Finite Group Databasebeta

← #11805663

Subgroups — #11805663

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 742 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×#63900C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic, complemented
5#10591722C212yesmaximal
6#10591703C212yesmaximal, complemented
7#10591325C211yesmaximal, characteristic, complemented
8#10591274C211yesmaximal, characteristic, complemented
9#10591233C212yesmaximal, complemented
10#10591230C211yesmaximal, characteristic, complemented
11#10591197C212yesmaximal, complemented
12#82272—31nomaximal
13#74012—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#624C2212yes—
18C2×#3757C2211yescharacteristic
19C4×#638C418yescomplemented
20C2×#3752C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C3×#926—24no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2212yes—
31C2×#3724C2212yes—
32C2×#3722C2212yes—
33C2×Dic32C2212yes—
34#63900—24no—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×C4×#67—31no—
42C2×C4×#67—31no—
43C2×C4×#67—61no—
44C2×#926D311yescharacteristic, complemented
45C2×D3×C4⋊C4—31no—
46C2×D3×C4⋊C4—31no—
47C3×#380—31no—
48#5212D311yescharacteristic, complemented
49#4987—31no—
50#4987—31no—
51#4977—31no—
52#4977—31no—
53Dic3×C4⋊C4—31no—
54Dic3×C4⋊C4—31no—
55#4956—32no—
56#4956—32no—
57#4945—32no—
58#4944—32no—
59C4×(C2×D3)⋊C4—32no—
60#4933—32no—
61#4666—32no—
62#4652—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yescomplemented
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—
83C2×#624—24no—
84C2×#624—24no—
85C2×#624—42no—
86#3757C2×C414yescomplemented
87#3752C2×C414yes—
88#3750C2×C414yescomplemented
89C4×C3⋊Dic3C2×C414yescomplemented
90C3×#217—24no—
91C3×#217—42no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3D414yescomplemented
96C3×C4×Dic3—24no—
97#3724—24no—
98#3722—24no—
99Dic32—42no—
100#2352—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—32no—
110C22×C4×D3—32no—
111C22×C4×D3—61no—
112C3×#117—64no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C42—32no—
120C2×#217—31no—
121C2×#217—31no—
122C2×#217—61no—
123C2×#217C2×D312yes—
124C2×#217C2×D312yes—
125C4×#67—38no—
126C4×#67—38no—
127C4×#67—68no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—31no—
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—61no—
143C2×C4×Dic3—31no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—61no—
148C2×C4×Dic3C2×D312yes—
149D3×C4⋊C4—64no—
150D3×C4⋊C4—64no—
151C3×#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
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⋊D3C22×C412yes—
174C22×C3⋊D3#4112yes—
175C22×C3⋊D3#4112yes—
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⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C22×C412yes—
191C2×C3⋊Dic3C22×C412yes—
192C2×C3⋊Dic3C22×C412yes—
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—
206#624—48no—
207C2×C4×D4—91no—
208C2×#117—31no—
209C22×C4⋊C4—91no—
210#388—92no—
211#387—92no—
212#386—92no—
213#382—91no—
214#380—31no—
215#380—91no—
216C4×C4⋊C4—91no—
217C4×C22⋊C4—92no—
218C24×C3—21no—
219C24×C3C22×D311yescharacteristic
220C24×C3C22×D311yescharacteristic
221C23×D3—31no—
222C23×D3—31no—
223C23×D3—61no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—24no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4—32no—
234C22×C3×C4—32no—
235C22×C3×C4—42no—
236C22×C3×C4—42no—
237C22×C3×C4C4×D314yescomplemented
238C22×C3×C4C4×D314yescomplemented
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C2×#67—34no—
244C2×#67—34no—
245C2×#67—64no—
246C2×#67—62no—
247C2×#67—62no—
248C2×#67—62no—
249C2×#67—62no—
250C2×#67—64no—
251C2×#67—64no—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—61no—
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D312yes—
264C22×Dic3C22×D312yes—
265C2×C4×D3—34no—
266C2×C4×D3—34no—
267C2×C4×D3—64no—
268C2×C4×D3—62no—
269C2×C4×D3—62no—
270C2×C4×D3—62no—
271C2×C4×D3—62no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×C4×D3—122no—
277C2×C4×D3—122no—
278C2×C4×D3—122no—
279C2×C4×D3—122no—
280C3×C4⋊C4—34no—
281C3×C4⋊C4—62no—
282C3×C4⋊C4—62no—
283C3×C4⋊C4—62no—
284C3×C22⋊C4—64no—
285C3×C22⋊C4—122no—
286C3×C42—64no—
287#217—24no—
288#217—34no—
289#217—34no—
290#217—42no—
291#217—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—
297C4⋊Dic3—22no—
298C4⋊Dic3—22no—
299C4⋊Dic3—22no—
300C4⋊Dic3#6714yescomplemented
301Dic3⋊C4—34no—
302Dic3⋊C4—34no—
303Dic3⋊C4—64no—
304Dic3⋊C4—64no—
305Dic3⋊C4—64no—
306C4×Dic3—24no—
307C4×Dic3—34no—
308C4×Dic3—34no—
309C4×Dic3—64no—
310C4×Dic3—122no—
311C4×Dic3—122no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32—41no—
316C22×C32—41no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32C23×C411yescharacteristic
320C22×C32C22×D411yescharacteristic
321C22×C32C2×#4111yescharacteristic
322C22×C32C2×#4111yescharacteristic
323C22×C32C2×#4111yescharacteristic
324C22×C32H(5,𝔽2)11yescharacteristic
325C22×C322−1+411yescharacteristic
326C2×C3⋊D3—22no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—22no—
329C2×C3⋊D3—22no—
330C2×C3⋊D3—22no—
331C2×C3⋊D3—22no—
332C2×C3⋊D3#11714yescomplemented
333C32×C4—22no—
334C32×C4C4×D414yes—
335C3⋊Dic3—22no—
336C3⋊Dic3—22no—
337C3⋊Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3—42no—
340C3×Dic3—42no—
341C3×Dic3—42no—
342C22×D4—91no—
343C23×C4—92no—
344C23×C4—91no—
345C23×C4D3211yescharacteristic
346C4×D4—98no—
347#117—64no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—91no—
353C2×C4⋊C4—92no—
354C2×C4⋊C4—184no—
355C2×C22⋊C4—32no—
356C2×C22⋊C4—32no—
357C2×C22⋊C4—91no—
358C2×C22⋊C4—91no—
359C2×C22⋊C4—92no—
360C2×C42—32no—
361C2×C42—91no—
362C2×C42—92no—
363#95—32no—
364#95—92no—
365#95—92no—
366#95—92no—
367#95—92no—
368C23×C3—22no—
369C23×C3—22no—
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—21no—
383C23×C3—22no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3C2×C4×D312yes—
389C23×C3C2×C4×D312yes—
390C23×C3C23×D311yescharacteristic
391C23×C3C23×D311yescharacteristic
392C22×D3—32no—
393C22×D3—32no—
394C22×D3—32no—
395C22×D3—32no—
396C22×D3—32no—
397C22×D3—32no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3—62no—
401C22×D3—61no—
402C22×D3—61no—
403C22×D3—61no—
404C22×D3—61no—
405C22×D3—61no—
406C22×D3—61no—
407C22×D3—61no—
408C22×D3—61no—
409C22×D3—121no—
410C22×D3—121no—
411C22×D3—121no—
412C22×D3—121no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—28no—
418C2×C3×C4—28no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—34no—
424C2×C3×C4—48no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
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×C4—62no—
438C2×C3×C4C2×C4×D312yes—
439C2×C3×C4C2×C4×D312yes—
440C2×C3×C4C2×C4×D312yes—
441C2×C3×C4C2×C4×D312yes—
442C2×C3×C4#23512yes—
443C2×C3×C4D3×D412yes—
444C2×C3×C4#23712yes—
445C2×C3×C4C2×#6712yes—
446#67—68no—
447#67—68no—
448#67—616no—
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—22no—
460C2×Dic3—32no—
461C2×Dic3—32no—
462C2×Dic3—32no—
463C2×Dic3—32no—
464C2×Dic3—32no—
465C2×Dic3—32no—
466C2×Dic3—62no—
467C2×Dic3—62no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—61no—
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—61no—
483C2×Dic3—121no—
484C2×Dic3—121no—
485C2×Dic3—121no—
486C2×Dic3—121no—
487C2×Dic3C2×#6714yes—
488C4×D3—68no—
489C4×D3—68no—
490C4×D3—128no—
491C4×D3—128no—
492C4×D3—128no—
493C2×C32—42no—
494C2×C32C2×#11711yescharacteristic
495C2×C32C2×C4×D411yescharacteristic
496C2×C32#52011yescharacteristic
497C2×C32#54611yescharacteristic
498C2×C32#54811yescharacteristic
499C2×C32#55211yescharacteristic
500C2×C32#55311yescharacteristic
501C3⋊D3—24no—
502C24—91no—
503C24C2×D3211yescharacteristic
504C2×D4—94no—
505C2×D4—182no—
506C2×D4—182no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—32no—
510C22×C4—32no—
511C22×C4—32no—
512C22×C4—32no—
513C22×C4—91no—
514C22×C4—91no—
515C22×C4—91no—
516C22×C4—94no—
517C22×C4—184no—
518C22×C4—184no—
519C22×C4—182no—
520C22×C4—182no—
521C22×C4—362no—
522C22×C4#62414yescomplemented
523C22×C4C2×D3211yescharacteristic
524C22×C4C2×D3211yescharacteristic
525C4⋊C4—34no—
526C4⋊C4—62no—
527C4⋊C4—62no—
528C4⋊C4—62no—
529C4⋊C4—94no—
530C4⋊C4—184no—
531C22⋊C4—64no—
532C22⋊C4—94no—
533C22⋊C4—94no—
534C22⋊C4—122no—
535C22⋊C4—184no—
536C42—64no—
537C42—94no—
538C42—362no—
539C22×C3—24no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3C22×C4×D311yescharacteristic
568C22×C3C22×C4×D311yescharacteristic
569C22×C3C2×#23511yescharacteristic
570C22×C3C2×D3×D411yescharacteristic
571C22×C3C2×#23711yescharacteristic
572C22×C3#100411yescharacteristic
573C22×C3#100711yescharacteristic
574C22×C3D3×#4111yescharacteristic
575C22×C3D3×#4111yescharacteristic
576C22×C3D3×#4111yescharacteristic
577C22×C3D3×#4111yescharacteristic
578C22×C3#100911yescharacteristic
579C22×C3#101011yescharacteristic
580C22×C3C22×#6711yescharacteristic
581C2×D3—34no—
582C2×D3—34no—
583C2×D3—64no—
584C2×D3—62no—
585C2×D3—62no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—62no—
589C2×D3—62no—
590C2×D3—62no—
591C2×D3—62no—
592C2×D3—62no—
593C2×D3—62no—
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—122no—
597C2×D3—122no—
598C2×D3—122no—
599C2×D3—122no—
600C2×D3—122no—
601C2×D3—122no—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—24no—
605C3×C4—42no—
606C3×C4—64no—
607C3×C4—122no—
608C3×C4—122no—
609C3×C4—122no—
610C3×C4#67⋊C414yes—
611C3×C4C4×#6714yes—
612Dic3—24no—
613Dic3—42no—
614Dic3—42no—
615Dic3—42no—
616Dic3—64no—
617Dic3—62no—
618Dic3—62no—
619Dic3—62no—
620Dic3—62no—
621Dic3—62no—
622Dic3—62no—
623Dic3—122no—
624Dic3—122no—
625C32#235211yescharacteristic, complemented, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—92no—
633C23—92no—
634C23—92no—
635C23—181no—
636C23—181no—
637C23—181no—
638C23—181no—
639C23C2×#62412yes—
640C23C22×D3211yescharacteristic
641D4—188no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—28no—
645C2×C4—34no—
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—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—92no—
658C2×C4—92no—
659C2×C4—92no—
660C2×C4—181no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—188no—
667C2×C4—368no—
668C2×C4#380412yes—
669C2×C4C2×#62412yes—
670C2×C4C2×#62412yes—
671C2×C4D3×#6712yes—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—44no—
680C2×C3—42no—
681C2×C3—42no—
682C2×C3C2×#67⋊C411yescharacteristic
683C2×C3#550411yescharacteristic
684C2×C3D3×#11711yescharacteristic
685C2×C3D3×#11711yescharacteristic
686C2×C3#552311yescharacteristic
687C2×C3#552911yescharacteristic
688C2×C3#553011yescharacteristic
689C2×C3#561211yescharacteristic
690C2×C3#561411yescharacteristic
691C2×C3#563311yescharacteristic
692C2×C3#563911yescharacteristic
693C2×C3C2×C4×#6711yescharacteristic
694C2×C3#582911yescharacteristic
695C2×C3#583111yescharacteristic
696D3—64no—
697D3—64no—
698D3—124no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—94no—
707C22—182no—
708C22—182no—
709C22—182no—
710C22—182no—
711C22—182no—
712C22—182no—
713C22#6429711yescharacteristic
714C22#6430611yescharacteristic
715C22#6430611yescharacteristic
716C22#6430711yescharacteristic
717C22C2×#380411yescharacteristic
718C22C22×#62411yescharacteristic
719C22C2×D3×#6711yescharacteristic
720C4—22no—
721C4—64no—
722C4—122no—
723C4—122no—
724C4—122no—
725C4—182no—
726C4—182no—
727C4—182no—
728C4#6395214yes—
729C3—21no—
730C3#7401211yescharacteristic, complemented
731C3#8227211yescharacteristic, complemented
732C2—42no—
733C2—184no—
734C2#1059483011yescharacteristic
735C2#1059496711yescharacteristic
736C2#1059496911yescharacteristic
737C2#1059497011yescharacteristic
738C2#1059499011yescharacteristic
739C2#1059507011yescharacteristic
740C2C2×#6395211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2352
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×#63900C2semidirect
4. C3×#5212C2semidirect
6. #10591703C2semidirect
7. #10591325C2semidirect
8. #10591274C2semidirect
9. #10591233C2semidirect
10. #10591230C2semidirect
11. #10591197C2semidirect
19. C4×#638C4semidirect
44. C2×#926D3semidirect
48. #5212D3semidirect
67. C22×C32×C4C2×C4semidirect
86. #3757C2×C4semidirect
88. #3750C2×C4semidirect
89. C4×C3⋊Dic3C2×C4semidirect
95. C3×C4⋊Dic3D4semidirect
237. C22×C3×C4C4×D3semidirect
238. C22×C3×C4C4×D3semidirect
300. C4⋊Dic3#67semidirect
332. C2×C3⋊D3#117semidirect
522. C22×C4#624semidirect
625. C32#2352semidirect
730. C3#74012semidirect
731. C3#82272semidirect

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×#639002
C3×#52122
#105917222
#105917032
#105913252
#105912742
#105912332
#105912302
#105911972
#822723
#740123