Finite Group Databasebeta

← #11906191

Subgroups — #11906191

Order 1152.

2314 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2C3×#5730C211yesmaximal, characteristic, complemented
3C3×#5728C211yesmaximal, characteristic, complemented
4#10595434C214yesmaximal, complemented
5#10595371C214yesmaximal, complemented
6#10594631C212yesmaximal, complemented
7D3×#897C212yesmaximal, complemented
8#10594604C212yesmaximal
9#10594536C212yesmaximal, complemented
10#10594505C212yesmaximal, complemented
11#10594484C212yesmaximal, complemented
12#10594452C212yesmaximal, complemented
13#10594383C212yesmaximal, complemented
14C4×D3×D12C211yesmaximal, characteristic
15#10593904C211yesmaximal, characteristic, complemented
16#10593903C211yesmaximal, characteristic, complemented
17#10593873C211yesmaximal, characteristic, complemented
18#86948—31nomaximal
19#86280—31nomaximal
20C2×D3×D12C2211yescharacteristic
21C2×C4×D32C2212yes—
22C2×#3797C2212yescomplemented
23C2×D3×Dic6C2212yescomplemented
24C32×C4⋊Q8C2211yescharacteristic, complemented
25#64155C2214yescomplemented
26#64106C2212yescomplemented
27#64102C2212yes—
28C4⋊C4×C3⋊D3C2212yescomplemented
29#64099C2212yescomplemented
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C4×#634C2211yescharacteristic, complemented
32C3×#946C2212yes—
33C3×#946C2214yescomplemented
34C3×Q8×Dic3C2212yescomplemented
35C3×#897C2212yes—
36C3×#897C2212yescomplemented
37C3×#893C2212yes—
38C3×#892C2212yes—
39C3×D3×C4⋊C4C2212yescomplemented
40C3×#890C2212yescomplemented
41C3×#890C2212yescomplemented
42C3×#887C2212yescomplemented
43C3×C4×D12C2211yescharacteristic
44C3×C42×D3C2211yescharacteristic
45C3×#869C2211yescharacteristic, complemented
46C3×C4×Dic6C2211yescharacteristic, complemented
47#63921C2214yes—
48D3×(C2×D3)⋊C4C2214yes—
49D3×(C2×D3)⋊C4C2212yes—
50#63919C2212yescomplemented
51#63918C2214yescomplemented
52#63918C2211yescharacteristic, complemented
53#63918C2212yescomplemented
54C4×#627C2212yescomplemented
55C4×#626C2214yes—
56C4×#626C2212yes—
57#63900C2214yescomplemented
58#63899C2214yes—
59#63899C2214yescomplemented
60#63899C2214yescomplemented
61#63898C2212yes—
62#63895C2214yescomplemented
63#63895C2214yescomplemented
64#63895C2214yescomplemented
65#63894C2212yes—
66#63894C2211yescharacteristic
67#63893C2214yes—
68#63893C2214yescomplemented
69Dic3×D12C2211yescharacteristic
70D3×C4⋊Dic3C2211yescharacteristic
71D3×C4⋊Dic3C2214yescomplemented
72#63880C2212yes—
73#63880C2214yes—
74#63871C2212yescomplemented
75#63867C2212yescomplemented
76#63867C2214yescomplemented
77#63866C2211yescharacteristic, complemented
78#63865C2214yescomplemented
79#63857C2211yescharacteristic
80#63856C2211yescharacteristic
81#63856C2212yescomplemented
82#63855C2212yes—
83#63851C2212yes—
84#63851C2214yescomplemented
85C3×#554—31no—
86C3×#533—31no—
87#5730—31no—
88#5730—31no—
89#5730—61no—
90#5730D311yescharacteristic, complemented
91#5728D311yescharacteristic, complemented
92#5727—31no—
93#5727—31no—
94#5690—32no—
95#5690—32no—
96#5690—32no—
97#5689—32no—
98#5635—34no—
99#5634—34no—
100#5634—34no—
101#5632—32no—
102D3×C22⋊Q8—32no—
103D3×C22⋊Q8—32no—
104D3×C22⋊Q8—32no—
105#5579—34no—
106#5579—32no—
107#5578—31no—
108Q8×D12—32no—
109Q8×D12—31no—
110#5545—32no—
111C4×D3×D4—31no—
112#5543—32no—
113D4×Dic6—31no—
114#5521—32no—
115#5519—32no—
116#5511—32no—
117C2×#897—32no—
118C2×C4×D12—31no—
119#5470—31no—
120C22×D32C2312yes—
121C2×C32×Q8C2312yes—
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634C2311yescharacteristic
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×#627C2314yes—
135C2×#627C2314yes—
136C2×#627C2312yes—
137C2×#626C2312yes—
138C2×#624C2314yes—
139C2×#624C2312yes—
140C2×D3×Dic3C2314yes—
141C2×D3×Dic3C2312yes—
142C2×D3×Dic3C2312yes—
143D3×D12Q818yescomplemented
144C4×D32—44no—
145#3797—44no—
146D3×Dic6—44no—
147C32×C4⋊C4C2312yes—
148C32×C4⋊C4C2312yes—
149C32×C42C2311yescharacteristic
150#3752C2312yes—
151#3752C2314yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C4⋊(C3⋊Dic3)C2314yes—
155#3750C2312yes—
156#3750C2314yes—
157C4×C3⋊Dic3C2312yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2314yes—
164C3×C4⋊Dic3C2314yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2312yes—
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2314yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2311yescharacteristic
175#3724C2312yes—
176#3724C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2312yes—
182Dic3⋊Dic3C2312yes—
183#3722C2312yes—
184#3722C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2312yes—
187(C2×D3)⋊Dic3C2312yes—
188(C2×D3)⋊Dic3C2314yes—
189#3501—91noSylow
190C2×D3×Q8—32no—
191C2×D3×Q8—32no—
192C2×D3×Q8—32no—
193C2×D3×D4—31no—
194C22×D12—31no—
195C22×C4×D3—32no—
196C22×C4×D3—32no—
197C22×Dic6—32no—
198C3×C4⋊Q8—21no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8C2×D311yescharacteristic, complemented
201C3×C4⋊Q8C2×D311yescharacteristic, complemented
202C3×#125—32no—
203C3×#125—32no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—34no—
206C3×C22⋊Q8—32no—
207C3×C22⋊Q8—32no—
208C3×C4×Q8—32no—
209C3×C4×Q8—32no—
210C3×C4×Q8—31no—
211C3×C4×D4—32no—
212C3×C4×D4—31no—
213C3×#117—32no—
214C2×C3×C4⋊C4—32no—
215C2×C3×C42—31no—
216#946—34no—
217#946—34no—
218#946—32no—
219#946—31no—
220#946—32no—
221#946—64no—
222#946C2×D312yes—
223#946C2×D314yescomplemented
224Q8×Dic3C2×D312yescomplemented
225#944—31no—
226D4×Dic3—32no—
227D4×Dic3—31no—
228C4×#67—32no—
229C4×#67—34no—
230C2×(C2×D3)⋊C4—32no—
231C2×(C2×D3)⋊C4—34no—
232#926—32no—
233C2×C4⋊Dic3—34no—
234C2×C4⋊Dic3—31no—
235#924—31no—
236#924—32no—
237#924—31no—
238#924—32no—
239#924—34no—
240#897—31no—
241#897—32no—
242#897—32no—
243#897—32no—
244#897—34no—
245#897—34no—
246#897—34no—
247#897—34no—
248#897—34no—
249#897—62no—
250#897C2×D312yes—
251#897C2×D312yescomplemented
252#896—32no—
253#896—34no—
254#896—34no—
255#896—34no—
256#896—34no—
257#896—34no—
258#896—34no—
259#896—34no—
260#896—34no—
261#896—34no—
262#893—32no—
263#893—32no—
264#893—32no—
265#893—31no—
266#893—32no—
267#893—62no—
268#893C2×D312yes—
269#892C2×D312yes—
270D3×C4⋊C4—31no—
271D3×C4⋊C4—34no—
272D3×C4⋊C4—32no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4—34no—
275D3×C4⋊C4—34no—
276D3×C4⋊C4—62no—
277D3×C4⋊C4C2×D312yescomplemented
278#890—32no—
279#890—32no—
280#890—62no—
281#890C2×D312yescomplemented
282#890C2×D312yescomplemented
283#889—32no—
284#889—34no—
285#888—32no—
286#888—32no—
287#888—34no—
288#888—32no—
289#888—31no—
290#887C2×D312yescomplemented
291#67⋊C4—34no—
292#67⋊C4—32no—
293D3×C22⋊C4—32no—
294D3×C22⋊C4—34no—
295D3×C22⋊C4—34no—
296D3×C22⋊C4—34no—
297#878—34no—
298#878—34no—
299#878—34no—
300#878—34no—
301#878—34no—
302C4×D12—31no—
303C4×D12—32no—
304C4×D12—34no—
305C4×D12—31no—
306C4×D12—31no—
307C4×D12—32no—
308C4×D12—34no—
309C4×D12—31no—
310C4×D12—32no—
311C4×D12—61no—
312C4×D12C2×D311yescharacteristic
313#872—32no—
314C42×D3C2×D311yescharacteristic
315#870—32no—
316#870—34no—
317#869—31no—
318#869—32no—
319#869—31no—
320#869—34no—
321#869C2×D311yescharacteristic, complemented
322C4×Dic6—31no—
323C4×Dic6—31no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic, complemented
328C22×C3⋊D3C2412yes—
329C22×C3×D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C2×D32—42no—
332C2×D32—42no—
333C2×D32C2×Q818yescomplemented
334C32×Q8—42no—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2414yes—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2412yes—
342C4⋊(C3⋊D3)C2×Q814yescomplemented
343C4×C3⋊D3—24no—
344C4×C3⋊D3—44no—
345#634—22no—
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2414yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2411yescharacteristic
352C2×C3×Dic3C2411yescharacteristic
353C3×D12C2×Q814yescomplemented
354C3×C4×D3—24no—
355C3×C4×D3—22no—
356C3×C4×D3—41no—
357C3×C4×D3—44no—
358C3×C4×D3C2×Q814yescomplemented
359C3×Dic6—24no—
360C3×Dic6—22no—
361#627—44no—
362#627—44no—
363#627—42no—
364#626C2×Q818yescomplemented
365#624—44no—
366#624—42no—
367D3×Dic3—44no—
368D3×Dic3—42no—
369D3×Dic3—42no—
370#554—31no—
371#554—92no—
372#554—92no—
373#554—94no—
374#554—92no—
375#554—91no—
376D4×Q8—91no—
377D4×Q8—92no—
378D4×Q8—91no—
379#544—92no—
380#543—94no—
381#533—31no—
382#533—91no—
383C2×C22⋊Q8—92no—
384C2×C22⋊Q8—92no—
385#518—92no—
386C2×C4×D4—91no—
387C23×D3—32no—
388C23×D3—32no—
389C2×C3×Q8—22no—
390C2×C3×Q8—31no—
391C2×C3×Q8—32no—
392C2×C3×Q8C22×D312yes—
393C2×C3×Q8C22×D312yes—
394C2×C3×D4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—32no—
398C22×C3×C4—31no—
399C22×C3×C4—34no—
400C2×#67—32no—
401C22×Dic3—32no—
402C22×Dic3—32no—
403C22×Dic3—34no—
404D3×Q8—124no—
405D3×Q8—124no—
406D3×Q8—124no—
407D3×D4—38no—
408C2×D12—32no—
409C2×D12—31no—
410C2×D12—31no—
411C2×D12—38no—
412C2×D12—61no—
413C2×D12C22×D311yescharacteristic
414C2×C4×D3—32no—
415C2×C4×D3—32no—
416C2×C4×D3—32no—
417C2×C4×D3—34no—
418C2×C4×D3—32no—
419C2×C4×D3—34no—
420C2×C4×D3—34no—
421C2×C4×D3—32no—
422C2×C4×D3—34no—
423C2×C4×D3—34no—
424C2×C4×D3—32no—
425C2×C4×D3—62no—
426C2×C4×D3—64no—
427C2×C4×D3—124no—
428C2×C4×D3—124no—
429C2×C4×D3C22×D311yescharacteristic
430C2×C4×D3C22×D312yes—
431C2×C4×D3C22×D311yescharacteristic
432C2×C4×D3C22×D314yes—
433C2×C4×D3C22×D311yescharacteristic
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—32no—
437C2×Dic6—32no—
438C2×Dic6—34no—
439C2×Dic6—34no—
440C2×Dic6—34no—
441C2×Dic6—34no—
442C2×Dic6—61no—
443C2×Dic6—124no—
444C2×Dic6C22×D311yescharacteristic
445C2×Dic6C22×D312yes—
446C3×C4⋊C4—22no—
447C3×C4⋊C4—22no—
448C3×C4⋊C4—31no—
449C3×C4⋊C4—32no—
450C3×C4⋊C4—34no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4—34no—
457C3×C4⋊C4C22×D312yes—
458C3×C4⋊C4C22×D312yes—
459C3×C4⋊C4C22×D312yes—
460C3×C4⋊C4C22×D312yes—
461C3×C22⋊C4—34no—
462C3×C22⋊C4—34no—
463C3×C22⋊C4—32no—
464C3×C42—21no—
465C3×C42—31no—
466C3×C42—32no—
467C3×C42—31no—
468C3×C42—34no—
469C3×C42—31no—
470C3×C42C22×D311yescharacteristic
471C3×C42C22×D311yescharacteristic
472#217—32no—
473#217—32no—
474#217—34no—
475#217—32no—
476(C2×D3)⋊C4—32no—
477(C2×D3)⋊C4—32no—
478(C2×D3)⋊C4—32no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—32no—
481(C2×D3)⋊C4—32no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—62no—
489(C2×D3)⋊C4—64no—
490(C2×D3)⋊C4C22×D312yes—
491(C2×D3)⋊C4C22×D314yes—
492(C2×D3)⋊C4C22×D314yes—
493C4⋊Dic3—31no—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—34no—
497C4⋊Dic3—31no—
498C4⋊Dic3—34no—
499C4⋊Dic3—32no—
500C4⋊Dic3—32no—
501C4⋊Dic3—32no—
502C4⋊Dic3—32no—
503C4⋊Dic3—32no—
504C4⋊Dic3—34no—
505C4⋊Dic3—61no—
506C4⋊Dic3—61no—
507C4⋊Dic3—64no—
508C4⋊Dic3C22×D311yescharacteristic
509C4⋊Dic3C22×D312yes—
510C4⋊Dic3C22×D314yes—
511C4⋊Dic3C22×D312yes—
512C4⋊Dic3C22×D311yescharacteristic
513C4⋊Dic3C22×D314yes—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—32no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—32no—
525Dic3⋊C4—32no—
526Dic3⋊C4—34no—
527Dic3⋊C4—32no—
528Dic3⋊C4—62no—
529Dic3⋊C4—64no—
530Dic3⋊C4C22×D312yes—
531Dic3⋊C4C22×D314yes—
532Dic3⋊C4C22×D314yes—
533C4×Dic3—32no—
534C4×Dic3—32no—
535C4×Dic3—62no—
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D311yescharacteristic
539C4×Dic3C22×D311yescharacteristic
540C4×Dic3C22×D314yes—
541C22×C32C2511yescharacteristic
542C2×C3⋊D3—22no—
543C2×C3⋊D3—22no—
544C2×C3⋊D3C22×Q814yes—
545C2×C3×D3—22no—
546C2×C3×D3—21no—
547C2×C3×D3—22no—
548C2×C3×D3—21no—
549C2×C3×D3C22×Q814yes—
550C2×C3×D3C22×Q812yes—
551D32—48no—
552C32×C4—24no—
553C32×C4—21no—
554C32×C4C22×Q812yes—
555C32×C4H(5,𝔽2)12yes—
556C3⋊Dic3—22no—
557C3⋊Dic3—22no—
558C3⋊Dic3—22no—
559C3×Dic3—21no—
560C3×Dic3—24no—
561C3×Dic3—22no—
562C3×Dic3—22no—
563C3×Dic3—21no—
564C3×Dic3—22no—
565C3×Dic3C22×Q812yes—
566C22×Q8—92no—
567C22×Q8—92no—
568C22×D4—91no—
569C23×C4—92no—
570C4⋊Q8—31no—
571C4⋊Q8—91no—
572C4⋊Q8—94no—
573C4⋊Q8—92no—
574C4⋊Q8—91no—
575C4⋊Q8—92no—
576C4⋊Q8D3211yescharacteristic, complemented
577#125—32no—
578#125—32no—
579#125—92no—
580#125—94no—
581#125—92no—
582C22⋊Q8—32no—
583C22⋊Q8—34no—
584C22⋊Q8—32no—
585C22⋊Q8—32no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C22⋊Q8—94no—
595C22⋊Q8—91no—
596C22⋊Q8—92no—
597C22⋊Q8—94no—
598C22⋊Q8—92no—
599C22⋊Q8—91no—
600C22⋊Q8—92no—
601C22⋊Q8—94no—
602C22⋊Q8—92no—
603C4×Q8—32no—
604C4×Q8—32no—
605C4×Q8—31no—
606C4×Q8—92no—
607C4×Q8—91no—
608C4×D4—32no—
609C4×D4—31no—
610C4×D4—92no—
611C4×D4—94no—
612C4×D4—91no—
613C4×D4—92no—
614C4×D4—92no—
615C4×D4—94no—
616C4×D4—91no—
617C4×D4—92no—
618C4×D4—92no—
619C4×D4—91no—
620#117—32no—
621#117—92no—
622C2×C4⋊C4—32no—
623C2×C4⋊C4—94no—
624C2×C4⋊C4—91no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—92no—
627C2×C22⋊C4—94no—
628C2×C22⋊C4—92no—
629C2×C22⋊C4—94no—
630C2×C42—31no—
631C23×C3—31no—
632C23×C3—32no—
633C22×D3—32no—
634C22×D3—32no—
635C22×D3—38no—
636C22×D3—38no—
637C22×D3—62no—
638C22×D3—122no—
639C22×D3—122no—
640C22×D3—122no—
641C22×D3—122no—
642C22×D3C23×D311yescharacteristic
643C22×D3C23×D312yes—
644C3×Q8—42no—
645C3×Q8—42no—
646C3×Q8—62no—
647C3×Q8—64no—
648C3×Q8—82no—
649C3×D4—34no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—24no—
654C2×C3×C4—31no—
655C2×C3×C4—34no—
656C2×C3×C4—31no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—34no—
660C2×C3×C4—32no—
661C2×C3×C4—31no—
662C2×C3×C4—64no—
663C2×C3×C4—62no—
664C2×C3×C4—124no—
665C2×C3×C4—121no—
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D314yes—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D314yes—
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673C2×C3×C4C23×D311yescharacteristic
674#67—38no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—124no—
685C2×Dic3—122no—
686C2×Dic3—122no—
687C2×Dic3C23×D311yescharacteristic
688C2×Dic3C23×D311yescharacteristic
689C2×Dic3C23×D312yes—
690C2×Dic3C23×D312yes—
691C2×Dic3C23×D314yes—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D311yescharacteristic
694D12—38no—
695D12—34no—
696D12—34no—
697D12—64no—
698D12D3×Q814yescomplemented
699C4×D3—22no—
700C4×D3—24no—
701C4×D3—41no—
702C4×D3—44no—
703C4×D3—64no—
704C4×D3—64no—
705C4×D3—124no—
706C4×D3—122no—
707C4×D3—122no—
708C4×D3—124no—
709C4×D3—124no—
710C4×D3—124no—
711C4×D3—124no—
712C4×D3—122no—
713C4×D3—122no—
714C4×D3—124no—
715C4×D3—244no—
716C4×D3D3×Q814yescomplemented
717Dic6—24no—
718Dic6—22no—
719Dic6—62no—
720Dic6—62no—
721Dic6—122no—
722Dic6—122no—
723Dic6—122no—
724Dic6—124no—
725Dic6—124no—
726Dic6—124no—
727Dic6—124no—
728C2×C32C23×Q811yescharacteristic
729C2×C32C2×H(5,𝔽2)11yescharacteristic
730C2×C32#58511yescharacteristic
731C3⋊D3—24no—
732C3×D3—22no—
733C3×D3—24no—
734C24—92no—
735C2×Q8—31no—
736C2×Q8—32no—
737C2×Q8—92no—
738C2×Q8—94no—
739C2×Q8—94no—
740C2×Q8—91no—
741C2×Q8—364no—
742C2×Q8—364no—
743C2×Q8C2×D3212yes—
744C2×D4—31no—
745C2×D4—98no—
746C2×D4—92no—
747C2×D4—91no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—32no—
751C22×C4—31no—
752C22×C4—34no—
753C22×C4—94no—
754C22×C4—92no—
755C22×C4—94no—
756C22×C4—92no—
757C22×C4—92no—
758C22×C4—92no—
759C22×C4—94no—
760C22×C4—364no—
761C4⋊C4—31no—
762C4⋊C4—34no—
763C4⋊C4—34no—
764C4⋊C4—31no—
765C4⋊C4—34no—
766C4⋊C4—32no—
767C4⋊C4—32no—
768C4⋊C4—34no—
769C4⋊C4—32no—
770C4⋊C4—92no—
771C4⋊C4—92no—
772C4⋊C4—92no—
773C4⋊C4—94no—
774C4⋊C4—94no—
775C4⋊C4—92no—
776C4⋊C4—92no—
777C4⋊C4—92no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—94no—
781C4⋊C4—94no—
782C4⋊C4—92no—
783C4⋊C4C2×D3212yes—
784C4⋊C4C2×D3212yes—
785C22⋊C4—34no—
786C22⋊C4—34no—
787C22⋊C4—32no—
788C22⋊C4—92no—
789C22⋊C4—94no—
790C22⋊C4—92no—
791C22⋊C4—92no—
792C22⋊C4—92no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—92no—
796C42—31no—
797C42—31no—
798C42—31no—
799C42—34no—
800C42—32no—
801C42—92no—
802C42C2×D3211yescharacteristic
803C22×C3—21no—
804C22×C3—34no—
805C22×C3—32no—
806C22×C3—62no—
807C22×C3—61no—
808C22×C3—62no—
809C22×C3—61no—
810C22×C3C24×D311yescharacteristic
811C22×C3C24×D311yescharacteristic
812C2×D3—22no—
813C2×D3—21no—
814C2×D3—21no—
815C2×D3—22no—
816C2×D3—34no—
817C2×D3—34no—
818C2×D3—64no—
819C2×D3—62no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—122no—
824C2×D3—122no—
825C2×D3—128no—
826C2×D3—128no—
827C2×D3C2×D3×Q812yes—
828C2×D3C2×D3×Q814yes—
829C3×C4—21no—
830C3×C4—24no—
831C3×C4—24no—
832C3×C4—21no—
833C3×C4—22no—
834C3×C4—22no—
835C3×C4—32no—
836C3×C4—44no—
837C3×C4—41no—
838C3×C4—62no—
839C3×C4—62no—
840C3×C4—64no—
841C3×C4—61no—
842C3×C4—62no—
843C3×C4—61no—
844C3×C4C2×D3×Q812yes—
845C3×C4C2×D3×Q812yes—
846C3×C4#100912yes—
847C3×C4#100912yes—
848Dic3—22no—
849Dic3—24no—
850Dic3—22no—
851Dic3—21no—
852Dic3—21no—
853Dic3—22no—
854Dic3—62no—
855Dic3—62no—
856Dic3—62no—
857Dic3—62no—
858Dic3—62no—
859Dic3—62no—
860Dic3—122no—
861Dic3—122no—
862Dic3—122no—
863Dic3C2×D3×Q812yes—
864C32#350111yescharacteristic, complemented, Sylow
865C23—31no—
866C23—32no—
867C23—98no—
868C23—92no—
869C23—362no—
870C23—362no—
871Q8—42no—
872Q8—62no—
873Q8—64no—
874Q8—182no—
875Q8—364no—
876Q8—364no—
877Q8—362no—
878D4—34no—
879D4—98no—
880D4—94no—
881C2×C4—31no—
882C2×C4—34no—
883C2×C4—31no—
884C2×C4—31no—
885C2×C4—32no—
886C2×C4—34no—
887C2×C4—32no—
888C2×C4—32no—
889C2×C4—62no—
890C2×C4—64no—
891C2×C4—92no—
892C2×C4—92no—
893C2×C4—92no—
894C2×C4—124no—
895C2×C4—121no—
896C2×C4—184no—
897C2×C4—364no—
898C2×C4—362no—
899C2×C4—364no—
900C2×C4—362no—
901C2×C4—362no—
902C2×C4—364no—
903C2×C4C22×D3211yescharacteristic
904C2×C4C22×D3214yes—
905C2×C4C22×D3211yescharacteristic
906C2×C4C22×D3211yescharacteristic
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—64no—
911C2×C3—62no—
912C2×C3C22×D3×Q811yescharacteristic
913C2×C3C22×D3×Q811yescharacteristic
914C2×C3C2×#100911yescharacteristic
915C2×C3C2×#100911yescharacteristic
916C2×C3#596411yescharacteristic
917C2×C3#596611yescharacteristic
918D3—22no—
919D3—24no—
920D3—64no—
921D3—64no—
922D3—124no—
923C22—32no—
924C22—34no—
925C22—62no—
926C22—61no—
927C22—62no—
928C22—61no—
929C22—94no—
930C22—182no—
931C22—182no—
932C22—368no—
933C22C23×D3211yescharacteristic
934C4—24no—
935C4—21no—
936C4—32no—
937C4—62no—
938C4—61no—
939C4—61no—
940C4—62no—
941C4—62no—
942C4—64no—
943C4—182no—
944C4—182no—
945C4—182no—
946C4D32×Q812yes—
947C4#6432012yes—
948C3—21no—
949C3#8628011yescharacteristic, complemented
950C3#8694811yescharacteristic, complemented
951C2—62no—
952C2—64no—
953C2—184no—
954C2#1059667811yescharacteristic
955C2C2×D32×Q811yescharacteristic
956C2C2×#6432011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC2×D3×D12C22
hypercenterC4⋊Q8D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. C3×#5730C2semidirect
3. C3×#5728C2semidirect
4. #10595434C2semidirect
5. #10595371C2semidirect
6. #10594631C2semidirect
7. D3×#897C2semidirect
9. #10594536C2semidirect
10. #10594505C2semidirect
11. #10594484C2semidirect
12. #10594452C2semidirect
13. #10594383C2semidirect
15. #10593904C2semidirect
16. #10593903C2semidirect
17. #10593873C2semidirect
22. C2×#3797C22semidirect
23. C2×D3×Dic6C22semidirect
24. C32×C4⋊Q8C22semidirect
25. #64155C22semidirect
26. #64106C22semidirect
28. C4⋊C4×C3⋊D3C22semidirect
29. #64099C22semidirect
31. C4×#634C22semidirect
33. C3×#946C22semidirect
34. C3×Q8×Dic3C22semidirect
36. C3×#897C22semidirect
39. C3×D3×C4⋊C4C22semidirect
40. C3×#890C22semidirect
41. C3×#890C22semidirect
42. C3×#887C22semidirect
45. C3×#869C22semidirect
46. C3×C4×Dic6C22semidirect
50. #63919C22semidirect
51. #63918C22semidirect
52. #63918C22semidirect
53. #63918C22semidirect
54. C4×#627C22semidirect
57. #63900C22semidirect
59. #63899C22semidirect
60. #63899C22semidirect
62. #63895C22semidirect
63. #63895C22semidirect
64. #63895C22semidirect
68. #63893C22semidirect
71. D3×C4⋊Dic3C22semidirect
74. #63871C22semidirect
75. #63867C22semidirect
76. #63867C22semidirect
77. #63866C22semidirect
78. #63865C22semidirect
81. #63856C22semidirect
84. #63851C22semidirect
90. #5730D3semidirect
91. #5728D3semidirect
143. D3×D12Q8semidirect
200. C3×C4⋊Q8C2×D3semidirect
201. C3×C4⋊Q8C2×D3semidirect
223. #946C2×D3semidirect
224. Q8×Dic3C2×D3semidirect
251. #897C2×D3semidirect
277. D3×C4⋊C4C2×D3semidirect
281. #890C2×D3semidirect
282. #890C2×D3semidirect
290. #887C2×D3semidirect
321. #869C2×D3semidirect
327. C4×Dic6C2×D3semidirect
333. C2×D32C2×Q8semidirect
342. C4⋊(C3⋊D3)C2×Q8semidirect
353. C3×D12C2×Q8semidirect
358. C3×C4×D3C2×Q8semidirect
364. #626C2×Q8semidirect
576. C4⋊Q8D32semidirect
698. D12D3×Q8semidirect
716. C4×D3D3×Q8semidirect
864. C32#3501semidirect
949. C3#86280semidirect
950. C3#86948semidirect

Maximal subgroups

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

subgroupindex
#105962012
C3×#57302
C3×#57282
#105954342
#105953712
#105946312
D3×#8972
#105946042
#105945362
#105945052
#105944842
#105944522
#105943832
C4×D3×D122
#105939042
#105939032
#105938732
#869483
#862803