Finite Group Databasebeta

← C2×#10594007 #11902466

Subgroups — C2×#10594007 #11902466

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C2×C3×#875C211yesmaximal, characteristic, complemented
5C2×C3×C4×D12C211yesmaximal, characteristic, complemented
6C2×#63922C212yesmaximal, complemented
7C2×#63921C212yesmaximal, complemented
8C2×#63912C212yesmaximal, complemented
9C2×#63908C211yesmaximal, characteristic, complemented
10C2×#63856C211yesmaximal, characteristic, complemented
11C2×#63854C212yesmaximal, complemented
12#10594007C2116yesmaximal, direct product factor
13C2×#5676—31nomaximal
14C2×#5550—31nomaximal
15C23×D32C2212yes—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C4×C3⋊D3C2212yescomplemented
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic, complemented
22C22×C3×Dic6C2211yescharacteristic, complemented
23C22×#626C2212yes—
24C22×#626C2212yescomplemented
25C22×#625C2212yescomplemented
26C22×#624C2212yescomplemented
27C2×D3×D12—28no—
28C2×D3×D12C2218yescomplemented
29C2×#3799—28no—
30C2×#3799C2218yescomplemented
31C2×C32×C42C2211yescharacteristic, complemented
32C2×#3752C2212yescomplemented
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C4×C4⋊(C3⋊D3)C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
40C3×#875C2218yescomplemented
41C3×C4×D12C2218yescomplemented
42C2×#3724C2212yescomplemented
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45#63922C22116yescomplemented
46#63921C22116yescomplemented
47#63912C22116yescomplemented
48#63908C2218yescomplemented
49#63856C2218yescomplemented
50#63854C22116yescomplemented
51C22×#239—31no—
52C22×D3×D4—31no—
53C22×#235—31no—
54C23×D12—31no—
55C2×C3×#124—31no—
56C2×C3×C4×D4—31no—
57C2×#946—31no—
58C2×#938—31no—
59C2×#937—32no—
60C2×#930—31no—
61C2×#924—31no—
62#5676—316no—
63#5550—316no—
64C2×#894—32no—
65C2×#884—32no—
66C2×#884—32no—
67C2×#883—32no—
68C2×#882—32no—
69C2×D3×C22⋊C4—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⋊D3C2312yes—
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C22×D32—28no—
81C22×D32—28no—
82C22×D32—44no—
83C22×D32C2318yes—
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C3⋊Dic3C2312yes—
88C2×C4⋊(C3⋊D3)D418yescomplemented
89C2×C4⋊(C3⋊D3)C2314yes—
90C2×C4×C3⋊D3—44no—
91C2×C4×C3⋊D3C2318yescomplemented
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2312yes—
95C2×C3×D12—24no—
96C2×C3×D12—24no—
97C2×C3×D12C2314yes—
98C2×C3×D12C2314yes—
99C2×C3×C4×D3—24no—
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3C2314yes—
102C2×C3×C4×D3C2314yescomplemented
103C2×C3×Dic6—24no—
104C2×C3×Dic6C2314yescomplemented
105C2×#626—28no—
106C2×#626—28no—
107C2×#626C2318yes—
108C2×#626C2318yescomplemented
109C2×#625—44no—
110C2×#625C2318yescomplemented
111C2×#624—28no—
112C2×#624C2318yescomplemented
113D3×D12—232no—
114#3799—232no—
115C32×C42C2314yescomplemented
116#3752C2318yescomplemented
117C4⋊(C3⋊Dic3)C2314yescomplemented
118C3×(C2×D3)⋊C4C2314yes—
119C3×(C2×D3)⋊C4C2318yescomplemented
120C3×(C2×D3)⋊C4C2314yescomplemented
121C3×(C2×D3)⋊C4C2318yescomplemented
122C3×C4⋊Dic3C2314yescomplemented
123#3724C2318yescomplemented
124(C2×D3)⋊Dic3C2318yes—
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—31no—
133C23×C3×C4—31no—
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—32no—
137C22×#67—32no—
138C2×#239—38no—
139C2×#239—68no—
140C2×D3×D4—38no—
141C2×D3×D4—68no—
142C2×#235—38no—
143C2×#235—68no—
144C22×D12—31no—
145C22×D12—31no—
146C22×D12—32no—
147C22×D12—32no—
148C22×D12—38no—
149C22×D12—61no—
150C22×D12—68no—
151C22×D12C2×D311yescharacteristic
152C22×D12C2×D311yescharacteristic
153C22×C4×D3—32no—
154C22×C4×D3—32no—
155C22×C4×D3—32no—
156C22×C4×D3—32no—
157C22×C4×D3—62no—
158C22×C4×D3C2×D311yescharacteristic
159C22×C4×D3C2×D311yescharacteristic, complemented
160C22×Dic6C2×D311yescharacteristic, complemented
161C3×#124—38no—
162C3×C4×D4—38no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—32no—
166C2×C3×C22⋊C4—32no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C42—21no—
169C2×C3×C42C2×D311yescharacteristic, complemented
170C2×C3×C42C2×D311yescharacteristic, complemented
171C2×#217—32no—
172C2×#217—32no—
173#946—38no—
174#938—38no—
175#937—316no—
176#930—38no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—62no—
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
184C2×(C2×D3)⋊C4C2×D312yescomplemented
185C2×(C2×D3)⋊C4C2×D312yescomplemented
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3—61no—
189C2×C4⋊Dic3C2×D311yescharacteristic, complemented
190#924—38no—
191C2×Dic3⋊C4—32no—
192C2×Dic3⋊C4—32no—
193#894—316no—
194#884—316no—
195#884—316no—
196#883—316no—
197#882—316no—
198D3×C22⋊C4—316no—
199D3×C22⋊C4—316no—
200#875C2×D318yescomplemented
201C4×D12—38no—
202C4×D12—38no—
203C4×D12—68no—
204C4×D12C2×D318yescomplemented
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—24no—
207C22×C3⋊D3—24no—
208C22×C3⋊D3C2×D418yes—
209C22×C3⋊D3C2414yes—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—24no—
213C22×C3×D3—22no—
214C22×C3×D3—24no—
215C22×C3×D3—22no—
216C22×C3×D3—24no—
217C22×C3×D3—22no—
218C22×C3×D3#4114yescomplemented
219C22×C3×D3C2414yes—
220C22×C3×D3C2412yes—
221C22×C3×D3C2412yes—
222C2×D32—216no—
223C2×D32—216no—
224C2×D32—48no—
225C2×D32—432no—
226C2×C32×C4—22no—
227C2×C32×C4—22no—
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2412yes—
230C2×C32×C4C2412yes—
231C2×C32×C4C2412yes—
232C2×C3⋊Dic3—24no—
233C2×C3⋊Dic3C2414yes—
234C4⋊(C3⋊D3)C2×D4116yescomplemented
235C4×C3⋊D3—48no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—24no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2412yes—
241C2×C3×Dic3C2412yes—
242C3×D12—28no—
243C3×D12—28no—
244C3×C4×D3—28no—
245C3×C4×D3—28no—
246C3×Dic6—28no—
247#626—216no—
248#626—216no—
249#625—48no—
250#624—216no—
251C22×#41—91no—
252C23×D4—91no—
253#546—916no—
254C2×#124—31no—
255C2×#123—92no—
256C2×C22⋊Q8—91no—
257C2×#121—92no—
258C2×#121—91no—
259C2×#120—92no—
260C2×C4×D4—31no—
261C2×C4×D4—91no—
262C22×C22⋊C4—92no—
263C24×C3—31no—
264C24×C3—32no—
265C24×C3—31no—
266C23×D3—32no—
267C23×D3—32no—
268C23×D3—38no—
269C23×D3—38no—
270C23×D3—62no—
271C23×D3—68no—
272C23×D3—68no—
273C23×D3—68no—
274C23×D3—68no—
275C23×D3—124no—
276C23×D3—124no—
277C23×D3C22×D312yes—
278C23×D3C22×D311yescharacteristic
279C23×D3C22×D311yescharacteristic
280C2×C3×Q8—34no—
281C2×C3×Q8—64no—
282C2×C3×D4—34no—
283C2×C3×D4—34no—
284C2×C3×D4—64no—
285C2×C3×D4—64no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—31no—
290C22×C3×C4—32no—
291C22×C3×C4—31no—
292C22×C3×C4—34no—
293C22×C3×C4—34no—
294C22×C3×C4—64no—
295C22×C3×C4—64no—
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—124no—
309C2×#67—124no—
310C22×Dic3—32no—
311C22×Dic3—32no—
312C22×Dic3—62no—
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D312yes—
315C22×Dic3C22×D311yescharacteristic
316#239—632no—
317D3×D4—632no—
318#235—632no—
319C2×D12—24no—
320C2×D12—24no—
321C2×D12—38no—
322C2×D12—38no—
323C2×D12—34no—
324C2×D12—34no—
325C2×D12—38no—
326C2×D12—38no—
327C2×D12—64no—
328C2×D12—68no—
329C2×D12—632no—
330C2×D12—68no—
331C2×D12—68no—
332C2×D12C22×D314yes—
333C2×D12C22×D314yes—
334C2×C4×D3—24no—
335C2×C4×D3—24no—
336C2×C4×D3—38no—
337C2×C4×D3—38no—
338C2×C4×D3—38no—
339C2×C4×D3—38no—
340C2×C4×D3—68no—
341C2×C4×D3—68no—
342C2×C4×D3—68no—
343C2×C4×D3—124no—
344C2×C4×D3—124no—
345C2×C4×D3—128no—
346C2×C4×D3C22×D314yes—
347C2×C4×D3C22×D314yescomplemented
348C2×Dic6—24no—
349C2×Dic6C22×D314yescomplemented
350C3×C4⋊C4—34no—
351C3×C22⋊C4—34no—
352C3×C22⋊C4—38no—
353C3×C22⋊C4—38no—
354C3×C22⋊C4—34no—
355C3×C42—24no—
356C3×C42C22×D314yescomplemented
357C3×C42C22×D314yescomplemented
358#217—38no—
359#217—38no—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—68no—
365(C2×D3)⋊C4C22×D314yes—
366(C2×D3)⋊C4C22×D314yescomplemented
367(C2×D3)⋊C4C22×D318yescomplemented
368(C2×D3)⋊C4C22×D318yescomplemented
369C4⋊Dic3—34no—
370C4⋊Dic3—34no—
371C4⋊Dic3—64no—
372C4⋊Dic3C22×D314yescomplemented
373Dic3⋊C4—38no—
374Dic3⋊C4—38no—
375C22×C32C22×D412yes—
376C22×C32C2×#4112yes—
377C22×C32H(5,𝔽2)12yes—
378C22×C32C2511yescharacteristic
379C2×C3⋊D3—216no—
380C2×C3⋊D3—24no—
381C2×C3⋊D3—24no—
382C2×C3⋊D3C22×D418yes—
383C2×C3×D3—28no—
384C2×C3×D3—22no—
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—24no—
388C2×C3×D3—22no—
389C2×C3×D3—24no—
390C2×C3×D3—22no—
391C2×C3×D3—24no—
392C2×C3×D3—48no—
393C2×C3×D3—44no—
394C2×C3×D3C2×#4114yescomplemented
395D32—432no—
396C32×C4—22no—
397C32×C4—22no—
398C32×C4C22×D414yes—
399C3⋊Dic3—24no—
400C3×Dic3—22no—
401C3×Dic3—24no—
402C3×Dic3—22no—
403C25—92no—
404C2×#41—98no—
405C2×#41—188no—
406C22×Q8—31no—
407C22×D4—31no—
408C22×D4—31no—
409C22×D4—98no—
410C22×D4—92no—
411C22×D4—92no—
412C22×D4—92no—
413C22×D4—91no—
414C22×D4—188no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—92no—
418C23×C4—92no—
419#124—38no—
420#123—916no—
421C22⋊Q8—98no—
422#121—916no—
423#121—98no—
424#120—916no—
425C4×D4—38no—
426C4×D4—98no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—92no—
429C2×C4⋊C4—91no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—32no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—32no—
434C2×C22⋊C4—916no—
435C2×C22⋊C4—92no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—92no—
438C2×C42D3211yescharacteristic, complemented
439C23×C3—21no—
440C23×C3—34no—
441C23×C3—32no—
442C23×C3—34no—
443C23×C3—32no—
444C23×C3—62no—
445C23×C3—62no—
446C23×C3—64no—
447C23×C3—62no—
448C23×C3—64no—
449C23×C3—62no—
450C23×C3—62no—
451C23×C3—64no—
452C23×C3C23×D311yescharacteristic
453C23×C3C23×D311yescharacteristic
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—22no—
461C22×D3—24no—
462C22×D3—38no—
463C22×D3—38no—
464C22×D3—34no—
465C22×D3—34no—
466C22×D3—68no—
467C22×D3—64no—
468C22×D3—616no—
469C22×D3—616no—
470C22×D3—616no—
471C22×D3—64no—
472C22×D3—64no—
473C22×D3—64no—
474C22×D3—64no—
475C22×D3—616no—
476C22×D3—124no—
477C22×D3—124no—
478C22×D3—128no—
479C22×D3—128no—
480C22×D3—1232no—
481C22×D3—1232no—
482C22×D3#23514yescomplemented
483C22×D3C23×D314yes—
484C22×D3C23×D312yes—
485C22×D3C23×D312yes—
486C3×Q8—68no—
487C3×D4—68no—
488C3×D4—68no—
489C2×C3×C4—24no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—24no—
498C2×C3×C4—32no—
499C2×C3×C4—34no—
500C2×C3×C4—32no—
501C2×C3×C4—42no—
502C2×C3×C4—62no—
503C2×C3×C4—64no—
504C2×C3×C4—62no—
505C2×C3×C4—68no—
506C2×C3×C4—68no—
507C2×C3×C4D3×D414yes—
508C2×C3×C4D3×D414yes—
509C2×C3×C4C23×D312yes—
510C2×C3×C4C23×D312yes—
511C2×C3×C4C23×D312yes—
512C2×C3×C4C23×D312yes—
513C2×C3×C4C23×D312yes—
514C2×C3×C4C23×D312yes—
515#67—616no—
516#67—616no—
517#67—128no—
518#67—128no—
519C2×Dic3—24no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—34no—
523C2×Dic3—34no—
524C2×Dic3—64no—
525C2×Dic3—64no—
526C2×Dic3—64no—
527C2×Dic3—124no—
528C2×Dic3C23×D312yes—
529C2×Dic3C23×D314yes—
530C2×Dic3C23×D312yes—
531D12—28no—
532D12—28no—
533D12—316no—
534D12—316no—
535D12—616no—
536D12—616no—
537D12—616no—
538C4×D3—28no—
539C4×D3—28no—
540C4×D3—616no—
541C4×D3—616no—
542C4×D3—128no—
543C4×D3—128no—
544C4×D3—1216no—
545Dic6—28no—
546C2×C32#54614yescomplemented
547C2×C32C23×D411yescharacteristic
548C2×C32C22×#4111yescharacteristic
549C2×C32C2×H(5,𝔽2)11yescharacteristic
550C3⋊D3—28no—
551C3×D3—24no—
552C3×D3—44no—
553C3×D3—42no—
554C24—31no—
555C24—32no—
556C24—31no—
557C24—98no—
558C24—92no—
559C24—188no—
560C24—188no—
561C24—364no—
562#41—1832no—
563C2×Q8—34no—
564C2×Q8—64no—
565C2×D4—34no—
566C2×D4—34no—
567C2×D4—64no—
568C2×D4—64no—
569C2×D4—98no—
570C2×D4—98no—
571C2×D4—98no—
572C2×D4—94no—
573C2×D4—98no—
574C2×D4—1832no—
575C2×D4—188no—
576C2×D4—188no—
577C2×D4—364no—
578C22×C4—32no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—34no—
582C22×C4—34no—
583C22×C4—64no—
584C22×C4—64no—
585C22×C4—98no—
586C22×C4—92no—
587C22×C4—98no—
588C22×C4—188no—
589C22×C4—364no—
590C22×C4C2×D3211yescharacteristic
591C22×C4C2×D3211yescharacteristic
592C22×C4C2×D3211yescharacteristic
593C4⋊C4—34no—
594C4⋊C4—98no—
595C4⋊C4—94no—
596C22⋊C4—34no—
597C22⋊C4—38no—
598C22⋊C4—34no—
599C22⋊C4—38no—
600C22⋊C4—98no—
601C22⋊C4—98no—
602C22⋊C4—98no—
603C42C2×D3214yescomplemented
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—21no—
608C22×C3—34no—
609C22×C3—68no—
610C22×C3—62no—
611C22×C3—62no—
612C22×C3—64no—
613C22×C3—62no—
614C22×C3—64no—
615C22×C3—62no—
616C22×C3—62no—
617C22×C3—64no—
618C22×C3—124no—
619C22×C3—128no—
620C22×C3C2×#23512yes—
621C22×C3C2×D3×D412yes—
622C22×C3C2×D3×D412yes—
623C22×C3D3×#4112yes—
624C22×C3#100912yes—
625C22×C3#100912yes—
626C22×C3C24×D311yescharacteristic
627C22×C3C24×D311yescharacteristic
628C2×D3—22no—
629C2×D3—22no—
630C2×D3—28no—
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—24no—
634C2×D3—24no—
635C2×D3—22no—
636C2×D3—24no—
637C2×D3—38no—
638C2×D3—38no—
639C2×D3—48no—
640C2×D3—44no—
641C2×D3—68no—
642C2×D3—616no—
643C2×D3—64no—
644C2×D3—64no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—616no—
648C2×D3—124no—
649C2×D3—124no—
650C2×D3—1216no—
651C2×D3—1232no—
652C2×D3—1232no—
653C2×D3C2×#23514yescomplemented
654C3×C4—24no—
655C3×C4—22no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—24no—
660C3×C4—42no—
661C3×C4—62no—
662C3×C4—64no—
663C3×C4—62no—
664C3×C4C2×D3×D414yes—
665C3×C4C2×D3×D414yes—
666Dic3—24no—
667Dic3—22no—
668Dic3—22no—
669Dic3—64no—
670Dic3—64no—
671Dic3—124no—
672C32C2×#54611yescharacteristic, complemented, Sylow
673C23—34no—
674C23—32no—
675C23—34no—
676C23—32no—
677C23—62no—
678C23—62no—
679C23—62no—
680C23—64no—
681C23—62no—
682C23—64no—
683C23—62no—
684C23—64no—
685C23—98no—
686C23—94no—
687C23—1816no—
688C23—1816no—
689C23—184no—
690C23—184no—
691C23—368no—
692C23—3632no—
693C23C22×D3211yescharacteristic
694Q8—68no—
695D4—68no—
696D4—68no—
697D4—916no—
698D4—1816no—
699D4—1816no—
700D4—368no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—34no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—64no—
709C2×C4—68no—
710C2×C4—68no—
711C2×C4—94no—
712C2×C4—1816no—
713C2×C4—184no—
714C2×C4—368no—
715C2×C4#380214yes—
716C2×C4C22×D3212yes—
717C2×C4C22×D3212yes—
718C2×C4C22×D3212yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—24no—
723C2×C3—64no—
724C2×C3—124no—
725C2×C3—122no—
726C2×C3#555014yescomplemented
727C2×C3#567614yescomplemented
728C2×C3C22×#23511yescharacteristic
729C2×C3C22×D3×D411yescharacteristic
730C2×C3C22×D3×D411yescharacteristic
731C2×C3C2×D3×#4111yescharacteristic
732C2×C3C2×#100911yescharacteristic
733C2×C3C2×#100911yescharacteristic
734D3—24no—
735D3—42no—
736D3—44no—
737D3—68no—
738D3—68no—
739D3—128no—
740C22—34no—
741C22—62no—
742C22—62no—
743C22—68no—
744C22—62no—
745C22—64no—
746C22—62no—
747C22—64no—
748C22—62no—
749C22—64no—
750C22—98no—
751C22—128no—
752C22—124no—
753C22—184no—
754C22—184no—
755C22—1816no—
756C22—3632no—
757C22C2×#380212yes—
758C22D3×#23512yes—
759C22#6430812yes—
760C22C23×D3211yescharacteristic
761C4—22no—
762C4—22no—
763C4—62no—
764C4—62no—
765C4—64no—
766C4—184no—
767C4C2×#380214yes—
768C3—21no—
769C3C2×#555011yescharacteristic, complemented
770C3C2×#567611yescharacteristic, complemented
771C2—64no—
772C2—124no—
773C2—122no—
774C2—188no—
775C2#1059400714yesdirect product factor
776C2C22×#380211yescharacteristic
777C2C2×D3×#23511yescharacteristic
778C2C2×#6430811yescharacteristic
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×D3×D12C2semidirect
2. C22×#3799C2semidirect
3. C2×C4×C4⋊(C3⋊D3)C2semidirect
4. C2×C3×#875C2semidirect
5. C2×C3×C4×D12C2semidirect
6. C2×#63922C2semidirect
7. C2×#63921C2semidirect
8. C2×#63912C2semidirect
9. C2×#63908C2semidirect
10. C2×#63856C2semidirect
11. C2×#63854C2semidirect
12. #10594007C2direct (N × H)
17. C22×C4×C3⋊D3C22semidirect
21. C22×C3×C4×D3C22semidirect
22. C22×C3×Dic6C22semidirect
24. C22×#626C22semidirect
25. C22×#625C22semidirect
26. C22×#624C22semidirect
28. C2×D3×D12C22semidirect
30. C2×#3799C22semidirect
31. C2×C32×C42C22semidirect
32. C2×#3752C22semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. 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×#3724C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. #63922C22semidirect
46. #63921C22semidirect
47. #63912C22semidirect
48. #63908C22semidirect
49. #63856C22semidirect
50. #63854C22semidirect
71. C2×#875D3semidirect
75. C2×C4×D12D3semidirect
88. C2×C4⋊(C3⋊D3)D4semidirect
91. C2×C4×C3⋊D3C23semidirect
102. C2×C3×C4×D3C23semidirect
104. C2×C3×Dic6C23semidirect
108. C2×#626C23semidirect
110. C2×#625C23semidirect
112. C2×#624C23semidirect
115. C32×C42C23semidirect
116. #3752C23semidirect
117. C4⋊(C3⋊Dic3)C23semidirect
119. C3×(C2×D3)⋊C4C23semidirect
120. C3×(C2×D3)⋊C4C23semidirect
121. C3×(C2×D3)⋊C4C23semidirect
122. C3×C4⋊Dic3C23semidirect
123. #3724C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
159. C22×C4×D3C2×D3semidirect
160. C22×Dic6C2×D3semidirect
169. C2×C3×C42C2×D3semidirect
170. C2×C3×C42C2×D3semidirect
183. C2×(C2×D3)⋊C4C2×D3semidirect
184. C2×(C2×D3)⋊C4C2×D3semidirect
185. C2×(C2×D3)⋊C4C2×D3semidirect
189. C2×C4⋊Dic3C2×D3semidirect
200. #875C2×D3semidirect
204. C4×D12C2×D3semidirect
218. C22×C3×D3#41semidirect
234. C4⋊(C3⋊D3)C2×D4semidirect
347. C2×C4×D3C22×D3semidirect
349. C2×Dic6C22×D3semidirect
356. C3×C42C22×D3semidirect
357. C3×C42C22×D3semidirect
366. (C2×D3)⋊C4C22×D3semidirect
367. (C2×D3)⋊C4C22×D3semidirect
368. (C2×D3)⋊C4C22×D3semidirect
372. C4⋊Dic3C22×D3semidirect
394. C2×C3×D3C2×#41semidirect
438. C2×C42D32semidirect
482. C22×D3#235semidirect
546. C2×C32#546semidirect
603. C42C2×D32semidirect
653. C2×D3C2×#235semidirect
672. C32C2×#546semidirect
726. C2×C3#5550semidirect
727. C2×C3#5676semidirect
769. C3C2×#5550semidirect
770. C3C2×#5676semidirect
775. C2#10594007direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D122
C22×#37992
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8752
C2×C3×C4×D122
C2×#639222
C2×#639212
C2×#639122
C2×#639082
C2×#638562
C2×#638542
#105940072
C2×#56763
C2×#55503