Finite Group Databasebeta

← #10596132⋊C3 #13153051

Subgroups — #10596132⋊C3 #13153051

Order 1728.

911 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#123C211yesmaximal, characteristic, complemented
2#64148⋊C3C211yesmaximal, characteristic, complemented
3#64147⋊C3C211yesmaximal, characteristic, complemented
4C4×#638⋊C3C211yesmaximal, characteristic, complemented
5C4×#638⋊C3C211yesmaximal, characteristic, complemented
6#64107⋊C3C211yesmaximal, characteristic, complemented
7#64102⋊C3C211yesmaximal, characteristic, complemented
8C4⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
9#64098⋊C3C211yesmaximal, characteristic, complemented
10#64093⋊C3C211yesmaximal, characteristic, complemented
11#64093⋊C3C211yesmaximal, characteristic, complemented
12#64092⋊C3C211yesmaximal, characteristic, complemented
13#64090⋊C3C211yesmaximal, characteristic, complemented
14#64088⋊C3C211yesmaximal, characteristic, complemented
15#64086⋊C3C211yesmaximal, characteristic, complemented
16#10596132C311yesmaximal, characteristic, complemented
17C3×#5661—31nomaximal
18C2×D4×H(3,𝔽3)C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
25C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
29C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
30C4⋊C4×H(3,𝔽3)C2211yescharacteristic
31C4⋊C4×H(3,𝔽3)C2211yescharacteristic
32C22⋊C4×H(3,𝔽3)C2211yescharacteristic
33C22⋊C4×H(3,𝔽3)C2211yescharacteristic
34C22⋊C4×H(3,𝔽3)C2211yescharacteristic
35#3757⋊C3C2211yescharacteristic
36#3757⋊C3C2211yescharacteristic
37#3757⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic
42C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
43C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
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×#123—21no—
54C32×#123D311yescharacteristic, complemented
55C32×#123C2×C311yescharacteristic, complemented
56#64148C2×C311yescharacteristic, complemented
57#64147C2×C311yescharacteristic, complemented
58C4×#638C2×C311yescharacteristic, complemented
59C4×#638C2×C311yescharacteristic, complemented
60#64107C2×C311yescharacteristic, complemented
61#64102C2×C311yescharacteristic, complemented
62C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
63#64098C2×C311yescharacteristic, complemented
64#64093C2×C311yescharacteristic, complemented
65#64093C2×C311yescharacteristic, complemented
66#64092C2×C311yescharacteristic, complemented
67#64090C2×C311yescharacteristic, complemented
68#64088C2×C311yescharacteristic, complemented
69#64086C2×C311yescharacteristic, complemented
70C3×#939—31no—
71C3×#938—31no—
72C3×C4×#67—31no—
73C3×C4×#67—31no—
74C3×#898—31no—
75C3×#893—31no—
76C3×D3×C4⋊C4—31no—
77C3×#889—31no—
78C3×#884—31no—
79C3×#884—31no—
80C3×#883—31no—
81C3×#67⋊C4—31no—
82C3×#879—31no—
83C3×#877—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C23×H(3,𝔽3)C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88D4×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
95#638⋊C3—22no—
96#638⋊C3—22no—
97#638⋊C3—22no—
98#638⋊C3—41no—
99C2×(C3⋊Dic3)⋊C3—22no—
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C4⋊((C3⋊D3)⋊C3)—22no—
107C4×(C3⋊D3)⋊C3—22no—
108C4×(C3⋊D3)⋊C3—41no—
109C4×(C3⋊D3)⋊C3—41no—
110C4×(C3⋊D3)⋊C3—41no—
111C3×#553—91no—
112#5661—31no—
113#5661—91no—
114C2×C32×D4—21no—
115C2×C32×D4C2×D311yescharacteristic
116C2×C32×D4C22×C311yescharacteristic
117C22×C32×C4—21no—
118C22×C32×C4C2×D311yescharacteristic
119C22×C32×C4C22×C311yescharacteristic
120C2×#638C22×C311yescharacteristic
121C2×#638C22×C311yescharacteristic
122C2×#638C22×C311yescharacteristic
123C2×#638C22×C311yescharacteristic
124C22×C3⋊Dic3C22×C311yescharacteristic
125C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
126C2×C4×C3⋊D3C22×C311yescharacteristic
127C2×C4×C3⋊D3C22×C311yescharacteristic
128C2×C4×C3⋊D3C22×C311yescharacteristic
129C2×C4×C3⋊D3C22×C311yescharacteristic
130C2×C3×#67—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C22×C3×Dic3—31no—
135C2×C3×D12—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C32×C4⋊C4—21no—
141C32×C4⋊C4—21no—
142C32×C4⋊C4C2×D311yescharacteristic
143C32×C4⋊C4C2×D311yescharacteristic
144C32×C4⋊C4C22×C311yescharacteristic
145C32×C4⋊C4C22×C311yescharacteristic
146C32×C22⋊C4—21no—
147C32×C22⋊C4—21no—
148C32×C22⋊C4—21no—
149C32×C22⋊C4C2×D311yescharacteristic
150C32×C22⋊C4C2×D311yescharacteristic
151C32×C22⋊C4C2×D311yescharacteristic
152C32×C22⋊C4C22×C311yescharacteristic
153C32×C22⋊C4C22×C311yescharacteristic
154C32×C22⋊C4C22×C311yescharacteristic
155#3757C22×C311yescharacteristic
156#3757C22×C311yescharacteristic
157#3757C22×C311yescharacteristic
158#3752C22×C311yescharacteristic
159#3752C22×C311yescharacteristic
160#3752C22×C311yescharacteristic
161#3752C22×C311yescharacteristic
162C4⋊(C3⋊Dic3)C22×C311yescharacteristic
163C4⋊(C3⋊Dic3)C22×C311yescharacteristic
164#3750C22×C311yescharacteristic
165#3750C22×C311yescharacteristic
166#3750C22×C311yescharacteristic
167#3750C22×C311yescharacteristic
168#3750C22×C311yescharacteristic
169#3750C22×C311yescharacteristic
170C4×C3⋊Dic3C22×C311yescharacteristic
171C4×C3⋊Dic3C22×C311yescharacteristic
172C4×C3⋊Dic3C22×C311yescharacteristic
173C3×#217—31no—
174C3×#217—31no—
175C3×#217—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×C4×Dic3—31no—
189C3×C4×Dic3—31no—
190C3×C4×Dic3—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)—21no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)—21no—
197C22×H(3,𝔽3)C2411yescharacteristic
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#4112yes—
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—
209(C3⋊Dic3)⋊C3—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#4112yes—
215C3×#126—91no—
216C3×#126—91no—
217C3×#125—91no—
218C3×#123—31no—
219C3×#123—31no—
220C3×#123—61no—
221C3×#123—91no—
222C3×#123C3×D311yescharacteristic
223C3×#121—91no—
224C3×#121—91no—
225C3×#121—91no—
226C3×#121—91no—
227C3×C4×D4—91no—
228C3×C4×D4—91no—
229C3×C4×D4—91no—
230C3×C4×D4—91no—
231C3×#117—91no—
232C2×C3×C4⋊C4—91no—
233#939—31no—
234#939—91no—
235#938—31no—
236#938—91no—
237C4×#67—31no—
238C4×#67—31no—
239C4×#67—91no—
240C4×#67—91no—
241#898—31no—
242#898—91no—
243#893—31no—
244#893—91no—
245D3×C4⋊C4—31no—
246D3×C4⋊C4—91no—
247#889—31no—
248#889—91no—
249#884—31no—
250#884—31no—
251#884—91no—
252#884—91no—
253#883—31no—
254#883—91no—
255#67⋊C4—31no—
256#67⋊C4—91no—
257#879—31no—
258#879—91no—
259#877—31no—
260#877—91no—
261C23×C32—21no—
262C23×C32—21no—
263C23×C32C22×D311yescharacteristic
264C23×C32C22×D311yescharacteristic
265C23×C32C23×C311yescharacteristic
266C23×C32C23×C311yescharacteristic
267C22×C3⋊D3C23×C311yescharacteristic
268C22×C3⋊D3C23×C311yescharacteristic
269C22×C3×D3—31no—
270C22×C3×D3—31no—
271C32×D4—41no—
272C32×D4—41no—
273C32×D4—42no—
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×C4C23×C311yescharacteristic
288C2×C32×C4C23×C311yescharacteristic
289C2×C32×C4C23×C311yescharacteristic
290C2×C32×C4C23×C311yescharacteristic
291C2×C32×C4C23×C311yescharacteristic
292#638—22no—
293#638—22no—
294#638—22no—
295#638—41no—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3C23×C311yescharacteristic
298C2×C3⋊Dic3C23×C311yescharacteristic
299C2×C3⋊Dic3C23×C311yescharacteristic
300C2×C3⋊Dic3C23×C311yescharacteristic
301C2×C3⋊Dic3C23×C311yescharacteristic
302C2×C3⋊Dic3C23×C311yescharacteristic
303C4⋊(C3⋊D3)—22no—
304C4×C3⋊D3—22no—
305C4×C3⋊D3—41no—
306C4×C3⋊D3—41no—
307C4×C3⋊D3—41no—
308C3×#67—62no—
309C3×#67—62no—
310C3×#67—62no—
311C3×#67—121no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—62no—
319C3×D12—62no—
320C3×C4×D3—62no—
321C3×C4×D3—121no—
322C3×C4×D3—121no—
323C3×C4×D3—121no—
324#553—91noSylow
325C2×H(3,𝔽3)—41no—
326C2×H(3,𝔽3)—41no—
327C2×H(3,𝔽3)C2×#4111yescharacteristic
328C2×H(3,𝔽3)C2×#4111yescharacteristic
329C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
330(C3⋊D3)⋊C3—22no—
331(C3⋊D3)⋊C3—41no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C2×C3×D4—91no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C2×C3×D4—91no—
340C2×C3×D4C2×C3×D311yescharacteristic
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—61no—
344C22×C3×C4—91no—
345C22×C3×C4—91no—
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—31no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C22×Dic3—31no—
359C22×Dic3—91no—
360C2×D12—31no—
361C2×D12—91no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×C4×D3—91no—
369C2×C4×D3—91no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4—91no—
377C3×C4⋊C4—91no—
378C3×C4⋊C4—91no—
379C3×C4⋊C4—91no—
380C3×C4⋊C4—91no—
381C3×C4⋊C4—91no—
382C3×C4⋊C4—91no—
383C3×C4⋊C4—91no—
384C3×C4⋊C4C2×C3×D311yescharacteristic
385C3×C4⋊C4C2×C3×D311yescharacteristic
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—61no—
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⋊C4C2×C3×D311yescharacteristic
403C3×C22⋊C4C2×C3×D311yescharacteristic
404C3×C22⋊C4C2×C3×D311yescharacteristic
405C3×C42—91no—
406C3×C42—91no—
407C3×C42—91no—
408#217—31no—
409#217—31no—
410#217—31no—
411#217—91no—
412#217—91no—
413#217—91no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422C4⋊Dic3—31no—
423C4⋊Dic3—31no—
424C4⋊Dic3—91no—
425C4⋊Dic3—91no—
426Dic3⋊C4—31no—
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429Dic3⋊C4—31no—
430Dic3⋊C4—31no—
431Dic3⋊C4—31no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438C4×Dic3—31no—
439C4×Dic3—31no—
440C4×Dic3—31no—
441C4×Dic3—91no—
442C4×Dic3—91no—
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—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C23×D311yescharacteristic
464C22×C32C24×C311yescharacteristic
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3C3×#4112yes—
471C2×C3×D3—32no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
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⋊Dic3C3×#4112yes—
498C3×Dic3—32no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504#126—91no—
505#126—91no—
506#125—91no—
507#123—91no—
508#123(C3⋊D3)⋊C311yescharacteristic, complemented
509#121—91no—
510#121—91no—
511#121—91no—
512#121—91no—
513C4×D4—91no—
514C4×D4—91no—
515C4×D4—91no—
516C4×D4—91no—
517#117—91no—
518C2×C4⋊C4—91no—
519H(3,𝔽3)#55311yescharacteristic, complemented, Sylow
520C23×C3—31no—
521C23×C3—31no—
522C23×C3—31no—
523C23×C3—31no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—91no—
527C23×C3—91no—
528C23×C3C22×C3×D311yescharacteristic
529C23×C3C22×C3×D311yescharacteristic
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—91no—
533C22×D3—91no—
534C3×D4—41no—
535C3×D4—121no—
536C3×D4—121no—
537C3×D4—122no—
538C3×D4—182no—
539C3×D4—182no—
540C3×D4—182no—
541C3×D4—182no—
542C3×D4—361no—
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—41no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—91no—
560C2×C3×C4—91no—
561C2×C3×C4—91no—
562C2×C3×C4—91no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—121no—
566C2×C3×C4—121no—
567C2×C3×C4—122no—
568C2×C3×C4—182no—
569C2×C3×C4—182no—
570C2×C3×C4—361no—
571C2×C3×C4—361no—
572C2×C3×C4—361no—
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—62no—
579#67—62no—
580#67—62no—
581#67—121no—
582#67—182no—
583#67—182no—
584#67—182no—
585#67—361no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—62no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—182no—
600D12—62no—
601D12—182no—
602C4×D3—62no—
603C4×D3—121no—
604C4×D3—121no—
605C4×D3—121no—
606C4×D3—182no—
607C4×D3—361no—
608C4×D3—361no—
609C4×D3—361no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—42no—
614C2×C32—41no—
615C2×C32—41no—
616C2×C32—41no—
617C2×C32—41no—
618C2×C32—81no—
619C2×C32#100411yescharacteristic
620C2×C32D3×#4111yescharacteristic
621C2×C32D3×#4111yescharacteristic
622C2×C32C2×C3×#4111yescharacteristic
623C2×C32C2×C3×#4111yescharacteristic
624C2×C32C3×H(5,𝔽2)11yescharacteristic
625C3⋊D3—22no—
626C3⋊D3—41no—
627C3×D3—62no—
628C3×D3—121no—
629C2×D4—91no—
630C2×D4—91no—
631C2×D4—91no—
632C2×D4—91no—
633C2×D4—91no—
634C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
635C22×C4—91no—
636C22×C4—91no—
637C22×C4—91no—
638C22×C4—91no—
639C22×C4—91no—
640C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
641C4⋊C4—91no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—91no—
645C4⋊C4—91no—
646C4⋊C4—91no—
647C4⋊C4—91no—
648C4⋊C4—91no—
649C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
650C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
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
660C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
661C42—91no—
662C42—91no—
663C42—91no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—31no—
671C22×C3—31no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—62no—
685C22×C3—61no—
686C22×C3—92no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3C23×C3×D311yescharacteristic
698C2×D3—32no—
699C2×D3—61no—
700C2×D3—61no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—92no—
705C2×D3—181no—
706C2×D3—181no—
707C2×D3—181no—
708C2×D3—181no—
709C2×D3—181no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—61no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—61no—
724C3×C4—61no—
725C3×C4—92no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4—181no—
732C3×C4—181no—
733C3×C4—181no—
734C3×C4—181no—
735C3×C4—181no—
736Dic3—32no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—92no—
743Dic3—181no—
744Dic3—181no—
745Dic3—181no—
746Dic3—181no—
747Dic3—181no—
748C32—21no—
749C32#566111yescharacteristic, complemented
750C32C3×#55311yescharacteristic, complemented
751C23—91no—
752C23—91no—
753C23C22×(C3⋊D3)⋊C311yescharacteristic
754C23C22×(C3⋊D3)⋊C311yescharacteristic
755D4—41no—
756D4—182no—
757D4—182no—
758D4—182no—
759D4—182no—
760D4—361no—
761C2×C4—41no—
762C2×C4—91no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—91no—
768C2×C4—182no—
769C2×C4—182no—
770C2×C4—361no—
771C2×C4—361no—
772C2×C4—361no—
773C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
774C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
775C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
776C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
777C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
778C2×C3—31no—
779C2×C3—31no—
780C2×C3—31no—
781C2×C3—31no—
782C2×C3—31no—
783C2×C3—31no—
784C2×C3—41no—
785C2×C3—41no—
786C2×C3—61no—
787C2×C3—61no—
788C2×C3—61no—
789C2×C3—121no—
790C2×C3—121no—
791C2×C3—121no—
792C2×C3—121no—
793C2×C3—122no—
794C2×C3—182no—
795C2×C3—241no—
796C2×C3—361no—
797C2×C3C3×#100411yescharacteristic
798C2×C3C3×D3×#4111yescharacteristic
799C2×C3C3×D3×#4111yescharacteristic
800D3—62no—
801D3—121no—
802D3—182no—
803D3—361no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—92no—
811C22—181no—
812C22—181no—
813C22—181no—
814C22—181no—
815C22—181no—
816C22C23×(C3⋊D3)⋊C311yescharacteristic
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—92no—
823C4—181no—
824C4—181no—
825C4—181no—
826C4—181no—
827C4—181no—
828C3—31no—
829C3—31no—
830C3—61no—
831C3C3×#566111yescharacteristic
832C2—41no—
833C2—41no—
834C2—182no—
835C2—361no—
836C2#64361⋊C311yescharacteristic
837C2#41×(C3⋊D3)⋊C311yescharacteristic
838C2#41×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#123C2
hypercenter#123(C3⋊D3)⋊C3
hypocenterC32C3×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#123C2semidirect
2. #64148⋊C3C2semidirect
3. #64147⋊C3C2semidirect
4. C4×#638⋊C3C2semidirect
5. C4×#638⋊C3C2semidirect
6. #64107⋊C3C2semidirect
7. #64102⋊C3C2semidirect
8. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
9. #64098⋊C3C2semidirect
10. #64093⋊C3C2semidirect
11. #64093⋊C3C2semidirect
12. #64092⋊C3C2semidirect
13. #64090⋊C3C2semidirect
14. #64088⋊C3C2semidirect
15. #64086⋊C3C2semidirect
16. #10596132C3semidirect
54. C32×#123D3semidirect
55. C32×#123C2×C3semidirect
56. #64148C2×C3semidirect
57. #64147C2×C3semidirect
58. C4×#638C2×C3semidirect
59. C4×#638C2×C3semidirect
60. #64107C2×C3semidirect
61. #64102C2×C3semidirect
62. C4⋊C4×C3⋊D3C2×C3semidirect
63. #64098C2×C3semidirect
64. #64093C2×C3semidirect
65. #64093C2×C3semidirect
66. #64092C2×C3semidirect
67. #64090C2×C3semidirect
68. #64088C2×C3semidirect
69. #64086C2×C3semidirect
508. #123(C3⋊D3)⋊C3semidirect
519. H(3,𝔽3)#553semidirect
749. C32#5661semidirect
750. C32C3×#553semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×#1232
#64148⋊C32
#64147⋊C32
C4×#638⋊C32
#64107⋊C32
#64102⋊C32
C4⋊C4×(C3⋊D3)⋊C32
#64098⋊C32
#64093⋊C32
#64092⋊C32
#64090⋊C32
#64088⋊C32
#64086⋊C32
#105961323
C3×#56613