Finite Group Databasebeta

← #10596241⋊C3 #13153484

Subgroups — #10596241⋊C3 #13153484

Order 1728.

965 conjugacy classes of subgroups.

The subgroup lattice has 699 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11722639C211yesmaximal, characteristic, complemented
2#11722638C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×#135C211yesmaximal, characteristic, complemented
4#64158⋊C3C211yesmaximal, characteristic, complemented
5#64160⋊C3C211yesmaximal, characteristic, complemented
6#64127⋊C3C212yesmaximal, complemented
7#64125⋊C3C212yesmaximal, complemented
8SD16×(C3⋊D3)⋊C3C212yesmaximal, complemented
9#64120⋊C3C212yesmaximal, complemented
10C2×#3744⋊C3C211yesmaximal, characteristic, complemented
11#64110⋊C3C211yesmaximal, characteristic, complemented
12#10596241C311yesmaximal, characteristic, complemented
13C3×#5770—31nomaximal
14#41×H(3,𝔽3)C2211yescharacteristic
15#41×H(3,𝔽3)C2211yescharacteristic, complemented
16#88722C2212yes—
17Q8×(C3⋊D3)⋊C3C2212yescomplemented
18#3830⋊C3—22no—
19#3830⋊C3C2212yescomplemented
20D4×(C3⋊D3)⋊C3—22no—
21D4×(C3⋊D3)⋊C3C2212yes—
22#3828⋊C3—21no—
23#3828⋊C3—21no—
24#3828⋊C3C2211yescharacteristic
25C2×C4⋊((C3⋊D3)⋊C3)—21no—
26C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
27C2×#634⋊C3—21no—
28C2×#634⋊C3C2211yescharacteristic, complemented
29Q16×H(3,𝔽3)C2211yescharacteristic, complemented
30SD16×H(3,𝔽3)C2211yescharacteristic, complemented
31SD16×H(3,𝔽3)C2211yescharacteristic, complemented
32D8×H(3,𝔽3)C2211yescharacteristic, complemented
33C2×C8×H(3,𝔽3)C2211yescharacteristic, complemented
34#3755⋊C3C2212yescomplemented
35#3756⋊C3C2212yescomplemented
36#3753⋊C3C2212yescomplemented
37#3754⋊C3C2212yescomplemented
38#3748⋊C3C2211yescharacteristic, complemented
39#3744⋊C3C2212yescomplemented
40#3744⋊C3C2212yescomplemented
41#3743⋊C3C2212yescomplemented
42C8×(C3⋊D3)⋊C3C2212yescomplemented
43#64367C2×C311yescharacteristic, complemented
44#64366C2×C311yescharacteristic, complemented
45C3×#1010—31no—
46C3×#1009—31no—
47C32×#135—21no—
48C32×#135D311yescharacteristic, complemented
49C32×#135C2×C311yescharacteristic, complemented
50#64160C2×C311yescharacteristic, complemented
51#64158C2×C311yescharacteristic, complemented
52#64127C2×C312yescomplemented
53#64125C2×C312yescomplemented
54SD16×C3⋊D3C2×C312yescomplemented
55#64120C2×C312yescomplemented
56C2×#3744C2×C311yescharacteristic, complemented
57#64110C2×C311yescharacteristic, complemented
58C3×#951—31no—
59C3×#949—31no—
60C3×#918—32no—
61C3×#916—32no—
62C3×D3×SD16—32no—
63C3×#911—32no—
64C2×C3×#204—31no—
65C3×#901—31no—
66C22×(C3⋊D3)⋊C3—21no—
67C22×(C3⋊D3)⋊C3—22no—
68Q8×H(3,𝔽3)C2311yescharacteristic
69Q8×H(3,𝔽3)C2311yescharacteristic
70D4×H(3,𝔽3)—21no—
71D4×H(3,𝔽3)—21no—
72D4×H(3,𝔽3)C2311yescharacteristic
73D4×H(3,𝔽3)C2311yescharacteristic
74C2×C4×H(3,𝔽3)—21no—
75C2×C4×H(3,𝔽3)—21no—
76C2×C4×H(3,𝔽3)C2311yescharacteristic
77#638⋊C3—22no—
78#638⋊C3—22no—
79#638⋊C3D412yes—
80C2×(C3⋊Dic3)⋊C3—21no—
81C2×(C3⋊Dic3)⋊C3—22no—
82C4⋊((C3⋊D3)⋊C3)—22no—
83C4⋊((C3⋊D3)⋊C3)—21no—
84C4⋊((C3⋊D3)⋊C3)D411yescharacteristic
85C4⋊((C3⋊D3)⋊C3)C2312yes—
86C4×(C3⋊D3)⋊C3—22no—
87C4×(C3⋊D3)⋊C3—22no—
88C4×(C3⋊D3)⋊C3C2312yes—
89#634⋊C3—21no—
90#634⋊C3—22no—
91#634⋊C3D411yescharacteristic
92#634⋊C3C2312yes—
93C8×H(3,𝔽3)C2311yescharacteristic
94C8×H(3,𝔽3)C2311yescharacteristic
95(C3⋊(C3⋊C8))⋊C3C2312yes—
96C3×#577—91no—
97#5770—31no—
98#5770—91no—
99C32×#41—21no—
100C32×#41—21no—
101C32×#41C2×D311yescharacteristic
102C32×#41C2×D311yescharacteristic, complemented
103C32×#41C22×C311yescharacteristic
104C32×#41C22×C311yescharacteristic, complemented
105#3832C22×C312yes—
106Q8×C3⋊D3C22×C312yescomplemented
107#3830—22no—
108#3830C22×C312yescomplemented
109D4×C3⋊D3—22no—
110D4×C3⋊D3C22×C312yes—
111#3828—21no—
112#3828—21no—
113#3828C22×C311yescharacteristic
114C2×C4⋊(C3⋊D3)—21no—
115C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
116C2×#634—21no—
117C2×#634C22×C311yescharacteristic, complemented
118C3×#239—32no—
119C3×D3×Q8—32no—
120C3×#237—32no—
121C3×#237—62no—
122C3×D3×D4—32no—
123C3×D3×D4—62no—
124C3×#235—31no—
125C3×#235—61no—
126C3×#235—61no—
127C2×C3×D12—31no—
128C2×C3×D12—61no—
129C2×C3×Dic6—31no—
130C2×C3×Dic6—61no—
131C32×Q16—21no—
132C32×Q16C2×D311yescharacteristic, complemented
133C32×Q16C22×C311yescharacteristic, complemented
134C32×SD16—21no—
135C32×SD16—21no—
136C32×SD16C2×D311yescharacteristic, complemented
137C32×SD16C2×D311yescharacteristic, complemented
138C32×SD16C22×C311yescharacteristic, complemented
139C32×SD16C22×C311yescharacteristic, complemented
140C32×D8—21no—
141C32×D8C2×D311yescharacteristic, complemented
142C32×D8C22×C311yescharacteristic, complemented
143C2×C32×C8—21no—
144C2×C32×C8C2×D311yescharacteristic, complemented
145C2×C32×C8C22×C311yescharacteristic, complemented
146#3756C22×C312yescomplemented
147#3755C22×C312yescomplemented
148#3754C22×C312yescomplemented
149#3753C22×C312yescomplemented
150#3748C22×C311yescharacteristic, complemented
151#3744C22×C312yescomplemented
152#3744C22×C312yescomplemented
153#3743C22×C312yescomplemented
154C8×C3⋊D3C22×C312yescomplemented
155C3×#216—32no—
156C3×#215—32no—
157C3×#214—32no—
158C3×#213—32no—
159C3×#208—31no—
160C3×#204—32no—
161C3×#204—32no—
162C3×ΓL(1,𝔽25)—32no—
163C3×D3×C8—32no—
164C22×H(3,𝔽3)—21no—
165C22×H(3,𝔽3)—21no—
166C22×H(3,𝔽3)C2×D411yescharacteristic
167C2×(C3⋊D3)⋊C3—22no—
168C2×(C3⋊D3)⋊C3—82no—
169C2×(C3⋊D3)⋊C3—81no—
170C2×(C3⋊D3)⋊C3C2×D412yes—
171C4×H(3,𝔽3)—21no—
172C4×H(3,𝔽3)—21no—
173C4×H(3,𝔽3)C2×D411yescharacteristic
174C4×H(3,𝔽3)C2411yescharacteristic
175(C3⋊Dic3)⋊C3—22no—
176(C3⋊Dic3)⋊C3C2×D412yes—
177C3×2−1+4—91no—
178C3×H(5,𝔽2)—91no—
179#1010—31no—
180#1010—91no—
181#1009—31no—
182#1009—91no—
183C3×#137—92no—
184C3×#137—91no—
185C3×AGL(1,ℤ/8)—92no—
186C3×AGL(1,ℤ/8)—91no—
187C3×#135—31no—
188C3×#135—31no—
189C3×#135—61no—
190C3×#135—92no—
191C3×#135C3×D311yescharacteristic
192C2×C3×SD16—91no—
193C2×C3×SD16—92no—
194C3×#131—91no—
195#951—31no—
196#951—91no—
197#949—31no—
198#949—91no—
199#918—32no—
200#918—92no—
201#916—32no—
202#916—92no—
203D3×SD16—32no—
204D3×SD16—92no—
205#911—32no—
206#911—92no—
207C2×#204—31no—
208C2×#204—91no—
209#901—31no—
210#901—91no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3—22no—
213C22×C3×D3—62no—
214C22×C3×D3—61no—
215C32×Q8—21no—
216C32×Q8—21no—
217C32×Q8C22×D311yescharacteristic
218C32×Q8C22×D311yescharacteristic
219C32×Q8C23×C311yescharacteristic
220C32×Q8C23×C311yescharacteristic
221C32×D4—21no—
222C32×D4—21no—
223C32×D4—21no—
224C32×D4—21no—
225C32×D4—21no—
226C32×D4—21no—
227C32×D4—41no—
228C32×D4—41no—
229C32×D4C22×D311yescharacteristic
230C32×D4C22×D311yescharacteristic
231C32×D4C23×C311yescharacteristic
232C32×D4C23×C311yescharacteristic
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—41no—
239C2×C32×C4—41no—
240C2×C32×C4C22×D311yescharacteristic
241C2×C32×C4C23×C311yescharacteristic
242#638—22no—
243#638—22no—
244#638C3×D412yes—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—22no—
247C4⋊(C3⋊D3)—22no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)C3×D411yescharacteristic
250C4⋊(C3⋊D3)C23×C312yes—
251C4×C3⋊D3—22no—
252C4×C3⋊D3—22no—
253C4×C3⋊D3C23×C312yes—
254#634—21no—
255#634—22no—
256#634C3×D411yescharacteristic
257#634C23×C312yes—
258C3×#67—32no—
259C3×#67—62no—
260C3×#67—62no—
261C2×C3×Dic3—62no—
262C2×C3×Dic3—61no—
263C3×D12—31no—
264C3×D12—32no—
265C3×D12—62no—
266C3×D12—61no—
267C3×C4×D3—32no—
268C3×C4×D3—62no—
269C3×C4×D3—62no—
270C3×Dic6—31no—
271C3×Dic6—32no—
272C3×Dic6—62no—
273C3×Dic6—61no—
274C32×C8—21no—
275C32×C8—21no—
276C32×C8C22×D311yescharacteristic
277C32×C8C22×D311yescharacteristic
278C32×C8C23×C311yescharacteristic
279C32×C8C23×C311yescharacteristic
280C3⋊(C3⋊C8)C23×C312yes—
281C3×C3⋊C8—32no—
282#577—91noSylow
283C2×H(3,𝔽3)—21no—
284C2×H(3,𝔽3)—41no—
285C2×H(3,𝔽3)—41no—
286C2×H(3,𝔽3)C22×D411yescharacteristic
287(C3⋊D3)⋊C3—22no—
288(C3⋊D3)⋊C3—42no—
289C3×#41—31no—
290C3×#41—31no—
291C3×#41—31no—
292C3×#41—31no—
293C3×#41—61no—
294C3×#41—61no—
295C3×#41—91no—
296C3×#41—92no—
297C3×#41—92no—
298C3×#41—181no—
299C3×#41—181no—
300C3×#41—182no—
301C3×#41C2×C3×D311yescharacteristic
302C3×#41C2×C3×D311yescharacteristic
303C2×C3×Q8—91no—
304C2×C3×Q8—92no—
305C2×C3×Q8—181no—
306C2×C3×D4—91no—
307C2×C3×D4—92no—
308C2×C3×D4—181no—
309C2×C3×D4—182no—
310#239—32no—
311#239—92no—
312D3×Q8—32no—
313D3×Q8—92no—
314#237—32no—
315#237—62no—
316#237—92no—
317#237—182no—
318D3×D4—32no—
319D3×D4—62no—
320D3×D4—92no—
321D3×D4—182no—
322#235—31no—
323#235—61no—
324#235—61no—
325#235—91no—
326#235—181no—
327#235—181no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—91no—
331C2×D12—181no—
332C2×Dic6—31no—
333C2×Dic6—61no—
334C2×Dic6—91no—
335C2×Dic6—181no—
336C3×Q16—31no—
337C3×Q16—31no—
338C3×Q16—61no—
339C3×Q16—92no—
340C3×Q16C2×C3×D311yescharacteristic
341C3×SD16—31no—
342C3×SD16—31no—
343C3×SD16—31no—
344C3×SD16—31no—
345C3×SD16—61no—
346C3×SD16—61no—
347C3×SD16—92no—
348C3×SD16—92no—
349C3×SD16—92no—
350C3×SD16—92no—
351C3×SD16C2×C3×D311yescharacteristic
352C3×SD16C2×C3×D311yescharacteristic
353C3×D8—31no—
354C3×D8—31no—
355C3×D8—61no—
356C3×D8—92no—
357C3×D8C2×C3×D311yescharacteristic
358C3×M16—92no—
359C3×M16—91no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—61no—
363C2×C3×C8—92no—
364C2×C3×C8C2×C3×D311yescharacteristic
365#216—32no—
366#216—92no—
367#215—32no—
368#215—92no—
369#214—32no—
370#214—92no—
371#213—32no—
372#213—92no—
373#208—31no—
374#208—91no—
375#204—32no—
376#204—32no—
377#204—92no—
378#204—92no—
379ΓL(1,𝔽25)—32no—
380ΓL(1,𝔽25)—92no—
381D3×C8—32no—
382D3×C8—92no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32D3×D411yescharacteristic
391C22×C32C2×C3×D411yescharacteristic
392C2×C3⋊D3—22no—
393C2×C3⋊D3—82no—
394C2×C3⋊D3—81no—
395C2×C3⋊D3C2×C3×D412yes—
396C2×C3×D3—32no—
397C2×C3×D3—62no—
398C2×C3×D3—242no—
399C2×C3×D3—241no—
400C32×C4—21no—
401C32×C4—21no—
402C32×C4—21no—
403C32×C4—21no—
404C32×C4—21no—
405C32×C4—21no—
406C32×C4—41no—
407C32×C4—41no—
408C32×C4D3×D411yescharacteristic
409C32×C4C2×C3×D411yescharacteristic
410C32×C4C23×D311yescharacteristic
411C32×C4C24×C311yescharacteristic
412C3⋊Dic3—22no—
413C3⋊Dic3C2×C3×D412yes—
414C3×Dic3—32no—
415C3×Dic3—62no—
4162−1+4—91no—
417H(5,𝔽2)—91no—
418#137—91no—
419#137—92no—
420AGL(1,ℤ/8)—91no—
421AGL(1,ℤ/8)—92no—
422#135—92no—
423#135(C3⋊D3)⋊C311yescharacteristic, complemented
424C2×SD16—92no—
425C2×SD16—91no—
426#131—91no—
427H(3,𝔽3)#57711yescharacteristic, complemented, Sylow
428C23×C3—181no—
429C23×C3—182no—
430C22×D3—62no—
431C22×D3—61no—
432C22×D3—182no—
433C22×D3—181no—
434C3×Q8—31no—
435C3×Q8—31no—
436C3×Q8—31no—
437C3×Q8—31no—
438C3×Q8—61no—
439C3×Q8—61no—
440C3×Q8—91no—
441C3×Q8—92no—
442C3×Q8—181no—
443C3×Q8—182no—
444C3×Q8C22×C3×D311yescharacteristic
445C3×Q8C22×C3×D311yescharacteristic
446C3×D4—21no—
447C3×D4—21no—
448C3×D4—31no—
449C3×D4—31no—
450C3×D4—31no—
451C3×D4—31no—
452C3×D4—61no—
453C3×D4—61no—
454C3×D4—61no—
455C3×D4—61no—
456C3×D4—61no—
457C3×D4—61no—
458C3×D4—91no—
459C3×D4—92no—
460C3×D4—92no—
461C3×D4—121no—
462C3×D4—121no—
463C3×D4—181no—
464C3×D4—182no—
465C3×D4—182no—
466C3×D4—182no—
467C3×D4C22×C3×D311yescharacteristic
468C3×D4C22×C3×D311yescharacteristic
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—92no—
479C2×C3×C4—121no—
480C2×C3×C4—121no—
481C2×C3×C4—182no—
482C2×C3×C4—182no—
483C2×C3×C4—182no—
484C2×C3×C4—181no—
485C2×C3×C4C22×C3×D311yescharacteristic
486#67—32no—
487#67—62no—
488#67—62no—
489#67—92no—
490#67—182no—
491#67—182no—
492C2×Dic3—62no—
493C2×Dic3—61no—
494C2×Dic3—182no—
495C2×Dic3—181no—
496D12—32no—
497D12—31no—
498D12—62no—
499D12—61no—
500D12—91no—
501D12—92no—
502D12—181no—
503D12—182no—
504C4×D3—32no—
505C4×D3—62no—
506C4×D3—62no—
507C4×D3—92no—
508C4×D3—182no—
509C4×D3—182no—
510Dic6—31no—
511Dic6—32no—
512Dic6—62no—
513Dic6—61no—
514Dic6—91no—
515Dic6—92no—
516Dic6—182no—
517Dic6—181no—
518C3×C8—31no—
519C3×C8—31no—
520C3×C8—31no—
521C3×C8—31no—
522C3×C8—61no—
523C3×C8—61no—
524C3×C8—92no—
525C3×C8C22×C3×D311yescharacteristic
526C3×C8C22×C3×D311yescharacteristic
527C3⋊C8—32no—
528C3⋊C8—92no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—41no—
533C2×C32—41no—
534C2×C32—41no—
535C2×C32—41no—
536C2×C32—41no—
537C2×C32—81no—
538C2×C32—81no—
539C2×C32C2×D3×D411yescharacteristic
540C2×C32C22×C3×D411yescharacteristic
541C3⋊D3—22no—
542C3⋊D3—42no—
543C3×D3—62no—
544C3×D3—122no—
545#41—91no—
546#41—92no—
547#41—92no—
548#41—181no—
549#41—181no—
550#41—182no—
551#41C2×(C3⋊D3)⋊C311yescharacteristic
552#41C2×(C3⋊D3)⋊C311yescharacteristic, complemented
553C2×Q8—92no—
554C2×Q8—91no—
555C2×Q8—181no—
556C2×D4—92no—
557C2×D4—91no—
558C2×D4—181no—
559C2×D4—182no—
560Q16—92no—
561Q16C2×(C3⋊D3)⋊C311yescharacteristic, complemented
562SD16—92no—
563SD16—92no—
564SD16—92no—
565SD16—92no—
566SD16C2×(C3⋊D3)⋊C311yescharacteristic, complemented
567SD16C2×(C3⋊D3)⋊C311yescharacteristic, complemented
568D8—92no—
569D8C2×(C3⋊D3)⋊C311yescharacteristic, complemented
570M16—91no—
571M16—92no—
572C2×C8—92no—
573C2×C8C2×(C3⋊D3)⋊C311yescharacteristic, complemented
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—31no—
577C22×C3—31no—
578C22×C3—61no—
579C22×C3—61no—
580C22×C3—61no—
581C22×C3—61no—
582C22×C3—61no—
583C22×C3—92no—
584C22×C3—121no—
585C22×C3—121no—
586C22×C3—182no—
587C22×C3—721no—
588C22×C3—722no—
589C22×C3C3×D3×D411yescharacteristic
590C2×D3—32no—
591C2×D3—62no—
592C2×D3—92no—
593C2×D3—182no—
594C2×D3—242no—
595C2×D3—241no—
596C2×D3—722no—
597C2×D3—721no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—31no—
601C3×C4—31no—
602C3×C4—31no—
603C3×C4—31no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—61no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—92no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—182no—
614C3×C4C3×D3×D411yescharacteristic
615C3×C4C23×C3×D311yescharacteristic
616Dic3—32no—
617Dic3—62no—
618Dic3—92no—
619Dic3—182no—
620C32—21no—
621C32#577011yescharacteristic, complemented
622C32C3×#57711yescharacteristic, complemented
623C23—182no—
624C23—181no—
625Q8—91no—
626Q8—92no—
627Q8—182no—
628Q8—181no—
629Q8C22×(C3⋊D3)⋊C311yescharacteristic
630Q8C22×(C3⋊D3)⋊C311yescharacteristic
631D4—21no—
632D4—21no—
633D4—92no—
634D4—92no—
635D4—91no—
636D4—182no—
637D4—182no—
638D4—182no—
639D4—181no—
640D4C22×(C3⋊D3)⋊C311yescharacteristic
641D4C22×(C3⋊D3)⋊C311yescharacteristic
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—92no—
645C2×C4—182no—
646C2×C4—182no—
647C2×C4—182no—
648C2×C4—181no—
649C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
650C8—92no—
651C8C22×(C3⋊D3)⋊C311yescharacteristic
652C8C22×(C3⋊D3)⋊C311yescharacteristic
653C2×C3—21no—
654C2×C3—31no—
655C2×C3—31no—
656C2×C3—41no—
657C2×C3—41no—
658C2×C3—61no—
659C2×C3—61no—
660C2×C3—61no—
661C2×C3—121no—
662C2×C3—121no—
663C2×C3—121no—
664C2×C3—121no—
665C2×C3—121no—
666C2×C3—182no—
667C2×C3—241no—
668C2×C3—241no—
669C2×C3—362no—
670C2×C3C2×C3×D3×D411yescharacteristic
671D3—62no—
672D3—122no—
673D3—182no—
674D3—362no—
675C22—21no—
676C22—21no—
677C22—92no—
678C22—182no—
679C22—721no—
680C22—722no—
681C22D4×(C3⋊D3)⋊C311yescharacteristic
682C4—21no—
683C4—21no—
684C4—92no—
685C4—182no—
686C4D4×(C3⋊D3)⋊C311yescharacteristic
687C4C23×(C3⋊D3)⋊C311yescharacteristic
688C3—31no—
689C3—31no—
690C3—61no—
691C3C3×#577011yescharacteristic
692C2—21no—
693C2—41no—
694C2—41no—
695C2—182no—
696C2—362no—
697C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC2C2×D4×(C3⋊D3)⋊C3
commutator, cosocleC32×C4C24×C3
FrattiniC3×C4C23×C3×D3
FittingH(3,𝔽3)×#135C2
socleC2×C3C2×C3×D3×D4
hypercenter#135(C3⋊D3)⋊C3
hypocenterC32C3×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #11722639C2semidirect
2. #11722638C2semidirect
3. H(3,𝔽3)×#135C2semidirect
4. #64158⋊C3C2semidirect
5. #64160⋊C3C2semidirect
6. #64127⋊C3C2semidirect
7. #64125⋊C3C2semidirect
8. SD16×(C3⋊D3)⋊C3C2semidirect
9. #64120⋊C3C2semidirect
10. C2×#3744⋊C3C2semidirect
11. #64110⋊C3C2semidirect
12. #10596241C3semidirect
15. #41×H(3,𝔽3)C22semidirect
17. Q8×(C3⋊D3)⋊C3C22semidirect
19. #3830⋊C3C22semidirect
28. C2×#634⋊C3C22semidirect
29. Q16×H(3,𝔽3)C22semidirect
30. SD16×H(3,𝔽3)C22semidirect
31. SD16×H(3,𝔽3)C22semidirect
32. D8×H(3,𝔽3)C22semidirect
33. C2×C8×H(3,𝔽3)C22semidirect
34. #3755⋊C3C22semidirect
35. #3756⋊C3C22semidirect
36. #3753⋊C3C22semidirect
37. #3754⋊C3C22semidirect
38. #3748⋊C3C22semidirect
39. #3744⋊C3C22semidirect
40. #3744⋊C3C22semidirect
41. #3743⋊C3C22semidirect
42. C8×(C3⋊D3)⋊C3C22semidirect
43. #64367C2×C3semidirect
44. #64366C2×C3semidirect
48. C32×#135D3semidirect
49. C32×#135C2×C3semidirect
50. #64160C2×C3semidirect
51. #64158C2×C3semidirect
52. #64127C2×C3semidirect
53. #64125C2×C3semidirect
54. SD16×C3⋊D3C2×C3semidirect
55. #64120C2×C3semidirect
56. C2×#3744C2×C3semidirect
57. #64110C2×C3semidirect
102. C32×#41C2×D3semidirect
104. C32×#41C22×C3semidirect
106. Q8×C3⋊D3C22×C3semidirect
108. #3830C22×C3semidirect
117. C2×#634C22×C3semidirect
132. C32×Q16C2×D3semidirect
133. C32×Q16C22×C3semidirect
136. C32×SD16C2×D3semidirect
137. C32×SD16C2×D3semidirect
138. C32×SD16C22×C3semidirect
139. C32×SD16C22×C3semidirect
141. C32×D8C2×D3semidirect
142. C32×D8C22×C3semidirect
144. C2×C32×C8C2×D3semidirect
145. C2×C32×C8C22×C3semidirect
146. #3756C22×C3semidirect
147. #3755C22×C3semidirect
148. #3754C22×C3semidirect
149. #3753C22×C3semidirect
150. #3748C22×C3semidirect
151. #3744C22×C3semidirect
152. #3744C22×C3semidirect
153. #3743C22×C3semidirect
154. C8×C3⋊D3C22×C3semidirect
423. #135(C3⋊D3)⋊C3semidirect
427. H(3,𝔽3)#577semidirect
552. #41C2×(C3⋊D3)⋊C3semidirect
561. Q16C2×(C3⋊D3)⋊C3semidirect
566. SD16C2×(C3⋊D3)⋊C3semidirect
567. SD16C2×(C3⋊D3)⋊C3semidirect
569. D8C2×(C3⋊D3)⋊C3semidirect
573. C2×C8C2×(C3⋊D3)⋊C3semidirect
621. C32#5770semidirect
622. C32C3×#577semidirect

Maximal subgroups

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

subgroupindex
#117226392
#117226382
H(3,𝔽3)×#1352
#64158⋊C32
#64160⋊C32
#64127⋊C32
#64125⋊C32
SD16×(C3⋊D3)⋊C32
#64120⋊C32
C2×#3744⋊C32
#64110⋊C32
#105962413
C3×#57703