Finite Group Databasebeta

← #137×(C3⋊D3)⋊C3 #13153515

Subgroups — #137×(C3⋊D3)⋊C3 #13153515

Order 1728.

963 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×(C3⋊D3)⋊C3C211yesmaximal, characteristic
2C2×Q8×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×#137C211yesmaximal, characteristic, complemented
4#64160⋊C3C211yesmaximal, characteristic, complemented
5#64151⋊C3C211yesmaximal, characteristic, complemented
6#64127⋊C3C212yesmaximal, complemented
7Q16×(C3⋊D3)⋊C3C212yesmaximal, complemented
8#64124⋊C3C212yesmaximal, complemented
9SD16×(C3⋊D3)⋊C3C212yesmaximal, complemented
10#64118⋊C3C211yesmaximal, characteristic, complemented
11M16×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
12C3⋊D3×#137C311yesmaximal, characteristic, complemented
13C3×D3×#137—31nomaximal
14#41×H(3,𝔽3)C2211yescharacteristic
15C2×Q8×H(3,𝔽3)C2211yescharacteristic, complemented
16#88722C2211yescharacteristic
17Q8×(C3⋊D3)⋊C3—21no—
18Q8×(C3⋊D3)⋊C3—21no—
19Q8×(C3⋊D3)⋊C3C2212yes—
20Q8×(C3⋊D3)⋊C3C2211yescharacteristic
21Q8×(C3⋊D3)⋊C3C2212yescomplemented
22#3830⋊C3—21no—
23#3830⋊C3C2211yescharacteristic
24D4×(C3⋊D3)⋊C3—21no—
25D4×(C3⋊D3)⋊C3C2211yescharacteristic
26#3828⋊C3—21no—
27#3828⋊C3C2211yescharacteristic
28C2×C4×(C3⋊D3)⋊C3—21no—
29C2×C4×(C3⋊D3)⋊C3—21no—
30C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
31C2×#634⋊C3—21no—
32C2×#634⋊C3C2211yescharacteristic, complemented
33Q16×H(3,𝔽3)C2212yescomplemented
34SD16×H(3,𝔽3)C2212yescomplemented
35M16×H(3,𝔽3)C2211yescharacteristic, complemented
36#3755⋊C3C2212yescomplemented
37#3756⋊C3C2212yescomplemented
38#3756⋊C3C2212yescomplemented
39#3754⋊C3C2212yescomplemented
40#3748⋊C3C2211yescharacteristic, complemented
41#3744⋊C3C2212yescomplemented
42#3743⋊C3C2212yescomplemented
43C8×(C3⋊D3)⋊C3C2212yes—
44#3746⋊C3C2212yescomplemented
45#41×C3⋊D3C2×C311yescharacteristic
46C2×Q8×C3⋊D3C2×C311yescharacteristic, complemented
47C3×D3×#41—31no—
48C2×C3×D3×Q8—31no—
49C32×#137—21no—
50C32×#137D311yescharacteristic, complemented
51C32×#137C2×C311yescharacteristic, complemented
52#64160C2×C311yescharacteristic, complemented
53#64151C2×C311yescharacteristic, complemented
54#64127C2×C312yescomplemented
55Q16×C3⋊D3C2×C312yescomplemented
56#64124C2×C312yescomplemented
57SD16×C3⋊D3C2×C312yescomplemented
58#64118C2×C311yescharacteristic, complemented
59M16×C3⋊D3C2×C311yescharacteristic, complemented
60C3×#951—31no—
61C3×#942—31no—
62C3×#918—32no—
63C3×D3×Q16—32no—
64C3×#915—32no—
65C3×D3×SD16—32no—
66C3×#909—31no—
67C3×D3×M16—31no—
68C22×(C3⋊D3)⋊C3—21no—
69C22×(C3⋊D3)⋊C3D411yescharacteristic
70Q8×H(3,𝔽3)—21no—
71Q8×H(3,𝔽3)C2312yes—
72Q8×H(3,𝔽3)C2311yescharacteristic
73D4×H(3,𝔽3)—21no—
74D4×H(3,𝔽3)C2311yescharacteristic
75C2×C4×H(3,𝔽3)—21no—
76C2×C4×H(3,𝔽3)—21no—
77C2×C4×H(3,𝔽3)C2311yescharacteristic
78#638⋊C3—21no—
79#638⋊C3—21no—
80#638⋊C3—21no—
81C2×(C3⋊Dic3)⋊C3—21no—
82C2×(C3⋊Dic3)⋊C3—21no—
83C2×(C3⋊Dic3)⋊C3D411yescharacteristic
84C4⋊((C3⋊D3)⋊C3)—21no—
85C4⋊((C3⋊D3)⋊C3)C2311yescharacteristic
86C4×(C3⋊D3)⋊C3—21no—
87C4×(C3⋊D3)⋊C3—22no—
88C4×(C3⋊D3)⋊C3—22no—
89C4×(C3⋊D3)⋊C3—21no—
90C4×(C3⋊D3)⋊C3—21no—
91C4×(C3⋊D3)⋊C3D411yescharacteristic
92C4×(C3⋊D3)⋊C3D411yescharacteristic
93C4×(C3⋊D3)⋊C3C2311yescharacteristic
94C4×(C3⋊D3)⋊C3C2311yescharacteristic
95#634⋊C3—21no—
96#634⋊C3—22no—
97#634⋊C3—22no—
98#634⋊C3—21no—
99#634⋊C3C2312yes—
100#634⋊C3C2311yescharacteristic
101C8×H(3,𝔽3)C2312yes—
102(C3⋊(C3⋊C8))⋊C3C2312yes—
103C2×C3×#137—91no—
104D3×#137—31no—
105D3×#137—91no—
106C32×#41—21no—
107C32×#41C2×D311yescharacteristic
108C32×#41C22×C311yescharacteristic
109C2×C32×Q8—21no—
110C2×C32×Q8C2×D311yescharacteristic, complemented
111C2×C32×Q8C22×C311yescharacteristic, complemented
112#3832C22×C311yescharacteristic
113Q8×C3⋊D3—21no—
114Q8×C3⋊D3—21no—
115Q8×C3⋊D3C22×C312yes—
116Q8×C3⋊D3C22×C311yescharacteristic
117Q8×C3⋊D3C22×C312yescomplemented
118#3830—21no—
119#3830C22×C311yescharacteristic
120D4×C3⋊D3—21no—
121D4×C3⋊D3C22×C311yescharacteristic
122#3828—21no—
123#3828C22×C311yescharacteristic
124C2×C4×C3⋊D3—21no—
125C2×C4×C3⋊D3—21no—
126C2×C4×C3⋊D3C22×C311yescharacteristic
127C2×#634—21no—
128C2×#634C22×C311yescharacteristic, complemented
129C3×#239—31no—
130C3×D3×Q8—32no—
131C3×D3×Q8—32no—
132C3×D3×Q8—31no—
133C3×D3×Q8—61no—
134C3×D3×Q8—61no—
135C3×#237—31no—
136C3×#237—61no—
137C3×D3×D4—31no—
138C3×D3×D4—61no—
139C3×#235—31no—
140C3×#235—61no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—61no—
143C2×C3×C4×D3—61no—
144C2×C3×Dic6—31no—
145C2×C3×Dic6—61no—
146C32×Q16—22no—
147C32×Q16C2×D312yescomplemented
148C32×Q16C22×C312yescomplemented
149C32×SD16—22no—
150C32×SD16C2×D312yescomplemented
151C32×SD16C22×C312yescomplemented
152C32×M16—21no—
153C32×M16C2×D311yescharacteristic, complemented
154C32×M16C22×C311yescharacteristic, complemented
155#3756C22×C312yescomplemented
156#3756C22×C312yescomplemented
157#3755C22×C312yescomplemented
158#3754C22×C312yescomplemented
159#3748C22×C311yescharacteristic, complemented
160#3746C22×C312yescomplemented
161#3744C22×C312yescomplemented
162#3743C22×C312yescomplemented
163C8×C3⋊D3C22×C312yes—
164C3×#216—32no—
165C3×#216—32no—
166C3×#215—32no—
167C3×#214—32no—
168C3×#208—31no—
169C3×Dic12—32no—
170C3×#204—32no—
171C3×ΓL(1,𝔽25)—32no—
172C3×D3×C8—32no—
173C22×H(3,𝔽3)—21no—
174C22×H(3,𝔽3)C2×D411yescharacteristic
175C2×(C3⋊D3)⋊C3—22no—
176C2×(C3⋊D3)⋊C3—21no—
177C2×(C3⋊D3)⋊C3—42no—
178C2×(C3⋊D3)⋊C3C2×D411yescharacteristic
179C2×(C3⋊D3)⋊C3C2×D411yescharacteristic
180C4×H(3,𝔽3)—22no—
181C4×H(3,𝔽3)—21no—
182C4×H(3,𝔽3)C2×D411yescharacteristic
183C4×H(3,𝔽3)C2411yescharacteristic
184(C3⋊Dic3)⋊C3—22no—
185(C3⋊Dic3)⋊C3—21no—
186(C3⋊Dic3)⋊C3C2×D411yescharacteristic
187(C3⋊Dic3)⋊C3C2×D411yescharacteristic
188C2×C3×#41—91no—
189C22×C3×Q8—91no—
190D3×#41—31no—
191D3×#41—91no—
192C2×D3×Q8—31no—
193C2×D3×Q8—91no—
194C3×#137—31no—
195C3×#137—31no—
196C3×#137—61no—
197C3×#137—91no—
198C3×#137—92no—
199C3×#137—92no—
200C3×#137—91no—
201C3×#137—91no—
202C3×#137C3×D311yescharacteristic
203C2×C3×Q16—92no—
204C2×C3×SD16—92no—
205C2×C3×M16—91no—
206#951—31no—
207#951—91no—
208#942—31no—
209#942—91no—
210#918—32no—
211#918—92no—
212D3×Q16—32no—
213D3×Q16—92no—
214#915—32no—
215#915—92no—
216D3×SD16—32no—
217D3×SD16—92no—
218#909—31no—
219#909—91no—
220D3×M16—31no—
221D3×M16—91no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3C3×D411yescharacteristic
224C22×C3×D3—31no—
225C22×C3×D3—61no—
226C32×Q8—21no—
227C32×Q8—21no—
228C32×Q8—22no—
229C32×Q8—21no—
230C32×Q8—41no—
231C32×Q8C22×D312yes—
232C32×Q8C22×D311yescharacteristic
233C32×Q8C23×C312yes—
234C32×Q8C23×C311yescharacteristic
235C32×D4—21no—
236C32×D4—21no—
237C32×D4—21no—
238C32×D4—41no—
239C32×D4C22×D311yescharacteristic
240C32×D4C23×C311yescharacteristic
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—41no—
247C2×C32×C4—41no—
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C23×C311yescharacteristic
250#638—21no—
251#638—21no—
252#638—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3C3×D411yescharacteristic
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)C23×C311yescharacteristic
258C4×C3⋊D3—21no—
259C4×C3⋊D3—22no—
260C4×C3⋊D3—22no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3C3×D411yescharacteristic
264C4×C3⋊D3C3×D411yescharacteristic
265C4×C3⋊D3C23×C311yescharacteristic
266C4×C3⋊D3C23×C311yescharacteristic
267#634—21no—
268#634—22no—
269#634—22no—
270#634—21no—
271#634C23×C312yes—
272#634C23×C311yescharacteristic
273C3×#67—61no—
274C3×#67—61no—
275C3×#67—61no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C3×D12—31no—
280C3×D12—61no—
281C3×C4×D3—31no—
282C3×C4×D3—31no—
283C3×C4×D3—31no—
284C3×C4×D3—31no—
285C3×C4×D3—61no—
286C3×C4×D3—61no—
287C3×C4×D3—62no—
288C3×C4×D3—62no—
289C3×C4×D3—61no—
290C3×Dic6—32no—
291C3×Dic6—31no—
292C3×Dic6—62no—
293C3×Dic6—62no—
294C3×Dic6—61no—
295C3×Dic6—61no—
296C32×C8—22no—
297C32×C8C22×D312yes—
298C32×C8C23×C312yes—
299C3⋊(C3⋊C8)C23×C312yes—
300C3×C3⋊C8—32no—
301C2×#137—91noSylow
302C2×H(3,𝔽3)—21no—
303C2×H(3,𝔽3)—41no—
304C2×H(3,𝔽3)C22×D411yescharacteristic
305(C3⋊D3)⋊C3—21no—
306(C3⋊D3)⋊C3—41no—
307(C3⋊D3)⋊C3#13712yesdirect product factor
308C3×#41—31no—
309C3×#41—31no—
310C3×#41—61no—
311C3×#41—91no—
312C3×#41—91no—
313C3×#41—91no—
314C3×#41—181no—
315C3×#41—181no—
316C3×#41C2×C3×D311yescharacteristic
317C2×C3×Q8—31no—
318C2×C3×Q8—31no—
319C2×C3×Q8—61no—
320C2×C3×Q8—91no—
321C2×C3×Q8—92no—
322C2×C3×Q8—91no—
323C2×C3×Q8—92no—
324C2×C3×Q8—181no—
325C2×C3×Q8—181no—
326C2×C3×Q8—181no—
327C2×C3×Q8C2×C3×D311yescharacteristic
328C2×C3×D4—91no—
329C2×C3×D4—181no—
330C22×C3×C4—91no—
331C22×C3×C4—181no—
332C22×C3×C4—181no—
333#239—31no—
334#239—91no—
335D3×Q8—32no—
336D3×Q8—32no—
337D3×Q8—31no—
338D3×Q8—61no—
339D3×Q8—61no—
340D3×Q8—92no—
341D3×Q8—92no—
342D3×Q8—91no—
343D3×Q8—181no—
344D3×Q8—181no—
345#237—31no—
346#237—61no—
347#237—91no—
348#237—181no—
349D3×D4—31no—
350D3×D4—61no—
351D3×D4—91no—
352D3×D4—181no—
353#235—31no—
354#235—61no—
355#235—91no—
356#235—181no—
357C2×C4×D3—31no—
358C2×C4×D3—61no—
359C2×C4×D3—61no—
360C2×C4×D3—91no—
361C2×C4×D3—181no—
362C2×C4×D3—181no—
363C2×Dic6—31no—
364C2×Dic6—61no—
365C2×Dic6—91no—
366C2×Dic6—181no—
367C3×Q16—32no—
368C3×Q16—32no—
369C3×Q16—62no—
370C3×Q16—92no—
371C3×Q16—92no—
372C3×Q16—92no—
373C3×Q16C2×C3×D312yes—
374C3×SD16—32no—
375C3×SD16—32no—
376C3×SD16—62no—
377C3×SD16—92no—
378C3×SD16—92no—
379C3×SD16—92no—
380C3×SD16C2×C3×D312yes—
381C3×M16—31no—
382C3×M16—31no—
383C3×M16—61no—
384C3×M16—92no—
385C3×M16—91no—
386C3×M16C2×C3×D311yescharacteristic
387C2×C3×C8—92no—
388#216—32no—
389#216—32no—
390#216—92no—
391#216—92no—
392#215—32no—
393#215—92no—
394#214—32no—
395#214—92no—
396#208—31no—
397#208—91no—
398Dic12—32no—
399Dic12—92no—
400#204—32no—
401#204—92no—
402ΓL(1,𝔽25)—32no—
403ΓL(1,𝔽25)—92no—
404D3×C8—32no—
405D3×C8—92no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—41no—
410C22×C32D3×D411yescharacteristic
411C22×C32C2×C3×D411yescharacteristic
412C2×C3⋊D3—22no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—42no—
415C2×C3⋊D3C2×C3×D411yescharacteristic
416C2×C3⋊D3C2×C3×D411yescharacteristic
417C2×C3×D3—31no—
418C2×C3×D3—31no—
419C2×C3×D3—62no—
420C2×C3×D3—61no—
421C2×C3×D3—122no—
422C32×C4—22no—
423C32×C4—21no—
424C32×C4—22no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—41no—
429C32×C4—42no—
430C32×C4D3×D411yescharacteristic
431C32×C4C2×C3×D411yescharacteristic
432C32×C4C23×D311yescharacteristic
433C32×C4C24×C311yescharacteristic
434C3⋊Dic3—22no—
435C3⋊Dic3—21no—
436C3⋊Dic3C2×C3×D411yescharacteristic
437C3⋊Dic3C2×C3×D411yescharacteristic
438C3×Dic3—31no—
439C3×Dic3—31no—
440C3×Dic3—62no—
441C3×Dic3—61no—
442C2×#41—91no—
443C22×Q8—91no—
444#137—91no—
445#137—91no—
446#137—92no—
447#137—92no—
448#137—91no—
449#137(C3⋊D3)⋊C311yescharacteristic, direct product factor
450C2×Q16—92no—
451C2×SD16—92no—
452C2×M16—91no—
453H(3,𝔽3)C2×#13711yescharacteristic, complemented, Sylow
454C23×C3—91no—
455C23×C3—181no—
456C22×D3—31no—
457C22×D3—61no—
458C22×D3—91no—
459C22×D3—181no—
460C3×Q8—21no—
461C3×Q8—32no—
462C3×Q8—31no—
463C3×Q8—32no—
464C3×Q8—31no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—62no—
468C3×Q8—61no—
469C3×Q8—92no—
470C3×Q8—91no—
471C3×Q8—121no—
472C3×Q8—181no—
473C3×Q8—182no—
474C3×Q8—182no—
475C3×Q8—181no—
476C3×Q8C22×C3×D312yes—
477C3×Q8C22×C3×D311yescharacteristic
478C3×D4—21no—
479C3×D4—31no—
480C3×D4—31no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—61no—
484C3×D4—91no—
485C3×D4—121no—
486C3×D4—181no—
487C3×D4—181no—
488C3×D4—181no—
489C3×D4—181no—
490C3×D4C22×C3×D311yescharacteristic
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—91no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4—121no—
506C2×C3×C4—121no—
507C2×C3×C4—181no—
508C2×C3×C4—181no—
509C2×C3×C4—181no—
510C2×C3×C4—182no—
511C2×C3×C4—182no—
512C2×C3×C4—181no—
513C2×C3×C4—181no—
514C2×C3×C4C22×C3×D311yescharacteristic
515#67—61no—
516#67—61no—
517#67—61no—
518#67—181no—
519#67—181no—
520#67—181no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—91no—
525C2×Dic3—181no—
526C2×Dic3—181no—
527D12—31no—
528D12—61no—
529D12—91no—
530D12—181no—
531C4×D3—31no—
532C4×D3—31no—
533C4×D3—31no—
534C4×D3—31no—
535C4×D3—61no—
536C4×D3—61no—
537C4×D3—62no—
538C4×D3—62no—
539C4×D3—61no—
540C4×D3—91no—
541C4×D3—91no—
542C4×D3—91no—
543C4×D3—91no—
544C4×D3—181no—
545C4×D3—181no—
546C4×D3—181no—
547C4×D3—182no—
548C4×D3—182no—
549Dic6—32no—
550Dic6—31no—
551Dic6—62no—
552Dic6—62no—
553Dic6—61no—
554Dic6—61no—
555Dic6—92no—
556Dic6—91no—
557Dic6—182no—
558Dic6—182no—
559Dic6—181no—
560Dic6—181no—
561C3×C8—32no—
562C3×C8—32no—
563C3×C8—62no—
564C3×C8—92no—
565C3×C8C22×C3×D312yes—
566C3⋊C8—32no—
567C3⋊C8—92no—
568C2×C32—21no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—41no—
572C2×C32—41no—
573C2×C32—41no—
574C2×C32—81no—
575C2×C32C2×D3×D411yescharacteristic
576C2×C32C22×C3×D411yescharacteristic
577C3⋊D3—21no—
578C3⋊D3—41no—
579C3⋊D3C3×#13712yescomplemented
580C3×D3—32no—
581C3×D3—61no—
582C3×D3—121no—
583#41—91no—
584#41—91no—
585#41—91no—
586#41—181no—
587#41—181no—
588#41C2×(C3⋊D3)⋊C311yescharacteristic
589C2×Q8—92no—
590C2×Q8—91no—
591C2×Q8—92no—
592C2×Q8—91no—
593C2×Q8—181no—
594C2×Q8—181no—
595C2×Q8—181no—
596C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic, complemented
597C2×D4—91no—
598C2×D4—181no—
599C22×C4—91no—
600C22×C4—181no—
601C22×C4—181no—
602Q16—92no—
603Q16—92no—
604Q16—92no—
605Q16C2×(C3⋊D3)⋊C312yescomplemented
606SD16—92no—
607SD16—92no—
608SD16—92no—
609SD16C2×(C3⋊D3)⋊C312yescomplemented
610M16—91no—
611M16—92no—
612M16C2×(C3⋊D3)⋊C311yescharacteristic, complemented
613C2×C8—92no—
614C22×C3—21no—
615C22×C3—31no—
616C22×C3—31no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—91no—
621C22×C3—91no—
622C22×C3—121no—
623C22×C3—181no—
624C22×C3—182no—
625C22×C3—362no—
626C22×C3C3×D3×D411yescharacteristic
627C2×D3—31no—
628C2×D3—31no—
629C2×D3—62no—
630C2×D3—61no—
631C2×D3—91no—
632C2×D3—91no—
633C2×D3—122no—
634C2×D3—182no—
635C2×D3—181no—
636C2×D3—362no—
637C3×C4—22no—
638C3×C4—21no—
639C3×C4—31no—
640C3×C4—31no—
641C3×C4—31no—
642C3×C4—31no—
643C3×C4—62no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—62no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—91no—
650C3×C4—91no—
651C3×C4—121no—
652C3×C4—122no—
653C3×C4—181no—
654C3×C4—182no—
655C3×C4C3×D3×D411yescharacteristic
656C3×C4C23×C3×D311yescharacteristic
657Dic3—31no—
658Dic3—31no—
659Dic3—62no—
660Dic3—61no—
661Dic3—91no—
662Dic3—91no—
663Dic3—182no—
664Dic3—181no—
665C32—21no—
666C32D3×#13711yescharacteristic, complemented
667C32C2×C3×#13711yescharacteristic, complemented
668C23—91no—
669C23—181no—
670Q8—21no—
671Q8—92no—
672Q8—91no—
673Q8—182no—
674Q8—182no—
675Q8—181no—
676Q8—181no—
677Q8C22×(C3⋊D3)⋊C312yes—
678Q8C22×(C3⋊D3)⋊C311yescharacteristic
679D4—21no—
680D4—91no—
681D4—181no—
682D4—181no—
683D4—181no—
684D4—181no—
685D4C22×(C3⋊D3)⋊C311yescharacteristic
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—91no—
689C2×C4—91no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—182no—
696C2×C4—182no—
697C2×C4—181no—
698C2×C4—181no—
699C2×C4—181no—
700C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
701C8—92no—
702C8C22×(C3⋊D3)⋊C312yes—
703C2×C3—21no—
704C2×C3—31no—
705C2×C3—31no—
706C2×C3—41no—
707C2×C3—61no—
708C2×C3—61no—
709C2×C3—61no—
710C2×C3—92no—
711C2×C3—121no—
712C2×C3—121no—
713C2×C3—121no—
714C2×C3—181no—
715C2×C3—241no—
716C2×C3—361no—
717C2×C3C2×C3×D3×D411yescharacteristic
718D3—32no—
719D3—61no—
720D3—92no—
721D3—121no—
722D3—181no—
723D3—361no—
724C22—21no—
725C22—91no—
726C22—91no—
727C22—182no—
728C22—181no—
729C22—362no—
730C22D4×(C3⋊D3)⋊C311yescharacteristic
731C4—21no—
732C4—22no—
733C4—91no—
734C4—91no—
735C4—181no—
736C4—182no—
737C4D4×(C3⋊D3)⋊C311yescharacteristic
738C4C23×(C3⋊D3)⋊C311yescharacteristic
739C3—31no—
740C3—31no—
741C3—61no—
742C3C3×D3×#13711yescharacteristic
743C2—21no—
744C2—41no—
745C2—92no—
746C2—181no—
747C2—361no—
748C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC2C2×D4×(C3⋊D3)⋊C3
commutator, cosocleC32×C4C24×C3
FrattiniC3×C4C23×C3×D3
FittingH(3,𝔽3)×#137C2
socleC2×C3C2×C3×D3×D4
prime radical#41×(C3⋊D3)⋊C3C2
hypercenter#137(C3⋊D3)⋊C3
hypocenterC32C2×C3×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. C2×Q8×(C3⋊D3)⋊C3C2semidirect
3. H(3,𝔽3)×#137C2semidirect
4. #64160⋊C3C2semidirect
5. #64151⋊C3C2semidirect
6. #64127⋊C3C2semidirect
7. Q16×(C3⋊D3)⋊C3C2semidirect
8. #64124⋊C3C2semidirect
9. SD16×(C3⋊D3)⋊C3C2semidirect
10. #64118⋊C3C2semidirect
11. M16×(C3⋊D3)⋊C3C2semidirect
12. C3⋊D3×#137C3semidirect
15. C2×Q8×H(3,𝔽3)C22semidirect
21. Q8×(C3⋊D3)⋊C3C22semidirect
32. C2×#634⋊C3C22semidirect
33. Q16×H(3,𝔽3)C22semidirect
34. SD16×H(3,𝔽3)C22semidirect
35. M16×H(3,𝔽3)C22semidirect
36. #3755⋊C3C22semidirect
37. #3756⋊C3C22semidirect
38. #3756⋊C3C22semidirect
39. #3754⋊C3C22semidirect
40. #3748⋊C3C22semidirect
41. #3744⋊C3C22semidirect
42. #3743⋊C3C22semidirect
44. #3746⋊C3C22semidirect
46. C2×Q8×C3⋊D3C2×C3semidirect
50. C32×#137D3semidirect
51. C32×#137C2×C3semidirect
52. #64160C2×C3semidirect
53. #64151C2×C3semidirect
54. #64127C2×C3semidirect
55. Q16×C3⋊D3C2×C3semidirect
56. #64124C2×C3semidirect
57. SD16×C3⋊D3C2×C3semidirect
58. #64118C2×C3semidirect
59. M16×C3⋊D3C2×C3semidirect
110. C2×C32×Q8C2×D3semidirect
111. C2×C32×Q8C22×C3semidirect
117. Q8×C3⋊D3C22×C3semidirect
128. C2×#634C22×C3semidirect
147. C32×Q16C2×D3semidirect
148. C32×Q16C22×C3semidirect
150. C32×SD16C2×D3semidirect
151. C32×SD16C22×C3semidirect
153. C32×M16C2×D3semidirect
154. C32×M16C22×C3semidirect
155. #3756C22×C3semidirect
156. #3756C22×C3semidirect
157. #3755C22×C3semidirect
158. #3754C22×C3semidirect
159. #3748C22×C3semidirect
160. #3746C22×C3semidirect
161. #3744C22×C3semidirect
162. #3743C22×C3semidirect
307. (C3⋊D3)⋊C3#137direct (N × H)
449. #137(C3⋊D3)⋊C3direct (N × H)
453. H(3,𝔽3)C2×#137semidirect
579. C3⋊D3C3×#137semidirect
596. C2×Q8C2×(C3⋊D3)⋊C3semidirect
605. Q16C2×(C3⋊D3)⋊C3semidirect
609. SD16C2×(C3⋊D3)⋊C3semidirect
612. M16C2×(C3⋊D3)⋊C3semidirect
666. C32D3×#137semidirect
667. C32C2×C3×#137semidirect

Maximal subgroups

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

subgroupindex
#41×(C3⋊D3)⋊C32
C2×Q8×(C3⋊D3)⋊C32
H(3,𝔽3)×#1372
#64160⋊C32
#64151⋊C32
#64127⋊C32
Q16×(C3⋊D3)⋊C32
#64124⋊C32
SD16×(C3⋊D3)⋊C32
#64118⋊C32
M16×(C3⋊D3)⋊C32
C3⋊D3×#1373
C3×D3×#1373