Finite Group Databasebeta

← #10596103⋊C3 #13152943

Subgroups — #10596103⋊C3 #13152943

Order 1728.

1054 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
2C22×#634⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×C22⋊Q8C211yesmaximal, characteristic, complemented
4#64153⋊C3C211yesmaximal, characteristic, complemented
5C4×#638⋊C3C211yesmaximal, characteristic
6#64106⋊C3C211yesmaximal, characteristic, complemented
7#64105⋊C3C212yesmaximal, complemented
8#64097⋊C3C212yesmaximal, complemented
9#64096⋊C3C211yesmaximal, characteristic, complemented
10#64090⋊C3C212yesmaximal
11#64087⋊C3C212yesmaximal, complemented
12#10596103C311yesmaximal, characteristic, complemented
13C3×#5632—31nomaximal
14C2×Q8×H(3,𝔽3)C2211yescharacteristic
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C2×#638⋊C3C2211yescharacteristic
17C22×(C3⋊Dic3)⋊C3C2212yes—
18Q8×(C3⋊D3)⋊C3—24no—
19C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
20C2×C4×(C3⋊D3)⋊C3C2212yes—
21C2×#634⋊C3—24no—
22C2×#634⋊C3C2211yescharacteristic
23C2×#634⋊C3C2212yes—
24C2×#634⋊C3C2212yes—
25C2×#634⋊C3C2211yescharacteristic
26C4⋊C4×H(3,𝔽3)C2211yescharacteristic
27C4⋊C4×H(3,𝔽3)C2212yes—
28C22⋊C4×H(3,𝔽3)C2212yes—
29#3757⋊C3C2211yescharacteristic
30#3752⋊C3C2211yescharacteristic
31#3752⋊C3C2212yes—
32C4⋊((C3⋊Dic3)⋊C3)C2212yes—
33#3750⋊C3C2211yescharacteristic
34#3750⋊C3C2212yes—
35#3750⋊C3C2212yes—
36#3750⋊C3C2212yes—
37C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
38C4×(C3⋊Dic3)⋊C3C2212yes—
39C2×Q8×C3⋊D3C2×C311yescharacteristic, complemented
40C22×#634C2×C311yescharacteristic, complemented
41C2×C3×D3×Q8—31no—
42C22×C3×Dic6—31no—
43C32×C22⋊Q8—21no—
44C32×C22⋊Q8D311yescharacteristic, complemented
45C32×C22⋊Q8C2×C311yescharacteristic, complemented
46#64153C2×C311yescharacteristic, complemented
47C4×#638C2×C311yescharacteristic
48#64106C2×C311yescharacteristic, complemented
49#64105C2×C312yescomplemented
50#64097C2×C312yescomplemented
51#64096C2×C311yescharacteristic, complemented
52#64090C2×C312yes—
53#64087C2×C312yescomplemented
54C3×#944—31no—
55C3×C4×#67—31no—
56C3×#897—31no—
57C3×#896—32no—
58C3×#888—32no—
59C3×#887—31no—
60C3×#67⋊C4—32no—
61C3×#878—32no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×(C3⋊D3)⋊C3C2311yescharacteristic
64Q8×H(3,𝔽3)—22no—
65C2×C4×H(3,𝔽3)—22no—
66C2×C4×H(3,𝔽3)C2311yescharacteristic
67C2×C4×H(3,𝔽3)C2312yes—
68C2×C4×H(3,𝔽3)C2312yes—
69C2×C4×H(3,𝔽3)C2311yescharacteristic
70#638⋊C3Q814yescomplemented
71C2×(C3⋊Dic3)⋊C3—24no—
72C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
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—
79#634⋊C3—22no—
80#634⋊C3—24no—
81#634⋊C3—24no—
82#634⋊C3D414yescomplemented
83C3×D4×Q8—91no—
84#5632—31no—
85#5632—91no—
86C2×C32×Q8—21no—
87C2×C32×Q8C2×D311yescharacteristic
88C2×C32×Q8C22×C311yescharacteristic
89C22×C32×C4—21no—
90C22×C32×C4C2×D311yescharacteristic
91C22×C32×C4C22×C311yescharacteristic
92C2×#638C22×C311yescharacteristic
93C22×C3⋊Dic3C22×C312yes—
94Q8×C3⋊D3—24no—
95C2×C4×C3⋊D3C22×C312yes—
96C2×C4×C3⋊D3C22×C311yescharacteristic
97C2×#634—24no—
98C2×#634C22×C312yes—
99C2×#634C22×C312yes—
100C2×#634C22×C311yescharacteristic
101C2×#634C22×C311yescharacteristic
102C2×C3×#67—31no—
103C22×C3×Dic3—32no—
104C3×D3×Q8—64no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3—31no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—32no—
109C2×C3×Dic6—32no—
110C2×C3×Dic6—31no—
111C2×C3×Dic6—64no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—22no—
114C32×C4⋊C4C2×D311yescharacteristic
115C32×C4⋊C4C2×D312yes—
116C32×C4⋊C4C22×C311yescharacteristic
117C32×C4⋊C4C22×C312yes—
118C32×C22⋊C4—22no—
119C32×C22⋊C4C2×D312yes—
120C32×C22⋊C4C22×C312yes—
121#3757C22×C311yescharacteristic
122#3752C22×C312yes—
123#3752C22×C311yescharacteristic
124C4⋊(C3⋊Dic3)C22×C312yes—
125#3750C22×C312yes—
126#3750C22×C312yes—
127#3750C22×C312yes—
128#3750C22×C311yescharacteristic
129C4×C3⋊Dic3C22×C312yes—
130C4×C3⋊Dic3C22×C311yescharacteristic
131C3×#217—31no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—31no—
134C3×C4⋊Dic3—32no—
135C3×Dic3⋊C4—32no—
136C3×Dic3⋊C4—32no—
137C3×Dic3⋊C4—32no—
138C3×Dic3⋊C4—31no—
139C3×C4×Dic3—32no—
140C3×C4×Dic3—31no—
141C22×H(3,𝔽3)—21no—
142C22×H(3,𝔽3)—21no—
143C22×H(3,𝔽3)C2×Q812yescomplemented
144C22×H(3,𝔽3)C2411yescharacteristic
145C2×(C3⋊D3)⋊C3—21no—
146C2×(C3⋊D3)⋊C3—21no—
147C2×(C3⋊D3)⋊C3C2×Q812yescomplemented
148C4×H(3,𝔽3)—21no—
149C4×H(3,𝔽3)—22no—
150C4×H(3,𝔽3)—22no—
151C4×H(3,𝔽3)C2×D412yes—
152(C3⋊Dic3)⋊C3—21no—
153(C3⋊Dic3)⋊C3—22no—
154(C3⋊Dic3)⋊C3—21no—
155(C3⋊Dic3)⋊C3C2×D414yes—
156(C3⋊Dic3)⋊C3C2×Q812yescomplemented
157C22×C3×Q8—91no—
158C22×C3×Q8—91no—
159C2×D3×Q8—31no—
160C2×D3×Q8—91no—
161C22×Dic6—31no—
162C22×Dic6—91no—
163C3×C4⋊Q8—92no—
164C3×C4⋊Q8—91no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—61no—
168C3×C22⋊Q8—92no—
169C3×C22⋊Q8—92no—
170C3×C22⋊Q8—91no—
171C3×C22⋊Q8C3×D311yescharacteristic
172C3×C4×Q8—91no—
173C3×C4×D4—92no—
174C3×C4×D4—91no—
175#944—31no—
176#944—91no—
177C4×#67—31no—
178C4×#67—91no—
179#897—31no—
180#897—91no—
181#896—32no—
182#896—92no—
183#888—32no—
184#888—92no—
185#887—31no—
186#887—91no—
187#67⋊C4—32no—
188#67⋊C4—92no—
189#878—32no—
190#878—92no—
191C23×C32—21no—
192C23×C32C22×D311yescharacteristic
193C23×C32C23×C311yescharacteristic
194C22×C3⋊D3C23×C311yescharacteristic
195C22×C3×D3—31no—
196C32×Q8—22no—
197C32×Q8—22no—
198C32×Q8—42no—
199C2×C32×C4—22no—
200C2×C32×C4—22no—
201C2×C32×C4—21no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4—21no—
205C2×C32×C4—42no—
206C2×C32×C4C22×D312yes—
207C2×C32×C4C22×D312yes—
208C2×C32×C4C22×D311yescharacteristic
209C2×C32×C4C22×D311yescharacteristic
210C2×C32×C4C23×C312yes—
211C2×C32×C4C23×C312yes—
212C2×C32×C4C23×C311yescharacteristic
213C2×C32×C4C23×C311yescharacteristic
214#638C3×Q814yescomplemented
215C2×C3⋊Dic3—24no—
216C2×C3⋊Dic3C23×C311yescharacteristic
217C2×C3⋊Dic3C23×C312yes—
218C2×C3⋊Dic3C23×C311yescharacteristic
219C2×C3⋊Dic3C23×C312yes—
220C2×C3⋊Dic3C23×C311yescharacteristic
221C4×C3⋊D3—22no—
222C4×C3⋊D3—24no—
223#634—22no—
224#634—24no—
225#634—24no—
226#634C3×D414yescomplemented
227C3×#67—34no—
228C2×C3×Dic3—31no—
229C2×C3×Dic3—32no—
230C2×C3×Dic3—31no—
231C2×C3×Dic3—32no—
232C2×C3×Dic3—31no—
233C2×C3×Dic3—64no—
234C3×C4×D3—64no—
235C3×C4×D3—62no—
236C3×Dic6—34no—
237C3×Dic6—64no—
238C3×Dic6—64no—
239C3×Dic6—62no—
240D4×Q8—91noSylow
241C2×H(3,𝔽3)—22no—
242C2×H(3,𝔽3)C22×D411yescharacteristic
243C2×H(3,𝔽3)C22×Q811yescharacteristic
244C2×H(3,𝔽3)2−1+411yescharacteristic
245(C3⋊D3)⋊C3—22no—
246C2×C3×Q8—31no—
247C2×C3×Q8—31no—
248C2×C3×Q8—61no—
249C2×C3×Q8—91no—
250C2×C3×Q8—91no—
251C2×C3×Q8—92no—
252C2×C3×Q8—92no—
253C2×C3×Q8—184no—
254C2×C3×Q8—184no—
255C2×C3×Q8C2×C3×D311yescharacteristic
256C2×C3×D4—91no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—61no—
260C22×C3×C4—91no—
261C22×C3×C4—92no—
262C22×C3×C4—92no—
263C22×C3×C4C2×C3×D311yescharacteristic
264C2×#67—31no—
265C2×#67—91no—
266C22×Dic3—32no—
267C22×Dic3—92no—
268D3×Q8—64no—
269D3×Q8—184no—
270C2×C4×D3—32no—
271C2×C4×D3—31no—
272C2×C4×D3—92no—
273C2×C4×D3—91no—
274C2×Dic6—31no—
275C2×Dic6—32no—
276C2×Dic6—32no—
277C2×Dic6—31no—
278C2×Dic6—64no—
279C2×Dic6—91no—
280C2×Dic6—92no—
281C2×Dic6—92no—
282C2×Dic6—91no—
283C2×Dic6—184no—
284C3×C4⋊C4—31no—
285C3×C4⋊C4—32no—
286C3×C4⋊C4—31no—
287C3×C4⋊C4—32no—
288C3×C4⋊C4—61no—
289C3×C4⋊C4—62no—
290C3×C4⋊C4—92no—
291C3×C4⋊C4—91no—
292C3×C4⋊C4—92no—
293C3×C4⋊C4—92no—
294C3×C4⋊C4—92no—
295C3×C4⋊C4C2×C3×D311yescharacteristic
296C3×C4⋊C4C2×C3×D312yes—
297C3×C22⋊C4—32no—
298C3×C22⋊C4—32no—
299C3×C22⋊C4—62no—
300C3×C22⋊C4—92no—
301C3×C22⋊C4—91no—
302C3×C22⋊C4—91no—
303C3×C22⋊C4C2×C3×D312yes—
304C3×C42—91no—
305C3×C42—92no—
306#217—31no—
307#217—91no—
308(C2×D3)⋊C4—32no—
309(C2×D3)⋊C4—31no—
310(C2×D3)⋊C4—92no—
311(C2×D3)⋊C4—91no—
312C4⋊Dic3—32no—
313C4⋊Dic3—92no—
314Dic3⋊C4—32no—
315Dic3⋊C4—32no—
316Dic3⋊C4—32no—
317Dic3⋊C4—31no—
318Dic3⋊C4—92no—
319Dic3⋊C4—92no—
320Dic3⋊C4—92no—
321Dic3⋊C4—91no—
322C4×Dic3—32no—
323C4×Dic3—31no—
324C4×Dic3—92no—
325C4×Dic3—91no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—22no—
332C22×C32—41no—
333C22×C32—41no—
334C22×C32D3×Q812yescomplemented
335C22×C32C2×C3×Q812yescomplemented
336C22×C32C23×D311yescharacteristic
337C22×C32C24×C311yescharacteristic
338C2×C3⋊D3—21no—
339C2×C3⋊D3—21no—
340C2×C3⋊D3C2×C3×Q812yescomplemented
341C2×C3×D3—32no—
342C2×C3×D3—61no—
343C2×C3×D3—61no—
344C32×C4—21no—
345C32×C4—22no—
346C32×C4—22no—
347C32×C4—21no—
348C32×C4—22no—
349C32×C4—22no—
350C32×C4—22no—
351C32×C4—42no—
352C32×C4—41no—
353C32×C4—42no—
354C32×C4D3×D412yes—
355C32×C4C2×C3×D412yes—
356C3⋊Dic3—21no—
357C3⋊Dic3—22no—
358C3⋊Dic3—21no—
359C3⋊Dic3C2×C3×D414yes—
360C3⋊Dic3C2×C3×Q812yescomplemented
361C3×Dic3—34no—
362C3×Dic3—32no—
363C3×Dic3—61no—
364C3×Dic3—62no—
365C3×Dic3—61no—
366C22×Q8—91no—
367C22×Q8—91no—
368C4⋊Q8—91no—
369C4⋊Q8—92no—
370C22⋊Q8—92no—
371C22⋊Q8—91no—
372C22⋊Q8—92no—
373C22⋊Q8(C3⋊D3)⋊C311yescharacteristic, complemented
374C4×Q8—91no—
375C4×D4—91no—
376C4×D4—92no—
377H(3,𝔽3)D4×Q811yescharacteristic, complemented, Sylow
378C23×C3—31no—
379C23×C3—31no—
380C23×C3—61no—
381C23×C3—91no—
382C23×C3C22×C3×D311yescharacteristic
383C22×D3—31no—
384C22×D3—91no—
385C3×Q8—22no—
386C3×Q8—62no—
387C3×Q8—62no—
388C3×Q8—94no—
389C3×Q8—122no—
390C3×Q8—182no—
391C3×Q8—184no—
392C3×Q8—184no—
393C3×D4—94no—
394C2×C3×C4—22no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—31no—
400C2×C3×C4—32no—
401C2×C3×C4—32no—
402C2×C3×C4—31no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—61no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—61no—
409C2×C3×C4—91no—
410C2×C3×C4—92no—
411C2×C3×C4—91no—
412C2×C3×C4—92no—
413C2×C3×C4—91no—
414C2×C3×C4—122no—
415C2×C3×C4—182no—
416C2×C3×C4—184no—
417C2×C3×C4—184no—
418C2×C3×C4C22×C3×D312yes—
419C2×C3×C4C22×C3×D312yes—
420C2×C3×C4C22×C3×D311yescharacteristic
421C2×C3×C4C22×C3×D311yescharacteristic
422#67—34no—
423#67—94no—
424C2×Dic3—31no—
425C2×Dic3—32no—
426C2×Dic3—31no—
427C2×Dic3—32no—
428C2×Dic3—31no—
429C2×Dic3—64no—
430C2×Dic3—91no—
431C2×Dic3—92no—
432C2×Dic3—91no—
433C2×Dic3—92no—
434C2×Dic3—91no—
435C2×Dic3—184no—
436C4×D3—64no—
437C4×D3—62no—
438C4×D3—184no—
439C4×D3—182no—
440Dic6—34no—
441Dic6—64no—
442Dic6—64no—
443Dic6—62no—
444Dic6—94no—
445Dic6—184no—
446Dic6—184no—
447Dic6—182no—
448C2×C32—22no—
449C2×C32—22no—
450C2×C32—21no—
451C2×C32—21no—
452C2×C32—21no—
453C2×C32—42no—
454C2×C32C2×D3×D411yescharacteristic
455C2×C32C2×D3×Q811yescharacteristic
456C2×C32#101011yescharacteristic
457C2×C32C22×C3×D411yescharacteristic
458C2×C32C22×C3×Q811yescharacteristic
459C2×C32C3×2−1+411yescharacteristic
460C3⋊D3—22no—
461C3×D3—62no—
462C2×Q8—91no—
463C2×Q8—92no—
464C2×Q8—92no—
465C2×Q8—91no—
466C2×Q8—184no—
467C2×Q8—184no—
468C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic
469C2×D4—91no—
470C22×C4—92no—
471C22×C4—92no—
472C22×C4—91no—
473C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
474C4⋊C4—91no—
475C4⋊C4—92no—
476C4⋊C4—92no—
477C4⋊C4—92no—
478C4⋊C4—92no—
479C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
480C4⋊C4C2×(C3⋊D3)⋊C312yes—
481C22⋊C4—91no—
482C22⋊C4—91no—
483C22⋊C4—92no—
484C22⋊C4C2×(C3⋊D3)⋊C312yes—
485C42—92no—
486C42—91no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—31no—
490C22×C3—31no—
491C22×C3—32no—
492C22×C3—32no—
493C22×C3—61no—
494C22×C3—61no—
495C22×C3—61no—
496C22×C3—61no—
497C22×C3—61no—
498C22×C3—62no—
499C22×C3—92no—
500C22×C3—121no—
501C22×C3—121no—
502C22×C3—181no—
503C22×C3—181no—
504C22×C3C3×D3×Q812yes—
505C22×C3C23×C3×D311yescharacteristic
506C2×D3—32no—
507C2×D3—61no—
508C2×D3—61no—
509C2×D3—92no—
510C2×D3—181no—
511C2×D3—181no—
512C3×C4—21no—
513C3×C4—22no—
514C3×C4—22no—
515C3×C4—32no—
516C3×C4—32no—
517C3×C4—61no—
518C3×C4—62no—
519C3×C4—61no—
520C3×C4—62no—
521C3×C4—62no—
522C3×C4—62no—
523C3×C4—62no—
524C3×C4—94no—
525C3×C4—92no—
526C3×C4—121no—
527C3×C4—122no—
528C3×C4—122no—
529C3×C4—181no—
530C3×C4—182no—
531C3×C4—181no—
532C3×C4C3×D3×D412yes—
533Dic3—34no—
534Dic3—32no—
535Dic3—61no—
536Dic3—62no—
537Dic3—61no—
538Dic3—94no—
539Dic3—92no—
540Dic3—181no—
541Dic3—182no—
542Dic3—181no—
543C32—21no—
544C32#563211yescharacteristic, complemented
545C32C3×D4×Q811yescharacteristic, complemented
546C23—91no—
547C23C22×(C3⋊D3)⋊C311yescharacteristic
548Q8—22no—
549Q8—94no—
550Q8—184no—
551Q8—184no—
552Q8—182no—
553D4—94no—
554C2×C4—22no—
555C2×C4—91no—
556C2×C4—92no—
557C2×C4—91no—
558C2×C4—91no—
559C2×C4—92no—
560C2×C4—184no—
561C2×C4—184no—
562C2×C4—182no—
563C2×C4C22×(C3⋊D3)⋊C312yes—
564C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
565C2×C4C22×(C3⋊D3)⋊C312yes—
566C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
567C2×C3—22no—
568C2×C3—31no—
569C2×C3—31no—
570C2×C3—31no—
571C2×C3—31no—
572C2×C3—31no—
573C2×C3—31no—
574C2×C3—62no—
575C2×C3—62no—
576C2×C3—61no—
577C2×C3—61no—
578C2×C3—61no—
579C2×C3—122no—
580C2×C3—182no—
581C2×C3C2×C3×D3×D411yescharacteristic
582C2×C3C2×C3×D3×Q811yescharacteristic
583C2×C3C3×#101011yescharacteristic
584D3—62no—
585D3—182no—
586C22—21no—
587C22—21no—
588C22—92no—
589C22—181no—
590C22—181no—
591C22Q8×(C3⋊D3)⋊C312yescomplemented
592C22C23×(C3⋊D3)⋊C311yescharacteristic
593C4—21no—
594C4—22no—
595C4—22no—
596C4—94no—
597C4—92no—
598C4—182no—
599C4—181no—
600C4—181no—
601C4D4×(C3⋊D3)⋊C312yes—
602C3—31no—
603C3—31no—
604C3—61no—
605C3C3×#563211yescharacteristic
606C2—22no—
607C2—182no—
608C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
609C2C2×Q8×(C3⋊D3)⋊C311yescharacteristic
610C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×C22⋊Q8C2
prime radicalC2×#638⋊C3C22
hypercenterC22⋊Q8(C3⋊D3)⋊C3
hypocenterC32C3×D4×Q8
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
2. C22×#634⋊C3C2semidirect
3. H(3,𝔽3)×C22⋊Q8C2semidirect
4. #64153⋊C3C2semidirect
6. #64106⋊C3C2semidirect
7. #64105⋊C3C2semidirect
8. #64097⋊C3C2semidirect
9. #64096⋊C3C2semidirect
11. #64087⋊C3C2semidirect
12. #10596103C3semidirect
39. C2×Q8×C3⋊D3C2×C3semidirect
40. C22×#634C2×C3semidirect
44. C32×C22⋊Q8D3semidirect
45. C32×C22⋊Q8C2×C3semidirect
46. #64153C2×C3semidirect
48. #64106C2×C3semidirect
49. #64105C2×C3semidirect
50. #64097C2×C3semidirect
51. #64096C2×C3semidirect
53. #64087C2×C3semidirect
70. #638⋊C3Q8semidirect
82. #634⋊C3D4semidirect
143. C22×H(3,𝔽3)C2×Q8semidirect
147. C2×(C3⋊D3)⋊C3C2×Q8semidirect
156. (C3⋊Dic3)⋊C3C2×Q8semidirect
214. #638C3×Q8semidirect
226. #634C3×D4semidirect
334. C22×C32D3×Q8semidirect
335. C22×C32C2×C3×Q8semidirect
340. C2×C3⋊D3C2×C3×Q8semidirect
360. C3⋊Dic3C2×C3×Q8semidirect
373. C22⋊Q8(C3⋊D3)⋊C3semidirect
377. H(3,𝔽3)D4×Q8semidirect
544. C32#5632semidirect
545. C32C3×D4×Q8semidirect
591. C22Q8×(C3⋊D3)⋊C3semidirect

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
C22×#634⋊C32
H(3,𝔽3)×C22⋊Q82
#64153⋊C32
C4×#638⋊C32
#64106⋊C32
#64105⋊C32
#64097⋊C32
#64096⋊C32
#64090⋊C32
#64087⋊C32
#105961033
C3×#56323