Finite Group Databasebeta

← #11803307

Subgroups — #11803307

Order 1152.

1953 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic, complemented
2C2×#63981C211yesmaximal, characteristic
3C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5213C211yesmaximal, characteristic, complemented
5C3×#5210C211yesmaximal, characteristic, complemented
6#10591714C211yesmaximal, characteristic, complemented
7#10591705C211yesmaximal, characteristic, complemented
8#10591384C212yesmaximal, complemented
9#10591364C212yesmaximal, complemented
10#10591259C212yesmaximal, complemented
11#10591258C212yesmaximal, complemented
12#74875—31nomaximal
13#74592—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×#626C2212yes—
19C22×D3×Dic3C2211yescharacteristic, complemented
20C2×#3752—24no—
21C2×#3752C2212yes—
22C2×#3752C2212yes—
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2212yescomplemented
27C2×C3×Dic3⋊C4C2212yescomplemented
28#63981C418yescomplemented
29#67⋊Dic3—24no—
30C2×Dic3⋊Dic3C2211yescharacteristic, complemented
31C2×#3722C2212yes—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
35C2×Dic32C2211yescharacteristic, complemented
36C2×Dic32C2212yescomplemented
37C3×C3⋊#95C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39#63579C2212yescomplemented
40C2×#937—31no—
41C2×D4×Dic3—31no—
42C22×(C2×D3)⋊C4—31no—
43C22×(C2×D3)⋊C4—31no—
44C22×(C2×D3)⋊C4—61no—
45C2×#882—31no—
46C2×#67⋊C4—31no—
47C3×#386—31no—
48C3×#385—31no—
49#5213D311yescharacteristic, complemented
50#5210D311yescharacteristic, complemented
51#4990—32no—
52#4988—32no—
53#4958—32no—
54#4957—32no—
55#4955—31no—
56#4955—31no—
57Dic3×C22⋊C4—31no—
58Dic3×C22⋊C4—31no—
59#4670—32no—
60#4669—32no—
61#4669—32no—
62#4665—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3—22no—
65C23×C3⋊D3—22no—
66C23×C3⋊D3—42no—
67C23×C3⋊D3—42no—
68C23×C3⋊D3C2×C414yescomplemented
69C23×C3⋊D3C2312yes—
70C23×C3×D3C2311yescharacteristic
71C22×C32×C4—22no—
72C22×C32×C4—42no—
73C22×C32×C4C2312yes—
74C22×C3⋊Dic3—42no—
75C22×C3⋊Dic3D414yescomplemented
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C2×C3×#67—22no—
79C2×C3×#67—22no—
80C2×C3×#67C2×C414yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C2×#626—42no—
87C2×#626—42no—
88C2×#626C2×C418yescomplemented
89C2×D3×Dic3—22no—
90C2×D3×Dic3—42no—
91#3752—24no—
92#3752—24no—
93C3×#217—22no—
94C3×#217—22no—
95C3×#217C2×C414yescomplemented
96C3×(C2×D3)⋊C4—42no—
97C3×Dic3⋊C4—42no—
98Dic3⋊Dic3—22no—
99#3722—42no—
100#3722—42no—
101#3722C2×C418yescomplemented
102(C2×D3)⋊Dic3—22no—
103Dic32—22no—
104Dic32—42no—
105#2321—91noSylow
106C24×D3—31no—
107C24×D3—31no—
108C24×D3—61no—
109C22×C3×D4—31no—
110C23×C3×C4—21no—
111C23×C3×C4C2×D311yescharacteristic
112C23×C3×C4C2×D311yescharacteristic
113C22×#67—32no—
114C22×#67C2×D311yescharacteristic
115C23×Dic3—31no—
116C23×Dic3—31no—
117C23×Dic3—31no—
118C23×Dic3—61no—
119C22×D12—32no—
120C22×C4×D3—31no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C22⋊C4—31no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C22⋊C4—32no—
126C2×#217—31no—
127C2×#217C2×D311yescharacteristic
128C2×#217C2×D311yescharacteristic
129C2×#217C2×D311yescharacteristic
130#937—38no—
131D4×Dic3—64no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—62no—
144C2×(C2×D3)⋊C4—62no—
145C2×(C2×D3)⋊C4—64no—
146C2×(C2×D3)⋊C4—64no—
147C2×(C2×D3)⋊C4—68no—
148C2×(C2×D3)⋊C4C2×D312yescomplemented
149C2×C4⋊Dic3—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4C2×D312yescomplemented
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—32no—
155C2×C4×Dic3—32no—
156#882—38no—
157#67⋊C4—64no—
158C3×#95—32no—
159C3×#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95C2×D312yescomplemented
163C3⋊#95C2×D312yescomplemented
164C23×C32—22no—
165C23×C32—22no—
166C23×C32C22×C412yes—
167C23×C32C2×D412yes—
168C23×C32#4112yes—
169C23×C32C2411yescharacteristic
170C22×C3⋊D3—28no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—22no—
174C22×C3⋊D3—22no—
175C22×C3⋊D3—22no—
176C22×C3⋊D3—22no—
177C22×C3⋊D3—48no—
178C22×C3⋊D3—44no—
179C22×C3⋊D3—44no—
180C22×C3⋊D3—48no—
181C22×C3⋊D3C22×C414yes—
182C22×C3×D3—21no—
183C22×C3×D3—21no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3C22×C412yes—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4—44no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—44no—
194C2×C3⋊Dic3C2×D412yes—
195C2×C3⋊Dic3C2×D412yes—
196C3×#67—28no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3C22×C412yes—
209C2×C3×Dic3C22×C414yes—
210#626—48no—
211D3×Dic3—44no—
212C2×#120—91no—
213C2×C4×D4—91no—
214C22×C22⋊C4—91no—
215#390—92no—
216#388—92no—
217#388—92no—
218#386—31no—
219#386—92no—
220#385—31no—
221#379—91no—
222C4×C22⋊C4—91no—
223C24×C3—21no—
224C24×C3—31no—
225C24×C3C22×D311yescharacteristic
226C24×C3C22×D311yescharacteristic
227C23×D3—32no—
228C23×D3—32no—
229C23×D3—34no—
230C23×D3—34no—
231C23×D3—64no—
232C23×D3—62no—
233C23×D3—64no—
234C23×D3—64no—
235C23×D3—62no—
236C23×D3—62no—
237C23×D3—62no—
238C23×D3—62no—
239C23×D3—122no—
240C23×D3—122no—
241C23×D3—122no—
242C23×D3—122no—
243C23×D3—124no—
244C23×D3—124no—
245C23×D3C22×D311yescharacteristic
246C2×C3×D4—34no—
247C2×C3×D4—62no—
248C2×C3×D4—62no—
249C22×C3×C4—24no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—32no—
254C22×C3×C4—31no—
255C22×C3×C4—32no—
256C22×C3×C4—31no—
257C22×C3×C4—31no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4—44no—
261C22×C3×C4C22×D312yes—
262C22×C3×C4C22×D312yes—
263C2×#67—22no—
264C2×#67—22no—
265C2×#67—38no—
266C2×#67—122no—
267C2×#67—122no—
268C2×#67C4×D314yes—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—34no—
274C22×Dic3—34no—
275C22×Dic3—64no—
276C22×Dic3—61no—
277C22×Dic3—61no—
278C22×Dic3—62no—
279C22×Dic3—122no—
280C22×Dic3—122no—
281C22×Dic3—122no—
282C22×Dic3—124no—
283C22×Dic3C22×D312yes—
284C22×Dic3C22×D311yescharacteristic
285C22×Dic3C22×D311yescharacteristic
286C22×Dic3C22×D312yes—
287C22×Dic3C22×D311yescharacteristic
288C2×D12—38no—
289C2×D12—122no—
290C2×D12—122no—
291C2×C4×D3—62no—
292C2×C4×D3—122no—
293C3×C4⋊C4—122no—
294C3×C22⋊C4—34no—
295C3×C22⋊C4—62no—
296C3×C22⋊C4—62no—
297C3×C22⋊C4—122no—
298#217—22no—
299#217—22no—
300#217—62no—
301#217C4×D314yescomplemented
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—64no—
306(C2×D3)⋊C4—64no—
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—62no—
310(C2×D3)⋊C4—68no—
311(C2×D3)⋊C4—68no—
312(C2×D3)⋊C4—122no—
313(C2×D3)⋊C4—122no—
314(C2×D3)⋊C4—122no—
315(C2×D3)⋊C4—122no—
316C4⋊Dic3—62no—
317Dic3⋊C4—42no—
318Dic3⋊C4—62no—
319C4×Dic3—62no—
320C4×Dic3—62no—
321C4×Dic3—122no—
322C4×Dic3—122no—
323C22×C32—24no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—24no—
327C22×C32C4×D414yes—
328C22×C32C23×C411yescharacteristic
329C22×C32C22×D411yescharacteristic
330C22×C32C2×#4111yescharacteristic
331C22×C32H(5,𝔽2)12yes—
332C22×C32H(5,𝔽2)12yes—
333C2×C3⋊D3—24no—
334C2×C3⋊D3—24no—
335C2×C3⋊D3—24no—
336C2×C3⋊D3—416no—
337C2×C3⋊D3—42no—
338C2×C3⋊D3—42no—
339C2×C3⋊D3—42no—
340C2×C3⋊D3—42no—
341C2×C3×D3—22no—
342C2×C3×D3—24no—
343C2×C3×D3—41no—
344C2×C3×D3—41no—
345C2×C3×D3—42no—
346C32×C4—42no—
347C3⋊Dic3—22no—
348C3⋊Dic3—22no—
349C3×Dic3—22no—
350C3×Dic3—24no—
351C3×Dic3—41no—
352C3×Dic3—41no—
353C3×Dic3—42no—
354C25—91no—
355C22×D4—31no—
356C22×D4—92no—
357C23×C4—91no—
358C23×C4—91no—
359C23×C4D3211yescharacteristic
360#120—98no—
361C4×D4—184no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—91no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—92no—
369C2×C22⋊C4—91no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—184no—
375C2×C42—91no—
376C2×C42—92no—
377#95—32no—
378#95—32no—
379#95—92no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—21no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—32no—
391C23×C3—61no—
392C23×C3—62no—
393C23×C3—61no—
394C23×C3—62no—
395C23×C3C2×C4×D312yes—
396C23×C3C2×C4×D312yes—
397C23×C3D3×D412yes—
398C23×C3D3×D412yes—
399C23×C3#23712yes—
400C23×C3#23912yes—
401C23×C3C23×D311yescharacteristic
402C23×C3C23×D311yescharacteristic
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—34no—
408C22×D3—34no—
409C22×D3—64no—
410C22×D3—64no—
411C22×D3—64no—
412C22×D3—616no—
413C22×D3—68no—
414C22×D3—68no—
415C22×D3—62no—
416C22×D3—62no—
417C22×D3—62no—
418C22×D3—62no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—62no—
422C22×D3—62no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—62no—
427C22×D3—122no—
428C22×D3—122no—
429C22×D3—122no—
430C22×D3—122no—
431C22×D3—128no—
432C22×D3—128no—
433C22×D3—1216no—
434C22×D3—128no—
435C22×D3—128no—
436C22×D3—1216no—
437C22×D3—128no—
438C22×D3—124no—
439C22×D3—124no—
440C22×D3—124no—
441C22×D3—124no—
442C22×D3—128no—
443C22×D3C2×C4×D312yes—
444C3×D4—68no—
445C2×C3×C4—24no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—32no—
453C2×C3×C4—34no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—48no—
457C2×C3×C4—44no—
458C2×C3×C4—44no—
459C2×C3×C4—61no—
460C2×C3×C4—62no—
461C2×C3×C4—61no—
462C2×C3×C4—62no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470#67—28no—
471#67—128no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—32no—
484C2×Dic3—32no—
485C2×Dic3—32no—
486C2×Dic3—32no—
487C2×Dic3—62no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—122no—
494C2×Dic3—122no—
495C2×Dic3—124no—
496C2×Dic3—124no—
497C2×Dic3—124no—
498C2×Dic3—128no—
499C2×Dic3C2×C4×D312yes—
500C2×Dic3C2×C4×D314yes—
501D12—128no—
502C4×D3—124no—
503C2×C32—24no—
504C2×C32C2×C4×D411yescharacteristic
505C2×C32#51812yes—
506C2×C32#53411yescharacteristic
507C2×C32#53511yescharacteristic
508C2×C32#53812yes—
509C3⋊D3—44no—
510C3×D3—42no—
511C24—31no—
512C24—92no—
513C24—94no—
514C24—182no—
515C24—182no—
516C24—362no—
517C24—362no—
518C24C2×D3211yescharacteristic
519C2×D4—34no—
520C2×D4—62no—
521C2×D4—62no—
522C2×D4—98no—
523C2×D4—362no—
524C2×D4—362no—
525C22×C4—22no—
526C22×C4—31no—
527C22×C4—32no—
528C22×C4—31no—
529C22×C4—32no—
530C22×C4—31no—
531C22×C4—42no—
532C22×C4—91no—
533C22×C4—91no—
534C22×C4—94no—
535C22×C4—182no—
536C22×C4—362no—
537C22×C4—362no—
538C22×C4C2×D3212yes—
539C4⋊C4—122no—
540C4⋊C4—182no—
541C22⋊C4—34no—
542C22⋊C4—62no—
543C22⋊C4—62no—
544C22⋊C4—98no—
545C22⋊C4—122no—
546C22⋊C4—184no—
547C22⋊C4—184no—
548C22⋊C4—182no—
549C22⋊C4—362no—
550C22⋊C4—362no—
551C42—182no—
552C42—362no—
553C22×C3—24no—
554C22×C3—24no—
555C22×C3—28no—
556C22×C3—28no—
557C22×C3—24no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—24no—
561C22×C3—24no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—24no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—22no—
568C22×C3—21no—
569C22×C3—22no—
570C22×C3—24no—
571C22×C3—62no—
572C22×C3—64no—
573C22×C3—122no—
574C22×C3—121no—
575C22×C3—121no—
576C22×C3#67⋊C414yes—
577C22×C3#89314yes—
578C22×C3C22×C4×D311yescharacteristic
579C22×C3C22×C4×D311yescharacteristic
580C22×C3C2×D3×D411yescharacteristic
581C22×C3C2×D3×D411yescharacteristic
582C22×C3C2×#23711yescharacteristic
583C22×C3#100412yes—
584C22×C3#100412yes—
585C22×C3C2×#23911yescharacteristic
586C22×C3#100912yes—
587C22×C3#100912yes—
588C2×D3—22no—
589C2×D3—24no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—42no—
593C2×D3—68no—
594C2×D3—64no—
595C2×D3—64no—
596C2×D3—64no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—124no—
601C2×D3—124no—
602C2×D3—1232no—
603C2×D3—1216no—
604C2×D3—1216no—
605C2×D3—124no—
606C2×D3—124no—
607C2×D3—124no—
608C2×D3—124no—
609C2×D3—122no—
610C2×D3—122no—
611C2×D3—122no—
612C2×D3—122no—
613C2×D3—122no—
614C2×D3—122no—
615C2×D3—122no—
616C2×D3—122no—
617C3×C4—44no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—62no—
621C3×C4—64no—
622C3×C4—122no—
623C3×C4—121no—
624C3×C4—121no—
625Dic3—22no—
626Dic3—24no—
627Dic3—41no—
628Dic3—41no—
629Dic3—42no—
630Dic3—62no—
631Dic3—62no—
632Dic3—62no—
633Dic3—62no—
634Dic3—122no—
635Dic3—122no—
636C32#232111yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—32no—
640C23—61no—
641C23—62no—
642C23—61no—
643C23—62no—
644C23—94no—
645C23—182no—
646C23—182no—
647C23—182no—
648C23—182no—
649C23—182no—
650C23—182no—
651C23—188no—
652C23—368no—
653C23—364no—
654C23—368no—
655C23—364no—
656C23#379612yes—
657C23C4×D3212yes—
658C23#381112yes—
659C23C22×D3211yescharacteristic
660D4—68no—
661D4—368no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—34no—
666C2×C4—32no—
667C2×C4—44no—
668C2×C4—61no—
669C2×C4—62no—
670C2×C4—61no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—92no—
680C2×C4—92no—
681C2×C4—182no—
682C2×C4—182no—
683C2×C4—364no—
684C2×C4—364no—
685C2×C3—28no—
686C2×C3—24no—
687C2×C3—24no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—22no—
691C2×C3—21no—
692C2×C3—22no—
693C2×C3—122no—
694C2×C3C2×#67⋊C411yescharacteristic
695C2×C3C2×#89311yescharacteristic
696C2×C3#554512yes—
697C2×C3#554512yes—
698C2×C3#559211yescharacteristic
699C2×C3#559211yescharacteristic
700C2×C3#561712yes—
701C2×C3#564412yes—
702C2×C3#565311yescharacteristic
703C2×C3#565311yescharacteristic
704D3—42no—
705D3—128no—
706D3—124no—
707D3—124no—
708C22—22no—
709C22—24no—
710C22—22no—
711C22—24no—
712C22—62no—
713C22—64no—
714C22—121no—
715C22—122no—
716C22—121no—
717C22—184no—
718C22—184no—
719C22—184no—
720C22—3616no—
721C22—362no—
722C22—362no—
723C22—362no—
724C22—362no—
725C22#6388114yes—
726C22C2×#379611yescharacteristic
727C22C2×C4×D3211yescharacteristic
728C22#6430812yes—
729C22C2×#381111yescharacteristic
730C22#6433012yes—
731C4—42no—
732C4—62no—
733C4—64no—
734C4—121no—
735C4—122no—
736C4—121no—
737C4—182no—
738C4—182no—
739C3—21no—
740C3#7459211yescharacteristic, complemented
741C3#7487511yescharacteristic, complemented
742C2—24no—
743C2—122no—
744C2—364no—
745C2C2×#6388111yescharacteristic
746C2#1059497912yes—
747C2#1059505812yes—
748C2#1059508011yescharacteristic
749C2#1059550211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63981C2
hypercenterC23×C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3752C2semidirect
3. C2×#67⋊Dic3C2semidirect
4. C3×#5213C2semidirect
5. C3×#5210C2semidirect
6. #10591714C2semidirect
7. #10591705C2semidirect
8. #10591384C2semidirect
9. #10591364C2semidirect
10. #10591259C2semidirect
11. #10591258C2semidirect
19. C22×D3×Dic3C22semidirect
26. C2×C3×(C2×D3)⋊C4C22semidirect
27. C2×C3×Dic3⋊C4C22semidirect
28. #63981C4semidirect
30. C2×Dic3⋊Dic3C22semidirect
34. C2×(C2×D3)⋊Dic3C22semidirect
35. C2×Dic32C22semidirect
36. C2×Dic32C22semidirect
37. C3×C3⋊#95C22semidirect
38. C3×C3⋊#95C22semidirect
39. #63579C22semidirect
49. #5213D3semidirect
50. #5210D3semidirect
68. C23×C3⋊D3C2×C4semidirect
75. C22×C3⋊Dic3D4semidirect
88. C2×#626C2×C4semidirect
95. C3×#217C2×C4semidirect
101. #3722C2×C4semidirect
148. C2×(C2×D3)⋊C4C2×D3semidirect
151. C2×Dic3⋊C4C2×D3semidirect
162. C3⋊#95C2×D3semidirect
163. C3⋊#95C2×D3semidirect
301. #217C4×D3semidirect
636. C32#2321semidirect
740. C3#74592semidirect
741. C3#74875semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C2×#639812
C2×#67⋊Dic32
C3×#52132
C3×#52102
#105917142
#105917052
#105913842
#105913642
#105912592
#105912582
#748753
#745923