Finite Group Databasebeta

← #11803582

Subgroups — #11803582

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic, complemented
2C2×#63909C211yesmaximal, characteristic
3C2×#63855C211yesmaximal, characteristic, complemented
4C3×#4987C211yesmaximal, characteristic, complemented
5C3×#4972C211yesmaximal, characteristic, complemented
6#10591387C212yesmaximal, complemented
7#10591384C212yesmaximal, complemented
8#10591320C211yesmaximal, characteristic, complemented
9#10591290C212yesmaximal, complemented
10#10591274C211yesmaximal, characteristic, complemented
11#10591259C212yesmaximal, complemented
12#76198—31nomaximal
13#73872—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2212yes—
16C22×C3×C4×D3C2211yescharacteristic
17C22×#626C2212yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21#64102—24no—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×#3722C2212yes—
30C2×#3722C2212yes—
31C2×#3722C2212yes—
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×Dic32C2212yes—
35#63909C418yescomplemented
36#63855—24no—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×#930—31no—
41C2×#926—31no—
42C2×#895—31no—
43C2×#893—31no—
44C2×#893—31no—
45C2×#893—61no—
46C2×#872—31no—
47C3×#389—31no—
48C3×#380—31no—
49#4989—32no—
50#4988—32no—
51#4988—31no—
52#4987D311yescharacteristic, complemented
53Dic3×C4⋊C4—31no—
54Dic3×C4⋊C4—31no—
55#4972D311yescharacteristic, complemented
56#4957—32no—
57#4956—32no—
58#4939—31no—
59#4670—32no—
60#4669—32no—
61#4668—32no—
62#4665—32no—
63C23×C3⋊D3C2312yes—
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4⋊(C3⋊D3)—22no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)C2×C414yes—
72C2×C4×C3⋊D3—24no—
73C2×C4×C3⋊D3—42no—
74C2×C4×C3⋊D3—42no—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3C2×C414yescomplemented
83C2×#626—42no—
84C2×#626—42no—
85C2×#626C2×C418yescomplemented
86C32×C4⋊C4—22no—
87#3752—24no—
88C4×C3⋊Dic3D414yescomplemented
89C3×(C2×D3)⋊C4—42no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3C2×C414yescomplemented
92C3×Dic3⋊C4—42no—
93C3×C4×Dic3—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96#3722—42no—
97#3722—42no—
98#3722C2×C418yescomplemented
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101Dic32—42no—
102#2324—91noSylow
103C23×C3×C4—31no—
104C22×#67—32no—
105C22×D12—31no—
106C22×D12—31no—
107C22×D12—32no—
108C22×D12—61no—
109C22×C4×D3—32no—
110C22×C4×D3—32no—
111C22×C4×D3—62no—
112C22×C4×D3C2×D311yescharacteristic
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C3×C22⋊C4—32no—
120C2×C3×C42—31no—
121C2×#217—31no—
122C2×#217—31no—
123#930—38no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
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—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—62no—
135C2×(C2×D3)⋊C4C2×D312yes—
136#926—64no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×C4⋊Dic3C2×D311yescharacteristic
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4C2×D312yes—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—31no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—61no—
149C2×C4×Dic3C2×D311yescharacteristic
150#895—38no—
151#893—64no—
152#893—64no—
153#893—68no—
154#872—64no—
155C3×#95—32no—
156C3×#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95C2×D312yes—
160C3⋊#95C2×D312yes—
161C23×C32C2411yescharacteristic
162C22×C3⋊D3—22no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3C22×C414yes—
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—22no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4C22×C412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4#4112yes—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3C2×D412yes—
187C2×C3⋊Dic3C2×D412yes—
188C4⋊(C3⋊D3)—28no—
189C4×C3⋊D3—48no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3C22×C412yes—
204C2×C3×Dic3C22×C414yes—
205C3×C4×D3—28no—
206#626—48no—
207C2×#121—91no—
208C2×C4×D4—91no—
209C2×#117—91no—
210#390—91no—
211#390—92no—
212#389—31no—
213#388—92no—
214#386—92no—
215#385—92no—
216#380—31no—
217C4×C4⋊C4—91no—
218C24×C3—31no—
219C23×D3—32no—
220C23×D3—32no—
221C23×D3—62no—
222C23×D3C22×D311yescharacteristic
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—32no—
226C22×C3×C4—31no—
227C22×C3×C4—34no—
228C22×C3×C4—32no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—62no—
232C22×C3×C4—62no—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C22×D312yes—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C2×#67—38no—
238C2×#67—122no—
239C2×#67—122no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—31no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D311yescharacteristic
248C22×Dic3C22×D311yescharacteristic
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D311yescharacteristic
251C2×D12—34no—
252C2×D12—34no—
253C2×D12—38no—
254C2×D12—64no—
255C2×D12—64no—
256C2×D12—64no—
257C2×D12—62no—
258C2×D12—62no—
259C2×D12—62no—
260C2×D12—62no—
261C2×D12—122no—
262C2×D12—122no—
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—64no—
266C2×C4×D3—64no—
267C2×C4×D3—68no—
268C2×C4×D3—122no—
269C2×C4×D3—122no—
270C2×C4×D3—122no—
271C2×C4×D3—122no—
272C2×C4×D3—124no—
273C2×C4×D3—124no—
274C2×C4×D3C4×D314yescomplemented
275C3×C4⋊C4—24no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—34no—
279C3×C4⋊C4—62no—
280C3×C4⋊C4—122no—
281C3×C22⋊C4—122no—
282C3×C42—62no—
283#217—62no—
284#217—62no—
285(C2×D3)⋊C4—38no—
286(C2×D3)⋊C4—38no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—64no—
289(C2×D3)⋊C4—64no—
290(C2×D3)⋊C4—62no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—68no—
293(C2×D3)⋊C4—122no—
294(C2×D3)⋊C4—122no—
295(C2×D3)⋊C4—122no—
296(C2×D3)⋊C4—122no—
297C4⋊Dic3—22no—
298C4⋊Dic3—62no—
299C4⋊Dic3—62no—
300C4⋊Dic3C4×D314yescomplemented
301Dic3⋊C4—42no—
302Dic3⋊C4—62no—
303Dic3⋊C4—62no—
304C4×Dic3—22no—
305C4×Dic3—34no—
306C4×Dic3—34no—
307C4×Dic3—64no—
308C4×Dic3—122no—
309C4×Dic3—122no—
310C22×C32C23×C411yescharacteristic
311C22×C32C22×D411yescharacteristic
312C22×C32C2×#4111yescharacteristic
313C22×C32H(5,𝔽2)11yescharacteristic
314C22×C32H(5,𝔽2)11yescharacteristic
315C22×C32H(5,𝔽2)11yescharacteristic
316C22×C322−1+411yescharacteristic
317C2×C3⋊D3—24no—
318C2×C3⋊D3—24no—
319C2×C3⋊D3—24no—
320C2×C3⋊D3—42no—
321C2×C3⋊D3—42no—
322C2×C3⋊D3—42no—
323C2×C3⋊D3—42no—
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—41no—
328C2×C3×D3—41no—
329C2×C3×D3—41no—
330C2×C3×D3—41no—
331C32×C4—42no—
332C32×C4C4×D414yes—
333C3⋊Dic3—22no—
334C3⋊Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3—24no—
337C3×Dic3—41no—
338C3×Dic3—41no—
339C3×Dic3—42no—
340C22×D4—92no—
341C22×D4—91no—
342C23×C4—31no—
343C23×C4—92no—
344#121—98no—
345C4×D4—184no—
346#117—184no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—32no—
350C2×C4⋊C4—91no—
351C2×C4⋊C4—91no—
352C2×C4⋊C4D3211yescharacteristic
353C2×C22⋊C4—32no—
354C2×C22⋊C4—92no—
355C2×C22⋊C4—91no—
356C2×C22⋊C4—91no—
357C2×C22⋊C4—92no—
358C2×C22⋊C4—92no—
359C2×C22⋊C4—92no—
360C2×C42—31no—
361C2×C42—91no—
362C2×C42—92no—
363#95—32no—
364#95—32no—
365#95—92no—
366C23×C3—21no—
367C23×C3—32no—
368C23×C3—61no—
369C23×C3—61no—
370C23×C3—61no—
371C23×C3—61no—
372C23×C3—61no—
373C23×C3—61no—
374C23×C3C23×D311yescharacteristic
375C23×C3C23×D311yescharacteristic
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—21no—
379C22×D3—21no—
380C22×D3—21no—
381C22×D3—21no—
382C22×D3—34no—
383C22×D3—34no—
384C22×D3—64no—
385C22×D3—64no—
386C22×D3—64no—
387C22×D3—62no—
388C22×D3—62no—
389C22×D3—62no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—62no—
394C22×D3—62no—
395C22×D3—62no—
396C22×D3—62no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3—122no—
400C22×D3—122no—
401C22×D3—122no—
402C22×D3—122no—
403C22×D3C2×C4×D312yes—
404C2×C3×C4—24no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—32no—
415C2×C3×C4—34no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—68no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
426C2×C3×C4—62no—
427C2×C3×C4—61no—
428C2×C3×C4—62no—
429C2×C3×C4—61no—
430C2×C3×C4—62no—
431C2×C3×C4—61no—
432C2×C3×C4C2×C4×D312yes—
433C2×C3×C4C2×C4×D312yes—
434C2×C3×C4D3×D412yes—
435C2×C3×C4D3×D412yes—
436C2×C3×C4#23712yes—
437C2×C3×C4#23912yes—
438#67—128no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—22no—
446C2×Dic3—21no—
447C2×Dic3—22no—
448C2×Dic3—21no—
449C2×Dic3—22no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—32no—
453C2×Dic3—32no—
454C2×Dic3—32no—
455C2×Dic3—32no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—61no—
464C2×Dic3—61no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—121no—
469C2×Dic3—121no—
470C2×Dic3C2×C4×D314yes—
471C2×Dic3C2×C4×D312yes—
472D12—616no—
473D12—68no—
474D12—68no—
475D12—128no—
476C4×D3—28no—
477C4×D3—1216no—
478C4×D3—128no—
479C4×D3—128no—
480C2×C32C2×C4×D411yescharacteristic
481C2×C32#51811yescharacteristic
482C2×C32#52011yescharacteristic
483C2×C32#53511yescharacteristic
484C2×C32#53711yescharacteristic
485C2×C32#54011yescharacteristic
486C2×C32#54211yescharacteristic
487C3⋊D3—44no—
488C3×D3—42no—
489C24—31no—
490C24—92no—
491C2×D4—98no—
492C2×D4—94no—
493C2×D4—182no—
494C2×D4—182no—
495C2×D4—362no—
496C2×D4—362no—
497C22×C4—31no—
498C22×C4—32no—
499C22×C4—34no—
500C22×C4—31no—
501C22×C4—32no—
502C22×C4—31no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—91no—
506C22×C4—91no—
507C22×C4—184no—
508C22×C4—362no—
509C22×C4—362no—
510C22×C4C2×D3212yes—
511C22×C4C2×D3211yescharacteristic
512C4⋊C4—22no—
513C4⋊C4—34no—
514C4⋊C4—62no—
515C4⋊C4—122no—
516C4⋊C4—182no—
517C4⋊C4—182no—
518C22⋊C4—98no—
519C22⋊C4—122no—
520C22⋊C4—184no—
521C22⋊C4—182no—
522C22⋊C4—182no—
523C22⋊C4—362no—
524C22⋊C4—362no—
525C42—62no—
526C42—94no—
527C42—362no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—62no—
536C22×C3—62no—
537C22×C3—62no—
538C22×C3—121no—
539C22×C3—121no—
540C22×C3—121no—
541C22×C3—121no—
542C22×C3C22×C4×D311yescharacteristic
543C22×C3C22×C4×D311yescharacteristic
544C22×C3C2×D3×D411yescharacteristic
545C22×C3C2×D3×D411yescharacteristic
546C22×C3C2×#23711yescharacteristic
547C22×C3#100411yescharacteristic
548C22×C3#100411yescharacteristic
549C22×C3C2×#23911yescharacteristic
550C22×C3#100711yescharacteristic
551C22×C3#100711yescharacteristic
552C22×C3#100911yescharacteristic
553C22×C3#100911yescharacteristic
554C22×C3#100911yescharacteristic
555C22×C3#100911yescharacteristic
556C2×D3—22no—
557C2×D3—22no—
558C2×D3—22no—
559C2×D3—41no—
560C2×D3—41no—
561C2×D3—41no—
562C2×D3—41no—
563C2×D3—68no—
564C2×D3—64no—
565C2×D3—64no—
566C2×D3—64no—
567C2×D3—64no—
568C2×D3—64no—
569C2×D3—64no—
570C2×D3—124no—
571C2×D3—124no—
572C2×D3—124no—
573C2×D3—124no—
574C2×D3—124no—
575C2×D3—124no—
576C2×D3—122no—
577C2×D3—122no—
578C2×D3—122no—
579C2×D3—122no—
580C2×D3—122no—
581C2×D3—122no—
582C2×D3—122no—
583C2×D3—122no—
584C3×C4—24no—
585C3×C4—44no—
586C3×C4—42no—
587C3×C4—42no—
588C3×C4—62no—
589C3×C4—64no—
590C3×C4—122no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4#67⋊C414yes—
594C3×C4#89314yes—
595Dic3—22no—
596Dic3—24no—
597Dic3—41no—
598Dic3—42no—
599Dic3—41no—
600Dic3—64no—
601Dic3—62no—
602Dic3—62no—
603Dic3—62no—
604Dic3—62no—
605Dic3—122no—
606C32#232411yescharacteristic, complemented, Sylow
607C23—32no—
608C23—61no—
609C23—61no—
610C23—61no—
611C23—61no—
612C23—61no—
613C23—61no—
614C23—94no—
615C23—182no—
616C23—182no—
617C23—182no—
618C23—182no—
619C23—182no—
620C23—182no—
621C23C22×D3211yescharacteristic
622D4—188no—
623D4—368no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—32no—
628C2×C4—34no—
629C2×C4—61no—
630C2×C4—62no—
631C2×C4—62no—
632C2×C4—61no—
633C2×C4—68no—
634C2×C4—62no—
635C2×C4—62no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—62no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—92no—
644C2×C4—92no—
645C2×C4—181no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—368no—
650C2×C4#379612yes—
651C2×C4C4×D3212yes—
652C2×C4#381112yes—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—122no—
661C2×C3C2×#67⋊C411yescharacteristic
662C2×C3C2×#89311yescharacteristic
663C2×C3#550411yescharacteristic
664C2×C3#552111yescharacteristic
665C2×C3#554511yescharacteristic
666C2×C3#557411yescharacteristic
667C2×C3#560711yescharacteristic
668C2×C3#560711yescharacteristic
669C2×C3#561911yescharacteristic
670C2×C3#562911yescharacteristic
671C2×C3#562911yescharacteristic
672C2×C3#564311yescharacteristic
673C2×C3#569711yescharacteristic
674C2×C3#573311yescharacteristic
675D3—42no—
676D3—128no—
677D3—124no—
678D3—124no—
679C22—62no—
680C22—62no—
681C22—62no—
682C22—121no—
683C22—121no—
684C22—121no—
685C22—121no—
686C22—184no—
687C22—184no—
688C22—184no—
689C22—362no—
690C22—362no—
691C22—362no—
692C22—362no—
693C22C2×#379611yescharacteristic
694C22C2×C4×D3211yescharacteristic
695C22#6431411yescharacteristic
696C22#6431411yescharacteristic
697C22#6431611yescharacteristic
698C22#6432011yescharacteristic
699C22C2×#381111yescharacteristic
700C4—42no—
701C4—64no—
702C4—62no—
703C4—121no—
704C4—121no—
705C4—122no—
706C4—182no—
707C4—182no—
708C4#6388114yes—
709C3—21no—
710C3#7387211yescharacteristic, complemented
711C3#7619811yescharacteristic, complemented
712C2—122no—
713C2—364no—
714C2#1059432711yescharacteristic
715C2#1059434311yescharacteristic
716C2#1059450111yescharacteristic
717C2#1059460411yescharacteristic
718C2C2×#6388111yescharacteristic
719C2#1059524111yescharacteristic
720C2#1059540411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63909C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
3. C2×#63855C2semidirect
4. C3×#4987C2semidirect
5. C3×#4972C2semidirect
6. #10591387C2semidirect
7. #10591384C2semidirect
8. #10591320C2semidirect
9. #10591290C2semidirect
10. #10591274C2semidirect
11. #10591259C2semidirect
35. #63909C4semidirect
52. #4987D3semidirect
55. #4972D3semidirect
82. C2×C3×C4×D3C2×C4semidirect
85. C2×#626C2×C4semidirect
88. C4×C3⋊Dic3D4semidirect
91. C3×C4⋊Dic3C2×C4semidirect
98. #3722C2×C4semidirect
274. C2×C4×D3C4×D3semidirect
300. C4⋊Dic3C4×D3semidirect
606. C32#2324semidirect
710. C3#73872semidirect
711. C3#76198semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#639092
C2×#638552
C3×#49872
C3×#49722
#105913872
#105913842
#105913202
#105912902
#105912742
#105912592
#761983
#738723