Finite Group Databasebeta

← #10596109⋊C3 #13152961

Subgroups — #10596109⋊C3 #13152961

Order 1728.

837 conjugacy classes of subgroups.

The subgroup lattice has 792 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#64155⋊C3C211yesmaximal, characteristic, complemented
4#64138⋊C3C211yesmaximal, characteristic, complemented
5C4×#638⋊C3C211yesmaximal, characteristic, complemented
6#64107⋊C3C211yesmaximal, characteristic, complemented
7#64103⋊C3C211yesmaximal, characteristic, complemented
8#64102⋊C3C211yesmaximal, characteristic, complemented
9C4⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
10#64098⋊C3C211yesmaximal, characteristic, complemented
11#64098⋊C3C211yesmaximal, characteristic, complemented
12#64093⋊C3C211yesmaximal, characteristic
13#64092⋊C3C211yesmaximal, characteristic, complemented
14#64092⋊C3C211yesmaximal, characteristic, complemented
15#64088⋊C3C211yesmaximal, characteristic, complemented
16#10596109C311yesmaximal, characteristic, complemented
17C3×#5638—31nomaximal
18C2×Q8×H(3,𝔽3)C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
27C4⋊C4×H(3,𝔽3)C2211yescharacteristic
28C4⋊C4×H(3,𝔽3)C2211yescharacteristic
29C4⋊C4×H(3,𝔽3)C2211yescharacteristic
30C22⋊C4×H(3,𝔽3)C2211yescharacteristic
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic
32#3757⋊C3C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
41C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
42C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
43#3750⋊C3C2211yescharacteristic
44#3750⋊C3C2211yescharacteristic
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×C22⋊Q8—21no—
54C32×C22⋊Q8D311yescharacteristic, complemented
55C32×C22⋊Q8C2×C311yescharacteristic, complemented
56#64155C2×C311yescharacteristic, complemented
57#64155C2×C311yescharacteristic, complemented
58#64138C2×C311yescharacteristic, complemented
59C4×#638C2×C311yescharacteristic, complemented
60#64107C2×C311yescharacteristic, complemented
61#64103C2×C311yescharacteristic, complemented
62#64102C2×C311yescharacteristic, complemented
63C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
64#64098C2×C311yescharacteristic, complemented
65#64098C2×C311yescharacteristic, complemented
66#64093C2×C311yescharacteristic
67#64092C2×C311yescharacteristic, complemented
68#64092C2×C311yescharacteristic, complemented
69#64088C2×C311yescharacteristic, complemented
70C3×#946—31no—
71C3×#946—31no—
72C3×#929—31no—
73C3×C4×#67—31no—
74C3×#898—31no—
75C3×#894—31no—
76C3×#893—31no—
77C3×D3×C4⋊C4—31no—
78C3×#889—31no—
79C3×#889—31no—
80C3×#884—31no—
81C3×#883—31no—
82C3×#883—31no—
83C3×#879—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87Q8×H(3,𝔽3)—41no—
88C2×C4×H(3,𝔽3)—41no—
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
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95#638⋊C3—22no—
96#638⋊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
103C4⋊((C3⋊D3)⋊C3)—22no—
104C4×(C3⋊D3)⋊C3—22no—
105C4×(C3⋊D3)⋊C3—41no—
106C4×(C3⋊D3)⋊C3—41no—
107C4×(C3⋊D3)⋊C3—41no—
108C3×#539—91no—
109#5638—31no—
110#5638—91no—
111C2×C32×Q8—21no—
112C2×C32×Q8C2×D311yescharacteristic
113C2×C32×Q8C22×C311yescharacteristic
114C22×C32×C4—21no—
115C22×C32×C4C2×D311yescharacteristic
116C22×C32×C4C22×C311yescharacteristic
117C2×#638C22×C311yescharacteristic
118C2×#638C22×C311yescharacteristic
119C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
120C2×C4×C3⋊D3C22×C311yescharacteristic
121C2×C4×C3⋊D3C22×C311yescharacteristic
122C2×C4×C3⋊D3C22×C311yescharacteristic
123C2×C4×C3⋊D3C22×C311yescharacteristic
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×D12—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—31no—
131C32×C4⋊C4—21no—
132C32×C4⋊C4—21no—
133C32×C4⋊C4—21no—
134C32×C4⋊C4C2×D311yescharacteristic
135C32×C4⋊C4C2×D311yescharacteristic
136C32×C4⋊C4C2×D311yescharacteristic
137C32×C4⋊C4C22×C311yescharacteristic
138C32×C4⋊C4C22×C311yescharacteristic
139C32×C4⋊C4C22×C311yescharacteristic
140C32×C22⋊C4—21no—
141C32×C22⋊C4—21no—
142C32×C22⋊C4C2×D311yescharacteristic
143C32×C22⋊C4C2×D311yescharacteristic
144C32×C22⋊C4C22×C311yescharacteristic
145C32×C22⋊C4C22×C311yescharacteristic
146#3757C22×C311yescharacteristic
147#3757C22×C311yescharacteristic
148#3752C22×C311yescharacteristic
149#3752C22×C311yescharacteristic
150#3752C22×C311yescharacteristic
151#3752C22×C311yescharacteristic
152#3752C22×C311yescharacteristic
153#3752C22×C311yescharacteristic
154C4⋊(C3⋊Dic3)C22×C311yescharacteristic
155C4⋊(C3⋊Dic3)C22×C311yescharacteristic
156C4⋊(C3⋊Dic3)C22×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
165C4×C3⋊Dic3C22×C311yescharacteristic
166C4×C3⋊Dic3C22×C311yescharacteristic
167C3×#217—31no—
168C3×#217—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—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—
188C22×H(3,𝔽3)—21no—
189C22×H(3,𝔽3)—21no—
190C22×H(3,𝔽3)—21no—
191C22×H(3,𝔽3)C2411yescharacteristic
192C2×(C3⋊D3)⋊C3—21no—
193C2×(C3⋊D3)⋊C3—21no—
194C2×(C3⋊D3)⋊C3—21no—
195C2×(C3⋊D3)⋊C3—21no—
196C2×(C3⋊D3)⋊C3—21no—
197C2×(C3⋊D3)⋊C3#4112yes—
198C4×H(3,𝔽3)—21no—
199C4×H(3,𝔽3)—21no—
200C4×H(3,𝔽3)—21no—
201C4×H(3,𝔽3)—21no—
202C4×H(3,𝔽3)—21no—
203C4×H(3,𝔽3)—21no—
204(C3⋊Dic3)⋊C3—21no—
205(C3⋊Dic3)⋊C3—21no—
206(C3⋊Dic3)⋊C3—21no—
207(C3⋊Dic3)⋊C3—21no—
208(C3⋊Dic3)⋊C3—21no—
209(C3⋊Dic3)⋊C3—21no—
210C3×#126—91no—
211C3×#126—91no—
212C3×#125—91no—
213C3×#125—91no—
214C3×#123—91no—
215C3×#123—91no—
216C3×#123—91no—
217C3×#123—91no—
218C3×C22⋊Q8—31no—
219C3×C22⋊Q8—31no—
220C3×C22⋊Q8—61no—
221C3×C22⋊Q8—91no—
222C3×C22⋊Q8—91no—
223C3×C22⋊Q8C3×D311yescharacteristic
224C3×#121—91no—
225C3×C4×D4—91no—
226C3×C4×D4—91no—
227C2×C3×C4⋊C4—91no—
228#946—31no—
229#946—31no—
230#946—91no—
231#946—91no—
232#929—31no—
233#929—91no—
234C4×#67—31no—
235C4×#67—91no—
236#898—31no—
237#898—91no—
238#894—31no—
239#894—91no—
240#893—31no—
241#893—91no—
242D3×C4⋊C4—31no—
243D3×C4⋊C4—91no—
244#889—31no—
245#889—31no—
246#889—91no—
247#889—91no—
248#884—31no—
249#884—91no—
250#883—31no—
251#883—31no—
252#883—91no—
253#883—91no—
254#879—31no—
255#879—91no—
256C23×C32—21no—
257C23×C32C22×D311yescharacteristic
258C23×C32C23×C311yescharacteristic
259C22×C3⋊D3C23×C311yescharacteristic
260C22×C3⋊D3C23×C311yescharacteristic
261C22×C3×D3—31no—
262C22×C3×D3—31no—
263C32×Q8—41no—
264C32×Q8—41no—
265C32×Q8—42no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—41no—
273C2×C32×C4—41no—
274C2×C32×C4—42no—
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C23×C311yescharacteristic
282C2×C32×C4C23×C311yescharacteristic
283C2×C32×C4C23×C311yescharacteristic
284C2×C32×C4C23×C311yescharacteristic
285C2×C32×C4C23×C311yescharacteristic
286C2×C32×C4C23×C311yescharacteristic
287#638—22no—
288#638—41no—
289C2×C3⋊Dic3C23×C311yescharacteristic
290C2×C3⋊Dic3C23×C311yescharacteristic
291C2×C3⋊Dic3C23×C311yescharacteristic
292C2×C3⋊Dic3C23×C311yescharacteristic
293C2×C3⋊Dic3C23×C311yescharacteristic
294C2×C3⋊Dic3C23×C311yescharacteristic
295C4⋊(C3⋊D3)—22no—
296C4×C3⋊D3—22no—
297C4×C3⋊D3—41no—
298C4×C3⋊D3—41no—
299C4×C3⋊D3—41no—
300C3×#67—62no—
301C3×#67—121no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—31no—
308C3×D12—62no—
309C3×C4×D3—62no—
310C3×C4×D3—121no—
311C3×C4×D3—121no—
312C3×C4×D3—121no—
313#539—91noSylow
314C2×H(3,𝔽3)—41no—
315C2×H(3,𝔽3)C2×#4111yescharacteristic
316C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
317C2×H(3,𝔽3)2−1+411yescharacteristic
318(C3⋊D3)⋊C3—22no—
319(C3⋊D3)⋊C3—41no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—61no—
323C2×C3×Q8C2×C3×D311yescharacteristic
324C2×C3×D4—91no—
325C2×C3×D4—91no—
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×C4C2×C3×D311yescharacteristic
335C2×#67—31no—
336C2×#67—31no—
337C2×#67—91no—
338C2×#67—91no—
339C2×D12—31no—
340C2×D12—91no—
341C2×C4×D3—31no—
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×C4×D3—91no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—91no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4—91no—
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⋊C4C2×C3×D311yescharacteristic
370C3×C4⋊C4C2×C3×D311yescharacteristic
371C3×C4⋊C4C2×C3×D311yescharacteristic
372C3×C22⋊C4—31no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C22⋊C4—91no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C22⋊C4—91no—
386C3×C22⋊C4C2×C3×D311yescharacteristic
387C3×C22⋊C4C2×C3×D311yescharacteristic
388C3×C42—91no—
389C3×C42—91no—
390#217—31no—
391#217—31no—
392#217—91no—
393#217—91no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406C4⋊Dic3—31no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—91no—
410C4⋊Dic3—91no—
411C4⋊Dic3—91no—
412Dic3⋊C4—31no—
413Dic3⋊C4—31no—
414Dic3⋊C4—31no—
415Dic3⋊C4—31no—
416Dic3⋊C4—31no—
417Dic3⋊C4—31no—
418Dic3⋊C4—31no—
419Dic3⋊C4—31no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428C4×Dic3—31no—
429C4×Dic3—31no—
430C4×Dic3—91no—
431C4×Dic3—91no—
432C22×C32—22no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—21no—
439C22×C32—21no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32C23×D311yescharacteristic
443C22×C32C24×C311yescharacteristic
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3C3×#4112yes—
450C2×C3×D3—32no—
451C2×C3×D3—61no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C32×C4—22no—
457C32×C4—21no—
458C32×C4—21no—
459C32×C4—21no—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—21no—
464C32×C4—21no—
465C32×C4—21no—
466C32×C4—21no—
467C32×C4—21no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4—41no—
473C32×C4—41no—
474C3⋊Dic3—21no—
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3⋊Dic3—21no—
479C3⋊Dic3—21no—
480C3×Dic3—61no—
481C3×Dic3—61no—
482C3×Dic3—61no—
483C3×Dic3—61no—
484C3×Dic3—61no—
485C3×Dic3—61no—
486#126—91no—
487#126—91no—
488#125—91no—
489#125—91no—
490#123—91no—
491#123—91no—
492#123—91no—
493#123—91no—
494C22⋊Q8—91no—
495C22⋊Q8—91no—
496C22⋊Q8(C3⋊D3)⋊C311yescharacteristic, complemented
497#121—91no—
498C4×D4—91no—
499C4×D4—91no—
500C2×C4⋊C4—91no—
501H(3,𝔽3)#53911yescharacteristic, complemented, Sylow
502C23×C3—31no—
503C23×C3—31no—
504C23×C3—61no—
505C23×C3—91no—
506C23×C3—91no—
507C23×C3C22×C3×D311yescharacteristic
508C22×D3—31no—
509C22×D3—31no—
510C22×D3—91no—
511C22×D3—91no—
512C3×Q8—41no—
513C3×Q8—121no—
514C3×Q8—121no—
515C3×Q8—122no—
516C3×D4—182no—
517C3×D4—182no—
518C3×D4—361no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—91no—
542C2×C3×C4—91no—
543C2×C3×C4—91no—
544C2×C3×C4—121no—
545C2×C3×C4—121no—
546C2×C3×C4—122no—
547C2×C3×C4—182no—
548C2×C3×C4—361no—
549C2×C3×C4—361no—
550C2×C3×C4—361no—
551C2×C3×C4C22×C3×D311yescharacteristic
552C2×C3×C4C22×C3×D311yescharacteristic
553C2×C3×C4C22×C3×D311yescharacteristic
554C2×C3×C4C22×C3×D311yescharacteristic
555C2×C3×C4C22×C3×D311yescharacteristic
556C2×C3×C4C22×C3×D311yescharacteristic
557#67—62no—
558#67—121no—
559#67—182no—
560#67—361no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—91no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—91no—
573D12—62no—
574D12—182no—
575C4×D3—62no—
576C4×D3—121no—
577C4×D3—121no—
578C4×D3—121no—
579C4×D3—182no—
580C4×D3—361no—
581C4×D3—361no—
582C4×D3—361no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—42no—
587C2×C32—41no—
588C2×C32—41no—
589C2×C32#100411yescharacteristic
590C2×C32#100711yescharacteristic
591C2×C32D3×#4111yescharacteristic
592C2×C32C2×C3×#4111yescharacteristic
593C2×C32C3×H(5,𝔽2)11yescharacteristic
594C2×C32C3×2−1+411yescharacteristic
595C3⋊D3—22no—
596C3⋊D3—41no—
597C3×D3—62no—
598C3×D3—121no—
599C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic
600C2×D4—91no—
601C2×D4—91no—
602C2×D4—91no—
603C22×C4—91no—
604C22×C4—91no—
605C22×C4—91no—
606C22×C4—91no—
607C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
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⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—91no—
630C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
631C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
632C42—91no—
633C42—91no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—31no—
638C22×C3—31no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—62no—
646C22×C3—61no—
647C22×C3—92no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3C23×C3×D311yescharacteristic
656C2×D3—32no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—92no—
663C2×D3—181no—
664C2×D3—181no—
665C2×D3—181no—
666C2×D3—181no—
667C2×D3—181no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—62no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4—181no—
693C3×C4—181no—
694C3×C4—181no—
695C3×C4—181no—
696C3×C4—181no—
697C3×C4—181no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—181no—
705Dic3—181no—
706Dic3—181no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710C32—21no—
711C32#563811yescharacteristic, complemented
712C32C3×#53911yescharacteristic, complemented
713C23—91no—
714C23—91no—
715C23C22×(C3⋊D3)⋊C311yescharacteristic
716Q8—41no—
717D4—182no—
718D4—182no—
719D4—361no—
720C2×C4—41no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—182no—
728C2×C4—361no—
729C2×C4—361no—
730C2×C4—361no—
731C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
732C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
733C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
734C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
735C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
736C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
737C2×C3—31no—
738C2×C3—31no—
739C2×C3—31no—
740C2×C3—31no—
741C2×C3—31no—
742C2×C3—31no—
743C2×C3—41no—
744C2×C3—61no—
745C2×C3—61no—
746C2×C3—61no—
747C2×C3—121no—
748C2×C3—121no—
749C2×C3—122no—
750C2×C3—182no—
751C2×C3—361no—
752C2×C3C3×#100411yescharacteristic
753C2×C3C3×#100711yescharacteristic
754C2×C3C3×D3×#4111yescharacteristic
755D3—62no—
756D3—121no—
757D3—182no—
758D3—361no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—92no—
763C22—181no—
764C22—181no—
765C22—181no—
766C22—181no—
767C22—181no—
768C22C23×(C3⋊D3)⋊C311yescharacteristic
769C4—21no—
770C4—21no—
771C4—21no—
772C4—21no—
773C4—21no—
774C4—21no—
775C4—181no—
776C4—181no—
777C4—181no—
778C4—181no—
779C4—181no—
780C4—181no—
781C3—31no—
782C3—31no—
783C3—61no—
784C3C3×#563811yescharacteristic
785C2—41no—
786C2—182no—
787C2—361no—
788C2#64361⋊C311yescharacteristic
789C2#1172262711yescharacteristic
790C2#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 radical#64093⋊C3C2
hypercenterC22⋊Q8(C3⋊D3)⋊C3
hypocenterC32C3×#539
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. #64155⋊C3C2semidirect
4. #64138⋊C3C2semidirect
5. C4×#638⋊C3C2semidirect
6. #64107⋊C3C2semidirect
7. #64103⋊C3C2semidirect
8. #64102⋊C3C2semidirect
9. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
10. #64098⋊C3C2semidirect
11. #64098⋊C3C2semidirect
13. #64092⋊C3C2semidirect
14. #64092⋊C3C2semidirect
15. #64088⋊C3C2semidirect
16. #10596109C3semidirect
54. C32×C22⋊Q8D3semidirect
55. C32×C22⋊Q8C2×C3semidirect
56. #64155C2×C3semidirect
57. #64155C2×C3semidirect
58. #64138C2×C3semidirect
59. C4×#638C2×C3semidirect
60. #64107C2×C3semidirect
61. #64103C2×C3semidirect
62. #64102C2×C3semidirect
63. C4⋊C4×C3⋊D3C2×C3semidirect
64. #64098C2×C3semidirect
65. #64098C2×C3semidirect
67. #64092C2×C3semidirect
68. #64092C2×C3semidirect
69. #64088C2×C3semidirect
496. C22⋊Q8(C3⋊D3)⋊C3semidirect
501. H(3,𝔽3)#539semidirect
711. C32#5638semidirect
712. C32C3×#539semidirect

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
#64138⋊C32
C4×#638⋊C32
#64107⋊C32
#64103⋊C32
#64102⋊C32
C4⋊C4×(C3⋊D3)⋊C32
#64098⋊C32
#64093⋊C32
#64092⋊C32
#64088⋊C32
#105961093
C3×#56383