Finite Group Databasebeta

← #10596172⋊C3 #13153231

Subgroups — #10596172⋊C3 #13153231

Order 1728.

732 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#126C211yesmaximal, characteristic
2#64099⋊C3C211yesmaximal, characteristic, complemented
3#64098⋊C3C211yesmaximal, characteristic, complemented
4#64098⋊C3C211yesmaximal, characteristic, complemented
5#64098⋊C3C211yesmaximal, characteristic, complemented
6#64097⋊C3C211yesmaximal, characteristic, complemented
7#64096⋊C3C211yesmaximal, characteristic, complemented
8#64088⋊C3C211yesmaximal, characteristic
9#64088⋊C3C211yesmaximal, characteristic
10#64088⋊C3C211yesmaximal, characteristic
11#64087⋊C3C211yesmaximal, characteristic
12#64087⋊C3C211yesmaximal, characteristic
13#64086⋊C3C211yesmaximal, characteristic
14#64079⋊C3C211yesmaximal, characteristic, complemented
15C4×#634⋊C3C211yesmaximal, characteristic, complemented
16#10596172C311yesmaximal, characteristic, complemented
17C3×#5701—31nomaximal
18C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
19C2×#634⋊C3C2211yescharacteristic
20C2×#634⋊C3C2211yescharacteristic
21C4⋊C4×H(3,𝔽3)C2211yescharacteristic
22C4⋊C4×H(3,𝔽3)C2211yescharacteristic
23C4⋊C4×H(3,𝔽3)C2211yescharacteristic
24C22⋊C4×H(3,𝔽3)C2211yescharacteristic
25C22⋊C4×H(3,𝔽3)C2211yescharacteristic
26C22⋊C4×H(3,𝔽3)C2211yescharacteristic
27C42×H(3,𝔽3)C2211yescharacteristic
28#3757⋊C3C2211yescharacteristic
29#3757⋊C3C2211yescharacteristic
30#3757⋊C3C2211yescharacteristic
31C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
33C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
34C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
35C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
36#3750⋊C3C2211yescharacteristic
37#3750⋊C3C2211yescharacteristic
38#3750⋊C3C2211yescharacteristic
39#3750⋊C3C2211yescharacteristic
40#3750⋊C3C2211yescharacteristic
41#3750⋊C3C2211yescharacteristic
42#3750⋊C3C2211yescharacteristic
43#3750⋊C3C2211yescharacteristic
44#3750⋊C3C2211yescharacteristic
45#3750⋊C3C2211yescharacteristic
46#3750⋊C3C2211yescharacteristic
47#3750⋊C3C2211yescharacteristic
48C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
49C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
50C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
53C32×#126—21no—
54C32×#126D311yescharacteristic
55C32×#126C2×C311yescharacteristic
56#64099C2×C311yescharacteristic, complemented
57#64098C2×C311yescharacteristic, complemented
58#64098C2×C311yescharacteristic, complemented
59#64098C2×C311yescharacteristic, complemented
60#64097C2×C311yescharacteristic, complemented
61#64096C2×C311yescharacteristic, complemented
62#64088C2×C311yescharacteristic
63#64088C2×C311yescharacteristic
64#64088C2×C311yescharacteristic
65#64087C2×C311yescharacteristic
66#64087C2×C311yescharacteristic
67#64086C2×C311yescharacteristic
68#64079C2×C311yescharacteristic, complemented
69C4×#634C2×C311yescharacteristic, complemented
70C3×#890—31no—
71C3×#889—31no—
72C3×#889—31no—
73C3×#889—31no—
74C3×#888—31no—
75C3×#887—31no—
76C3×#879—31no—
77C3×#879—31no—
78C3×#879—31no—
79C3×#878—31no—
80C3×#878—31no—
81C3×#877—31no—
82C3×#870—31no—
83C3×C4×Dic6—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C2×C4×H(3,𝔽3)C2311yescharacteristic
86C2×C4×H(3,𝔽3)C2311yescharacteristic
87C2×C4×H(3,𝔽3)C2311yescharacteristic
88C2×C4×H(3,𝔽3)C2311yescharacteristic
89C2×C4×H(3,𝔽3)C2311yescharacteristic
90C2×C4×H(3,𝔽3)C2311yescharacteristic
91C2×(C3⋊Dic3)⋊C3—22no—
92C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
93C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
94C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100#634⋊C3—22no—
101#634⋊C3—22no—
102C3×#541—91no—
103#5701—31no—
104#5701—91no—
105C22×C3⋊Dic3C22×C311yescharacteristic
106C2×#634C22×C311yescharacteristic
107C2×#634C22×C311yescharacteristic
108C22×C3×Dic3—31no—
109C2×C3×Dic6—31no—
110C2×C3×Dic6—31no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2×D311yescharacteristic
115C32×C4⋊C4C2×D311yescharacteristic
116C32×C4⋊C4C2×D311yescharacteristic
117C32×C4⋊C4C22×C311yescharacteristic
118C32×C4⋊C4C22×C311yescharacteristic
119C32×C4⋊C4C22×C311yescharacteristic
120C32×C22⋊C4—21no—
121C32×C22⋊C4—21no—
122C32×C22⋊C4—21no—
123C32×C22⋊C4C2×D311yescharacteristic
124C32×C22⋊C4C2×D311yescharacteristic
125C32×C22⋊C4C2×D311yescharacteristic
126C32×C22⋊C4C22×C311yescharacteristic
127C32×C22⋊C4C22×C311yescharacteristic
128C32×C22⋊C4C22×C311yescharacteristic
129C32×C42—21no—
130C32×C42C2×D311yescharacteristic
131C32×C42C22×C311yescharacteristic
132#3757C22×C311yescharacteristic
133#3757C22×C311yescharacteristic
134#3757C22×C311yescharacteristic
135C4⋊(C3⋊Dic3)C22×C311yescharacteristic
136C4⋊(C3⋊Dic3)C22×C311yescharacteristic
137C4⋊(C3⋊Dic3)C22×C311yescharacteristic
138C4⋊(C3⋊Dic3)C22×C311yescharacteristic
139C4⋊(C3⋊Dic3)C22×C311yescharacteristic
140#3750C22×C311yescharacteristic
141#3750C22×C311yescharacteristic
142#3750C22×C311yescharacteristic
143#3750C22×C311yescharacteristic
144#3750C22×C311yescharacteristic
145#3750C22×C311yescharacteristic
146#3750C22×C311yescharacteristic
147#3750C22×C311yescharacteristic
148#3750C22×C311yescharacteristic
149#3750C22×C311yescharacteristic
150#3750C22×C311yescharacteristic
151#3750C22×C311yescharacteristic
152C4×C3⋊Dic3C22×C311yescharacteristic
153C4×C3⋊Dic3C22×C311yescharacteristic
154C4×C3⋊Dic3C22×C311yescharacteristic
155C4×C3⋊Dic3C22×C311yescharacteristic
156C4×C3⋊Dic3C22×C311yescharacteristic
157C3×#217—31no—
158C3×#217—31no—
159C3×#217—31no—
160C3×C4⋊Dic3—31no—
161C3×C4⋊Dic3—31no—
162C3×C4⋊Dic3—31no—
163C3×C4⋊Dic3—31no—
164C3×C4⋊Dic3—31no—
165C3×Dic3⋊C4—31no—
166C3×Dic3⋊C4—31no—
167C3×Dic3⋊C4—31no—
168C3×Dic3⋊C4—31no—
169C3×Dic3⋊C4—31no—
170C3×Dic3⋊C4—31no—
171C3×Dic3⋊C4—31no—
172C3×Dic3⋊C4—31no—
173C3×Dic3⋊C4—31no—
174C3×Dic3⋊C4—31no—
175C3×Dic3⋊C4—31no—
176C3×Dic3⋊C4—31no—
177C3×C4×Dic3—31no—
178C3×C4×Dic3—31no—
179C3×C4×Dic3—31no—
180C3×C4×Dic3—31no—
181C3×C4×Dic3—31no—
182C22×H(3,𝔽3)—21no—
183C22×H(3,𝔽3)—21no—
184C22×H(3,𝔽3)—21no—
185C22×H(3,𝔽3)C2411yescharacteristic
186C4×H(3,𝔽3)—21no—
187C4×H(3,𝔽3)—21no—
188C4×H(3,𝔽3)—21no—
189C4×H(3,𝔽3)—21no—
190C4×H(3,𝔽3)—21no—
191C4×H(3,𝔽3)—21no—
192(C3⋊Dic3)⋊C3—21no—
193(C3⋊Dic3)⋊C3—21no—
194(C3⋊Dic3)⋊C3—21no—
195(C3⋊Dic3)⋊C3—21no—
196(C3⋊Dic3)⋊C3—21no—
197(C3⋊Dic3)⋊C3—21no—
198(C3⋊Dic3)⋊C3—21no—
199(C3⋊Dic3)⋊C3#4112yes—
200C3×C4⋊Q8—91no—
201C3×#126—31no—
202C3×#126—31no—
203C3×#126—61no—
204C3×#126—91no—
205C3×#126—91no—
206C3×#126—91no—
207C3×#126C3×D311yescharacteristic
208C3×#125—91no—
209C3×#125—91no—
210C3×#125—91no—
211C3×#125—91no—
212C3×#125—91no—
213C3×C22⋊Q8—91no—
214C3×C22⋊Q8—91no—
215C3×C4×Q8—91no—
216C3×C4×Q8—91no—
217C3×#117—91no—
218#890—31no—
219#890—91no—
220#889—31no—
221#889—31no—
222#889—31no—
223#889—91no—
224#889—91no—
225#889—91no—
226#888—31no—
227#888—91no—
228#887—31no—
229#887—91no—
230#879—31no—
231#879—31no—
232#879—31no—
233#879—91no—
234#879—91no—
235#879—91no—
236#878—31no—
237#878—31no—
238#878—91no—
239#878—91no—
240#877—31no—
241#877—91no—
242#870—31no—
243#870—91no—
244C4×Dic6—31no—
245C4×Dic6—91no—
246C23×C32—21no—
247C23×C32C22×D311yescharacteristic
248C23×C32C23×C311yescharacteristic
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C23×C311yescharacteristic
262C2×C32×C4C23×C311yescharacteristic
263C2×C32×C4C23×C311yescharacteristic
264C2×C32×C4C23×C311yescharacteristic
265C2×C32×C4C23×C311yescharacteristic
266C2×C32×C4C23×C311yescharacteristic
267C2×C3⋊Dic3—22no—
268C2×C3⋊Dic3C23×C311yescharacteristic
269C2×C3⋊Dic3C23×C311yescharacteristic
270C2×C3⋊Dic3C23×C311yescharacteristic
271C2×C3⋊Dic3C23×C311yescharacteristic
272C2×C3⋊Dic3C23×C311yescharacteristic
273C2×C3⋊Dic3C23×C311yescharacteristic
274C2×C3⋊Dic3C23×C311yescharacteristic
275C2×C3⋊Dic3C23×C311yescharacteristic
276#634—22no—
277#634—22no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—62no—
287C3×Dic6—62no—
288C3×Dic6—62no—
289#541—91noSylow
290C2×H(3,𝔽3)—41no—
291C2×H(3,𝔽3)C2×#4111yescharacteristic
292C2×H(3,𝔽3)2−1+411yescharacteristic
293C2×H(3,𝔽3)2−1+411yescharacteristic
294C2×C3×Q8—91no—
295C2×C3×Q8—91no—
296C22×C3×C4—91no—
297C22×Dic3—31no—
298C22×Dic3—91no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—91no—
302C2×Dic6—91no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—91no—
313C3×C4⋊C4—91no—
314C3×C4⋊C4—91no—
315C3×C4⋊C4—91no—
316C3×C4⋊C4—91no—
317C3×C4⋊C4—91no—
318C3×C4⋊C4—91no—
319C3×C4⋊C4—91no—
320C3×C4⋊C4—91no—
321C3×C4⋊C4—91no—
322C3×C4⋊C4—91no—
323C3×C4⋊C4—91no—
324C3×C4⋊C4—91no—
325C3×C4⋊C4—91no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4C2×C3×D311yescharacteristic
330C3×C4⋊C4C2×C3×D311yescharacteristic
331C3×C4⋊C4C2×C3×D311yescharacteristic
332C3×C22⋊C4—31no—
333C3×C22⋊C4—31no—
334C3×C22⋊C4—31no—
335C3×C22⋊C4—31no—
336C3×C22⋊C4—31no—
337C3×C22⋊C4—31no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—91no—
342C3×C22⋊C4—91no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4C2×C3×D311yescharacteristic
345C3×C22⋊C4C2×C3×D311yescharacteristic
346C3×C22⋊C4C2×C3×D311yescharacteristic
347C3×C42—31no—
348C3×C42—31no—
349C3×C42—61no—
350C3×C42—91no—
351C3×C42—91no—
352C3×C42—91no—
353C3×C42—91no—
354C3×C42—91no—
355C3×C42C2×C3×D311yescharacteristic
356#217—31no—
357#217—31no—
358#217—31no—
359#217—91no—
360#217—91no—
361#217—91no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—91no—
368C4⋊Dic3—91no—
369C4⋊Dic3—91no—
370C4⋊Dic3—91no—
371C4⋊Dic3—91no—
372Dic3⋊C4—31no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—31no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—31no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—91no—
402C4×Dic3—91no—
403C4×Dic3—91no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C23×D311yescharacteristic
417C22×C32C24×C311yescharacteristic
418C32×C4—21no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—41no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4—41no—
435C32×C4—41no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3C3×#4112yes—
444C3×Dic3—32no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—61no—
451C3×Dic3—61no—
452C4⋊Q8—91no—
453#126—91no—
454#126—91no—
455#126—91no—
456#126(C3⋊D3)⋊C311yescharacteristic
457#125—91no—
458#125—91no—
459#125—91no—
460#125—91no—
461#125—91no—
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464C4×Q8—91no—
465C4×Q8—91no—
466#117—91no—
467H(3,𝔽3)#54111yescharacteristic, complemented, Sylow
468C23×C3—31no—
469C23×C3—31no—
470C23×C3—61no—
471C23×C3C22×C3×D311yescharacteristic
472C3×Q8—182no—
473C3×Q8—182no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—91no—
499C2×C3×C4—91no—
500C2×C3×C4—182no—
501C2×C3×C4C22×C3×D311yescharacteristic
502C2×C3×C4C22×C3×D311yescharacteristic
503C2×C3×C4C22×C3×D311yescharacteristic
504C2×C3×C4C22×C3×D311yescharacteristic
505C2×C3×C4C22×C3×D311yescharacteristic
506C2×C3×C4C22×C3×D311yescharacteristic
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—62no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—91no—
522C2×Dic3—91no—
523C2×Dic3—91no—
524C2×Dic3—182no—
525Dic6—62no—
526Dic6—62no—
527Dic6—182no—
528Dic6—182no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—41no—
533C2×C32—41no—
534C2×C32—81no—
535C2×C32D3×#4111yescharacteristic
536C2×C32#101011yescharacteristic
537C2×C32#101011yescharacteristic
538C2×C32C2×C3×#4111yescharacteristic
539C2×C32C3×2−1+411yescharacteristic
540C2×C32C3×2−1+411yescharacteristic
541C2×Q8—91no—
542C2×Q8—91no—
543C22×C4—91no—
544C4⋊C4—91no—
545C4⋊C4—91no—
546C4⋊C4—91no—
547C4⋊C4—91no—
548C4⋊C4—91no—
549C4⋊C4—91no—
550C4⋊C4—91no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
562C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
563C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
564C22⋊C4—91no—
565C22⋊C4—91no—
566C22⋊C4—91no—
567C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
568C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
569C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
570C42—91no—
571C42—91no—
572C42—91no—
573C42—91no—
574C42—91no—
575C42C2×(C3⋊D3)⋊C311yescharacteristic
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—31no—
580C22×C3—31no—
581C22×C3—61no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3—61no—
585C22×C3—61no—
586C22×C3—61no—
587C22×C3—61no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3C23×C3×D311yescharacteristic
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—61no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—92no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4—121no—
616C3×C4—121no—
617C3×C4—181no—
618C3×C4—181no—
619C3×C4—181no—
620C3×C4—181no—
621C3×C4—181no—
622C3×C4—181no—
623C3×C4—181no—
624Dic3—32no—
625Dic3—61no—
626Dic3—61no—
627Dic3—61no—
628Dic3—61no—
629Dic3—61no—
630Dic3—61no—
631Dic3—61no—
632Dic3—92no—
633Dic3—181no—
634Dic3—181no—
635Dic3—181no—
636Dic3—181no—
637Dic3—181no—
638Dic3—181no—
639Dic3—181no—
640C32—21no—
641C32#570111yescharacteristic, complemented
642C32C3×#54111yescharacteristic, complemented
643C23C22×(C3⋊D3)⋊C311yescharacteristic
644Q8—182no—
645Q8—182no—
646C2×C4—91no—
647C2×C4—91no—
648C2×C4—91no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—182no—
655C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
656C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
657C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
658C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
659C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
660C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
661C2×C3—31no—
662C2×C3—31no—
663C2×C3—31no—
664C2×C3—31no—
665C2×C3—31no—
666C2×C3—31no—
667C2×C3—41no—
668C2×C3—61no—
669C2×C3—61no—
670C2×C3—61no—
671C2×C3—121no—
672C2×C3—121no—
673C2×C3—241no—
674C2×C3C3×D3×#4111yescharacteristic
675C2×C3C3×#101011yescharacteristic
676C2×C3C3×#101011yescharacteristic
677C22—21no—
678C22—21no—
679C22—21no—
680C22C23×(C3⋊D3)⋊C311yescharacteristic
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—21no—
687C4—92no—
688C4—181no—
689C4—181no—
690C4—181no—
691C4—181no—
692C4—181no—
693C4—181no—
694C4—181no—
695C3—31no—
696C3—31no—
697C3—61no—
698C3C3×#570111yescharacteristic
699C2—41no—
700C2#41×(C3⋊D3)⋊C311yescharacteristic
701C2#1172263911yescharacteristic
702C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#126C2
prime radicalC23×H(3,𝔽3)C23
hypercenter#126(C3⋊D3)⋊C3
hypocenterC32C3×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
2. #64099⋊C3C2semidirect
3. #64098⋊C3C2semidirect
4. #64098⋊C3C2semidirect
5. #64098⋊C3C2semidirect
6. #64097⋊C3C2semidirect
7. #64096⋊C3C2semidirect
14. #64079⋊C3C2semidirect
15. C4×#634⋊C3C2semidirect
16. #10596172C3semidirect
56. #64099C2×C3semidirect
57. #64098C2×C3semidirect
58. #64098C2×C3semidirect
59. #64098C2×C3semidirect
60. #64097C2×C3semidirect
61. #64096C2×C3semidirect
68. #64079C2×C3semidirect
69. C4×#634C2×C3semidirect
467. H(3,𝔽3)#541semidirect
641. C32#5701semidirect
642. C32C3×#541semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×#1262
#64099⋊C32
#64098⋊C32
#64097⋊C32
#64096⋊C32
#64088⋊C32
#64087⋊C32
#64086⋊C32
#64079⋊C32
C4×#634⋊C32
#105961723
C3×#57013