Finite Group Databasebeta

← #10596149⋊C3 #13153120

Subgroups — #10596149⋊C3 #13153120

Order 1728.

951 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#124C211yesmaximal, characteristic, complemented
2#64156⋊C3C211yesmaximal, characteristic, complemented
3#64155⋊C3C211yesmaximal, characteristic, complemented
4#64148⋊C3C211yesmaximal, characteristic, complemented
5#64146⋊C3C211yesmaximal, characteristic, complemented
6#64095⋊C3C211yesmaximal, characteristic, complemented
7#64093⋊C3C211yesmaximal, characteristic, complemented
8#64093⋊C3C211yesmaximal, characteristic, complemented
9#64092⋊C3C211yesmaximal, characteristic, complemented
10#64091⋊C3C211yesmaximal, characteristic, complemented
11#64090⋊C3C211yesmaximal, characteristic, complemented
12C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
13#64088⋊C3C211yesmaximal, characteristic, complemented
14#11721387C211yesmaximal, characteristic, complemented
15C4×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
16#10596149C311yesmaximal, characteristic, complemented
17C3×#5678—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C2×Q8×H(3,𝔽3)C2211yescharacteristic, complemented
20C2×D4×H(3,𝔽3)C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C2×#638⋊C3C2211yescharacteristic, complemented
25C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
26C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
27C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
29C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
30C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic
32C22⋊C4×H(3,𝔽3)C2211yescharacteristic
33C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
34C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
35C42×H(3,𝔽3)C2211yescharacteristic, complemented
36#3757⋊C3C2211yescharacteristic
37#3757⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic
44#3752⋊C3C2211yescharacteristic, complemented
45#3752⋊C3C2211yescharacteristic, complemented
46C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
47C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
48#3750⋊C3C2211yescharacteristic, complemented
49#3750⋊C3C2211yescharacteristic, complemented
50#3750⋊C3C2211yescharacteristic, complemented
51#3750⋊C3C2211yescharacteristic, complemented
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
53C32×#124—21no—
54C32×#124D311yescharacteristic, complemented
55C32×#124C2×C311yescharacteristic, complemented
56#64156C2×C311yescharacteristic, complemented
57#64155C2×C311yescharacteristic, complemented
58#64148C2×C311yescharacteristic, complemented
59#64146C2×C311yescharacteristic, complemented
60#64095C2×C311yescharacteristic, complemented
61#64093C2×C311yescharacteristic, complemented
62#64093C2×C311yescharacteristic, complemented
63#64092C2×C311yescharacteristic, complemented
64#64091C2×C311yescharacteristic, complemented
65#64090C2×C311yescharacteristic, complemented
66C22⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
67#64088C2×C311yescharacteristic, complemented
68#64085C2×C311yescharacteristic, complemented
69C4×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
70C3×#947—31no—
71C3×#946—31no—
72C3×#939—31no—
73C3×#937—31no—
74C3×#886—31no—
75C3×#884—31no—
76C3×#884—31no—
77C3×#883—31no—
78C3×#882—31no—
79C3×#67⋊C4—31no—
80C3×D3×C22⋊C4—31no—
81C3×#879—31no—
82C3×#876—31no—
83C3×C4×D12—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C23×H(3,𝔽3)C2311yescharacteristic
86C22×(C3⋊D3)⋊C3—22no—
87C22×(C3⋊D3)⋊C3—41no—
88C22×(C3⋊D3)⋊C3—41no—
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
92Q8×H(3,𝔽3)—41no—
93D4×H(3,𝔽3)—41no—
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95C2×C4×H(3,𝔽3)C2311yescharacteristic
96C2×C4×H(3,𝔽3)C2311yescharacteristic
97C2×C4×H(3,𝔽3)C2311yescharacteristic
98C2×C4×H(3,𝔽3)C2311yescharacteristic
99#638⋊C3—22no—
100#638⋊C3—41no—
101#638⋊C3—41no—
102#638⋊C3—41no—
103C2×(C3⋊Dic3)⋊C3—41no—
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C4⋊((C3⋊D3)⋊C3)—22no—
110C4⋊((C3⋊D3)⋊C3)—41no—
111C4×(C3⋊D3)⋊C3—41no—
112C4×(C3⋊D3)⋊C3—41no—
113C4×(C3⋊D3)⋊C3—41no—
114C3×#538—91no—
115#5678—31no—
116#5678—91no—
117C23×C3⋊D3C22×C311yescharacteristic
118C23×C3×D3—31no—
119C2×C32×Q8—21no—
120C2×C32×Q8C2×D311yescharacteristic, complemented
121C2×C32×Q8C22×C311yescharacteristic, complemented
122C2×C32×D4—21no—
123C2×C32×D4C2×D311yescharacteristic
124C2×C32×D4C22×C311yescharacteristic
125C2×#638C22×C311yescharacteristic
126C2×#638C22×C311yescharacteristic
127C2×#638C22×C311yescharacteristic
128C2×#638C22×C311yescharacteristic, complemented
129C22×C3⋊Dic3C22×C311yescharacteristic, complemented
130C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
131C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
132C2×C4×C3⋊D3C22×C311yescharacteristic
133C2×C4×C3⋊D3C22×C311yescharacteristic
134C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C22×C3×Dic3—31no—
140C2×C3×D12—31no—
141C2×C3×D12—31no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C32×C22⋊C4—21no—
146C32×C22⋊C4—21no—
147C32×C22⋊C4—21no—
148C32×C22⋊C4—21no—
149C32×C22⋊C4C2×D311yescharacteristic
150C32×C22⋊C4C2×D311yescharacteristic
151C32×C22⋊C4C2×D311yescharacteristic, complemented
152C32×C22⋊C4C2×D311yescharacteristic, complemented
153C32×C22⋊C4C22×C311yescharacteristic
154C32×C22⋊C4C22×C311yescharacteristic
155C32×C22⋊C4C22×C311yescharacteristic, complemented
156C32×C22⋊C4C22×C311yescharacteristic, complemented
157C32×C42—21no—
158C32×C42C2×D311yescharacteristic, complemented
159C32×C42C22×C311yescharacteristic, complemented
160#3757C22×C311yescharacteristic
161#3757C22×C311yescharacteristic
162#3752C22×C311yescharacteristic
163#3752C22×C311yescharacteristic
164#3752C22×C311yescharacteristic
165#3752C22×C311yescharacteristic
166#3752C22×C311yescharacteristic
167#3752C22×C311yescharacteristic
168#3752C22×C311yescharacteristic, complemented
169#3752C22×C311yescharacteristic, complemented
170C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
171C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
172#3750C22×C311yescharacteristic, complemented
173#3750C22×C311yescharacteristic, complemented
174#3750C22×C311yescharacteristic, complemented
175#3750C22×C311yescharacteristic, complemented
176C4×C3⋊Dic3C22×C311yescharacteristic, complemented
177C3×#217—31no—
178C3×#217—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×C4×Dic3—31no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)—21no—
197C22×H(3,𝔽3)—21no—
198C22×H(3,𝔽3)—21no—
199C22×H(3,𝔽3)—21no—
200C22×H(3,𝔽3)C2411yescharacteristic
201C2×(C3⋊D3)⋊C3—21no—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3—21no—
204C2×(C3⋊D3)⋊C3—21no—
205C2×(C3⋊D3)⋊C3—21no—
206C2×(C3⋊D3)⋊C3—21no—
207C2×(C3⋊D3)⋊C3—21no—
208C2×(C3⋊D3)⋊C3—21no—
209C2×(C3⋊D3)⋊C3—44no—
210C2×(C3⋊D3)⋊C3#4112yes—
211C4×H(3,𝔽3)—21no—
212C4×H(3,𝔽3)—21no—
213C4×H(3,𝔽3)—21no—
214C4×H(3,𝔽3)—21no—
215C4×H(3,𝔽3)—21no—
216(C3⋊Dic3)⋊C3—21no—
217(C3⋊Dic3)⋊C3—21no—
218(C3⋊Dic3)⋊C3—21no—
219(C3⋊Dic3)⋊C3—21no—
220(C3⋊Dic3)⋊C3—21no—
221C3×#126—91no—
222C3×#126—91no—
223C3×#124—31no—
224C3×#124—31no—
225C3×#124—61no—
226C3×#124—91no—
227C3×#124C3×D311yescharacteristic
228C3×#123—91no—
229C3×#123—91no—
230C3×C22⋊Q8—91no—
231C3×#121—91no—
232C3×#121—91no—
233C3×#121—91no—
234C3×#120—91no—
235C3×#120—91no—
236C3×C4×D4—91no—
237C3×C4×D4—91no—
238C2×C3×C22⋊C4—91no—
239#947—31no—
240#947—91no—
241#946—31no—
242#946—91no—
243#939—31no—
244#939—91no—
245#937—31no—
246#937—91no—
247#886—31no—
248#886—91no—
249#884—31no—
250#884—31no—
251#884—91no—
252#884—91no—
253#883—31no—
254#883—91no—
255#882—31no—
256#882—91no—
257#67⋊C4—31no—
258#67⋊C4—91no—
259D3×C22⋊C4—31no—
260D3×C22⋊C4—91no—
261#879—31no—
262#879—91no—
263#876—31no—
264#876—91no—
265C4×D12—31no—
266C4×D12—91no—
267C23×C32—21no—
268C23×C32—21no—
269C23×C32C22×D311yescharacteristic
270C23×C32C22×D311yescharacteristic
271C23×C32C23×C311yescharacteristic
272C23×C32C23×C311yescharacteristic
273C22×C3⋊D3—22no—
274C22×C3⋊D3—41no—
275C22×C3⋊D3—41no—
276C22×C3⋊D3C23×C311yescharacteristic
277C22×C3⋊D3C23×C311yescharacteristic
278C22×C3⋊D3C23×C311yescharacteristic
279C22×C3×D3—31no—
280C22×C3×D3—31no—
281C22×C3×D3—31no—
282C22×C3×D3—62no—
283C22×C3×D3—121no—
284C22×C3×D3—121no—
285C32×Q8—41no—
286C32×Q8—41no—
287C32×Q8—42no—
288C32×D4—41no—
289C32×D4—41no—
290C32×D4—42no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4C22×D311yescharacteristic
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C22×D311yescharacteristic
301C2×C32×C4C23×C311yescharacteristic
302C2×C32×C4C23×C311yescharacteristic
303C2×C32×C4C23×C311yescharacteristic
304C2×C32×C4C23×C311yescharacteristic
305C2×C32×C4C23×C311yescharacteristic
306#638—22no—
307#638—41no—
308#638—41no—
309#638—41no—
310C2×C3⋊Dic3—41no—
311C2×C3⋊Dic3C23×C311yescharacteristic
312C2×C3⋊Dic3C23×C311yescharacteristic
313C2×C3⋊Dic3C23×C311yescharacteristic
314C2×C3⋊Dic3C23×C311yescharacteristic
315C2×C3⋊Dic3C23×C311yescharacteristic
316C4⋊(C3⋊D3)—22no—
317C4⋊(C3⋊D3)—41no—
318C4×C3⋊D3—41no—
319C4×C3⋊D3—41no—
320C4×C3⋊D3—41no—
321C3×#67—62no—
322C3×#67—121no—
323C3×#67—121no—
324C3×#67—121no—
325C2×C3×Dic3—31no—
326C2×C3×Dic3—31no—
327C2×C3×Dic3—31no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—31no—
330C2×C3×Dic3—121no—
331C3×D12—62no—
332C3×D12—121no—
333C3×C4×D3—121no—
334C3×C4×D3—121no—
335C3×C4×D3—121no—
336#538—91noSylow
337C2×H(3,𝔽3)—41no—
338C2×H(3,𝔽3)—41no—
339C2×H(3,𝔽3)C2×#4111yescharacteristic
340C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
341C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
342(C3⋊D3)⋊C3—22no—
343(C3⋊D3)⋊C3—41no—
344(C3⋊D3)⋊C3—41no—
345C24×C3—91no—
346C23×D3—31no—
347C23×D3—91no—
348C2×C3×Q8—31no—
349C2×C3×Q8—31no—
350C2×C3×Q8—61no—
351C2×C3×Q8C2×C3×D311yescharacteristic
352C2×C3×D4—31no—
353C2×C3×D4—31no—
354C2×C3×D4—61no—
355C2×C3×D4—91no—
356C2×C3×D4—91no—
357C2×C3×D4—91no—
358C2×C3×D4—91no—
359C2×C3×D4—91no—
360C2×C3×D4—91no—
361C2×C3×D4C2×C3×D311yescharacteristic
362C22×C3×C4—91no—
363C22×C3×C4—91no—
364C22×C3×C4—91no—
365C22×C3×C4—91no—
366C2×#67—31no—
367C2×#67—31no—
368C2×#67—31no—
369C2×#67—31no—
370C2×#67—91no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C22×Dic3—31no—
375C22×Dic3—91no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—91no—
379C2×D12—91no—
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C3×C4⋊C4—91no—
387C3×C4⋊C4—91no—
388C3×C4⋊C4—91no—
389C3×C4⋊C4—91no—
390C3×C4⋊C4—91no—
391C3×C4⋊C4—91no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—31no—
397C3×C22⋊C4—31no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—91no—
405C3×C22⋊C4—91no—
406C3×C22⋊C4—91no—
407C3×C22⋊C4—91no—
408C3×C22⋊C4—91no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4—91no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4—91no—
414C3×C22⋊C4C2×C3×D311yescharacteristic
415C3×C22⋊C4C2×C3×D311yescharacteristic
416C3×C22⋊C4C2×C3×D311yescharacteristic
417C3×C22⋊C4C2×C3×D311yescharacteristic
418C3×C42—31no—
419C3×C42—31no—
420C3×C42—61no—
421C3×C42—91no—
422C3×C42C2×C3×D311yescharacteristic
423#217—31no—
424#217—31no—
425#217—91no—
426#217—91no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—31no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443C4⋊Dic3—31no—
444C4⋊Dic3—31no—
445C4⋊Dic3—91no—
446C4⋊Dic3—91no—
447Dic3⋊C4—31no—
448Dic3⋊C4—31no—
449Dic3⋊C4—31no—
450Dic3⋊C4—31no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—91no—
454Dic3⋊C4—91no—
455C4×Dic3—31no—
456C4×Dic3—91no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32C23×D311yescharacteristic
477C22×C32C24×C311yescharacteristic
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—44no—
487C2×C3⋊D3C3×#4112yes—
488C2×C3×D3—32no—
489C2×C3×D3—61no—
490C2×C3×D3—61no—
491C2×C3×D3—61no—
492C2×C3×D3—61no—
493C2×C3×D3—61no—
494C2×C3×D3—61no—
495C2×C3×D3—61no—
496C2×C3×D3—61no—
497C2×C3×D3—124no—
498C32×C4—22no—
499C32×C4—21no—
500C32×C4—21no—
501C32×C4—21no—
502C32×C4—21no—
503C32×C4—21no—
504C32×C4—21no—
505C32×C4—21no—
506C32×C4—21no—
507C32×C4—21no—
508C32×C4—21no—
509C32×C4—41no—
510C32×C4—41no—
511C32×C4—41no—
512C32×C4—41no—
513C3⋊Dic3—21no—
514C3⋊Dic3—21no—
515C3⋊Dic3—21no—
516C3⋊Dic3—21no—
517C3⋊Dic3—21no—
518C3×Dic3—61no—
519C3×Dic3—61no—
520C3×Dic3—61no—
521C3×Dic3—61no—
522C3×Dic3—61no—
523#126—91no—
524#126—91no—
525#124—91no—
526#124(C3⋊D3)⋊C311yescharacteristic, complemented
527#123—91no—
528#123—91no—
529C22⋊Q8—91no—
530#121—91no—
531#121—91no—
532#121—91no—
533#120—91no—
534#120—91no—
535C4×D4—91no—
536C4×D4—91no—
537C2×C22⋊C4—91no—
538H(3,𝔽3)#53811yescharacteristic, complemented, Sylow
539C23×C3—31no—
540C23×C3—31no—
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—91no—
546C23×C3—91no—
547C23×C3—91no—
548C23×C3—182no—
549C23×C3—361no—
550C23×C3—361no—
551C23×C3C22×C3×D311yescharacteristic
552C23×C3C22×C3×D311yescharacteristic
553C22×D3—31no—
554C22×D3—31no—
555C22×D3—31no—
556C22×D3—62no—
557C22×D3—91no—
558C22×D3—91no—
559C22×D3—91no—
560C22×D3—121no—
561C22×D3—121no—
562C22×D3—182no—
563C22×D3—361no—
564C22×D3—361no—
565C3×Q8—41no—
566C3×Q8—121no—
567C3×Q8—121no—
568C3×Q8—122no—
569C3×D4—41no—
570C3×D4—121no—
571C3×D4—121no—
572C3×D4—122no—
573C3×D4—182no—
574C3×D4—182no—
575C3×D4—361no—
576C3×D4—361no—
577C3×D4—361no—
578C3×D4—361no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—91no—
595C2×C3×C4—91no—
596C2×C3×C4—91no—
597C2×C3×C4—91no—
598C2×C3×C4—91no—
599C2×C3×C4—361no—
600C2×C3×C4—361no—
601C2×C3×C4—361no—
602C2×C3×C4—361no—
603C2×C3×C4C22×C3×D311yescharacteristic
604C2×C3×C4C22×C3×D311yescharacteristic
605C2×C3×C4C22×C3×D311yescharacteristic
606C2×C3×C4C22×C3×D311yescharacteristic
607C2×C3×C4C22×C3×D311yescharacteristic
608#67—62no—
609#67—121no—
610#67—121no—
611#67—121no—
612#67—182no—
613#67—361no—
614#67—361no—
615#67—361no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—91no—
622C2×Dic3—91no—
623C2×Dic3—91no—
624C2×Dic3—91no—
625C2×Dic3—91no—
626C2×Dic3—121no—
627C2×Dic3—361no—
628D12—62no—
629D12—121no—
630D12—182no—
631D12—361no—
632C4×D3—121no—
633C4×D3—121no—
634C4×D3—121no—
635C4×D3—361no—
636C4×D3—361no—
637C4×D3—361no—
638C2×C32—21no—
639C2×C32—21no—
640C2×C32—21no—
641C2×C32—41no—
642C2×C32—41no—
643C2×C32—41no—
644C2×C32—41no—
645C2×C32—81no—
646C2×C32—81no—
647C2×C32#100411yescharacteristic
648C2×C32D3×#4111yescharacteristic
649C2×C32#100911yescharacteristic
650C2×C32C2×C3×#4111yescharacteristic
651C2×C32C3×H(5,𝔽2)11yescharacteristic
652C2×C32C3×H(5,𝔽2)11yescharacteristic
653C3⋊D3—22no—
654C3⋊D3—41no—
655C3⋊D3—41no—
656C3×D3—62no—
657C3×D3—121no—
658C3×D3—121no—
659C24—91no—
660C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic, complemented
661C2×D4—91no—
662C2×D4—91no—
663C2×D4—91no—
664C2×D4—91no—
665C2×D4—91no—
666C2×D4—91no—
667C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
668C22×C4—91no—
669C22×C4—91no—
670C22×C4—91no—
671C22×C4—91no—
672C4⋊C4—91no—
673C4⋊C4—91no—
674C4⋊C4—91no—
675C4⋊C4—91no—
676C4⋊C4—91no—
677C4⋊C4—91no—
678C22⋊C4—91no—
679C22⋊C4—91no—
680C22⋊C4—91no—
681C22⋊C4—91no—
682C22⋊C4—91no—
683C22⋊C4—91no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
689C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
690C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
691C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
692C42—91no—
693C42C2×(C3⋊D3)⋊C311yescharacteristic, complemented
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—31no—
701C22×C3—31no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—92no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3—181no—
726C22×C3—181no—
727C22×C3—181no—
728C22×C3—181no—
729C22×C3—181no—
730C22×C3—364no—
731C22×C3C23×C3×D311yescharacteristic
732C2×D3—32no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—92no—
742C2×D3—124no—
743C2×D3—181no—
744C2×D3—181no—
745C2×D3—181no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—181no—
751C2×D3—364no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—61no—
767C3×C4—62no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4—121no—
771C3×C4—121no—
772C3×C4—181no—
773C3×C4—181no—
774C3×C4—181no—
775C3×C4—181no—
776C3×C4—181no—
777Dic3—61no—
778Dic3—61no—
779Dic3—61no—
780Dic3—61no—
781Dic3—61no—
782Dic3—181no—
783Dic3—181no—
784Dic3—181no—
785Dic3—181no—
786Dic3—181no—
787C32—21no—
788C32#567811yescharacteristic, complemented
789C32C3×#53811yescharacteristic, complemented
790C23—91no—
791C23—91no—
792C23—91no—
793C23—182no—
794C23—361no—
795C23—361no—
796C23C22×(C3⋊D3)⋊C311yescharacteristic
797C23C22×(C3⋊D3)⋊C311yescharacteristic
798Q8—41no—
799D4—41no—
800D4—182no—
801D4—182no—
802D4—361no—
803D4—361no—
804D4—361no—
805D4—361no—
806C2×C4—91no—
807C2×C4—91no—
808C2×C4—91no—
809C2×C4—91no—
810C2×C4—91no—
811C2×C4—361no—
812C2×C4—361no—
813C2×C4—361no—
814C2×C4—361no—
815C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
816C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
817C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
818C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
819C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
820C2×C3—31no—
821C2×C3—31no—
822C2×C3—31no—
823C2×C3—31no—
824C2×C3—31no—
825C2×C3—31no—
826C2×C3—41no—
827C2×C3—41no—
828C2×C3—61no—
829C2×C3—61no—
830C2×C3—61no—
831C2×C3—121no—
832C2×C3—121no—
833C2×C3—121no—
834C2×C3—121no—
835C2×C3—182no—
836C2×C3—241no—
837C2×C3—241no—
838C2×C3—361no—
839C2×C3—361no—
840C2×C3C3×#100411yescharacteristic
841C2×C3C3×D3×#4111yescharacteristic
842C2×C3C3×#100911yescharacteristic
843D3—62no—
844D3—121no—
845D3—121no—
846D3—182no—
847D3—361no—
848D3—361no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—92no—
856C22—181no—
857C22—181no—
858C22—181no—
859C22—181no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—364no—
865C22C23×(C3⋊D3)⋊C311yescharacteristic
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—181no—
872C4—181no—
873C4—181no—
874C4—181no—
875C4—181no—
876C3—31no—
877C3—31no—
878C3—61no—
879C3C3×#567811yescharacteristic
880C2—41no—
881C2—41no—
882C2—182no—
883C2—361no—
884C2—361no—
885C2#64361⋊C311yescharacteristic
886C2#41×(C3⋊D3)⋊C311yescharacteristic
887C2#1172263811yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#124C2
hypercenter#124(C3⋊D3)⋊C3
hypocenterC32C3×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#124C2semidirect
2. #64156⋊C3C2semidirect
3. #64155⋊C3C2semidirect
4. #64148⋊C3C2semidirect
5. #64146⋊C3C2semidirect
6. #64095⋊C3C2semidirect
7. #64093⋊C3C2semidirect
8. #64093⋊C3C2semidirect
9. #64092⋊C3C2semidirect
10. #64091⋊C3C2semidirect
11. #64090⋊C3C2semidirect
12. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
13. #64088⋊C3C2semidirect
14. #11721387C2semidirect
15. C4×C4⋊((C3⋊D3)⋊C3)C2semidirect
16. #10596149C3semidirect
19. C2×Q8×H(3,𝔽3)C22semidirect
24. C2×#638⋊C3C22semidirect
25. C22×(C3⋊Dic3)⋊C3C22semidirect
30. C2×C4×(C3⋊D3)⋊C3C22semidirect
33. C22⋊C4×H(3,𝔽3)C22semidirect
34. C22⋊C4×H(3,𝔽3)C22semidirect
35. C42×H(3,𝔽3)C22semidirect
44. #3752⋊C3C22semidirect
45. #3752⋊C3C22semidirect
46. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
47. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
48. #3750⋊C3C22semidirect
49. #3750⋊C3C22semidirect
50. #3750⋊C3C22semidirect
51. #3750⋊C3C22semidirect
52. C4×(C3⋊Dic3)⋊C3C22semidirect
54. C32×#124D3semidirect
55. C32×#124C2×C3semidirect
56. #64156C2×C3semidirect
57. #64155C2×C3semidirect
58. #64148C2×C3semidirect
59. #64146C2×C3semidirect
60. #64095C2×C3semidirect
61. #64093C2×C3semidirect
62. #64093C2×C3semidirect
63. #64092C2×C3semidirect
64. #64091C2×C3semidirect
65. #64090C2×C3semidirect
66. C22⋊C4×C3⋊D3C2×C3semidirect
67. #64088C2×C3semidirect
68. #64085C2×C3semidirect
69. C4×C4⋊(C3⋊D3)C2×C3semidirect
120. C2×C32×Q8C2×D3semidirect
121. C2×C32×Q8C22×C3semidirect
128. C2×#638C22×C3semidirect
129. C22×C3⋊Dic3C22×C3semidirect
134. C2×C4×C3⋊D3C22×C3semidirect
151. C32×C22⋊C4C2×D3semidirect
152. C32×C22⋊C4C2×D3semidirect
155. C32×C22⋊C4C22×C3semidirect
156. C32×C22⋊C4C22×C3semidirect
158. C32×C42C2×D3semidirect
159. C32×C42C22×C3semidirect
168. #3752C22×C3semidirect
169. #3752C22×C3semidirect
170. C4⋊(C3⋊Dic3)C22×C3semidirect
171. C4⋊(C3⋊Dic3)C22×C3semidirect
172. #3750C22×C3semidirect
173. #3750C22×C3semidirect
174. #3750C22×C3semidirect
175. #3750C22×C3semidirect
176. C4×C3⋊Dic3C22×C3semidirect
526. #124(C3⋊D3)⋊C3semidirect
538. H(3,𝔽3)#538semidirect
660. C2×Q8C2×(C3⋊D3)⋊C3semidirect
690. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
691. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
693. C42C2×(C3⋊D3)⋊C3semidirect
788. C32#5678semidirect
789. C32C3×#538semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×#1242
#64156⋊C32
#64155⋊C32
#64148⋊C32
#64146⋊C32
#64095⋊C32
#64093⋊C32
#64092⋊C32
#64091⋊C32
#64090⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#64088⋊C32
#117213872
C4×C4⋊((C3⋊D3)⋊C3)2
#105961493
C3×#56783