Finite Group Databasebeta

← #11803590

Subgroups — #11803590

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic, complemented
5#10591722C212yesmaximal, complemented
6#10591704C212yesmaximal, complemented
7#10591378C212yesmaximal, complemented
8#10591320C211yesmaximal, characteristic, complemented
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#10591266C212yesmaximal, complemented
11#10591212C211yesmaximal, characteristic, complemented
12#82236—31nomaximal
13#73872—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2212yes—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×#624C2212yes—
18#64139C418yescomplemented
19C2×#3752C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
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×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2212yes—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yes—
35C2×Dic32C2212yes—
36#63894—24no—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×#930—31no—
42C2×#930—31no—
43C2×#930—61no—
44C2×#926D311yescharacteristic, complemented
45C2×#893—31no—
46C2×C4×D12—31no—
47C3×#380—31no—
48#5212D311yescharacteristic, complemented
49#4990—32no—
50#4989—32no—
51#4988—31no—
52Dic3×C4⋊C4—31no—
53#4972—31no—
54#4957—32no—
55#4957—32no—
56#4956—32no—
57#4956—32no—
58#4939—31no—
59C4×C4⋊Dic3—31no—
60#4928—31no—
61#4670—32no—
62#4668—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2312yes—
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yescomplemented
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C2×#638—42no—
71C2×#638—42no—
72C2×#638C2×C418yescomplemented
73C22×C3⋊Dic3C2312yes—
74C2×C4⋊(C3⋊D3)—22no—
75C2×C4⋊(C3⋊D3)—22no—
76C2×C4⋊(C3⋊D3)C2×C414yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C2×#624—24no—
84C2×#624—42no—
85C2×#624—42no—
86#3752C2×C418yescomplemented
87C4⋊(C3⋊Dic3)C2×C414yescomplemented
88C3×#217—22no—
89C3×#217—22no—
90C3×#217—42no—
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3D414yescomplemented
97#3724—42no—
98#3722—24no—
99#3722—42no—
100#3722—42no—
101Dic32—42no—
102#2324—91noSylow
103C23×C3×C4—21no—
104C23×C3×C4C2×D311yescharacteristic
105C23×C3×C4C2×D311yescharacteristic
106C22×#67—32no—
107C22×#67—32no—
108C22×#67—62no—
109C22×D12—31no—
110C22×D12—31no—
111C22×D12—61no—
112C22×C4×D3—32no—
113C22×C4×D3—32no—
114C3×#117—64no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C22⋊C4—31no—
120C2×C3×C22⋊C4—31no—
121C2×C3×C22⋊C4—32no—
122C2×C3×C42—31no—
123C2×C3×C42—31no—
124C2×#217C2×D311yescharacteristic
125C2×#217C2×D311yescharacteristic
126C2×#217C2×D312yes—
127#930—38no—
128#930—38no—
129#930—68no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—62no—
139#926—24no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—61no—
143C2×C4⋊Dic3C2×D311yescharacteristic
144C2×C4⋊Dic3C2×D311yescharacteristic
145C2×C4⋊Dic3C2×D311yescharacteristic
146C2×C4⋊Dic3C2×D311yescharacteristic
147C2×Dic3⋊C4—32no—
148C2×Dic3⋊C4—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151C2×C4×Dic3C2×D311yescharacteristic
152C2×C4×Dic3C2×D311yescharacteristic
153#893—64no—
154C4×D12—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—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—22no—
174C22×C3⋊D3—22no—
175C22×C3⋊D3C22×C414yes—
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—48no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3C22×C414yes—
187C4⋊(C3⋊D3)—28no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3C2×D412yes—
205C2×C3×Dic3C2×D412yes—
206#624—48no—
207C2×#121—91no—
208C2×C4×D4—91no—
209C2×#117—31no—
210#390—91no—
211#390—92no—
212#389—91no—
213#388—92no—
214#386—92no—
215#385—92no—
216#380—31no—
217C4×C4⋊C4—91no—
218C24×C3—21no—
219C24×C3C22×D311yescharacteristic
220C24×C3C22×D311yescharacteristic
221C23×D3—32no—
222C23×D3—32no—
223C23×D3—62no—
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—31no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—32no—
235C22×C3×C4—32no—
236C22×C3×C4—31no—
237C22×C3×C4—42no—
238C22×C3×C4—42no—
239C22×C3×C4C4×D314yescomplemented
240C22×C3×C4C4×D314yescomplemented
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—38no—
246C2×#67—38no—
247C2×#67—68no—
248C2×#67—122no—
249C2×#67—122no—
250C2×#67—122no—
251C2×#67—122no—
252C2×#67—124no—
253C2×#67—124no—
254C22×Dic3—32no—
255C22×Dic3—32no—
256C22×Dic3—62no—
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D311yescharacteristic
263C2×D12—34no—
264C2×D12—34no—
265C2×D12—64no—
266C2×D12—62no—
267C2×D12—62no—
268C2×D12—62no—
269C2×D12—62no—
270C2×D12—122no—
271C2×D12—122no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×C4×D3—122no—
275C2×C4×D3—122no—
276C2×C4×D3—122no—
277C2×C4×D3—122no—
278C3×C4⋊C4—62no—
279C3×C4⋊C4—62no—
280C3×C4⋊C4—62no—
281C3×C4⋊C4—62no—
282C3×C22⋊C4—62no—
283C3×C22⋊C4—62no—
284C3×C22⋊C4—122no—
285C3×C42—34no—
286C3×C42—62no—
287#217—22no—
288#217—22no—
289#217—42no—
290(C2×D3)⋊C4—38no—
291(C2×D3)⋊C4—38no—
292(C2×D3)⋊C4—68no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—122no—
296(C2×D3)⋊C4—122no—
297(C2×D3)⋊C4—122no—
298(C2×D3)⋊C4—122no—
299C4⋊Dic3—22no—
300C4⋊Dic3—22no—
301C4⋊Dic3—22no—
302C4⋊Dic3—22no—
303C4⋊Dic3—34no—
304C4⋊Dic3—34no—
305C4⋊Dic3—64no—
306Dic3⋊C4—122no—
307Dic3⋊C4—122no—
308C4×Dic3—22no—
309C4×Dic3—122no—
310C4×Dic3—122no—
311C4×Dic3#6714yescomplemented
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×C32H(5,𝔽2)11yescharacteristic
323C22×C32H(5,𝔽2)11yescharacteristic
324C22×C32H(5,𝔽2)11yescharacteristic
325C22×C322−1+411yescharacteristic
326C2×C3⋊D3—24no—
327C2×C3⋊D3—24no—
328C2×C3⋊D3—24no—
329C2×C3⋊D3—42no—
330C2×C3⋊D3—42no—
331C2×C3⋊D3—42no—
332C2×C3⋊D3—42no—
333C32×C4—22no—
334C32×C4C4×D414yes—
335C3⋊Dic3—24no—
336C3×Dic3—22no—
337C3×Dic3—22no—
338C3×Dic3—42no—
339C3×Dic3—41no—
340C3×Dic3—41no—
341C3×Dic3—42no—
342C22×D4—92no—
343C22×D4—91no—
344C23×C4—92no—
345C23×C4D3211yescharacteristic
346#121—98no—
347C4×D4—184no—
348#117—64no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—91no—
354C2×C4⋊C4—92no—
355C2×C22⋊C4—31no—
356C2×C22⋊C4—31no—
357C2×C22⋊C4—32no—
358C2×C22⋊C4—92no—
359C2×C22⋊C4—92no—
360C2×C22⋊C4—92no—
361C2×C22⋊C4—92no—
362C2×C42—31no—
363C2×C42—31no—
364C2×C42—92no—
365#95—32no—
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—34no—
393C22×D3—34no—
394C22×D3—64no—
395C22×D3—62no—
396C22×D3—62no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3—62no—
401C22×D3—62no—
402C22×D3—62no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—62no—
406C22×D3—62no—
407C22×D3—122no—
408C22×D3—122no—
409C22×D3—122no—
410C22×D3—122no—
411C22×D3—122no—
412C22×D3—122no—
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—32no—
424C2×C3×C4—32no—
425C2×C3×C4—48no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—62no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4—62no—
438C2×C3×C4—61no—
439C2×C3×C4—62no—
440C2×C3×C4—61no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4—62no—
444C2×C3×C4C2×C4×D312yes—
445C2×C3×C4C2×C4×D312yes—
446C2×C3×C4C2×C4×D312yes—
447C2×C3×C4C2×C4×D312yes—
448C2×C3×C4#23512yes—
449C2×C3×C4D3×D412yes—
450C2×C3×C4#23712yes—
451C2×C3×C4C2×#6712yes—
452#67—128no—
453#67—128no—
454#67—1216no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—21no—
465C2×Dic3—22no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—34no—
472C2×Dic3—34no—
473C2×Dic3—64no—
474C2×Dic3—62no—
475C2×Dic3—62no—
476C2×Dic3—62no—
477C2×Dic3—62no—
478C2×Dic3—122no—
479C2×Dic3—122no—
480C2×Dic3C2×#6712yes—
481C2×Dic3C2×#6712yes—
482D12—68no—
483D12—68no—
484D12—128no—
485C4×D3—128no—
486C4×D3—128no—
487C2×C32—42no—
488C2×C32C2×C4×D411yescharacteristic
489C2×C32#51811yescharacteristic
490C2×C32#52011yescharacteristic
491C2×C32#53511yescharacteristic
492C2×C32#53711yescharacteristic
493C2×C32#54011yescharacteristic
494C2×C32#54211yescharacteristic
495C3⋊D3—44no—
496C24—92no—
497C24C2×D3211yescharacteristic
498C2×D4—98no—
499C2×D4—94no—
500C2×D4—182no—
501C2×D4—182no—
502C2×D4—362no—
503C2×D4—362no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—31no—
511C22×C4—31no—
512C22×C4—92no—
513C22×C4—184no—
514C22×C4—362no—
515C22×C4—362no—
516C22×C4#62414yescomplemented
517C22×C4C2×D3211yescharacteristic
518C22×C4C2×D3211yescharacteristic
519C4⋊C4—62no—
520C4⋊C4—62no—
521C4⋊C4—62no—
522C4⋊C4—62no—
523C4⋊C4—94no—
524C4⋊C4—362no—
525C22⋊C4—62no—
526C22⋊C4—62no—
527C22⋊C4—98no—
528C22⋊C4—122no—
529C22⋊C4—184no—
530C22⋊C4—362no—
531C22⋊C4—362no—
532C42—34no—
533C42—62no—
534C42—362no—
535C22×C3—24no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—41no—
556C22×C3—41no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3C22×C4×D311yescharacteristic
564C22×C3C22×C4×D311yescharacteristic
565C22×C3C2×#23511yescharacteristic
566C22×C3C2×D3×D411yescharacteristic
567C22×C3C2×#23711yescharacteristic
568C22×C3#100411yescharacteristic
569C22×C3#100711yescharacteristic
570C22×C3#100911yescharacteristic
571C22×C3#100911yescharacteristic
572C22×C3#100911yescharacteristic
573C22×C3#100911yescharacteristic
574C22×C3#100911yescharacteristic
575C22×C3#101011yescharacteristic
576C22×C3C22×#6711yescharacteristic
577C2×D3—64no—
578C2×D3—64no—
579C2×D3—64no—
580C2×D3—64no—
581C2×D3—64no—
582C2×D3—64no—
583C2×D3—124no—
584C2×D3—124no—
585C2×D3—124no—
586C2×D3—122no—
587C2×D3—122no—
588C2×D3—122no—
589C2×D3—122no—
590C2×D3—122no—
591C2×D3—122no—
592C2×D3—122no—
593C2×D3—122no—
594C2×D3—242no—
595C2×D3—242no—
596C2×D3—242no—
597C2×D3—242no—
598C3×C4—22no—
599C3×C4—22no—
600C3×C4—24no—
601C3×C4—42no—
602C3×C4—62no—
603C3×C4—62no—
604C3×C4—122no—
605C3×C4—122no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4#67⋊C414yes—
609C3×C4C4×#6714yes—
610Dic3—22no—
611Dic3—22no—
612Dic3—41no—
613Dic3—41no—
614Dic3—42no—
615Dic3—42no—
616Dic3—64no—
617Dic3—64no—
618Dic3—124no—
619C32#232411yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—94no—
627C23—182no—
628C23—182no—
629C23—182no—
630C23—182no—
631C23—182no—
632C23—182no—
633C23C2×#62412yes—
634C23C22×D3211yescharacteristic
635D4—188no—
636D4—368no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—28no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—61no—
650C2×C4—62no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—62no—
658C2×C4—94no—
659C2×C4—182no—
660C2×C4—182no—
661C2×C4—368no—
662C2×C4#380412yes—
663C2×C4C2×#62412yes—
664C2×C4C2×#62412yes—
665C2×C4D3×#6712yes—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—44no—
674C2×C3—42no—
675C2×C3—42no—
676C2×C3C2×#67⋊C411yescharacteristic
677C2×C3#550411yescharacteristic
678C2×C3#552111yescharacteristic
679C2×C3#552111yescharacteristic
680C2×C3#552311yescharacteristic
681C2×C3#553411yescharacteristic
682C2×C3#553511yescharacteristic
683C2×C3#560711yescharacteristic
684C2×C3#561911yescharacteristic
685C2×C3#562911yescharacteristic
686C2×C3#564311yescharacteristic
687C2×C3C2×C4×#6711yescharacteristic
688C2×C3#583011yescharacteristic
689C2×C3#583311yescharacteristic
690D3—124no—
691D3—124no—
692D3—244no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—184no—
701C22—184no—
702C22—184no—
703C22—362no—
704C22—362no—
705C22—362no—
706C22—362no—
707C22#6429711yescharacteristic
708C22#6430711yescharacteristic
709C22#6430811yescharacteristic
710C22#6430811yescharacteristic
711C22C2×#380411yescharacteristic
712C22C22×#62411yescharacteristic
713C22C2×D3×#6711yescharacteristic
714C4—22no—
715C4—62no—
716C4—62no—
717C4—121no—
718C4—122no—
719C4—122no—
720C4—121no—
721C4—184no—
722C4#6395214yes—
723C3—21no—
724C3#7387211yescharacteristic, complemented
725C3#8223611yescharacteristic, complemented
726C2—42no—
727C2—364no—
728C2#1059481411yescharacteristic
729C2#1059489411yescharacteristic
730C2#1059498511yescharacteristic
731C2#1059499011yescharacteristic
732C2#1059499611yescharacteristic
733C2#1059506411yescharacteristic
734C2C2×#6395211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#64139C2
hypercenterC23×C4D32
hypocenterC32#2324
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×#63894C2semidirect
4. C3×#5212C2semidirect
5. #10591722C2semidirect
6. #10591704C2semidirect
7. #10591378C2semidirect
8. #10591320C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591266C2semidirect
11. #10591212C2semidirect
18. #64139C4semidirect
44. C2×#926D3semidirect
48. #5212D3semidirect
67. C22×C32×C4C2×C4semidirect
72. C2×#638C2×C4semidirect
86. #3752C2×C4semidirect
87. C4⋊(C3⋊Dic3)C2×C4semidirect
96. C3×C4×Dic3D4semidirect
239. C22×C3×C4C4×D3semidirect
240. C22×C3×C4C4×D3semidirect
311. C4×Dic3#67semidirect
516. C22×C4#624semidirect
619. C32#2324semidirect
724. C3#73872semidirect
725. C3#82236semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C2×C3×#9262
C2×#638942
C3×#52122
#105917222
#105917042
#105913782
#105913202
Dic3×C4⋊Dic32
#105912662
#105912122
#822363
#738723