Finite Group Databasebeta

← #10596086⋊C3 #13152844

Subgroups — #10596086⋊C3 #13152844

Order 1728.

934 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#121C211yesmaximal, characteristic, complemented
2#64149⋊C3C211yesmaximal, characteristic, complemented
3#64148⋊C3C211yesmaximal, characteristic, complemented
4#64148⋊C3C211yesmaximal, characteristic, complemented
5#64148⋊C3C211yesmaximal, characteristic, complemented
6#64147⋊C3C211yesmaximal, characteristic, complemented
7#64144⋊C3C211yesmaximal, characteristic, complemented
8#64138⋊C3C211yesmaximal, characteristic, complemented
9C4×#638⋊C3C211yesmaximal, characteristic, complemented
10#64103⋊C3C211yesmaximal, characteristic, complemented
11#64098⋊C3C211yesmaximal, characteristic, complemented
12#64093⋊C3C211yesmaximal, characteristic, complemented
13#64092⋊C3C211yesmaximal, characteristic, complemented
14#64090⋊C3C211yesmaximal, characteristic, complemented
15#64086⋊C3C211yesmaximal, characteristic, complemented
16#10596086C311yesmaximal, characteristic, complemented
17C3×#5615—31nomaximal
18C2×D4×H(3,𝔽3)C2211yescharacteristic
19C2×D4×H(3,𝔽3)C2211yescharacteristic
20C2×D4×H(3,𝔽3)C2211yescharacteristic
21C22×C4×H(3,𝔽3)C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C2×#638⋊C3C2211yescharacteristic
25C2×#638⋊C3C2211yescharacteristic
26C2×#638⋊C3C2211yescharacteristic
27C2×#638⋊C3C2211yescharacteristic
28C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
29C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
30C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
31C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
32C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
33C4⋊C4×H(3,𝔽3)C2211yescharacteristic
34C22⋊C4×H(3,𝔽3)C2211yescharacteristic
35C22⋊C4×H(3,𝔽3)C2211yescharacteristic
36#3757⋊C3C2211yescharacteristic
37#3757⋊C3C2211yescharacteristic
38#3757⋊C3C2211yescharacteristic
39#3757⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic
44C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
45#3750⋊C3C2211yescharacteristic
46#3750⋊C3C2211yescharacteristic
47#3750⋊C3C2211yescharacteristic
48#3750⋊C3C2211yescharacteristic
49#3750⋊C3C2211yescharacteristic
50#3750⋊C3C2211yescharacteristic
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
53C32×#121—21no—
54C32×#121D311yescharacteristic, complemented
55C32×#121C2×C311yescharacteristic, complemented
56#64149C2×C311yescharacteristic, complemented
57#64148C2×C311yescharacteristic, complemented
58#64148C2×C311yescharacteristic, complemented
59#64148C2×C311yescharacteristic, complemented
60#64147C2×C311yescharacteristic, complemented
61#64144C2×C311yescharacteristic, complemented
62#64138C2×C311yescharacteristic, complemented
63C4×#638C2×C311yescharacteristic, complemented
64#64103C2×C311yescharacteristic, complemented
65#64098C2×C311yescharacteristic, complemented
66#64093C2×C311yescharacteristic, complemented
67#64092C2×C311yescharacteristic, complemented
68#64090C2×C311yescharacteristic, complemented
69#64086C2×C311yescharacteristic, complemented
70C3×#940—31no—
71C3×#939—31no—
72C3×#939—31no—
73C3×#939—31no—
74C3×#938—31no—
75C3×#935—31no—
76C3×#929—31no—
77C3×C4×#67—31no—
78C3×#894—31no—
79C3×#889—31no—
80C3×#884—31no—
81C3×#883—31no—
82C3×#67⋊C4—31no—
83C3×#877—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C23×H(3,𝔽3)C2311yescharacteristic
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89D4×H(3,𝔽3)—41no—
90D4×H(3,𝔽3)—41no—
91D4×H(3,𝔽3)—41no—
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—
100#638⋊C3—41no—
101#638⋊C3—41no—
102#638⋊C3—41no—
103C2×(C3⋊Dic3)⋊C3—22no—
104C2×(C3⋊Dic3)⋊C3—41no—
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C4⋊((C3⋊D3)⋊C3)—41no—
112C4×(C3⋊D3)⋊C3—41no—
113C4×(C3⋊D3)⋊C3—41no—
114C3×#540—91no—
115#5615—31no—
116#5615—91no—
117C2×C32×D4—21no—
118C2×C32×D4—21no—
119C2×C32×D4—21no—
120C2×C32×D4C2×D311yescharacteristic
121C2×C32×D4C2×D311yescharacteristic
122C2×C32×D4C2×D311yescharacteristic
123C2×C32×D4C22×C311yescharacteristic
124C2×C32×D4C22×C311yescharacteristic
125C2×C32×D4C22×C311yescharacteristic
126C22×C32×C4—21no—
127C22×C32×C4C2×D311yescharacteristic
128C22×C32×C4C22×C311yescharacteristic
129C2×#638C22×C311yescharacteristic
130C2×#638C22×C311yescharacteristic
131C2×#638C22×C311yescharacteristic
132C2×#638C22×C311yescharacteristic
133C2×#638C22×C311yescharacteristic
134C2×#638C22×C311yescharacteristic
135C22×C3⋊Dic3C22×C311yescharacteristic
136C22×C3⋊Dic3C22×C311yescharacteristic
137C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
138C2×C4×C3⋊D3C22×C311yescharacteristic
139C2×C4×C3⋊D3C22×C311yescharacteristic
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C22×C3×Dic3—31no—
147C22×C3×Dic3—31no—
148C2×C3×D12—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C32×C4⋊C4—21no—
152C32×C4⋊C4C2×D311yescharacteristic
153C32×C4⋊C4C22×C311yescharacteristic
154C32×C22⋊C4—21no—
155C32×C22⋊C4—21no—
156C32×C22⋊C4C2×D311yescharacteristic
157C32×C22⋊C4C2×D311yescharacteristic
158C32×C22⋊C4C22×C311yescharacteristic
159C32×C22⋊C4C22×C311yescharacteristic
160#3757C22×C311yescharacteristic
161#3757C22×C311yescharacteristic
162#3757C22×C311yescharacteristic
163#3757C22×C311yescharacteristic
164#3752C22×C311yescharacteristic
165#3752C22×C311yescharacteristic
166#3752C22×C311yescharacteristic
167#3752C22×C311yescharacteristic
168C4⋊(C3⋊Dic3)C22×C311yescharacteristic
169#3750C22×C311yescharacteristic
170#3750C22×C311yescharacteristic
171#3750C22×C311yescharacteristic
172#3750C22×C311yescharacteristic
173#3750C22×C311yescharacteristic
174#3750C22×C311yescharacteristic
175C4×C3⋊Dic3C22×C311yescharacteristic
176C4×C3⋊Dic3C22×C311yescharacteristic
177C3×#217—31no—
178C3×#217—31no—
179C3×#217—31no—
180C3×#217—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×C4⋊Dic3—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×C4×Dic3—31no—
193C3×C4×Dic3—31no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)—21no—
197C22×H(3,𝔽3)—21no—
198C22×H(3,𝔽3)—21no—
199C22×H(3,𝔽3)—21no—
200C22×H(3,𝔽3)—21no—
201C22×H(3,𝔽3)—21no—
202C22×H(3,𝔽3)—21no—
203C22×H(3,𝔽3)C2411yescharacteristic
204C2×(C3⋊D3)⋊C3—21no—
205C2×(C3⋊D3)⋊C3—21no—
206C2×(C3⋊D3)⋊C3—21no—
207C2×(C3⋊D3)⋊C3—21no—
208C2×(C3⋊D3)⋊C3—21no—
209C2×(C3⋊D3)⋊C3—21no—
210C4×H(3,𝔽3)—21no—
211C4×H(3,𝔽3)—21no—
212C4×H(3,𝔽3)—21no—
213C4×H(3,𝔽3)—21no—
214(C3⋊Dic3)⋊C3—21no—
215(C3⋊Dic3)⋊C3—21no—
216(C3⋊Dic3)⋊C3—21no—
217(C3⋊Dic3)⋊C3—21no—
218(C3⋊Dic3)⋊C3—21no—
219(C3⋊Dic3)⋊C3#4112yes—
220C3×#127—91no—
221C3×#125—91no—
222C3×#123—91no—
223C3×#123—91no—
224C3×#123—91no—
225C3×#123—91no—
226C3×#121—31no—
227C3×#121—31no—
228C3×#121—61no—
229C3×#121—91no—
230C3×#121—91no—
231C3×#121—91no—
232C3×#121—91no—
233C3×#121—91no—
234C3×#121C3×D311yescharacteristic
235C3×C4×D4—91no—
236C3×C4×D4—91no—
237C3×#117—91no—
238#940—31no—
239#940—91no—
240#939—31no—
241#939—31no—
242#939—31no—
243#939—91no—
244#939—91no—
245#939—91no—
246#938—31no—
247#938—91no—
248#935—31no—
249#935—91no—
250#929—31no—
251#929—91no—
252C4×#67—31no—
253C4×#67—91no—
254#894—31no—
255#894—91no—
256#889—31no—
257#889—91no—
258#884—31no—
259#884—91no—
260#883—31no—
261#883—91no—
262#67⋊C4—31no—
263#67⋊C4—91no—
264#877—31no—
265#877—91no—
266C23×C32—21no—
267C23×C32—21no—
268C23×C32—21no—
269C23×C32C22×D311yescharacteristic
270C23×C32C22×D311yescharacteristic
271C23×C32C22×D311yescharacteristic
272C23×C32C23×C311yescharacteristic
273C23×C32C23×C311yescharacteristic
274C23×C32C23×C311yescharacteristic
275C22×C3⋊D3C23×C311yescharacteristic
276C22×C3⋊D3C23×C311yescharacteristic
277C22×C3×D3—31no—
278C22×C3×D3—31no—
279C32×D4—41no—
280C32×D4—41no—
281C32×D4—41no—
282C32×D4—41no—
283C32×D4—41no—
284C32×D4—41no—
285C32×D4—42no—
286C32×D4—42no—
287C32×D4—42no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—41no—
293C2×C32×C4—41no—
294C2×C32×C4—42no—
295C2×C32×C4C22×D311yescharacteristic
296C2×C32×C4C22×D311yescharacteristic
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299C2×C32×C4C23×C311yescharacteristic
300C2×C32×C4C23×C311yescharacteristic
301C2×C32×C4C23×C311yescharacteristic
302C2×C32×C4C23×C311yescharacteristic
303#638—22no—
304#638—22no—
305#638—41no—
306#638—41no—
307#638—41no—
308#638—41no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3—41no—
311C2×C3⋊Dic3C23×C311yescharacteristic
312C2×C3⋊Dic3C23×C311yescharacteristic
313C2×C3⋊Dic3C23×C311yescharacteristic
314C2×C3⋊Dic3C23×C311yescharacteristic
315C2×C3⋊Dic3C23×C311yescharacteristic
316C2×C3⋊Dic3C23×C311yescharacteristic
317C4⋊(C3⋊D3)—41no—
318C4×C3⋊D3—41no—
319C4×C3⋊D3—41no—
320C3×#67—62no—
321C3×#67—62no—
322C3×#67—121no—
323C3×#67—121no—
324C3×#67—121no—
325C3×#67—121no—
326C2×C3×Dic3—31no—
327C2×C3×Dic3—31no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—31no—
330C2×C3×Dic3—31no—
331C2×C3×Dic3—31no—
332C2×C3×Dic3—62no—
333C2×C3×Dic3—121no—
334C3×D12—121no—
335C3×C4×D3—121no—
336C3×C4×D3—121no—
337#540—91noSylow
338C2×H(3,𝔽3)—41no—
339C2×H(3,𝔽3)—41no—
340C2×H(3,𝔽3)—41no—
341C2×H(3,𝔽3)C2×#4111yescharacteristic
342C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
343C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
344(C3⋊D3)⋊C3—41no—
345(C3⋊D3)⋊C3—41no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—31no—
351C2×C3×D4—31no—
352C2×C3×D4—61no—
353C2×C3×D4—61no—
354C2×C3×D4—61no—
355C2×C3×D4—91no—
356C2×C3×D4—91no—
357C2×C3×D4—91no—
358C2×C3×D4—91no—
359C2×C3×D4—91no—
360C2×C3×D4—91no—
361C2×C3×D4—91no—
362C2×C3×D4C2×C3×D311yescharacteristic
363C2×C3×D4C2×C3×D311yescharacteristic
364C2×C3×D4C2×C3×D311yescharacteristic
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—61no—
368C22×C3×C4—91no—
369C22×C3×C4—91no—
370C22×C3×C4—91no—
371C22×C3×C4—91no—
372C22×C3×C4C2×C3×D311yescharacteristic
373C2×#67—31no—
374C2×#67—31no—
375C2×#67—31no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C2×D12—31no—
390C2×D12—91no—
391C2×C4×D3—31no—
392C2×C4×D3—31no—
393C2×C4×D3—91no—
394C2×C4×D3—91no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4—61no—
398C3×C4⋊C4—91no—
399C3×C4⋊C4—91no—
400C3×C4⋊C4—91no—
401C3×C4⋊C4—91no—
402C3×C4⋊C4—91no—
403C3×C4⋊C4—91no—
404C3×C4⋊C4—91no—
405C3×C4⋊C4C2×C3×D311yescharacteristic
406C3×C22⋊C4—31no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4—91no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4—91no—
416C3×C22⋊C4—91no—
417C3×C22⋊C4—91no—
418C3×C22⋊C4—91no—
419C3×C22⋊C4—91no—
420C3×C22⋊C4C2×C3×D311yescharacteristic
421C3×C22⋊C4C2×C3×D311yescharacteristic
422C3×C42—91no—
423C3×C42—91no—
424#217—31no—
425#217—31no—
426#217—31no—
427#217—31no—
428#217—91no—
429#217—91no—
430#217—91no—
431#217—91no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—31no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440C4⋊Dic3—31no—
441C4⋊Dic3—91no—
442Dic3⋊C4—31no—
443Dic3⋊C4—31no—
444Dic3⋊C4—31no—
445Dic3⋊C4—31no—
446Dic3⋊C4—31no—
447Dic3⋊C4—31no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—91no—
454C4×Dic3—31no—
455C4×Dic3—31no—
456C4×Dic3—91no—
457C4×Dic3—91no—
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—21no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—21no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32C23×D311yescharacteristic
487C22×C32C24×C311yescharacteristic
488C2×C3⋊D3—21no—
489C2×C3⋊D3—21no—
490C2×C3⋊D3—21no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—21no—
494C2×C3×D3—61no—
495C2×C3×D3—61no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3—61no—
499C2×C3×D3—61no—
500C32×C4—22no—
501C32×C4—21no—
502C32×C4—21no—
503C32×C4—21no—
504C32×C4—21no—
505C32×C4—21no—
506C32×C4—21no—
507C32×C4—21no—
508C32×C4—21no—
509C32×C4—41no—
510C32×C4—41no—
511C32×C4—41no—
512C3⋊Dic3—21no—
513C3⋊Dic3—21no—
514C3⋊Dic3—21no—
515C3⋊Dic3—21no—
516C3⋊Dic3—21no—
517C3⋊Dic3C3×#4112yes—
518C3×Dic3—32no—
519C3×Dic3—61no—
520C3×Dic3—61no—
521C3×Dic3—61no—
522C3×Dic3—61no—
523C3×Dic3—61no—
524#127—91no—
525#125—91no—
526#123—91no—
527#123—91no—
528#123—91no—
529#123—91no—
530#121—91no—
531#121—91no—
532#121—91no—
533#121—91no—
534#121—91no—
535#121(C3⋊D3)⋊C311yescharacteristic, complemented
536C4×D4—91no—
537C4×D4—91no—
538#117—91no—
539H(3,𝔽3)#54011yescharacteristic, complemented, Sylow
540C23×C3—31no—
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—31no—
544C23×C3—31no—
545C23×C3—31no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—91no—
550C23×C3—91no—
551C23×C3C22×C3×D311yescharacteristic
552C23×C3C22×C3×D311yescharacteristic
553C23×C3C22×C3×D311yescharacteristic
554C22×D3—31no—
555C22×D3—31no—
556C22×D3—91no—
557C22×D3—91no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—41no—
561C3×D4—121no—
562C3×D4—121no—
563C3×D4—121no—
564C3×D4—121no—
565C3×D4—121no—
566C3×D4—121no—
567C3×D4—122no—
568C3×D4—122no—
569C3×D4—122no—
570C3×D4—182no—
571C3×D4—182no—
572C3×D4—361no—
573C3×D4—361no—
574C3×D4—361no—
575C3×D4—361no—
576C3×D4—361no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—41no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—91no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4—91no—
594C2×C3×C4—91no—
595C2×C3×C4—91no—
596C2×C3×C4—121no—
597C2×C3×C4—121no—
598C2×C3×C4—122no—
599C2×C3×C4—182no—
600C2×C3×C4—361no—
601C2×C3×C4—361no—
602C2×C3×C4—361no—
603C2×C3×C4C22×C3×D311yescharacteristic
604C2×C3×C4C22×C3×D311yescharacteristic
605C2×C3×C4C22×C3×D311yescharacteristic
606C2×C3×C4C22×C3×D311yescharacteristic
607#67—62no—
608#67—62no—
609#67—121no—
610#67—121no—
611#67—121no—
612#67—121no—
613#67—182no—
614#67—182no—
615#67—361no—
616#67—361no—
617#67—361no—
618#67—361no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—31no—
625C2×Dic3—62no—
626C2×Dic3—91no—
627C2×Dic3—91no—
628C2×Dic3—91no—
629C2×Dic3—91no—
630C2×Dic3—91no—
631C2×Dic3—91no—
632C2×Dic3—121no—
633C2×Dic3—182no—
634C2×Dic3—361no—
635D12—121no—
636D12—361no—
637C4×D3—121no—
638C4×D3—121no—
639C4×D3—361no—
640C4×D3—361no—
641C2×C32—21no—
642C2×C32—21no—
643C2×C32—21no—
644C2×C32—42no—
645C2×C32—41no—
646C2×C32—41no—
647C2×C32—41no—
648C2×C32—41no—
649C2×C32—41no—
650C2×C32—41no—
651C2×C32—81no—
652C2×C32—81no—
653C2×C32#100411yescharacteristic
654C2×C32#100411yescharacteristic
655C2×C32D3×#4111yescharacteristic
656C2×C32C2×C3×#4111yescharacteristic
657C2×C32C3×H(5,𝔽2)11yescharacteristic
658C2×C32C3×H(5,𝔽2)11yescharacteristic
659C3⋊D3—41no—
660C3⋊D3—41no—
661C3×D3—121no—
662C3×D3—121no—
663C2×D4—91no—
664C2×D4—91no—
665C2×D4—91no—
666C2×D4—91no—
667C2×D4—91no—
668C2×D4—91no—
669C2×D4—91no—
670C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
671C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
672C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—91no—
676C22×C4—91no—
677C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
678C4⋊C4—91no—
679C4⋊C4—91no—
680C4⋊C4—91no—
681C4⋊C4—91no—
682C4⋊C4—91no—
683C4⋊C4—91no—
684C4⋊C4—91no—
685C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C22⋊C4—91no—
690C22⋊C4—91no—
691C22⋊C4—91no—
692C22⋊C4—91no—
693C22⋊C4—91no—
694C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
695C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
696C42—91no—
697C42—91no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—31no—
708C22×C3—31no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—62no—
728C22×C3—61no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—181no—
738C22×C3—181no—
739C22×C3—181no—
740C22×C3—181no—
741C22×C3—181no—
742C22×C3—181no—
743C22×C3C23×C3×D311yescharacteristic
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—61no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—61no—
767C3×C4—61no—
768C3×C4—62no—
769C3×C4—92no—
770C3×C4—121no—
771C3×C4—121no—
772C3×C4—121no—
773C3×C4—181no—
774C3×C4—181no—
775C3×C4—181no—
776C3×C4—181no—
777C3×C4—181no—
778Dic3—32no—
779Dic3—61no—
780Dic3—61no—
781Dic3—61no—
782Dic3—61no—
783Dic3—61no—
784Dic3—92no—
785Dic3—181no—
786Dic3—181no—
787Dic3—181no—
788Dic3—181no—
789Dic3—181no—
790C32—21no—
791C32#561511yescharacteristic, complemented
792C32C3×#54011yescharacteristic, complemented
793C23—91no—
794C23—91no—
795C23C22×(C3⋊D3)⋊C311yescharacteristic
796C23C22×(C3⋊D3)⋊C311yescharacteristic
797C23C22×(C3⋊D3)⋊C311yescharacteristic
798D4—41no—
799D4—41no—
800D4—41no—
801D4—182no—
802D4—182no—
803D4—361no—
804D4—361no—
805D4—361no—
806D4—361no—
807D4—361no—
808C2×C4—41no—
809C2×C4—91no—
810C2×C4—91no—
811C2×C4—91no—
812C2×C4—91no—
813C2×C4—91no—
814C2×C4—91no—
815C2×C4—182no—
816C2×C4—361no—
817C2×C4—361no—
818C2×C4—361no—
819C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
820C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
821C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
822C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
823C2×C3—31no—
824C2×C3—31no—
825C2×C3—31no—
826C2×C3—31no—
827C2×C3—31no—
828C2×C3—31no—
829C2×C3—41no—
830C2×C3—41no—
831C2×C3—41no—
832C2×C3—61no—
833C2×C3—61no—
834C2×C3—61no—
835C2×C3—121no—
836C2×C3—121no—
837C2×C3—121no—
838C2×C3—121no—
839C2×C3—121no—
840C2×C3—121no—
841C2×C3—122no—
842C2×C3—241no—
843C2×C3—241no—
844C2×C3—361no—
845C2×C3—361no—
846C2×C3C3×#100411yescharacteristic
847C2×C3C3×#100411yescharacteristic
848C2×C3C3×D3×#4111yescharacteristic
849D3—121no—
850D3—121no—
851D3—361no—
852D3—361no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—181no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—181no—
868C22C23×(C3⋊D3)⋊C311yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—92no—
874C4—181no—
875C4—181no—
876C4—181no—
877C4—181no—
878C4—181no—
879C3—31no—
880C3—31no—
881C3—61no—
882C3C3×#561511yescharacteristic
883C2—41no—
884C2—41no—
885C2—41no—
886C2—361no—
887C2—361no—
888C2#64361⋊C311yescharacteristic
889C2#64361⋊C311yescharacteristic
890C2#41×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#121C2
hypercenter#121(C3⋊D3)⋊C3
hypocenterC32C3×#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#121C2semidirect
2. #64149⋊C3C2semidirect
3. #64148⋊C3C2semidirect
4. #64148⋊C3C2semidirect
5. #64148⋊C3C2semidirect
6. #64147⋊C3C2semidirect
7. #64144⋊C3C2semidirect
8. #64138⋊C3C2semidirect
9. C4×#638⋊C3C2semidirect
10. #64103⋊C3C2semidirect
11. #64098⋊C3C2semidirect
12. #64093⋊C3C2semidirect
13. #64092⋊C3C2semidirect
14. #64090⋊C3C2semidirect
15. #64086⋊C3C2semidirect
16. #10596086C3semidirect
54. C32×#121D3semidirect
55. C32×#121C2×C3semidirect
56. #64149C2×C3semidirect
57. #64148C2×C3semidirect
58. #64148C2×C3semidirect
59. #64148C2×C3semidirect
60. #64147C2×C3semidirect
61. #64144C2×C3semidirect
62. #64138C2×C3semidirect
63. C4×#638C2×C3semidirect
64. #64103C2×C3semidirect
65. #64098C2×C3semidirect
66. #64093C2×C3semidirect
67. #64092C2×C3semidirect
68. #64090C2×C3semidirect
69. #64086C2×C3semidirect
535. #121(C3⋊D3)⋊C3semidirect
539. H(3,𝔽3)#540semidirect
791. C32#5615semidirect
792. C32C3×#540semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×#1212
#64149⋊C32
#64148⋊C32
#64147⋊C32
#64144⋊C32
#64138⋊C32
C4×#638⋊C32
#64103⋊C32
#64098⋊C32
#64093⋊C32
#64092⋊C32
#64090⋊C32
#64086⋊C32
#105960863
C3×#56153