Finite Group Databasebeta

← #10596300⋊C3 #13153719

Subgroups — #10596300⋊C3 #13153719

Order 1728.

1333 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×D4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3#64156⋊C3C211yesmaximal, characteristic, complemented
4#64155⋊C3C211yesmaximal, characteristic, complemented
5#64148⋊C3C212yesmaximal, complemented
6#64146⋊C3C212yesmaximal, complemented
7D4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
8#64139⋊C3C211yesmaximal, characteristic, complemented
9#64138⋊C3C212yesmaximal, complemented
10C4×#638⋊C3C211yesmaximal, characteristic, complemented
11C2×#3752⋊C3C212yesmaximal, complemented
12#10596300C311yesmaximal, characteristic, complemented
13C3×#5829—31nomaximal
14C23×(C3⋊D3)⋊C3C2212yes—
15#41×H(3,𝔽3)—24no—
16C2×Q8×H(3,𝔽3)C2211yescharacteristic, complemented
17C2×D4×H(3,𝔽3)C2211yescharacteristic
18C2×D4×H(3,𝔽3)C2212yescomplemented
19C22×C4×H(3,𝔽3)C2212yescomplemented
20C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
21C2×#638⋊C3C2212yes—
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2212yescomplemented
24C22×(C3⋊Dic3)⋊C3C2212yescomplemented
25D4×(C3⋊D3)⋊C3—24no—
26C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
28#3757⋊C3C2211yescharacteristic, complemented
29#3757⋊C3C2212yescomplemented
30#3752⋊C3C2211yescharacteristic
31#3752⋊C3C2212yes—
32#3752⋊C3C2212yescomplemented
33#3752⋊C3C2212yescomplemented
34#3752⋊C3C2212yescomplemented
35C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
36#3750⋊C3C2211yescharacteristic, complemented
37#3750⋊C3C2212yescomplemented
38C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
39C2×C32×#41—21no—
40C2×C32×#41D311yescharacteristic, complemented
41C2×C32×#41C2×C311yescharacteristic, complemented
42C2×D4×C3⋊D3C2×C311yescharacteristic, complemented
43C2×C3×D3×D4—31no—
44#64156C2×C311yescharacteristic, complemented
45#64155C2×C311yescharacteristic, complemented
46#64148C2×C312yescomplemented
47#64146C2×C312yescomplemented
48D4×C3⋊Dic3C2×C311yescharacteristic, complemented
49#64139C2×C311yescharacteristic, complemented
50#64138C2×C312yescomplemented
51C4×#638C2×C311yescharacteristic, complemented
52C2×#3752C2×C312yescomplemented
53C3×#947—31no—
54C3×#946—31no—
55C3×#939—32no—
56C3×#937—32no—
57C3×D4×Dic3—31no—
58C3×#930—31no—
59C3×#929—32no—
60C3×C4×#67—31no—
61C2×C3×(C2×D3)⋊C4—32no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C23×H(3,𝔽3)C2312yes—
64C22×(C3⋊D3)⋊C3—24no—
65C22×(C3⋊D3)⋊C3—24no—
66C22×(C3⋊D3)⋊C3—42no—
67C22×(C3⋊D3)⋊C3C2312yes—
68C22×(C3⋊D3)⋊C3C2311yescharacteristic
69Q8×H(3,𝔽3)—22no—
70D4×H(3,𝔽3)—24no—
71D4×H(3,𝔽3)D414yescomplemented
72C2×C4×H(3,𝔽3)—24no—
73C2×C4×H(3,𝔽3)—22no—
74C2×C4×H(3,𝔽3)C2311yescharacteristic
75C2×C4×H(3,𝔽3)C2312yes—
76C2×C4×H(3,𝔽3)C2311yescharacteristic
77#638⋊C3—24no—
78#638⋊C3—22no—
79#638⋊C3—42no—
80C2×(C3⋊Dic3)⋊C3—42no—
81C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
82C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
83C2×(C3⋊Dic3)⋊C3C2312yes—
84C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
85C4⋊((C3⋊D3)⋊C3)—22no—
86C4×(C3⋊D3)⋊C3—22no—
87C3×#546—91no—
88#5829—31no—
89#5829—91no—
90C23×C3⋊D3C22×C312yes—
91C23×C3×D3—32no—
92C32×#41—28no—
93C32×#41—24no—
94C32×#41—24no—
95C2×C32×Q8—21no—
96C2×C32×Q8C2×D311yescharacteristic, complemented
97C2×C32×Q8C22×C311yescharacteristic, complemented
98C2×C32×D4—21no—
99C2×C32×D4—22no—
100C2×C32×D4C2×D311yescharacteristic
101C2×C32×D4C2×D312yescomplemented
102C2×C32×D4C22×C311yescharacteristic
103C2×C32×D4C22×C312yescomplemented
104C22×C32×C4—22no—
105C22×C32×C4—21no—
106C22×C32×C4C2×D312yescomplemented
107C22×C32×C4C2×D311yescharacteristic, complemented
108C22×C32×C4C22×C312yescomplemented
109C22×C32×C4C22×C311yescharacteristic, complemented
110C2×#638C22×C312yes—
111C2×#638C22×C311yescharacteristic
112C2×#638C22×C312yescomplemented
113C22×C3⋊Dic3C22×C312yescomplemented
114D4×C3⋊D3—24no—
115C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
116C2×C4×C3⋊D3C22×C311yescharacteristic
117C2×C3×#67—31no—
118C2×C3×#67—32no—
119C2×C3×#67—32no—
120C22×C3×Dic3—32no—
121C3×D3×D4—64no—
122C2×C3×D12—31no—
123C2×C3×C4×D3—31no—
124#3757C22×C311yescharacteristic, complemented
125#3757C22×C312yescomplemented
126#3752C22×C311yescharacteristic
127#3752C22×C312yes—
128#3752C22×C312yescomplemented
129#3752C22×C312yescomplemented
130#3752C22×C312yescomplemented
131C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
132#3750C22×C311yescharacteristic, complemented
133#3750C22×C312yescomplemented
134C4×C3⋊Dic3C22×C311yescharacteristic, complemented
135C3×#217—31no—
136C3×#217—32no—
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×C4⋊Dic3—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—32no—
145C3×C4×Dic3—31no—
146C22×H(3,𝔽3)—22no—
147C22×H(3,𝔽3)—22no—
148C22×H(3,𝔽3)—21no—
149C22×H(3,𝔽3)—21no—
150C22×H(3,𝔽3)—21no—
151C22×H(3,𝔽3)C2×D414yes—
152C22×H(3,𝔽3)C2411yescharacteristic
153C2×(C3⋊D3)⋊C3—21no—
154C2×(C3⋊D3)⋊C3—21no—
155C2×(C3⋊D3)⋊C3—22no—
156C2×(C3⋊D3)⋊C3—22no—
157C2×(C3⋊D3)⋊C3—22no—
158C2×(C3⋊D3)⋊C3—48no—
159C2×(C3⋊D3)⋊C3#4112yescomplemented
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—
166(C3⋊Dic3)⋊C3—22no—
167C2×C3×#41—31no—
168C2×C3×#41—31no—
169C2×C3×#41—61no—
170C2×C3×#41C3×D311yescharacteristic
171C22×C3×D4—91no—
172C2×D3×D4—31no—
173C2×D3×D4—91no—
174C3×#124—91no—
175C3×#123—92no—
176C3×C22⋊Q8—91no—
177C3×#121—91no—
178C3×#121—92no—
179C3×#120—92no—
180C3×C4×D4—91no—
181C3×C4×D4—91no—
182C2×C3×C22⋊C4—92no—
183#947—31no—
184#947—91no—
185#946—31no—
186#946—91no—
187#939—32no—
188#939—92no—
189#937—32no—
190#937—92no—
191D4×Dic3—31no—
192D4×Dic3—91no—
193#930—31no—
194#930—91no—
195#929—32no—
196#929—92no—
197C4×#67—31no—
198C4×#67—91no—
199C2×(C2×D3)⋊C4—32no—
200C2×(C2×D3)⋊C4—92no—
201C23×C32—21no—
202C23×C32—22no—
203C23×C32C22×D311yescharacteristic
204C23×C32C22×D312yes—
205C23×C32C23×C311yescharacteristic
206C23×C32C23×C312yes—
207C22×C3⋊D3—24no—
208C22×C3⋊D3—24no—
209C22×C3⋊D3—42no—
210C22×C3⋊D3C23×C312yes—
211C22×C3⋊D3C23×C311yescharacteristic
212C22×C3×D3—31no—
213C22×C3×D3—32no—
214C22×C3×D3—64no—
215C22×C3×D3—64no—
216C22×C3×D3—122no—
217C32×Q8—24no—
218C32×Q8—22no—
219C32×Q8—22no—
220C32×D4—28no—
221C32×D4—24no—
222C32×D4—24no—
223C32×D4—24no—
224C32×D4#6714yescomplemented
225C32×D4C3×D414yescomplemented
226C2×C32×C4—28no—
227C2×C32×C4—24no—
228C2×C32×C4—24no—
229C2×C32×C4—24no—
230C2×C32×C4—22no—
231C2×C32×C4—22no—
232C2×C32×C4—21no—
233C2×C32×C4—22no—
234C2×C32×C4—21no—
235C2×C32×C4C22×D311yescharacteristic
236C2×C32×C4C22×D312yes—
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C23×C311yescharacteristic
239C2×C32×C4C23×C312yes—
240C2×C32×C4C23×C311yescharacteristic
241#638—24no—
242#638—22no—
243#638—42no—
244C2×C3⋊Dic3—42no—
245C2×C3⋊Dic3C23×C311yescharacteristic
246C2×C3⋊Dic3C23×C311yescharacteristic
247C2×C3⋊Dic3C23×C311yescharacteristic
248C2×C3⋊Dic3C23×C312yes—
249C4⋊(C3⋊D3)—22no—
250C4×C3⋊D3—22no—
251C3×#67—62no—
252C3×#67—64no—
253C3×#67—122no—
254C2×C3×Dic3—31no—
255C2×C3×Dic3—31no—
256C2×C3×Dic3—31no—
257C2×C3×Dic3—32no—
258C2×C3×Dic3—122no—
259C3×D12—62no—
260C3×C4×D3—62no—
261#546—91noSylow
262C2×H(3,𝔽3)—24no—
263C2×H(3,𝔽3)—41no—
264C2×H(3,𝔽3)C22×D411yescharacteristic
265C2×H(3,𝔽3)C2×#4111yescharacteristic
266C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
267(C3⋊D3)⋊C3—22no—
268(C3⋊D3)⋊C3—42no—
269C24×C3—92no—
270C23×D3—32no—
271C23×D3—92no—
272C3×#41—24no—
273C3×#41—64no—
274C3×#41—64no—
275C3×#41—68no—
276C2×C3×Q8—31no—
277C2×C3×Q8—31no—
278C2×C3×Q8—61no—
279C2×C3×Q8C2×C3×D311yescharacteristic
280C2×C3×D4—31no—
281C2×C3×D4—31no—
282C2×C3×D4—32no—
283C2×C3×D4—32no—
284C2×C3×D4—61no—
285C2×C3×D4—62no—
286C2×C3×D4—91no—
287C2×C3×D4—91no—
288C2×C3×D4—92no—
289C2×C3×D4—92no—
290C2×C3×D4—184no—
291C2×C3×D4C2×C3×D311yescharacteristic
292C2×C3×D4C2×C3×D312yes—
293C22×C3×C4—32no—
294C22×C3×C4—31no—
295C22×C3×C4—32no—
296C22×C3×C4—31no—
297C22×C3×C4—62no—
298C22×C3×C4—61no—
299C22×C3×C4—91no—
300C22×C3×C4—92no—
301C22×C3×C4C2×C3×D312yes—
302C22×C3×C4C2×C3×D311yescharacteristic
303C2×#67—31no—
304C2×#67—32no—
305C2×#67—32no—
306C2×#67—91no—
307C2×#67—92no—
308C2×#67—92no—
309C22×Dic3—32no—
310C22×Dic3—92no—
311D3×D4—64no—
312D3×D4—184no—
313C2×D12—31no—
314C2×D12—91no—
315C2×C4×D3—31no—
316C2×C4×D3—91no—
317C3×C4⋊C4—91no—
318C3×C4⋊C4—92no—
319C3×C4⋊C4—91no—
320C3×C22⋊C4—91no—
321C3×C22⋊C4—92no—
322C3×C22⋊C4—92no—
323C3×C22⋊C4—92no—
324C3×C22⋊C4—92no—
325C3×C22⋊C4—92no—
326C3×C22⋊C4—91no—
327C3×C42—91no—
328#217—31no—
329#217—32no—
330#217—91no—
331#217—92no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—32no—
334(C2×D3)⋊C4—32no—
335(C2×D3)⋊C4—32no—
336(C2×D3)⋊C4—32no—
337(C2×D3)⋊C4—91no—
338(C2×D3)⋊C4—92no—
339(C2×D3)⋊C4—92no—
340(C2×D3)⋊C4—92no—
341(C2×D3)⋊C4—92no—
342C4⋊Dic3—31no—
343C4⋊Dic3—91no—
344Dic3⋊C4—31no—
345Dic3⋊C4—32no—
346Dic3⋊C4—91no—
347Dic3⋊C4—92no—
348C4×Dic3—31no—
349C4×Dic3—91no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—24no—
363C22×C32—42no—
364C22×C32—42no—
365C22×C32—41no—
366C22×C32—41no—
367C22×C32C2×#6714yes—
368C22×C32C2×C3×D414yes—
369C22×C32C23×D311yescharacteristic
370C22×C32C24×C311yescharacteristic
371C2×C3⋊D3—21no—
372C2×C3⋊D3—21no—
373C2×C3⋊D3—22no—
374C2×C3⋊D3—22no—
375C2×C3⋊D3—22no—
376C2×C3⋊D3—48no—
377C2×C3⋊D3C3×#4112yescomplemented
378C2×C3×D3—32no—
379C2×C3×D3—61no—
380C2×C3×D3—61no—
381C2×C3×D3—62no—
382C2×C3×D3—62no—
383C2×C3×D3—62no—
384C2×C3×D3—128no—
385C32×C4—22no—
386C32×C4—24no—
387C32×C4—21no—
388C32×C4—22no—
389C32×C4—21no—
390C32×C4—22no—
391C32×C4—22no—
392C32×C4C2×#6712yes—
393C32×C4C2×C3×D412yes—
394C3⋊Dic3—21no—
395C3⋊Dic3—21no—
396C3⋊Dic3—21no—
397C3⋊Dic3—22no—
398C3×Dic3—61no—
399C3×Dic3—61no—
400C3×Dic3—62no—
401C3×Dic3—61no—
402C2×#41(C3⋊D3)⋊C311yescharacteristic, complemented
403C22×D4—91no—
404#124—91no—
405#123—92no—
406C22⋊Q8—91no—
407#121—92no—
408#121—91no—
409#120—92no—
410C4×D4—91no—
411C4×D4—91no—
412C2×C22⋊C4—92no—
413H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
414C23×C3—32no—
415C23×C3—32no—
416C23×C3—31no—
417C23×C3—31no—
418C23×C3—61no—
419C23×C3—62no—
420C23×C3—91no—
421C23×C3—92no—
422C23×C3—184no—
423C23×C3—184no—
424C23×C3—362no—
425C23×C3C22×C3×D311yescharacteristic
426C23×C3C22×C3×D312yes—
427C22×D3—31no—
428C22×D3—32no—
429C22×D3—64no—
430C22×D3—64no—
431C22×D3—91no—
432C22×D3—92no—
433C22×D3—122no—
434C22×D3—184no—
435C22×D3—184no—
436C22×D3—362no—
437C3×Q8—22no—
438C3×Q8—62no—
439C3×Q8—62no—
440C3×Q8—64no—
441C3×D4—24no—
442C3×D4—34no—
443C3×D4—34no—
444C3×D4—64no—
445C3×D4—64no—
446C3×D4—68no—
447C3×D4—64no—
448C3×D4—182no—
449C3×D4—184no—
450C3×D4—182no—
451C3×D4—362no—
452C3×D4C3×#6714yes—
453C2×C3×C4—24no—
454C2×C3×C4—22no—
455C2×C3×C4—31no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—32no—
459C2×C3×C4—31no—
460C2×C3×C4—32no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—64no—
464C2×C3×C4—64no—
465C2×C3×C4—68no—
466C2×C3×C4—64no—
467C2×C3×C4—61no—
468C2×C3×C4—62no—
469C2×C3×C4—61no—
470C2×C3×C4—91no—
471C2×C3×C4—91no—
472C2×C3×C4—92no—
473C2×C3×C4—91no—
474C2×C3×C4—182no—
475C2×C3×C4—362no—
476C2×C3×C4C22×C3×D311yescharacteristic
477C2×C3×C4C22×C3×D312yes—
478C2×C3×C4C22×C3×D311yescharacteristic
479#67—62no—
480#67—64no—
481#67—122no—
482#67—182no—
483#67—184no—
484#67—362no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—32no—
489C2×Dic3—91no—
490C2×Dic3—91no—
491C2×Dic3—91no—
492C2×Dic3—92no—
493C2×Dic3—122no—
494C2×Dic3—362no—
495D12—62no—
496D12—182no—
497C4×D3—62no—
498C4×D3—182no—
499C2×C32—24no—
500C2×C32—24no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—44no—
505C2×C32—42no—
506C2×C32—41no—
507C2×C32—41no—
508C2×C32D3×#4111yescharacteristic
509C2×C32#100911yescharacteristic
510C2×C32C22×#6711yescharacteristic
511C2×C32C22×C3×D411yescharacteristic
512C2×C32C2×C3×#4111yescharacteristic
513C2×C32C3×H(5,𝔽2)11yescharacteristic
514C3⋊D3—22no—
515C3⋊D3—42no—
516C3×D3—62no—
517C3×D3—122no—
518C24—92no—
519#41—24no—
520C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic, complemented
521C2×D4—91no—
522C2×D4—92no—
523C2×D4—92no—
524C2×D4—91no—
525C2×D4—184no—
526C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
527C2×D4C2×(C3⋊D3)⋊C312yescomplemented
528C22×C4—92no—
529C22×C4—91no—
530C22×C4C2×(C3⋊D3)⋊C312yescomplemented
531C22×C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
532C4⋊C4—91no—
533C4⋊C4—91no—
534C4⋊C4—92no—
535C22⋊C4—92no—
536C22⋊C4—91no—
537C22⋊C4—91no—
538C22⋊C4—92no—
539C22⋊C4—92no—
540C22⋊C4—92no—
541C22⋊C4—92no—
542C42—91no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—31no—
549C22×C3—31no—
550C22×C3—34no—
551C22×C3—34no—
552C22×C3—62no—
553C22×C3—62no—
554C22×C3—62no—
555C22×C3—62no—
556C22×C3—61no—
557C22×C3—61no—
558C22×C3—61no—
559C22×C3—61no—
560C22×C3—61no—
561C22×C3—61no—
562C22×C3—62no—
563C22×C3—61no—
564C22×C3—64no—
565C22×C3—92no—
566C22×C3—122no—
567C22×C3—122no—
568C22×C3—121no—
569C22×C3—121no—
570C22×C3—181no—
571C22×C3—181no—
572C22×C3—182no—
573C22×C3—182no—
574C22×C3—182no—
575C22×C3—368no—
576C22×C3C2×C3×#6714yes—
577C22×C3C23×C3×D311yescharacteristic
578C2×D3—32no—
579C2×D3—61no—
580C2×D3—61no—
581C2×D3—62no—
582C2×D3—62no—
583C2×D3—62no—
584C2×D3—92no—
585C2×D3—128no—
586C2×D3—181no—
587C2×D3—181no—
588C2×D3—182no—
589C2×D3—182no—
590C2×D3—182no—
591C2×D3—368no—
592C3×C4—21no—
593C3×C4—22no—
594C3×C4—32no—
595C3×C4—32no—
596C3×C4—61no—
597C3×C4—61no—
598C3×C4—62no—
599C3×C4—62no—
600C3×C4—62no—
601C3×C4—64no—
602C3×C4—62no—
603C3×C4—181no—
604C3×C4—181no—
605C3×C4—182no—
606C3×C4—181no—
607C3×C4C2×C3×#6712yes—
608Dic3—61no—
609Dic3—61no—
610Dic3—62no—
611Dic3—61no—
612Dic3—181no—
613Dic3—181no—
614Dic3—182no—
615Dic3—181no—
616C32—21no—
617C32#582911yescharacteristic, complemented
618C32C3×#54611yescharacteristic, complemented
619C23—91no—
620C23—92no—
621C23—184no—
622C23—184no—
623C23—362no—
624C23C22×(C3⋊D3)⋊C311yescharacteristic
625C23C22×(C3⋊D3)⋊C312yes—
626Q8—22no—
627D4—24no—
628D4—182no—
629D4—184no—
630D4—182no—
631D4—362no—
632D4#638⋊C314yescomplemented
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—91no—
636C2×C4—91no—
637C2×C4—92no—
638C2×C4—91no—
639C2×C4—182no—
640C2×C4—362no—
641C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
642C2×C4C22×(C3⋊D3)⋊C312yes—
643C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
644C2×C3—24no—
645C2×C3—31no—
646C2×C3—31no—
647C2×C3—31no—
648C2×C3—31no—
649C2×C3—31no—
650C2×C3—31no—
651C2×C3—41no—
652C2×C3—64no—
653C2×C3—64no—
654C2×C3—61no—
655C2×C3—61no—
656C2×C3—61no—
657C2×C3—124no—
658C2×C3—121no—
659C2×C3—121no—
660C2×C3—122no—
661C2×C3—182no—
662C2×C3—362no—
663C2×C3C3×D3×#4111yescharacteristic
664C2×C3C3×#100911yescharacteristic
665C2×C3C22×C3×#6711yescharacteristic
666D3—62no—
667D3—122no—
668D3—182no—
669D3—362no—
670C22—22no—
671C22—22no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—92no—
676C22—181no—
677C22—181no—
678C22—182no—
679C22—182no—
680C22—182no—
681C22—368no—
682C22C2×#638⋊C314yes—
683C22C23×(C3⋊D3)⋊C311yescharacteristic
684C4—21no—
685C4—22no—
686C4—181no—
687C4—181no—
688C4—182no—
689C4—181no—
690C4C2×#638⋊C312yes—
691C3—31no—
692C3—31no—
693C3—61no—
694C3C3×#582911yescharacteristic
695C2—24no—
696C2—41no—
697C2—182no—
698C2—362no—
699C2#41×(C3⋊D3)⋊C311yescharacteristic
700C2#1172263811yescharacteristic
701C2C22×#638⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingC2×#41×H(3,𝔽3)C2
hypercenterC2×#41(C3⋊D3)⋊C3
hypocenterC32C3×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×H(3,𝔽3)C2semidirect
2. C2×D4×(C3⋊D3)⋊C3C2semidirect
3. #64156⋊C3C2semidirect
4. #64155⋊C3C2semidirect
5. #64148⋊C3C2semidirect
6. #64146⋊C3C2semidirect
7. D4×(C3⋊Dic3)⋊C3C2semidirect
8. #64139⋊C3C2semidirect
9. #64138⋊C3C2semidirect
10. C4×#638⋊C3C2semidirect
11. C2×#3752⋊C3C2semidirect
12. #10596300C3semidirect
16. C2×Q8×H(3,𝔽3)C22semidirect
18. C2×D4×H(3,𝔽3)C22semidirect
19. C22×C4×H(3,𝔽3)C22semidirect
20. C22×C4×H(3,𝔽3)C22semidirect
23. C2×#638⋊C3C22semidirect
24. C22×(C3⋊Dic3)⋊C3C22semidirect
28. #3757⋊C3C22semidirect
29. #3757⋊C3C22semidirect
32. #3752⋊C3C22semidirect
33. #3752⋊C3C22semidirect
34. #3752⋊C3C22semidirect
35. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
36. #3750⋊C3C22semidirect
37. #3750⋊C3C22semidirect
38. C4×(C3⋊Dic3)⋊C3C22semidirect
40. C2×C32×#41D3semidirect
41. C2×C32×#41C2×C3semidirect
42. C2×D4×C3⋊D3C2×C3semidirect
44. #64156C2×C3semidirect
45. #64155C2×C3semidirect
46. #64148C2×C3semidirect
47. #64146C2×C3semidirect
48. D4×C3⋊Dic3C2×C3semidirect
49. #64139C2×C3semidirect
50. #64138C2×C3semidirect
51. C4×#638C2×C3semidirect
52. C2×#3752C2×C3semidirect
71. D4×H(3,𝔽3)D4semidirect
96. C2×C32×Q8C2×D3semidirect
97. C2×C32×Q8C22×C3semidirect
101. C2×C32×D4C2×D3semidirect
103. C2×C32×D4C22×C3semidirect
106. C22×C32×C4C2×D3semidirect
107. C22×C32×C4C2×D3semidirect
108. C22×C32×C4C22×C3semidirect
109. C22×C32×C4C22×C3semidirect
112. C2×#638C22×C3semidirect
113. C22×C3⋊Dic3C22×C3semidirect
124. #3757C22×C3semidirect
125. #3757C22×C3semidirect
128. #3752C22×C3semidirect
129. #3752C22×C3semidirect
130. #3752C22×C3semidirect
131. C4⋊(C3⋊Dic3)C22×C3semidirect
132. #3750C22×C3semidirect
133. #3750C22×C3semidirect
134. C4×C3⋊Dic3C22×C3semidirect
159. C2×(C3⋊D3)⋊C3#41semidirect
224. C32×D4#67semidirect
225. C32×D4C3×D4semidirect
377. C2×C3⋊D3C3×#41semidirect
402. C2×#41(C3⋊D3)⋊C3semidirect
413. H(3,𝔽3)#546semidirect
520. C2×Q8C2×(C3⋊D3)⋊C3semidirect
527. C2×D4C2×(C3⋊D3)⋊C3semidirect
530. C22×C4C2×(C3⋊D3)⋊C3semidirect
531. C22×C4C2×(C3⋊D3)⋊C3semidirect
617. C32#5829semidirect
618. C32C3×#546semidirect
632. D4#638⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#41×H(3,𝔽3)2
C2×D4×(C3⋊D3)⋊C32
#64156⋊C32
#64155⋊C32
#64148⋊C32
#64146⋊C32
D4×(C3⋊Dic3)⋊C32
#64139⋊C32
#64138⋊C32
C4×#638⋊C32
C2×#3752⋊C32
#105963003
C3×#58293