Finite Group Databasebeta

← #10596099⋊C3 #13152953

Subgroups — #10596099⋊C3 #13152953

Order 1728.

1019 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
2C2×#3828⋊C3C211yesmaximal, characteristic
3H(3,𝔽3)×C22⋊Q8C211yesmaximal, characteristic, complemented
4#64155⋊C3C211yesmaximal, characteristic, complemented
5#64133⋊C3C211yesmaximal, characteristic, complemented
6#64106⋊C3C211yesmaximal, characteristic, complemented
7#64103⋊C3C212yesmaximal, complemented
8#64101⋊C3C211yesmaximal, characteristic, complemented
9#64097⋊C3C212yesmaximal, complemented
10#64094⋊C3C212yesmaximal, complemented
11#64092⋊C3C212yesmaximal, complemented
12#10596099C311yesmaximal, characteristic, complemented
13C3×#5628—31nomaximal
14C2×Q8×H(3,𝔽3)C2211yescharacteristic
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C2×#638⋊C3C2211yescharacteristic
17C2×#638⋊C3C2211yescharacteristic
18Q8×(C3⋊D3)⋊C3—24no—
19#3828⋊C3—24no—
20C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2212yes—
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×#634⋊C3C2211yescharacteristic
25C2×#634⋊C3C2211yescharacteristic
26C2×#634⋊C3C2212yes—
27C4⋊C4×H(3,𝔽3)C2212yes—
28C4⋊C4×H(3,𝔽3)C2211yescharacteristic
29C22⋊C4×H(3,𝔽3)C2212yes—
30#3757⋊C3C2212yes—
31#3752⋊C3C2212yes—
32#3752⋊C3C2212yes—
33#3752⋊C3C2212yes—
34C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
35C4⋊((C3⋊Dic3)⋊C3)C2212yes—
36#3750⋊C3C2212yes—
37#3750⋊C3C2212yes—
38C4×(C3⋊Dic3)⋊C3C2212yes—
39C2×Q8×C3⋊D3C2×C311yescharacteristic, complemented
40C2×#3828C2×C311yescharacteristic
41C2×C3×D3×Q8—31no—
42C2×C3×#235—31no—
43C32×C22⋊Q8—21no—
44C32×C22⋊Q8D311yescharacteristic, complemented
45C32×C22⋊Q8C2×C311yescharacteristic, complemented
46#64155C2×C311yescharacteristic, complemented
47#64133C2×C311yescharacteristic, complemented
48#64106C2×C311yescharacteristic, complemented
49#64103C2×C312yescomplemented
50#64101C2×C311yescharacteristic, complemented
51#64097C2×C312yescomplemented
52#64094C2×C312yescomplemented
53#64092C2×C312yescomplemented
54C3×#946—31no—
55C3×#924—31no—
56C3×#897—31no—
57C3×#894—32no—
58C3×#892—31no—
59C3×#888—32no—
60C3×#885—32no—
61C3×#883—32no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×(C3⋊D3)⋊C3C2311yescharacteristic
64C22×(C3⋊D3)⋊C3C2311yescharacteristic
65Q8×H(3,𝔽3)—22no—
66C2×C4×H(3,𝔽3)—22no—
67C2×C4×H(3,𝔽3)C2312yes—
68C2×C4×H(3,𝔽3)C2311yescharacteristic
69C2×C4×H(3,𝔽3)C2312yes—
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71#638⋊C3—22no—
72#638⋊C3—22no—
73C2×(C3⋊Dic3)⋊C3C2312yes—
74C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
75C2×(C3⋊Dic3)⋊C3C2312yes—
76C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
77C4⋊((C3⋊D3)⋊C3)—22no—
78C4×(C3⋊D3)⋊C3—24no—
79C4×(C3⋊D3)⋊C3—22no—
80C4×(C3⋊D3)⋊C3D414yes—
81#634⋊C3—22no—
82#634⋊C3—22no—
83#634⋊C3—24no—
84C3×#536—91no—
85#5628—31no—
86#5628—91no—
87C2×C32×Q8—21no—
88C2×C32×Q8C2×D311yescharacteristic
89C2×C32×Q8C22×C311yescharacteristic
90C22×C32×C4—21no—
91C22×C32×C4C2×D311yescharacteristic
92C22×C32×C4C22×C311yescharacteristic
93C2×#638C22×C311yescharacteristic
94C2×#638C22×C311yescharacteristic
95Q8×C3⋊D3—24no—
96#3828—24no—
97C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
98C2×C4×C3⋊D3C22×C312yes—
99C2×C4×C3⋊D3C22×C311yescharacteristic
100C2×C4×C3⋊D3C22×C311yescharacteristic
101C2×#634C22×C312yes—
102C2×#634C22×C311yescharacteristic
103C2×#634C22×C311yescharacteristic
104C2×C3×#67—31no—
105C2×C3×#67—31no—
106C3×D3×Q8—64no—
107C3×#235—64no—
108C2×C3×D12—31no—
109C2×C3×C4×D3—31no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—31no—
112C2×C3×Dic6—32no—
113C2×C3×Dic6—31no—
114C2×C3×Dic6—31no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4—22no—
117C32×C4⋊C4C2×D312yes—
118C32×C4⋊C4C2×D311yescharacteristic
119C32×C4⋊C4C22×C312yes—
120C32×C4⋊C4C22×C311yescharacteristic
121C32×C22⋊C4—22no—
122C32×C22⋊C4C2×D312yes—
123C32×C22⋊C4C22×C312yes—
124#3757C22×C312yes—
125#3752C22×C312yes—
126#3752C22×C312yes—
127#3752C22×C312yes—
128C4⋊(C3⋊Dic3)C22×C312yes—
129C4⋊(C3⋊Dic3)C22×C311yescharacteristic
130#3750C22×C312yes—
131#3750C22×C312yes—
132C4×C3⋊Dic3C22×C312yes—
133C3×#217—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—31no—
139C3×Dic3⋊C4—32no—
140C3×Dic3⋊C4—32no—
141C3×C4×Dic3—32no—
142C22×H(3,𝔽3)—21no—
143C22×H(3,𝔽3)—21no—
144C22×H(3,𝔽3)—21no—
145C22×H(3,𝔽3)C2411yescharacteristic
146C2×(C3⋊D3)⋊C3—21no—
147C2×(C3⋊D3)⋊C3—21no—
148C2×(C3⋊D3)⋊C3—21no—
149C2×(C3⋊D3)⋊C3—21no—
150C2×(C3⋊D3)⋊C3—21no—
151C2×(C3⋊D3)⋊C3C2×D412yes—
152C4×H(3,𝔽3)—22no—
153C4×H(3,𝔽3)—21no—
154C4×H(3,𝔽3)—22no—
155C4×H(3,𝔽3)C2×D412yes—
156(C3⋊Dic3)⋊C3—22no—
157(C3⋊Dic3)⋊C3—21no—
158(C3⋊Dic3)⋊C3—22no—
159(C3⋊Dic3)⋊C3C2×D412yes—
160C2×C3×#41—91no—
161C22×C3×Q8—91no—
162C2×D3×Q8—31no—
163C2×D3×Q8—91no—
164C2×#235—31no—
165C2×#235—91no—
166C3×C4⋊Q8—92no—
167C3×#124—92no—
168C3×#123—92no—
169C3×#123—92no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—61no—
173C3×C22⋊Q8—91no—
174C3×C22⋊Q8—91no—
175C3×C22⋊Q8—91no—
176C3×C22⋊Q8C3×D311yescharacteristic
177C3×#117—91no—
178#946—31no—
179#946—91no—
180#924—31no—
181#924—91no—
182#897—31no—
183#897—91no—
184#894—32no—
185#894—92no—
186#892—31no—
187#892—91no—
188#888—32no—
189#888—92no—
190#885—32no—
191#885—92no—
192#883—32no—
193#883—92no—
194C23×C32—21no—
195C23×C32C22×D311yescharacteristic
196C23×C32C23×C311yescharacteristic
197C22×C3⋊D3C23×C311yescharacteristic
198C22×C3⋊D3C23×C311yescharacteristic
199C22×C3×D3—31no—
200C22×C3×D3—31no—
201C32×Q8—22no—
202C32×Q8—22no—
203C32×Q8—42no—
204C2×C32×C4—22no—
205C2×C32×C4—22no—
206C2×C32×C4—21no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—21no—
210C2×C32×C4—42no—
211C2×C32×C4C22×D312yes—
212C2×C32×C4C22×D311yescharacteristic
213C2×C32×C4C22×D312yes—
214C2×C32×C4C22×D311yescharacteristic
215C2×C32×C4C23×C312yes—
216C2×C32×C4C23×C311yescharacteristic
217C2×C32×C4C23×C312yes—
218C2×C32×C4C23×C311yescharacteristic
219#638—22no—
220#638—22no—
221C2×C3⋊Dic3C23×C312yes—
222C2×C3⋊Dic3C23×C311yescharacteristic
223C2×C3⋊Dic3C23×C312yes—
224C2×C3⋊Dic3C23×C311yescharacteristic
225C4⋊(C3⋊D3)—22no—
226C4×C3⋊D3—24no—
227C4×C3⋊D3—22no—
228C4×C3⋊D3C3×D414yes—
229#634—22no—
230#634—22no—
231#634—24no—
232C3×#67—62no—
233C3×#67—62no—
234C2×C3×Dic3—31no—
235C2×C3×Dic3—32no—
236C2×C3×Dic3—31no—
237C2×C3×Dic3—32no—
238C3×D12—62no—
239C3×C4×D3—34no—
240C3×C4×D3—64no—
241C3×C4×D3—62no—
242C3×Dic6—62no—
243C3×Dic6—64no—
244C3×Dic6—62no—
245#536—91noSylow
246C2×H(3,𝔽3)—41no—
247C2×H(3,𝔽3)C22×D411yescharacteristic
248C2×H(3,𝔽3)2−1+411yescharacteristic
249C2×H(3,𝔽3)2−1+411yescharacteristic
250(C3⋊D3)⋊C3—22no—
251(C3⋊D3)⋊C3—41no—
252C3×#41—184no—
253C2×C3×Q8—31no—
254C2×C3×Q8—31no—
255C2×C3×Q8—61no—
256C2×C3×Q8—91no—
257C2×C3×Q8—92no—
258C2×C3×Q8—91no—
259C2×C3×Q8—184no—
260C2×C3×Q8C2×C3×D311yescharacteristic
261C2×C3×D4—91no—
262C2×C3×D4—91no—
263C2×C3×D4—91no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—61no—
267C22×C3×C4—91no—
268C22×C3×C4—91no—
269C22×C3×C4—92no—
270C22×C3×C4C2×C3×D311yescharacteristic
271C2×#67—31no—
272C2×#67—31no—
273C2×#67—91no—
274C2×#67—91no—
275D3×Q8—64no—
276D3×Q8—184no—
277#235—64no—
278#235—184no—
279C2×D12—31no—
280C2×D12—91no—
281C2×C4×D3—31no—
282C2×C4×D3—32no—
283C2×C4×D3—31no—
284C2×C4×D3—91no—
285C2×C4×D3—92no—
286C2×C4×D3—91no—
287C2×Dic6—32no—
288C2×Dic6—31no—
289C2×Dic6—31no—
290C2×Dic6—92no—
291C2×Dic6—91no—
292C2×Dic6—91no—
293C3×C4⋊C4—32no—
294C3×C4⋊C4—31no—
295C3×C4⋊C4—31no—
296C3×C4⋊C4—32no—
297C3×C4⋊C4—61no—
298C3×C4⋊C4—62no—
299C3×C4⋊C4—92no—
300C3×C4⋊C4—92no—
301C3×C4⋊C4—91no—
302C3×C4⋊C4—92no—
303C3×C4⋊C4C2×C3×D312yes—
304C3×C4⋊C4C2×C3×D311yescharacteristic
305C3×C22⋊C4—32no—
306C3×C22⋊C4—32no—
307C3×C22⋊C4—62no—
308C3×C22⋊C4—92no—
309C3×C22⋊C4—92no—
310C3×C22⋊C4—92no—
311C3×C22⋊C4—92no—
312C3×C22⋊C4C2×C3×D312yes—
313C3×C42—92no—
314#217—32no—
315#217—92no—
316(C2×D3)⋊C4—32no—
317(C2×D3)⋊C4—32no—
318(C2×D3)⋊C4—32no—
319(C2×D3)⋊C4—92no—
320(C2×D3)⋊C4—92no—
321(C2×D3)⋊C4—92no—
322C4⋊Dic3—32no—
323C4⋊Dic3—31no—
324C4⋊Dic3—92no—
325C4⋊Dic3—91no—
326Dic3⋊C4—32no—
327Dic3⋊C4—32no—
328Dic3⋊C4—92no—
329Dic3⋊C4—92no—
330C4×Dic3—32no—
331C4×Dic3—92no—
332C22×C32—22no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—21no—
336C22×C32—21no—
337C22×C32—21no—
338C22×C32—21no—
339C22×C32—21no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32C23×D311yescharacteristic
343C22×C32C24×C311yescharacteristic
344C2×C3⋊D3—21no—
345C2×C3⋊D3—21no—
346C2×C3⋊D3—21no—
347C2×C3⋊D3—21no—
348C2×C3⋊D3—21no—
349C2×C3⋊D3C2×C3×D412yes—
350C2×C3×D3—32no—
351C2×C3×D3—61no—
352C2×C3×D3—61no—
353C2×C3×D3—61no—
354C2×C3×D3—61no—
355C2×C3×D3—61no—
356C32×C4—22no—
357C32×C4—21no—
358C32×C4—22no—
359C32×C4—22no—
360C32×C4—21no—
361C32×C4—22no—
362C32×C4—22no—
363C32×C4—42no—
364C32×C4—41no—
365C32×C4—42no—
366C32×C4D3×D412yes—
367C32×C4C2×C3×D412yes—
368C3⋊Dic3—22no—
369C3⋊Dic3—21no—
370C3⋊Dic3—22no—
371C3⋊Dic3C2×C3×D412yes—
372C3×Dic3—32no—
373C3×Dic3—62no—
374C3×Dic3—61no—
375C3×Dic3—62no—
376C2×#41—91no—
377C22×Q8—91no—
378C4⋊Q8—92no—
379#124—92no—
380#123—92no—
381#123—92no—
382C22⋊Q8—91no—
383C22⋊Q8—91no—
384C22⋊Q8—91no—
385C22⋊Q8(C3⋊D3)⋊C311yescharacteristic, complemented
386#117—91no—
387H(3,𝔽3)#53611yescharacteristic, complemented, Sylow
388C23×C3—31no—
389C23×C3—31no—
390C23×C3—61no—
391C23×C3—91no—
392C23×C3—91no—
393C23×C3C22×C3×D311yescharacteristic
394C22×D3—31no—
395C22×D3—31no—
396C22×D3—91no—
397C22×D3—91no—
398C3×Q8—22no—
399C3×Q8—62no—
400C3×Q8—62no—
401C3×Q8—122no—
402C3×Q8—182no—
403C3×Q8—184no—
404C3×Q8—182no—
405C3×D4—182no—
406C3×D4—182no—
407C3×D4—182no—
408C2×C3×C4—22no—
409C2×C3×C4—31no—
410C2×C3×C4—31no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—31no—
414C2×C3×C4—32no—
415C2×C3×C4—31no—
416C2×C3×C4—32no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—61no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—61no—
423C2×C3×C4—94no—
424C2×C3×C4—91no—
425C2×C3×C4—92no—
426C2×C3×C4—92no—
427C2×C3×C4—91no—
428C2×C3×C4—122no—
429C2×C3×C4—182no—
430C2×C3×C4—184no—
431C2×C3×C4C22×C3×D312yes—
432C2×C3×C4C22×C3×D311yescharacteristic
433C2×C3×C4C22×C3×D312yes—
434C2×C3×C4C22×C3×D311yescharacteristic
435#67—62no—
436#67—62no—
437#67—182no—
438#67—182no—
439C2×Dic3—31no—
440C2×Dic3—32no—
441C2×Dic3—31no—
442C2×Dic3—32no—
443C2×Dic3—91no—
444C2×Dic3—92no—
445C2×Dic3—91no—
446C2×Dic3—92no—
447D12—62no—
448D12—182no—
449C4×D3—34no—
450C4×D3—64no—
451C4×D3—62no—
452C4×D3—94no—
453C4×D3—182no—
454C4×D3—184no—
455Dic6—62no—
456Dic6—64no—
457Dic6—62no—
458Dic6—182no—
459Dic6—184no—
460Dic6—182no—
461C2×C32—21no—
462C2×C32—21no—
463C2×C32—21no—
464C2×C32—42no—
465C2×C32—41no—
466C2×C32—41no—
467C2×C32C2×D3×D411yescharacteristic
468C2×C32#100711yescharacteristic
469C2×C32#101011yescharacteristic
470C2×C32C22×C3×D411yescharacteristic
471C2×C32C3×2−1+411yescharacteristic
472C2×C32C3×2−1+411yescharacteristic
473C3⋊D3—22no—
474C3⋊D3—41no—
475C3×D3—62no—
476C3×D3—121no—
477#41—184no—
478C2×Q8—91no—
479C2×Q8—92no—
480C2×Q8—91no—
481C2×Q8—184no—
482C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic
483C2×D4—91no—
484C2×D4—91no—
485C2×D4—91no—
486C22×C4—91no—
487C22×C4—91no—
488C22×C4—92no—
489C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
490C4⋊C4—91no—
491C4⋊C4—92no—
492C4⋊C4—92no—
493C4⋊C4—92no—
494C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
495C4⋊C4C2×(C3⋊D3)⋊C312yes—
496C22⋊C4—92no—
497C22⋊C4—92no—
498C22⋊C4—92no—
499C22⋊C4—92no—
500C22⋊C4C2×(C3⋊D3)⋊C312yes—
501C42—92no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—31no—
506C22×C3—31no—
507C22×C3—61no—
508C22×C3—61no—
509C22×C3—61no—
510C22×C3—61no—
511C22×C3—61no—
512C22×C3—61no—
513C22×C3—62no—
514C22×C3—61no—
515C22×C3—92no—
516C22×C3—121no—
517C22×C3—121no—
518C22×C3—181no—
519C22×C3—181no—
520C22×C3—181no—
521C22×C3—181no—
522C22×C3—181no—
523C22×C3C23×C3×D311yescharacteristic
524C2×D3—32no—
525C2×D3—61no—
526C2×D3—61no—
527C2×D3—61no—
528C2×D3—61no—
529C2×D3—61no—
530C2×D3—92no—
531C2×D3—181no—
532C2×D3—181no—
533C2×D3—181no—
534C2×D3—181no—
535C2×D3—181no—
536C3×C4—22no—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—32no—
540C3×C4—32no—
541C3×C4—62no—
542C3×C4—61no—
543C3×C4—61no—
544C3×C4—62no—
545C3×C4—62no—
546C3×C4—62no—
547C3×C4—62no—
548C3×C4—92no—
549C3×C4—121no—
550C3×C4—122no—
551C3×C4—122no—
552C3×C4—181no—
553C3×C4—182no—
554C3×C4—182no—
555C3×C4C3×D3×D412yes—
556Dic3—32no—
557Dic3—62no—
558Dic3—61no—
559Dic3—62no—
560Dic3—92no—
561Dic3—182no—
562Dic3—181no—
563Dic3—182no—
564C32—21no—
565C32#562811yescharacteristic, complemented
566C32C3×#53611yescharacteristic, complemented
567C23—91no—
568C23—91no—
569C23C22×(C3⋊D3)⋊C311yescharacteristic
570Q8—22no—
571Q8—184no—
572Q8—182no—
573Q8—182no—
574D4—182no—
575D4—182no—
576D4—182no—
577C2×C4—22no—
578C2×C4—91no—
579C2×C4—94no—
580C2×C4—92no—
581C2×C4—92no—
582C2×C4—91no—
583C2×C4—184no—
584C2×C4—182no—
585C2×C4C22×(C3⋊D3)⋊C312yes—
586C2×C4C22×(C3⋊D3)⋊C312yes—
587C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
588C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
589C2×C3—31no—
590C2×C3—31no—
591C2×C3—31no—
592C2×C3—31no—
593C2×C3—31no—
594C2×C3—31no—
595C2×C3—41no—
596C2×C3—61no—
597C2×C3—61no—
598C2×C3—61no—
599C2×C3—121no—
600C2×C3—121no—
601C2×C3—122no—
602C2×C3—182no—
603C2×C3—361no—
604C2×C3C2×C3×D3×D411yescharacteristic
605C2×C3C3×#100711yescharacteristic
606C2×C3C3×#101011yescharacteristic
607D3—62no—
608D3—121no—
609D3—182no—
610D3—361no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—92no—
615C22—181no—
616C22—181no—
617C22—181no—
618C22—181no—
619C22—181no—
620C22C23×(C3⋊D3)⋊C311yescharacteristic
621C4—21no—
622C4—22no—
623C4—22no—
624C4—92no—
625C4—181no—
626C4—182no—
627C4—182no—
628C4D4×(C3⋊D3)⋊C312yes—
629C3—31no—
630C3—31no—
631C3—61no—
632C3C3×#562811yescharacteristic
633C2—41no—
634C2—182no—
635C2—361no—
636C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
637C2#1172262711yescharacteristic
638C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×C22⋊Q8C2
prime radicalC2×#3828⋊C3C2
hypercenterC22⋊Q8(C3⋊D3)⋊C3
hypocenterC32C3×#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×(C3⋊D3)⋊C3C2semidirect
3. H(3,𝔽3)×C22⋊Q8C2semidirect
4. #64155⋊C3C2semidirect
5. #64133⋊C3C2semidirect
6. #64106⋊C3C2semidirect
7. #64103⋊C3C2semidirect
8. #64101⋊C3C2semidirect
9. #64097⋊C3C2semidirect
10. #64094⋊C3C2semidirect
11. #64092⋊C3C2semidirect
12. #10596099C3semidirect
39. C2×Q8×C3⋊D3C2×C3semidirect
44. C32×C22⋊Q8D3semidirect
45. C32×C22⋊Q8C2×C3semidirect
46. #64155C2×C3semidirect
47. #64133C2×C3semidirect
48. #64106C2×C3semidirect
49. #64103C2×C3semidirect
50. #64101C2×C3semidirect
51. #64097C2×C3semidirect
52. #64094C2×C3semidirect
53. #64092C2×C3semidirect
385. C22⋊Q8(C3⋊D3)⋊C3semidirect
387. H(3,𝔽3)#536semidirect
565. C32#5628semidirect
566. C32C3×#536semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×(C3⋊D3)⋊C32
C2×#3828⋊C32
H(3,𝔽3)×C22⋊Q82
#64155⋊C32
#64133⋊C32
#64106⋊C32
#64103⋊C32
#64101⋊C32
#64097⋊C32
#64094⋊C32
#64092⋊C32
#105960993
C3×#56283