Finite Group Databasebeta

← #11805852

Subgroups — #11805852

Order 1152.

1477 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
1C2×C4×#638C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×#63849C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic, complemented
5#10591704C212yesmaximal
6#10591703C212yesmaximal, complemented
7#10591359C211yesmaximal, characteristic, complemented
8#10591325C211yesmaximal, characteristic, complemented
9#10591274C211yesmaximal, characteristic, complemented
10#10591243C212yesmaximal, complemented
11#10591202C212yesmaximal, complemented
12#82241—31nomaximal
13#73885—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C4×#638C418yescomplemented
19C2×#3752C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C3×#926—24no—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2212yes—
30C2×#3724C2212yes—
31C2×#3724C2212yes—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×Dic32C2212yes—
35C2×Dic32C2212yes—
36#63849—24no—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×C4×#67—31no—
42C2×C4×#67—31no—
43C2×C4×#67—61no—
44C2×#926D311yescharacteristic, complemented
45C2×#892—31no—
46C2×#892—31no—
47C3×#380—31no—
48#5212D311yescharacteristic, complemented
49#4987—31no—
50#4987—31no—
51#4975—31no—
52#4975—31no—
53Dic3×C4⋊C4—31no—
54Dic3×C4⋊C4—31no—
55#4957—32no—
56#4957—32no—
57#4945—32no—
58#4944—32no—
59#4940—32no—
60C4×Dic3⋊C4—32no—
61#4669—32no—
62#4649—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yes—
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C2×#638—22no—
71C2×#638—22no—
72C2×#638C2×C414yes—
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C2×C4×C3⋊D3—22no—
77C2×C4×C3⋊D3—22no—
78C2×C4×C3⋊D3C2×C414yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83#3757C2×C414yes—
84#3752C2×C414yes—
85#3750C2×C414yes—
86C4×C3⋊Dic3C2×C414yes—
87C3×#217—24no—
88C3×#217—42no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3D414yescomplemented
93C3×C4×Dic3—24no—
94#3724—24no—
95#3724—42no—
96#3722—24no—
97#3722—42no—
98Dic32—24no—
99Dic32—24no—
100#2354—91noSylow
101C23×C3×C4—21no—
102C23×C3×C4C2×D311yescharacteristic
103C23×C3×C4C2×D311yescharacteristic
104C22×#67—31no—
105C22×#67—31no—
106C22×#67—61no—
107C22×C4×D3—31no—
108C22×C4×D3—31no—
109C22×C4×D3—61no—
110C3×#117—64no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C22⋊C4—32no—
116C2×C3×C22⋊C4—32no—
117C2×C3×C42—32no—
118C2×#217—31no—
119C2×#217—31no—
120C2×#217—61no—
121C2×#217C2×D312yes—
122C2×#217C2×D312yes—
123C4×#67—38no—
124C4×#67—38no—
125C4×#67—68no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—61no—
133#926—24no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—61no—
145C2×C4×Dic3—31no—
146C2×C4×Dic3—31no—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151C2×C4×Dic3—61no—
152C2×C4×Dic3C2×D312yes—
153#892—64no—
154#892—64no—
155C3×#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95C2×D312yes—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32C22×C412yes—
168C23×C32C2411yescharacteristic
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3—21no—
173C22×C3⋊D3—21no—
174C22×C3⋊D3—21no—
175C22×C3⋊D3C22×C412yes—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—28no—
179C2×C32×C4C22×C412yes—
180C2×C32×C4C22×C412yes—
181C2×C32×C4C2×D412yes—
182C2×C32×C4#4112yes—
183#638—28no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3C22×C412yes—
189C2×C3⋊Dic3C22×C412yes—
190C2×C3⋊Dic3C22×C412yes—
191C2×C3⋊Dic3#4112yes—
192C2×C3⋊Dic3#4112yes—
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×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3C2×D414yes—
206C2×C4×D4—91no—
207C2×#117—31no—
208C2×#117—91no—
209#390—92no—
210#388—92no—
211#388—92no—
212#384—91no—
213#380—31no—
214#380—91no—
215C4×C4⋊C4—92no—
216C4×C4⋊C4—91no—
217C24×C3—21no—
218C24×C3C22×D311yescharacteristic
219C24×C3C22×D311yescharacteristic
220C23×D3—31no—
221C23×D3—31no—
222C23×D3—61no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—24no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—32no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4—32no—
234C22×C3×C4—42no—
235C22×C3×C4—42no—
236C22×C3×C4C4×D314yes—
237C22×C3×C4C4×D314yes—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C2×#67—34no—
243C2×#67—34no—
244C2×#67—64no—
245C2×#67—62no—
246C2×#67—62no—
247C2×#67—62no—
248C2×#67—62no—
249C2×#67—64no—
250C2×#67—64no—
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—61no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D312yes—
264C2×C4×D3—34no—
265C2×C4×D3—34no—
266C2×C4×D3—64no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—62no—
270C2×C4×D3—62no—
271C2×C4×D3—122no—
272C2×C4×D3—122no—
273C3×C4⋊C4—34no—
274C3×C4⋊C4—62no—
275C3×C4⋊C4—62no—
276C3×C4⋊C4—62no—
277C3×C22⋊C4—64no—
278C3×C22⋊C4—122no—
279C3×C42—64no—
280#217—24no—
281#217—34no—
282#217—34no—
283#217—42no—
284#217—64no—
285(C2×D3)⋊C4—34no—
286(C2×D3)⋊C4—34no—
287(C2×D3)⋊C4—64no—
288(C2×D3)⋊C4—64no—
289(C2×D3)⋊C4—64no—
290(C2×D3)⋊C4—122no—
291(C2×D3)⋊C4—122no—
292C4⋊Dic3—22no—
293C4⋊Dic3—22no—
294C4⋊Dic3—22no—
295C4⋊Dic3#6714yescomplemented
296Dic3⋊C4—34no—
297Dic3⋊C4—34no—
298Dic3⋊C4—64no—
299Dic3⋊C4—64no—
300Dic3⋊C4—64no—
301Dic3⋊C4—122no—
302Dic3⋊C4—122no—
303C4×Dic3—24no—
304C4×Dic3—34no—
305C4×Dic3—34no—
306C4×Dic3—64no—
307C4×Dic3—64no—
308C4×Dic3—64no—
309C4×Dic3—64no—
310C4×Dic3—64no—
311C22×C32—22no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32—41no—
317C22×C32—41no—
318C22×C32C23×C411yescharacteristic
319C22×C32C22×D411yescharacteristic
320C22×C32C2×#4111yescharacteristic
321C22×C32C2×#4111yescharacteristic
322C22×C32C2×#4111yescharacteristic
323C22×C32H(5,𝔽2)11yescharacteristic
324C22×C322−1+411yescharacteristic
325C2×C3⋊D3—22no—
326C2×C3⋊D3—22no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—41no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3⋊D3—41no—
332C32×C4—22no—
333C32×C4C4×D414yes—
334C3⋊Dic3—22no—
335C3⋊Dic3—22no—
336C3⋊Dic3#11714yescomplemented
337C3×Dic3—24no—
338C3×Dic3—42no—
339C3×Dic3—42no—
340C3×Dic3—42no—
341C22×D4—91no—
342C23×C4—91no—
343C23×C4D3211yescharacteristic
344C4×D4—98no—
345#117—64no—
346#117—184no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—91no—
352C2×C4⋊C4—92no—
353C2×C4⋊C4—92no—
354C2×C22⋊C4—32no—
355C2×C22⋊C4—32no—
356C2×C22⋊C4—91no—
357C2×C22⋊C4—91no—
358C2×C22⋊C4—92no—
359C2×C22⋊C4—92no—
360C2×C42—32no—
361C2×C42—91no—
362C2×C42—92no—
363C2×C42—92no—
364#95—32no—
365#95—92no—
366#95—92no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3C2×C4×D312yes—
388C23×C3C2×C4×D312yes—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C22×D3—32no—
392C22×D3—32no—
393C22×D3—62no—
394C22×D3—62no—
395C22×D3—62no—
396C22×D3—61no—
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—61no—
400C22×D3—61no—
401C22×D3—61no—
402C22×D3—61no—
403C22×D3—61no—
404C22×D3—61no—
405C22×D3—61no—
406C22×D3—61no—
407C22×D3—61no—
408C22×D3—121no—
409C22×D3—121no—
410C22×D3—121no—
411C22×D3—121no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—28no—
417C2×C3×C4—28no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—34no—
423C2×C3×C4—48no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4—62no—
435C2×C3×C4—62no—
436C2×C3×C4—62no—
437C2×C3×C4C2×C4×D312yes—
438C2×C3×C4C2×C4×D312yes—
439C2×C3×C4C2×C4×D312yes—
440C2×C3×C4C2×C4×D312yes—
441C2×C3×C4#23512yes—
442C2×C3×C4D3×D412yes—
443C2×C3×C4#23712yes—
444C2×C3×C4C2×#6712yes—
445#67—68no—
446#67—68no—
447#67—616no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—32no—
460C2×Dic3—32no—
461C2×Dic3—32no—
462C2×Dic3—32no—
463C2×Dic3—32no—
464C2×Dic3—32no—
465C2×Dic3—32no—
466C2×Dic3—32no—
467C2×Dic3—32no—
468C2×Dic3—32no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—121no—
483C2×Dic3—121no—
484C2×Dic3—121no—
485C2×Dic3—121no—
486C2×Dic3C2×#6714yes—
487C4×D3—68no—
488C4×D3—68no—
489C4×D3—128no—
490C2×C32—42no—
491C2×C32C2×#11711yescharacteristic
492C2×C32C2×C4×D411yescharacteristic
493C2×C32#52011yescharacteristic
494C2×C32#54711yescharacteristic
495C2×C32#55011yescharacteristic
496C2×C32#55511yescharacteristic
497C2×C32#55611yescharacteristic
498C3⋊D3—42no—
499C24—91no—
500C24C2×D3211yescharacteristic
501C2×D4—94no—
502C2×D4—182no—
503C2×D4—182no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—32no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—91no—
511C22×C4—91no—
512C22×C4—91no—
513C22×C4—94no—
514C22×C4—182no—
515C22×C4—182no—
516C22×C4#62414yes—
517C22×C4C2×D3211yescharacteristic
518C22×C4C2×D3211yescharacteristic
519C4⋊C4—34no—
520C4⋊C4—62no—
521C4⋊C4—62no—
522C4⋊C4—62no—
523C4⋊C4—94no—
524C4⋊C4—184no—
525C4⋊C4—362no—
526C22⋊C4—64no—
527C22⋊C4—94no—
528C22⋊C4—94no—
529C22⋊C4—122no—
530C22⋊C4—184no—
531C22⋊C4—362no—
532C42—64no—
533C42—94no—
534C42—184no—
535C42—184no—
536C22×C3—24no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—41no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3C22×C4×D311yescharacteristic
565C22×C3C22×C4×D311yescharacteristic
566C22×C3C2×#23511yescharacteristic
567C22×C3C2×D3×D411yescharacteristic
568C22×C3C2×#23711yescharacteristic
569C22×C3#100411yescharacteristic
570C22×C3#100711yescharacteristic
571C22×C3D3×#4111yescharacteristic
572C22×C3D3×#4111yescharacteristic
573C22×C3D3×#4111yescharacteristic
574C22×C3D3×#4111yescharacteristic
575C22×C3#100911yescharacteristic
576C22×C3#101011yescharacteristic
577C22×C3C22×#6711yescharacteristic
578C2×D3—64no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—62no—
583C2×D3—62no—
584C2×D3—62no—
585C2×D3—122no—
586C2×D3—122no—
587C2×D3—122no—
588C2×D3—122no—
589C2×D3—122no—
590C2×D3—122no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—121no—
596C2×D3—121no—
597C2×D3—121no—
598C2×D3—121no—
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—24no—
602C3×C4—42no—
603C3×C4—64no—
604C3×C4—122no—
605C3×C4—122no—
606C3×C4—122no—
607C3×C4#67⋊C414yes—
608C3×C4C4×#6714yes—
609Dic3—24no—
610Dic3—34no—
611Dic3—34no—
612Dic3—42no—
613Dic3—42no—
614Dic3—42no—
615Dic3—64no—
616Dic3—62no—
617Dic3—62no—
618Dic3—62no—
619Dic3—62no—
620Dic3—122no—
621Dic3—122no—
622C32#235411yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—92no—
630C23—181no—
631C23—181no—
632C23—181no—
633C23—181no—
634C23—181no—
635C23—181no—
636C23C2×#62412yes—
637C23C22×D3211yescharacteristic
638D4—188no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—28no—
642C2×C4—34no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—92no—
655C2×C4—92no—
656C2×C4—92no—
657C2×C4—92no—
658C2×C4—92no—
659C2×C4—181no—
660C2×C4—181no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—188no—
664C2×C4#380412yes—
665C2×C4C2×#62412yes—
666C2×C4C2×#62412yes—
667C2×C4D3×#6712yes—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—44no—
676C2×C3—42no—
677C2×C3—42no—
678C2×C3C2×#67⋊C411yescharacteristic
679C2×C3#550411yescharacteristic
680C2×C3D3×#11711yescharacteristic
681C2×C3D3×#11711yescharacteristic
682C2×C3#552311yescharacteristic
683C2×C3#553211yescharacteristic
684C2×C3#553311yescharacteristic
685C2×C3#559911yescharacteristic
686C2×C3#561611yescharacteristic
687C2×C3#563111yescharacteristic
688C2×C3#564111yescharacteristic
689C2×C3C2×C4×#6711yescharacteristic
690C2×C3#582411yescharacteristic
691C2×C3#583411yescharacteristic
692D3—124no—
693D3—122no—
694D3—122no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—182no—
703C22—182no—
704C22—182no—
705C22—361no—
706C22—361no—
707C22—361no—
708C22—361no—
709C22#6429711yescharacteristic
710C22#6430611yescharacteristic
711C22#6430611yescharacteristic
712C22#6430711yescharacteristic
713C22C2×#380411yescharacteristic
714C22C22×#62411yescharacteristic
715C22C2×D3×#6711yescharacteristic
716C4—22no—
717C4—64no—
718C4—94no—
719C4—122no—
720C4—122no—
721C4—122no—
722C4—182no—
723C4—182no—
724C4#6395214yes—
725C3—21no—
726C3#7388511yescharacteristic, complemented
727C3#8224111yescharacteristic, complemented
728C2—42no—
729C2—362no—
730C2#1059480911yescharacteristic
731C2#1059489011yescharacteristic
732C2#1059496111yescharacteristic
733C2#1059496911yescharacteristic
734C2#1059499011yescharacteristic
735C2#1059500611yescharacteristic
736C2C2×#6395211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2354
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×#63849C2semidirect
4. C3×#5212C2semidirect
6. #10591703C2semidirect
7. #10591359C2semidirect
8. #10591325C2semidirect
9. #10591274C2semidirect
10. #10591243C2semidirect
11. #10591202C2semidirect
18. C4×#638C4semidirect
44. C2×#926D3semidirect
48. #5212D3semidirect
92. C3×C4⋊Dic3D4semidirect
295. C4⋊Dic3#67semidirect
336. C3⋊Dic3#117semidirect
622. C32#2354semidirect
726. C3#73885semidirect
727. C3#82241semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×#9262
C2×#638492
C3×#52122
#105917042
#105917032
#105913592
#105913252
#105912742
#105912432
#105912022
#822413
#738853