Finite Group Databasebeta

← C2×#10595070 #11902462

Subgroups — C2×#10595070 #11902462

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×C3×#235C211yesmaximal, characteristic, complemented
2C22×#3802C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5C2×#63983C212yesmaximal, complemented
6C2×#63970C212yesmaximal, complemented
7#10595070C2116yesmaximal, direct product factor
8C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
9C2×#63905C212yesmaximal, complemented
10C2×#63898C211yesmaximal, characteristic, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12C2×#63863C211yesmaximal, characteristic, complemented
13C2×#5829—31nomaximal
14C2×#5612—31nomaximal
15C23×D32C2212yes—
16C23×C32×C4C2211yescharacteristic, complemented
17C22×#638C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×#67C2212yescomplemented
20C22×C3×#67C2212yescomplemented
21C2×C3×#235—28no—
22C2×C3×#235C2218yescomplemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2212yescomplemented
26C22×C3×Dic6C2211yescharacteristic, complemented
27C22×#625C2212yes—
28C22×D3×Dic3C2212yescomplemented
29C2×#3802—28no—
30C2×#3802C2218yescomplemented
31C2×#3757C2211yescharacteristic, complemented
32C4×#638C2218yescomplemented
33C2×#3752C2211yescharacteristic
34C2×#3750C2211yescharacteristic, complemented
35C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C3×#930C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yescomplemented
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39#63983C22116yescomplemented
40#63970C22116yescomplemented
41C2×Dic3⋊Dic3C2212yescomplemented
42C2×#3722C2212yes—
43C2×(C2×D3)⋊Dic3C2212yescomplemented
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45C2×(C2×D3)⋊Dic3C2212yescomplemented
46D3×(C2×D3)⋊C4C22116yescomplemented
47#63905C22116yescomplemented
48#63898C2218yescomplemented
49#63871C2218yescomplemented
50#63863C2218yescomplemented
51C22×C3×#41—31no—
52C22×D3×D4—31no—
53C22×D3×D4—31no—
54C22×#235D311yescharacteristic, complemented
55C2×C3×#121—31no—
56#5829—316no—
57C2×#947—31no—
58C2×#946—31no—
59C2×#939—32no—
60C2×#938—32no—
61C2×#937—32no—
62C2×#937—32no—
63C2×#936—31no—
64C2×D4×Dic3—31no—
65C2×#930D311yescharacteristic, complemented
66C2×#929—32no—
67C2×C4×#67—31no—
68C2×C4×#67—31no—
69C2×C4×#67—61no—
70C22×(C2×D3)⋊C4—32no—
71#5612—316no—
72C2×#897—31no—
73C2×#893—31no—
74C2×#883—32no—
75C2×D3×C22⋊C4—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C23×C3×D3C2312yes—
80C22×D32—28no—
81C22×D32—28no—
82C22×D32—44no—
83C22×D32C2318yes—
84C22×C32×C4—24no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2314yescomplemented
88C2×#638—24no—
89C2×#638C2314yes—
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×C4×C3⋊D3—24no—
94C2×C4×C3⋊D3C2314yes—
95C2×C3×#67—28no—
96C2×C3×#67—44no—
97C2×C3×#67C2318yescomplemented
98C2×C3×#67C2318yescomplemented
99C22×C3×Dic3C2312yes—
100C22×C3×Dic3C2312yes—
101C3×#235—232no—
102C2×C3×D12—24no—
103C2×C3×D12D418yescomplemented
104C2×C3×D12C2314yes—
105C2×C3×D12C2314yes—
106C2×C3×C4×D3—28no—
107C2×C3×C4×D3C2318yescomplemented
108C2×C3×Dic6—24no—
109C2×C3×Dic6C2314yescomplemented
110C2×#625—28no—
111C2×#625C2318yes—
112C2×D3×Dic3—44no—
113C2×D3×Dic3C2318yescomplemented
114#3802—232no—
115#3757C2314yescomplemented
116#3752C2314yes—
117#3750C2314yescomplemented
118C4×C3⋊Dic3C2314yescomplemented
119C3×(C2×D3)⋊C4C2318yescomplemented
120C3×C4⋊Dic3C2314yescomplemented
121Dic3⋊Dic3C2318yescomplemented
122#3722C2318yes—
123(C2×D3)⋊Dic3C2318yescomplemented
124(C2×D3)⋊Dic3C2318yescomplemented
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#546—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C2×C3×#41—38no—
130C2×C3×#41—68no—
131C22×C3×Q8—31no—
132C22×C3×D4—32no—
133C22×C3×D4—32no—
134C22×C3×D4—31no—
135C22×C3×D4—31no—
136C23×C3×C4—21no—
137C23×C3×C4—32no—
138C23×C3×C4C2×D311yescharacteristic, complemented
139C23×C3×C4C2×D311yescharacteristic, complemented
140C22×#67—31no—
141C22×#67—31no—
142C22×#67—32no—
143C22×#67—32no—
144C22×#67—61no—
145C22×#67C2×D312yescomplemented
146C22×#67C2×D312yescomplemented
147C23×Dic3—32no—
148C2×D3×D4—38no—
149C2×D3×D4—38no—
150C2×D3×D4—68no—
151C2×D3×D4—68no—
152C2×#235—28no—
153C2×#235C2×D318yescomplemented
154C22×D12C2×D311yescharacteristic
155C22×D12C2×D311yescharacteristic
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—32no—
159C22×C4×D3—61no—
160C22×C4×D3C2×D312yescomplemented
161C22×Dic6C2×D311yescharacteristic, complemented
162C3×#121—38no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C22⋊C4—32no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—32no—
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—61no—
171#947—38no—
172#946—38no—
173#939—316no—
174#938—316no—
175#937—316no—
176#937—316no—
177#936—38no—
178D4×Dic3—38no—
179#930C2×D318yescomplemented
180#929—316no—
181C4×#67—38no—
182C4×#67—38no—
183C4×#67—68no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—32no—
190C2×(C2×D3)⋊C4—32no—
191C2×(C2×D3)⋊C4—316no—
192C2×(C2×D3)⋊C4—61no—
193C2×(C2×D3)⋊C4C2×D312yescomplemented
194C2×C4⋊Dic3—32no—
195C2×C4⋊Dic3C2×D311yescharacteristic, complemented
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—32no—
199C2×Dic3⋊C4—61no—
200C2×C4×Dic3—31no—
201C2×C4×Dic3—31no—
202C2×C4×Dic3—61no—
203#897—38no—
204#893—38no—
205#883—316no—
206D3×C22⋊C4—316no—
207C23×C32—22no—
208C23×C32—22no—
209C23×C32—22no—
210C23×C32C2412yes—
211C23×C32C2411yescharacteristic
212C22×C3⋊D3—22no—
213C22×C3⋊D3—22no—
214C22×C3⋊D3#4114yescomplemented
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—28no—
230C2×C32×C4C2×D414yes—
231C2×C32×C4C2412yes—
232C2×C32×C4C2412yes—
233#638—28no—
234C2×C3⋊Dic3—22no—
235C2×C3⋊Dic3—22no—
236C2×C3⋊Dic3—22no—
237C2×C3⋊Dic3C2412yes—
238C2×C3⋊Dic3C2412yes—
239C2×C3⋊Dic3C2412yes—
240C4×C3⋊D3—28no—
241C3×#67—216no—
242C3×#67—48no—
243C2×C3×Dic3—24no—
244C2×C3×Dic3—24no—
245C2×C3×Dic3C2414yes—
246C2×C3×Dic3C2414yes—
247C3×D12—28no—
248C3×D12C2×D4116yescomplemented
249C3×C4×D3—216no—
250C3×Dic6—28no—
251#625—216no—
252D3×Dic3—48no—
253C22×#41—31no—
254C23×D4—91no—
255#546—916no—
256C2×#124—91no—
257C2×#123—92no—
258C2×C22⋊Q8—91no—
259C2×#121—31no—
260C2×#121—92no—
261C2×#120—92no—
262C2×C4×D4—91no—
263C2×C4×D4—91no—
264C22×C22⋊C4—92no—
265C24×C3—21no—
266C24×C3—32no—
267C24×C3—32no—
268C24×C3C22×D311yescharacteristic
269C24×C3C22×D311yescharacteristic
270C23×D3—31no—
271C23×D3—31no—
272C23×D3—38no—
273C23×D3—38no—
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—
283C3×#41—632no—
284C2×C3×Q8—34no—
285C2×C3×Q8—64no—
286C2×C3×D4—38no—
287C2×C3×D4—38no—
288C2×C3×D4—38no—
289C2×C3×D4—34no—
290C2×C3×D4—34no—
291C2×C3×D4—68no—
292C2×C3×D4—64no—
293C2×C3×D4—124no—
294C22×C3×C4—24no—
295C22×C3×C4—24no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—24no—
299C22×C3×C4—32no—
300C22×C3×C4—32no—
301C22×C3×C4—38no—
302C22×C3×C4—44no—
303C22×C3×C4—68no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D314yescomplemented
309C22×C3×C4C22×D314yescomplemented
310C2×#67—28no—
311C2×#67—34no—
312C2×#67—34no—
313C2×#67—38no—
314C2×#67—38no—
315C2×#67—44no—
316C2×#67—64no—
317C2×#67—68no—
318C2×#67—64no—
319C2×#67—64no—
320C2×#67—68no—
321C2×#67—68no—
322C2×#67C22×D318yescomplemented
323C2×#67C22×D318yescomplemented
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—38no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—124no—
335C22×Dic3C22×D312yes—
336C22×Dic3C22×D312yes—
337D3×D4—632no—
338D3×D4—632no—
339#235—232no—
340C2×D12—24no—
341C2×D12#6718yescomplemented
342C2×D12C22×D314yes—
343C2×D12C22×D314yes—
344C2×C4×D3—28no—
345C2×C4×D3—34no—
346C2×C4×D3—34no—
347C2×C4×D3—38no—
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—
358#217—34no—
359#217—34no—
360#217—38no—
361#217—38no—
362#217—38no—
363#217—64no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4—38no—
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)⋊C4C22×D318yescomplemented
373C4⋊Dic3—38no—
374C4⋊Dic3C22×D314yescomplemented
375Dic3⋊C4—34no—
376Dic3⋊C4—34no—
377Dic3⋊C4—38no—
378Dic3⋊C4—64no—
379C4×Dic3—34no—
380C4×Dic3—34no—
381C4×Dic3—64no—
382C22×C32—22no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32—44no—
386C22×C32C22×D412yes—
387C22×C32C2×#4112yes—
388C22×C32H(5,𝔽2)12yes—
389C22×C32C2511yescharacteristic
390C2×C3⋊D3—28no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
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×C4C22×D414yes—
405C3⋊Dic3—22no—
406C3⋊Dic3—22no—
407C3⋊Dic3—22no—
408C3×Dic3—24no—
409C3×Dic3—24no—
410C25—92no—
411C2×#41—38no—
412C2×#41—68no—
413C22×Q8—31no—
414C22×D4—32no—
415C22×D4—32no—
416C22×D4—31no—
417C22×D4—31no—
418C22×D4—98no—
419C22×D4—92no—
420C22×D4—91no—
421C22×D4—188no—
422C23×C4—32no—
423C23×C4—92no—
424C23×C4—91no—
425C23×C4D3211yescharacteristic, complemented
426#124—98no—
427#123—916no—
428C22⋊Q8—98no—
429#121—38no—
430#121—916no—
431#120—916no—
432C4×D4—98no—
433C4×D4—98no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—92no—
436C2×C4⋊C4—91no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—916no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—92no—
441C2×C22⋊C4—92no—
442C2×C22⋊C4—92no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C42—91no—
446C23×C3—24no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—21no—
455C23×C3—38no—
456C23×C3—34no—
457C23×C3—34no—
458C23×C3—42no—
459C23×C3—42no—
460C23×C3—64no—
461C23×C3—64no—
462C23×C3—64no—
463C23×C3—64no—
464C23×C3—64no—
465C23×C3C23×D312yes—
466C23×C3C23×D312yes—
467C23×C3C23×D311yescharacteristic
468C23×C3C23×D311yescharacteristic
469C22×D3—24no—
470C22×D3—24no—
471C22×D3—24no—
472C22×D3—24no—
473C22×D3—24no—
474C22×D3—34no—
475C22×D3—34no—
476C22×D3—32no—
477C22×D3—32no—
478C22×D3—64no—
479C22×D3—62no—
480C22×D3—616no—
481C22×D3—616no—
482C22×D3—616no—
483C22×D3—62no—
484C22×D3—62no—
485C22×D3—62no—
486C22×D3—62no—
487C22×D3—616no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—128no—
491C22×D3—128no—
492C22×D3—1232no—
493C22×D3—1232no—
494C22×D3C2×#6718yes—
495C22×D3C23×D314yes—
496C22×D3C23×D314yes—
497C3×Q8—68no—
498C3×D4—316no—
499C3×D4—616no—
500C3×D4—68no—
501C3×D4—128no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—28no—
505C2×C3×C4—28no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—24no—
509C2×C3×C4—34no—
510C2×C3×C4—34no—
511C2×C3×C4—48no—
512C2×C3×C4—42no—
513C2×C3×C4—616no—
514C2×C3×C4—64no—
515C2×C3×C4—64no—
516C2×C3×C4D3×D414yes—
517C2×C3×C4C2×#6714yes—
518C2×C3×C4C23×D312yes—
519C2×C3×C4C23×D312yes—
520C2×C3×C4C23×D312yes—
521C2×C3×C4C23×D312yes—
522#67—216no—
523#67—48no—
524#67—616no—
525#67—68no—
526#67—68no—
527#67—616no—
528#67—616no—
529C2×Dic3—24no—
530C2×Dic3—24no—
531C2×Dic3—32no—
532C2×Dic3—32no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—62no—
540C2×Dic3—64no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3—62no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3—128no—
550C2×Dic3C23×D314yes—
551C2×Dic3C23×D314yes—
552D12—28no—
553D12C2×#67116yescomplemented
554C4×D3—216no—
555C4×D3—68no—
556C4×D3—68no—
557C4×D3—128no—
558C4×D3—128no—
559Dic6—28no—
560C2×C32—42no—
561C2×C32#54614yescomplemented
562C2×C32C23×D411yescharacteristic
563C2×C32C22×#4111yescharacteristic
564C2×C32C2×H(5,𝔽2)11yescharacteristic
565C3⋊D3—24no—
566C3×D3—28no—
567C3×D3—44no—
568C24—32no—
569C24—32no—
570C24—98no—
571C24—91no—
572C24—188no—
573C24—188no—
574C24—364no—
575C24C2×D3211yescharacteristic
576#41—632no—
577C2×Q8—34no—
578C2×Q8—64no—
579C2×D4—38no—
580C2×D4—38no—
581C2×D4—34no—
582C2×D4—34no—
583C2×D4—38no—
584C2×D4—68no—
585C2×D4—64no—
586C2×D4—98no—
587C2×D4—94no—
588C2×D4—124no—
589C2×D4—1832no—
590C2×D4—184no—
591C2×D4—188no—
592C22×C4—24no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—38no—
596C22×C4—68no—
597C22×C4—98no—
598C22×C4—91no—
599C22×C4—91no—
600C22×C4—91no—
601C22×C4—94no—
602C22×C4—184no—
603C22×C4—364no—
604C22×C4C2×D3211yescharacteristic
605C22×C4C2×D3211yescharacteristic
606C22×C4C2×D3214yescomplemented
607C4⋊C4—34no—
608C4⋊C4—98no—
609C4⋊C4—94no—
610C22⋊C4—38no—
611C22⋊C4—98no—
612C22⋊C4—98no—
613C22⋊C4—98no—
614C22⋊C4—98no—
615C22⋊C4—94no—
616C22⋊C4—94no—
617C42—94no—
618C22×C3—24no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—38no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—48no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—64no—
636C22×C3—64no—
637C22×C3—616no—
638C22×C3—64no—
639C22×C3—64no—
640C22×C3—64no—
641C22×C3—128no—
642C22×C3C2×D3×D412yes—
643C22×C3#100412yes—
644C22×C3D3×#4112yes—
645C22×C3D3×#4112yes—
646C22×C3#100912yes—
647C22×C3C22×#6712yes—
648C22×C3C24×D311yescharacteristic
649C22×C3C24×D311yescharacteristic
650C2×D3—24no—
651C2×D3—24no—
652C2×D3—216no—
653C2×D3—24no—
654C2×D3—24no—
655C2×D3—24no—
656C2×D3—34no—
657C2×D3—34no—
658C2×D3—48no—
659C2×D3—64no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—68no—
665C2×D3—68no—
666C2×D3—122no—
667C2×D3—122no—
668C2×D3—128no—
669C2×D3—1232no—
670C2×D3—1232no—
671C2×D3C22×#6718yes—
672C3×C4—22no—
673C3×C4—22no—
674C3×C4—24no—
675C3×C4—42no—
676C3×C4—64no—
677C3×C4—64no—
678C3×C4C2×D3×D414yes—
679C3×C4C22×#6714yes—
680Dic3—24no—
681Dic3—24no—
682Dic3—64no—
683Dic3—62no—
684Dic3—62no—
685Dic3—62no—
686Dic3—62no—
687Dic3—62no—
688Dic3—62no—
689Dic3—122no—
690Dic3—122no—
691C32C2×#54611yescharacteristic, complemented, Sylow
692C23—22no—
693C23—22no—
694C23—22no—
695C23—38no—
696C23—34no—
697C23—34no—
698C23—64no—
699C23—64no—
700C23—64no—
701C23—64no—
702C23—64no—
703C23—94no—
704C23—92no—
705C23—1816no—
706C23—1816no—
707C23—182no—
708C23—182no—
709C23—368no—
710C23—3632no—
711C23C22×D3212yes—
712C23C22×D3211yescharacteristic
713Q8—68no—
714D4—316no—
715D4—616no—
716D4—68no—
717D4—128no—
718D4—188no—
719D4—1816no—
720C2×C4—22no—
721C2×C4—28no—
722C2×C4—34no—
723C2×C4—34no—
724C2×C4—616no—
725C2×C4—64no—
726C2×C4—64no—
727C2×C4—92no—
728C2×C4—92no—
729C2×C4—92no—
730C2×C4—182no—
731C2×C4—182no—
732C2×C4—182no—
733C2×C4—188no—
734C2×C4—368no—
735C2×C4D3×#6714yes—
736C2×C4C22×D3212yes—
737C2×C4C22×D3212yes—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—24no—
742C2×C3—44no—
743C2×C3—42no—
744C2×C3—42no—
745C2×C3—68no—
746C2×C3—124no—
747C2×C3#561214yescomplemented
748C2×C3#582914yescomplemented
749C2×C3C22×D3×D411yescharacteristic
750C2×C3C2×#100411yescharacteristic
751C2×C3C2×D3×#4111yescharacteristic
752C2×C3C2×D3×#4111yescharacteristic
753C2×C3C2×#100911yescharacteristic
754C2×C3C23×#6711yescharacteristic
755D3—28no—
756D3—44no—
757D3—64no—
758D3—64no—
759D3—124no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—38no—
764C22—44no—
765C22—64no—
766C22—64no—
767C22—616no—
768C22—64no—
769C22—64no—
770C22—64no—
771C22—94no—
772C22—128no—
773C22—182no—
774C22—182no—
775C22—188no—
776C22—3632no—
777C22#6430612yes—
778C22#6430712yes—
779C22C2×D3×#6712yes—
780C22C23×D3211yescharacteristic
781C4—22no—
782C4—64no—
783C4—64no—
784C4—182no—
785C4—182no—
786C4—182no—
787C4C2×D3×#6714yes—
788C3—21no—
789C3C2×#561211yescharacteristic, complemented
790C3C2×#582911yescharacteristic, complemented
791C2—42no—
792C2—68no—
793C2—124no—
794C2—184no—
795C2#1059507014yesdirect product factor
796C2C2×#6430611yescharacteristic
797C2C2×#6430711yescharacteristic
798C2C22×D3×#6711yescharacteristic
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. C22×C3×#235C2semidirect
2. C22×#3802C2semidirect
3. C2×C4×#638C2semidirect
4. C2×C3×#930C2semidirect
5. C2×#63983C2semidirect
6. C2×#63970C2semidirect
7. #10595070C2direct (N × H)
8. C2×D3×(C2×D3)⋊C4C2semidirect
9. C2×#63905C2semidirect
10. C2×#63898C2semidirect
11. C2×#63871C2semidirect
12. C2×#63863C2semidirect
16. C23×C32×C4C22semidirect
19. C22×C3×#67C22semidirect
20. C22×C3×#67C22semidirect
22. C2×C3×#235C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C22×C3×Dic6C22semidirect
28. C22×D3×Dic3C22semidirect
30. C2×#3802C22semidirect
31. C2×#3757C22semidirect
32. C4×#638C22semidirect
34. C2×#3750C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
36. C3×#930C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. #63983C22semidirect
40. #63970C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. D3×(C2×D3)⋊C4C22semidirect
47. #63905C22semidirect
48. #63898C22semidirect
49. #63871C22semidirect
50. #63863C22semidirect
54. C22×#235D3semidirect
65. C2×#930D3semidirect
87. C22×C32×C4C23semidirect
97. C2×C3×#67C23semidirect
98. C2×C3×#67C23semidirect
103. C2×C3×D12D4semidirect
107. C2×C3×C4×D3C23semidirect
109. C2×C3×Dic6C23semidirect
113. C2×D3×Dic3C23semidirect
115. #3757C23semidirect
117. #3750C23semidirect
118. C4×C3⋊Dic3C23semidirect
119. C3×(C2×D3)⋊C4C23semidirect
120. C3×C4⋊Dic3C23semidirect
121. Dic3⋊Dic3C23semidirect
123. (C2×D3)⋊Dic3C23semidirect
124. (C2×D3)⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
138. C23×C3×C4C2×D3semidirect
139. C23×C3×C4C2×D3semidirect
145. C22×#67C2×D3semidirect
146. C22×#67C2×D3semidirect
153. C2×#235C2×D3semidirect
160. C22×C4×D3C2×D3semidirect
161. C22×Dic6C2×D3semidirect
179. #930C2×D3semidirect
193. C2×(C2×D3)⋊C4C2×D3semidirect
195. C2×C4⋊Dic3C2×D3semidirect
214. C22×C3⋊D3#41semidirect
248. C3×D12C2×D4semidirect
308. C22×C3×C4C22×D3semidirect
309. C22×C3×C4C22×D3semidirect
322. C2×#67C22×D3semidirect
323. C2×#67C22×D3semidirect
341. C2×D12#67semidirect
353. C2×C4×D3C22×D3semidirect
355. C2×Dic6C22×D3semidirect
372. (C2×D3)⋊C4C22×D3semidirect
374. C4⋊Dic3C22×D3semidirect
393. C2×C3⋊D3C2×#41semidirect
425. C23×C4D32semidirect
553. D12C2×#67semidirect
561. C2×C32#546semidirect
606. C22×C4C2×D32semidirect
691. C32C2×#546semidirect
747. C2×C3#5612semidirect
748. C2×C3#5829semidirect
789. C3C2×#5612semidirect
790. C3C2×#5829semidirect
795. C2#10595070direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×#38022
C2×C4×#6382
C2×C3×#9302
C2×#639832
C2×#639702
#105950702
C2×D3×(C2×D3)⋊C42
C2×#639052
C2×#638982
C2×#638712
C2×#638632
C2×#58293
C2×#56123