Finite Group Databasebeta

← #10596181⋊C3 #13153233

Subgroups — #10596181⋊C3 #13153233

Order 1728.

816 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#126C211yesmaximal, characteristic, complemented
2#64107⋊C3C211yesmaximal, characteristic, complemented
3#64106⋊C3C211yesmaximal, characteristic, complemented
4#64105⋊C3C211yesmaximal, characteristic, complemented
5#64103⋊C3C211yesmaximal, characteristic, complemented
6#64101⋊C3C211yesmaximal, characteristic, complemented
7#64097⋊C3C211yesmaximal, characteristic, complemented
8#64095⋊C3C211yesmaximal, characteristic, complemented
9#64094⋊C3C211yesmaximal, characteristic, complemented
10#64094⋊C3C211yesmaximal, characteristic, complemented
11#64093⋊C3C211yesmaximal, characteristic
12#64090⋊C3C211yesmaximal, characteristic, complemented
13#64087⋊C3C211yesmaximal, characteristic, complemented
14#64084⋊C3C211yesmaximal, characteristic, complemented
15C4×#634⋊C3C211yesmaximal, characteristic, complemented
16#10596181C311yesmaximal, characteristic, complemented
17C3×#5710—31nomaximal
18C2×#638⋊C3C2211yescharacteristic
19C2×#638⋊C3C2211yescharacteristic
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
21C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×#634⋊C3C2211yescharacteristic
25C2×#634⋊C3C2211yescharacteristic
26C2×#634⋊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
32C22⋊C4×H(3,𝔽3)C2211yescharacteristic
33C42×H(3,𝔽3)C2211yescharacteristic
34#3757⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
44C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
45C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
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×#126—21no—
54C32×#126D311yescharacteristic, complemented
55C32×#126C2×C311yescharacteristic, complemented
56#64107C2×C311yescharacteristic, complemented
57#64106C2×C311yescharacteristic, complemented
58#64105C2×C311yescharacteristic, complemented
59#64103C2×C311yescharacteristic, complemented
60#64101C2×C311yescharacteristic, complemented
61#64097C2×C311yescharacteristic, complemented
62#64095C2×C311yescharacteristic, complemented
63#64094C2×C311yescharacteristic, complemented
64#64094C2×C311yescharacteristic, complemented
65#64093C2×C311yescharacteristic
66#64090C2×C311yescharacteristic, complemented
67#64087C2×C311yescharacteristic, complemented
68#64084C2×C311yescharacteristic, complemented
69C4×#634C2×C311yescharacteristic, complemented
70C3×#898—31no—
71C3×#897—31no—
72C3×#896—31no—
73C3×#894—31no—
74C3×#892—31no—
75C3×#888—31no—
76C3×#886—31no—
77C3×#885—31no—
78C3×#885—31no—
79C3×#884—31no—
80C3×#67⋊C4—31no—
81C3×#878—31no—
82C3×#875—31no—
83C3×C4×Dic6—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
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×C4×H(3,𝔽3)C2311yescharacteristic
93#638⋊C3—22no—
94#638⋊C3—41no—
95C2×(C3⋊Dic3)⋊C3—41no—
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—
103C4×(C3⋊D3)⋊C3—22no—
104C4×(C3⋊D3)⋊C3—41no—
105#634⋊C3—22no—
106#634⋊C3—41no—
107#634⋊C3—41no—
108C3×#542—91no—
109#5710—31no—
110#5710—91no—
111C2×#638C22×C311yescharacteristic
112C2×#638C22×C311yescharacteristic
113C22×C3⋊Dic3C22×C311yescharacteristic
114C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
115C2×C4×C3⋊D3C22×C311yescharacteristic
116C2×C4×C3⋊D3C22×C311yescharacteristic
117C2×#634C22×C311yescharacteristic
118C2×#634C22×C311yescharacteristic
119C2×#634C22×C311yescharacteristic
120C2×C3×#67—31no—
121C2×C3×#67—31no—
122C22×C3×Dic3—31no—
123C2×C3×D12—31no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—31no—
126C2×C3×Dic6—31no—
127C2×C3×Dic6—31no—
128C2×C3×Dic6—31no—
129C32×C4⋊C4—21no—
130C32×C4⋊C4—21no—
131C32×C4⋊C4—21no—
132C32×C4⋊C4C2×D311yescharacteristic
133C32×C4⋊C4C2×D311yescharacteristic
134C32×C4⋊C4C2×D311yescharacteristic
135C32×C4⋊C4C22×C311yescharacteristic
136C32×C4⋊C4C22×C311yescharacteristic
137C32×C4⋊C4C22×C311yescharacteristic
138C32×C22⋊C4—21no—
139C32×C22⋊C4—21no—
140C32×C22⋊C4—21no—
141C32×C22⋊C4C2×D311yescharacteristic
142C32×C22⋊C4C2×D311yescharacteristic
143C32×C22⋊C4C2×D311yescharacteristic
144C32×C22⋊C4C22×C311yescharacteristic
145C32×C22⋊C4C22×C311yescharacteristic
146C32×C22⋊C4C22×C311yescharacteristic
147C32×C42—21no—
148C32×C42C2×D311yescharacteristic
149C32×C42C22×C311yescharacteristic
150#3757C22×C311yescharacteristic
151#3752C22×C311yescharacteristic
152#3752C22×C311yescharacteristic
153#3752C22×C311yescharacteristic
154#3752C22×C311yescharacteristic
155#3752C22×C311yescharacteristic
156#3752C22×C311yescharacteristic
157#3752C22×C311yescharacteristic
158#3752C22×C311yescharacteristic
159C4⋊(C3⋊Dic3)C22×C311yescharacteristic
160C4⋊(C3⋊Dic3)C22×C311yescharacteristic
161C4⋊(C3⋊Dic3)C22×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×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×Dic3⋊C4—31no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×C4×Dic3—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—21no—
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#4112yes—
210C3×C4⋊Q8—91no—
211C3×#126—31no—
212C3×#126—31no—
213C3×#126—61no—
214C3×#126—91no—
215C3×#126C3×D311yescharacteristic
216C3×#124—91no—
217C3×#124—91no—
218C3×#124—91no—
219C3×#123—91no—
220C3×#123—91no—
221C3×C22⋊Q8—91no—
222C3×C22⋊Q8—91no—
223C3×C22⋊Q8—91no—
224C3×#121—91no—
225C3×C4×Q8—91no—
226C3×C4×D4—91no—
227C3×#117—91no—
228#898—31no—
229#898—91no—
230#897—31no—
231#897—91no—
232#896—31no—
233#896—91no—
234#894—31no—
235#894—91no—
236#892—31no—
237#892—91no—
238#888—31no—
239#888—91no—
240#886—31no—
241#886—91no—
242#885—31no—
243#885—31no—
244#885—91no—
245#885—91no—
246#884—31no—
247#884—91no—
248#67⋊C4—31no—
249#67⋊C4—91no—
250#878—31no—
251#878—91no—
252#875—31no—
253#875—91no—
254C4×Dic6—31no—
255C4×Dic6—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—
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×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C23×C311yescharacteristic
276C2×C32×C4C23×C311yescharacteristic
277C2×C32×C4C23×C311yescharacteristic
278C2×C32×C4C23×C311yescharacteristic
279C2×C32×C4C23×C311yescharacteristic
280C2×C32×C4C23×C311yescharacteristic
281#638—22no—
282#638—41no—
283C2×C3⋊Dic3—41no—
284C2×C3⋊Dic3C23×C311yescharacteristic
285C2×C3⋊Dic3C23×C311yescharacteristic
286C2×C3⋊Dic3C23×C311yescharacteristic
287C2×C3⋊Dic3C23×C311yescharacteristic
288C2×C3⋊Dic3C23×C311yescharacteristic
289C2×C3⋊Dic3C23×C311yescharacteristic
290C4⋊(C3⋊D3)—41no—
291C4×C3⋊D3—22no—
292C4×C3⋊D3—41no—
293#634—22no—
294#634—41no—
295#634—41no—
296C3×#67—62no—
297C3×#67—121no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—121no—
305C3×D12—121no—
306C3×C4×D3—62no—
307C3×C4×D3—121no—
308C3×Dic6—62no—
309C3×Dic6—121no—
310C3×Dic6—121no—
311#542—91noSylow
312C2×H(3,𝔽3)—41no—
313C2×H(3,𝔽3)C2×#4111yescharacteristic
314C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
315C2×H(3,𝔽3)2−1+411yescharacteristic
316(C3⋊D3)⋊C3—41no—
317(C3⋊D3)⋊C3—41no—
318C2×C3×Q8—91no—
319C2×C3×Q8—91no—
320C2×C3×Q8—91no—
321C2×C3×D4—91no—
322C2×C3×D4—91no—
323C2×C3×D4—91no—
324C22×C3×C4—91no—
325C22×C3×C4—91no—
326C22×C3×C4—91no—
327C2×#67—31no—
328C2×#67—31no—
329C2×#67—91no—
330C2×#67—91no—
331C22×Dic3—31no—
332C22×Dic3—91no—
333C2×D12—31no—
334C2×D12—91no—
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×Dic6—31no—
340C2×Dic6—31no—
341C2×Dic6—31no—
342C2×Dic6—91no—
343C2×Dic6—91no—
344C2×Dic6—91no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—91no—
355C3×C4⋊C4—91no—
356C3×C4⋊C4—91no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4—91no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4—91no—
361C3×C4⋊C4C2×C3×D311yescharacteristic
362C3×C4⋊C4C2×C3×D311yescharacteristic
363C3×C4⋊C4C2×C3×D311yescharacteristic
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C22⋊C4—91no—
382C3×C22⋊C4C2×C3×D311yescharacteristic
383C3×C22⋊C4C2×C3×D311yescharacteristic
384C3×C22⋊C4C2×C3×D311yescharacteristic
385C3×C42—31no—
386C3×C42—31no—
387C3×C42—61no—
388C3×C42—91no—
389C3×C42—91no—
390C3×C42—91no—
391C3×C42C2×C3×D311yescharacteristic
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—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410C4⋊Dic3—31no—
411C4⋊Dic3—31no—
412C4⋊Dic3—31no—
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416Dic3⋊C4—31no—
417Dic3⋊C4—31no—
418Dic3⋊C4—31no—
419Dic3⋊C4—31no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424C4×Dic3—31no—
425C4×Dic3—31no—
426C4×Dic3—31no—
427C4×Dic3—91no—
428C4×Dic3—91no—
429C4×Dic3—91no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32C23×D311yescharacteristic
441C22×C32C24×C311yescharacteristic
442C2×C3⋊D3—21no—
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C2×C3×D3—61no—
451C2×C3×D3—61no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
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—21no—
464C32×C4—21no—
465C32×C4—21no—
466C32×C4—41no—
467C32×C4—41no—
468C32×C4—41no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4—41no—
472C3⋊Dic3—21no—
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3⋊Dic3C3×#4112yes—
478C3×Dic3—32no—
479C3×Dic3—61no—
480C3×Dic3—61no—
481C3×Dic3—61no—
482C3×Dic3—61no—
483C3×Dic3—61no—
484C4⋊Q8—91no—
485#126—91no—
486#126(C3⋊D3)⋊C311yescharacteristic, complemented
487#124—91no—
488#124—91no—
489#124—91no—
490#123—91no—
491#123—91no—
492C22⋊Q8—91no—
493C22⋊Q8—91no—
494C22⋊Q8—91no—
495#121—91no—
496C4×Q8—91no—
497C4×D4—91no—
498#117—91no—
499H(3,𝔽3)#54211yescharacteristic, complemented, Sylow
500C23×C3—31no—
501C23×C3—31no—
502C23×C3—61no—
503C23×C3—91no—
504C23×C3—91no—
505C23×C3C22×C3×D311yescharacteristic
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—91no—
509C22×D3—91no—
510C3×Q8—182no—
511C3×Q8—361no—
512C3×Q8—361no—
513C3×D4—182no—
514C3×D4—361no—
515C3×D4—361no—
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—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—91no—
535C2×C3×C4—91no—
536C2×C3×C4—91no—
537C2×C3×C4—91no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—182no—
541C2×C3×C4—361no—
542C2×C3×C4—361no—
543C2×C3×C4C22×C3×D311yescharacteristic
544C2×C3×C4C22×C3×D311yescharacteristic
545C2×C3×C4C22×C3×D311yescharacteristic
546C2×C3×C4C22×C3×D311yescharacteristic
547C2×C3×C4C22×C3×D311yescharacteristic
548C2×C3×C4C22×C3×D311yescharacteristic
549#67—62no—
550#67—121no—
551#67—182no—
552#67—361no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—91no—
560C2×Dic3—91no—
561C2×Dic3—91no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—121no—
566C2×Dic3—361no—
567D12—121no—
568D12—361no—
569C4×D3—62no—
570C4×D3—121no—
571C4×D3—182no—
572C4×D3—361no—
573Dic6—62no—
574Dic6—121no—
575Dic6—121no—
576Dic6—182no—
577Dic6—361no—
578Dic6—361no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—41no—
583C2×C32—41no—
584C2×C32—81no—
585C2×C32D3×#4111yescharacteristic
586C2×C32#100911yescharacteristic
587C2×C32#101011yescharacteristic
588C2×C32C2×C3×#4111yescharacteristic
589C2×C32C3×H(5,𝔽2)11yescharacteristic
590C2×C32C3×2−1+411yescharacteristic
591C3⋊D3—41no—
592C3⋊D3—41no—
593C3×D3—121no—
594C3×D3—121no—
595C2×Q8—91no—
596C2×Q8—91no—
597C2×Q8—91no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—91no—
601C22×C4—91no—
602C22×C4—91no—
603C22×C4—91no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
612C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
613C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
614C22⋊C4—91no—
615C22⋊C4—91no—
616C22⋊C4—91no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
624C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
625C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
626C42—91no—
627C42—91no—
628C42—91no—
629C42C2×(C3⋊D3)⋊C311yescharacteristic
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—31no—
634C22×C3—31no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—181no—
646C22×C3—181no—
647C22×C3—181no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3C23×C3×D311yescharacteristic
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—181no—
659C2×D3—181no—
660C2×D3—181no—
661C2×D3—181no—
662C2×D3—181no—
663C2×D3—181no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—61no—
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—92no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—181no—
690C3×C4—181no—
691C3×C4—181no—
692C3×C4—181no—
693C3×C4—181no—
694Dic3—32no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—92no—
701Dic3—181no—
702Dic3—181no—
703Dic3—181no—
704Dic3—181no—
705Dic3—181no—
706C32—21no—
707C32#571011yescharacteristic, complemented
708C32C3×#54211yescharacteristic, complemented
709C23—91no—
710C23—91no—
711C23C22×(C3⋊D3)⋊C311yescharacteristic
712Q8—182no—
713Q8—361no—
714Q8—361no—
715D4—182no—
716D4—361no—
717D4—361no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—182no—
725C2×C4—361no—
726C2×C4—361no—
727C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
728C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
729C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
730C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
731C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
732C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
733C2×C3—31no—
734C2×C3—31no—
735C2×C3—31no—
736C2×C3—31no—
737C2×C3—31no—
738C2×C3—31no—
739C2×C3—41no—
740C2×C3—61no—
741C2×C3—61no—
742C2×C3—61no—
743C2×C3—121no—
744C2×C3—121no—
745C2×C3—241no—
746C2×C3—361no—
747C2×C3—361no—
748C2×C3C3×D3×#4111yescharacteristic
749C2×C3C3×#100911yescharacteristic
750C2×C3C3×#101011yescharacteristic
751D3—121no—
752D3—121no—
753D3—361no—
754D3—361no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—181no—
759C22—181no—
760C22—181no—
761C22—181no—
762C22—181no—
763C22—181no—
764C22C23×(C3⋊D3)⋊C311yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—21no—
770C4—21no—
771C4—92no—
772C4—181no—
773C4—181no—
774C4—181no—
775C4—181no—
776C4—181no—
777C3—31no—
778C3—31no—
779C3—61no—
780C3C3×#571011yescharacteristic
781C2—41no—
782C2—361no—
783C2—361no—
784C2#41×(C3⋊D3)⋊C311yescharacteristic
785C2#1172263811yescharacteristic
786C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#126C2
prime radical#64093⋊C3C2
hypercenter#126(C3⋊D3)⋊C3
hypocenterC32C3×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#126C2semidirect
2. #64107⋊C3C2semidirect
3. #64106⋊C3C2semidirect
4. #64105⋊C3C2semidirect
5. #64103⋊C3C2semidirect
6. #64101⋊C3C2semidirect
7. #64097⋊C3C2semidirect
8. #64095⋊C3C2semidirect
9. #64094⋊C3C2semidirect
10. #64094⋊C3C2semidirect
12. #64090⋊C3C2semidirect
13. #64087⋊C3C2semidirect
14. #64084⋊C3C2semidirect
15. C4×#634⋊C3C2semidirect
16. #10596181C3semidirect
54. C32×#126D3semidirect
55. C32×#126C2×C3semidirect
56. #64107C2×C3semidirect
57. #64106C2×C3semidirect
58. #64105C2×C3semidirect
59. #64103C2×C3semidirect
60. #64101C2×C3semidirect
61. #64097C2×C3semidirect
62. #64095C2×C3semidirect
63. #64094C2×C3semidirect
64. #64094C2×C3semidirect
66. #64090C2×C3semidirect
67. #64087C2×C3semidirect
68. #64084C2×C3semidirect
69. C4×#634C2×C3semidirect
486. #126(C3⋊D3)⋊C3semidirect
499. H(3,𝔽3)#542semidirect
707. C32#5710semidirect
708. C32C3×#542semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×#1262
#64107⋊C32
#64106⋊C32
#64105⋊C32
#64103⋊C32
#64101⋊C32
#64097⋊C32
#64095⋊C32
#64094⋊C32
#64093⋊C32
#64090⋊C32
#64087⋊C32
#64084⋊C32
C4×#634⋊C32
#105961813
C3×#57103