Finite Group Databasebeta

← #10596117⋊C3 #13152967

Subgroups — #10596117⋊C3 #13152967

Order 1728.

760 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×C22⋊Q8C211yesmaximal, characteristic, complemented
2#64155⋊C3C211yesmaximal, characteristic, complemented
3#64153⋊C3C211yesmaximal, characteristic, complemented
4#64138⋊C3C211yesmaximal, characteristic
5#64133⋊C3C211yesmaximal, characteristic, complemented
6#64107⋊C3C211yesmaximal, characteristic, complemented
7#64107⋊C3C211yesmaximal, characteristic, complemented
8#64105⋊C3C211yesmaximal, characteristic, complemented
9#64099⋊C3C211yesmaximal, characteristic, complemented
10#64098⋊C3C211yesmaximal, characteristic, complemented
11#64097⋊C3C211yesmaximal, characteristic, complemented
12#64094⋊C3C211yesmaximal, characteristic
13#64092⋊C3C211yesmaximal, characteristic
14#64088⋊C3C211yesmaximal, characteristic, complemented
15#64088⋊C3C211yesmaximal, characteristic, complemented
16#10596117C311yesmaximal, characteristic, complemented
17C3×#5646—31nomaximal
18C2×Q8×H(3,𝔽3)C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
22C2×#634⋊C3C2211yescharacteristic
23C2×#634⋊C3C2211yescharacteristic
24C4⋊C4×H(3,𝔽3)C2211yescharacteristic
25C4⋊C4×H(3,𝔽3)C2211yescharacteristic
26C4⋊C4×H(3,𝔽3)C2211yescharacteristic
27C22⋊C4×H(3,𝔽3)C2211yescharacteristic
28C22⋊C4×H(3,𝔽3)C2211yescharacteristic
29#3757⋊C3C2211yescharacteristic
30#3757⋊C3C2211yescharacteristic
31#3757⋊C3C2211yescharacteristic
32#3752⋊C3C2211yescharacteristic
33#3752⋊C3C2211yescharacteristic
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
38C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
39C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
40C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
41#3750⋊C3C2211yescharacteristic
42#3750⋊C3C2211yescharacteristic
43#3750⋊C3C2211yescharacteristic
44#3750⋊C3C2211yescharacteristic
45#3750⋊C3C2211yescharacteristic
46#3750⋊C3C2211yescharacteristic
47#3750⋊C3C2211yescharacteristic
48#3750⋊C3C2211yescharacteristic
49#3750⋊C3C2211yescharacteristic
50C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
53C32×C22⋊Q8—21no—
54C32×C22⋊Q8D311yescharacteristic, complemented
55C32×C22⋊Q8C2×C311yescharacteristic, complemented
56#64155C2×C311yescharacteristic, complemented
57#64153C2×C311yescharacteristic, complemented
58#64138C2×C311yescharacteristic
59#64133C2×C311yescharacteristic, complemented
60#64107C2×C311yescharacteristic, complemented
61#64107C2×C311yescharacteristic, complemented
62#64105C2×C311yescharacteristic, complemented
63#64099C2×C311yescharacteristic, complemented
64#64098C2×C311yescharacteristic, complemented
65#64097C2×C311yescharacteristic, complemented
66#64094C2×C311yescharacteristic
67#64092C2×C311yescharacteristic
68#64088C2×C311yescharacteristic, complemented
69#64088C2×C311yescharacteristic, complemented
70C3×#946—31no—
71C3×#944—31no—
72C3×#929—31no—
73C3×#924—31no—
74C3×#898—31no—
75C3×#898—31no—
76C3×#896—31no—
77C3×#890—31no—
78C3×#889—31no—
79C3×#888—31no—
80C3×#885—31no—
81C3×#883—31no—
82C3×#879—31no—
83C3×#879—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86Q8×H(3,𝔽3)—41no—
87C2×C4×H(3,𝔽3)—41no—
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×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94#638⋊C3—41no—
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C4×(C3⋊D3)⋊C3—41no—
103#634⋊C3—41no—
104#634⋊C3—41no—
105C3×#563—91no—
106#5646—31no—
107#5646—91no—
108C2×C32×Q8—21no—
109C2×C32×Q8C2×D311yescharacteristic
110C2×C32×Q8C22×C311yescharacteristic
111C22×C32×C4—21no—
112C22×C32×C4C2×D311yescharacteristic
113C22×C32×C4C22×C311yescharacteristic
114C2×#638C22×C311yescharacteristic
115C2×C4×C3⋊D3C22×C311yescharacteristic
116C2×#634C22×C311yescharacteristic
117C2×#634C22×C311yescharacteristic
118C2×C3×#67—31no—
119C2×C3×C4×D3—31no—
120C2×C3×Dic6—31no—
121C2×C3×Dic6—31no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4—21no—
125C32×C4⋊C4C2×D311yescharacteristic
126C32×C4⋊C4C2×D311yescharacteristic
127C32×C4⋊C4C2×D311yescharacteristic
128C32×C4⋊C4C22×C311yescharacteristic
129C32×C4⋊C4C22×C311yescharacteristic
130C32×C4⋊C4C22×C311yescharacteristic
131C32×C22⋊C4—21no—
132C32×C22⋊C4—21no—
133C32×C22⋊C4C2×D311yescharacteristic
134C32×C22⋊C4C2×D311yescharacteristic
135C32×C22⋊C4C22×C311yescharacteristic
136C32×C22⋊C4C22×C311yescharacteristic
137#3757C22×C311yescharacteristic
138#3757C22×C311yescharacteristic
139#3757C22×C311yescharacteristic
140#3752C22×C311yescharacteristic
141#3752C22×C311yescharacteristic
142#3752C22×C311yescharacteristic
143#3752C22×C311yescharacteristic
144#3752C22×C311yescharacteristic
145C4⋊(C3⋊Dic3)C22×C311yescharacteristic
146C4⋊(C3⋊Dic3)C22×C311yescharacteristic
147C4⋊(C3⋊Dic3)C22×C311yescharacteristic
148C4⋊(C3⋊Dic3)C22×C311yescharacteristic
149#3750C22×C311yescharacteristic
150#3750C22×C311yescharacteristic
151#3750C22×C311yescharacteristic
152#3750C22×C311yescharacteristic
153#3750C22×C311yescharacteristic
154#3750C22×C311yescharacteristic
155#3750C22×C311yescharacteristic
156#3750C22×C311yescharacteristic
157#3750C22×C311yescharacteristic
158C4×C3⋊Dic3C22×C311yescharacteristic
159C4×C3⋊Dic3C22×C311yescharacteristic
160C4×C3⋊Dic3C22×C311yescharacteristic
161C3×#217—31no—
162C3×#217—31no—
163C3×#217—31no—
164C3×(C2×D3)⋊C4—31no—
165C3×(C2×D3)⋊C4—31no—
166C3×(C2×D3)⋊C4—31no—
167C3×(C2×D3)⋊C4—31no—
168C3×(C2×D3)⋊C4—31no—
169C3×C4⋊Dic3—31no—
170C3×C4⋊Dic3—31no—
171C3×C4⋊Dic3—31no—
172C3×C4⋊Dic3—31no—
173C3×Dic3⋊C4—31no—
174C3×Dic3⋊C4—31no—
175C3×Dic3⋊C4—31no—
176C3×Dic3⋊C4—31no—
177C3×Dic3⋊C4—31no—
178C3×Dic3⋊C4—31no—
179C3×Dic3⋊C4—31no—
180C3×Dic3⋊C4—31no—
181C3×Dic3⋊C4—31no—
182C3×C4×Dic3—31no—
183C3×C4×Dic3—31no—
184C3×C4×Dic3—31no—
185C22×H(3,𝔽3)—21no—
186C22×H(3,𝔽3)—21no—
187C22×H(3,𝔽3)—21no—
188C22×H(3,𝔽3)C2411yescharacteristic
189C2×(C3⋊D3)⋊C3—21no—
190C2×(C3⋊D3)⋊C3—21no—
191C2×(C3⋊D3)⋊C3—21no—
192C4×H(3,𝔽3)—21no—
193C4×H(3,𝔽3)—21no—
194C4×H(3,𝔽3)—21no—
195C4×H(3,𝔽3)—21no—
196C4×H(3,𝔽3)—21no—
197C4×H(3,𝔽3)—21no—
198(C3⋊Dic3)⋊C3—21no—
199(C3⋊Dic3)⋊C3—21no—
200(C3⋊Dic3)⋊C3—21no—
201(C3⋊Dic3)⋊C3—21no—
202(C3⋊Dic3)⋊C3—21no—
203(C3⋊Dic3)⋊C3—21no—
204(C3⋊Dic3)⋊C3—21no—
205C3×C4⋊Q8—91no—
206C3×C4⋊Q8—91no—
207C3×#126—91no—
208C3×#126—91no—
209C3×#126—91no—
210C3×#126—91no—
211C3×#125—91no—
212C3×#125—91no—
213C3×#124—91no—
214C3×#123—91no—
215C3×#123—91no—
216C3×C22⋊Q8—31no—
217C3×C22⋊Q8—31no—
218C3×C22⋊Q8—61no—
219C3×C22⋊Q8—91no—
220C3×C22⋊Q8—91no—
221C3×C22⋊Q8—91no—
222C3×C22⋊Q8C3×D311yescharacteristic
223#946—31no—
224#946—91no—
225#944—31no—
226#944—91no—
227#929—31no—
228#929—91no—
229#924—31no—
230#924—91no—
231#898—31no—
232#898—31no—
233#898—91no—
234#898—91no—
235#896—31no—
236#896—91no—
237#890—31no—
238#890—91no—
239#889—31no—
240#889—91no—
241#888—31no—
242#888—91no—
243#885—31no—
244#885—91no—
245#883—31no—
246#883—91no—
247#879—31no—
248#879—31no—
249#879—91no—
250#879—91no—
251C23×C32—21no—
252C23×C32C22×D311yescharacteristic
253C23×C32C23×C311yescharacteristic
254C22×C3⋊D3C23×C311yescharacteristic
255C22×C3×D3—31no—
256C32×Q8—41no—
257C32×Q8—41no—
258C32×Q8—42no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—41no—
266C2×C32×C4—41no—
267C2×C32×C4—42no—
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C23×C311yescharacteristic
275C2×C32×C4C23×C311yescharacteristic
276C2×C32×C4C23×C311yescharacteristic
277C2×C32×C4C23×C311yescharacteristic
278C2×C32×C4C23×C311yescharacteristic
279C2×C32×C4C23×C311yescharacteristic
280#638—41no—
281C2×C3⋊Dic3C23×C311yescharacteristic
282C2×C3⋊Dic3C23×C311yescharacteristic
283C2×C3⋊Dic3C23×C311yescharacteristic
284C2×C3⋊Dic3C23×C311yescharacteristic
285C2×C3⋊Dic3C23×C311yescharacteristic
286C2×C3⋊Dic3C23×C311yescharacteristic
287C2×C3⋊Dic3C23×C311yescharacteristic
288C4×C3⋊D3—41no—
289#634—41no—
290#634—41no—
291C3×#67—121no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—31no—
299C3×C4×D3—121no—
300C3×Dic6—121no—
301C3×Dic6—121no—
302#563—91noSylow
303C2×H(3,𝔽3)—41no—
304C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
305C2×H(3,𝔽3)2−1+411yescharacteristic
306C2×H(3,𝔽3)2−1+411yescharacteristic
307(C3⋊D3)⋊C3—41no—
308C2×C3×Q8—31no—
309C2×C3×Q8—31no—
310C2×C3×Q8—61no—
311C2×C3×Q8—91no—
312C2×C3×Q8—91no—
313C2×C3×Q8C2×C3×D311yescharacteristic
314C2×C3×D4—91no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—61no—
318C22×C3×C4—91no—
319C22×C3×C4C2×C3×D311yescharacteristic
320C2×#67—31no—
321C2×#67—91no—
322C2×C4×D3—31no—
323C2×C4×D3—91no—
324C2×Dic6—31no—
325C2×Dic6—31no—
326C2×Dic6—91no—
327C2×Dic6—91no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—91no—
338C3×C4⋊C4—91no—
339C3×C4⋊C4—91no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4—91no—
347C3×C4⋊C4—91no—
348C3×C4⋊C4—91no—
349C3×C4⋊C4—91no—
350C3×C4⋊C4C2×C3×D311yescharacteristic
351C3×C4⋊C4C2×C3×D311yescharacteristic
352C3×C4⋊C4C2×C3×D311yescharacteristic
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—91no—
360C3×C22⋊C4—91no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4C2×C3×D311yescharacteristic
368C3×C22⋊C4C2×C3×D311yescharacteristic
369C3×C42—91no—
370C3×C42—91no—
371C3×C42—91no—
372#217—31no—
373#217—31no—
374#217—31no—
375#217—91no—
376#217—91no—
377#217—91no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394C4⋊Dic3—91no—
395C4⋊Dic3—91no—
396Dic3⋊C4—31no—
397Dic3⋊C4—31no—
398Dic3⋊C4—31no—
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—31no—
417C4×Dic3—91no—
418C4×Dic3—91no—
419C4×Dic3—91no—
420C22×C32—22no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32C23×D311yescharacteristic
431C22×C32C24×C311yescharacteristic
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—21no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C32×C4—22no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—21no—
448C32×C4—21no—
449C32×C4—21no—
450C32×C4—21no—
451C32×C4—41no—
452C32×C4—41no—
453C32×C4—41no—
454C32×C4—41no—
455C32×C4—41no—
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3—21no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—61no—
466C3×Dic3—61no—
467C3×Dic3—61no—
468C3×Dic3—61no—
469C3×Dic3—61no—
470C4⋊Q8—91no—
471C4⋊Q8—91no—
472#126—91no—
473#126—91no—
474#126—91no—
475#126—91no—
476#125—91no—
477#125—91no—
478#124—91no—
479#123—91no—
480#123—91no—
481C22⋊Q8—91no—
482C22⋊Q8—91no—
483C22⋊Q8—91no—
484C22⋊Q8(C3⋊D3)⋊C311yescharacteristic, complemented
485H(3,𝔽3)#56311yescharacteristic, complemented, Sylow
486C23×C3—31no—
487C23×C3—31no—
488C23×C3—61no—
489C23×C3—91no—
490C23×C3C22×C3×D311yescharacteristic
491C22×D3—31no—
492C22×D3—91no—
493C3×Q8—41no—
494C3×Q8—121no—
495C3×Q8—121no—
496C3×Q8—122no—
497C3×Q8—361no—
498C3×Q8—361no—
499C3×D4—361no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—91no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—91no—
526C2×C3×C4—121no—
527C2×C3×C4—121no—
528C2×C3×C4—122no—
529C2×C3×C4—361no—
530C2×C3×C4C22×C3×D311yescharacteristic
531C2×C3×C4C22×C3×D311yescharacteristic
532C2×C3×C4C22×C3×D311yescharacteristic
533C2×C3×C4C22×C3×D311yescharacteristic
534C2×C3×C4C22×C3×D311yescharacteristic
535C2×C3×C4C22×C3×D311yescharacteristic
536#67—121no—
537#67—361no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—91no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—91no—
549C2×Dic3—91no—
550C2×Dic3—91no—
551C2×Dic3—91no—
552C4×D3—121no—
553C4×D3—361no—
554Dic6—121no—
555Dic6—121no—
556Dic6—361no—
557Dic6—361no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—42no—
562C2×C32—41no—
563C2×C32—41no—
564C2×C32#100411yescharacteristic
565C2×C32#100711yescharacteristic
566C2×C32#101011yescharacteristic
567C2×C32C3×H(5,𝔽2)11yescharacteristic
568C2×C32C3×2−1+411yescharacteristic
569C2×C32C3×2−1+411yescharacteristic
570C3⋊D3—41no—
571C3×D3—121no—
572C2×Q8—91no—
573C2×Q8—91no—
574C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic
575C2×D4—91no—
576C22×C4—91no—
577C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4—91no—
588C4⋊C4—91no—
589C4⋊C4—91no—
590C4⋊C4—91no—
591C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
592C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
593C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
594C22⋊C4—91no—
595C22⋊C4—91no—
596C22⋊C4—91no—
597C22⋊C4—91no—
598C22⋊C4—91no—
599C22⋊C4—91no—
600C22⋊C4—91no—
601C22⋊C4—91no—
602C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
603C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
604C42—91no—
605C42—91no—
606C42—91no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—31no—
611C22×C3—31no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—62no—
619C22×C3—61no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3—181no—
623C22×C3—181no—
624C22×C3—181no—
625C22×C3C23×C3×D311yescharacteristic
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—181no—
630C2×D3—181no—
631C2×D3—181no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—62no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—181no—
657C3×C4—181no—
658C3×C4—181no—
659C3×C4—181no—
660C3×C4—181no—
661C3×C4—181no—
662C3×C4—181no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—61no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675Dic3—181no—
676Dic3—181no—
677C32—21no—
678C32#564611yescharacteristic, complemented
679C32C3×#56311yescharacteristic, complemented
680C23—91no—
681C23C22×(C3⋊D3)⋊C311yescharacteristic
682Q8—41no—
683Q8—361no—
684Q8—361no—
685D4—361no—
686C2×C4—41no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—91no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—91no—
694C2×C4—361no—
695C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
696C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
697C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
698C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
699C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
700C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
701C2×C3—31no—
702C2×C3—31no—
703C2×C3—31no—
704C2×C3—31no—
705C2×C3—31no—
706C2×C3—31no—
707C2×C3—41no—
708C2×C3—61no—
709C2×C3—61no—
710C2×C3—61no—
711C2×C3—121no—
712C2×C3—121no—
713C2×C3—122no—
714C2×C3—361no—
715C2×C3C3×#100411yescharacteristic
716C2×C3C3×#100711yescharacteristic
717C2×C3C3×#101011yescharacteristic
718D3—121no—
719D3—361no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—181no—
724C22—181no—
725C22—181no—
726C22C23×(C3⋊D3)⋊C311yescharacteristic
727C4—21no—
728C4—21no—
729C4—21no—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—181no—
734C4—181no—
735C4—181no—
736C4—181no—
737C4—181no—
738C4—181no—
739C4—181no—
740C3—31no—
741C3—31no—
742C3—61no—
743C3C3×#564611yescharacteristic
744C2—41no—
745C2—361no—
746C2#64361⋊C311yescharacteristic
747C2#1172262711yescharacteristic
748C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×C22⋊Q8C2
prime radicalC2×#638⋊C3C22
hypercenterC22⋊Q8(C3⋊D3)⋊C3
hypocenterC32C3×#563
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×C22⋊Q8C2semidirect
2. #64155⋊C3C2semidirect
3. #64153⋊C3C2semidirect
5. #64133⋊C3C2semidirect
6. #64107⋊C3C2semidirect
7. #64107⋊C3C2semidirect
8. #64105⋊C3C2semidirect
9. #64099⋊C3C2semidirect
10. #64098⋊C3C2semidirect
11. #64097⋊C3C2semidirect
14. #64088⋊C3C2semidirect
15. #64088⋊C3C2semidirect
16. #10596117C3semidirect
54. C32×C22⋊Q8D3semidirect
55. C32×C22⋊Q8C2×C3semidirect
56. #64155C2×C3semidirect
57. #64153C2×C3semidirect
59. #64133C2×C3semidirect
60. #64107C2×C3semidirect
61. #64107C2×C3semidirect
62. #64105C2×C3semidirect
63. #64099C2×C3semidirect
64. #64098C2×C3semidirect
65. #64097C2×C3semidirect
68. #64088C2×C3semidirect
69. #64088C2×C3semidirect
484. C22⋊Q8(C3⋊D3)⋊C3semidirect
485. H(3,𝔽3)#563semidirect
678. C32#5646semidirect
679. C32C3×#563semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×C22⋊Q82
#64155⋊C32
#64153⋊C32
#64138⋊C32
#64133⋊C32
#64107⋊C32
#64105⋊C32
#64099⋊C32
#64098⋊C32
#64097⋊C32
#64094⋊C32
#64092⋊C32
#64088⋊C32
#105961173
C3×#56463