Finite Group Databasebeta

← #11803292

Subgroups — #11803292

Order 1152.

1869 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
2C2×#63981C211yesmaximal, characteristic
3C22×#3722C211yesmaximal, characteristic, complemented
4#10592654C211yesmaximal, characteristic, complemented
5C3×#4946C211yesmaximal, characteristic, complemented
6#10591710C211yesmaximal, characteristic, complemented
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591384C212yesmaximal, complemented
9#10591382C212yesmaximal, complemented
10#10591289C212yesmaximal, complemented
11#10591258C212yesmaximal, complemented
12#82395—31nomaximal
13#74592—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic, complemented
19C22×#626C2212yes—
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×#3752C2212yes—
23C2×#3752C2212yes—
24C2×C3×#217C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
26C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
27C2×C3×Dic3⋊C4C2212yescomplemented
28C2×C3×C4×Dic3C2211yescharacteristic, complemented
29C3×#67⋊C4—24no—
30#63981C418yescomplemented
31C2×#3722—24no—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yes—
35C2×(C2×D3)⋊Dic3C2212yescomplemented
36C2×Dic32C2212yescomplemented
37C3×C3⋊#95C2212yescomplemented
38#63579C2212yescomplemented
39#63579C2212yescomplemented
40C2×C3×C4×D4—31no—
41C2×#937—31no—
42C22×(C2×D3)⋊C4—31no—
43C22×(C2×D3)⋊C4—31no—
44C2×#882—31no—
45C2×#67⋊C4D311yescharacteristic, complemented
46C3×#385—31no—
47#5220—31no—
48#5213—31no—
49#5213—32no—
50C4×#217—31no—
51#4990—32no—
52#4990—32no—
53#4988—32no—
54#4957—32no—
55#4955—31no—
56#4955—31no—
57#4955—61no—
58#4946D311yescharacteristic, complemented
59Dic3×C22⋊C4—31no—
60#4940—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×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3C2312yes—
74C2×C3×#67—22no—
75C2×C3×#67—22no—
76C2×C3×#67C2×C414yes—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—42no—
79C22×C3×Dic3—42no—
80C22×C3×Dic3D414yescomplemented
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C2×C3×C4×D3—22no—
87C2×C3×C4×D3—42no—
88C2×#626—42no—
89C2×#626—42no—
90C2×#626C2×C418yescomplemented
91C32×C22⋊C4—22no—
92#3757—22no—
93#3752—42no—
94#3752—42no—
95C3×#217C2×C414yescomplemented
96C3×(C2×D3)⋊C4—22no—
97C3×Dic3⋊C4—22no—
98C3×Dic3⋊C4—42no—
99C3×C4×Dic3—22no—
100#3722—24no—
101#3722—24no—
102#3722C2×C418yescomplemented
103(C2×D3)⋊Dic3—42no—
104Dic32—42no—
105#2321—91noSylow
106C24×D3—31no—
107C24×D3—31no—
108C24×D3—61no—
109C22×C3×D4—31no—
110C23×C3×C4—31no—
111C23×C3×C4—31no—
112C23×C3×C4—31no—
113C22×#67—32no—
114C22×#67C2×D311yescharacteristic
115C23×Dic3C2×D311yescharacteristic
116C23×Dic3C2×D311yescharacteristic
117C22×D12—32no—
118C22×C4×D3C2×D311yescharacteristic, complemented
119C3×C4×D4—64no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C22⋊C4C2×D311yescharacteristic
126C2×C3×C22⋊C4C2×D311yescharacteristic
127C2×C3×C42—31no—
128C2×#217—31no—
129C2×#217—31no—
130C2×#217—32no—
131C2×#217—61no—
132C2×#217C2×D311yescharacteristic
133#937—38no—
134C2×(C2×D3)⋊C4—32no—
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—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—62no—
146C2×(C2×D3)⋊C4—62no—
147C2×(C2×D3)⋊C4—64no—
148C2×(C2×D3)⋊C4—64no—
149C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
150C2×Dic3⋊C4C2×D311yescharacteristic, complemented
151C2×Dic3⋊C4C2×D312yescomplemented
152C2×C4×Dic3—32no—
153C2×C4×Dic3—32no—
154C2×C4×Dic3C2×D311yescharacteristic, complemented
155#882—38no—
156#67⋊C4—24no—
157C3×#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95C2×D312yescomplemented
163C23×C32—22no—
164C23×C32—22no—
165C23×C32C22×C412yes—
166C23×C32C2×D412yes—
167C23×C32#4112yes—
168C23×C32C2411yescharacteristic
169C22×C3⋊D3—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3—28no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—22no—
174C22×C3⋊D3—22no—
175C22×C3⋊D3—22no—
176C22×C3⋊D3—48no—
177C22×C3⋊D3—44no—
178C22×C3⋊D3—44no—
179C22×C3⋊D3—48no—
180C22×C3⋊D3C22×C414yes—
181C22×C3×D3—21no—
182C22×C3×D3—21no—
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3C22×C412yes—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—22no—
193C3×#67—28no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
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—44no—
204C2×C3×Dic3—44no—
205C2×C3×Dic3C22×C412yes—
206C2×C3×Dic3C22×C414yes—
207C2×C3×Dic3C2×D412yes—
208C2×C3×Dic3C2×D412yes—
209C3×C4×D3—44no—
210#626—48no—
211C2×#120—91no—
212C2×C4×D4—31no—
213C22×C22⋊C4—91no—
214#390—92no—
215#388—92no—
216#388—92no—
217#386—92no—
218#386—91no—
219#385—31no—
220#379—91no—
221C4×C22⋊C4—91no—
222C24×C3—21no—
223C24×C3—31no—
224C24×C3C22×D311yescharacteristic
225C24×C3C22×D311yescharacteristic
226C23×D3—32no—
227C23×D3—32no—
228C23×D3—34no—
229C23×D3—34no—
230C23×D3—62no—
231C23×D3—64no—
232C23×D3—62no—
233C23×D3—62no—
234C23×D3—62no—
235C23×D3—62no—
236C23×D3—122no—
237C23×D3—122no—
238C23×D3—122no—
239C23×D3—122no—
240C23×D3—122no—
241C23×D3—122no—
242C23×D3—124no—
243C23×D3—124no—
244C23×D3C22×D311yescharacteristic
245C2×C3×D4—34no—
246C2×C3×D4—62no—
247C2×C3×D4—62no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—32no—
253C22×C3×C4—31no—
254C22×C3×C4—34no—
255C22×C3×C4—32no—
256C22×C3×C4—62no—
257C22×C3×C4—62no—
258C22×C3×C4—122no—
259C22×C3×C4—122no—
260C22×C3×C4—122no—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C2×#67—22no—
266C2×#67—22no—
267C2×#67—38no—
268C2×#67—122no—
269C2×#67—122no—
270C2×#67C4×D314yes—
271C22×Dic3—22no—
272C22×Dic3—32no—
273C22×Dic3—32no—
274C22×Dic3—42no—
275C22×Dic3—42no—
276C22×Dic3—62no—
277C22×Dic3#6714yescomplemented
278C22×Dic3C22×D312yes—
279C22×Dic3C22×D311yescharacteristic
280C22×Dic3C22×D312yes—
281C22×Dic3C22×D311yescharacteristic
282C22×Dic3C22×D311yescharacteristic
283C2×D12—38no—
284C2×D12—122no—
285C2×D12—122no—
286C2×C4×D3—22no—
287C2×C4×D3—42no—
288C3×C4⋊C4—62no—
289C3×C4⋊C4—122no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—34no—
293C3×C22⋊C4—42no—
294C3×C22⋊C4—62no—
295C3×C42—62no—
296#217—62no—
297#217—62no—
298#217—122no—
299#217—122no—
300#217C4×D314yescomplemented
301(C2×D3)⋊C4—22no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—64no—
305(C2×D3)⋊C4—64no—
306(C2×D3)⋊C4—64no—
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—122no—
309(C2×D3)⋊C4—122no—
310(C2×D3)⋊C4—122no—
311(C2×D3)⋊C4—122no—
312(C2×D3)⋊C4—122no—
313(C2×D3)⋊C4—124no—
314(C2×D3)⋊C4—124no—
315Dic3⋊C4—22no—
316Dic3⋊C4—42no—
317C4×Dic3—22no—
318C4×Dic3—122no—
319C4×Dic3—122no—
320C22×C32—24no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—24no—
324C22×C32C4×D414yes—
325C22×C32C23×C411yescharacteristic
326C22×C32C22×D411yescharacteristic
327C22×C32C2×#4111yescharacteristic
328C22×C32H(5,𝔽2)12yes—
329C22×C32H(5,𝔽2)12yes—
330C2×C3⋊D3—24no—
331C2×C3⋊D3—24no—
332C2×C3⋊D3—24no—
333C2×C3⋊D3—416no—
334C2×C3⋊D3—42no—
335C2×C3⋊D3—42no—
336C2×C3⋊D3—42no—
337C2×C3⋊D3—42no—
338C2×C3×D3—22no—
339C2×C3×D3—24no—
340C2×C3×D3—41no—
341C2×C3×D3—41no—
342C2×C3×D3—42no—
343C32×C4—41no—
344C32×C4—41no—
345C3⋊Dic3—42no—
346C3×Dic3—22no—
347C3×Dic3—24no—
348C3×Dic3—22no—
349C3×Dic3—22no—
350C3×Dic3—42no—
351C25—91no—
352C22×D4—31no—
353C22×D4—92no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357#120—98no—
358C4×D4—64no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—32no—
361C2×C22⋊C4—31no—
362C2×C22⋊C4—31no—
363C2×C22⋊C4—92no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—91no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4—92no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—184no—
371C2×C22⋊C4D3211yescharacteristic
372C2×C42—31no—
373C2×C42—92no—
374#95—32no—
375#95—92no—
376#95—92no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—32no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—61no—
389C23×C3—62no—
390C23×C3—61no—
391C23×C3—62no—
392C23×C3C2×C4×D312yes—
393C23×C3C2×C4×D312yes—
394C23×C3#23512yes—
395C23×C3D3×D412yes—
396C23×C3#23912yes—
397C23×C3C2×#6712yes—
398C23×C3C23×D311yescharacteristic
399C23×C3C23×D311yescharacteristic
400C22×D3—21no—
401C22×D3—22no—
402C22×D3—22no—
403C22×D3—21no—
404C22×D3—34no—
405C22×D3—34no—
406C22×D3—64no—
407C22×D3—64no—
408C22×D3—64no—
409C22×D3—68no—
410C22×D3—68no—
411C22×D3—62no—
412C22×D3—62no—
413C22×D3—62no—
414C22×D3—62no—
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—122no—
424C22×D3—122no—
425C22×D3—122no—
426C22×D3—122no—
427C22×D3—128no—
428C22×D3—128no—
429C22×D3—128no—
430C22×D3—1216no—
431C22×D3—128no—
432C22×D3—124no—
433C22×D3—124no—
434C22×D3—128no—
435C22×D3—124no—
436C22×D3—124no—
437C22×D3—128no—
438C22×D3—128no—
439C22×D3—1216no—
440C22×D3C2×C4×D312yes—
441C3×D4—68no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—32no—
451C2×C3×C4—34no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—61no—
459C2×C3×C4—62no—
460C2×C3×C4—61no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—62no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—124no—
468C2×C3×C4—124no—
469C2×C3×C4—124no—
470#67—28no—
471#67—128no—
472C2×Dic3—21no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—44no—
482C2×Dic3—44no—
483C2×Dic3—62no—
484C2×Dic3—62no—
485C2×Dic3—62no—
486C2×Dic3—62no—
487C2×Dic3—62no—
488C2×Dic3—62no—
489C2×Dic3—122no—
490C2×Dic3—122no—
491C2×Dic3—122no—
492C2×Dic3C2×C4×D312yes—
493C2×Dic3C2×C4×D314yes—
494C2×Dic3C2×#6712yes—
495C2×Dic3C2×#6712yes—
496D12—128no—
497C4×D3—44no—
498C2×C32—24no—
499C2×C32C2×C4×D411yescharacteristic
500C2×C32#51812yes—
501C2×C32#53411yescharacteristic
502C2×C32#53511yescharacteristic
503C2×C32#53812yes—
504C3⋊D3—44no—
505C3×D3—42no—
506C24—31no—
507C24—92no—
508C24—94no—
509C24—182no—
510C24—182no—
511C24—362no—
512C24—362no—
513C24C2×D3211yescharacteristic
514C2×D4—34no—
515C2×D4—62no—
516C2×D4—62no—
517C2×D4—98no—
518C2×D4—362no—
519C2×D4—362no—
520C22×C4—32no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—34no—
525C22×C4—32no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—92no—
529C22×C4—122no—
530C22×C4—122no—
531C22×C4—122no—
532C22×C4C2×D3211yescharacteristic
533C22×C4C2×D3211yescharacteristic
534C4⋊C4—62no—
535C4⋊C4—122no—
536C22⋊C4—22no—
537C22⋊C4—34no—
538C22⋊C4—62no—
539C22⋊C4—98no—
540C22⋊C4—184no—
541C22⋊C4—184no—
542C22⋊C4—182no—
543C22⋊C4—362no—
544C22⋊C4—362no—
545C22⋊C4—362no—
546C42—62no—
547C42—362no—
548C22×C3—24no—
549C22×C3—22no—
550C22×C3—24no—
551C22×C3—24no—
552C22×C3—22no—
553C22×C3—24no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—21no—
561C22×C3—24no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—62no—
567C22×C3—64no—
568C22×C3—122no—
569C22×C3—121no—
570C22×C3—121no—
571C22×C3#89314yes—
572C22×C3C4×#6714yes—
573C22×C3C22×C4×D311yescharacteristic
574C22×C3C22×C4×D311yescharacteristic
575C22×C3C2×#23511yescharacteristic
576C22×C3C2×D3×D411yescharacteristic
577C22×C3#100412yes—
578C22×C3#100412yes—
579C22×C3C2×#23911yescharacteristic
580C22×C3#100912yes—
581C22×C3#100912yes—
582C22×C3C22×#6711yescharacteristic
583C2×D3—22no—
584C2×D3—24no—
585C2×D3—41no—
586C2×D3—42no—
587C2×D3—41no—
588C2×D3—68no—
589C2×D3—64no—
590C2×D3—64no—
591C2×D3—64no—
592C2×D3—64no—
593C2×D3—64no—
594C2×D3—64no—
595C2×D3—124no—
596C2×D3—124no—
597C2×D3—1216no—
598C2×D3—1216no—
599C2×D3—124no—
600C2×D3—124no—
601C2×D3—124no—
602C2×D3—124no—
603C2×D3—1232no—
604C2×D3—122no—
605C2×D3—122no—
606C2×D3—122no—
607C2×D3—122no—
608C2×D3—122no—
609C2×D3—122no—
610C2×D3—122no—
611C2×D3—122no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—62no—
617C3×C4—62no—
618C3×C4—62no—
619C3×C4—64no—
620C3×C4—81no—
621C3×C4—81no—
622C3×C4—122no—
623Dic3—22no—
624Dic3—24no—
625Dic3—22no—
626Dic3—22no—
627Dic3—42no—
628Dic3—122no—
629Dic3—122no—
630Dic3—242no—
631C32#232111yescharacteristic, complemented, Sylow
632C23—22no—
633C23—22no—
634C23—32no—
635C23—61no—
636C23—62no—
637C23—62no—
638C23—61no—
639C23—94no—
640C23—182no—
641C23—182no—
642C23—182no—
643C23—182no—
644C23—182no—
645C23—182no—
646C23—188no—
647C23—368no—
648C23—364no—
649C23—364no—
650C23—368no—
651C23#379912yes—
652C23C4×D3212yes—
653C23D3×#6712yes—
654C23C22×D3211yescharacteristic
655D4—68no—
656D4—368no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—34no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—32no—
665C2×C4—61no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—61no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—124no—
675C2×C4—124no—
676C2×C4—124no—
677C2×C4—182no—
678C2×C4—182no—
679C2×C4—182no—
680C2×C3—24no—
681C2×C3—24no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—22no—
686C2×C3—22no—
687C2×C3—44no—
688C2×C3—122no—
689C2×C3C2×#89311yescharacteristic
690C2×C3#554512yes—
691C2×C3#554512yes—
692C2×C3#556012yes—
693C2×C3#559211yescharacteristic
694C2×C3#564412yes—
695C2×C3#565311yescharacteristic
696C2×C3C2×C4×#6711yescharacteristic
697C2×C3#580411yescharacteristic
698C2×C3#583011yescharacteristic
699D3—42no—
700D3—128no—
701D3—124no—
702D3—124no—
703C22—22no—
704C22—22no—
705C22—24no—
706C22—24no—
707C22—62no—
708C22—64no—
709C22—121no—
710C22—121no—
711C22—122no—
712C22—184no—
713C22—184no—
714C22—184no—
715C22—3616no—
716C22—362no—
717C22—362no—
718C22—362no—
719C22—362no—
720C22#6390414yes—
721C22C2×#379911yescharacteristic
722C22C2×C4×D3211yescharacteristic
723C22#6431412yes—
724C22#6431412yes—
725C22C2×D3×#6711yescharacteristic
726C4—41no—
727C4—41no—
728C4—62no—
729C4—62no—
730C4—62no—
731C4—64no—
732C4—122no—
733C4—362no—
734C3—21no—
735C3#7459211yescharacteristic, complemented
736C3#8239511yescharacteristic, complemented
737C2—24no—
738C2—122no—
739C2—364no—
740C2#1059424312yes—
741C2#1059425612yes—
742C2C2×#6390411yescharacteristic
743C2#1059523411yescharacteristic
744C2#1059523811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63981C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#67⋊C4C2semidirect
3. C22×#3722C2semidirect
4. #10592654C2semidirect
5. C3×#4946C2semidirect
6. #10591710C2semidirect
7. Dic3×#217C2semidirect
8. #10591384C2semidirect
9. #10591382C2semidirect
10. #10591289C2semidirect
11. #10591258C2semidirect
18. C22×C3×C4×D3C22semidirect
25. C2×C3×(C2×D3)⋊C4C22semidirect
26. C2×C3×Dic3⋊C4C22semidirect
27. C2×C3×Dic3⋊C4C22semidirect
28. C2×C3×C4×Dic3C22semidirect
30. #63981C4semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. C2×Dic32C22semidirect
37. C3×C3⋊#95C22semidirect
38. #63579C22semidirect
39. #63579C22semidirect
45. C2×#67⋊C4D3semidirect
58. #4946D3semidirect
68. C23×C3⋊D3C2×C4semidirect
80. C22×C3×Dic3D4semidirect
90. C2×#626C2×C4semidirect
95. C3×#217C2×C4semidirect
102. #3722C2×C4semidirect
118. C22×C4×D3C2×D3semidirect
149. C2×(C2×D3)⋊C4C2×D3semidirect
150. C2×Dic3⋊C4C2×D3semidirect
151. C2×Dic3⋊C4C2×D3semidirect
154. C2×C4×Dic3C2×D3semidirect
162. C3⋊#95C2×D3semidirect
277. C22×Dic3#67semidirect
300. #217C4×D3semidirect
631. C32#2321semidirect
735. C3#74592semidirect
736. C3#82395semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C2×#639812
C22×#37222
#105926542
C3×#49462
#105917102
Dic3×#2172
#105913842
#105913822
#105912892
#105912582
#823953
#745923