Finite Group Databasebeta

← C2×#10594005 #11902465

Subgroups — C2×#10594005 #11902465

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C2×C3×#875C211yesmaximal, characteristic, complemented
5C2×C3×C4×D12C211yesmaximal, characteristic, complemented
6C2×#63923C212yesmaximal, complemented
7C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
8C2×#63916C211yesmaximal, characteristic, complemented
9C2×#63906C212yesmaximal, complemented
10C2×#63891C212yesmaximal, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12#10594005C2116yesmaximal, direct product factor
13C2×#5676—31nomaximal
14C2×#5554—31nomaximal
15C23×D32C2212yes—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2212yescomplemented
22C22×C3×Dic6C2211yescharacteristic, complemented
23C22×#626C2212yescomplemented
24C22×#626C2212yescomplemented
25C22×#625C2212yes—
26C22×D3×Dic3C2212yescomplemented
27C2×#3802—28no—
28C2×#3802C2218yescomplemented
29C2×#3796—28no—
30C2×#3796C2218yescomplemented
31C2×C32×C42C2211yescharacteristic, complemented
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic, complemented
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C4×C4⋊(C3⋊D3)C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yescomplemented
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
40C3×#875C2218yescomplemented
41C3×C4×D12C2218yescomplemented
42C2×Dic3⋊Dic3C2212yescomplemented
43C2×#3722C2212yes—
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45#63923C22116yescomplemented
46D3×(C2×D3)⋊C4C22116yescomplemented
47#63916C2218yescomplemented
48#63906C22116yescomplemented
49#63891C22116yescomplemented
50#63871C2218yescomplemented
51C22×#239—31no—
52C22×#237—31no—
53C22×D3×D4—31no—
54C22×D3×D4—31no—
55C2×C3×#124—31no—
56C2×C3×C4×D4—31no—
57C2×#946—31no—
58C2×#938—31no—
59C2×#930—32no—
60C22×(C2×D3)⋊C4—32no—
61#5676—316no—
62#5554—316no—
63C2×#897—31no—
64C2×#895—31no—
65C2×#886—32no—
66C2×#884—32no—
67C2×#883—32no—
68C2×#882—32no—
69C2×#882—32no—
70C2×D3×C22⋊C4—32no—
71C2×#875D311yescharacteristic, complemented
72C2×C4×D12—31no—
73C2×C4×D12—31no—
74C2×C4×D12—61no—
75C2×C4×D12D311yescharacteristic, complemented
76C23×C3⋊D3C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C23×C3×D3C2312yes—
80C22×D32—28no—
81C22×D32—28no—
82C22×D32—44no—
83C22×D32C2318yes—
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C2×C4⋊(C3⋊D3)—24no—
90C2×C4⋊(C3⋊D3)C2314yes—
91C2×C4×C3⋊D3—24no—
92C2×C4×C3⋊D3—24no—
93C2×C4×C3⋊D3C2314yes—
94C2×C4×C3⋊D3C2314yescomplemented
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2312yes—
97C2×C3×D12—24no—
98C2×C3×D12D418yescomplemented
99C2×C3×D12C2314yes—
100C2×C3×D12C2314yes—
101C2×C3×C4×D3—44no—
102C2×C3×C4×D3C2318yescomplemented
103C2×C3×Dic6—24no—
104C2×C3×Dic6C2314yescomplemented
105C2×#626—28no—
106C2×#626—44no—
107C2×#626C2318yescomplemented
108C2×#626C2318yescomplemented
109C2×#625—28no—
110C2×#625C2318yes—
111C2×D3×Dic3—28no—
112C2×D3×Dic3C2318yescomplemented
113#3802—232no—
114#3796—232no—
115C32×C42C2314yescomplemented
116#3752C2314yes—
117#3752C2314yescomplemented
118C4⋊(C3⋊Dic3)C2314yescomplemented
119C3×(C2×D3)⋊C4C2318yescomplemented
120C3×(C2×D3)⋊C4C2318yescomplemented
121C3×(C2×D3)⋊C4C2318yescomplemented
122C3×C4⋊Dic3C2314yescomplemented
123Dic3⋊Dic3C2318yescomplemented
124#3722C2318yes—
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#546—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C22×C3×Q8—31no—
130C22×C3×D4—31no—
131C22×C3×D4—31no—
132C23×C3×C4—32no—
133C22×#67—32no—
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—32no—
137C23×Dic3—32no—
138C2×#239—38no—
139C2×#239—68no—
140C2×#237—38no—
141C2×#237—68no—
142C2×D3×D4—38no—
143C2×D3×D4—38no—
144C2×D3×D4—68no—
145C2×D3×D4—68no—
146C22×D12—32no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—32no—
150C22×D12—61no—
151C22×D12C2×D311yescharacteristic
152C22×D12C2×D311yescharacteristic
153C22×C4×D3—32no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—61no—
159C22×C4×D3—61no—
160C22×C4×D3C2×D312yescomplemented
161C22×Dic6C2×D311yescharacteristic, complemented
162C3×#124—38no—
163C3×C4×D4—38no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C22⋊C4—32no—
166C2×C3×C22⋊C4—32no—
167C2×C3×C22⋊C4—32no—
168C2×C3×C42—21no—
169C2×C3×C42C2×D311yescharacteristic, complemented
170C2×C3×C42C2×D311yescharacteristic, complemented
171C2×#217—32no—
172#946—38no—
173#938—38no—
174#930—316no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—316no—
183C2×(C2×D3)⋊C4—61no—
184C2×(C2×D3)⋊C4—61no—
185C2×(C2×D3)⋊C4C2×D312yescomplemented
186C2×(C2×D3)⋊C4C2×D312yescomplemented
187C2×(C2×D3)⋊C4C2×D312yescomplemented
188C2×C4⋊Dic3—31no—
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—32no—
191C2×C4⋊Dic3—61no—
192C2×C4⋊Dic3C2×D311yescharacteristic, complemented
193C2×Dic3⋊C4—32no—
194#897—38no—
195#895—38no—
196#886—316no—
197#884—316no—
198#883—316no—
199#882—316no—
200#882—316no—
201D3×C22⋊C4—316no—
202#875C2×D318yescomplemented
203C4×D12—38no—
204C4×D12—38no—
205C4×D12—68no—
206C4×D12C2×D318yescomplemented
207C23×C32C2411yescharacteristic
208C22×C3⋊D3—22no—
209C22×C3⋊D3—22no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—22no—
212C22×C3⋊D3—22no—
213C22×C3⋊D3#4114yescomplemented
214C22×C3⋊D3C2412yes—
215C22×C3⋊D3C2412yes—
216C22×C3×D3—24no—
217C22×C3×D3—24no—
218C22×C3×D3—24no—
219C22×C3×D3—24no—
220C22×C3×D3—24no—
221C22×C3×D3C2×D418yes—
222C22×C3×D3C2414yes—
223C22×C3×D3C2414yes—
224C2×D32—216no—
225C2×D32—216no—
226C2×D32—48no—
227C2×D32—432no—
228C2×C32×C4—22no—
229C2×C32×C4—22no—
230C2×C32×C4C2×D414yes—
231C2×C32×C4C2412yes—
232C2×C32×C4C2412yes—
233C2×C32×C4C2412yes—
234C2×C3⋊Dic3—22no—
235C2×C3⋊Dic3—22no—
236C2×C3⋊Dic3C2412yes—
237C2×C3⋊Dic3C2412yes—
238C4⋊(C3⋊D3)—28no—
239C4×C3⋊D3—28no—
240C4×C3⋊D3—28no—
241C2×C3×Dic3—24no—
242C2×C3×Dic3—24no—
243C2×C3×Dic3C2414yes—
244C2×C3×Dic3C2414yes—
245C3×D12—28no—
246C3×D12C2×D4116yescomplemented
247C3×C4×D3—48no—
248C3×Dic6—28no—
249#626—216no—
250#626—48no—
251#625—216no—
252D3×Dic3—216no—
253C22×#41—91no—
254C23×D4—91no—
255#546—916no—
256C2×#124—31no—
257C2×#123—92no—
258C2×C22⋊Q8—91no—
259C2×#121—92no—
260C2×#121—91no—
261C2×#120—92no—
262C2×C4×D4—31no—
263C2×C4×D4—91no—
264C22×C22⋊C4—92no—
265C24×C3—32no—
266C24×C3—32no—
267C23×D3—31no—
268C23×D3—31no—
269C23×D3—31no—
270C23×D3—31no—
271C23×D3—38no—
272C23×D3—38no—
273C23×D3—61no—
274C23×D3—61no—
275C23×D3—68no—
276C23×D3—68no—
277C23×D3—68no—
278C23×D3—68no—
279C23×D3—124no—
280C23×D3—124no—
281C23×D3C22×D312yes—
282C23×D3C22×D312yes—
283C2×C3×Q8—34no—
284C2×C3×Q8—64no—
285C2×C3×D4—38no—
286C2×C3×D4—34no—
287C2×C3×D4—34no—
288C2×C3×D4—64no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—32no—
293C22×C3×C4—32no—
294C22×C3×C4—38no—
295C22×C3×C4—124no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C2×#67—38no—
303C2×#67—38no—
304C2×#67—38no—
305C2×#67—38no—
306C2×#67—68no—
307C2×#67—68no—
308C2×#67—68no—
309C2×#67—124no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—38no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—68no—
318C22×Dic3C22×D312yes—
319C22×Dic3C22×D312yes—
320#239—632no—
321#237—632no—
322D3×D4—632no—
323D3×D4—632no—
324C2×D12—24no—
325C2×D12—38no—
326C2×D12—34no—
327C2×D12—34no—
328C2×D12—38no—
329C2×D12—64no—
330C2×D12—64no—
331C2×D12—64no—
332C2×D12—68no—
333C2×D12—68no—
334C2×D12—124no—
335C2×D12D1218yescomplemented
336C2×D12C22×D314yes—
337C2×D12C22×D314yes—
338C2×C4×D3—38no—
339C2×C4×D3—34no—
340C2×C4×D3—34no—
341C2×C4×D3—34no—
342C2×C4×D3—34no—
343C2×C4×D3—44no—
344C2×C4×D3—64no—
345C2×C4×D3—64no—
346C2×C4×D3—68no—
347C2×C4×D3—64no—
348C2×C4×D3—64no—
349C2×C4×D3—64no—
350C2×C4×D3—64no—
351C2×C4×D3—124no—
352C2×C4×D3—124no—
353C2×C4×D3C22×D318yescomplemented
354C2×Dic6—24no—
355C2×Dic6C22×D314yescomplemented
356C3×C4⋊C4—34no—
357C3×C22⋊C4—38no—
358C3×C22⋊C4—38no—
359C3×C22⋊C4—38no—
360C3×C42—24no—
361C3×C42C22×D314yescomplemented
362C3×C42C22×D314yescomplemented
363#217—38no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—34no—
366(C2×D3)⋊C4—34no—
367(C2×D3)⋊C4—34no—
368(C2×D3)⋊C4—34no—
369(C2×D3)⋊C4—38no—
370(C2×D3)⋊C4—38no—
371(C2×D3)⋊C4—64no—
372(C2×D3)⋊C4—64no—
373(C2×D3)⋊C4C22×D318yescomplemented
374(C2×D3)⋊C4C22×D318yescomplemented
375(C2×D3)⋊C4C22×D318yescomplemented
376C4⋊Dic3—34no—
377C4⋊Dic3—34no—
378C4⋊Dic3—38no—
379C4⋊Dic3—64no—
380C4⋊Dic3C22×D314yescomplemented
381Dic3⋊C4—38no—
382C22×C32C22×D412yes—
383C22×C32C2×#4112yes—
384C22×C32H(5,𝔽2)12yes—
385C22×C32C2511yescharacteristic
386C2×C3⋊D3—22no—
387C2×C3⋊D3—28no—
388C2×C3⋊D3—22no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—44no—
393C2×C3⋊D3C2×#4114yescomplemented
394C2×C3×D3—216no—
395C2×C3×D3—24no—
396C2×C3×D3—24no—
397C2×C3×D3—24no—
398C2×C3×D3—24no—
399C2×C3×D3—24no—
400C2×C3×D3—48no—
401C2×C3×D3C22×D418yes—
402D32—432no—
403C32×C4—22no—
404C32×C4—22no—
405C32×C4C22×D414yes—
406C3⋊Dic3—22no—
407C3⋊Dic3—22no—
408C3×Dic3—24no—
409C3×Dic3—24no—
410C25—92no—
411C2×#41—98no—
412C2×#41—188no—
413C22×Q8—31no—
414C22×D4—31no—
415C22×D4—31no—
416C22×D4—92no—
417C22×D4—92no—
418C22×D4—98no—
419C22×D4—92no—
420C22×D4—91no—
421C22×D4—188no—
422C23×C4—32no—
423C23×C4—92no—
424C23×C4—91no—
425C23×C4—91no—
426#124—38no—
427#123—916no—
428C22⋊Q8—98no—
429#121—916no—
430#121—98no—
431#120—916no—
432C4×D4—38no—
433C4×D4—98no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—92no—
436C2×C4⋊C4—91no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—916no—
441C2×C22⋊C4—92no—
442C2×C22⋊C4—92no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C42D3211yescharacteristic, complemented
446C23×C3—21no—
447C23×C3—38no—
448C23×C3—34no—
449C23×C3—34no—
450C23×C3—64no—
451C23×C3—64no—
452C23×C3—64no—
453C23×C3—64no—
454C23×C3—64no—
455C23×C3C23×D311yescharacteristic
456C23×C3C23×D311yescharacteristic
457C22×D3—24no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—24no—
461C22×D3—24no—
462C22×D3—34no—
463C22×D3—34no—
464C22×D3—32no—
465C22×D3—32no—
466C22×D3—32no—
467C22×D3—32no—
468C22×D3—64no—
469C22×D3—62no—
470C22×D3—62no—
471C22×D3—616no—
472C22×D3—616no—
473C22×D3—616no—
474C22×D3—62no—
475C22×D3—62no—
476C22×D3—62no—
477C22×D3—62no—
478C22×D3—64no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3—62no—
485C22×D3—616no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—128no—
491C22×D3—128no—
492C22×D3—1232no—
493C22×D3—1232no—
494C22×D3C2×D1218yes—
495C22×D3C23×D314yes—
496C22×D3C23×D314yes—
497C3×Q8—68no—
498C3×D4—316no—
499C3×D4—68no—
500C2×C3×C4—24no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—24no—
509C2×C3×C4—34no—
510C2×C3×C4—34no—
511C2×C3×C4—42no—
512C2×C3×C4—64no—
513C2×C3×C4—64no—
514C2×C3×C4—128no—
515C2×C3×C4C2×D1214yes—
516C2×C3×C4D3×D414yes—
517C2×C3×C4C23×D312yes—
518C2×C3×C4C23×D312yes—
519C2×C3×C4C23×D312yes—
520C2×C3×C4C23×D312yes—
521C2×C3×C4C23×D312yes—
522C2×C3×C4C23×D312yes—
523#67—616no—
524#67—616no—
525#67—616no—
526#67—128no—
527C2×Dic3—24no—
528C2×Dic3—24no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—32no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—616no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—62no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542C2×Dic3C23×D314yes—
543C2×Dic3C23×D314yes—
544D12—28no—
545D12—68no—
546D12—68no—
547D12—616no—
548D12—616no—
549D12—128no—
550D12C2×D12116yescomplemented
551C4×D3—48no—
552C4×D3—616no—
553C4×D3—68no—
554C4×D3—68no—
555C4×D3—68no—
556C4×D3—68no—
557C4×D3—128no—
558C4×D3—128no—
559Dic6—28no—
560C2×C32#54614yescomplemented
561C2×C32C23×D411yescharacteristic
562C2×C32C22×#4111yescharacteristic
563C2×C32C2×H(5,𝔽2)11yescharacteristic
564C3⋊D3—24no—
565C3⋊D3—42no—
566C3×D3—28no—
567C3×D3—44no—
568C24—32no—
569C24—32no—
570C24—98no—
571C24—91no—
572C24—91no—
573C24—188no—
574C24—188no—
575C24—364no—
576#41—1832no—
577C2×Q8—34no—
578C2×Q8—64no—
579C2×D4—34no—
580C2×D4—34no—
581C2×D4—38no—
582C2×D4—64no—
583C2×D4—98no—
584C2×D4—98no—
585C2×D4—98no—
586C2×D4—94no—
587C2×D4—184no—
588C2×D4—188no—
589C2×D4—1832no—
590C2×D4—188no—
591C2×D4—364no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—38no—
595C22×C4—98no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—94no—
599C22×C4—94no—
600C22×C4—124no—
601C22×C4—188no—
602C22×C4—184no—
603C22×C4—184no—
604C22×C4C2×D3211yescharacteristic
605C22×C4C2×D3211yescharacteristic
606C22×C4C2×D3211yescharacteristic
607C4⋊C4—34no—
608C4⋊C4—98no—
609C4⋊C4—94no—
610C22⋊C4—38no—
611C22⋊C4—38no—
612C22⋊C4—38no—
613C22⋊C4—98no—
614C22⋊C4—98no—
615C22⋊C4—94no—
616C22⋊C4—94no—
617C42C2×D3214yescomplemented
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—38no—
623C22×C3—616no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—64no—
627C22×C3—64no—
628C22×C3—64no—
629C22×C3—128no—
630C22×C3C22×D1212yes—
631C22×C3C2×D3×D412yes—
632C22×C3#100412yes—
633C22×C3D3×#4112yes—
634C22×C3D3×#4112yes—
635C22×C3#100912yes—
636C22×C3C24×D311yescharacteristic
637C22×C3C24×D311yescharacteristic
638C2×D3—24no—
639C2×D3—24no—
640C2×D3—216no—
641C2×D3—24no—
642C2×D3—24no—
643C2×D3—24no—
644C2×D3—34no—
645C2×D3—34no—
646C2×D3—48no—
647C2×D3—64no—
648C2×D3—68no—
649C2×D3—62no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—68no—
654C2×D3—64no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—122no—
662C2×D3—122no—
663C2×D3—122no—
664C2×D3—128no—
665C2×D3—122no—
666C2×D3—1232no—
667C2×D3—1232no—
668C2×D3—128no—
669C2×D3—124no—
670C2×D3—124no—
671C2×D3C22×D1218yes—
672C3×C4—24no—
673C3×C4—22no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—24no—
678C3×C4—42no—
679C3×C4—64no—
680C3×C4—64no—
681C3×C4C22×D1214yes—
682C3×C4C2×D3×D414yes—
683Dic3—24no—
684Dic3—24no—
685Dic3—62no—
686Dic3—62no—
687Dic3—62no—
688Dic3—62no—
689Dic3—122no—
690Dic3—122no—
691C32C2×#54611yescharacteristic, complemented, Sylow
692C23—38no—
693C23—34no—
694C23—34no—
695C23—64no—
696C23—64no—
697C23—64no—
698C23—64no—
699C23—64no—
700C23—94no—
701C23—92no—
702C23—92no—
703C23—1816no—
704C23—1816no—
705C23—182no—
706C23—182no—
707C23—182no—
708C23—182no—
709C23—182no—
710C23—368no—
711C23—3632no—
712C23C22×D3211yescharacteristic
713Q8—68no—
714D4—316no—
715D4—68no—
716D4—188no—
717D4—1816no—
718D4—1816no—
719D4—368no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—34no—
723C2×C4—34no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—92no—
727C2×C4—92no—
728C2×C4—128no—
729C2×C4—1816no—
730C2×C4—182no—
731C2×C4—182no—
732C2×C4—188no—
733C2×C4—188no—
734C2×C4D3×D1214yes—
735C2×C4C22×D3212yes—
736C2×C4C22×D3212yes—
737C2×C4C22×D3212yes—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—24no—
742C2×C3—68no—
743C2×C3—124no—
744C2×C3#555414yescomplemented
745C2×C3#567614yescomplemented
746C2×C3C23×D1211yescharacteristic
747C2×C3C22×D3×D411yescharacteristic
748C2×C3C2×#100411yescharacteristic
749C2×C3C2×D3×#4111yescharacteristic
750C2×C3C2×D3×#4111yescharacteristic
751C2×C3C2×#100911yescharacteristic
752D3—28no—
753D3—44no—
754D3—64no—
755D3—64no—
756D3—124no—
757D3—124no—
758D3—122no—
759D3—122no—
760C22—38no—
761C22—64no—
762C22—64no—
763C22—616no—
764C22—64no—
765C22—64no—
766C22—64no—
767C22—94no—
768C22—128no—
769C22—182no—
770C22—182no—
771C22—188no—
772C22—182no—
773C22—182no—
774C22—182no—
775C22—3632no—
776C22—364no—
777C22C2×D3×D1212yes—
778C22#6430612yes—
779C22#6430712yes—
780C22C23×D3211yescharacteristic
781C4—22no—
782C4—22no—
783C4—64no—
784C4—64no—
785C4—182no—
786C4—182no—
787C4C2×D3×D1214yes—
788C3—21no—
789C3C2×#555411yescharacteristic, complemented
790C3C2×#567611yescharacteristic, complemented
791C2—68no—
792C2—124no—
793C2—184no—
794C2—362no—
795C2#1059400514yesdirect product factor
796C2C22×D3×D1211yescharacteristic
797C2C2×#6430611yescharacteristic
798C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3802C2semidirect
2. C22×#3796C2semidirect
3. C2×C4×C4⋊(C3⋊D3)C2semidirect
4. C2×C3×#875C2semidirect
5. C2×C3×C4×D12C2semidirect
6. C2×#63923C2semidirect
7. C2×D3×(C2×D3)⋊C4C2semidirect
8. C2×#63916C2semidirect
9. C2×#63906C2semidirect
10. C2×#63891C2semidirect
11. C2×#63871C2semidirect
12. #10594005C2direct (N × H)
18. C22×C4×C3⋊D3C22semidirect
21. C22×C3×C4×D3C22semidirect
22. C22×C3×Dic6C22semidirect
23. C22×#626C22semidirect
24. C22×#626C22semidirect
26. C22×D3×Dic3C22semidirect
28. C2×#3802C22semidirect
30. C2×#3796C22semidirect
31. C2×C32×C42C22semidirect
33. C2×#3752C22semidirect
34. C2×C4⋊(C3⋊Dic3)C22semidirect
35. C4×C4⋊(C3⋊D3)C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C3×#875C22semidirect
41. C3×C4×D12C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. #63923C22semidirect
46. D3×(C2×D3)⋊C4C22semidirect
47. #63916C22semidirect
48. #63906C22semidirect
49. #63891C22semidirect
50. #63871C22semidirect
71. C2×#875D3semidirect
75. C2×C4×D12D3semidirect
94. C2×C4×C3⋊D3C23semidirect
98. C2×C3×D12D4semidirect
102. C2×C3×C4×D3C23semidirect
104. C2×C3×Dic6C23semidirect
107. C2×#626C23semidirect
108. C2×#626C23semidirect
112. C2×D3×Dic3C23semidirect
115. C32×C42C23semidirect
117. #3752C23semidirect
118. C4⋊(C3⋊Dic3)C23semidirect
119. C3×(C2×D3)⋊C4C23semidirect
120. C3×(C2×D3)⋊C4C23semidirect
121. C3×(C2×D3)⋊C4C23semidirect
122. C3×C4⋊Dic3C23semidirect
123. Dic3⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
160. C22×C4×D3C2×D3semidirect
161. C22×Dic6C2×D3semidirect
169. C2×C3×C42C2×D3semidirect
170. C2×C3×C42C2×D3semidirect
185. C2×(C2×D3)⋊C4C2×D3semidirect
186. C2×(C2×D3)⋊C4C2×D3semidirect
187. C2×(C2×D3)⋊C4C2×D3semidirect
192. C2×C4⋊Dic3C2×D3semidirect
202. #875C2×D3semidirect
206. C4×D12C2×D3semidirect
213. C22×C3⋊D3#41semidirect
246. C3×D12C2×D4semidirect
335. C2×D12D12semidirect
353. C2×C4×D3C22×D3semidirect
355. C2×Dic6C22×D3semidirect
361. C3×C42C22×D3semidirect
362. C3×C42C22×D3semidirect
373. (C2×D3)⋊C4C22×D3semidirect
374. (C2×D3)⋊C4C22×D3semidirect
375. (C2×D3)⋊C4C22×D3semidirect
380. C4⋊Dic3C22×D3semidirect
393. C2×C3⋊D3C2×#41semidirect
445. C2×C42D32semidirect
550. D12C2×D12semidirect
560. C2×C32#546semidirect
617. C42C2×D32semidirect
691. C32C2×#546semidirect
744. C2×C3#5554semidirect
745. C2×C3#5676semidirect
789. C3C2×#5554semidirect
790. C3C2×#5676semidirect
795. C2#10594005direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C22×#37962
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8752
C2×C3×C4×D122
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639162
C2×#639062
C2×#638912
C2×#638712
#105940052
C2×#56763
C2×#55543