Finite Group Databasebeta

← #10595978⋊C3 #13152439

Subgroups — #10595978⋊C3 #13152439

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3828⋊C3C212yesmaximal, complemented
2C2×C4⋊C4×H(3,𝔽3)C211yesmaximal, characteristic, complemented
3#64139⋊C3C211yesmaximal, characteristic, complemented
4#64138⋊C3C212yesmaximal, complemented
5C4×#638⋊C3C211yesmaximal, characteristic, complemented
6#64105⋊C3C212yesmaximal, complemented
7#64104⋊C3C211yesmaximal, characteristic, complemented
8#64103⋊C3C212yesmaximal, complemented
9#64102⋊C3C211yesmaximal, characteristic, complemented
10C4⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
11#64097⋊C3C211yesmaximal, characteristic, complemented
12#10595978C311yesmaximal, characteristic, complemented
13C3×#5507—31nomaximal
14C22×C4×H(3,𝔽3)C2212yes—
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C2×#638⋊C3C2212yes—
17C2×#638⋊C3C2211yescharacteristic
18#3828⋊C3—28no—
19C2×C4⋊((C3⋊D3)⋊C3)C2212yes—
20C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2212yes—
22C2×C4×(C3⋊D3)⋊C3C2212yes—
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×#634⋊C3C2212yes—
25C4⋊C4×H(3,𝔽3)C2211yescharacteristic
26C4⋊C4×H(3,𝔽3)C2211yescharacteristic
27C4⋊C4×H(3,𝔽3)C2212yes—
28#3757⋊C3C2211yescharacteristic
29#3752⋊C3C2211yescharacteristic
30#3752⋊C3C2212yes—
31#3752⋊C3C2212yes—
32#3752⋊C3C2212yes—
33C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
34#3750⋊C3C2211yescharacteristic
35#3750⋊C3C2212yes—
36#3750⋊C3C2212yes—
37C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
38C2×#3828C2×C312yescomplemented
39C2×C3×#235—32no—
40C2×C32×C4⋊C4—21no—
41C2×C32×C4⋊C4D311yescharacteristic, complemented
42C2×C32×C4⋊C4C2×C311yescharacteristic, complemented
43#64139C2×C311yescharacteristic, complemented
44#64138C2×C312yescomplemented
45C4×#638C2×C311yescharacteristic, complemented
46#64105C2×C312yescomplemented
47#64104C2×C311yescharacteristic, complemented
48#64103C2×C312yescomplemented
49#64102C2×C311yescharacteristic, complemented
50C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
51#64097C2×C311yescharacteristic, complemented
52C3×#930—31no—
53C3×#929—32no—
54C3×C4×#67—31no—
55C3×#896—32no—
56C3×#895—31no—
57C3×#894—32no—
58C3×#893—31no—
59C3×D3×C4⋊C4—31no—
60C3×#888—31no—
61C23×H(3,𝔽3)C2311yescharacteristic
62C22×(C3⋊D3)⋊C3C2312yes—
63C22×(C3⋊D3)⋊C3C2311yescharacteristic
64C2×C4×H(3,𝔽3)—24no—
65C2×C4×H(3,𝔽3)—22no—
66C2×C4×H(3,𝔽3)C2312yes—
67C2×C4×H(3,𝔽3)C2312yes—
68C2×C4×H(3,𝔽3)C2311yescharacteristic
69C2×C4×H(3,𝔽3)C2311yescharacteristic
70#638⋊C3—24no—
71#638⋊C3D414yescomplemented
72C2×(C3⋊Dic3)⋊C3C2312yes—
73C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
74C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
75C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
76C4⋊((C3⋊D3)⋊C3)—24no—
77C4⋊((C3⋊D3)⋊C3)—22no—
78C4×(C3⋊D3)⋊C3—24no—
79C4×(C3⋊D3)⋊C3—22no—
80C4×(C3⋊D3)⋊C3—24no—
81#634⋊C3—24no—
82C3×#547—91no—
83#5507—31no—
84#5507—91no—
85C22×C32×C4—21no—
86C22×C32×C4—22no—
87C22×C32×C4C2×D311yescharacteristic
88C22×C32×C4C2×D312yes—
89C22×C32×C4C22×C312yes—
90C22×C32×C4C22×C311yescharacteristic
91C2×#638C22×C312yes—
92C2×#638C22×C311yescharacteristic
93#3828—28no—
94C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
95C2×C4⋊(C3⋊D3)C22×C312yes—
96C2×C4×C3⋊D3C22×C312yes—
97C2×C4×C3⋊D3C22×C311yescharacteristic
98C2×C4×C3⋊D3C22×C312yes—
99C2×#634C22×C312yes—
100C2×C3×#67—31no—
101C2×C3×#67—32no—
102C3×#235—68no—
103C2×C3×D12—31no—
104C2×C3×D12—32no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—32no—
108C2×C3×Dic6—32no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4—22no—
112C32×C4⋊C4C2×D311yescharacteristic
113C32×C4⋊C4C2×D311yescharacteristic
114C32×C4⋊C4C2×D312yes—
115C32×C4⋊C4C22×C311yescharacteristic
116C32×C4⋊C4C22×C311yescharacteristic
117C32×C4⋊C4C22×C312yes—
118#3757C22×C311yescharacteristic
119#3752C22×C312yes—
120#3752C22×C311yescharacteristic
121#3752C22×C312yes—
122#3752C22×C312yes—
123C4⋊(C3⋊Dic3)C22×C311yescharacteristic
124#3750C22×C312yes—
125#3750C22×C312yes—
126#3750C22×C311yescharacteristic
127C4×C3⋊Dic3C22×C311yescharacteristic
128C3×#217—31no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×C4⋊Dic3—31no—
134C3×Dic3⋊C4—32no—
135C3×Dic3⋊C4—32no—
136C3×Dic3⋊C4—31no—
137C3×C4×Dic3—31no—
138C22×H(3,𝔽3)—21no—
139C22×H(3,𝔽3)—21no—
140C22×H(3,𝔽3)C2×D412yes—
141C22×H(3,𝔽3)C2411yescharacteristic
142C2×(C3⋊D3)⋊C3—21no—
143C2×(C3⋊D3)⋊C3—21no—
144C2×(C3⋊D3)⋊C3—22no—
145C2×(C3⋊D3)⋊C3—22no—
146C2×(C3⋊D3)⋊C3—22no—
147C2×(C3⋊D3)⋊C3C2×D412yes—
148C4×H(3,𝔽3)—22no—
149C4×H(3,𝔽3)—22no—
150C4×H(3,𝔽3)—21no—
151C4×H(3,𝔽3)#4112yescomplemented
152(C3⋊Dic3)⋊C3—22no—
153(C3⋊Dic3)⋊C3—21no—
154(C3⋊Dic3)⋊C3—21no—
155(C3⋊Dic3)⋊C3C2×D412yes—
156C2×C3×#41—92no—
157C2×#235—32no—
158C2×#235—92no—
159C3×C4⋊Q8—91no—
160C3×#123—92no—
161C3×#123—92no—
162C3×C22⋊Q8—92no—
163C3×#121—91no—
164C3×#121—91no—
165C3×C4×D4—91no—
166C3×C4×D4—91no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—61no—
170C2×C3×C4⋊C4—91no—
171C2×C3×C4⋊C4C3×D311yescharacteristic
172#930—31no—
173#930—91no—
174#929—32no—
175#929—92no—
176C4×#67—31no—
177C4×#67—91no—
178#896—32no—
179#896—92no—
180#895—31no—
181#895—91no—
182#894—32no—
183#894—92no—
184#893—31no—
185#893—91no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—91no—
188#888—31no—
189#888—91no—
190C23×C32—21no—
191C23×C32C22×D311yescharacteristic
192C23×C32C23×C311yescharacteristic
193C22×C3⋊D3C23×C312yes—
194C22×C3⋊D3C23×C311yescharacteristic
195C22×C3×D3—31no—
196C22×C3×D3—32no—
197C2×C32×C4—24no—
198C2×C32×C4—24no—
199C2×C32×C4—24no—
200C2×C32×C4—22no—
201C2×C32×C4—22no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—22no—
205C2×C32×C4—22no—
206C2×C32×C4—44no—
207C2×C32×C4C22×D311yescharacteristic
208C2×C32×C4C22×D312yes—
209C2×C32×C4C22×D312yes—
210C2×C32×C4C22×D311yescharacteristic
211C2×C32×C4C23×C311yescharacteristic
212C2×C32×C4C23×C312yes—
213C2×C32×C4C23×C312yes—
214C2×C32×C4C23×C311yescharacteristic
215#638—24no—
216#638C3×D414yescomplemented
217C2×C3⋊Dic3C23×C311yescharacteristic
218C2×C3⋊Dic3C23×C311yescharacteristic
219C2×C3⋊Dic3C23×C312yes—
220C2×C3⋊Dic3C23×C311yescharacteristic
221C4⋊(C3⋊D3)—24no—
222C4⋊(C3⋊D3)—22no—
223C4×C3⋊D3—24no—
224C4×C3⋊D3—22no—
225C4×C3⋊D3—24no—
226#634—24no—
227C3×#67—34no—
228C3×#67—64no—
229C2×C3×Dic3—31no—
230C2×C3×Dic3—31no—
231C2×C3×Dic3—31no—
232C2×C3×Dic3—32no—
233C3×D12—64no—
234C3×D12—62no—
235C3×C4×D3—64no—
236C3×C4×D3—64no—
237C3×C4×D3—62no—
238C3×Dic6—64no—
239#547—91noSylow
240C2×H(3,𝔽3)—22no—
241C2×H(3,𝔽3)C22×D411yescharacteristic
242C2×H(3,𝔽3)C2×#4111yescharacteristic
243C2×H(3,𝔽3)2−1+411yescharacteristic
244(C3⋊D3)⋊C3—22no—
245(C3⋊D3)⋊C3—42no—
246C3×#41—188no—
247C2×C3×Q8—92no—
248C2×C3×D4—91no—
249C2×C3×D4—92no—
250C2×C3×D4—91no—
251C2×C3×D4—92no—
252C22×C3×C4—31no—
253C22×C3×C4—32no—
254C22×C3×C4—31no—
255C22×C3×C4—32no—
256C22×C3×C4—61no—
257C22×C3×C4—62no—
258C22×C3×C4—91no—
259C22×C3×C4—92no—
260C22×C3×C4—92no—
261C22×C3×C4C2×C3×D311yescharacteristic
262C22×C3×C4C2×C3×D312yes—
263C2×#67—31no—
264C2×#67—32no—
265C2×#67—91no—
266C2×#67—92no—
267#235—68no—
268#235—188no—
269C2×D12—31no—
270C2×D12—32no—
271C2×D12—91no—
272C2×D12—92no—
273C2×C4×D3—32no—
274C2×C4×D3—31no—
275C2×C4×D3—32no—
276C2×C4×D3—92no—
277C2×C4×D3—91no—
278C2×C4×D3—92no—
279C2×Dic6—32no—
280C2×Dic6—92no—
281C3×C4⋊C4—31no—
282C3×C4⋊C4—31no—
283C3×C4⋊C4—32no—
284C3×C4⋊C4—31no—
285C3×C4⋊C4—31no—
286C3×C4⋊C4—32no—
287C3×C4⋊C4—61no—
288C3×C4⋊C4—61no—
289C3×C4⋊C4—62no—
290C3×C4⋊C4—92no—
291C3×C4⋊C4—91no—
292C3×C4⋊C4—92no—
293C3×C4⋊C4—91no—
294C3×C4⋊C4C2×C3×D311yescharacteristic
295C3×C4⋊C4C2×C3×D311yescharacteristic
296C3×C4⋊C4C2×C3×D312yes—
297C3×C22⋊C4—91no—
298C3×C22⋊C4—92no—
299C3×C22⋊C4—92no—
300C3×C22⋊C4—92no—
301C3×C22⋊C4—91no—
302C3×C42—91no—
303#217—31no—
304#217—91no—
305(C2×D3)⋊C4—32no—
306(C2×D3)⋊C4—31no—
307(C2×D3)⋊C4—32no—
308(C2×D3)⋊C4—32no—
309(C2×D3)⋊C4—92no—
310(C2×D3)⋊C4—91no—
311(C2×D3)⋊C4—92no—
312(C2×D3)⋊C4—92no—
313C4⋊Dic3—31no—
314C4⋊Dic3—91no—
315Dic3⋊C4—32no—
316Dic3⋊C4—32no—
317Dic3⋊C4—31no—
318Dic3⋊C4—92no—
319Dic3⋊C4—92no—
320Dic3⋊C4—91no—
321C4×Dic3—31no—
322C4×Dic3—91no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—22no—
331C22×C32D3×D412yes—
332C22×C32C2×C3×D412yes—
333C22×C32C23×D311yescharacteristic
334C22×C32C24×C311yescharacteristic
335C2×C3⋊D3—21no—
336C2×C3⋊D3—21no—
337C2×C3⋊D3—22no—
338C2×C3⋊D3—22no—
339C2×C3⋊D3—22no—
340C2×C3⋊D3C2×C3×D412yes—
341C2×C3×D3—32no—
342C2×C3×D3—61no—
343C2×C3×D3—61no—
344C2×C3×D3—62no—
345C2×C3×D3—62no—
346C2×C3×D3—62no—
347C32×C4—22no—
348C32×C4—21no—
349C32×C4—22no—
350C32×C4—22no—
351C32×C4—22no—
352C32×C4—22no—
353C32×C4—21no—
354C32×C4—22no—
355C32×C4—42no—
356C32×C4—42no—
357C32×C4#23512yescomplemented
358C32×C4C3×#4112yescomplemented
359C3⋊Dic3—22no—
360C3⋊Dic3—21no—
361C3⋊Dic3—21no—
362C3⋊Dic3C2×C3×D412yes—
363C3×Dic3—32no—
364C3×Dic3—61no—
365C3×Dic3—62no—
366C3×Dic3—61no—
367C2×#41—92no—
368C4⋊Q8—91no—
369#123—92no—
370#123—92no—
371C22⋊Q8—92no—
372#121—91no—
373#121—91no—
374C4×D4—91no—
375C4×D4—91no—
376C2×C4⋊C4—91no—
377C2×C4⋊C4(C3⋊D3)⋊C311yescharacteristic, complemented
378H(3,𝔽3)#54711yescharacteristic, complemented, Sylow
379C23×C3—31no—
380C23×C3—31no—
381C23×C3—61no—
382C23×C3—91no—
383C23×C3—92no—
384C23×C3C22×C3×D311yescharacteristic
385C22×D3—31no—
386C22×D3—32no—
387C22×D3—91no—
388C22×D3—92no—
389C3×Q8—184no—
390C3×D4—94no—
391C3×D4—182no—
392C3×D4—184no—
393C3×D4—184no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—31no—
399C2×C3×C4—32no—
400C2×C3×C4—32no—
401C2×C3×C4—31no—
402C2×C3×C4—32no—
403C2×C3×C4—32no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—64no—
407C2×C3×C4—64no—
408C2×C3×C4—64no—
409C2×C3×C4—61no—
410C2×C3×C4—61no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4—91no—
414C2×C3×C4—91no—
415C2×C3×C4—91no—
416C2×C3×C4—92no—
417C2×C3×C4—124no—
418C2×C3×C4—182no—
419C2×C3×C4—184no—
420C2×C3×C4—184no—
421C2×C3×C4C22×C3×D311yescharacteristic
422C2×C3×C4C22×C3×D312yes—
423C2×C3×C4C22×C3×D312yes—
424C2×C3×C4C22×C3×D311yescharacteristic
425#67—34no—
426#67—64no—
427#67—94no—
428#67—184no—
429C2×Dic3—31no—
430C2×Dic3—31no—
431C2×Dic3—31no—
432C2×Dic3—32no—
433C2×Dic3—91no—
434C2×Dic3—91no—
435C2×Dic3—91no—
436C2×Dic3—92no—
437D12—64no—
438D12—62no—
439D12—182no—
440D12—184no—
441C4×D3—64no—
442C4×D3—64no—
443C4×D3—62no—
444C4×D3—184no—
445C4×D3—182no—
446C4×D3—184no—
447Dic6—64no—
448Dic6—184no—
449C2×C32—24no—
450C2×C32—22no—
451C2×C32—22no—
452C2×C32—21no—
453C2×C32—21no—
454C2×C32—21no—
455C2×C32C2×#23511yescharacteristic
456C2×C32C2×D3×D411yescharacteristic
457C2×C32#100711yescharacteristic
458C2×C32C22×C3×D411yescharacteristic
459C2×C32C2×C3×#4111yescharacteristic
460C2×C32C3×2−1+411yescharacteristic
461C3⋊D3—22no—
462C3⋊D3—42no—
463C3×D3—62no—
464C3×D3—122no—
465#41—188no—
466C2×Q8—92no—
467C2×D4—91no—
468C2×D4—92no—
469C2×D4—91no—
470C2×D4—92no—
471C22×C4—91no—
472C22×C4—92no—
473C22×C4—92no—
474C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
475C22×C4C2×(C3⋊D3)⋊C312yes—
476C4⋊C4—91no—
477C4⋊C4—92no—
478C4⋊C4—91no—
479C4⋊C4—92no—
480C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
481C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
482C4⋊C4C2×(C3⋊D3)⋊C312yes—
483C22⋊C4—91no—
484C22⋊C4—91no—
485C22⋊C4—92no—
486C22⋊C4—92no—
487C22⋊C4—92no—
488C42—91no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—31no—
492C22×C3—31no—
493C22×C3—32no—
494C22×C3—32no—
495C22×C3—61no—
496C22×C3—61no—
497C22×C3—61no—
498C22×C3—61no—
499C22×C3—62no—
500C22×C3—62no—
501C22×C3—61no—
502C22×C3—62no—
503C22×C3—92no—
504C22×C3—181no—
505C22×C3—181no—
506C22×C3—182no—
507C22×C3—182no—
508C22×C3—182no—
509C22×C3C3×D3×D412yes—
510C22×C3C23×C3×D311yescharacteristic
511C2×D3—32no—
512C2×D3—61no—
513C2×D3—61no—
514C2×D3—62no—
515C2×D3—62no—
516C2×D3—62no—
517C2×D3—92no—
518C2×D3—181no—
519C2×D3—181no—
520C2×D3—182no—
521C2×D3—182no—
522C2×D3—182no—
523C3×C4—21no—
524C3×C4—22no—
525C3×C4—22no—
526C3×C4—32no—
527C3×C4—32no—
528C3×C4—62no—
529C3×C4—62no—
530C3×C4—62no—
531C3×C4—62no—
532C3×C4—61no—
533C3×C4—61no—
534C3×C4—62no—
535C3×C4—62no—
536C3×C4—92no—
537C3×C4—122no—
538C3×C4—122no—
539C3×C4—182no—
540C3×C4—181no—
541C3×C4—181no—
542C3×C4C3×#23512yes—
543Dic3—32no—
544Dic3—61no—
545Dic3—62no—
546Dic3—61no—
547Dic3—92no—
548Dic3—182no—
549Dic3—181no—
550Dic3—181no—
551C32—21no—
552C32#550711yescharacteristic, complemented
553C32C3×#54711yescharacteristic, complemented
554C23—91no—
555C23—92no—
556C23C22×(C3⋊D3)⋊C311yescharacteristic
557Q8—184no—
558D4—94no—
559D4—184no—
560D4—184no—
561D4—182no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—91no—
565C2×C4—91no—
566C2×C4—91no—
567C2×C4—92no—
568C2×C4—184no—
569C2×C4—184no—
570C2×C4—182no—
571C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
572C2×C4C22×(C3⋊D3)⋊C312yes—
573C2×C4C22×(C3⋊D3)⋊C312yes—
574C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
575C2×C3—22no—
576C2×C3—31no—
577C2×C3—31no—
578C2×C3—31no—
579C2×C3—31no—
580C2×C3—31no—
581C2×C3—31no—
582C2×C3—62no—
583C2×C3—62no—
584C2×C3—64no—
585C2×C3—61no—
586C2×C3—61no—
587C2×C3—61no—
588C2×C3—182no—
589C2×C3—362no—
590C2×C3C2×C3×#23511yescharacteristic
591C2×C3C2×C3×D3×D411yescharacteristic
592C2×C3C3×#100711yescharacteristic
593D3—62no—
594D3—122no—
595D3—182no—
596D3—362no—
597C22—21no—
598C22—21no—
599C22—92no—
600C22—181no—
601C22—181no—
602C22—182no—
603C22—182no—
604C22—182no—
605C22D4×(C3⋊D3)⋊C312yes—
606C22C23×(C3⋊D3)⋊C311yescharacteristic
607C4—21no—
608C4—22no—
609C4—22no—
610C4—92no—
611C4—181no—
612C4—182no—
613C4—181no—
614C4#3828⋊C312yescomplemented
615C3—31no—
616C3—31no—
617C3—61no—
618C3C3×#550711yescharacteristic
619C2—22no—
620C2—182no—
621C2—362no—
622C2C2×#3828⋊C311yescharacteristic
623C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
624C2#1172262711yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingC2×C4⋊C4×H(3,𝔽3)C2
hypercenterC2×C4⋊C4(C3⋊D3)⋊C3
hypocenterC32C3×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#3828⋊C3C2semidirect
2. C2×C4⋊C4×H(3,𝔽3)C2semidirect
3. #64139⋊C3C2semidirect
4. #64138⋊C3C2semidirect
5. C4×#638⋊C3C2semidirect
6. #64105⋊C3C2semidirect
7. #64104⋊C3C2semidirect
8. #64103⋊C3C2semidirect
9. #64102⋊C3C2semidirect
10. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
11. #64097⋊C3C2semidirect
12. #10595978C3semidirect
38. C2×#3828C2×C3semidirect
41. C2×C32×C4⋊C4D3semidirect
42. C2×C32×C4⋊C4C2×C3semidirect
43. #64139C2×C3semidirect
44. #64138C2×C3semidirect
45. C4×#638C2×C3semidirect
46. #64105C2×C3semidirect
47. #64104C2×C3semidirect
48. #64103C2×C3semidirect
49. #64102C2×C3semidirect
50. C4⋊C4×C3⋊D3C2×C3semidirect
51. #64097C2×C3semidirect
71. #638⋊C3D4semidirect
151. C4×H(3,𝔽3)#41semidirect
216. #638C3×D4semidirect
357. C32×C4#235semidirect
358. C32×C4C3×#41semidirect
377. C2×C4⋊C4(C3⋊D3)⋊C3semidirect
378. H(3,𝔽3)#547semidirect
552. C32#5507semidirect
553. C32C3×#547semidirect
614. C4#3828⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#3828⋊C32
C2×C4⋊C4×H(3,𝔽3)2
#64139⋊C32
#64138⋊C32
C4×#638⋊C32
#64105⋊C32
#64104⋊C32
#64103⋊C32
#64102⋊C32
C4⋊C4×(C3⋊D3)⋊C32
#64097⋊C32
#105959783
C3×#55073