Finite Group Databasebeta

← #11906387

Subgroups — #11906387

Order 1152.

2234 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596050C211yesmaximal, characteristic, complemented
2C3×#5578C211yesmaximal, characteristic, complemented
3C3×Q8×Dic6C211yesmaximal, characteristic, complemented
4#10595374C212yesmaximal, complemented
5#10595371C212yesmaximal, complemented
6#10594400C214yesmaximal, complemented
7#10594393C212yesmaximal, complemented
8#10594378C214yesmaximal, complemented
9#10594374C212yesmaximal, complemented
10C4×#3799C211yesmaximal, characteristic
11#10593958C211yesmaximal, characteristic, complemented
12#10593954C212yesmaximal, complemented
13#10593903C212yesmaximal, complemented
14D3×#869C211yesmaximal, characteristic, complemented
15#10593890C212yesmaximal
16Dic62C211yesmaximal, characteristic, complemented
17#10593851C212yesmaximal, complemented
18#87041—31nomaximal
19#86281—31nomaximal
20C2×#3799C2211yescharacteristic
21C2×#3797C2214yes—
22C2×D3×Dic6C2212yes—
23C32×C4×Q8C2211yescharacteristic
24#64155C2212yes—
25#64105C2214yes—
26C4⋊C4×C3⋊D3C2212yes—
27C4×C4⋊(C3⋊D3)C2212yes—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29#64079C2212yes—
30#64078C2211yescharacteristic
31C3×#946C2211yescharacteristic
32C3×Q8×Dic3C2212yes—
33C3×#944C2211yescharacteristic
34C3×#897C2211yescharacteristic
35C3×#896C2212yes—
36C3×#889C2212yes—
37C3×#888C2211yescharacteristic
38C3×#888C2212yes—
39C3×#888C2214yes—
40C3×#872C2212yes—
41C3×C42×D3C2211yescharacteristic
42C3×#869C2211yescharacteristic
43C3×#869C2212yes—
44C3×C4×Dic6C2212yes—
45C3×C4×Dic6C2212yes—
46C3×C4×Dic6C2211yescharacteristic
47C3×C4×Dic6C2211yescharacteristic
48#63918C2212yes—
49#63918C2212yes—
50#63918C2212yes—
51#63918C2212yes—
52#63904C2212yes—
53C4×#626C2212yes—
54#63900C2212yes—
55#63899C2214yes—
56#63895C2214yes—
57#63895C2214yes—
58#63894C2212yes—
59#63894C2211yescharacteristic
60D3×C4⋊Dic3C2212yes—
61D3×C4⋊Dic3C2212yes—
62#63888C2214yes—
63#63887C2214yes—
64#63883C2214yes—
65C4×#624C2212yes—
66#63881C2214yes—
67#63880C2214yes—
68#63871C2212yes—
69#63871C2214yes—
70#63869C2212yes—
71#63867C2214yes—
72#63866C2212yes—
73#63846C2214yes—
74#63846C2214yes—
75Dic3×Dic6C2212yes—
76Dic3×Dic6C2211yescharacteristic
77Dic3×Dic6C2212yes—
78#63841C2211yescharacteristic
79#63840C2214yes—
80#63839C2214yes—
81#63839C2214yes—
82#63837C2214yes—
83#63836C2214yes—
84#63836C2212yes—
85C3×Q82—31no—
86C3×#533—31no—
87#5730—32no—
88#5730—31no—
89#5729—34no—
90#5729—32no—
91#5728—32no—
92#5727—34no—
93#5727—32no—
94D3×C4⋊Q8—32no—
95D3×C4⋊Q8—32no—
96D3×C4⋊Q8—31no—
97#5689—34no—
98#5635—32no—
99#5635—32no—
100#5632—34no—
101#5579—31no—
102#5579—31no—
103#5579—32no—
104#5579—31no—
105#5579—61no—
106#5578—32no—
107#5578D311yescharacteristic, complemented
108Q8×D12—32no—
109#5574—32no—
110C4×#239—31no—
111#5569—32no—
112#5567—32no—
113Q8×Dic6—31no—
114Q8×Dic6—31no—
115Q8×Dic6D311yescharacteristic, complemented
116#5523—32no—
117#5519—32no—
118C4×#235—31no—
119C2×#869—31no—
120C2×C32×Q8C2311yescharacteristic
121C2×C4⋊(C3⋊D3)C2311yescharacteristic
122C2×C4×C3⋊D3C2312yes—
123C2×C4×C3⋊D3C2314yes—
124C2×#634C2312yes—
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×Dic6C2312yes—
129C2×C3×Dic6C2311yescharacteristic
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2314yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2314yes—
134C2×#627C2314yes—
135C2×#626C2312yes—
136C2×#624C2312yes—
137C2×#624C2314yes—
138C2×#624C2312yes—
139C2×D3×Dic3C2314yes—
140#3799Q818yescomplemented
141#3797—48no—
142D3×Dic6—44no—
143C32×C4⋊C4C2311yescharacteristic
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146C32×C42C2312yes—
147#3752C2312yes—
148#3752C2314yes—
149C4⋊(C3⋊Dic3)C2312yes—
150C4⋊(C3⋊Dic3)C2312yes—
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152#3750C2314yes—
153#3750C2314yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×(C2×D3)⋊C4C2312yes—
156C3×C4⋊Dic3C2314yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2312yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2312yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2314yes—
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2311yescharacteristic
175#3724C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182#3722C2314yes—
183#3722C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185Dic32C2314yes—
186Dic32C2312yes—
187Dic32C2312yes—
188#3503—91noSylow
189C2×#239—31no—
190C2×D3×Q8—32no—
191C2×D3×Q8—34no—
192C2×D3×Q8—34no—
193C2×#235—31no—
194C22×Dic6—32no—
195C3×C4⋊Q8—31no—
196C3×C4⋊Q8—32no—
197C3×C4⋊Q8—34no—
198C3×C4⋊Q8—31no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8—32no—
201C3×#125—32no—
202C3×C22⋊Q8—31no—
203C3×C22⋊Q8—32no—
204C3×C22⋊Q8—31no—
205C3×C4×Q8—21no—
206C3×C4×Q8—32no—
207C3×C4×Q8—31no—
208C3×C4×Q8—32no—
209C3×C4×Q8—31no—
210C3×C4×Q8—32no—
211C3×C4×Q8C2×D311yescharacteristic
212C3×C4×Q8C2×D311yescharacteristic
213C3×#117—32no—
214C2×C3×C42—31no—
215#946—32no—
216#946—32no—
217#946—34no—
218#946—32no—
219#946—34no—
220#946—34no—
221#946—62no—
222#946C2×D311yescharacteristic
223Q8×Dic3—32no—
224Q8×Dic3—32no—
225Q8×Dic3—31no—
226Q8×Dic3C2×D312yes—
227#944—34no—
228#944—34no—
229#944—32no—
230#944C2×D311yescharacteristic
231C4×#67—32no—
232C4×#67—32no—
233#926—31no—
234C2×C4⋊Dic3—32no—
235C2×C4⋊Dic3—32no—
236#897—34no—
237#897—32no—
238#897—34no—
239#897—34no—
240#897C2×D311yescharacteristic
241#896—34no—
242#896—34no—
243#896—34no—
244#896—34no—
245#896—34no—
246#896—34no—
247#896—64no—
248#896C2×D312yes—
249#893—32no—
250#893—34no—
251#893—31no—
252#893—32no—
253#892—31no—
254#892—34no—
255#892—32no—
256D3×C4⋊C4—32no—
257D3×C4⋊C4—32no—
258D3×C4⋊C4—32no—
259D3×C4⋊C4—32no—
260D3×C4⋊C4—32no—
261D3×C4⋊C4—32no—
262D3×C4⋊C4—34no—
263D3×C4⋊C4—34no—
264D3×C4⋊C4—62no—
265#890—34no—
266#890—34no—
267#890—32no—
268#889—34no—
269#889—34no—
270#889—34no—
271#889C2×D312yes—
272#888—34no—
273#888—34no—
274#888—34no—
275#888—34no—
276#888—32no—
277#888—32no—
278#888—32no—
279#888—32no—
280#888C2×D314yes—
281#888C2×D312yes—
282#888C2×D311yescharacteristic
283#887—34no—
284#67⋊C4—34no—
285#67⋊C4—34no—
286#878—34no—
287#878—34no—
288C4×D12—32no—
289C4×D12—32no—
290C4×D12—31no—
291C4×D12—31no—
292C4×D12—32no—
293C4×D12—34no—
294C4×D12—31no—
295C4×D12—32no—
296C4×D12—61no—
297C4×D12—62no—
298#872—32no—
299#872—34no—
300#872C2×D312yes—
301C42×D3—32no—
302C42×D3—32no—
303C42×D3C2×D311yescharacteristic
304#870—32no—
305#870—32no—
306#870—32no—
307#870—34no—
308#870—62no—
309#869—32no—
310#869—31no—
311#869—31no—
312#869—32no—
313#869—32no—
314#869—32no—
315#869—32no—
316#869—61no—
317#869C2×D311yescharacteristic
318#869C2×D312yes—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—34no—
323C4×Dic6C2×D312yes—
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D312yes—
327C22×C3⋊D3C2412yes—
328C22×C3×D3C2411yescharacteristic
329C32×Q8—22no—
330C2×C32×C4C2412yes—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2412yes—
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2414yes—
337C4⋊(C3⋊D3)C2×Q814yescomplemented
338C4×C3⋊D3—24no—
339C4×C3⋊D3—44no—
340#634—42no—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2414yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2411yescharacteristic
349C3×C4×D3—22no—
350C3×C4×D3—22no—
351C3×C4×D3C2×Q814yescomplemented
352C3×Dic6—22no—
353C3×Dic6—24no—
354C3×Dic6—42no—
355C3×Dic6—44no—
356C3×Dic6C2×Q814yescomplemented
357#627—28no—
358#627—44no—
359#626C2×Q818yescomplemented
360#624—24no—
361#624—44no—
362#624C2×Q818yescomplemented
363D3×Dic3—44no—
364Q82—31no—
365Q82—91no—
366#557—92no—
367#554—92no—
368#554—91no—
369#554—92no—
370#554—91no—
371D4×Q8—92no—
372D4×Q8—94no—
373#544—92no—
374#544—94no—
375#533—31no—
376#533—92no—
377C2×C4⋊Q8—91no—
378C2×C4⋊Q8—92no—
379#520—92no—
380C4×#41—91no—
381C2×C3×Q8—21no—
382C2×C3×Q8—31no—
383C2×C3×Q8—32no—
384C2×C3×Q8—31no—
385C2×C3×Q8—34no—
386C2×C3×Q8—32no—
387C2×C3×Q8C22×D311yescharacteristic
388C2×C3×Q8C22×D311yescharacteristic
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C2×#67—32no—
393C22×Dic3—34no—
394#239—38no—
395D3×Q8—128no—
396D3×Q8—128no—
397D3×Q8—124no—
398#235—38no—
399C2×D12—32no—
400C2×D12—31no—
401C2×D12—31no—
402C2×D12—61no—
403C2×C4×D3—32no—
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—32no—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—62no—
415C2×C4×D3—64no—
416C2×C4×D3C22×D311yescharacteristic
417C2×C4×D3C22×D311yescharacteristic
418C2×C4×D3C22×D311yescharacteristic
419C2×Dic6—34no—
420C2×Dic6—34no—
421C2×Dic6—32no—
422C2×Dic6—32no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—62no—
426C2×Dic6—124no—
427C2×Dic6C22×D311yescharacteristic
428C2×Dic6C22×D312yes—
429C2×Dic6C22×D312yes—
430C2×Dic6C22×D314yes—
431C2×Dic6C22×D311yescharacteristic
432C3×C4⋊C4—21no—
433C3×C4⋊C4—22no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—32no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—32no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—34no—
441C3×C4⋊C4—32no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—34no—
446C3×C4⋊C4—32no—
447C3×C4⋊C4C22×D311yescharacteristic
448C3×C4⋊C4C22×D312yes—
449C3×C4⋊C4C22×D311yescharacteristic
450C3×C4⋊C4C22×D312yes—
451C3×C22⋊C4—32no—
452C3×C22⋊C4—32no—
453C3×C42—21no—
454C3×C42—22no—
455C3×C42—31no—
456C3×C42—32no—
457C3×C42—32no—
458C3×C42—34no—
459C3×C42—31no—
460C3×C42—31no—
461C3×C42C22×D311yescharacteristic
462C3×C42C22×D311yescharacteristic
463C3×C42C22×D312yes—
464C3×C42C22×D312yes—
465#217—32no—
466(C2×D3)⋊C4—32no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—32no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—32no—
475(C2×D3)⋊C4—62no—
476(C2×D3)⋊C4—64no—
477(C2×D3)⋊C4C22×D312yes—
478(C2×D3)⋊C4C22×D312yes—
479C4⋊Dic3—32no—
480C4⋊Dic3—32no—
481C4⋊Dic3—31no—
482C4⋊Dic3—32no—
483C4⋊Dic3—32no—
484C4⋊Dic3—31no—
485C4⋊Dic3—34no—
486C4⋊Dic3—34no—
487C4⋊Dic3—34no—
488C4⋊Dic3—34no—
489C4⋊Dic3—34no—
490C4⋊Dic3—32no—
491C4⋊Dic3—62no—
492C4⋊Dic3—62no—
493C4⋊Dic3—61no—
494C4⋊Dic3C22×D311yescharacteristic
495C4⋊Dic3C22×D311yescharacteristic
496C4⋊Dic3C22×D312yes—
497C4⋊Dic3C22×D312yes—
498C4⋊Dic3C22×D312yes—
499C4⋊Dic3C22×D314yes—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—32no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—64no—
513Dic3⋊C4—64no—
514Dic3⋊C4C22×D312yes—
515Dic3⋊C4C22×D312yes—
516Dic3⋊C4C22×D312yes—
517Dic3⋊C4C22×D314yes—
518Dic3⋊C4C22×D312yes—
519Dic3⋊C4C22×D312yes—
520Dic3⋊C4C22×D312yes—
521C4×Dic3—32no—
522C4×Dic3—34no—
523C4×Dic3—32no—
524C4×Dic3—34no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3C22×D311yescharacteristic
528C4×Dic3C22×D312yes—
529C4×Dic3C22×D312yes—
530C4×Dic3C22×D314yes—
531C4×Dic3C22×D311yescharacteristic
532C4×Dic3C22×D311yescharacteristic
533C22×C32C2511yescharacteristic
534C2×C3⋊D3—22no—
535C2×C3⋊D3—22no—
536C2×C3⋊D3C22×Q814yes—
537C2×C3×D3—21no—
538C2×C3×D3—21no—
539C2×C3×D3C22×Q812yes—
540C32×C4—22no—
541C32×C4—21no—
542C32×C4—22no—
543C32×C4C22×Q812yes—
544C32×C42−1+412yes—
545C3⋊Dic3—24no—
546C3⋊Dic3—22no—
547C3×Dic3—24no—
548C3×Dic3—22no—
549C3×Dic3—22no—
550C3×Dic3—22no—
551C3×Dic3—21no—
552C3×Dic3C22×Q812yes—
553C3×Dic3C22×Q814yes—
554C3×Dic3H(5,𝔽2)12yes—
555C2×#41—91no—
556C22×Q8—92no—
557C22×Q8—94no—
558C4⋊Q8—31no—
559C4⋊Q8—31no—
560C4⋊Q8—32no—
561C4⋊Q8—34no—
562C4⋊Q8—31no—
563C4⋊Q8—32no—
564C4⋊Q8—92no—
565C4⋊Q8—92no—
566C4⋊Q8—92no—
567C4⋊Q8—92no—
568C4⋊Q8—92no—
569C4⋊Q8—94no—
570C4⋊Q8—94no—
571C4⋊Q8—94no—
572C4⋊Q8—91no—
573#125—32no—
574#125—94no—
575#125—92no—
576#125—94no—
577#125—94no—
578#125—92no—
579C22⋊Q8—31no—
580C22⋊Q8—32no—
581C22⋊Q8—31no—
582C22⋊Q8—94no—
583C22⋊Q8—94no—
584C22⋊Q8—94no—
585C22⋊Q8—94no—
586C22⋊Q8—92no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—92no—
590C22⋊Q8—94no—
591C4×Q8—32no—
592C4×Q8—31no—
593C4×Q8—32no—
594C4×Q8—32no—
595C4×Q8—31no—
596C4×Q8—94no—
597C4×Q8—91no—
598C4×Q8—92no—
599C4×Q8—92no—
600C4×Q8D3211yescharacteristic
601C4×D4—94no—
602C4×D4—91no—
603C4×D4—92no—
604C4×D4—92no—
605C4×D4—94no—
606C4×D4—92no—
607C4×D4—91no—
608C4×D4—92no—
609#117—32no—
610#117—92no—
611#117—94no—
612#117—91no—
613C2×C4⋊C4—94no—
614C2×C4⋊C4—92no—
615C2×C4⋊C4—92no—
616C2×C4⋊C4—92no—
617C2×C4⋊C4—92no—
618C2×C42—31no—
619C2×C42—92no—
620C23×C3—31no—
621C22×D3—32no—
622C22×D3—32no—
623C22×D3—62no—
624C22×D3C23×D311yescharacteristic
625C3×Q8—22no—
626C3×Q8—22no—
627C3×Q8—34no—
628C3×Q8—42no—
629C3×Q8—64no—
630C3×Q8—62no—
631C3×Q8—124no—
632C3×Q8—122no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—21no—
638C2×C3×C4—32no—
639C2×C3×C4—31no—
640C2×C3×C4—31no—
641C2×C3×C4—34no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—34no—
646C2×C3×C4—31no—
647C2×C3×C4—62no—
648C2×C3×C4—62no—
649C2×C3×C4C23×D312yes—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D312yes—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659#67—38no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—34no—
663C2×Dic3—34no—
664C2×Dic3—62no—
665C2×Dic3—64no—
666C2×Dic3—124no—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D311yescharacteristic
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D314yes—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D311yescharacteristic
674C2×Dic3C23×D311yescharacteristic
675D12—38no—
676D12—34no—
677D12—34no—
678D12—64no—
679C4×D3—22no—
680C4×D3—22no—
681C4×D3—38no—
682C4×D3—38no—
683C4×D3—64no—
684C4×D3—64no—
685C4×D3—64no—
686C4×D3—64no—
687C4×D3—124no—
688C4×D3—124no—
689C4×D3—124no—
690C4×D3—124no—
691C4×D3—124no—
692C4×D3—124no—
693C4×D3—244no—
694C4×D3D3×Q814yescomplemented
695Dic6—22no—
696Dic6—24no—
697Dic6—42no—
698Dic6—44no—
699Dic6—68no—
700Dic6—68no—
701Dic6—124no—
702Dic6—124no—
703Dic6—122no—
704Dic6—122no—
705Dic6—242no—
706Dic6D3×Q814yescomplemented
707C2×C32C23×Q811yescharacteristic
708C2×C32C2×H(5,𝔽2)11yescharacteristic
709C2×C32C2×2−1+411yescharacteristic
710C3⋊D3—24no—
711C3×D3—22no—
712#41—98no—
713C2×Q8—31no—
714C2×Q8—31no—
715C2×Q8—32no—
716C2×Q8—34no—
717C2×Q8—32no—
718C2×Q8—94no—
719C2×Q8—94no—
720C2×Q8—92no—
721C2×Q8—364no—
722C2×Q8—368no—
723C2×Q8C2×D3211yescharacteristic
724C2×D4—92no—
725C2×D4—91no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—92no—
730C22×C4—92no—
731C22×C4—94no—
732C22×C4—94no—
733C22×C4—92no—
734C22×C4—94no—
735C4⋊C4—32no—
736C4⋊C4—31no—
737C4⋊C4—32no—
738C4⋊C4—34no—
739C4⋊C4—32no—
740C4⋊C4—32no—
741C4⋊C4—32no—
742C4⋊C4—31no—
743C4⋊C4—32no—
744C4⋊C4—32no—
745C4⋊C4—32no—
746C4⋊C4—32no—
747C4⋊C4—34no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—92no—
753C4⋊C4—94no—
754C4⋊C4—94no—
755C4⋊C4—92no—
756C4⋊C4—92no—
757C4⋊C4—94no—
758C4⋊C4—91no—
759C4⋊C4—94no—
760C4⋊C4C2×D3211yescharacteristic
761C4⋊C4C2×D3212yes—
762C22⋊C4—32no—
763C22⋊C4—32no—
764C22⋊C4—92no—
765C22⋊C4—94no—
766C22⋊C4—92no—
767C22⋊C4—92no—
768C22⋊C4—94no—
769C42—31no—
770C42—31no—
771C42—31no—
772C42—32no—
773C42—32no—
774C42—34no—
775C42—92no—
776C42—92no—
777C42—94no—
778C42C2×D3211yescharacteristic
779C42C2×D3212yes—
780C22×C3—21no—
781C22×C3—32no—
782C22×C3—61no—
783C22×C3—61no—
784C22×C3C24×D311yescharacteristic
785C22×C3C24×D311yescharacteristic
786C2×D3—21no—
787C2×D3—21no—
788C2×D3—34no—
789C2×D3—34no—
790C2×D3—64no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—122no—
796C2×D3—122no—
797C2×D3C2×D3×Q812yes—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—21no—
801C3×C4—22no—
802C3×C4—21no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—32no—
807C3×C4—34no—
808C3×C4—32no—
809C3×C4—41no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4—61no—
813C3×C4—62no—
814C3×C4—64no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4C2×D3×Q812yes—
818C3×C4C2×D3×Q812yes—
819C3×C4#100712yes—
820C3×C4#101012yes—
821Dic3—22no—
822Dic3—22no—
823Dic3—21no—
824Dic3—24no—
825Dic3—22no—
826Dic3—62no—
827Dic3—64no—
828Dic3—62no—
829Dic3—64no—
830Dic3—124no—
831Dic3—122no—
832Dic3C2×D3×Q814yes—
833Dic3C2×D3×Q812yes—
834Dic3#100912yes—
835C32#350311yescharacteristic, complemented, Sylow
836C23—31no—
837C23—92no—
838Q8—22no—
839Q8—34no—
840Q8—64no—
841Q8—62no—
842Q8—122no—
843Q8—124no—
844Q8—188no—
845Q8—362no—
846Q8—364no—
847D4—98no—
848D4—94no—
849C2×C4—32no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—34no—
853C2×C4—31no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—34no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—98no—
861C2×C4—92no—
862C2×C4—94no—
863C2×C4—184no—
864C2×C4—184no—
865C2×C4—364no—
866C2×C4—364no—
867C2×C4—364no—
868C2×C4C22×D3212yes—
869C2×C4C22×D3211yescharacteristic
870C2×C4C22×D3212yes—
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3211yescharacteristic
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—62no—
877C2×C3C22×D3×Q811yescharacteristic
878C2×C3C22×D3×Q811yescharacteristic
879C2×C3C2×#100711yescharacteristic
880C2×C3C2×#100911yescharacteristic
881C2×C3C2×#101011yescharacteristic
882C2×C3D3×H(5,𝔽2)11yescharacteristic
883D3—22no—
884D3—64no—
885D3—64no—
886D3—124no—
887C22—32no—
888C22—61no—
889C22—61no—
890C22—94no—
891C22—182no—
892C22—182no—
893C22C23×D3211yescharacteristic
894C4—22no—
895C4—21no—
896C4—22no—
897C4—32no—
898C4—34no—
899C4—32no—
900C4—61no—
901C4—62no—
902C4—62no—
903C4—62no—
904C4—64no—
905C4—182no—
906C4—184no—
907C4#6429712yes—
908C4D32×Q812yes—
909C3—21no—
910C3#8628111yescharacteristic, complemented
911C3#8704111yescharacteristic, complemented
912C2—62no—
913C2—184no—
914C2C2×#6429711yescharacteristic
915C2C2×D32×Q811yescharacteristic
916C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3799C22
hypercenterC4×Q8D32
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596050C2semidirect
2. C3×#5578C2semidirect
3. C3×Q8×Dic6C2semidirect
4. #10595374C2semidirect
5. #10595371C2semidirect
6. #10594400C2semidirect
7. #10594393C2semidirect
8. #10594378C2semidirect
9. #10594374C2semidirect
11. #10593958C2semidirect
12. #10593954C2semidirect
13. #10593903C2semidirect
14. D3×#869C2semidirect
16. Dic62C2semidirect
17. #10593851C2semidirect
107. #5578D3semidirect
115. Q8×Dic6D3semidirect
140. #3799Q8semidirect
337. C4⋊(C3⋊D3)C2×Q8semidirect
351. C3×C4×D3C2×Q8semidirect
356. C3×Dic6C2×Q8semidirect
359. #626C2×Q8semidirect
362. #624C2×Q8semidirect
694. C4×D3D3×Q8semidirect
706. Dic6D3×Q8semidirect
835. C32#3503semidirect
910. C3#86281semidirect
911. C3#87041semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#55782
C3×Q8×Dic62
#105953742
#105953712
#105944002
#105943932
#105943782
#105943742
C4×#37992
#105939582
#105939542
#105939032
D3×#8692
#105938902
Dic622
#105938512
#870413
#862813