Finite Group Databasebeta

← #10596107⋊C3 #13152958

Subgroups — #10596107⋊C3 #13152958

Order 1728.

872 conjugacy classes of subgroups.

The subgroup lattice has 778 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
4C4×#638⋊C3C211yesmaximal, characteristic
5C2×#3750⋊C3C211yesmaximal, characteristic, complemented
6#64105⋊C3C211yesmaximal, characteristic, complemented
7#64105⋊C3C211yesmaximal, characteristic, complemented
8C4⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
9#64098⋊C3C211yesmaximal, characteristic, complemented
10#64098⋊C3C211yesmaximal, characteristic, complemented
11#64096⋊C3C211yesmaximal, characteristic, complemented
12#64090⋊C3C211yesmaximal, characteristic
13#64090⋊C3C211yesmaximal, characteristic
14#64087⋊C3C211yesmaximal, characteristic, complemented
15#64087⋊C3C211yesmaximal, characteristic, complemented
16#10596107C311yesmaximal, characteristic, complemented
17C3×#5636—31nomaximal
18C2×Q8×H(3,𝔽3)C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×#634⋊C3C2211yescharacteristic
27C2×#634⋊C3C2211yescharacteristic
28C4⋊C4×H(3,𝔽3)C2211yescharacteristic
29C4⋊C4×H(3,𝔽3)C2211yescharacteristic
30C4⋊C4×H(3,𝔽3)C2211yescharacteristic
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic
32C22⋊C4×H(3,𝔽3)C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
38C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
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
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
58C4×#638C2×C311yescharacteristic
59C2×#3750C2×C311yescharacteristic, complemented
60#64105C2×C311yescharacteristic, complemented
61#64105C2×C311yescharacteristic, complemented
62C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
63#64098C2×C311yescharacteristic, complemented
64#64098C2×C311yescharacteristic, complemented
65#64096C2×C311yescharacteristic, complemented
66#64090C2×C311yescharacteristic
67#64090C2×C311yescharacteristic
68#64087C2×C311yescharacteristic, complemented
69#64087C2×C311yescharacteristic, complemented
70C3×#946—31no—
71C3×#944—31no—
72C3×C4×#67—31no—
73C2×C3×Dic3⋊C4—31no—
74C3×#896—31no—
75C3×#896—31no—
76C3×D3×C4⋊C4—31no—
77C3×#889—31no—
78C3×#889—31no—
79C3×#887—31no—
80C3×#67⋊C4—31no—
81C3×#67⋊C4—31no—
82C3×#878—31no—
83C3×#878—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⋊C3Q814yescomplemented
95C2×(C3⋊Dic3)⋊C3—22no—
96C2×(C3⋊Dic3)⋊C3—41no—
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C4×(C3⋊D3)⋊C3—22no—
105C4×(C3⋊D3)⋊C3—41no—
106C4×(C3⋊D3)⋊C3—41no—
107#634⋊C3—22no—
108#634⋊C3—41no—
109C3×#554—91no—
110#5636—31no—
111#5636—91no—
112C2×C32×Q8—21no—
113C2×C32×Q8C2×D311yescharacteristic
114C2×C32×Q8C22×C311yescharacteristic
115C22×C32×C4—21no—
116C22×C32×C4C2×D311yescharacteristic
117C22×C32×C4C22×C311yescharacteristic
118C2×#638C22×C311yescharacteristic
119C22×C3⋊Dic3C22×C311yescharacteristic
120C22×C3⋊Dic3C22×C311yescharacteristic
121C2×C4×C3⋊D3C22×C311yescharacteristic
122C2×C4×C3⋊D3C22×C311yescharacteristic
123C2×C4×C3⋊D3C22×C311yescharacteristic
124C2×#634C22×C311yescharacteristic
125C2×#634C22×C311yescharacteristic
126C2×C3×#67—31no—
127C22×C3×Dic3—31no—
128C22×C3×Dic3—31no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×Dic6—31no—
133C2×C3×Dic6—31no—
134C32×C4⋊C4—21no—
135C32×C4⋊C4—21no—
136C32×C4⋊C4—21no—
137C32×C4⋊C4C2×D311yescharacteristic
138C32×C4⋊C4C2×D311yescharacteristic
139C32×C4⋊C4C2×D311yescharacteristic
140C32×C4⋊C4C22×C311yescharacteristic
141C32×C4⋊C4C22×C311yescharacteristic
142C32×C4⋊C4C22×C311yescharacteristic
143C32×C22⋊C4—21no—
144C32×C22⋊C4—21no—
145C32×C22⋊C4C2×D311yescharacteristic
146C32×C22⋊C4C2×D311yescharacteristic
147C32×C22⋊C4C22×C311yescharacteristic
148C32×C22⋊C4C22×C311yescharacteristic
149#3757C22×C311yescharacteristic
150#3752C22×C311yescharacteristic
151#3752C22×C311yescharacteristic
152#3752C22×C311yescharacteristic
153C4⋊(C3⋊Dic3)C22×C311yescharacteristic
154C4⋊(C3⋊Dic3)C22×C311yescharacteristic
155#3750C22×C311yescharacteristic
156#3750C22×C311yescharacteristic
157#3750C22×C311yescharacteristic
158#3750C22×C311yescharacteristic
159#3750C22×C311yescharacteristic
160#3750C22×C311yescharacteristic
161#3750C22×C311yescharacteristic
162#3750C22×C311yescharacteristic
163#3750C22×C311yescharacteristic
164#3750C22×C311yescharacteristic
165#3750C22×C311yescharacteristic
166C4×C3⋊Dic3C22×C311yescharacteristic
167C4×C3⋊Dic3C22×C311yescharacteristic
168C4×C3⋊Dic3C22×C311yescharacteristic
169C3×#217—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—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×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×C4×Dic3—31no—
187C3×C4×Dic3—31no—
188C3×C4×Dic3—31no—
189C22×H(3,𝔽3)—21no—
190C22×H(3,𝔽3)—21no—
191C22×H(3,𝔽3)C2×Q812yes—
192C22×H(3,𝔽3)C2411yescharacteristic
193C2×(C3⋊D3)⋊C3—21no—
194C2×(C3⋊D3)⋊C3—21no—
195C2×(C3⋊D3)⋊C3C2×Q812yes—
196C4×H(3,𝔽3)—21no—
197C4×H(3,𝔽3)—21no—
198C4×H(3,𝔽3)—21no—
199C4×H(3,𝔽3)—21no—
200C4×H(3,𝔽3)—21no—
201C4×H(3,𝔽3)—21no—
202(C3⋊Dic3)⋊C3—21no—
203(C3⋊Dic3)⋊C3—21no—
204(C3⋊Dic3)⋊C3—21no—
205(C3⋊Dic3)⋊C3—21no—
206(C3⋊Dic3)⋊C3—21no—
207(C3⋊Dic3)⋊C3C2×Q812yes—
208(C3⋊Dic3)⋊C3#4112yes—
209C3×C4⋊Q8—91no—
210C3×#125—91no—
211C3×#125—91no—
212C3×C22⋊Q8—31no—
213C3×C22⋊Q8—31no—
214C3×C22⋊Q8—61no—
215C3×C22⋊Q8—91no—
216C3×C22⋊Q8—91no—
217C3×C22⋊Q8—91no—
218C3×C22⋊Q8—91no—
219C3×C22⋊Q8—91no—
220C3×C22⋊Q8C3×D311yescharacteristic
221C3×C4×Q8—91no—
222C3×C4×D4—91no—
223C3×C4×D4—91no—
224C3×C4×D4—91no—
225C2×C3×C4⋊C4—91no—
226C2×C3×C4⋊C4—91no—
227#946—31no—
228#946—91no—
229#944—31no—
230#944—91no—
231C4×#67—31no—
232C4×#67—91no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—91no—
235#896—31no—
236#896—31no—
237#896—91no—
238#896—91no—
239D3×C4⋊C4—31no—
240D3×C4⋊C4—91no—
241#889—31no—
242#889—31no—
243#889—91no—
244#889—91no—
245#887—31no—
246#887—91no—
247#67⋊C4—31no—
248#67⋊C4—31no—
249#67⋊C4—91no—
250#67⋊C4—91no—
251#878—31no—
252#878—31no—
253#878—91no—
254#878—91no—
255C23×C32—21no—
256C23×C32C22×D311yescharacteristic
257C23×C32C23×C311yescharacteristic
258C22×C3⋊D3C23×C311yescharacteristic
259C22×C3×D3—31no—
260C32×Q8—41no—
261C32×Q8—41no—
262C32×Q8—42no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—41no—
270C2×C32×C4—41no—
271C2×C32×C4—42no—
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C23×C311yescharacteristic
279C2×C32×C4C23×C311yescharacteristic
280C2×C32×C4C23×C311yescharacteristic
281C2×C32×C4C23×C311yescharacteristic
282C2×C32×C4C23×C311yescharacteristic
283C2×C32×C4C23×C311yescharacteristic
284#638C3×Q814yescomplemented
285C2×C3⋊Dic3—22no—
286C2×C3⋊Dic3—41no—
287C2×C3⋊Dic3C23×C311yescharacteristic
288C2×C3⋊Dic3C23×C311yescharacteristic
289C2×C3⋊Dic3C23×C311yescharacteristic
290C2×C3⋊Dic3C23×C311yescharacteristic
291C2×C3⋊Dic3C23×C311yescharacteristic
292C2×C3⋊Dic3C23×C311yescharacteristic
293C2×C3⋊Dic3C23×C311yescharacteristic
294C4×C3⋊D3—22no—
295C4×C3⋊D3—41no—
296C4×C3⋊D3—41no—
297#634—22no—
298#634—41no—
299C3×#67—34no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—62no—
308C2×C3×Dic3—121no—
309C3×C4×D3—62no—
310C3×C4×D3—121no—
311C3×C4×D3—121no—
312C3×Dic6—62no—
313C3×Dic6—121no—
314#554—91noSylow
315C2×H(3,𝔽3)—22no—
316C2×H(3,𝔽3)C22×Q811yescharacteristic
317C2×H(3,𝔽3)C2×#4111yescharacteristic
318C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
319(C3⋊D3)⋊C3—22no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—61no—
323C2×C3×Q8—91no—
324C2×C3×Q8—91no—
325C2×C3×Q8C2×C3×D311yescharacteristic
326C2×C3×D4—91no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—91no—
331C22×C3×C4—91no—
332C22×C3×C4—91no—
333C22×C3×C4—91no—
334C22×C3×C4—91no—
335C22×C3×C4C2×C3×D311yescharacteristic
336C2×#67—31no—
337C2×#67—91no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—91no—
341C22×Dic3—91no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—91no—
346C2×C4×D3—91no—
347C2×C4×D3—91no—
348C2×Dic6—31no—
349C2×Dic6—31no—
350C2×Dic6—91no—
351C2×Dic6—91no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—91no—
362C3×C4⋊C4—91no—
363C3×C4⋊C4—91no—
364C3×C4⋊C4—91no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C4⋊C4—91no—
368C3×C4⋊C4—91no—
369C3×C4⋊C4—91no—
370C3×C4⋊C4—91no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—91no—
373C3×C4⋊C4—91no—
374C3×C4⋊C4C2×C3×D311yescharacteristic
375C3×C4⋊C4C2×C3×D311yescharacteristic
376C3×C4⋊C4C2×C3×D311yescharacteristic
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C22⋊C4—91no—
386C3×C22⋊C4—91no—
387C3×C22⋊C4C2×C3×D311yescharacteristic
388C3×C22⋊C4C2×C3×D311yescharacteristic
389C3×C42—91no—
390C3×C42—91no—
391C3×C42—91no—
392#217—31no—
393#217—91no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—91no—
403C4⋊Dic3—91no—
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—31no—
410Dic3⋊C4—31no—
411Dic3⋊C4—31no—
412Dic3⋊C4—31no—
413Dic3⋊C4—31no—
414Dic3⋊C4—31no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426C4×Dic3—31no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—91no—
430C4×Dic3—91no—
431C4×Dic3—91no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—22no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32D3×Q812yes—
441C22×C32C2×C3×Q812yes—
442C22×C32C23×D311yescharacteristic
443C22×C32C24×C311yescharacteristic
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3C2×C3×Q812yes—
447C2×C3×D3—32no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C32×C4—22no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4—21no—
454C32×C4—21no—
455C32×C4—21no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4—21no—
459C32×C4—21no—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—41no—
464C32×C4—41no—
465C32×C4—41no—
466C32×C4—41no—
467C32×C4—41no—
468C3⋊Dic3—21no—
469C3⋊Dic3—21no—
470C3⋊Dic3—21no—
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3C2×C3×Q812yes—
474C3⋊Dic3C3×#4112yes—
475C3×Dic3—32no—
476C3×Dic3—32no—
477C3×Dic3—61no—
478C3×Dic3—61no—
479C3×Dic3—61no—
480C3×Dic3—61no—
481C3×Dic3—61no—
482C4⋊Q8—91no—
483#125—91no—
484#125—91no—
485C22⋊Q8—91no—
486C22⋊Q8—91no—
487C22⋊Q8—91no—
488C22⋊Q8—91no—
489C22⋊Q8—91no—
490C22⋊Q8(C3⋊D3)⋊C311yescharacteristic, complemented
491C4×Q8—91no—
492C4×D4—91no—
493C4×D4—91no—
494C4×D4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497H(3,𝔽3)#55411yescharacteristic, complemented, Sylow
498C23×C3—31no—
499C23×C3—31no—
500C23×C3—61no—
501C23×C3—91no—
502C23×C3C22×C3×D311yescharacteristic
503C22×D3—31no—
504C22×D3—91no—
505C3×Q8—41no—
506C3×Q8—121no—
507C3×Q8—121no—
508C3×Q8—122no—
509C3×Q8—182no—
510C3×Q8—361no—
511C3×D4—94no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—41no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—91no—
532C2×C3×C4—91no—
533C2×C3×C4—91no—
534C2×C3×C4—91no—
535C2×C3×C4—91no—
536C2×C3×C4—91no—
537C2×C3×C4—91no—
538C2×C3×C4—121no—
539C2×C3×C4—121no—
540C2×C3×C4—122no—
541C2×C3×C4—182no—
542C2×C3×C4—182no—
543C2×C3×C4—361no—
544C2×C3×C4—361no—
545C2×C3×C4—361no—
546C2×C3×C4C22×C3×D311yescharacteristic
547C2×C3×C4C22×C3×D311yescharacteristic
548C2×C3×C4C22×C3×D311yescharacteristic
549C2×C3×C4C22×C3×D311yescharacteristic
550C2×C3×C4C22×C3×D311yescharacteristic
551C2×C3×C4C22×C3×D311yescharacteristic
552#67—34no—
553#67—94no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—62no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—121no—
570C2×Dic3—182no—
571C2×Dic3—361no—
572C4×D3—62no—
573C4×D3—121no—
574C4×D3—121no—
575C4×D3—182no—
576C4×D3—361no—
577C4×D3—361no—
578Dic6—62no—
579Dic6—121no—
580Dic6—182no—
581Dic6—361no—
582C2×C32—22no—
583C2×C32—22no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—42no—
588C2×C32#100411yescharacteristic
589C2×C32C2×D3×Q811yescharacteristic
590C2×C32D3×#4111yescharacteristic
591C2×C32C22×C3×Q811yescharacteristic
592C2×C32C2×C3×#4111yescharacteristic
593C2×C32C3×H(5,𝔽2)11yescharacteristic
594C3⋊D3—22no—
595C3×D3—62no—
596C2×Q8—91no—
597C2×Q8—91no—
598C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic
599C2×D4—91no—
600C22×C4—91no—
601C22×C4—91no—
602C22×C4—91no—
603C22×C4—91no—
604C22×C4—91no—
605C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
620C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
621C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
627C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
628C42—91no—
629C42—91no—
630C42—91no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—31no—
634C22×C3—31no—
635C22×C3—32no—
636C22×C3—32no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—62no—
643C22×C3—92no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—181no—
647C22×C3—181no—
648C22×C3C3×D3×Q812yes—
649C22×C3C23×C3×D311yescharacteristic
650C2×D3—32no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—92no—
654C2×D3—181no—
655C2×D3—181no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—62no—
675C3×C4—92no—
676C3×C4—92no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—181no—
683C3×C4—181no—
684C3×C4—181no—
685C3×C4—181no—
686C3×C4—181no—
687Dic3—32no—
688Dic3—32no—
689Dic3—61no—
690Dic3—61no—
691Dic3—61no—
692Dic3—61no—
693Dic3—61no—
694Dic3—92no—
695Dic3—92no—
696Dic3—181no—
697Dic3—181no—
698Dic3—181no—
699Dic3—181no—
700Dic3—181no—
701C32—21no—
702C32#563611yescharacteristic, complemented
703C32C3×#55411yescharacteristic, complemented
704C23—91no—
705C23C22×(C3⋊D3)⋊C311yescharacteristic
706Q8—41no—
707Q8—182no—
708Q8—361no—
709D4—94no—
710C2×C4—41no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—182no—
719C2×C4—182no—
720C2×C4—361no—
721C2×C4—361no—
722C2×C4—361no—
723C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
724C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
725C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
726C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
727C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
728C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
729C2×C3—22no—
730C2×C3—31no—
731C2×C3—31no—
732C2×C3—31no—
733C2×C3—31no—
734C2×C3—31no—
735C2×C3—31no—
736C2×C3—62no—
737C2×C3—62no—
738C2×C3—61no—
739C2×C3—61no—
740C2×C3—61no—
741C2×C3—122no—
742C2×C3—182no—
743C2×C3C3×#100411yescharacteristic
744C2×C3C2×C3×D3×Q811yescharacteristic
745C2×C3C3×D3×#4111yescharacteristic
746D3—62no—
747D3—182no—
748C22—21no—
749C22—21no—
750C22—92no—
751C22—181no—
752C22—181no—
753C22Q8×(C3⋊D3)⋊C312yes—
754C22C23×(C3⋊D3)⋊C311yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—92no—
762C4—92no—
763C4—181no—
764C4—181no—
765C4—181no—
766C4—181no—
767C4—181no—
768C3—31no—
769C3—31no—
770C3—61no—
771C3C3×#563611yescharacteristic
772C2—22no—
773C2—182no—
774C2#64361⋊C311yescharacteristic
775C2C2×Q8×(C3⋊D3)⋊C311yescharacteristic
776C2#41×(C3⋊D3)⋊C311yescharacteristic
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×#554
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. C2×#3750⋊C3C2semidirect
6. #64105⋊C3C2semidirect
7. #64105⋊C3C2semidirect
8. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
9. #64098⋊C3C2semidirect
10. #64098⋊C3C2semidirect
11. #64096⋊C3C2semidirect
14. #64087⋊C3C2semidirect
15. #64087⋊C3C2semidirect
16. #10596107C3semidirect
54. C32×C22⋊Q8D3semidirect
55. C32×C22⋊Q8C2×C3semidirect
56. #64155C2×C3semidirect
57. #64153C2×C3semidirect
59. C2×#3750C2×C3semidirect
60. #64105C2×C3semidirect
61. #64105C2×C3semidirect
62. C4⋊C4×C3⋊D3C2×C3semidirect
63. #64098C2×C3semidirect
64. #64098C2×C3semidirect
65. #64096C2×C3semidirect
68. #64087C2×C3semidirect
69. #64087C2×C3semidirect
94. #638⋊C3Q8semidirect
284. #638C3×Q8semidirect
490. C22⋊Q8(C3⋊D3)⋊C3semidirect
497. H(3,𝔽3)#554semidirect
702. C32#5636semidirect
703. C32C3×#554semidirect

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
C4×#638⋊C32
C2×#3750⋊C32
#64105⋊C32
C4⋊C4×(C3⋊D3)⋊C32
#64098⋊C32
#64096⋊C32
#64090⋊C32
#64087⋊C32
#105961073
C3×#56363