacteristic
343C2×C22⋊C4—91no—
344C2×C22⋊C4—91no—
345C2×C22⋊C4—92no—
346C2×C22⋊C4—92no—
347C2×C22⋊C4—92no—
348C2×C42—31no—
349C2×C42—92no—
350C2×C42—92no—
351#95—32no—
352#95—32no—
353#95—92no—
354#95—92no—
355#95—92no—
356C23×C3—21no—
357C23×C3—32no—
358C23×C3—32no—
359C23×C3—32no—
360C23×C3—61no—
361C23×C3—61no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3C23×D311yescharacteristic
365C23×C3C23×D311yescharacteristic
366C22×D3—21no—
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—21no—
370C22×D3—32no—
371C22×D3—32no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—61no—
376C22×D3—61no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—61no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—61no—
385C22×D3—61no—
386C22×D3—61no—
387C22×D3—121no—
388C22×D3—121no—
389C22×D3—121no—
390C22×D3—121no—
391C22×D3C2×C4×D312yes—
392C22×D3#23712yes—
393C22×D3#23912yes—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—32no—
404C2×C3×C4—32no—
405C2×C3×C4—32no—
406C2×C3×C4—34no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—61no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—68no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—128no—
423C2×C3×C4C2×C4×D312yes—
424C2×C3×C4C2×C4×D312yes—
425C2×C3×C4#23512yes—
426C2×C3×C4D3×D412yes—
427C2×C3×C4#23912yes—
428C2×C3×C4C2×#6712yes—
429#67—68no—
430C2×Dic3—21no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—32no—
442C2×Dic3—32no—
443C2×Dic3—62no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—61no—
447C2×Dic3—61no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—121no—
455C2×Dic3—121no—
456C2×Dic3—122no—
457C2×Dic3—122no—
458C2×Dic3—122no—
459C2×Dic3C2×C4×D312yes—
460C2×Dic3C2×C4×D312yes—
461C2×Dic3C2×C4×D312yes—
462C2×Dic3C2×#6714yes—
463D12—68no—
464C4×D3—28no—
465C4×D3—48no—
466C4×D3—68no—
467C4×D3—68no—
468C4×D3—128no—
469C2×C32C2×#11711yescharacteristic
470C2×C32C2×C4×D411yescharacteristic
471C2×C32#52011yescharacteristic
472C2×C32#54611yescharacteristic
473C2×C32#54811yescharacteristic
474C2×C32#55211yescharacteristic
475C2×C32#55311yescharacteristic
476C3⋊D3—42no—
477C3×D3—24no—
478C24—31no—
479C24—91no—
480C2×D4—94no—
481C2×D4—182no—
482C2×D4—182no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—32no—
487C22×C4—34no—
488C22×C4—32no—
489C22×C4—64no—
490C22×C4—64no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—91no—
494C22×C4—94no—
495C22×C4—92no—
496C22×C4—122no—
497C22×C4—182no—
498C22×C4—182no—
499C22×C4C2×D3212yes—
500C22×C4C2×D3211yescharacteristic
501C4⋊C4—22no—
502C4⋊C4—34no—
503C4⋊C4—64no—
504C4⋊C4—62no—
505C4⋊C4—94no—
506C4⋊C4—182no—
507C22⋊C4—94no—
508C22⋊C4—94no—
509C22⋊C4—184no—
510C22⋊C4—184no—
511C22⋊C4—362no—
512C42—34no—
513C42—184no—
514C42—362no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—34no—
523C22×C3—62no—
524C22×C3—62no—
525C22×C3—62no—
526C22×C3—62no—
527C22×C3—62no—
528C22×C3—62no—
529C22×C3C22×C4×D311yescharacteristic
530C22×C3C22×C4×D311yescharacteristic
531C22×C3C2×#23511yescharacteristic
532C22×C3C2×D3×D411yescharacteristic
533C22×C3C2×#23711yescharacteristic
534C22×C3#100411yescharacteristic
535C22×C3C2×#23911yescharacteristic
536C22×C3C2×#23911yescharacteristic
537C22×C3#100711yescharacteristic
538C22×C3D3×#4111yescharacteristic
539C22×C3D3×#4111yescharacteristic
540C22×C3#100911yescharacteristic
541C22×C3#101011yescharacteristic
542C22×C3C22×#6711yescharacteristic
543C2×D3—22no—
544C2×D3—22no—
545C2×D3—22no—
546C2×D3—22no—
547C2×D3—22no—
548C2×D3—22no—
549C2×D3—64no—
550C2×D3—62no—
551C2×D3—62no—
552C2×D3—62no—
553C2×D3—62no—
554C2×D3—62no—
555C2×D3—62no—
556C2×D3—122no—
557C2×D3—122no—
558C2×D3—122no—
559C2×D3—122no—
560C2×D3—122no—
561C2×D3—122no—
562C2×D3—121no—
563C2×D3—121no—
564C2×D3—121no—
565C2×D3—121no—
566C2×D3—121no—
567C2×D3—121no—
568C2×D3—121no—
569C2×D3—121no—
570C2×D3#89214yescomplemented
571C3×C4—24no—
572C3×C4—42no—
573C3×C4—42no—
574C3×C4—64no—
575C3×C4—62no—
576C3×C4—62no—
577C3×C4—62no—
578C3×C4—82no—
579C3×C4—122no—
580C3×C4#89314yes—
581C3×C4C4×#6714yes—
582Dic3—22no—
583Dic3—22no—
584Dic3—22no—
585Dic3—24no—
586Dic3—42no—
587Dic3—62no—
588Dic3—62no—
589Dic3—122no—
590Dic3—122no—
591Dic3—122no—
592Dic3—242no—
593C32#235211yescharacteristic, complemented, Sylow
594C23—32no—
595C23—32no—
596C23—32no—
597C23—61no—
598C23—61no—
599C23—61no—
600C23—61no—
601C23—92no—
602C23—181no—
603C23—181no—
604C23—181no—
605C23—181no—
606C23—181no—
607C23—181no—
608C23C22×D3211yescharacteristic
609D4—188no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—32no—
614C2×C4—32no—
615C2×C4—32no—
616C2×C4—34no—
617C2×C4—61no—
618C2×C4—62no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—62no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—68no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—92no—
630C2×C4—128no—
631C2×C4—181no—
632C2×C4—181no—
633C2×C4—188no—
634C2×C4—182no—
635C2×C4—182no—
636C2×C4—182no—
637C2×C4#379912yes—
638C2×C4C4×D3212yes—
639C2×C4D3×#6712yes—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—64no—
648C2×C3C2×#89211yescharacteristic
649C2×C3C2×#89311yescharacteristic
650C2×C3#550411yescharacteristic
651C2×C3#551311yescharacteristic
652C2×C3#551411yescharacteristic
653C2×C3D3×#11711yescharacteristic
654C2×C3#552311yescharacteristic
655C2×C3#567611yescharacteristic
656C2×C3#567711yescharacteristic
657C2×C3#569411yescharacteristic
658C2×C3#569511yescharacteristic
659C2×C3C2×C4×#6711yescharacteristic
660C2×C3#580611yescharacteristic
661C2×C3#581711yescharacteristic
662D3—24no—
663D3—124no—
664D3—122no—
665D3—122no—
666C22—34no—
667C22—62no—
668C22—62no—
669C22—62no—
670C22—62no—
671C22—62no—
672C22—62no—
673C22—182no—
674C22—182no—
675C22—182no—
676C22—361no—
677C22—361no—
678C22—361no—
679C22—361no—
680C22C2×#379911yescharacteristic
681C22C2×C4×D3211yescharacteristic
682C22D3×#23711yescharacteristic
683C22#6431411yescharacteristic
684C22#6431511yescharacteristic
685C22D3×#23911yescharacteristic
686C22C2×D3×#6711yescharacteristic
687C4—42no—
688C4—62no—
689C4—64no—
690C4—62no—
691C4—62no—
692C4—122no—
693C4—182no—
694C4—362no—
695C4#6390414yes—
696C3—21no—
697C3#7422911yescharacteristic, complemented
698C3#8216111yescharacteristic, complemented
699C2—64no—
700C2—362no—
701C2#1059451011yescharacteristic
702C2#1059455311yescharacteristic
703C2#1059456211yescharacteristic
704C2D3×#89211yescharacteristic
705C2C2×#6390411yescharacteristic
706C2#1059522911yescharacteristic
707C2#1059540111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C4⋊C4C2semidirect
3. C2×#63849C2semidirect
4. #10592686C2semidirect
5. C3×#4977C2semidirect
7. #10591313C2semidirect
8. Dic3×C4⋊Dic3C2semidirect
9. #10591258C2semidirect
10. #10591254C2semidirect
11. #10591237C2semidirect
33. C4×#626C4semidirect
44. C2×D3×C4⋊C4D3semidirect
56. #4977D3semidirect
71. C2×C4×C3⋊D3C2×C4semidirect
90. C3×C4⋊Dic3D4semidirect
92. C3×C4×Dic3C2×C4semidirect
93. Dic3⋊Dic3C2×C4semidirect
95. #3722C2×C4semidirect
292. C4⋊Dic3#67semidirect
299. C4×Dic3C4×D3semidirect
320. C2×C3×D3#117semidirect
570. C2×D3#892semidirect
593. C32#2352semidirect
697. C3#74229semidirect
698. C3#82161semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×C4×#6262
C2×#638492
#105926862
C3×#49772
#105913822
#105913132
Dic3×C4⋊Dic32
#105912582
#105912542
#105912372
#821613
#742293