Finite Group Databasebeta

← #10595966⋊C3 #13152370

Subgroups — #10595966⋊C3 #13152370

Order 1728.

1000 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2#11721702C211yesmaximal, characteristic
3C2×#3757⋊C3C211yesmaximal, characteristic, complemented
4#64138⋊C3C211yesmaximal, characteristic, complemented
5C4×#638⋊C3C211yesmaximal, characteristic, complemented
6#64135⋊C3C211yesmaximal, characteristic, complemented
7#64133⋊C3C211yesmaximal, characteristic, complemented
8#64095⋊C3C211yesmaximal, characteristic, complemented
9#64094⋊C3C211yesmaximal, characteristic, complemented
10#64092⋊C3C211yesmaximal, characteristic, complemented
11#64090⋊C3C211yesmaximal, characteristic, complemented
12#64088⋊C3C211yesmaximal, characteristic, complemented
13#64088⋊C3C211yesmaximal, characteristic, complemented
14#64087⋊C3C211yesmaximal, characteristic, complemented
15#64086⋊C3C211yesmaximal, characteristic, complemented
16#10595966C311yesmaximal, characteristic, complemented
17C3×#5495—31nomaximal
18C24×H(3,𝔽3)C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C22×C4×H(3,𝔽3)C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
25C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
27C2×#634⋊C3C2211yescharacteristic, complemented
28C22⋊C4×H(3,𝔽3)C2211yescharacteristic
29C22⋊C4×H(3,𝔽3)C2211yescharacteristic
30C22⋊C4×H(3,𝔽3)C2211yescharacteristic
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic
32#3757⋊C3C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic
34#3757⋊C3C2211yescharacteristic
35#3757⋊C3C2211yescharacteristic
36#3757⋊C3C2211yescharacteristic
37#3757⋊C3C2211yescharacteristic
38#3757⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic, complemented
40#3752⋊C3C2211yescharacteristic, complemented
41#3752⋊C3C2211yescharacteristic, complemented
42C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
43C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
44C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
45#3750⋊C3C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47#3750⋊C3C2211yescharacteristic, complemented
48#3750⋊C3C2211yescharacteristic, complemented
49#3750⋊C3C2211yescharacteristic, complemented
50C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
53C2×C32×C22⋊C4—21no—
54C2×C32×C22⋊C4D311yescharacteristic, complemented
55C2×C32×C22⋊C4C2×C311yescharacteristic, complemented
56#64162C2×C311yescharacteristic
57C2×#3757C2×C311yescharacteristic, complemented
58#64138C2×C311yescharacteristic, complemented
59C4×#638C2×C311yescharacteristic, complemented
60#64135C2×C311yescharacteristic, complemented
61#64133C2×C311yescharacteristic, complemented
62#64095C2×C311yescharacteristic, complemented
63#64094C2×C311yescharacteristic, complemented
64#64092C2×C311yescharacteristic, complemented
65#64090C2×C311yescharacteristic, complemented
66#64088C2×C311yescharacteristic, complemented
67#64088C2×C311yescharacteristic, complemented
68#64087C2×C311yescharacteristic, complemented
69#64086C2×C311yescharacteristic, complemented
70C3×#953—31no—
71C2×C3×#217—31no—
72C3×#929—31no—
73C3×C4×#67—31no—
74C3×#926—31no—
75C3×#924—31no—
76C3×#886—31no—
77C3×#885—31no—
78C3×#883—31no—
79C3×#67⋊C4—31no—
80C3×#879—31no—
81C3×#879—31no—
82C3×#878—31no—
83C3×#877—31no—
84C23×H(3,𝔽3)—22no—
85C23×H(3,𝔽3)—22no—
86C23×H(3,𝔽3)—41no—
87C23×H(3,𝔽3)C2311yescharacteristic
88C23×H(3,𝔽3)C2311yescharacteristic
89C23×H(3,𝔽3)C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C2×C4×H(3,𝔽3)—22no—
92C2×C4×H(3,𝔽3)—41no—
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95C2×C4×H(3,𝔽3)C2311yescharacteristic
96C2×C4×H(3,𝔽3)C2311yescharacteristic
97#638⋊C3—22no—
98#638⋊C3—22no—
99#638⋊C3—41no—
100C2×(C3⋊Dic3)⋊C3—22no—
101C2×(C3⋊Dic3)⋊C3—41no—
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C4×(C3⋊D3)⋊C3—41no—
110#634⋊C3—41no—
111C3×#551—91no—
112#5495—31no—
113#5495—91no—
114C24×C32—21no—
115C24×C32C2×D311yescharacteristic
116C24×C32C22×C311yescharacteristic
117C22×C32×C4—21no—
118C22×C32×C4—21no—
119C22×C32×C4C2×D311yescharacteristic
120C22×C32×C4C2×D311yescharacteristic
121C22×C32×C4C22×C311yescharacteristic
122C22×C32×C4C22×C311yescharacteristic
123C2×#638C22×C311yescharacteristic
124C2×#638C22×C311yescharacteristic
125C2×#638C22×C311yescharacteristic
126C22×C3⋊Dic3C22×C311yescharacteristic
127C22×C3⋊Dic3C22×C311yescharacteristic
128C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
129C2×#634C22×C311yescharacteristic, complemented
130C2×C3×#67—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C22×C3×Dic3—31no—
134C22×C3×Dic3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×Dic6—31no—
137C32×C22⋊C4—21no—
138C32×C22⋊C4—21no—
139C32×C22⋊C4—21no—
140C32×C22⋊C4—21no—
141C32×C22⋊C4C2×D311yescharacteristic
142C32×C22⋊C4C2×D311yescharacteristic
143C32×C22⋊C4C2×D311yescharacteristic
144C32×C22⋊C4C2×D311yescharacteristic
145C32×C22⋊C4C22×C311yescharacteristic
146C32×C22⋊C4C22×C311yescharacteristic
147C32×C22⋊C4C22×C311yescharacteristic
148C32×C22⋊C4C22×C311yescharacteristic
149#3757C22×C311yescharacteristic
150#3757C22×C311yescharacteristic
151#3757C22×C311yescharacteristic
152#3757C22×C311yescharacteristic
153#3757C22×C311yescharacteristic
154#3757C22×C311yescharacteristic
155#3757C22×C311yescharacteristic
156#3752C22×C311yescharacteristic, complemented
157#3752C22×C311yescharacteristic, complemented
158#3752C22×C311yescharacteristic, complemented
159C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
160C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
161C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
162#3750C22×C311yescharacteristic, complemented
163#3750C22×C311yescharacteristic, complemented
164#3750C22×C311yescharacteristic, complemented
165#3750C22×C311yescharacteristic, complemented
166#3750C22×C311yescharacteristic, complemented
167C4×C3⋊Dic3C22×C311yescharacteristic, complemented
168C4×C3⋊Dic3C22×C311yescharacteristic, complemented
169C4×C3⋊Dic3C22×C311yescharacteristic, complemented
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—31no—
174C3×#217—31no—
175C3×#217—31no—
176C3×#217—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×C4×Dic3—31no—
189C3×C4×Dic3—31no—
190C3×C4×Dic3—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)—21no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)—21no—
197C22×H(3,𝔽3)—21no—
198C22×H(3,𝔽3)—44no—
199C22×H(3,𝔽3)#4112yes—
200C22×H(3,𝔽3)#4112yes—
201C22×H(3,𝔽3)C2411yescharacteristic
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3—21no—
204C2×(C3⋊D3)⋊C3—21no—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207C4×H(3,𝔽3)—21no—
208C4×H(3,𝔽3)—21no—
209(C3⋊Dic3)⋊C3—21no—
210(C3⋊Dic3)⋊C3—21no—
211(C3⋊Dic3)⋊C3—21no—
212(C3⋊Dic3)⋊C3—21no—
213(C3⋊Dic3)⋊C3—21no—
214(C3⋊Dic3)⋊C3—21no—
215(C3⋊Dic3)⋊C3—21no—
216C3×#126—91no—
217C3×#126—91no—
218C3×#124—91no—
219C3×#123—91no—
220C3×#123—91no—
221C3×#123—91no—
222C3×C22⋊Q8—91no—
223C3×C22⋊Q8—91no—
224C3×#120—91no—
225C3×C4×D4—91no—
226C3×C4×D4—91no—
227C3×#117—91no—
228C3×#117—91no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—61no—
232C2×C3×C22⋊C4—91no—
233C2×C3×C22⋊C4C3×D311yescharacteristic
234#953—31no—
235#953—91no—
236C2×#217—31no—
237C2×#217—91no—
238#929—31no—
239#929—91no—
240C4×#67—31no—
241C4×#67—91no—
242#926—31no—
243#926—91no—
244#924—31no—
245#924—91no—
246#886—31no—
247#886—91no—
248#885—31no—
249#885—91no—
250#883—31no—
251#883—91no—
252#67⋊C4—31no—
253#67⋊C4—91no—
254#879—31no—
255#879—31no—
256#879—91no—
257#879—91no—
258#878—31no—
259#878—91no—
260#877—31no—
261#877—91no—
262C23×C32—24no—
263C23×C32—22no—
264C23×C32—22no—
265C23×C32—22no—
266C23×C32—22no—
267C23×C32—21no—
268C23×C32—21no—
269C23×C32—21no—
270C23×C32—42no—
271C23×C32—41no—
272C23×C32—41no—
273C23×C32—42no—
274C23×C32C22×D311yescharacteristic
275C23×C32C22×D311yescharacteristic
276C23×C32C22×D311yescharacteristic
277C23×C32C23×C311yescharacteristic
278C23×C32C23×C311yescharacteristic
279C23×C32C23×C311yescharacteristic
280C22×C3⋊D3C23×C311yescharacteristic
281C22×C3×D3—31no—
282C2×C32×C4—22no—
283C2×C32×C4—22no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—42no—
289C2×C32×C4—41no—
290C2×C32×C4—41no—
291C2×C32×C4—42no—
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295C2×C32×C4C22×D311yescharacteristic
296C2×C32×C4C23×C311yescharacteristic
297C2×C32×C4C23×C311yescharacteristic
298C2×C32×C4C23×C311yescharacteristic
299C2×C32×C4C23×C311yescharacteristic
300#638—22no—
301#638—22no—
302#638—41no—
303C2×C3⋊Dic3—22no—
304C2×C3⋊Dic3—41no—
305C2×C3⋊Dic3C23×C311yescharacteristic
306C2×C3⋊Dic3C23×C311yescharacteristic
307C2×C3⋊Dic3C23×C311yescharacteristic
308C2×C3⋊Dic3C23×C311yescharacteristic
309C2×C3⋊Dic3C23×C311yescharacteristic
310C2×C3⋊Dic3C23×C311yescharacteristic
311C2×C3⋊Dic3C23×C311yescharacteristic
312C4×C3⋊D3—41no—
313#634—41no—
314C3×#67—62no—
315C3×#67—62no—
316C3×#67—121no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—62no—
325C2×C3×Dic3—121no—
326C3×C4×D3—121no—
327C3×Dic6—121no—
328#551—91noSylow
329C2×H(3,𝔽3)—22no—
330C2×H(3,𝔽3)—22no—
331C2×H(3,𝔽3)—41no—
332C2×H(3,𝔽3)C2×#4111yescharacteristic
333C2×H(3,𝔽3)C2×#4111yescharacteristic
334C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
335(C3⋊D3)⋊C3—41no—
336C24×C3—31no—
337C24×C3—31no—
338C24×C3—61no—
339C24×C3C2×C3×D311yescharacteristic
340C2×C3×Q8—91no—
341C2×C3×D4—91no—
342C2×C3×D4—91no—
343C2×C3×D4—91no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4—91no—
351C22×C3×C4—91no—
352C22×C3×C4—91no—
353C22×C3×C4C2×C3×D311yescharacteristic
354C22×C3×C4C2×C3×D311yescharacteristic
355C2×#67—31no—
356C2×#67—31no—
357C2×#67—31no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—91no—
364C22×Dic3—91no—
365C2×C4×D3—31no—
366C2×C4×D3—91no—
367C2×Dic6—31no—
368C2×Dic6—91no—
369C3×C4⋊C4—91no—
370C3×C4⋊C4—91no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—91no—
373C3×C4⋊C4—91no—
374C3×C4⋊C4—91no—
375C3×C4⋊C4—91no—
376C3×C4⋊C4—91no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—31no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C22⋊C4—91no—
393C3×C22⋊C4—91no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4C2×C3×D311yescharacteristic
400C3×C22⋊C4C2×C3×D311yescharacteristic
401C3×C22⋊C4C2×C3×D311yescharacteristic
402C3×C22⋊C4C2×C3×D311yescharacteristic
403C3×C42—91no—
404C3×C42—91no—
405C3×C42—91no—
406#217—31no—
407#217—31no—
408#217—31no—
409#217—31no—
410#217—31no—
411#217—31no—
412#217—31no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—31no—
429C4⋊Dic3—91no—
430C4⋊Dic3—91no—
431C4⋊Dic3—91no—
432Dic3⋊C4—31no—
433Dic3⋊C4—31no—
434Dic3⋊C4—31no—
435Dic3⋊C4—31no—
436Dic3⋊C4—31no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442C4×Dic3—31no—
443C4×Dic3—31no—
444C4×Dic3—31no—
445C4×Dic3—91no—
446C4×Dic3—91no—
447C4×Dic3—91no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—22no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—44no—
473C22×C32—44no—
474C22×C32—48no—
475C22×C32#23512yes—
476C22×C32#23712yes—
477C22×C32C3×#4112yes—
478C22×C32C3×#4112yes—
479C22×C32C23×D311yescharacteristic
480C22×C32C24×C311yescharacteristic
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—21no—
484C2×C3×D3—61no—
485C2×C3×D3—61no—
486C2×C3×D3—61no—
487C32×C4—21no—
488C32×C4—21no—
489C32×C4—21no—
490C32×C4—21no—
491C32×C4—21no—
492C32×C4—21no—
493C32×C4—21no—
494C32×C4—21no—
495C32×C4—41no—
496C32×C4—41no—
497C32×C4—41no—
498C32×C4—41no—
499C3⋊Dic3—21no—
500C3⋊Dic3—21no—
501C3⋊Dic3—21no—
502C3⋊Dic3—21no—
503C3⋊Dic3—21no—
504C3⋊Dic3—21no—
505C3⋊Dic3—21no—
506C3×Dic3—61no—
507C3×Dic3—61no—
508C3×Dic3—61no—
509C3×Dic3—61no—
510C3×Dic3—61no—
511C3×Dic3—61no—
512C3×Dic3—61no—
513#126—91no—
514#126—91no—
515#124—91no—
516#123—91no—
517#123—91no—
518#123—91no—
519C22⋊Q8—91no—
520C22⋊Q8—91no—
521#120—91no—
522C4×D4—91no—
523C4×D4—91no—
524#117—91no—
525#117—91no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4(C3⋊D3)⋊C311yescharacteristic, complemented
528H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—31no—
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—31no—
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—41no—
538C23×C3—62no—
539C23×C3—62no—
540C23×C3—62no—
541C23×C3—62no—
542C23×C3—64no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—91no—
547C23×C3—122no—
548C23×C3—121no—
549C23×C3—121no—
550C23×C3—122no—
551C23×C3C22×C3×D311yescharacteristic
552C23×C3C22×C3×D311yescharacteristic
553C23×C3C22×C3×D311yescharacteristic
554C22×D3—31no—
555C22×D3—91no—
556C3×Q8—361no—
557C3×D4—182no—
558C3×D4—182no—
559C3×D4—361no—
560C2×C3×C4—22no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—31no—
569C2×C3×C4—41no—
570C2×C3×C4—62no—
571C2×C3×C4—62no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—91no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—91no—
581C2×C3×C4—91no—
582C2×C3×C4—91no—
583C2×C3×C4—122no—
584C2×C3×C4—121no—
585C2×C3×C4—121no—
586C2×C3×C4—122no—
587C2×C3×C4—182no—
588C2×C3×C4—361no—
589C2×C3×C4—361no—
590C2×C3×C4C22×C3×D311yescharacteristic
591C2×C3×C4C22×C3×D311yescharacteristic
592C2×C3×C4C22×C3×D311yescharacteristic
593C2×C3×C4C22×C3×D311yescharacteristic
594#67—62no—
595#67—62no—
596#67—121no—
597#67—182no—
598#67—182no—
599#67—361no—
600C2×Dic3—31no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—62no—
608C2×Dic3—91no—
609C2×Dic3—91no—
610C2×Dic3—91no—
611C2×Dic3—91no—
612C2×Dic3—91no—
613C2×Dic3—91no—
614C2×Dic3—91no—
615C2×Dic3—121no—
616C2×Dic3—182no—
617C2×Dic3—361no—
618C4×D3—121no—
619C4×D3—361no—
620Dic6—121no—
621Dic6—361no—
622C2×C32—24no—
623C2×C32—22no—
624C2×C32—22no—
625C2×C32—22no—
626C2×C32—22no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—21no—
630C2×C32—42no—
631C2×C32—42no—
632C2×C32—41no—
633C2×C32—41no—
634C2×C32C2×#23511yescharacteristic
635C2×C32C2×#23711yescharacteristic
636C2×C32#100411yescharacteristic
637C2×C32C2×C3×#4111yescharacteristic
638C2×C32C2×C3×#4111yescharacteristic
639C2×C32C3×H(5,𝔽2)11yescharacteristic
640C3⋊D3—41no—
641C3×D3—121no—
642C24C2×(C3⋊D3)⋊C311yescharacteristic
643C2×Q8—91no—
644C2×D4—91no—
645C2×D4—91no—
646C2×D4—91no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
651C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
652C4⋊C4—91no—
653C4⋊C4—91no—
654C4⋊C4—91no—
655C4⋊C4—91no—
656C4⋊C4—91no—
657C4⋊C4—91no—
658C4⋊C4—91no—
659C4⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4—91no—
662C22⋊C4—91no—
663C22⋊C4—91no—
664C22⋊C4—91no—
665C22⋊C4—91no—
666C22⋊C4—91no—
667C22⋊C4—91no—
668C22⋊C4—91no—
669C22⋊C4—91no—
670C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
671C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
672C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
673C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
674C42—91no—
675C42—91no—
676C42—91no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—31no—
685C22×C3—31no—
686C22×C3—32no—
687C22×C3—32no—
688C22×C3—32no—
689C22×C3—32no—
690C22×C3—44no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—62no—
706C22×C3—62no—
707C22×C3—62no—
708C22×C3—61no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—124no—
716C22×C3—124no—
717C22×C3—128no—
718C22×C3—181no—
719C22×C3—181no—
720C22×C3—181no—
721C22×C3C3×#23512yes—
722C22×C3C3×#23712yes—
723C22×C3C23×C3×D311yescharacteristic
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—181no—
728C2×D3—181no—
729C2×D3—181no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—61no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—61no—
738C3×C4—61no—
739C3×C4—61no—
740C3×C4—61no—
741C3×C4—61no—
742C3×C4—121no—
743C3×C4—121no—
744C3×C4—121no—
745C3×C4—121no—
746C3×C4—181no—
747C3×C4—181no—
748C3×C4—181no—
749C3×C4—181no—
750C3×C4—181no—
751C3×C4—181no—
752C3×C4—181no—
753Dic3—61no—
754Dic3—61no—
755Dic3—61no—
756Dic3—61no—
757Dic3—61no—
758Dic3—61no—
759Dic3—61no—
760Dic3—181no—
761Dic3—181no—
762Dic3—181no—
763Dic3—181no—
764Dic3—181no—
765Dic3—181no—
766Dic3—181no—
767C32—21no—
768C32#549511yescharacteristic, complemented
769C32C3×#55111yescharacteristic, complemented
770C23—22no—
771C23—22no—
772C23—41no—
773C23—91no—
774C23C22×(C3⋊D3)⋊C311yescharacteristic
775C23C22×(C3⋊D3)⋊C311yescharacteristic
776C23C22×(C3⋊D3)⋊C311yescharacteristic
777Q8—361no—
778D4—182no—
779D4—182no—
780D4—361no—
781C2×C4—22no—
782C2×C4—41no—
783C2×C4—91no—
784C2×C4—91no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—91no—
788C2×C4—91no—
789C2×C4—91no—
790C2×C4—182no—
791C2×C4—361no—
792C2×C4—361no—
793C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
794C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
795C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
796C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
797C2×C3—22no—
798C2×C3—22no—
799C2×C3—31no—
800C2×C3—31no—
801C2×C3—31no—
802C2×C3—31no—
803C2×C3—31no—
804C2×C3—31no—
805C2×C3—41no—
806C2×C3—62no—
807C2×C3—62no—
808C2×C3—62no—
809C2×C3—62no—
810C2×C3—64no—
811C2×C3—61no—
812C2×C3—61no—
813C2×C3—61no—
814C2×C3—122no—
815C2×C3—121no—
816C2×C3—121no—
817C2×C3—122no—
818C2×C3—361no—
819C2×C3C2×C3×#23511yescharacteristic
820C2×C3C2×C3×#23711yescharacteristic
821C2×C3C3×#100411yescharacteristic
822D3—121no—
823D3—361no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—44no—
832C22—181no—
833C22—181no—
834C22—181no—
835C22#3828⋊C312yes—
836C22#3830⋊C312yes—
837C22C23×(C3⋊D3)⋊C311yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—181no—
843C4—181no—
844C4—181no—
845C4—181no—
846C4—181no—
847C4—181no—
848C4—181no—
849C3—31no—
850C3—31no—
851C3—61no—
852C3C3×#549511yescharacteristic
853C2—22no—
854C2—22no—
855C2—41no—
856C2—361no—
857C2C2×#3828⋊C311yescharacteristic
858C2C2×#3830⋊C311yescharacteristic
859C2#64361⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingC2×C22⋊C4×H(3,𝔽3)C2
prime radical#11721702C2
hypercenterC2×C22⋊C4(C3⋊D3)⋊C3
hypocenterC32C3×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊C4×H(3,𝔽3)C2semidirect
3. C2×#3757⋊C3C2semidirect
4. #64138⋊C3C2semidirect
5. C4×#638⋊C3C2semidirect
6. #64135⋊C3C2semidirect
7. #64133⋊C3C2semidirect
8. #64095⋊C3C2semidirect
9. #64094⋊C3C2semidirect
10. #64092⋊C3C2semidirect
11. #64090⋊C3C2semidirect
12. #64088⋊C3C2semidirect
13. #64088⋊C3C2semidirect
14. #64087⋊C3C2semidirect
15. #64086⋊C3C2semidirect
16. #10595966C3semidirect
26. C2×C4×(C3⋊D3)⋊C3C22semidirect
27. C2×#634⋊C3C22semidirect
39. #3752⋊C3C22semidirect
40. #3752⋊C3C22semidirect
41. #3752⋊C3C22semidirect
42. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
43. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
44. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
45. #3750⋊C3C22semidirect
46. #3750⋊C3C22semidirect
47. #3750⋊C3C22semidirect
48. #3750⋊C3C22semidirect
49. #3750⋊C3C22semidirect
50. C4×(C3⋊Dic3)⋊C3C22semidirect
51. C4×(C3⋊Dic3)⋊C3C22semidirect
52. C4×(C3⋊Dic3)⋊C3C22semidirect
54. C2×C32×C22⋊C4D3semidirect
55. C2×C32×C22⋊C4C2×C3semidirect
57. C2×#3757C2×C3semidirect
58. #64138C2×C3semidirect
59. C4×#638C2×C3semidirect
60. #64135C2×C3semidirect
61. #64133C2×C3semidirect
62. #64095C2×C3semidirect
63. #64094C2×C3semidirect
64. #64092C2×C3semidirect
65. #64090C2×C3semidirect
66. #64088C2×C3semidirect
67. #64088C2×C3semidirect
68. #64087C2×C3semidirect
69. #64086C2×C3semidirect
128. C2×C4×C3⋊D3C22×C3semidirect
129. C2×#634C22×C3semidirect
156. #3752C22×C3semidirect
157. #3752C22×C3semidirect
158. #3752C22×C3semidirect
159. C4⋊(C3⋊Dic3)C22×C3semidirect
160. C4⋊(C3⋊Dic3)C22×C3semidirect
161. C4⋊(C3⋊Dic3)C22×C3semidirect
162. #3750C22×C3semidirect
163. #3750C22×C3semidirect
164. #3750C22×C3semidirect
165. #3750C22×C3semidirect
166. #3750C22×C3semidirect
167. C4×C3⋊Dic3C22×C3semidirect
168. C4×C3⋊Dic3C22×C3semidirect
169. C4×C3⋊Dic3C22×C3semidirect
527. C2×C22⋊C4(C3⋊D3)⋊C3semidirect
528. H(3,𝔽3)#551semidirect
768. C32#5495semidirect
769. C32C3×#551semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×H(3,𝔽3)2
#117217022
C2×#3757⋊C32
#64138⋊C32
C4×#638⋊C32
#64135⋊C32
#64133⋊C32
#64095⋊C32
#64094⋊C32
#64092⋊C32
#64090⋊C32
#64088⋊C32
#64087⋊C32
#64086⋊C32
#105959663
C3×#54953