Finite Group Databasebeta

← #11804884

Subgroups — #11804884

Order 1152.

1769 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C2×#63843C211yesmaximal, characteristic, complemented
4C4×#3752C211yesmaximal, characteristic
5C3×#4929C211yesmaximal, characteristic, complemented
6#10591367C212yesmaximal
7#10591325C211yesmaximal, characteristic
8#10591235C212yesmaximal, complemented
9#10591233C212yesmaximal
10#10591221C211yesmaximal, characteristic, complemented
11#10591191C212yesmaximal, complemented
12Q8×(C2×D3)⋊C4—31nomaximal
13#76614—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C22×#627C2212yes—
18C22×#624C2212yes—
19C2×#3797—24no—
20C2×#3797—24no—
21C2×#3797C418yescomplemented
22C2×C32×C42C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C3×C4×Dic6—24no—
31C2×Dic3⋊Dic3C2212yes—
32C2×#3722C2212yes—
33C2×Dic32C2212yes—
34#63843—24no—
35#63658C2211yescharacteristic
36#63658C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40#63579C2212yes—
41#63579C2212yes—
42C22×D3×Q8—31no—
43C22×D3×Q8—31no—
44C2×C3×C4×Q8—31no—
45C2×Q8×Dic3—31no—
46C2×#887—31no—
47C2×C4×Dic6D311yescharacteristic, complemented
48C3×#391—31no—
49#5229—31no—
50#4987—31no—
51#4987—31no—
52#4987—32no—
53#4973—31no—
54#4973—32no—
55C4×(C2×D3)⋊C4—31no—
56C4×(C2×D3)⋊C4—31no—
57C4×(C2×D3)⋊C4—32no—
58C4×(C2×D3)⋊C4—61no—
59#4929—32no—
60#4929D311yescharacteristic, complemented
61#4667—32no—
62#4666—32no—
63#4646—32no—
64#4646—32no—
65C23×C3⋊D3C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3C2×C414yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—22no—
81C2×C3×Dic6C2×C414yes—
82C2×C3×Dic6C2×C414yes—
83C2×C3×Dic6D414yes—
84C2×C3×Dic6D414yes—
85C2×#627—24no—
86C2×#627—24no—
87C2×#627C2×C418yes—
88C2×#624—24no—
89C2×#624—24no—
90C2×#624C2×C418yes—
91#3797—232no—
92C32×C42—22no—
93#3752—22no—
94#3752Q814yescomplemented
95C4×C3⋊Dic3—22no—
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3—22no—
98C3×Dic3⋊C4—24no—
99C3×C4×Dic3—24no—
100Dic3⋊Dic3—24no—
101#3722—24no—
102Dic32—24no—
103Q8×C22⋊C4—91noSylow
104C22×C3×Q8—31no—
105C22×C3×Q8—31no—
106C2×D3×Q8—38no—
107C2×D3×Q8—38no—
108C2×D3×Q8—64no—
109C2×D3×Q8—64no—
110C2×D3×Q8—64no—
111C2×D3×Q8—64no—
112C22×C4×D3—31no—
113C22×C4×D3—31no—
114C22×C4×D3—32no—
115C22×C4×D3—32no—
116C22×C4×D3—61no—
117C22×Dic6—32no—
118C22×Dic6—32no—
119C22×Dic6C2×D311yescharacteristic
120C22×Dic6C2×D311yescharacteristic
121C3×C4×Q8—64no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C42—21no—
126C2×C3×C42—32no—
127C2×C3×C42C2×D311yescharacteristic
128C2×C3×C42C2×D311yescharacteristic
129Q8×Dic3—64no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—31no—
132C2×(C2×D3)⋊C4—31no—
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—61no—
137C2×(C2×D3)⋊C4—61no—
138C2×C4⋊Dic3—32no—
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×C4⋊Dic3C2×D311yescharacteristic
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4C2×D312yes—
143C2×C4×Dic3—31no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—61no—
148C2×C4×Dic3C2×D312yes—
149#887—64no—
150C4×Dic6—24no—
151C3×#95—32no—
152C3×#95—32no—
153C3⋊#95—31no—
154C3⋊#95—31no—
155C3⋊#95—31no—
156C3⋊#95—31no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—61no—
164C3⋊#95—61no—
165C3⋊#95C2×D312yes—
166C3⋊#95C2×D312yes—
167C23×C32C2411yescharacteristic
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3C22×C412yes—
173C22×C3⋊D3C2×Q812yes—
174C22×C3⋊D3#4112yes—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4C22×C412yes—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2×Q812yescomplemented
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3C22×C412yes—
192C2×C3⋊Dic3C2×Q812yescomplemented
193C4×C3⋊D3—28no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3C22×C414yes—
203C2×C3×Dic3C22×C414yes—
204C2×C3×Dic3C2×D414yes—
205C2×C3×Dic3C2×D414yes—
206C3×Dic6—28no—
207C3×Dic6C22⋊C4116yescomplemented
208#627—216no—
209#624—216no—
210C23×Q8—91no—
211C2×C4×Q8—31no—
212C2×C4×Q8—91no—
213#391—31no—
214#391—92no—
215#391—92no—
216#391—91no—
217#380—92no—
218#380—91no—
219C4×C22⋊C4—92no—
220C4×C22⋊C4—91no—
221C23×D3—31no—
222C23×D3—31no—
223C23×D3—61no—
224C2×C3×Q8—34no—
225C2×C3×Q8—34no—
226C2×C3×Q8—34no—
227C2×C3×Q8—34no—
228C2×C3×Q8—62no—
229C2×C3×Q8—62no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—32no—
234C22×C3×C4—32no—
235C22×C3×C4—32no—
236C22×C3×C4—32no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—31no—
249C22×Dic3—61no—
250C22×Dic3—61no—
251C22×Dic3—61no—
252C22×Dic3C22×D312yes—
253C22×Dic3C22×D312yes—
254C22×Dic3C22×D312yes—
255C22×Dic3C22×D312yes—
256D3×Q8—632no—
257D3×Q8—632no—
258C2×C4×D3—34no—
259C2×C4×D3—34no—
260C2×C4×D3—38no—
261C2×C4×D3—38no—
262C2×C4×D3—64no—
263C2×C4×D3—64no—
264C2×C4×D3—64no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×C4×D3—122no—
272C2×C4×D3—122no—
273C2×Dic6—22no—
274C2×Dic6—22no—
275C2×Dic6—38no—
276C2×Dic6—38no—
277C2×Dic6—64no—
278C2×Dic6—64no—
279C2×Dic6—64no—
280C2×Dic6—64no—
281C2×Dic6C4×D314yes—
282C2×Dic6C4×D314yes—
283C2×Dic6D1214yes—
284C2×Dic6#6714yes—
285C3×C4⋊C4—64no—
286C3×C4⋊C4—62no—
287C3×C4⋊C4—62no—
288C3×C42—22no—
289C3×C42—22no—
290C3×C42—42no—
291C3×C42—64no—
292(C2×D3)⋊C4—34no—
293(C2×D3)⋊C4—34no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—64no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—64no—
300C4⋊Dic3—22no—
301C4⋊Dic3—22no—
302C4⋊Dic3—64no—
303Dic3⋊C4—24no—
304Dic3⋊C4—64no—
305C4×Dic3—24no—
306C4×Dic3—64no—
307C4×Dic3—62no—
308C4×Dic3—62no—
309C4×Dic3—64no—
310C4×Dic3—122no—
311C22×C32C23×C411yescharacteristic
312C22×C32C22×D411yescharacteristic
313C22×C32C22×D411yescharacteristic
314C22×C32C22×Q811yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C22×C322−1+411yescharacteristic
317C22×C322−1+411yescharacteristic
318C2×C3⋊D3—22no—
319C2×C3⋊D3—22no—
320C2×C3⋊D3—22no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—22no—
324C2×C3⋊D3C4×Q814yescomplemented
325C32×C4—22no—
326C32×C4—41no—
327C32×C4C2×C22⋊C414yes—
328C3⋊Dic3—22no—
329C3⋊Dic3—22no—
330C3⋊Dic3—41no—
331C3×Dic3—24no—
332C3×Dic3—42no—
333C3×Dic3—42no—
334C3×Dic3C2×C22⋊C418yes—
335C22×Q8—31no—
336C22×Q8—31no—
337C22×Q8—92no—
338C22×Q8—98no—
339C22×Q8—184no—
340C22×Q8—184no—
341C23×C4—92no—
342C23×C4—91no—
343C4×Q8—64no—
344C4×Q8—184no—
345C2×C4⋊C4—32no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—92no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4—92no—
351C2×C22⋊C4—91no—
352C2×C42—32no—
353C2×C42—92no—
354C2×C42—91no—
355C2×C42D3211yescharacteristic
356#95—32no—
357#95—32no—
358#95—92no—
359#95—92no—
360#95—92no—
361#95—91no—
362#95—91no—
363C23×C3—21no—
364C23×C3C23×D311yescharacteristic
365C23×C3C23×D311yescharacteristic
366C22×D3—32no—
367C22×D3—32no—
368C22×D3—32no—
369C22×D3—32no—
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—121no—
384C22×D3—121no—
385C22×D3—121no—
386C22×D3—121no—
387C3×Q8—316no—
388C3×Q8—68no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—34no—
405C2×C3×C4—34no—
406C2×C3×C4—34no—
407C2×C3×C4—34no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4C2×C4×D312yes—
421C2×C3×C4C2×C4×D312yes—
422C2×C3×C4C2×D1212yes—
423C2×C3×C4D3×D412yes—
424C2×C3×C4D3×D412yes—
425C2×C3×C4D3×Q812yescomplemented
426C2×C3×C4D3×Q812yescomplemented
427C2×C3×C4C2×#6712yes—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—32no—
437C2×Dic3—32no—
438C2×Dic3—32no—
439C2×Dic3—32no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—61no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—61no—
447C2×Dic3—61no—
448C2×Dic3—61no—
449C2×Dic3—61no—
450C2×Dic3—62no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—61no—
456C2×Dic3—61no—
457C2×Dic3—121no—
458C2×Dic3—121no—
459C2×Dic3—121no—
460C2×Dic3—121no—
461C2×Dic3—121no—
462C2×Dic3—121no—
463C2×Dic3C2×C4×D314yes—
464C2×Dic3C2×C4×D314yes—
465C2×Dic3C2×D1214yes—
466C2×Dic3C2×#6714yes—
467C4×D3—616no—
468C4×D3—68no—
469C4×D3—68no—
470C4×D3—616no—
471C4×D3—128no—
472Dic6—28no—
473Dic6—616no—
474Dic6—616no—
475Dic6(C2×D3)⋊C4116yescomplemented
476C2×C32C22×C22⋊C411yescharacteristic
477C2×C32C2×C4×Q811yescharacteristic
478C2×C32#51911yescharacteristic
479C2×C32#54811yescharacteristic
480C2×C32#54811yescharacteristic
481C2×C32D4×Q811yescharacteristic
482C2×C32D4×Q811yescharacteristic
483C3⋊D3—24no—
484C24—91no—
485C2×Q8—34no—
486C2×Q8—34no—
487C2×Q8—34no—
488C2×Q8—34no—
489C2×Q8—62no—
490C2×Q8—62no—
491C2×Q8—98no—
492C2×Q8—184no—
493C2×Q8—184no—
494C2×Q8—1832no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—32no—
499C22×C4—98no—
500C22×C4—91no—
501C22×C4—91no—
502C22×C4—94no—
503C22×C4—91no—
504C22×C4—184no—
505C22×C4—184no—
506C22×C4—182no—
507C22×C4—182no—
508C22×C4C2×D3211yescharacteristic
509C22×C4C2×D3211yescharacteristic
510C22×C4C2×D3211yescharacteristic
511C4⋊C4—64no—
512C4⋊C4—62no—
513C4⋊C4—62no—
514C4⋊C4—184no—
515C22⋊C4—94no—
516C22⋊C4—182no—
517C22⋊C4—184no—
518C42—22no—
519C42—64no—
520C42—184no—
521C42—182no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3C22×C4×D311yescharacteristic
530C22×C3C22×C4×D311yescharacteristic
531C22×C3C22×D1211yescharacteristic
532C22×C3C2×D3×D411yescharacteristic
533C22×C3C2×D3×D411yescharacteristic
534C22×C3C2×D3×Q811yescharacteristic
535C22×C3C2×D3×Q811yescharacteristic
536C22×C3#100711yescharacteristic
537C22×C3#100711yescharacteristic
538C22×C3D3×#4111yescharacteristic
539C22×C3D3×#4111yescharacteristic
540C22×C3#101011yescharacteristic
541C22×C3#101011yescharacteristic
542C22×C3C22×#6711yescharacteristic
543C2×D3—34no—
544C2×D3—34no—
545C2×D3—64no—
546C2×D3—62no—
547C2×D3—62no—
548C2×D3—62no—
549C2×D3—62no—
550C2×D3—62no—
551C2×D3—62no—
552C2×D3—62no—
553C2×D3—62no—
554C2×D3—62no—
555C2×D3—62no—
556C2×D3—62no—
557C2×D3—62no—
558C2×D3—122no—
559C2×D3—122no—
560C2×D3—122no—
561C2×D3—122no—
562C2×D3—122no—
563C2×D3—122no—
564C3×C4—22no—
565C3×C4—22no—
566C3×C4—24no—
567C3×C4—38no—
568C3×C4—42no—
569C3×C4—42no—
570C3×C4—41no—
571C3×C4—41no—
572C3×C4—64no—
573C3×C4—122no—
574C3×C4—122no—
575C3×C4D3×C22⋊C414yes—
576C3×C4C2×(C2×D3)⋊C414yes—
577Dic3—24no—
578Dic3—42no—
579Dic3—42no—
580Dic3—62no—
581Dic3—62no—
582Dic3—62no—
583Dic3—62no—
584Dic3—122no—
585Dic3—122no—
586Dic3—122no—
587Dic3—121no—
588Dic3—121no—
589Dic3C2×(C2×D3)⋊C418yes—
590C32Q8×C22⋊C411yescharacteristic, complemented, Sylow
591C23—92no—
592C23—92no—
593C23—92no—
594C23—181no—
595C23—181no—
596C23—181no—
597C23—181no—
598C23C22×D3211yescharacteristic
599Q8—316no—
600Q8—68no—
601Q8—1816no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—34no—
608C2×C4—34no—
609C2×C4—34no—
610C2×C4—34no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—92no—
620C2×C4—92no—
621C2×C4—1816no—
622C2×C4—181no—
623C2×C4—181no—
624C2×C4—181no—
625C2×C4—181no—
626C2×C4—188no—
627C2×C4—181no—
628C2×C4—181no—
629C2×C4—181no—
630C2×C4#379712yescomplemented
631C2×C4C4×D3212yes—
632C2×C4D3×D1212yes—
633C2×C4D3×#6712yes—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3C2×D3×C22⋊C411yescharacteristic
642C2×C3C4×D3×Q811yescharacteristic
643C2×C3C4×D3×Q811yescharacteristic
644C2×C3#557211yescharacteristic
645C2×C3#557211yescharacteristic
646C2×C3Q8×D1211yescharacteristic
647C2×C3#557611yescharacteristic
648C2×C3#563211yescharacteristic
649C2×C3#563311yescharacteristic
650C2×C3#567711yescharacteristic
651C2×C3#572711yescharacteristic
652C2×C3C22×(C2×D3)⋊C411yescharacteristic
653C2×C3Q8×#6711yescharacteristic
654C2×C3#583111yescharacteristic
655D3—64no—
656D3—64no—
657D3—124no—
658C22—94no—
659C22—182no—
660C22—182no—
661C22—182no—
662C22—182no—
663C22—182no—
664C22—182no—
665C22#6429711yescharacteristic
666C22#6429711yescharacteristic
667C22C2×#379711yescharacteristic
668C22C2×C4×D3211yescharacteristic
669C22C2×D3×D1211yescharacteristic
670C22#6430611yescharacteristic
671C22C2×D3×#6711yescharacteristic
672C4—22no—
673C4—38no—
674C4—41no—
675C4—64no—
676C4—122no—
677C4—122no—
678C4—182no—
679C4—182no—
680C4—361no—
681C4D3×(C2×D3)⋊C414yes—
682C3—21no—
683C3#7661411yescharacteristic, complemented
684C3Q8×(C2×D3)⋊C411yescharacteristic, complemented
685C2—184no—
686C2#1059384811yescharacteristic
687C2C4×#379711yescharacteristic
688C2#1059390111yescharacteristic
689C2#1059390311yescharacteristic
690C2#1059480311yescharacteristic
691C2#1059483011yescharacteristic
692C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32Q8×C22⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C2×#63843C2semidirect
5. C3×#4929C2semidirect
8. #10591235C2semidirect
10. #10591221C2semidirect
11. #10591191C2semidirect
21. C2×#3797C4semidirect
47. C2×C4×Dic6D3semidirect
60. #4929D3semidirect
94. #3752Q8semidirect
183. C2×C32×C4C2×Q8semidirect
192. C2×C3⋊Dic3C2×Q8semidirect
207. C3×Dic6C22⋊C4semidirect
324. C2×C3⋊D3C4×Q8semidirect
425. C2×C3×C4D3×Q8semidirect
426. C2×C3×C4D3×Q8semidirect
475. Dic6(C2×D3)⋊C4semidirect
590. C32Q8×C22⋊C4semidirect
630. C2×C4#3797semidirect
683. C3#76614semidirect
684. C3Q8×(C2×D3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×C3×C4×Dic62
C2×#638432
C4×#37522
C3×#49292
#105913672
#105913252
#105912352
#105912332
#105912212
#105911912
Q8×(C2×D3)⋊C43
#766143