Finite Group Databasebeta

← #10596167⋊C3 #13153176

Subgroups — #10596167⋊C3 #13153176

Order 1728.

728 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#125C211yesmaximal, characteristic, complemented
2#64107⋊C3C211yesmaximal, characteristic
3#64107⋊C3C211yesmaximal, characteristic
4#64107⋊C3C211yesmaximal, characteristic
5#64105⋊C3C211yesmaximal, characteristic
6#64105⋊C3C211yesmaximal, characteristic
7#64101⋊C3C211yesmaximal, characteristic
8#64099⋊C3C211yesmaximal, characteristic, complemented
9#64098⋊C3C211yesmaximal, characteristic, complemented
10#64098⋊C3C211yesmaximal, characteristic, complemented
11#64098⋊C3C211yesmaximal, characteristic, complemented
12#64097⋊C3C211yesmaximal, characteristic, complemented
13#64096⋊C3C211yesmaximal, characteristic, complemented
14#11721387C211yesmaximal, characteristic
15C4×#634⋊C3C211yesmaximal, characteristic, complemented
16#10596167C311yesmaximal, characteristic, complemented
17C3×#5696—31nomaximal
18C2×C4×(C3⋊D3)⋊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
24C4⋊C4×H(3,𝔽3)C2211yescharacteristic
25C4⋊C4×H(3,𝔽3)C2211yescharacteristic
26C4⋊C4×H(3,𝔽3)C2211yescharacteristic
27C42×H(3,𝔽3)C2211yescharacteristic
28#3752⋊C3C2211yescharacteristic
29#3752⋊C3C2211yescharacteristic
30#3752⋊C3C2211yescharacteristic
31#3752⋊C3C2211yescharacteristic
32#3752⋊C3C2211yescharacteristic
33#3752⋊C3C2211yescharacteristic
34C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
35C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
36C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
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×#125—21no—
54C32×#125D311yescharacteristic, complemented
55C32×#125C2×C311yescharacteristic, complemented
56#64107C2×C311yescharacteristic
57#64107C2×C311yescharacteristic
58#64107C2×C311yescharacteristic
59#64105C2×C311yescharacteristic
60#64105C2×C311yescharacteristic
61#64101C2×C311yescharacteristic
62#64099C2×C311yescharacteristic, complemented
63#64098C2×C311yescharacteristic, complemented
64#64098C2×C311yescharacteristic, complemented
65#64098C2×C311yescharacteristic, complemented
66#64097C2×C311yescharacteristic, complemented
67#64096C2×C311yescharacteristic, complemented
68#64085C2×C311yescharacteristic
69C4×#634C2×C311yescharacteristic, complemented
70C3×#898—31no—
71C3×#898—31no—
72C3×#898—31no—
73C3×#896—31no—
74C3×#896—31no—
75C3×#892—31no—
76C3×#890—31no—
77C3×#889—31no—
78C3×#889—31no—
79C3×#889—31no—
80C3×#888—31no—
81C3×#887—31no—
82C3×#876—31no—
83C3×C4×Dic6—31no—
84C22×(C3⋊D3)⋊C3C2311yescharacteristic
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×C4×H(3,𝔽3)C2311yescharacteristic
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
99C4×(C3⋊D3)⋊C3—22no—
100#634⋊C3—22no—
101#634⋊C3—22no—
102C3×#541—91no—
103#5696—31no—
104#5696—91no—
105C2×C4×C3⋊D3C22×C311yescharacteristic
106C2×#634C22×C311yescharacteristic
107C2×#634C22×C311yescharacteristic
108C2×C3×C4×D3—31no—
109C2×C3×Dic6—31no—
110C2×C3×Dic6—31no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2×D311yescharacteristic
118C32×C4⋊C4C2×D311yescharacteristic
119C32×C4⋊C4C2×D311yescharacteristic
120C32×C4⋊C4C2×D311yescharacteristic
121C32×C4⋊C4C2×D311yescharacteristic
122C32×C4⋊C4C2×D311yescharacteristic
123C32×C4⋊C4C22×C311yescharacteristic
124C32×C4⋊C4C22×C311yescharacteristic
125C32×C4⋊C4C22×C311yescharacteristic
126C32×C4⋊C4C22×C311yescharacteristic
127C32×C4⋊C4C22×C311yescharacteristic
128C32×C4⋊C4C22×C311yescharacteristic
129C32×C42—21no—
130C32×C42C2×D311yescharacteristic
131C32×C42C22×C311yescharacteristic
132#3752C22×C311yescharacteristic
133#3752C22×C311yescharacteristic
134#3752C22×C311yescharacteristic
135#3752C22×C311yescharacteristic
136#3752C22×C311yescharacteristic
137#3752C22×C311yescharacteristic
138C4⋊(C3⋊Dic3)C22×C311yescharacteristic
139C4⋊(C3⋊Dic3)C22×C311yescharacteristic
140C4⋊(C3⋊Dic3)C22×C311yescharacteristic
141C4⋊(C3⋊Dic3)C22×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×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—31no—
161C3×(C2×D3)⋊C4—31no—
162C3×(C2×D3)⋊C4—31no—
163C3×C4⋊Dic3—31no—
164C3×C4⋊Dic3—31no—
165C3×C4⋊Dic3—31no—
166C3×C4⋊Dic3—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)C2411yescharacteristic
183C2×(C3⋊D3)⋊C3—21no—
184C2×(C3⋊D3)⋊C3—21no—
185C2×(C3⋊D3)⋊C3—21no—
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—
192C4×H(3,𝔽3)—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—91no—
202C3×#126—91no—
203C3×#126—91no—
204C3×#126—91no—
205C3×#125—31no—
206C3×#125—31no—
207C3×#125—61no—
208C3×#125—91no—
209C3×#125—91no—
210C3×#125—91no—
211C3×#125—91no—
212C3×#125C3×D311yescharacteristic
213C3×C22⋊Q8—91no—
214C3×C22⋊Q8—91no—
215C3×C4×Q8—91no—
216C3×C4×Q8—91no—
217C3×#117—91no—
218#898—31no—
219#898—31no—
220#898—31no—
221#898—91no—
222#898—91no—
223#898—91no—
224#896—31no—
225#896—31no—
226#896—91no—
227#896—91no—
228#892—31no—
229#892—91no—
230#890—31no—
231#890—91no—
232#889—31no—
233#889—31no—
234#889—31no—
235#889—91no—
236#889—91no—
237#889—91no—
238#888—31no—
239#888—91no—
240#887—31no—
241#887—91no—
242#876—31no—
243#876—91no—
244C4×Dic6—31no—
245C4×Dic6—91no—
246C22×C3⋊D3C23×C311yescharacteristic
247C22×C3×D3—31no—
248C2×C32×C4—21no—
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×C4C22×D311yescharacteristic
262C2×C32×C4C23×C311yescharacteristic
263C2×C32×C4C23×C311yescharacteristic
264C2×C32×C4C23×C311yescharacteristic
265C2×C32×C4C23×C311yescharacteristic
266C2×C32×C4C23×C311yescharacteristic
267C2×C32×C4C23×C311yescharacteristic
268C2×C32×C4C23×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
276C4×C3⋊D3—22no—
277#634—22no—
278#634—22no—
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—
286C3×C4×D3—62no—
287C3×Dic6—62no—
288C3×Dic6—62no—
289#541—91noSylow
290C2×H(3,𝔽3)C2×#4111yescharacteristic
291C2×H(3,𝔽3)2−1+411yescharacteristic
292C2×H(3,𝔽3)2−1+411yescharacteristic
293(C3⋊D3)⋊C3—41no—
294C2×C3×Q8—91no—
295C2×C3×Q8—91no—
296C22×C3×C4—91no—
297C2×C4×D3—31no—
298C2×C4×D3—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—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
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⋊C4—91no—
330C3×C4⋊C4—91no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C4⋊C4C2×C3×D311yescharacteristic
336C3×C4⋊C4C2×C3×D311yescharacteristic
337C3×C4⋊C4C2×C3×D311yescharacteristic
338C3×C4⋊C4C2×C3×D311yescharacteristic
339C3×C4⋊C4C2×C3×D311yescharacteristic
340C3×C4⋊C4C2×C3×D311yescharacteristic
341C3×C22⋊C4—91no—
342C3×C22⋊C4—91no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—91no—
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(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—91no—
373C4⋊Dic3—91no—
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
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—31no—
385Dic3⋊C4—31no—
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×C32C23×D311yescharacteristic
408C22×C32C24×C311yescharacteristic
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3×D3—61no—
413C2×C3×D3—61no—
414C2×C3×D3—61no—
415C32×C4—22no—
416C32×C4—21no—
417C32×C4—21no—
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⋊Dic3C3×#4112yes—
443C3×Dic3—32no—
444C3×Dic3—61no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C4⋊Q8—91no—
451#126—91no—
452#126—91no—
453#126—91no—
454#126—91no—
455#125—91no—
456#125—91no—
457#125—91no—
458#125—91no—
459#125(C3⋊D3)⋊C311yescharacteristic, complemented
460C22⋊Q8—91no—
461C22⋊Q8—91no—
462C4×Q8—91no—
463C4×Q8—91no—
464#117—91no—
465H(3,𝔽3)#54111yescharacteristic, complemented, Sylow
466C23×C3—91no—
467C22×D3—31no—
468C22×D3—91no—
469C3×Q8—182no—
470C3×Q8—182no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
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—61no—
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—182no—
500C2×C3×C4C22×C3×D311yescharacteristic
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—91no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C4×D3—62no—
522C4×D3—182no—
523Dic6—62no—
524Dic6—62no—
525Dic6—182no—
526Dic6—182no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32#100711yescharacteristic
531C2×C32D3×#4111yescharacteristic
532C2×C32#101011yescharacteristic
533C2×C32C2×C3×#4111yescharacteristic
534C2×C32C3×2−1+411yescharacteristic
535C2×C32C3×2−1+411yescharacteristic
536C3⋊D3—41no—
537C3×D3—121no—
538C2×Q8—91no—
539C2×Q8—91no—
540C22×C4—91no—
541C4⋊C4—91no—
542C4⋊C4—91no—
543C4⋊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⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
556C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
557C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
558C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
559C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
560C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
561C22⋊C4—91no—
562C22⋊C4—91no—
563C22⋊C4—91no—
564C22⋊C4—91no—
565C22⋊C4—91no—
566C22⋊C4—91no—
567C42—91no—
568C42—91no—
569C42—91no—
570C42—91no—
571C42—91no—
572C42C2×(C3⋊D3)⋊C311yescharacteristic
573C22×C3—31no—
574C22×C3—31no—
575C22×C3—61no—
576C22×C3—181no—
577C22×C3—181no—
578C22×C3—181no—
579C22×C3C23×C3×D311yescharacteristic
580C2×D3—61no—
581C2×D3—61no—
582C2×D3—61no—
583C2×D3—181no—
584C2×D3—181no—
585C2×D3—181no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—61no—
594C3×C4—61no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—61no—
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—62no—
608C3×C4—92no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4—181no—
616C3×C4—181no—
617C3×C4—181no—
618C3×C4—181no—
619C3×C4—181no—
620C3×C4—181no—
621Dic3—32no—
622Dic3—61no—
623Dic3—61no—
624Dic3—61no—
625Dic3—61no—
626Dic3—61no—
627Dic3—61no—
628Dic3—92no—
629Dic3—181no—
630Dic3—181no—
631Dic3—181no—
632Dic3—181no—
633Dic3—181no—
634Dic3—181no—
635C32—21no—
636C32#569611yescharacteristic, complemented
637C32C3×#54111yescharacteristic, complemented
638C23—91no—
639Q8—182no—
640Q8—182no—
641C2×C4—91no—
642C2×C4—91no—
643C2×C4—91no—
644C2×C4—91no—
645C2×C4—91no—
646C2×C4—91no—
647C2×C4—91no—
648C2×C4—182no—
649C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
650C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
651C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
652C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
653C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
654C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
655C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
656C2×C3—31no—
657C2×C3—31no—
658C2×C3—31no—
659C2×C3—31no—
660C2×C3—31no—
661C2×C3—31no—
662C2×C3—61no—
663C2×C3—61no—
664C2×C3—61no—
665C2×C3—361no—
666C2×C3C3×#100711yescharacteristic
667C2×C3C3×D3×#4111yescharacteristic
668C2×C3C3×#101011yescharacteristic
669D3—121no—
670D3—361no—
671C22—181no—
672C22—181no—
673C22—181no—
674C22C23×(C3⋊D3)⋊C311yescharacteristic
675C4—21no—
676C4—21no—
677C4—21no—
678C4—21no—
679C4—21no—
680C4—21no—
681C4—21no—
682C4—92no—
683C4—181no—
684C4—181no—
685C4—181no—
686C4—181no—
687C4—181no—
688C4—181no—
689C3—31no—
690C3—31no—
691C3—61no—
692C3C3×#569611yescharacteristic
693C2—361no—
694C2#1172262711yescharacteristic
695C2#41×(C3⋊D3)⋊C311yescharacteristic
696C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#125C2
prime radicalC22×(C3⋊D3)⋊C3C23
hypercenter#125(C3⋊D3)⋊C3
hypocenterC32C3×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#125C2semidirect
8. #64099⋊C3C2semidirect
9. #64098⋊C3C2semidirect
10. #64098⋊C3C2semidirect
11. #64098⋊C3C2semidirect
12. #64097⋊C3C2semidirect
13. #64096⋊C3C2semidirect
15. C4×#634⋊C3C2semidirect
16. #10596167C3semidirect
54. C32×#125D3semidirect
55. C32×#125C2×C3semidirect
62. #64099C2×C3semidirect
63. #64098C2×C3semidirect
64. #64098C2×C3semidirect
65. #64098C2×C3semidirect
66. #64097C2×C3semidirect
67. #64096C2×C3semidirect
69. C4×#634C2×C3semidirect
459. #125(C3⋊D3)⋊C3semidirect
465. H(3,𝔽3)#541semidirect
636. C32#5696semidirect
637. 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)×#1252
#64107⋊C32
#64105⋊C32
#64101⋊C32
#64099⋊C32
#64098⋊C32
#64097⋊C32
#64096⋊C32
#117213872
C4×#634⋊C32
#105961673
C3×#56963