Finite Group Databasebeta

← #11903637

Subgroups — #11903637

Order 1152.

2410 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596197C211yesmaximal, characteristic, complemented
2C3×#5732C211yesmaximal, characteristic, complemented
3C3×#5728C211yesmaximal, characteristic, complemented
4#10595431C212yesmaximal, complemented
5#10595386C212yesmaximal, complemented
6#10595382C212yesmaximal, complemented
7#10595379C212yesmaximal, complemented
8#10594654C214yesmaximal, complemented
9#10594627C212yesmaximal, complemented
10#10594602C212yesmaximal, complemented
11#10594579C212yesmaximal, complemented
12#10594578C212yesmaximal, complemented
13#10594423C214yesmaximal, complemented
14C4×D3×D12C211yesmaximal, characteristic, complemented
15#10593987C211yesmaximal, characteristic, complemented
16C4×#3799C211yesmaximal, characteristic, complemented
17#10593958C211yesmaximal, characteristic, complemented
18#86979—31nomaximal
19#86276—31nomaximal
20C2×#3832C2212yes—
21C2×D3×D12C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×#3799C2211yescharacteristic
24C32×C4⋊Q8C2211yescharacteristic, complemented
25#64155C2212yescomplemented
26#64104C2212yescomplemented
27#64103C2214yescomplemented
28C4⋊C4×C3⋊D3C2212yescomplemented
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
31C3×#947C2212yes—
32C3×#946C2212yes—
33C3×Q8×Dic3C2212yescomplemented
34C3×Q8×Dic3C2212yescomplemented
35C3×#898C2214yescomplemented
36C3×#897C2212yes—
37C3×#897C2212yescomplemented
38C3×#892C2212yes—
39C3×#892C2212yescomplemented
40C3×#890C2212yescomplemented
41C3×#887C2212yescomplemented
42C3×C4×D12C2211yescharacteristic
43C3×C42×D3C2211yescharacteristic
44C3×#869C2211yescharacteristic, complemented
45C3×C4×Dic6C2211yescharacteristic, complemented
46#63923C2214yes—
47#63921C2214yes—
48D3×(C2×D3)⋊C4C2212yes—
49#63916C2212yes—
50#63910C2214yes—
51#63909C2212yescomplemented
52#63907C2214yescomplemented
53#63904C2212yes—
54C4×#626C2212yes—
55C4×#626C2212yes—
56#63900C2212yescomplemented
57#63894C2211yescharacteristic
58#63894C2212yes—
59#63894C2211yescharacteristic, complemented
60#63894C2214yescomplemented
61#63894C2214yescomplemented
62Dic3×D12C2211yescharacteristic
63#63890C2214yes—
64D3×C4⋊Dic3C2211yescharacteristic
65#63888C2214yescomplemented
66C4×#624C2214yescomplemented
67C4×#624C2212yescomplemented
68#63880C2212yes—
69#63880C2214yescomplemented
70#63877C2214yes—
71#63877C2214yescomplemented
72#63871C2212yescomplemented
73#63869C2212yescomplemented
74#63868C2214yescomplemented
75#63858C2214yescomplemented
76#63854C2214yescomplemented
77#63853C2214yes—
78#63849C2214yescomplemented
79#63849C2212yescomplemented
80#63846C2214yescomplemented
81Dic3×Dic6C2211yescharacteristic, complemented
82#63841C2211yescharacteristic
83#63841C2212yescomplemented
84#63836C2212yescomplemented
85C3×#556—31no—
86C3×#533—31no—
87#5734—31no—
88#5732D311yescharacteristic, complemented
89#5730—31no—
90#5728D311yescharacteristic, complemented
91#5726—31no—
92#5726—31no—
93#5726—61no—
94#5706—34no—
95#5705—34no—
96#5695—32no—
97#5694—32no—
98#5680—32no—
99#5676—32no—
100#5642—32no—
101#5639—32no—
102#5637—34no—
103#5630—32no—
104#5627—32no—
105#5581—32no—
106#5580—32no—
107#5580—34no—
108#5579—31no—
109C4×#239—32no—
110C4×#239—32no—
111C4×#239—31no—
112#5563—31no—
113C4×D3×D4—31no—
114#5530—32no—
115#5524—32no—
116D3×#117—32no—
117D3×#117—32no—
118C4×#235—31no—
119C2×C4×D12—31no—
120C22×D32C2312yes—
121C2×C32×Q8C2312yes—
122#3832—28no—
123C2×C4⋊(C3⋊D3)C2311yescharacteristic
124C2×C4⋊(C3⋊D3)C2314yes—
125C2×C4⋊(C3⋊D3)C2311yescharacteristic
126C2×C4×C3⋊D3C2312yes—
127C2×C4×C3⋊D3C2312yes—
128C2×C4×C3⋊D3C2314yes—
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×Dic6C2311yescharacteristic
135C2×C3×Dic6C2312yes—
136C2×#626C2312yes—
137C2×#626C2312yes—
138C2×#626C2314yes—
139C2×#624C2312yes—
140C2×#624C2312yes—
141C2×#624C2312yes—
142C2×#624C2314yes—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2312yes—
145D3×D12—24no—
146C4×D32—28no—
147#3799—24no—
148C32×C4⋊C4C2312yes—
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151#3752C2312yes—
152#3752C2312yes—
153#3752C2314yes—
154C4⋊(C3⋊Dic3)C2311yescharacteristic
155C4⋊(C3⋊Dic3)C2311yescharacteristic
156#3750C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2314yes—
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2314yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2312yes—
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2314yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2314yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2312yes—
175#3724C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179#3722C2312yes—
180#3722C2312yes—
181#3722C2314yes—
182#3722C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186Dic32C2312yes—
187Dic32C2314yes—
188Dic32C2312yes—
189#3475—91noSylow
190C2×#239—32no—
191C2×#239—32no—
192C2×#239—31no—
193C2×#239—62no—
194C2×D3×D4—31no—
195C2×#235—31no—
196C22×D12—31no—
197C22×C4×D3—32no—
198C22×C4×D3—32no—
199C3×C4⋊Q8—21no—
200C3×C4⋊Q8—31no—
201C3×C4⋊Q8C2×D311yescharacteristic, complemented
202C3×C4⋊Q8C2×D311yescharacteristic, complemented
203C3×#126—34no—
204C3×#125—32no—
205C3×#124—32no—
206C3×C22⋊Q8—32no—
207C3×C22⋊Q8—32no—
208C3×C22⋊Q8—32no—
209C3×C4×Q8—32no—
210C3×C4×Q8—32no—
211C3×C4×Q8—32no—
212C3×C4×Q8—31no—
213C3×C4×D4—31no—
214C3×#117—32no—
215C3×#117—32no—
216C2×C3×C42—31no—
217#947—34no—
218#947C2×D312yes—
219#946—32no—
220#946—32no—
221#946—32no—
222#946—34no—
223#946—62no—
224#946C2×D312yes—
225Q8×Dic3—31no—
226Q8×Dic3C2×D312yescomplemented
227Q8×Dic3C2×D312yescomplemented
228#938—32no—
229D4×Dic3—31no—
230#930—32no—
231C4×#67—32no—
232C4×#67—32no—
233C4×#67—32no—
234C2×(C2×D3)⋊C4—32no—
235#926—32no—
236#926—31no—
237C2×C4⋊Dic3—31no—
238#898—34no—
239#898—34no—
240#898C2×D314yescomplemented
241#897—32no—
242#897C2×D312yes—
243#897C2×D312yescomplemented
244#896—34no—
245#895—32no—
246#895—32no—
247#895—32no—
248#895—32no—
249#895—34no—
250#895—62no—
251#894—34no—
252#894—34no—
253#894—34no—
254#894—34no—
255#894—34no—
256#894—64no—
257#893—32no—
258#893—34no—
259#893—34no—
260#893—32no—
261#893—31no—
262#893—31no—
263#892—32no—
264#892—31no—
265#892—34no—
266#892—34no—
267#892—32no—
268#892—32no—
269#892—32no—
270#892C2×D312yes—
271#892C2×D312yescomplemented
272D3×C4⋊C4—31no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4—32no—
275D3×C4⋊C4—32no—
276D3×C4⋊C4—32no—
277D3×C4⋊C4—62no—
278#890—34no—
279#890—32no—
280#890C2×D312yescomplemented
281#889—34no—
282#887C2×D312yescomplemented
283#886—34no—
284#885—34no—
285#884—34no—
286#883—34no—
287#883—34no—
288#882—34no—
289#882—34no—
290#67⋊C4—34no—
291#67⋊C4—32no—
292D3×C22⋊C4—32no—
293D3×C22⋊C4—34no—
294D3×C22⋊C4—34no—
295#879—34no—
296#877—34no—
297#877—34no—
298#876—34no—
299C4×D12—31no—
300C4×D12—32no—
301C4×D12—32no—
302C4×D12—31no—
303C4×D12—31no—
304C4×D12—31no—
305C4×D12—31no—
306C4×D12—32no—
307C4×D12—34no—
308C4×D12—32no—
309C4×D12—31no—
310C4×D12—34no—
311C4×D12—31no—
312C4×D12—34no—
313C4×D12—61no—
314C4×D12—61no—
315C4×D12C2×D311yescharacteristic
316#872—34no—
317#872—34no—
318#872—32no—
319C42×D3—32no—
320C42×D3—34no—
321C42×D3—32no—
322C42×D3—34no—
323C42×D3C2×D311yescharacteristic
324#870—32no—
325#869C2×D311yescharacteristic, complemented
326C4×Dic6—31no—
327C4×Dic6C2×D311yescharacteristic, complemented
328C22×C3⋊D3C2412yes—
329C22×C3⋊D3C2412yes—
330C22×C3×D3C2412yes—
331C22×C3×D3C2411yescharacteristic
332C2×D32—24no—
333C2×D32—24no—
334C2×D32—42no—
335C32×Q8—24no—
336C2×C32×C4C2414yes—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2412yes—
342C4⋊(C3⋊D3)—28no—
343C4⋊(C3⋊D3)—22no—
344C4⋊(C3⋊D3)#4114yescomplemented
345C4×C3⋊D3—28no—
346C4×C3⋊D3—24no—
347C4×C3⋊D3—24no—
348C2×C3×Dic3C2411yescharacteristic
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2411yescharacteristic
355C3×D12—22no—
356C3×C4×D3—24no—
357C3×C4×D3—22no—
358C3×C4×D3—41no—
359C3×C4×D3#4114yescomplemented
360C3×Dic6—22no—
361C3×Dic6—42no—
362#626—24no—
363#626—24no—
364#626—44no—
365#624—24no—
366#624—24no—
367#624—42no—
368#624—44no—
369D3×Dic3—24no—
370D3×Dic3—24no—
371#556—31no—
372#555—91no—
373#554—91no—
374#553—92no—
375#552—92no—
376#552—92no—
377#551—94no—
378#547—91no—
379#546—92no—
380#533—31no—
381#529—92no—
382#529—94no—
383#525—92no—
384C4×#41—91no—
385C4×#41—92no—
386C2×C4×D4—91no—
387C2×#117—92no—
388C23×D3—32no—
389C23×D3—32no—
390C2×C3×Q8—22no—
391C2×C3×Q8—31no—
392C2×C3×Q8—32no—
393C2×C3×Q8C22×D312yes—
394C2×C3×Q8C22×D312yes—
395C2×C3×D4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—32no—
399C22×C3×C4—31no—
400C2×#67—32no—
401C2×#67—32no—
402C2×#67—34no—
403C22×Dic3—32no—
404C22×Dic3—32no—
405#239—68no—
406#239—68no—
407#239—64no—
408#239—128no—
409D3×D4—64no—
410#235—64no—
411C2×D12—31no—
412C2×D12—31no—
413C2×D12—32no—
414C2×D12—32no—
415C2×D12—31no—
416C2×D12—34no—
417C2×D12—34no—
418C2×D12—31no—
419C2×D12—34no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—64no—
423C2×D12—64no—
424C2×D12C22×D311yescharacteristic
425C2×C4×D3—32no—
426C2×C4×D3—32no—
427C2×C4×D3—32no—
428C2×C4×D3—32no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—32no—
432C2×C4×D3—32no—
433C2×C4×D3—32no—
434C2×C4×D3—32no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—34no—
438C2×C4×D3—32no—
439C2×C4×D3—32no—
440C2×C4×D3—34no—
441C2×C4×D3—62no—
442C2×C4×D3—62no—
443C2×C4×D3—64no—
444C2×C4×D3—68no—
445C2×C4×D3—68no—
446C2×C4×D3C22×D311yescharacteristic
447C2×C4×D3C22×D312yes—
448C2×C4×D3C22×D311yescharacteristic
449C2×C4×D3C22×D311yescharacteristic
450C2×Dic6C22×D311yescharacteristic
451C2×Dic6C22×D312yes—
452C3×C4⋊C4—22no—
453C3×C4⋊C4—22no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4—34no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—34no—
461C3×C4⋊C4—32no—
462C3×C4⋊C4C22×D312yes—
463C3×C4⋊C4C22×D312yes—
464C3×C4⋊C4C22×D312yes—
465C3×C4⋊C4C22×D312yes—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—32no—
470C3×C42—21no—
471C3×C42—31no—
472C3×C42—32no—
473C3×C42—31no—
474C3×C42—34no—
475C3×C42—34no—
476C3×C42—31no—
477C3×C42C22×D311yescharacteristic
478C3×C42C22×D311yescharacteristic
479#217—32no—
480#217—34no—
481#217—32no—
482(C2×D3)⋊C4—32no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—62no—
500(C2×D3)⋊C4—62no—
501(C2×D3)⋊C4—64no—
502(C2×D3)⋊C4C22×D314yes—
503(C2×D3)⋊C4C22×D314yes—
504(C2×D3)⋊C4C22×D312yes—
505(C2×D3)⋊C4C22×D314yes—
506C4⋊Dic3—31no—
507C4⋊Dic3—31no—
508C4⋊Dic3—31no—
509C4⋊Dic3—31no—
510C4⋊Dic3—32no—
511C4⋊Dic3—32no—
512C4⋊Dic3—34no—
513C4⋊Dic3—61no—
514C4⋊Dic3—61no—
515C4⋊Dic3C22×D311yescharacteristic
516C4⋊Dic3C22×D312yes—
517C4⋊Dic3C22×D312yes—
518C4⋊Dic3C22×D311yescharacteristic
519C4⋊Dic3C22×D314yes—
520C4⋊Dic3C22×D314yes—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—32no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—32no—
528Dic3⋊C4—64no—
529Dic3⋊C4C22×D312yes—
530Dic3⋊C4C22×D314yes—
531C4×Dic3—32no—
532C4×Dic3—32no—
533C4×Dic3—32no—
534C4×Dic3—34no—
535C4×Dic3—34no—
536C4×Dic3—32no—
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D311yescharacteristic
539C4×Dic3C22×D314yes—
540C4×Dic3C22×D314yes—
541C4×Dic3C22×D311yescharacteristic
542C4×Dic3C22×D311yescharacteristic
543C22×C32C2511yescharacteristic
544C2×C3⋊D3—22no—
545C2×C3⋊D3—22no—
546C2×C3⋊D3—22no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3C2×#4114yes—
550C2×C3×D3—21no—
551C2×C3×D3—21no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3C2×#4112yes—
556D32—48no—
557C32×C4—24no—
558C32×C4—21no—
559C32×C4C2×#4112yes—
560C32×C4C2×#4112yes—
561C3⋊Dic3—22no—
562C3⋊Dic3—22no—
563C3×Dic3—22no—
564C3×Dic3—22no—
565C3×Dic3—21no—
566C3×Dic3—22no—
567C3×Dic3—21no—
568C3×Dic3—24no—
569C3×Dic3C2×#4112yes—
570C2×#41—91no—
571C2×#41—92no—
572C22×D4—91no—
573C23×C4—92no—
574C4⋊Q8—31no—
575C4⋊Q8D3211yescharacteristic, complemented
576#126—34no—
577#126—94no—
578#126—94no—
579#125—32no—
580#125—92no—
581#125—94no—
582#124—32no—
583#124—94no—
584#123—94no—
585#123—94no—
586#123—94no—
587#123—94no—
588C22⋊Q8—32no—
589C22⋊Q8—32no—
590C22⋊Q8—32no—
591C22⋊Q8—92no—
592C22⋊Q8—94no—
593C22⋊Q8—92no—
594#121—94no—
595#121—92no—
596#121—92no—
597#121—92no—
598#120—94no—
599C4×Q8—32no—
600C4×Q8—32no—
601C4×Q8—32no—
602C4×Q8—31no—
603C4×Q8—91no—
604C4×D4—31no—
605C4×D4—92no—
606C4×D4—94no—
607C4×D4—91no—
608C4×D4—94no—
609C4×D4—92no—
610C4×D4—94no—
611C4×D4—91no—
612C4×D4—92no—
613C4×D4—92no—
614C4×D4—91no—
615C4×D4—92no—
616C4×D4—91no—
617C4×D4—91no—
618#117—32no—
619#117—32no—
620#117—94no—
621#117—94no—
622#117—92no—
623#117—94no—
624#117—92no—
625#117—91no—
626#117—92no—
627C2×C4⋊C4—92no—
628C2×C4⋊C4—91no—
629C2×C4⋊C4—92no—
630C2×C22⋊C4—94no—
631C2×C22⋊C4—92no—
632C2×C42—31no—
633C2×C42—94no—
634C2×C42—92no—
635C23×C3—31no—
636C23×C3—32no—
637C22×D3—32no—
638C22×D3—32no—
639C22×D3—32no—
640C22×D3—32no—
641C22×D3—62no—
642C22×D3—62no—
643C22×D3—64no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3—122no—
648C22×D3—122no—
649C22×D3C23×D312yes—
650C22×D3C23×D311yescharacteristic
651C3×Q8—24no—
652C3×Q8—24no—
653C3×Q8—44no—
654C3×Q8—62no—
655C3×Q8—122no—
656C3×D4—62no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—24no—
660C2×C3×C4—21no—
661C2×C3×C4—31no—
662C2×C3×C4—34no—
663C2×C3×C4—32no—
664C2×C3×C4—31no—
665C2×C3×C4—32no—
666C2×C3×C4—32no—
667C2×C3×C4—34no—
668C2×C3×C4—31no—
669C2×C3×C4—64no—
670C2×C3×C4—62no—
671C2×C3×C4—121no—
672C2×C3×C4C23×D314yes—
673C2×C3×C4C23×D314yes—
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680#67—64no—
681#67—64no—
682#67—124no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—64no—
690C2×Dic3—64no—
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D311yescharacteristic
693C2×Dic3C23×D312yes—
694C2×Dic3C23×D314yes—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D311yescharacteristic
697C2×Dic3C23×D311yescharacteristic
698D12—22no—
699D12—34no—
700D12—34no—
701D12—64no—
702D12—68no—
703D12—68no—
704D12—64no—
705D12—64no—
706D12—62no—
707D12—62no—
708D12—122no—
709D12—128no—
710D12—124no—
711C4×D3—24no—
712C4×D3—22no—
713C4×D3—41no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—68no—
717C4×D3—68no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—64no—
724C4×D3—64no—
725C4×D3—64no—
726C4×D3—124no—
727C4×D3—124no—
728C4×D3—128no—
729C4×D3—124no—
730C4×D3—122no—
731C4×D3—122no—
732C4×D3—124no—
733C4×D3#23914yescomplemented
734Dic6—22no—
735Dic6—42no—
736C2×C32C22×#4111yescharacteristic
737C2×C32C22×#4111yescharacteristic
738C2×C32#58511yescharacteristic
739C3⋊D3—24no—
740C3⋊D3—42no—
741C3×D3—22no—
742C3×D3—42no—
743C24—92no—
744#41—184no—
745#41—188no—
746C2×Q8—31no—
747C2×Q8—32no—
748C2×Q8C2×D3212yes—
749C2×D4—31no—
750C2×D4—92no—
751C2×D4—92no—
752C2×D4—94no—
753C2×D4—91no—
754C2×D4—94no—
755C2×D4—91no—
756C2×D4—184no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—32no—
760C22×C4—31no—
761C22×C4—92no—
762C22×C4—92no—
763C22×C4—94no—
764C22×C4—92no—
765C22×C4—92no—
766C22×C4—92no—
767C22×C4—94no—
768C22×C4—92no—
769C22×C4—92no—
770C22×C4—188no—
771C4⋊C4—31no—
772C4⋊C4—32no—
773C4⋊C4—31no—
774C4⋊C4—32no—
775C4⋊C4—34no—
776C4⋊C4—34no—
777C4⋊C4—32no—
778C4⋊C4—34no—
779C4⋊C4—94no—
780C4⋊C4—92no—
781C4⋊C4—92no—
782C4⋊C4—94no—
783C4⋊C4—91no—
784C4⋊C4—94no—
785C4⋊C4—91no—
786C4⋊C4C2×D3212yes—
787C4⋊C4C2×D3212yes—
788C22⋊C4—34no—
789C22⋊C4—34no—
790C22⋊C4—32no—
791C22⋊C4—34no—
792C22⋊C4—92no—
793C22⋊C4—94no—
794C22⋊C4—92no—
795C22⋊C4—94no—
796C22⋊C4—92no—
797C22⋊C4—94no—
798C22⋊C4—92no—
799C22⋊C4—92no—
800C22⋊C4—92no—
801C22⋊C4—94no—
802C42—31no—
803C42—31no—
804C42—31no—
805C42—34no—
806C42—34no—
807C42—32no—
808C42—92no—
809C42—94no—
810C42—92no—
811C42C2×D3211yescharacteristic
812C22×C3—21no—
813C22×C3—32no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3C24×D311yescharacteristic
820C22×C3C24×D311yescharacteristic
821C2×D3—21no—
822C2×D3—21no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—34no—
827C2×D3—34no—
828C2×D3—64no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—122no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—122no—
843C2×D3—122no—
844C2×D3—128no—
845C2×D3—128no—
846C2×D3C2×#23912yes—
847C3×C4—24no—
848C3×C4—24no—
849C3×C4—21no—
850C3×C4—21no—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—32no—
854C3×C4—44no—
855C3×C4—41no—
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—61no—
859C3×C4—62no—
860C3×C4—61no—
861C3×C4—64no—
862C3×C4C2×#23912yes—
863C3×C4D3×#4112yes—
864C3×C4D3×#4112yes—
865C3×C4D3×#4112yes—
866Dic3—22no—
867Dic3—22no—
868Dic3—21no—
869Dic3—24no—
870Dic3—21no—
871Dic3—22no—
872Dic3—62no—
873Dic3—62no—
874Dic3—62no—
875Dic3—62no—
876Dic3—122no—
877Dic3—122no—
878Dic3C2×#23912yes—
879C32#347511yescharacteristic, complemented, Sylow
880C23—31no—
881C23—32no—
882C23—92no—
883C23—92no—
884C23—184no—
885C23—184no—
886C23—362no—
887Q8—24no—
888Q8—62no—
889Q8—122no—
890D4—62no—
891D4—94no—
892D4—188no—
893D4—184no—
894D4—184no—
895D4—182no—
896D4—364no—
897C2×C4—31no—
898C2×C4—34no—
899C2×C4—32no—
900C2×C4—32no—
901C2×C4—31no—
902C2×C4—31no—
903C2×C4—32no—
904C2×C4—34no—
905C2×C4—62no—
906C2×C4—64no—
907C2×C4—92no—
908C2×C4—92no—
909C2×C4—121no—
910C2×C4—188no—
911C2×C4—184no—
912C2×C4—184no—
913C2×C4—184no—
914C2×C4—184no—
915C2×C4—184no—
916C2×C4—184no—
917C2×C4—362no—
918C2×C4—364no—
919C2×C4C22×D3214yes—
920C2×C4C22×D3211yescharacteristic
921C2×C4C22×D3211yescharacteristic
922C2×C4C22×D3211yescharacteristic
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—62no—
927C2×C3—122no—
928C2×C3C22×#23911yescharacteristic
929C2×C3C2×D3×#4111yescharacteristic
930C2×C3C2×D3×#4111yescharacteristic
931C2×C3C2×D3×#4111yescharacteristic
932C2×C3#596411yescharacteristic
933C2×C3#596811yescharacteristic
934D3—22no—
935D3—42no—
936D3—64no—
937D3—64no—
938D3—124no—
939D3—122no—
940D3—122no—
941D3—242no—
942C22—32no—
943C22—61no—
944C22—61no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—94no—
949C22—182no—
950C22—182no—
951C22—182no—
952C22—182no—
953C22—182no—
954C22—368no—
955C22C23×D3211yescharacteristic
956C4—24no—
957C4—21no—
958C4—32no—
959C4—61no—
960C4—62no—
961C4—62no—
962C4—61no—
963C4—62no—
964C4—64no—
965C4—182no—
966C4—182no—
967C4#6431212yes—
968C4D3×#23912yes—
969C3—21no—
970C3#8627611yescharacteristic, complemented
971C3#8697911yescharacteristic, complemented
972C2—62no—
973C2—122no—
974C2—184no—
975C2—362no—
976C2C2×#6431211yescharacteristic
977C2C2×D3×#23911yescharacteristic
978C2#1059668811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596197C2semidirect
2. C3×#5732C2semidirect
3. C3×#5728C2semidirect
4. #10595431C2semidirect
5. #10595386C2semidirect
6. #10595382C2semidirect
7. #10595379C2semidirect
8. #10594654C2semidirect
9. #10594627C2semidirect
10. #10594602C2semidirect
11. #10594579C2semidirect
12. #10594578C2semidirect
13. #10594423C2semidirect
14. C4×D3×D12C2semidirect
15. #10593987C2semidirect
16. C4×#3799C2semidirect
17. #10593958C2semidirect
24. C32×C4⋊Q8C22semidirect
25. #64155C22semidirect
26. #64104C22semidirect
27. #64103C22semidirect
28. C4⋊C4×C3⋊D3C22semidirect
30. C4×C4⋊(C3⋊D3)C22semidirect
33. C3×Q8×Dic3C22semidirect
34. C3×Q8×Dic3C22semidirect
35. C3×#898C22semidirect
37. C3×#897C22semidirect
39. C3×#892C22semidirect
40. C3×#890C22semidirect
41. C3×#887C22semidirect
44. C3×#869C22semidirect
45. C3×C4×Dic6C22semidirect
51. #63909C22semidirect
52. #63907C22semidirect
56. #63900C22semidirect
59. #63894C22semidirect
60. #63894C22semidirect
61. #63894C22semidirect
65. #63888C22semidirect
66. C4×#624C22semidirect
67. C4×#624C22semidirect
69. #63880C22semidirect
71. #63877C22semidirect
72. #63871C22semidirect
73. #63869C22semidirect
74. #63868C22semidirect
75. #63858C22semidirect
76. #63854C22semidirect
78. #63849C22semidirect
79. #63849C22semidirect
80. #63846C22semidirect
81. Dic3×Dic6C22semidirect
83. #63841C22semidirect
84. #63836C22semidirect
88. #5732D3semidirect
90. #5728D3semidirect
201. C3×C4⋊Q8C2×D3semidirect
202. C3×C4⋊Q8C2×D3semidirect
226. Q8×Dic3C2×D3semidirect
227. Q8×Dic3C2×D3semidirect
240. #898C2×D3semidirect
243. #897C2×D3semidirect
271. #892C2×D3semidirect
280. #890C2×D3semidirect
282. #887C2×D3semidirect
325. #869C2×D3semidirect
327. C4×Dic6C2×D3semidirect
344. C4⋊(C3⋊D3)#41semidirect
359. C3×C4×D3#41semidirect
575. C4⋊Q8D32semidirect
733. C4×D3#239semidirect
879. C32#3475semidirect
970. C3#86276semidirect
971. C3#86979semidirect

Maximal subgroups

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

subgroupindex
#105961972
C3×#57322
C3×#57282
#105954312
#105953862
#105953822
#105953792
#105946542
#105946272
#105946022
#105945792
#105945782
#105944232
C4×D3×D122
#105939872
C4×#37992
#105939582
#869793
#862763