Finite Group Databasebeta

← C2×#10595473 #11918888

Subgroups — C2×#10595473 #11918888

Order 1152.

3369 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C2×C3×#951C211yesmaximal, characteristic, complemented
4C2×C3×#950C211yesmaximal, characteristic, complemented
5#10595473C2116yesmaximal, direct product factor
6C2×#63950C212yesmaximal, complemented
7C2×#63945C212yesmaximal, complemented
8C2×#63937C212yesmaximal, complemented
9C2×#63930C212yesmaximal, complemented
10C22×#3717C211yesmaximal, characteristic, complemented
11C2×#63825C211yesmaximal, characteristic, complemented
12C2×#63817C211yesmaximal, characteristic, complemented
13C2×#5778—31nomaximal
14C2×#5770—31nomaximal
15C2×C32×#41C2211yescharacteristic
16#64366—24no—
17#64366C2218yescomplemented
18C2×#3832C2212yes—
19C2×D4×C3⋊D3—22no—
20C2×D4×C3⋊D3C2212yes—
21C2×#3828—21no—
22C2×#3828C2211yescharacteristic
23C22×C4⋊(C3⋊D3)—21no—
24C22×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic, complemented
26C22×C3×Dic6C2211yescharacteristic, complemented
27C2×#3804—22no—
28C2×#3799—21no—
29C2×#3797C2212yescomplemented
30#64297—24no—
31#64297C2218yescomplemented
32C2×#3796C2212yescomplemented
33C2×D3×Dic6—21no—
34C3×#951C2218yescomplemented
35C3×#950C2218yescomplemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#216C2212yescomplemented
38C2×C3×#215C2211yescharacteristic, complemented
39C2×C3×#214C2211yescharacteristic, complemented
40C2×C3×#214C2212yescomplemented
41C2×C3×#213C2211yescharacteristic, complemented
42C2×C3×#208C2211yescharacteristic, complemented
43C22×C3×C3⋊C8C2211yescharacteristic, complemented
44#63950C22116yescomplemented
45#63945C22116yescomplemented
46#63937C22116yescomplemented
47#63930C22116yescomplemented
48C2×#3717C2212yescomplemented
49C2×#3717C2212yescomplemented
50C2×#3717C2212yescomplemented
51C2×#3717C2218yescomplemented
52#63825C2218yescomplemented
53C2×#3714C2212yescomplemented
54C2×#3712C2212yescomplemented
55#63817C2218yescomplemented
56C2×#3710C2212yescomplemented
57C2×#1010—31no—
58C2×#1009—31no—
59C2×#1009—31no—
60C2×#1009—61no—
61C2×#1007—31no—
62C2×C3×#137—31no—
63C2×C3×#135—31no—
64C2×#951D311yescharacteristic, complemented
65C2×#950D311yescharacteristic, complemented
66C2×#949—31no—
67C22×#215—31no—
68#5778—316no—
69#5770—316no—
70C2×#919—32no—
71C2×#918—32no—
72C2×#918—32no—
73C2×#916—32no—
74C2×#914—32no—
75C2×D3×SD16—32no—
76C2×D3×SD16—32no—
77C2×#911—32no—
78C2×#908—31no—
79C2×#907—31no—
80C22×#204—31no—
81C2×#901—31no—
82C23×C3⋊D3—21no—
83C23×C3⋊D3—22no—
84C32×#41—22no—
85C32×#41C2314yes—
86C2×C32×Q8C2311yescharacteristic
87C2×C32×D4—21no—
88C2×C32×D4C2311yescharacteristic
89C22×C32×C4—21no—
90C22×C32×C4C2311yescharacteristic
91C2×#638—22no—
92C2×#638D412yes—
93#3832—24no—
94#3832C2318yes—
95D4×C3⋊D3—216no—
96D4×C3⋊D3—24no—
97D4×C3⋊D3C2318yes—
98#3828—28no—
99#3828D414yes—
100#3828C2314yes—
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)—22no—
104C2×C4⋊(C3⋊D3)—28no—
105C2×C4⋊(C3⋊D3)D411yescharacteristic
106C2×C4⋊(C3⋊D3)C2312yes—
107C2×C4⋊(C3⋊D3)C2314yes—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3C2312yes—
110C2×#634D411yescharacteristic
111C2×C3×#67—21no—
112C22×C3×Dic3—21no—
113C3×#235—22no—
114C3×#235C2314yescomplemented
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×Dic6—21no—
118C2×C3×Dic6—22no—
119C2×C3×Dic6C2312yes—
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2314yescomplemented
122C2×#627—22no—
123C2×#626—22no—
124C2×#624—22no—
125#3804—216no—
126C2×D3×Dic3—22no—
127#3799—28no—
128#3797—24no—
129#3797C2318yescomplemented
130#3796—24no—
131#3796C2318yescomplemented
132D3×Dic6—28no—
133C3×#216C2314yescomplemented
134C3×#216C2318yescomplemented
135C3×#215C2314yescomplemented
136C3×#214C2314yescomplemented
137C3×#214C2318yescomplemented
138C3×#213C2314yescomplemented
139C3×#208C2314yescomplemented
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2312yes—
143C2×C3×C3⋊C8C2314yescomplemented
144#3717C2318yescomplemented
145#3717C2318yescomplemented
146#3717C2318yescomplemented
147#3714C2318yescomplemented
148#3712C2318yescomplemented
149#3710C2318yescomplemented
150C2×#577—91noSylow
151C2×C3×#41—21no—
152C2×C3×#41—31no—
153C2×C3×#41C2×D311yescharacteristic
154C2×C3×#41C2×D311yescharacteristic
155C22×C3×Q8—31no—
156#1010—38no—
157#1010—64no—
158#1009—38no—
159#1009—38no—
160#1009—68no—
161#1009—64no—
162#1009—64no—
163#1009—68no—
164#1007—38no—
165#1007—64no—
166C2×#239—32no—
167C2×#239—32no—
168C2×#239—32no—
169C2×#239—62no—
170C2×#239—61no—
171C2×D3×Q8—32no—
172C2×D3×Q8—32no—
173C2×D3×Q8—61no—
174C2×#237—32no—
175C2×#237—62no—
176C2×D3×D4—32no—
177C2×D3×D4—32no—
178C2×D3×D4—62no—
179C2×D3×D4—62no—
180C2×D3×D4—62no—
181C2×D3×D4—64no—
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—61no—
185C2×#235—61no—
186C2×#235—61no—
187C2×#235—61no—
188C2×#235—62no—
189C2×#235—62no—
190C2×#235C2×D311yescharacteristic, complemented
191C22×D12—31no—
192C22×D12—31no—
193C22×D12—61no—
194C22×D12—61no—
195C22×D12—61no—
196C22×D12—62no—
197C22×Dic6—61no—
198C22×Dic6C2×D311yescharacteristic, complemented
199C3×#137—38no—
200C3×#135—38no—
201C2×C3×Q16—31no—
202C2×C3×Q16—32no—
203C2×C3×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×SD16—32no—
206C2×C3×D8—31no—
207C2×C3×M16—31no—
208C22×C3×C8—31no—
209#951C2×D318yescomplemented
210#950C2×D318yescomplemented
211#949—38no—
212C2×#216C2×D312yescomplemented
213C2×#216C2×D311yescharacteristic, complemented
214C2×#215—32no—
215C2×#215—32no—
216C2×#215—32no—
217C2×#215—38no—
218C2×#215C2×D311yescharacteristic, complemented
219C2×#214C2×D312yescomplemented
220C2×#214C2×D311yescharacteristic, complemented
221C2×#213—32no—
222C2×#213C2×D311yescharacteristic, complemented
223C2×#208C2×D311yescharacteristic, complemented
224C22×C3⋊C8C2×D311yescharacteristic, complemented
225#919—316no—
226#918—316no—
227#918—316no—
228#916—316no—
229#914—316no—
230D3×SD16—316no—
231D3×SD16—316no—
232#911—316no—
233#908—38no—
234#907—38no—
235C2×D24—32no—
236C2×#204—32no—
237C2×#204—32no—
238C2×#204—32no—
239C2×#204—38no—
240#901—38no—
241C2×ΓL(1,𝔽25)—32no—
242C2×ΓL(1,𝔽25)—32no—
243C2×D3×C8—32no—
244C2×D3×C8—32no—
245C23×C32—21no—
246C23×C32C2×D411yescharacteristic
247C22×C3⋊D3—22no—
248C22×C3⋊D3—24no—
249C22×C3⋊D3—28no—
250C22×C3⋊D3—84no—
251C22×C3⋊D3—82no—
252C22×C3⋊D3C2×D412yes—
253C22×C3×D3—21no—
254C32×Q8—21no—
255C32×Q8C2412yes—
256C32×D4—24no—
257C32×D4—21no—
258C32×D4C2412yes—
259C2×C32×C4—21no—
260C2×C32×C4—24no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2×D412yes—
263C2×C32×C4C2411yescharacteristic
264C2×C32×C4C2412yes—
265#638—28no—
266#638C2×D418yes—
267C2×C3⋊Dic3C2×D412yes—
268C4⋊(C3⋊D3)—28no—
269C4⋊(C3⋊D3)—24no—
270C4⋊(C3⋊D3)—22no—
271C4⋊(C3⋊D3)C2×D414yes—
272C4⋊(C3⋊D3)C2414yes—
273C4×C3⋊D3—28no—
274C4×C3⋊D3C2×D414yes—
275C4×C3⋊D3C2414yes—
276#634C2×D414yes—
277C3×#67—24no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—24no—
280C2×C3×Dic3—21no—
281C3×D12—21no—
282C3×D12C2412yes—
283C3×C4×D3—24no—
284C3×Dic6—24no—
285C3×Dic6—22no—
286C3×Dic6—21no—
287C3×Dic6C2414yes—
288C3×Dic6C2412yes—
289#627—28no—
290#626—28no—
291#624—28no—
292D3×Dic3—28no—
293C3×C3⋊C8C2412yes—
294C3×C3⋊C8C2414yes—
295C3×C3⋊C8C2412yes—
296C2×2−1+4—91no—
297C2×H(5,𝔽2)—91no—
298#577—916no—
299C2×#137—31no—
300C2×#137—92no—
301C2×AGL(1,ℤ/8)—91no—
302C2×AGL(1,ℤ/8)—92no—
303C2×#135—31no—
304C2×#135—92no—
305C22×SD16—91no—
306C22×SD16—92no—
307C2×#131—91no—
308C23×D3—62no—
309C23×D3—62no—
310C23×D3—64no—
311C23×D3—62no—
312C23×D3—61no—
313C23×D3—61no—
314C3×#41—24no—
315C3×#41—22no—
316C3×#41—22no—
317C3×#41—24no—
318C3×#41—34no—
319C3×#41—62no—
320C3×#41C22×D314yes—
321C3×#41C22×D314yes—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—32no—
325C2×C3×Q8—34no—
326C2×C3×Q8—61no—
327C2×C3×Q8—62no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—22no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—61no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—22no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C2×#67—21no—
347C2×#67—32no—
348C2×#67—32no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—64no—
354C22×Dic3—21no—
355C22×Dic3—62no—
356#239—38no—
357#239—38no—
358#239—38no—
359#239—68no—
360#239—68no—
361#239—64no—
362#239—64no—
363#239—64no—
364#239—68no—
365D3×Q8—38no—
366D3×Q8—38no—
367D3×Q8—64no—
368D3×Q8—64no—
369D3×Q8—68no—
370#237—38no—
371#237—64no—
372#237—616no—
373D3×D4—38no—
374D3×D4—38no—
375D3×D4—68no—
376D3×D4—64no—
377D3×D4—64no—
378D3×D4—616no—
379D3×D4—616no—
380D3×D4—68no—
381D3×D4—632no—
382#235—22no—
383#235—34no—
384#235—34no—
385#235—34no—
386#235—34no—
387#235—64no—
388#235—64no—
389#235—68no—
390#235—68no—
391#235—68no—
392#235—616no—
393#235—616no—
394#235C22×D314yescomplemented
395C2×D12—31no—
396C2×D12—31no—
397C2×D12—32no—
398C2×D12—34no—
399C2×D12—32no—
400C2×D12—34no—
401C2×D12—61no—
402C2×D12—62no—
403C2×D12—64no—
404C2×D12—68no—
405C2×D12—68no—
406C2×D12—62no—
407C2×D12—62no—
408C2×D12—62no—
409C2×D12—64no—
410C2×D12—616no—
411C2×D12—64no—
412C2×D12—62no—
413C2×D12—61no—
414C2×D12—61no—
415C2×D12—62no—
416C2×D12—62no—
417C2×D12C22×D311yescharacteristic
418C2×C4×D3—21no—
419C2×C4×D3—32no—
420C2×C4×D3—32no—
421C2×C4×D3—62no—
422C2×C4×D3—62no—
423C2×C4×D3—62no—
424C2×C4×D3—62no—
425C2×C4×D3—62no—
426C2×C4×D3—62no—
427C2×C4×D3—64no—
428C2×Dic6—21no—
429C2×Dic6—22no—
430C2×Dic6—31no—
431C2×Dic6—31no—
432C2×Dic6—61no—
433C2×Dic6—68no—
434C2×Dic6—62no—
435C2×Dic6—62no—
436C2×Dic6C22×D312yes—
437C2×Dic6C22×D311yescharacteristic
438C2×Dic6C22×D314yescomplemented
439C3×Q16—34no—
440C3×Q16—38no—
441C3×SD16—34no—
442C3×SD16—34no—
443C3×SD16—38no—
444C3×D8—34no—
445C3×M16—34no—
446C2×C3×C8—31no—
447C2×C3×C8—32no—
448C2×C3×C8—31no—
449C2×C3×C8—34no—
450#216C22×D318yescomplemented
451#216C22×D314yescomplemented
452#215—38no—
453#215—38no—
454#215—38no—
455#215C22×D314yescomplemented
456#214C22×D318yescomplemented
457#214C22×D314yescomplemented
458#213—38no—
459#213C22×D314yescomplemented
460#208C22×D314yescomplemented
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D312yes—
463C2×C3⋊C8C22×D311yescharacteristic
464C2×C3⋊C8C22×D314yescomplemented
465D24—38no—
466#204—38no—
467#204—38no—
468#204—38no—
469ΓL(1,𝔽25)—38no—
470ΓL(1,𝔽25)—38no—
471D3×C8—38no—
472D3×C8—38no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—42no—
476C22×C32C22×D412yes—
477C22×C32C22×D411yescharacteristic
478C2×C3⋊D3—24no—
479C2×C3⋊D3—24no—
480C2×C3⋊D3—44no—
481C2×C3⋊D3—88no—
482C2×C3⋊D3—84no—
483C2×C3⋊D3C22×D414yes—
484C2×C3×D3—22no—
485C2×C3×D3—42no—
486C32×C4—22no—
487C32×C4C22×D411yescharacteristic
488C32×C4C22×D412yes—
489C32×C4C2511yescharacteristic
490C3⋊Dic3C22×D414yes—
491C3×Dic3—24no—
492C3×Dic3—22no—
4932−1+4—98no—
4942−1+4—184no—
495H(5,𝔽2)—98no—
496H(5,𝔽2)—184no—
497C2×#41—31no—
498C2×#41—91no—
499C2×#41—92no—
500C2×#41—92no—
501C2×#41—181no—
502C2×#41—182no—
503C2×#41—181no—
504C2×#41D3211yescharacteristic
505C22×Q8—31no—
506C22×Q8—92no—
507C22×Q8—181no—
508C22×D4—92no—
509C22×D4—91no—
510C22×D4—181no—
511C22×D4—182no—
512#137—38no—
513#137—916no—
514AGL(1,ℤ/8)—98no—
515AGL(1,ℤ/8)—916no—
516#135—38no—
517#135—916no—
518C2×Q16—31no—
519C2×Q16—32no—
520C2×SD16—31no—
521C2×SD16—31no—
522C2×SD16—32no—
523C2×SD16—92no—
524C2×SD16—92no—
525C2×SD16—92no—
526C2×SD16—98no—
527C2×SD16—916no—
528C2×D8—31no—
529C2×D8—92no—
530#131—98no—
531C2×M16—31no—
532C2×M16—92no—
533C22×C8—31no—
534C22×C8—92no—
535C23×C3—22no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—61no—
540C23×C3D3×D411yescharacteristic
541C23×C3D3×D411yescharacteristic
542C22×D3—21no—
543C22×D3—32no—
544C22×D3—32no—
545C22×D3—62no—
546C22×D3—68no—
547C22×D3—68no—
548C22×D3—64no—
549C22×D3—62no—
550C22×D3—62no—
551C22×D3—616no—
552C22×D3—68no—
553C22×D3—64no—
554C22×D3—64no—
555C22×D3—244no—
556C22×D3—244no—
557C22×D3—242no—
558C22×D3—242no—
559C22×D3—244no—
560C22×D3—248no—
561C3×Q8—22no—
562C3×Q8—21no—
563C3×Q8—21no—
564C3×Q8—22no—
565C3×Q8—32no—
566C3×Q8—34no—
567C3×Q8—61no—
568C3×Q8—62no—
569C3×Q8—64no—
570C3×Q8C23×D312yes—
571C3×Q8C23×D312yes—
572C3×D4—28no—
573C3×D4—22no—
574C3×D4—24no—
575C3×D4—24no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—22no—
579C3×D4—32no—
580C3×D4—64no—
581C3×D4—61no—
582C3×D4C23×D312yes—
583C3×D4C23×D312yes—
584C2×C3×C4—22no—
585C2×C3×C4—28no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—24no—
589C2×C3×C4—24no—
590C2×C3×C4—21no—
591C2×C3×C4—22no—
592C2×C3×C4—21no—
593C2×C3×C4—22no—
594C2×C3×C4—61no—
595C2×C3×C4—62no—
596C2×C3×C4—64no—
597C2×C3×C4—64no—
598C2×C3×C4D3×D411yescharacteristic
599C2×C3×C4D3×D412yes—
600C2×C3×C4D3×D411yescharacteristic
601C2×C3×C4D3×D412yes—
602C2×C3×C4C23×D311yescharacteristic
603C2×C3×C4C23×D311yescharacteristic
604C2×C3×C4C23×D312yes—
605C2×C3×C4C23×D312yes—
606#67—24no—
607#67—38no—
608#67—38no—
609#67—68no—
610#67—68no—
611#67—68no—
612#67—68no—
613#67—616no—
614C2×Dic3—22no—
615C2×Dic3—24no—
616C2×Dic3—21no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—62no—
620C2×Dic3—68no—
621D12—21no—
622D12—34no—
623D12—34no—
624D12—34no—
625D12—34no—
626D12—64no—
627D12—64no—
628D12—68no—
629D12—68no—
630D12—68no—
631D12—616no—
632D12—64no—
633D12—68no—
634D12—64no—
635D12—64no—
636D12—62no—
637D12—62no—
638D12C23×D312yes—
639C4×D3—24no—
640C4×D3—34no—
641C4×D3—34no—
642C4×D3—34no—
643C4×D3—34no—
644C4×D3—64no—
645C4×D3—64no—
646C4×D3—68no—
647C4×D3—68no—
648C4×D3—68no—
649C4×D3—68no—
650C4×D3—68no—
651C4×D3—616no—
652Dic6—24no—
653Dic6—22no—
654Dic6—21no—
655Dic6—34no—
656Dic6—34no—
657Dic6—64no—
658Dic6—68no—
659Dic6—68no—
660Dic6C23×D314yes—
661Dic6C23×D312yes—
662C3×C8—32no—
663C3×C8—34no—
664C3×C8—32no—
665C3⋊C8C23×D312yes—
666C3⋊C8C23×D314yes—
667C3⋊C8C23×D312yes—
668C2×C32—22no—
669C2×C32—42no—
670C2×C32#57712yescomplemented
671C2×C32C23×D411yescharacteristic
672C3⋊D3—24no—
673C3⋊D3—44no—
674C3×D3—42no—
675C24—182no—
676C24—181no—
677#41—22no—
678#41—34no—
679#41—62no—
680#41—94no—
681#41—94no—
682#41—98no—
683#41—98no—
684#41—188no—
685#41—1816no—
686#41—188no—
687#41—184no—
688#41—184no—
689#41C2×D3214yes—
690C2×Q8—32no—
691C2×Q8—31no—
692C2×Q8—34no—
693C2×Q8—61no—
694C2×Q8—62no—
695C2×Q8—91no—
696C2×Q8—98no—
697C2×Q8—182no—
698C2×Q8—188no—
699C2×Q8—184no—
700C2×Q8C2×D3211yescharacteristic
701C2×D4—21no—
702C2×D4—31no—
703C2×D4—61no—
704C2×D4—92no—
705C2×D4—98no—
706C2×D4—92no—
707C2×D4—94no—
708C2×D4—91no—
709C2×D4—188no—
710C2×D4—182no—
711C2×D4—182no—
712C2×D4—184no—
713C2×D4—182no—
714C2×D4—1816no—
715C2×D4—181no—
716C2×D4—182no—
717C2×D4C2×D3211yescharacteristic
718C22×C4—21no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—92no—
722C22×C4—182no—
723C22×C4—182no—
724C22×C4—182no—
725C22×C4C2×D3211yescharacteristic
726Q16—34no—
727Q16—38no—
728SD16—34no—
729SD16—34no—
730SD16—38no—
731SD16—98no—
732SD16—98no—
733SD16—98no—
734D8—34no—
735D8—98no—
736M16—34no—
737M16—98no—
738C2×C8—31no—
739C2×C8—31no—
740C2×C8—34no—
741C2×C8—32no—
742C2×C8—98no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—24no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—42no—
751C22×C3—44no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—62no—
755C22×C3—122no—
756C22×C3C2×D3×D412yes—
757C22×C3C2×D3×D412yes—
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C2×D3—22no—
761C2×D3—34no—
762C2×D3—34no—
763C2×D3—42no—
764C2×D3—64no—
765C2×D3—64no—
766C2×D3—64no—
767C2×D3—68no—
768C2×D3—64no—
769C2×D3—64no—
770C2×D3—124no—
771C2×D3—128no—
772C2×D3—124no—
773C2×D3—124no—
774C2×D3—248no—
775C2×D3—248no—
776C2×D3—244no—
777C2×D3—244no—
778C2×D3—248no—
779C2×D3—2416no—
780C3×C4—24no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—62no—
787C3×C4—64no—
788C3×C4C2×D3×D412yes—
789C3×C4C2×D3×D411yescharacteristic
790C3×C4C2×D3×D411yescharacteristic
791C3×C4C2×D3×D412yes—
792C3×C4C24×D311yescharacteristic
793C3×C4C24×D311yescharacteristic
794Dic3—24no—
795Dic3—22no—
796Dic3—34no—
797Dic3—34no—
798Dic3—64no—
799C32C2×#57711yescharacteristic, complemented, Sylow
800C23—21no—
801C23—61no—
802C23—92no—
803C23—188no—
804C23—182no—
805C23—184no—
806C23—722no—
807C23—724no—
808C23#381111yescharacteristic
809Q8—21no—
810Q8—34no—
811Q8—32no—
812Q8—64no—
813Q8—62no—
814Q8—61no—
815Q8—94no—
816Q8—188no—
817Q8C22×D3212yes—
818D4—24no—
819D4—21no—
820D4—32no—
821D4—64no—
822D4—61no—
823D4—98no—
824D4—94no—
825D4—94no—
826D4—188no—
827D4—188no—
828D4—188no—
829D4—184no—
830D4—182no—
831D4C22×D3212yes—
832C2×C4—21no—
833C2×C4—24no—
834C2×C4—64no—
835C2×C4—61no—
836C2×C4—62no—
837C2×C4—64no—
838C2×C4—92no—
839C2×C4—94no—
840C2×C4—94no—
841C2×C4—188no—
842C2×C4—188no—
843C2×C4—188no—
844C2×C4#381112yes—
845C2×C4#381111yescharacteristic
846C2×C4C22×D3212yes—
847C2×C4C22×D3211yescharacteristic
848C8—32no—
849C8—32no—
850C8—34no—
851C2×C3—22no—
852C2×C3—22no—
853C2×C3—21no—
854C2×C3—22no—
855C2×C3—42no—
856C2×C3—44no—
857C2×C3—42no—
858C2×C3—42no—
859C2×C3—122no—
860C2×C3#577012yescomplemented
861C2×C3#577812yescomplemented
862C2×C3C22×D3×D411yescharacteristic
863C2×C3C22×D3×D411yescharacteristic
864D3—42no—
865D3—64no—
866D3—64no—
867D3—124no—
868D3—128no—
869D3—124no—
870D3—124no—
871C22—22no—
872C22—22no—
873C22—42no—
874C22—62no—
875C22—94no—
876C22—122no—
877C22—184no—
878C22—184no—
879C22—364no—
880C22—724no—
881C22—728no—
882C22C2×#381112yes—
883C22C2×#381111yescharacteristic
884C4—22no—
885C4—62no—
886C4—64no—
887C4—94no—
888C4C2×#381112yes—
889C4C2×#381111yescharacteristic
890C4C23×D3211yescharacteristic
891C3—21no—
892C3C2×#577011yescharacteristic, complemented
893C3C2×#577811yescharacteristic, complemented
894C2—22no—
895C2—42no—
896C2—122no—
897C2—184no—
898C2—364no—
899C2#1059547312yesdirect product factor
900C2C22×#381111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C2×#64297C2semidirect
3. C2×C3×#951C2semidirect
4. C2×C3×#950C2semidirect
5. #10595473C2direct (N × H)
6. C2×#63950C2semidirect
7. C2×#63945C2semidirect
8. C2×#63937C2semidirect
9. C2×#63930C2semidirect
10. C22×#3717C2semidirect
11. C2×#63825C2semidirect
12. C2×#63817C2semidirect
17. #64366C22semidirect
25. C2×C3×#235C22semidirect
26. C22×C3×Dic6C22semidirect
29. C2×#3797C22semidirect
31. #64297C22semidirect
32. C2×#3796C22semidirect
34. C3×#951C22semidirect
35. C3×#950C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#216C22semidirect
38. C2×C3×#215C22semidirect
39. C2×C3×#214C22semidirect
40. C2×C3×#214C22semidirect
41. C2×C3×#213C22semidirect
42. C2×C3×#208C22semidirect
43. C22×C3×C3⋊C8C22semidirect
44. #63950C22semidirect
45. #63945C22semidirect
46. #63937C22semidirect
47. #63930C22semidirect
48. C2×#3717C22semidirect
49. C2×#3717C22semidirect
50. C2×#3717C22semidirect
51. C2×#3717C22semidirect
52. #63825C22semidirect
53. C2×#3714C22semidirect
54. C2×#3712C22semidirect
55. #63817C22semidirect
56. C2×#3710C22semidirect
64. C2×#951D3semidirect
65. C2×#950D3semidirect
114. C3×#235C23semidirect
121. C2×C3×Dic6C23semidirect
129. #3797C23semidirect
131. #3796C23semidirect
133. C3×#216C23semidirect
134. C3×#216C23semidirect
135. C3×#215C23semidirect
136. C3×#214C23semidirect
137. C3×#214C23semidirect
138. C3×#213C23semidirect
139. C3×#208C23semidirect
143. C2×C3×C3⋊C8C23semidirect
144. #3717C23semidirect
145. #3717C23semidirect
146. #3717C23semidirect
147. #3714C23semidirect
148. #3712C23semidirect
149. #3710C23semidirect
190. C2×#235C2×D3semidirect
198. C22×Dic6C2×D3semidirect
209. #951C2×D3semidirect
210. #950C2×D3semidirect
212. C2×#216C2×D3semidirect
213. C2×#216C2×D3semidirect
218. C2×#215C2×D3semidirect
219. C2×#214C2×D3semidirect
220. C2×#214C2×D3semidirect
222. C2×#213C2×D3semidirect
223. C2×#208C2×D3semidirect
224. C22×C3⋊C8C2×D3semidirect
394. #235C22×D3semidirect
438. C2×Dic6C22×D3semidirect
450. #216C22×D3semidirect
451. #216C22×D3semidirect
455. #215C22×D3semidirect
456. #214C22×D3semidirect
457. #214C22×D3semidirect
459. #213C22×D3semidirect
460. #208C22×D3semidirect
464. C2×C3⋊C8C22×D3semidirect
670. C2×C32#577semidirect
799. C32C2×#577semidirect
860. C2×C3#5770semidirect
861. C2×C3#5778semidirect
892. C3C2×#5770semidirect
893. C3C2×#5778semidirect
899. C2#10595473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643662
C2×#642972
C2×C3×#9512
C2×C3×#9502
#105954732
C2×#639502
C2×#639452
C2×#639372
C2×#639302
C22×#37172
C2×#638252
C2×#638172
C2×#57783
C2×#57703