Finite Group Databasebeta

← #10596101⋊C3 #13152955

Subgroups — #10596101⋊C3 #13152955

Order 1728.

1243 conjugacy classes of subgroups.

The subgroup lattice has 689 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88722C211yesmaximal, characteristic, complemented
2C22×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×C22⋊Q8C211yesmaximal, characteristic, complemented
4#64156⋊C3C211yesmaximal, characteristic, complemented
5C4×#638⋊C3C211yesmaximal, characteristic, complemented
6#64104⋊C3C211yesmaximal, characteristic, complemented
7#64104⋊C3C212yesmaximal, complemented
8#64103⋊C3C212yesmaximal, complemented
9#64102⋊C3C211yesmaximal, characteristic, complemented
10#64091⋊C3C212yesmaximal, complemented
11C22⋊C4×(C3⋊D3)⋊C3C212yesmaximal, complemented
12#10596101C311yesmaximal, characteristic, complemented
13C3×#5630—31nomaximal
14C23×(C3⋊D3)⋊C3C2212yes—
15C2×Q8×H(3,𝔽3)C2211yescharacteristic, complemented
16C22×C4×H(3,𝔽3)C2211yescharacteristic
17C2×#638⋊C3C2211yescharacteristic
18#88722—24no—
19C2×C4⋊((C3⋊D3)⋊C3)—24no—
20C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
21C2×C4⋊((C3⋊D3)⋊C3)C2212yes—
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
23C2×C4⋊((C3⋊D3)⋊C3)C2212yescomplemented
24C2×C4⋊((C3⋊D3)⋊C3)C2212yescomplemented
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
26C2×C4×(C3⋊D3)⋊C3C2212yescomplemented
27C2×C4×(C3⋊D3)⋊C3C2212yescomplemented
28C4⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
29C4⋊C4×H(3,𝔽3)C2212yescomplemented
30C22⋊C4×H(3,𝔽3)C2212yes—
31#3757⋊C3C2211yescharacteristic
32#3752⋊C3C2211yescharacteristic, complemented
33#3752⋊C3C2212yescomplemented
34#3752⋊C3C2212yescomplemented
35#3752⋊C3C2212yescomplemented
36#3752⋊C3C2212yescomplemented
37#3750⋊C3C2211yescharacteristic, complemented
38C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
39C2×#3832C2×C311yescharacteristic, complemented
40C22×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
41C2×C3×#239—31no—
42C22×C3×D12—31no—
43C32×C22⋊Q8—21no—
44C32×C22⋊Q8D311yescharacteristic, complemented
45C32×C22⋊Q8C2×C311yescharacteristic, complemented
46#64156C2×C311yescharacteristic, complemented
47C4×#638C2×C311yescharacteristic, complemented
48#64104C2×C311yescharacteristic, complemented
49#64104C2×C312yescomplemented
50#64103C2×C312yescomplemented
51#64102C2×C311yescharacteristic, complemented
52#64091C2×C312yescomplemented
53C22⋊C4×C3⋊D3C2×C312yescomplemented
54C3×#947—31no—
55C3×C4×#67—31no—
56C3×#895—31no—
57C3×#895—32no—
58C3×#894—32no—
59C3×#893—31no—
60C3×#882—32no—
61C3×D3×C22⋊C4—32no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×(C3⋊D3)⋊C3—24no—
64C22×(C3⋊D3)⋊C3—24no—
65C22×(C3⋊D3)⋊C3—42no—
66C22×(C3⋊D3)⋊C3C2312yes—
67C22×(C3⋊D3)⋊C3C2311yescharacteristic
68C22×(C3⋊D3)⋊C3C2312yes—
69Q8×H(3,𝔽3)—22no—
70C2×C4×H(3,𝔽3)—22no—
71C2×C4×H(3,𝔽3)C2312yes—
72C2×C4×H(3,𝔽3)C2312yes—
73C2×C4×H(3,𝔽3)C2311yescharacteristic
74C2×C4×H(3,𝔽3)C2311yescharacteristic
75#638⋊C3—22no—
76C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
77C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C4⋊((C3⋊D3)⋊C3)—24no—
80C4⋊((C3⋊D3)⋊C3)—24no—
81C4⋊((C3⋊D3)⋊C3)—22no—
82C4⋊((C3⋊D3)⋊C3)—42no—
83C4⋊((C3⋊D3)⋊C3)D414yescomplemented
84C4×(C3⋊D3)⋊C3—24no—
85C4×(C3⋊D3)⋊C3—22no—
86C4×(C3⋊D3)⋊C3—42no—
87C3×#546—91no—
88#5630—31no—
89#5630—91no—
90C23×C3⋊D3C22×C312yes—
91C23×C3×D3—32no—
92C2×C32×Q8—21no—
93C2×C32×Q8C2×D311yescharacteristic, complemented
94C2×C32×Q8C22×C311yescharacteristic, complemented
95C22×C32×C4—21no—
96C22×C32×C4C2×D311yescharacteristic
97C22×C32×C4C22×C311yescharacteristic
98C2×#638C22×C311yescharacteristic
99#3832—24no—
100C2×C4⋊(C3⋊D3)—24no—
101C2×C4⋊(C3⋊D3)C22×C312yes—
102C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
103C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
104C2×C4⋊(C3⋊D3)C22×C312yescomplemented
105C2×C4⋊(C3⋊D3)C22×C312yescomplemented
106C2×C4×C3⋊D3C22×C312yescomplemented
107C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
108C2×C4×C3⋊D3C22×C312yescomplemented
109C2×C3×#67—31no—
110C3×#239—64no—
111C2×C3×D12—31no—
112C2×C3×D12—32no—
113C2×C3×D12—32no—
114C2×C3×D12—31no—
115C2×C3×D12—32no—
116C2×C3×D12—64no—
117C2×C3×C4×D3—32no—
118C2×C3×C4×D3—31no—
119C2×C3×C4×D3—32no—
120C32×C4⋊C4—21no—
121C32×C4⋊C4—22no—
122C32×C4⋊C4C2×D311yescharacteristic, complemented
123C32×C4⋊C4C2×D312yescomplemented
124C32×C4⋊C4C22×C311yescharacteristic, complemented
125C32×C4⋊C4C22×C312yescomplemented
126C32×C22⋊C4—22no—
127C32×C22⋊C4C2×D312yes—
128C32×C22⋊C4C22×C312yes—
129#3757C22×C311yescharacteristic
130#3752C22×C312yescomplemented
131#3752C22×C312yescomplemented
132#3752C22×C312yescomplemented
133#3752C22×C312yescomplemented
134#3752C22×C311yescharacteristic, complemented
135#3750C22×C311yescharacteristic, complemented
136C4×C3⋊Dic3C22×C311yescharacteristic, complemented
137C3×#217—31no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—31no—
143C3×Dic3⋊C4—31no—
144C3×C4×Dic3—31no—
145C22×H(3,𝔽3)—21no—
146C22×H(3,𝔽3)—21no—
147C22×H(3,𝔽3)#4112yescomplemented
148C22×H(3,𝔽3)C2411yescharacteristic
149C2×(C3⋊D3)⋊C3—22no—
150C2×(C3⋊D3)⋊C3—22no—
151C2×(C3⋊D3)⋊C3—21no—
152C2×(C3⋊D3)⋊C3—22no—
153C2×(C3⋊D3)⋊C3—21no—
154C2×(C3⋊D3)⋊C3—22no—
155C2×(C3⋊D3)⋊C3—21no—
156C2×(C3⋊D3)⋊C3—22no—
157C2×(C3⋊D3)⋊C3—48no—
158C2×(C3⋊D3)⋊C3C2×D414yes—
159C4×H(3,𝔽3)—22no—
160C4×H(3,𝔽3)—21no—
161C4×H(3,𝔽3)—22no—
162C4×H(3,𝔽3)C2×D412yes—
163(C3⋊Dic3)⋊C3—21no—
164(C3⋊Dic3)⋊C3—21no—
165(C3⋊Dic3)⋊C3—21no—
166C2×C3×#41—91no—
167C22×C3×D4—91no—
168C2×#239—31no—
169C2×#239—91no—
170C22×D12—31no—
171C22×D12—91no—
172C3×#124—91no—
173C3×#123—92no—
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8—61no—
177C3×C22⋊Q8C3×D311yescharacteristic
178C3×#121—91no—
179C3×#121—92no—
180C3×#120—92no—
181C3×C4×D4—91no—
182C3×C4×D4—91no—
183C2×C3×C22⋊C4—92no—
184#947—31no—
185#947—91no—
186C4×#67—31no—
187C4×#67—91no—
188#895—31no—
189#895—32no—
190#895—91no—
191#895—92no—
192#894—32no—
193#894—92no—
194#893—31no—
195#893—91no—
196#882—32no—
197#882—92no—
198D3×C22⋊C4—32no—
199D3×C22⋊C4—92no—
200C23×C32—21no—
201C23×C32C22×D311yescharacteristic
202C23×C32C23×C311yescharacteristic
203C22×C3⋊D3—24no—
204C22×C3⋊D3—24no—
205C22×C3⋊D3—42no—
206C22×C3⋊D3C23×C312yes—
207C22×C3⋊D3C23×C311yescharacteristic
208C22×C3⋊D3C23×C312yes—
209C22×C3×D3—32no—
210C22×C3×D3—32no—
211C22×C3×D3—31no—
212C22×C3×D3—64no—
213C22×C3×D3—64no—
214C22×C3×D3—122no—
215C32×Q8—22no—
216C32×Q8—22no—
217C32×Q8—42no—
218C2×C32×C4—22no—
219C2×C32×C4—22no—
220C2×C32×C4—21no—
221C2×C32×C4—22no—
222C2×C32×C4—22no—
223C2×C32×C4—21no—
224C2×C32×C4—42no—
225C2×C32×C4C22×D311yescharacteristic
226C2×C32×C4C22×D312yes—
227C2×C32×C4C22×D312yes—
228C2×C32×C4C22×D311yescharacteristic
229C2×C32×C4C23×C311yescharacteristic
230C2×C32×C4C23×C312yes—
231C2×C32×C4C23×C312yes—
232C2×C32×C4C23×C311yescharacteristic
233#638—22no—
234C2×C3⋊Dic3C23×C311yescharacteristic
235C2×C3⋊Dic3C23×C311yescharacteristic
236C2×C3⋊Dic3C23×C311yescharacteristic
237C4⋊(C3⋊D3)—24no—
238C4⋊(C3⋊D3)—24no—
239C4⋊(C3⋊D3)—22no—
240C4⋊(C3⋊D3)—42no—
241C4⋊(C3⋊D3)C3×D414yescomplemented
242C4×C3⋊D3—24no—
243C4×C3⋊D3—22no—
244C4×C3⋊D3—42no—
245C3×#67—62no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3—31no—
248C2×C3×Dic3—31no—
249C3×D12—34no—
250C3×D12—64no—
251C3×D12—64no—
252C3×D12—62no—
253C3×D12—122no—
254C3×C4×D3—64no—
255C3×C4×D3—62no—
256C3×C4×D3—122no—
257#546—91noSylow
258C2×H(3,𝔽3)—22no—
259C2×H(3,𝔽3)C22×D411yescharacteristic
260C2×H(3,𝔽3)C2×#4111yescharacteristic
261C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
262(C3⋊D3)⋊C3—24no—
263(C3⋊D3)⋊C3—41no—
264(C3⋊D3)⋊C3—42no—
265C24×C3—92no—
266C23×D3—32no—
267C23×D3—92no—
268C3×#41—184no—
269C2×C3×Q8—31no—
270C2×C3×Q8—31no—
271C2×C3×Q8—61no—
272C2×C3×Q8C2×C3×D311yescharacteristic
273C2×C3×D4—91no—
274C2×C3×D4—92no—
275C2×C3×D4—92no—
276C2×C3×D4—91no—
277C2×C3×D4—92no—
278C2×C3×D4—91no—
279C2×C3×D4—184no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—61no—
283C22×C3×C4—92no—
284C22×C3×C4—91no—
285C22×C3×C4—92no—
286C22×C3×C4C2×C3×D311yescharacteristic
287C2×#67—31no—
288C2×#67—91no—
289#239—64no—
290#239—184no—
291C2×D12—31no—
292C2×D12—32no—
293C2×D12—32no—
294C2×D12—31no—
295C2×D12—32no—
296C2×D12—64no—
297C2×D12—91no—
298C2×D12—92no—
299C2×D12—92no—
300C2×D12—91no—
301C2×D12—92no—
302C2×D12—184no—
303C2×C4×D3—32no—
304C2×C4×D3—31no—
305C2×C4×D3—32no—
306C2×C4×D3—92no—
307C2×C4×D3—91no—
308C2×C4×D3—92no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—32no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—32no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—62no—
315C3×C4⋊C4—91no—
316C3×C4⋊C4C2×C3×D311yescharacteristic
317C3×C4⋊C4C2×C3×D312yes—
318C3×C22⋊C4—32no—
319C3×C22⋊C4—32no—
320C3×C22⋊C4—62no—
321C3×C22⋊C4—92no—
322C3×C22⋊C4—92no—
323C3×C22⋊C4—92no—
324C3×C22⋊C4—91no—
325C3×C22⋊C4—92no—
326C3×C22⋊C4—91no—
327C3×C22⋊C4C2×C3×D312yes—
328C3×C42—91no—
329#217—31no—
330#217—91no—
331(C2×D3)⋊C4—32no—
332(C2×D3)⋊C4—32no—
333(C2×D3)⋊C4—32no—
334(C2×D3)⋊C4—32no—
335(C2×D3)⋊C4—31no—
336(C2×D3)⋊C4—92no—
337(C2×D3)⋊C4—92no—
338(C2×D3)⋊C4—92no—
339(C2×D3)⋊C4—92no—
340(C2×D3)⋊C4—91no—
341Dic3⋊C4—31no—
342Dic3⋊C4—91no—
343C4×Dic3—31no—
344C4×Dic3—91no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—22no—
351C22×C32—41no—
352C22×C32—41no—
353C22×C32#23912yescomplemented
354C22×C32C3×#4112yescomplemented
355C22×C32C23×D311yescharacteristic
356C22×C32C24×C311yescharacteristic
357C2×C3⋊D3—22no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—21no—
360C2×C3⋊D3—22no—
361C2×C3⋊D3—21no—
362C2×C3⋊D3—22no—
363C2×C3⋊D3—21no—
364C2×C3⋊D3—22no—
365C2×C3⋊D3—48no—
366C2×C3⋊D3C2×C3×D414yes—
367C2×C3×D3—34no—
368C2×C3×D3—62no—
369C2×C3×D3—62no—
370C2×C3×D3—61no—
371C2×C3×D3—62no—
372C2×C3×D3—61no—
373C2×C3×D3—62no—
374C2×C3×D3—61no—
375C2×C3×D3—62no—
376C2×C3×D3—128no—
377C32×C4—22no—
378C32×C4—21no—
379C32×C4—22no—
380C32×C4—22no—
381C32×C4—21no—
382C32×C4—22no—
383C32×C4—22no—
384C32×C4—42no—
385C32×C4—41no—
386C32×C4—42no—
387C32×C4D3×D412yes—
388C32×C4C2×C3×D412yes—
389C3⋊Dic3—21no—
390C3⋊Dic3—21no—
391C3⋊Dic3—21no—
392C3×Dic3—61no—
393C3×Dic3—61no—
394C3×Dic3—61no—
395C2×#41—91no—
396C22×D4—91no—
397#124—91no—
398#123—92no—
399C22⋊Q8(C3⋊D3)⋊C311yescharacteristic, complemented
400#121—91no—
401#121—92no—
402#120—92no—
403C4×D4—91no—
404C4×D4—91no—
405C2×C22⋊C4—92no—
406H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
407C23×C3—31no—
408C23×C3—31no—
409C23×C3—61no—
410C23×C3—92no—
411C23×C3—92no—
412C23×C3—91no—
413C23×C3—184no—
414C23×C3—184no—
415C23×C3—362no—
416C23×C3C22×C3×D311yescharacteristic
417C22×D3—32no—
418C22×D3—32no—
419C22×D3—31no—
420C22×D3—64no—
421C22×D3—64no—
422C22×D3—92no—
423C22×D3—92no—
424C22×D3—91no—
425C22×D3—122no—
426C22×D3—184no—
427C22×D3—184no—
428C22×D3—362no—
429C3×Q8—22no—
430C3×Q8—62no—
431C3×Q8—62no—
432C3×Q8—122no—
433C3×D4—94no—
434C3×D4—182no—
435C3×D4—184no—
436C3×D4—184no—
437C3×D4—182no—
438C3×D4—362no—
439C2×C3×C4—22no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—32no—
443C2×C3×C4—32no—
444C2×C3×C4—31no—
445C2×C3×C4—31no—
446C2×C3×C4—32no—
447C2×C3×C4—32no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—61no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—61no—
454C2×C3×C4—91no—
455C2×C3×C4—91no—
456C2×C3×C4—91no—
457C2×C3×C4—122no—
458C2×C3×C4—182no—
459C2×C3×C4—184no—
460C2×C3×C4—362no—
461C2×C3×C4C22×C3×D311yescharacteristic
462C2×C3×C4C22×C3×D312yes—
463C2×C3×C4C22×C3×D312yes—
464C2×C3×C4C22×C3×D311yescharacteristic
465#67—62no—
466#67—182no—
467C2×Dic3—31no—
468C2×Dic3—31no—
469C2×Dic3—31no—
470C2×Dic3—91no—
471C2×Dic3—91no—
472C2×Dic3—91no—
473D12—34no—
474D12—64no—
475D12—64no—
476D12—62no—
477D12—94no—
478D12—122no—
479D12—182no—
480D12—184no—
481D12—184no—
482D12—362no—
483C4×D3—64no—
484C4×D3—62no—
485C4×D3—122no—
486C4×D3—182no—
487C4×D3—184no—
488C4×D3—362no—
489C2×C32—22no—
490C2×C32—22no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—21no—
494C2×C32—42no—
495C2×C32C2×D3×D411yescharacteristic
496C2×C32C2×#23911yescharacteristic
497C2×C32#100911yescharacteristic
498C2×C32C22×C3×D411yescharacteristic
499C2×C32C2×C3×#4111yescharacteristic
500C2×C32C3×H(5,𝔽2)11yescharacteristic
501C3⋊D3—24no—
502C3⋊D3—41no—
503C3⋊D3—42no—
504C3×D3—64no—
505C3×D3—121no—
506C3×D3—122no—
507C24—92no—
508#41—184no—
509C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic, complemented
510C2×D4—91no—
511C2×D4—91no—
512C2×D4—92no—
513C2×D4—92no—
514C2×D4—91no—
515C2×D4—92no—
516C2×D4—184no—
517C22×C4—92no—
518C22×C4—91no—
519C22×C4—92no—
520C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
521C4⋊C4—91no—
522C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
523C4⋊C4C2×(C3⋊D3)⋊C312yescomplemented
524C22⋊C4—91no—
525C22⋊C4—92no—
526C22⋊C4—92no—
527C22⋊C4—92no—
528C22⋊C4—91no—
529C22⋊C4—92no—
530C22⋊C4C2×(C3⋊D3)⋊C312yes—
531C42—91no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—31no—
535C22×C3—31no—
536C22×C3—32no—
537C22×C3—32no—
538C22×C3—61no—
539C22×C3—61no—
540C22×C3—61no—
541C22×C3—61no—
542C22×C3—61no—
543C22×C3—62no—
544C22×C3—94no—
545C22×C3—121no—
546C22×C3—121no—
547C22×C3—182no—
548C22×C3—182no—
549C22×C3—181no—
550C22×C3—182no—
551C22×C3—181no—
552C22×C3—181no—
553C22×C3—182no—
554C22×C3—182no—
555C22×C3—368no—
556C22×C3C3×#23912yes—
557C22×C3C23×C3×D311yescharacteristic
558C2×D3—34no—
559C2×D3—62no—
560C2×D3—62no—
561C2×D3—61no—
562C2×D3—62no—
563C2×D3—61no—
564C2×D3—62no—
565C2×D3—61no—
566C2×D3—62no—
567C2×D3—94no—
568C2×D3—128no—
569C2×D3—182no—
570C2×D3—182no—
571C2×D3—181no—
572C2×D3—182no—
573C2×D3—181no—
574C2×D3—182no—
575C2×D3—181no—
576C2×D3—182no—
577C2×D3—368no—
578C3×C4—22no—
579C3×C4—21no—
580C3×C4—22no—
581C3×C4—32no—
582C3×C4—32no—
583C3×C4—62no—
584C3×C4—62no—
585C3×C4—61no—
586C3×C4—61no—
587C3×C4—62no—
588C3×C4—62no—
589C3×C4—62no—
590C3×C4—121no—
591C3×C4—122no—
592C3×C4—122no—
593C3×C4—181no—
594C3×C4—181no—
595C3×C4—181no—
596C3×C4C3×D3×D412yes—
597Dic3—61no—
598Dic3—61no—
599Dic3—61no—
600Dic3—181no—
601Dic3—181no—
602Dic3—181no—
603C32—21no—
604C32#563011yescharacteristic, complemented
605C32C3×#54611yescharacteristic, complemented
606C23—92no—
607C23—92no—
608C23—91no—
609C23—184no—
610C23—184no—
611C23—362no—
612C23C22×(C3⋊D3)⋊C311yescharacteristic
613Q8—22no—
614D4—94no—
615D4—184no—
616D4—184no—
617D4—182no—
618D4—182no—
619D4—362no—
620C2×C4—22no—
621C2×C4—91no—
622C2×C4—91no—
623C2×C4—91no—
624C2×C4—184no—
625C2×C4—182no—
626C2×C4—362no—
627C2×C4C22×(C3⋊D3)⋊C312yes—
628C2×C4C22×(C3⋊D3)⋊C312yes—
629C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
630C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
631C2×C3—22no—
632C2×C3—31no—
633C2×C3—31no—
634C2×C3—31no—
635C2×C3—31no—
636C2×C3—31no—
637C2×C3—31no—
638C2×C3—62no—
639C2×C3—62no—
640C2×C3—61no—
641C2×C3—61no—
642C2×C3—61no—
643C2×C3—122no—
644C2×C3—184no—
645C2×C3—362no—
646C2×C3—361no—
647C2×C3C2×C3×D3×D411yescharacteristic
648C2×C3C2×C3×#23911yescharacteristic
649C2×C3C3×#100911yescharacteristic
650D3—64no—
651D3—122no—
652D3—121no—
653D3—184no—
654D3—362no—
655D3—361no—
656C22—21no—
657C22—21no—
658C22—94no—
659C22—182no—
660C22—182no—
661C22—181no—
662C22—182no—
663C22—181no—
664C22—182no—
665C22—181no—
666C22—182no—
667C22—368no—
668C22#8872212yescomplemented
669C22C23×(C3⋊D3)⋊C311yescharacteristic
670C4—21no—
671C4—22no—
672C4—22no—
673C4—181no—
674C4—181no—
675C4—181no—
676C4D4×(C3⋊D3)⋊C312yes—
677C3—31no—
678C3—31no—
679C3—61no—
680C3C3×#563011yescharacteristic
681C2—22no—
682C2—184no—
683C2—362no—
684C2—361no—
685C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
686C2C2×#8872211yescharacteristic
687C2#1172263811yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×C22⋊Q8C2
hypercenterC22⋊Q8(C3⋊D3)⋊C3
hypocenterC32C3×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#88722C2semidirect
2. C22×C4⋊((C3⋊D3)⋊C3)C2semidirect
3. H(3,𝔽3)×C22⋊Q8C2semidirect
4. #64156⋊C3C2semidirect
5. C4×#638⋊C3C2semidirect
6. #64104⋊C3C2semidirect
7. #64104⋊C3C2semidirect
8. #64103⋊C3C2semidirect
9. #64102⋊C3C2semidirect
10. #64091⋊C3C2semidirect
11. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
12. #10596101C3semidirect
15. C2×Q8×H(3,𝔽3)C22semidirect
23. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
24. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
25. C2×C4×(C3⋊D3)⋊C3C22semidirect
26. C2×C4×(C3⋊D3)⋊C3C22semidirect
27. C2×C4×(C3⋊D3)⋊C3C22semidirect
28. C4⋊C4×H(3,𝔽3)C22semidirect
29. C4⋊C4×H(3,𝔽3)C22semidirect
32. #3752⋊C3C22semidirect
33. #3752⋊C3C22semidirect
34. #3752⋊C3C22semidirect
35. #3752⋊C3C22semidirect
36. #3752⋊C3C22semidirect
37. #3750⋊C3C22semidirect
38. C4×(C3⋊Dic3)⋊C3C22semidirect
39. C2×#3832C2×C3semidirect
40. C22×C4⋊(C3⋊D3)C2×C3semidirect
44. C32×C22⋊Q8D3semidirect
45. C32×C22⋊Q8C2×C3semidirect
46. #64156C2×C3semidirect
47. C4×#638C2×C3semidirect
48. #64104C2×C3semidirect
49. #64104C2×C3semidirect
50. #64103C2×C3semidirect
51. #64102C2×C3semidirect
52. #64091C2×C3semidirect
53. C22⋊C4×C3⋊D3C2×C3semidirect
83. C4⋊((C3⋊D3)⋊C3)D4semidirect
93. C2×C32×Q8C2×D3semidirect
94. C2×C32×Q8C22×C3semidirect
104. C2×C4⋊(C3⋊D3)C22×C3semidirect
105. C2×C4⋊(C3⋊D3)C22×C3semidirect
106. C2×C4×C3⋊D3C22×C3semidirect
107. C2×C4×C3⋊D3C22×C3semidirect
108. C2×C4×C3⋊D3C22×C3semidirect
122. C32×C4⋊C4C2×D3semidirect
123. C32×C4⋊C4C2×D3semidirect
124. C32×C4⋊C4C22×C3semidirect
125. C32×C4⋊C4C22×C3semidirect
130. #3752C22×C3semidirect
131. #3752C22×C3semidirect
132. #3752C22×C3semidirect
133. #3752C22×C3semidirect
134. #3752C22×C3semidirect
135. #3750C22×C3semidirect
136. C4×C3⋊Dic3C22×C3semidirect
147. C22×H(3,𝔽3)#41semidirect
241. C4⋊(C3⋊D3)C3×D4semidirect
353. C22×C32#239semidirect
354. C22×C32C3×#41semidirect
399. C22⋊Q8(C3⋊D3)⋊C3semidirect
406. H(3,𝔽3)#546semidirect
509. C2×Q8C2×(C3⋊D3)⋊C3semidirect
522. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
523. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
604. C32#5630semidirect
605. C32C3×#546semidirect
668. C22#88722semidirect

Maximal subgroups

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

subgroupindex
C2×#887222
C22×C4⋊((C3⋊D3)⋊C3)2
H(3,𝔽3)×C22⋊Q82
#64156⋊C32
C4×#638⋊C32
#64104⋊C32
#64103⋊C32
#64102⋊C32
#64091⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#105961013
C3×#56303