Finite Group Databasebeta

← #10596118⋊C3 #13152968

Subgroups — #10596118⋊C3 #13152968

Order 1728.

844 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×C22⋊Q8C211yesmaximal, characteristic, complemented
2#64156⋊C3C211yesmaximal, characteristic, complemented
3#64155⋊C3C211yesmaximal, characteristic, complemented
4#64139⋊C3C211yesmaximal, characteristic, complemented
5#64138⋊C3C211yesmaximal, characteristic, complemented
6#64106⋊C3C211yesmaximal, characteristic, complemented
7#64105⋊C3C211yesmaximal, characteristic, complemented
8#64104⋊C3C211yesmaximal, characteristic, complemented
9#64103⋊C3C211yesmaximal, characteristic, complemented
10#64103⋊C3C211yesmaximal, characteristic, complemented
11#64098⋊C3C211yesmaximal, characteristic, complemented
12#64094⋊C3C211yesmaximal, characteristic, complemented
13#64093⋊C3C211yesmaximal, characteristic, complemented
14#64093⋊C3C211yesmaximal, characteristic, complemented
15#64092⋊C3C211yesmaximal, characteristic, complemented
16#10596118C311yesmaximal, characteristic, complemented
17C3×#5647—31nomaximal
18C2×Q8×H(3,𝔽3)C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
24C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
25C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
29C2×#634⋊C3C2211yescharacteristic
30C4⋊C4×H(3,𝔽3)C2211yescharacteristic
31C4⋊C4×H(3,𝔽3)C2211yescharacteristic
32C4⋊C4×H(3,𝔽3)C2211yescharacteristic
33C22⋊C4×H(3,𝔽3)C2211yescharacteristic
34C22⋊C4×H(3,𝔽3)C2211yescharacteristic
35#3757⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic
44#3752⋊C3C2211yescharacteristic
45C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
46C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
47#3750⋊C3C2211yescharacteristic
48#3750⋊C3C2211yescharacteristic
49#3750⋊C3C2211yescharacteristic
50#3750⋊C3C2211yescharacteristic
51#3750⋊C3C2211yescharacteristic
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
53C32×C22⋊Q8—21no—
54C32×C22⋊Q8D311yescharacteristic, complemented
55C32×C22⋊Q8C2×C311yescharacteristic, complemented
56#64156C2×C311yescharacteristic, complemented
57#64155C2×C311yescharacteristic, complemented
58#64139C2×C311yescharacteristic, complemented
59#64138C2×C311yescharacteristic, complemented
60#64106C2×C311yescharacteristic, complemented
61#64105C2×C311yescharacteristic, complemented
62#64104C2×C311yescharacteristic, complemented
63#64103C2×C311yescharacteristic, complemented
64#64103C2×C311yescharacteristic, complemented
65#64098C2×C311yescharacteristic, complemented
66#64094C2×C311yescharacteristic, complemented
67#64093C2×C311yescharacteristic, complemented
68#64093C2×C311yescharacteristic, complemented
69#64092C2×C311yescharacteristic, complemented
70C3×#947—31no—
71C3×#946—31no—
72C3×#930—31no—
73C3×#929—31no—
74C3×#897—31no—
75C3×#896—31no—
76C3×#895—31no—
77C3×#894—31no—
78C3×#894—31no—
79C3×#889—31no—
80C3×#885—31no—
81C3×#884—31no—
82C3×#884—31no—
83C3×#883—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88Q8×H(3,𝔽3)—41no—
89C2×C4×H(3,𝔽3)—41no—
90C2×C4×H(3,𝔽3)C2311yescharacteristic
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95C2×C4×H(3,𝔽3)C2311yescharacteristic
96#638⋊C3—41no—
97#638⋊C3—41no—
98#638⋊C3—41no—
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C4⋊((C3⋊D3)⋊C3)—41no—
105C4⋊((C3⋊D3)⋊C3)—41no—
106C4⋊((C3⋊D3)⋊C3)—41no—
107C4×(C3⋊D3)⋊C3—41no—
108C4×(C3⋊D3)⋊C3—41no—
109C4×(C3⋊D3)⋊C3—41no—
110#634⋊C3—41no—
111C3×#562—91no—
112#5647—31no—
113#5647—91no—
114C2×C32×Q8—21no—
115C2×C32×Q8C2×D311yescharacteristic
116C2×C32×Q8C22×C311yescharacteristic
117C22×C32×C4—21no—
118C22×C32×C4C2×D311yescharacteristic
119C22×C32×C4C22×C311yescharacteristic
120C2×#638C22×C311yescharacteristic
121C2×#638C22×C311yescharacteristic
122C2×#638C22×C311yescharacteristic
123C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
124C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
125C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
126C2×C4×C3⋊D3C22×C311yescharacteristic
127C2×C4×C3⋊D3C22×C311yescharacteristic
128C2×C4×C3⋊D3C22×C311yescharacteristic
129C2×#634C22×C311yescharacteristic
130C2×C3×#67—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×D12—31no—
134C2×C3×D12—31no—
135C2×C3×D12—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×Dic6—31no—
140C32×C4⋊C4—21no—
141C32×C4⋊C4—21no—
142C32×C4⋊C4—21no—
143C32×C4⋊C4C2×D311yescharacteristic
144C32×C4⋊C4C2×D311yescharacteristic
145C32×C4⋊C4C2×D311yescharacteristic
146C32×C4⋊C4C22×C311yescharacteristic
147C32×C4⋊C4C22×C311yescharacteristic
148C32×C4⋊C4C22×C311yescharacteristic
149C32×C22⋊C4—21no—
150C32×C22⋊C4—21no—
151C32×C22⋊C4C2×D311yescharacteristic
152C32×C22⋊C4C2×D311yescharacteristic
153C32×C22⋊C4C22×C311yescharacteristic
154C32×C22⋊C4C22×C311yescharacteristic
155#3757C22×C311yescharacteristic
156#3752C22×C311yescharacteristic
157#3752C22×C311yescharacteristic
158#3752C22×C311yescharacteristic
159#3752C22×C311yescharacteristic
160#3752C22×C311yescharacteristic
161#3752C22×C311yescharacteristic
162#3752C22×C311yescharacteristic
163#3752C22×C311yescharacteristic
164#3752C22×C311yescharacteristic
165C4⋊(C3⋊Dic3)C22×C311yescharacteristic
166C4⋊(C3⋊Dic3)C22×C311yescharacteristic
167#3750C22×C311yescharacteristic
168#3750C22×C311yescharacteristic
169#3750C22×C311yescharacteristic
170#3750C22×C311yescharacteristic
171#3750C22×C311yescharacteristic
172C4×C3⋊Dic3C22×C311yescharacteristic
173C3×#217—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×C4×Dic3—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)—21no—
194C22×H(3,𝔽3)C2411yescharacteristic
195C2×(C3⋊D3)⋊C3—21no—
196C2×(C3⋊D3)⋊C3—21no—
197C2×(C3⋊D3)⋊C3—21no—
198C2×(C3⋊D3)⋊C3—21no—
199C2×(C3⋊D3)⋊C3—21no—
200C2×(C3⋊D3)⋊C3—21no—
201C2×(C3⋊D3)⋊C3—21no—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3—21no—
204C4×H(3,𝔽3)—21no—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207C4×H(3,𝔽3)—21no—
208C4×H(3,𝔽3)—21no—
209C4×H(3,𝔽3)—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—
215C3×#125—91no—
216C3×#124—91no—
217C3×#124—91no—
218C3×#123—91no—
219C3×#123—91no—
220C3×#123—91no—
221C3×#123—91no—
222C3×C22⋊Q8—31no—
223C3×C22⋊Q8—31no—
224C3×C22⋊Q8—61no—
225C3×C22⋊Q8—91no—
226C3×C22⋊Q8—91no—
227C3×C22⋊Q8—91no—
228C3×C22⋊Q8C3×D311yescharacteristic
229C3×#121—91no—
230C3×#121—91no—
231C3×#121—91no—
232C3×#121—91no—
233#947—31no—
234#947—91no—
235#946—31no—
236#946—91no—
237#930—31no—
238#930—91no—
239#929—31no—
240#929—91no—
241#897—31no—
242#897—91no—
243#896—31no—
244#896—91no—
245#895—31no—
246#895—91no—
247#894—31no—
248#894—31no—
249#894—91no—
250#894—91no—
251#889—31no—
252#889—91no—
253#885—31no—
254#885—91no—
255#884—31no—
256#884—31no—
257#884—91no—
258#884—91no—
259#883—31no—
260#883—91no—
261C23×C32—21no—
262C23×C32C22×D311yescharacteristic
263C23×C32C23×C311yescharacteristic
264C22×C3⋊D3C23×C311yescharacteristic
265C22×C3⋊D3C23×C311yescharacteristic
266C22×C3⋊D3C23×C311yescharacteristic
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—31no—
270C32×Q8—41no—
271C32×Q8—41no—
272C32×Q8—42no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—41no—
280C2×C32×C4—41no—
281C2×C32×C4—42no—
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C23×C311yescharacteristic
289C2×C32×C4C23×C311yescharacteristic
290C2×C32×C4C23×C311yescharacteristic
291C2×C32×C4C23×C311yescharacteristic
292C2×C32×C4C23×C311yescharacteristic
293C2×C32×C4C23×C311yescharacteristic
294#638—41no—
295#638—41no—
296#638—41no—
297C2×C3⋊Dic3C23×C311yescharacteristic
298C2×C3⋊Dic3C23×C311yescharacteristic
299C2×C3⋊Dic3C23×C311yescharacteristic
300C2×C3⋊Dic3C23×C311yescharacteristic
301C2×C3⋊Dic3C23×C311yescharacteristic
302C4⋊(C3⋊D3)—41no—
303C4⋊(C3⋊D3)—41no—
304C4⋊(C3⋊D3)—41no—
305C4×C3⋊D3—41no—
306C4×C3⋊D3—41no—
307C4×C3⋊D3—41no—
308#634—41no—
309C3×#67—121no—
310C3×#67—121no—
311C3×#67—121no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—31no—
317C3×D12—121no—
318C3×D12—121no—
319C3×D12—121no—
320C3×C4×D3—121no—
321C3×C4×D3—121no—
322C3×C4×D3—121no—
323C3×Dic6—121no—
324#562—91noSylow
325C2×H(3,𝔽3)—41no—
326C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
327C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
328C2×H(3,𝔽3)2−1+411yescharacteristic
329(C3⋊D3)⋊C3—41no—
330(C3⋊D3)⋊C3—41no—
331(C3⋊D3)⋊C3—41no—
332C2×C3×Q8—31no—
333C2×C3×Q8—31no—
334C2×C3×Q8—61no—
335C2×C3×Q8—91no—
336C2×C3×Q8C2×C3×D311yescharacteristic
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C2×C3×D4—91no—
340C2×C3×D4—91no—
341C2×C3×D4—91no—
342C2×C3×D4—91no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—91no—
347C22×C3×C4—91no—
348C22×C3×C4—91no—
349C22×C3×C4C2×C3×D311yescharacteristic
350C2×#67—31no—
351C2×#67—31no—
352C2×#67—31no—
353C2×#67—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—91no—
360C2×D12—91no—
361C2×D12—91no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—91no—
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×Dic6—31no—
369C2×Dic6—91no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4—61no—
378C3×C4⋊C4—61no—
379C3×C4⋊C4—91no—
380C3×C4⋊C4—91no—
381C3×C4⋊C4—91no—
382C3×C4⋊C4—91no—
383C3×C4⋊C4—91no—
384C3×C4⋊C4—91no—
385C3×C4⋊C4—91no—
386C3×C4⋊C4C2×C3×D311yescharacteristic
387C3×C4⋊C4C2×C3×D311yescharacteristic
388C3×C4⋊C4C2×C3×D311yescharacteristic
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4—91no—
400C3×C22⋊C4—91no—
401C3×C22⋊C4—91no—
402C3×C22⋊C4—91no—
403C3×C22⋊C4—91no—
404C3×C22⋊C4—91no—
405C3×C22⋊C4C2×C3×D311yescharacteristic
406C3×C22⋊C4C2×C3×D311yescharacteristic
407C3×C42—91no—
408#217—31no—
409#217—91no—
410(C2×D3)⋊C4—31no—
411(C2×D3)⋊C4—31no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—91no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428C4⋊Dic3—31no—
429C4⋊Dic3—31no—
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—91no—
444C22×C32—22no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C23×D311yescharacteristic
455C22×C32C24×C311yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3×D3—61no—
466C2×C3×D3—61no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C32×C4—22no—
475C32×C4—21no—
476C32×C4—21no—
477C32×C4—21no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—21no—
483C32×C4—21no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4—21no—
487C32×C4—41no—
488C32×C4—41no—
489C32×C4—41no—
490C32×C4—41no—
491C32×C4—41no—
492C3⋊Dic3—21no—
493C3⋊Dic3—21no—
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3×Dic3—61no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502#125—91no—
503#124—91no—
504#124—91no—
505#123—91no—
506#123—91no—
507#123—91no—
508#123—91no—
509C22⋊Q8—91no—
510C22⋊Q8—91no—
511C22⋊Q8—91no—
512C22⋊Q8(C3⋊D3)⋊C311yescharacteristic, complemented
513#121—91no—
514#121—91no—
515#121—91no—
516#121—91no—
517H(3,𝔽3)#56211yescharacteristic, complemented, Sylow
518C23×C3—31no—
519C23×C3—31no—
520C23×C3—61no—
521C23×C3—91no—
522C23×C3—91no—
523C23×C3—91no—
524C23×C3C22×C3×D311yescharacteristic
525C22×D3—31no—
526C22×D3—31no—
527C22×D3—31no—
528C22×D3—91no—
529C22×D3—91no—
530C22×D3—91no—
531C3×Q8—41no—
532C3×Q8—121no—
533C3×Q8—121no—
534C3×Q8—122no—
535C3×Q8—361no—
536C3×D4—361no—
537C3×D4—361no—
538C3×D4—361no—
539C3×D4—361no—
540C3×D4—361no—
541C3×D4—361no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—41no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—91no—
562C2×C3×C4—91no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—91no—
566C2×C3×C4—121no—
567C2×C3×C4—121no—
568C2×C3×C4—122no—
569C2×C3×C4—361no—
570C2×C3×C4—361no—
571C2×C3×C4—361no—
572C2×C3×C4C22×C3×D311yescharacteristic
573C2×C3×C4C22×C3×D311yescharacteristic
574C2×C3×C4C22×C3×D311yescharacteristic
575C2×C3×C4C22×C3×D311yescharacteristic
576C2×C3×C4C22×C3×D311yescharacteristic
577C2×C3×C4C22×C3×D311yescharacteristic
578#67—121no—
579#67—121no—
580#67—121no—
581#67—361no—
582#67—361no—
583#67—361no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594D12—121no—
595D12—121no—
596D12—121no—
597D12—361no—
598D12—361no—
599D12—361no—
600C4×D3—121no—
601C4×D3—121no—
602C4×D3—121no—
603C4×D3—361no—
604C4×D3—361no—
605C4×D3—361no—
606Dic6—121no—
607Dic6—361no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—42no—
612C2×C32—41no—
613C2×C32—41no—
614C2×C32#100411yescharacteristic
615C2×C32#100711yescharacteristic
616C2×C32#100911yescharacteristic
617C2×C32C3×H(5,𝔽2)11yescharacteristic
618C2×C32C3×H(5,𝔽2)11yescharacteristic
619C2×C32C3×2−1+411yescharacteristic
620C3⋊D3—41no—
621C3⋊D3—41no—
622C3⋊D3—41no—
623C3×D3—121no—
624C3×D3—121no—
625C3×D3—121no—
626C2×Q8—91no—
627C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic
628C2×D4—91no—
629C2×D4—91no—
630C2×D4—91no—
631C2×D4—91no—
632C2×D4—91no—
633C2×D4—91no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4—91no—
637C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—91no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—91no—
645C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
646C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
647C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
648C22⋊C4—91no—
649C22⋊C4—91no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—91no—
656C22⋊C4—91no—
657C22⋊C4—91no—
658C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
659C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
660C42—91no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—31no—
665C22×C3—31no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—62no—
673C22×C3—61no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—181no—
677C22×C3—181no—
678C22×C3—181no—
679C22×C3—181no—
680C22×C3—181no—
681C22×C3—181no—
682C22×C3—181no—
683C22×C3—181no—
684C22×C3—181no—
685C22×C3C23×C3×D311yescharacteristic
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—181no—
700C2×D3—181no—
701C2×D3—181no—
702C2×D3—181no—
703C2×D3—181no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—62no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—181no—
729C3×C4—181no—
730C3×C4—181no—
731C3×C4—181no—
732C3×C4—181no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—181no—
739Dic3—181no—
740Dic3—181no—
741Dic3—181no—
742Dic3—181no—
743C32—21no—
744C32#564711yescharacteristic, complemented
745C32C3×#56211yescharacteristic, complemented
746C23—91no—
747C23—91no—
748C23—91no—
749C23C22×(C3⋊D3)⋊C311yescharacteristic
750Q8—41no—
751Q8—361no—
752D4—361no—
753D4—361no—
754D4—361no—
755D4—361no—
756D4—361no—
757D4—361no—
758C2×C4—41no—
759C2×C4—91no—
760C2×C4—91no—
761C2×C4—91no—
762C2×C4—91no—
763C2×C4—91no—
764C2×C4—361no—
765C2×C4—361no—
766C2×C4—361no—
767C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
768C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
769C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
770C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
771C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
772C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
773C2×C3—31no—
774C2×C3—31no—
775C2×C3—31no—
776C2×C3—31no—
777C2×C3—31no—
778C2×C3—31no—
779C2×C3—41no—
780C2×C3—61no—
781C2×C3—61no—
782C2×C3—61no—
783C2×C3—121no—
784C2×C3—121no—
785C2×C3—122no—
786C2×C3—361no—
787C2×C3—361no—
788C2×C3—361no—
789C2×C3C3×#100411yescharacteristic
790C2×C3C3×#100711yescharacteristic
791C2×C3C3×#100911yescharacteristic
792D3—121no—
793D3—121no—
794D3—121no—
795D3—361no—
796D3—361no—
797D3—361no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—181no—
802C22—181no—
803C22—181no—
804C22—181no—
805C22—181no—
806C22—181no—
807C22—181no—
808C22—181no—
809C22—181no—
810C22C23×(C3⋊D3)⋊C311yescharacteristic
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—181no—
818C4—181no—
819C4—181no—
820C4—181no—
821C4—181no—
822C3—31no—
823C3—31no—
824C3—61no—
825C3C3×#564711yescharacteristic
826C2—41no—
827C2—361no—
828C2—361no—
829C2—361no—
830C2#64361⋊C311yescharacteristic
831C2#1172262711yescharacteristic
832C2#1172263811yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×C22⋊Q8C2
hypercenterC22⋊Q8(C3⋊D3)⋊C3
hypocenterC32C3×#562
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. #64156⋊C3C2semidirect
3. #64155⋊C3C2semidirect
4. #64139⋊C3C2semidirect
5. #64138⋊C3C2semidirect
6. #64106⋊C3C2semidirect
7. #64105⋊C3C2semidirect
8. #64104⋊C3C2semidirect
9. #64103⋊C3C2semidirect
10. #64103⋊C3C2semidirect
11. #64098⋊C3C2semidirect
12. #64094⋊C3C2semidirect
13. #64093⋊C3C2semidirect
14. #64093⋊C3C2semidirect
15. #64092⋊C3C2semidirect
16. #10596118C3semidirect
54. C32×C22⋊Q8D3semidirect
55. C32×C22⋊Q8C2×C3semidirect
56. #64156C2×C3semidirect
57. #64155C2×C3semidirect
58. #64139C2×C3semidirect
59. #64138C2×C3semidirect
60. #64106C2×C3semidirect
61. #64105C2×C3semidirect
62. #64104C2×C3semidirect
63. #64103C2×C3semidirect
64. #64103C2×C3semidirect
65. #64098C2×C3semidirect
66. #64094C2×C3semidirect
67. #64093C2×C3semidirect
68. #64093C2×C3semidirect
69. #64092C2×C3semidirect
512. C22⋊Q8(C3⋊D3)⋊C3semidirect
517. H(3,𝔽3)#562semidirect
744. C32#5647semidirect
745. C32C3×#562semidirect

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
#64156⋊C32
#64155⋊C32
#64139⋊C32
#64138⋊C32
#64106⋊C32
#64105⋊C32
#64104⋊C32
#64103⋊C32
#64098⋊C32
#64094⋊C32
#64093⋊C32
#64092⋊C32
#105961183
C3×#56473