Finite Group Databasebeta

← C2×#10595018 #11902436

Subgroups — C2×#10595018 #11902436

Order 1152.

4481 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×#63981C212yesmaximal, complemented
6C2×#63974C212yesmaximal, complemented
7#10595018C2116yesmaximal, direct product factor
8C2×#63910C212yesmaximal, complemented
9C2×#63909C211yesmaximal, characteristic, complemented
10C2×#63897C212yesmaximal, complemented
11C2×#63894C211yesmaximal, characteristic, complemented
12C2×#63864C211yesmaximal, characteristic, complemented
13C2×#5630—31nomaximal
14C2×#5550—31nomaximal
15C24×C3⋊D3C2212yes—
16C23×C32×C4C2211yescharacteristic
17C22×C4⋊(C3⋊D3)—28no—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2212yes—
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2218yescomplemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic, complemented
24C22×C3×Dic6C2211yescharacteristic, complemented
25C22×#626C2212yescomplemented
26C22×#626C2212yescomplemented
27C22×#624C2212yescomplemented
28C22×#624C2212yescomplemented
29C2×#3799—28no—
30C2×#3799C2218yescomplemented
31C2×C3×#217C2212yes—
32C2×C3×#217C2211yescharacteristic
33C3×C4×#67C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
36C3×#924C2218yescomplemented
37C2×C3×Dic3⋊C4C2212yescomplemented
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39C2×C3×C4×Dic3C2211yescharacteristic, complemented
40#63981C22116yescomplemented
41#63974C22116yescomplemented
42C2×#3722C2212yescomplemented
43C2×#3722C2212yescomplemented
44C2×#3722C2212yescomplemented
45C2×#3722C2212yescomplemented
46#63910C22116yescomplemented
47#63909C2218yescomplemented
48#63897C22116yescomplemented
49#63894C2218yescomplemented
50#63864C2218yescomplemented
51C22×#239—31no—
52C22×#235—31no—
53C23×D12—31no—
54C23×D12—31no—
55C23×D12—61no—
56C2×C3×C22⋊Q8—31no—
57C2×C3×C4×D4—31no—
58C2×#947—31no—
59C2×#937—32no—
60C2×#930—31no—
61C2×C4×#67D311yescharacteristic, complemented
62C2×#924D311yescharacteristic, complemented
63#5630—316no—
64#5550—316no—
65C2×#895—31no—
66C2×#895—32no—
67C2×#894—32no—
68C2×#894—32no—
69C2×#893—31no—
70C2×#884—32no—
71C2×#882—32no—
72C2×D3×C22⋊C4—32no—
73C2×D3×C22⋊C4—32no—
74C2×#875—31no—
75C2×C4×D12—31no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3—28no—
78C23×C3⋊D3—28no—
79C23×C3⋊D3—44no—
80C23×C3⋊D3C2312yes—
81C23×C3⋊D3C2318yes—
82C23×C3⋊D3C2312yes—
83C23×C3×D3C2311yescharacteristic
84C22×C32×C4—24no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2314yes—
87C22×C32×C4C2311yescharacteristic
88C2×C4⋊(C3⋊D3)—28no—
89C2×C4⋊(C3⋊D3)—24no—
90C2×C4⋊(C3⋊D3)—232no—
91C2×C4⋊(C3⋊D3)D418yescomplemented
92C2×C4⋊(C3⋊D3)C2314yes—
93C2×C4⋊(C3⋊D3)C2318yes—
94C2×C4⋊(C3⋊D3)C2314yes—
95C2×C3×#67—24no—
96C2×C3×#67C2314yes—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2312yes—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2312yes—
102C2×C3×C4×D3—24no—
103C2×C3×C4×D3C2314yescomplemented
104C2×C3×Dic6—24no—
105C2×C3×Dic6C2314yescomplemented
106C2×#626—28no—
107C2×#626—44no—
108C2×#626C2318yescomplemented
109C2×#626C2318yescomplemented
110C2×#624—28no—
111C2×#624—44no—
112C2×#624C2318yescomplemented
113C2×#624C2318yescomplemented
114#3799—232no—
115C3×#217C2318yes—
116C3×#217C2314yes—
117C3×(C2×D3)⋊C4C2314yescomplemented
118C3×C4⋊Dic3C2314yescomplemented
119C3×Dic3⋊C4C2318yescomplemented
120C3×Dic3⋊C4C2314yescomplemented
121C3×C4×Dic3C2314yescomplemented
122#3722C2318yescomplemented
123#3722C2318yescomplemented
124#3722C2318yescomplemented
125#3722C2318yescomplemented
126C2×#546—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C24×D3—62no—
130C22×C3×Q8—31no—
131C22×C3×D4—31no—
132C23×C3×C4—21no—
133C23×C3×C4—31no—
134C23×C3×C4C2×D311yescharacteristic
135C23×C3×C4C2×D311yescharacteristic
136C22×#67—32no—
137C22×#67—32no—
138C22×#67C2×D311yescharacteristic
139C2×#239—38no—
140C2×#239—68no—
141C2×#235—38no—
142C2×#235—68no—
143C22×D12—31no—
144C22×D12—31no—
145C22×D12—32no—
146C22×D12—31no—
147C22×D12—32no—
148C22×D12—32no—
149C22×D12—31no—
150C22×D12—38no—
151C22×D12—38no—
152C22×D12—32no—
153C22×D12—61no—
154C22×D12—62no—
155C22×D12—61no—
156C22×D12—68no—
157C22×D12—68no—
158C22×D12—68no—
159C22×D12—616no—
160C22×C4×D3—32no—
161C22×C4×D3—32no—
162C22×C4×D3—32no—
163C22×C4×D3—32no—
164C22×C4×D3C2×D311yescharacteristic, complemented
165C22×Dic6C2×D311yescharacteristic, complemented
166C3×C22⋊Q8—38no—
167C3×C4×D4—38no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—32no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—32no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C42—31no—
175C2×#217C2×D311yescharacteristic
176C2×#217C2×D312yes—
177#947—38no—
178#937—316no—
179#930—38no—
180C4×#67C2×D318yescomplemented
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
190C2×C4⋊Dic3C2×D311yescharacteristic, complemented
191#924C2×D318yescomplemented
192C2×Dic3⋊C4C2×D312yescomplemented
193C2×Dic3⋊C4C2×D311yescharacteristic, complemented
194C2×C4×Dic3C2×D311yescharacteristic, complemented
195#895—38no—
196#895—316no—
197#894—316no—
198#894—316no—
199#893—38no—
200#884—316no—
201#882—316no—
202D3×C22⋊C4—316no—
203D3×C22⋊C4—316no—
204#875—38no—
205C4×D12—38no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32#4114yescomplemented
209C23×C32C2412yes—
210C23×C32C2411yescharacteristic
211C22×C3⋊D3—24no—
212C22×C3⋊D3—216no—
213C22×C3⋊D3—24no—
214C22×C3⋊D3—24no—
215C22×C3⋊D3—24no—
216C22×C3⋊D3—216no—
217C22×C3⋊D3—24no—
218C22×C3⋊D3—48no—
219C22×C3⋊D3—432no—
220C22×C3⋊D3C2×D418yes—
221C22×C3⋊D3C2414yes—
222C22×C3⋊D3C2414yes—
223C22×C3×D3—22no—
224C22×C3×D3—22no—
225C22×C3×D3—22no—
226C22×C3×D3C2412yes—
227C2×C32×C4—22no—
228C2×C32×C4—28no—
229C2×C32×C4C2×D414yes—
230C2×C32×C4C2412yes—
231C2×C32×C4C2412yes—
232C4⋊(C3⋊D3)—216no—
233C4⋊(C3⋊D3)—28no—
234C4⋊(C3⋊D3)C2×D4116yescomplemented
235C3×#67—28no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—24no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—24no—
241C2×C3×Dic3C2412yes—
242C2×C3×Dic3C2412yes—
243C2×C3×Dic3C2414yes—
244C2×C3×Dic3C2412yes—
245C2×C3×Dic3C2414yes—
246C3×C4×D3—28no—
247C3×Dic6—28no—
248#626—216no—
249#626—48no—
250#624—216no—
251#624—48no—
252C22×#41—91no—
253C23×D4—91no—
254#546—916no—
255C2×#124—91no—
256C2×#123—92no—
257C2×C22⋊Q8—31no—
258C2×#121—92no—
259C2×#121—91no—
260C2×#120—92no—
261C2×C4×D4—31no—
262C2×C4×D4—91no—
263C22×C22⋊C4—92no—
264C24×C3—21no—
265C24×C3—31no—
266C24×C3C22×D311yescharacteristic
267C24×C3C22×D311yescharacteristic
268C23×D3—32no—
269C23×D3—32no—
270C23×D3—32no—
271C23×D3—32no—
272C23×D3—38no—
273C23×D3—38no—
274C23×D3—62no—
275C23×D3—62no—
276C23×D3—68no—
277C23×D3—68no—
278C23×D3—68no—
279C23×D3—616no—
280C23×D3—68no—
281C23×D3—68no—
282C23×D3—128no—
283C23×D3—124no—
284C23×D3—124no—
285C23×D3—128no—
286C23×D3C22×D311yescharacteristic
287C2×C3×Q8—34no—
288C2×C3×Q8—64no—
289C2×C3×D4—34no—
290C2×C3×D4—64no—
291C22×C3×C4—28no—
292C22×C3×C4—24no—
293C22×C3×C4—24no—
294C22×C3×C4—24no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—32no—
300C22×C3×C4—31no—
301C22×C3×C4—32no—
302C22×C3×C4—34no—
303C22×C3×C4—64no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D314yes—
307C22×C3×C4C22×D314yes—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C2×#67—24no—
311C2×#67—38no—
312C2×#67—38no—
313C2×#67—68no—
314C2×#67—124no—
315C2×#67C22×D314yes—
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D312yes—
319C22×Dic3C22×D312yes—
320C22×Dic3C22×D311yescharacteristic
321#239—632no—
322#235—632no—
323C2×D12—38no—
324C2×D12—38no—
325C2×D12—34no—
326C2×D12—34no—
327C2×D12—38no—
328C2×D12—34no—
329C2×D12—38no—
330C2×D12—38no—
331C2×D12—34no—
332C2×D12—38no—
333C2×D12—68no—
334C2×D12—64no—
335C2×D12—68no—
336C2×D12—64no—
337C2×D12—632no—
338C2×D12—632no—
339C2×D12—68no—
340C2×D12—68no—
341C2×D12—664no—
342C2×D12—616no—
343C2×D12—68no—
344C2×D12—68no—
345C2×D12—64no—
346C2×D12—64no—
347C2×D12—124no—
348C2×C4×D3—24no—
349C2×C4×D3—38no—
350C2×C4×D3—38no—
351C2×C4×D3—38no—
352C2×C4×D3—38no—
353C2×C4×D3—68no—
354C2×C4×D3—68no—
355C2×C4×D3—124no—
356C2×C4×D3—124no—
357C2×C4×D3C22×D314yescomplemented
358C2×Dic6—24no—
359C2×Dic6C22×D314yescomplemented
360C3×C4⋊C4—34no—
361C3×C4⋊C4—34no—
362C3×C4⋊C4—38no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—38no—
365C3×C22⋊C4—34no—
366C3×C42—34no—
367#217C22×D314yes—
368#217C22×D318yes—
369(C2×D3)⋊C4—38no—
370(C2×D3)⋊C4—38no—
371(C2×D3)⋊C4—38no—
372(C2×D3)⋊C4—38no—
373(C2×D3)⋊C4—38no—
374(C2×D3)⋊C4—38no—
375(C2×D3)⋊C4—38no—
376(C2×D3)⋊C4—38no—
377(C2×D3)⋊C4C22×D314yescomplemented
378C4⋊Dic3C22×D314yescomplemented
379Dic3⋊C4C22×D318yescomplemented
380Dic3⋊C4C22×D314yescomplemented
381C4×Dic3C22×D314yescomplemented
382C22×C32—28no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32C22×D412yes—
386C22×C32C2×#4112yes—
387C22×C32C2×#4114yescomplemented
388C22×C32H(5,𝔽2)12yes—
389C22×C32C2511yescharacteristic
390C2×C3⋊D3—24no—
391C2×C3⋊D3—216no—
392C2×C3⋊D3—24no—
393C2×C3⋊D3—24no—
394C2×C3⋊D3—24no—
395C2×C3⋊D3—24no—
396C2×C3⋊D3—432no—
397C2×C3⋊D3—48no—
398C2×C3⋊D3C22×D418yes—
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—44no—
403C32×C4—22no—
404C32×C4C22×D414yes—
405C3×Dic3—22no—
406C3×Dic3—24no—
407C3×Dic3—22no—
408C3×Dic3—22no—
409C3×Dic3—24no—
410C25—92no—
411C2×#41—98no—
412C2×#41—188no—
413C22×Q8—31no—
414C22×D4—31no—
415C22×D4—92no—
416C22×D4—92no—
417C22×D4—91no—
418C22×D4—92no—
419C22×D4—91no—
420C22×D4—98no—
421C22×D4—188no—
422C23×C4—31no—
423C23×C4—92no—
424C23×C4—92no—
425C23×C4D3211yescharacteristic
426#124—98no—
427#123—916no—
428C22⋊Q8—38no—
429#121—916no—
430#121—98no—
431#120—916no—
432C4×D4—38no—
433C4×D4—98no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—32no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—916no—
441C2×C22⋊C4—92no—
442C2×C22⋊C4—92no—
443C2×C22⋊C4—92no—
444C2×C22⋊C4—92no—
445C2×C42—31no—
446C23×C3—24no—
447C23×C3—24no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—21no—
454C23×C3—24no—
455C23×C3—32no—
456C23×C3—62no—
457C23×C3—62no—
458C23×C3—62no—
459C23×C3#23514yescomplemented
460C23×C3#23914yescomplemented
461C23×C3C23×D312yes—
462C23×C3C23×D312yes—
463C23×C3C23×D311yescharacteristic
464C23×C3C23×D311yescharacteristic
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—38no—
469C22×D3—38no—
470C22×D3—34no—
471C22×D3—34no—
472C22×D3—34no—
473C22×D3—34no—
474C22×D3—68no—
475C22×D3—64no—
476C22×D3—64no—
477C22×D3—616no—
478C22×D3—616no—
479C22×D3—64no—
480C22×D3—64no—
481C22×D3—64no—
482C22×D3—64no—
483C22×D3—632no—
484C22×D3—68no—
485C22×D3—64no—
486C22×D3—616no—
487C22×D3—64no—
488C22×D3—64no—
489C22×D3—64no—
490C22×D3—616no—
491C22×D3—64no—
492C22×D3—64no—
493C22×D3—124no—
494C22×D3—124no—
495C22×D3—124no—
496C22×D3—1216no—
497C22×D3—124no—
498C22×D3—128no—
499C22×D3—128no—
500C22×D3—1232no—
501C22×D3—1232no—
502C22×D3—1216no—
503C22×D3—1264no—
504C22×D3C23×D312yes—
505C3×Q8—68no—
506C3×D4—68no—
507C2×C3×C4—24no—
508C2×C3×C4—216no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—28no—
512C2×C3×C4—28no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—24no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—34no—
519C2×C3×C4—32no—
520C2×C3×C4—34no—
521C2×C3×C4—62no—
522C2×C3×C4—64no—
523C2×C3×C4—62no—
524C2×C3×C4—62no—
525C2×C3×C4—64no—
526C2×C3×C4—68no—
527C2×C3×C4D3×D414yes—
528C2×C3×C4D3×D414yes—
529C2×C3×C4C23×D312yes—
530C2×C3×C4C23×D312yes—
531C2×C3×C4C23×D312yes—
532C2×C3×C4C23×D312yes—
533#67—28no—
534#67—616no—
535#67—128no—
536C2×Dic3—22no—
537C2×Dic3—24no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—24no—
541C2×Dic3C23×D312yes—
542C2×Dic3C23×D312yes—
543C2×Dic3C23×D314yes—
544C2×Dic3C23×D314yes—
545C2×Dic3C23×D312yes—
546D12—316no—
547D12—316no—
548D12—616no—
549D12—616no—
550D12—616no—
551D12—632no—
552D12—616no—
553D12—616no—
554D12—68no—
555D12—68no—
556D12—128no—
557C4×D3—28no—
558C4×D3—616no—
559C4×D3—616no—
560C4×D3—128no—
561C4×D3—128no—
562Dic6—28no—
563C2×C32—24no—
564C2×C32#54614yescomplemented
565C2×C32C23×D411yescharacteristic
566C2×C32C22×#4111yescharacteristic
567C2×C32C2×H(5,𝔽2)11yescharacteristic
568C3⋊D3—28no—
569C3⋊D3—44no—
570C3×D3—42no—
571C24—31no—
572C24—92no—
573C24—92no—
574C24—98no—
575C24—188no—
576C24—188no—
577C24—364no—
578C24C2×D3211yescharacteristic
579#41—1832no—
580C2×Q8—34no—
581C2×Q8—64no—
582C2×D4—34no—
583C2×D4—64no—
584C2×D4—98no—
585C2×D4—98no—
586C2×D4—94no—
587C2×D4—98no—
588C2×D4—94no—
589C2×D4—98no—
590C2×D4—1832no—
591C2×D4—188no—
592C2×D4—188no—
593C2×D4—184no—
594C2×D4—364no—
595C22×C4—24no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—32no—
599C22×C4—31no—
600C22×C4—32no—
601C22×C4—34no—
602C22×C4—64no—
603C22×C4—98no—
604C22×C4—98no—
605C22×C4—188no—
606C22×C4—364no—
607C22×C4C2×D3214yes—
608C22×C4C2×D3211yescharacteristic
609C22×C4C2×D3211yescharacteristic
610C4⋊C4—34no—
611C4⋊C4—34no—
612C4⋊C4—38no—
613C22⋊C4—34no—
614C22⋊C4—38no—
615C22⋊C4—34no—
616C22⋊C4—98no—
617C22⋊C4—98no—
618C22⋊C4—98no—
619C22⋊C4—98no—
620C42—34no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—216no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—28no—
629C22×C3—28no—
630C22×C3—22no—
631C22×C3—24no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—124no—
639C22×C3C2×#23512yes—
640C22×C3C2×#23514yescomplemented
641C22×C3C2×D3×D412yes—
642C22×C3C2×D3×D412yes—
643C22×C3C2×#23912yes—
644C22×C3C2×#23914yescomplemented
645C22×C3#100912yes—
646C22×C3#100912yes—
647C22×C3C24×D311yescharacteristic
648C22×C3C24×D311yescharacteristic
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—38no—
653C2×D3—38no—
654C2×D3—44no—
655C2×D3—68no—
656C2×D3—64no—
657C2×D3—64no—
658C2×D3—64no—
659C2×D3—64no—
660C2×D3—616no—
661C2×D3—616no—
662C2×D3—68no—
663C2×D3—64no—
664C2×D3—64no—
665C2×D3—64no—
666C2×D3—64no—
667C2×D3—64no—
668C2×D3—64no—
669C2×D3—124no—
670C2×D3—124no—
671C2×D3—1216no—
672C2×D3—124no—
673C2×D3—124no—
674C2×D3—1232no—
675C2×D3—1232no—
676C2×D3—1264no—
677C2×D3—1216no—
678C2×D3—128no—
679C2×D3—128no—
680C3×C4—24no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—24no—
684C3×C4—62no—
685C3×C4—64no—
686C3×C4—62no—
687C3×C4—62no—
688C3×C4—64no—
689C3×C4C2×D3×D414yes—
690C3×C4C2×D3×D414yes—
691Dic3—22no—
692Dic3—24no—
693Dic3—22no—
694Dic3—22no—
695Dic3—24no—
696C32C2×#54611yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—32no—
700C23—62no—
701C23—62no—
702C23—62no—
703C23—98no—
704C23—94no—
705C23—94no—
706C23—1816no—
707C23—184no—
708C23—184no—
709C23—184no—
710C23—1816no—
711C23—184no—
712C23—184no—
713C23—368no—
714C23—3632no—
715C23#379914yescomplemented
716C23C22×D3212yes—
717C23C22×D3211yescharacteristic
718Q8—68no—
719D4—68no—
720D4—916no—
721D4—1816no—
722D4—1816no—
723D4—188no—
724D4—368no—
725C2×C4—22no—
726C2×C4—28no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—34no—
730C2×C4—32no—
731C2×C4—34no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—64no—
735C2×C4—62no—
736C2×C4—64no—
737C2×C4—68no—
738C2×C4—1816no—
739C2×C4—368no—
740C2×C4#381114yes—
741C2×C4C22×D3212yes—
742C2×C4C22×D3212yes—
743C2×C3—28no—
744C2×C3—24no—
745C2×C3—24no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—24no—
750C2×C3—122no—
751C2×C3#555014yescomplemented
752C2×C3#563014yescomplemented
753C2×C3C22×#23511yescharacteristic
754C2×C3C22×D3×D411yescharacteristic
755C2×C3C22×D3×D411yescharacteristic
756C2×C3C22×#23911yescharacteristic
757C2×C3C2×#100911yescharacteristic
758C2×C3C2×#100911yescharacteristic
759D3—42no—
760D3—68no—
761D3—68no—
762D3—128no—
763D3—128no—
764D3—124no—
765D3—124no—
766C22—22no—
767C22—22no—
768C22—28no—
769C22—62no—
770C22—62no—
771C22—62no—
772C22—98no—
773C22—124no—
774C22—184no—
775C22—184no—
776C22—1816no—
777C22—184no—
778C22—184no—
779C22—184no—
780C22—3632no—
781C22—368no—
782C22C2×#379912yes—
783C22C2×#379914yescomplemented
784C22#6430812yes—
785C22C2×#381112yes—
786C22C23×D3211yescharacteristic
787C4—22no—
788C4—62no—
789C4—62no—
790C4—64no—
791C4—62no—
792C4—64no—
793C4C2×#381114yes—
794C3—21no—
795C3C2×#555011yescharacteristic, complemented
796C3C2×#563011yescharacteristic, complemented
797C2—24no—
798C2—122no—
799C2—188no—
800C2—364no—
801C2#1059501814yesdirect product factor
802C2C22×#379911yescharacteristic
803C2C2×#6430811yescharacteristic
804C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊(C3⋊D3)C2semidirect
2. C22×#3799C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63981C2semidirect
6. C2×#63974C2semidirect
7. #10595018C2direct (N × H)
8. C2×#63910C2semidirect
9. C2×#63909C2semidirect
10. C2×#63897C2semidirect
11. C2×#63894C2semidirect
12. C2×#63864C2semidirect
21. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C3×C4×D3C22semidirect
24. C22×C3×Dic6C22semidirect
25. C22×#626C22semidirect
26. C22×#626C22semidirect
27. C22×#624C22semidirect
28. C22×#624C22semidirect
30. C2×#3799C22semidirect
33. C3×C4×#67C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C3×#924C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. #63981C22semidirect
41. #63974C22semidirect
42. C2×#3722C22semidirect
43. C2×#3722C22semidirect
44. C2×#3722C22semidirect
45. C2×#3722C22semidirect
46. #63910C22semidirect
47. #63909C22semidirect
48. #63897C22semidirect
49. #63894C22semidirect
50. #63864C22semidirect
61. C2×C4×#67D3semidirect
62. C2×#924D3semidirect
91. C2×C4⋊(C3⋊D3)D4semidirect
103. C2×C3×C4×D3C23semidirect
105. C2×C3×Dic6C23semidirect
108. C2×#626C23semidirect
109. C2×#626C23semidirect
112. C2×#624C23semidirect
113. C2×#624C23semidirect
117. C3×(C2×D3)⋊C4C23semidirect
118. C3×C4⋊Dic3C23semidirect
119. C3×Dic3⋊C4C23semidirect
120. C3×Dic3⋊C4C23semidirect
121. C3×C4×Dic3C23semidirect
122. #3722C23semidirect
123. #3722C23semidirect
124. #3722C23semidirect
125. #3722C23semidirect
164. C22×C4×D3C2×D3semidirect
165. C22×Dic6C2×D3semidirect
180. C4×#67C2×D3semidirect
189. C2×(C2×D3)⋊C4C2×D3semidirect
190. C2×C4⋊Dic3C2×D3semidirect
191. #924C2×D3semidirect
192. C2×Dic3⋊C4C2×D3semidirect
193. C2×Dic3⋊C4C2×D3semidirect
194. C2×C4×Dic3C2×D3semidirect
208. C23×C32#41semidirect
234. C4⋊(C3⋊D3)C2×D4semidirect
357. C2×C4×D3C22×D3semidirect
359. C2×Dic6C22×D3semidirect
377. (C2×D3)⋊C4C22×D3semidirect
378. C4⋊Dic3C22×D3semidirect
379. Dic3⋊C4C22×D3semidirect
380. Dic3⋊C4C22×D3semidirect
381. C4×Dic3C22×D3semidirect
387. C22×C32C2×#41semidirect
459. C23×C3#235semidirect
460. C23×C3#239semidirect
564. C2×C32#546semidirect
640. C22×C3C2×#235semidirect
644. C22×C3C2×#239semidirect
696. C32C2×#546semidirect
715. C23#3799semidirect
751. C2×C3#5550semidirect
752. C2×C3#5630semidirect
783. C22C2×#3799semidirect
795. C3C2×#5550semidirect
796. C3C2×#5630semidirect
801. C2#10595018direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊(C3⋊D3)2
C22×#37992
C2×C3×C4×#672
C2×C3×#9242
C2×#639812
C2×#639742
#105950182
C2×#639102
C2×#639092
C2×#638972
C2×#638942
C2×#638642
C2×#56303
C2×#55503