Finite Group Databasebeta

← C3×#80184 #11864184

Subgroups — C3×#80184 #11864184

Order 1152.

1582 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic
2C2×C3×#918C212yesmaximal, complemented
3C3×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
4C32×#451C211yesmaximal, characteristic, complemented
5C3×#5228C211yesmaximal, characteristic, complemented
6C3×#5187C212yesmaximal, complemented
7C3×#5046C211yesmaximal, characteristic, complemented
8C3×#4808C212yesmaximal, complemented
9C3×#4803C212yesmaximal, complemented
10C3×#4731C211yesmaximal, characteristic, complemented
11C3×#4726C211yesmaximal, characteristic, complemented
12C3×#3007—31nomaximal
13#80184C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8C2211yescharacteristic
15C2×C3×#239—28no—
16C2×C3×#239—21no—
17C2×C3×#239—21no—
18C2×C3×#239C2212yes—
19C2×C3×#239C2212yes—
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C22×C3×D12—21no—
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3—21no—
24C22×C3×C4×D3C2211yescharacteristic
25C2×C32×Q16C2212yescomplemented
26C32×C22⋊Q8C2211yescharacteristic
27C3×#946C2211yescharacteristic, complemented
28C2×C3×#216C2212yescomplemented
29C2×C3×#215C2212yescomplemented
30C3×#924C2211yescharacteristic
31C3×#918—28no—
32C2×C3×#204C2212yescomplemented
33C2×C3×ΓL(1,𝔽25)C2212yescomplemented
34C3×#897C2211yescharacteristic, complemented
35C3×#896—21no—
36C3×D3×C4⋊C4—21no—
37C3×D3×C4⋊C4C2211yescharacteristic, complemented
38C3×D3×C22⋊C4—21no—
39C3×#878—21no—
40C32×#103C2212yescomplemented
41C32×C22⋊C8C2211yescharacteristic
42C3×#835C2212yescomplemented
43C3×#830C2211yescharacteristic
44C3×#821C2212yescomplemented
45C3×(C2×D3)⋊C8C2212yescomplemented
46C3×#809C2212yescomplemented
47C22×C3×#41—31no—
48C22×#239C2×C311yescharacteristic
49C2×C3×#137—32no—
50C2×C3×C22⋊Q8—31no—
51C2×#918C2×C312yescomplemented
52D3×C22⋊Q8C2×C311yescharacteristic, complemented
53C3×#452—32no—
54C3×#452—32no—
55C3×#451—21no—
56C3×#451—31no—
57C3×#451D311yescharacteristic, complemented
58C3×#451C2×C311yescharacteristic, complemented
59C3×#450—31no—
60C3×#450—31no—
61C3×#417—32no—
62C3×#407—31no—
63#5228C2×C311yescharacteristic, complemented
64#5187C2×C312yescomplemented
65#5046C2×C311yescharacteristic, complemented
66#4808C2×C312yescomplemented
67#4803C2×C312yescomplemented
68#4731C2×C311yescharacteristic, complemented
69#4726C2×C311yescharacteristic, complemented
70C23×C3×D3—21no—
71C23×C3×D3D411yescharacteristic
72C2×C32×Q8—24no—
73C2×C32×Q8—21no—
74C2×C32×Q8C2311yescharacteristic
75C2×C32×Q8C2312yes—
76C22×C32×C4—21no—
77C22×C32×C4C2311yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C3×#239—28no—
80C3×#239—28no—
81C3×#239—24no—
82C3×#239—24no—
83C3×#239—24no—
84C3×#239D418yes—
85C3×D3×Q8—24no—
86C2×C3×D12—28no—
87C2×C3×D12—22no—
88C2×C3×D12—22no—
89C2×C3×D12—21no—
90C2×C3×D12—24no—
91C2×C3×D12C2312yes—
92C2×C3×C4×D3—28no—
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3—22no—
95C2×C3×C4×D3—24no—
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3D411yescharacteristic
99C2×C3×C4×D3D411yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C32×Q16—24no—
105C2×C32×C8C2312yes—
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109C3×#217—21no—
110C3×#216—24no—
111C3×#215—24no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C2×C3×C3⋊C8C2312yes—
120C3×#204—24no—
121C3×ΓL(1,𝔽25)—24no—
122#3007—31noSylow
123C2×C3×#41—32no—
124C2×C3×#41—32no—
125C2×C3×#41—61no—
126C2×C3×#41—61no—
127C2×C3×#41—68no—
128C22×C3×Q8—21no—
129C22×C3×Q8—31no—
130C22×C3×Q8C2×D311yescharacteristic
131C22×C3×Q8C22×C311yescharacteristic
132C22×C3×D4—31no—
133C22×C3×D4—61no—
134C23×C3×C4—31no—
135C23×C3×C4—61no—
136C2×#239—28no—
137C2×#239—21no—
138C2×#239—21no—
139C2×#239C22×C312yes—
140C2×#239C22×C312yes—
141C2×D3×Q8C22×C311yescharacteristic, complemented
142C22×D12—21no—
143C22×D12C22×C311yescharacteristic
144C22×C4×D3—21no—
145C22×C4×D3C22×C311yescharacteristic
146C3×#137—68no—
147C2×C3×Q16—22no—
148C2×C3×Q16—32no—
149C2×C3×Q16C2×D312yescomplemented
150C2×C3×Q16C22×C312yescomplemented
151C2×C3×SD16—32no—
152C2×C3×SD16—32no—
153C2×C3×M16—32no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C22⋊Q8C22×C311yescharacteristic
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—61no—
164C2×C3×C22⋊C4—61no—
165#946C22×C311yescharacteristic, complemented
166C2×#216C22×C312yescomplemented
167C2×#215C22×C312yescomplemented
168#924C22×C311yescharacteristic
169#918—28no—
170C2×#204C22×C312yescomplemented
171C2×ΓL(1,𝔽25)C22×C312yescomplemented
172#897C22×C311yescharacteristic, complemented
173#896—21no—
174D3×C4⋊C4—21no—
175D3×C4⋊C4C22×C311yescharacteristic, complemented
176D3×C22⋊C4—21no—
177#878—21no—
178C3×#103—22no—
179C3×#103—32no—
180C3×#103C2×D312yescomplemented
181C3×#103C22×C312yescomplemented
182C3×#102—32no—
183C3×#102—32no—
184C3×C22⋊C8—21no—
185C3×C22⋊C8—31no—
186C3×C22⋊C8—32no—
187C3×C22⋊C8C2×D311yescharacteristic
188C3×C22⋊C8C22×C311yescharacteristic
189#835C22×C312yescomplemented
190#830C22×C311yescharacteristic
191#821C22×C312yescomplemented
192(C2×D3)⋊C8C22×C312yescomplemented
193#809C22×C312yescomplemented
194C23×C32C2×D411yescharacteristic
195C22×C3×D3—24no—
196C22×C3×D3—22no—
197C22×C3×D3—22no—
198C22×C3×D3—22no—
199C22×C3×D3—41no—
200C22×C3×D3—42no—
201C22×C3×D3—42no—
202C22×C3×D3C2×D411yescharacteristic
203C22×C3×D3C2×D411yescharacteristic
204C32×Q8—24no—
205C32×Q8—22no—
206C32×Q8—22no—
207C32×Q8C2×D414yes—
208C2×C32×C4—24no—
209C2×C32×C4—22no—
210C2×C32×C4—22no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4C2×D411yescharacteristic
214C2×C32×C4C2411yescharacteristic
215C2×C3×Dic3—22no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—21no—
218C2×C3×Dic3C2×D411yescharacteristic
219C2×C3×Dic3C2×D411yescharacteristic
220C3×D12—28no—
221C3×D12—24no—
222C3×D12—28no—
223C3×D12—22no—
224C3×D12C2×D414yes—
225C3×C4×D3—28no—
226C3×C4×D3—22no—
227C3×C4×D3—22no—
228C3×C4×D3—28no—
229C3×C4×D3—22no—
230C3×C4×D3—42no—
231C3×C4×D3—42no—
232C3×C4×D3C2×D414yes—
233C3×Dic6—22no—
234C3×Dic6—42no—
235C32×C8—22no—
236C3×C3⋊C8—22no—
237C22×#41—31no—
238C2×#137—32no—
239C2×C22⋊Q8—31no—
240#452—32no—
241#452—32no—
242#451—31no—
243#451C3×D311yescharacteristic, complemented
244#450—31no—
245#450—31no—
246#417—32no—
247#407—31no—
248C24×C3—31no—
249C24×C3—61no—
250C23×D3—21no—
251C23×D3C3×D411yescharacteristic
252C3×#41—38no—
253C3×#41—64no—
254C3×#41—64no—
255C3×#41—68no—
256C3×#41—68no—
257C3×#41—64no—
258C2×C3×Q8—24no—
259C2×C3×Q8—24no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—22no—
263C2×C3×Q8—21no—
264C2×C3×Q8—31no—
265C2×C3×Q8—41no—
266C2×C3×Q8—44no—
267C2×C3×Q8—61no—
268C2×C3×Q8—64no—
269C2×C3×Q8C22×D311yescharacteristic
270C2×C3×Q8C22×D312yes—
271C2×C3×Q8C23×C311yescharacteristic
272C2×C3×Q8C23×C312yes—
273C2×C3×D4—32no—
274C2×C3×D4—64no—
275C2×C3×D4—62no—
276C2×C3×D4—62no—
277C2×C3×D4—68no—
278C2×C3×D4—61no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—41no—
288C22×C3×C4—64no—
289C22×C3×C4—62no—
290C22×C3×C4—62no—
291C22×C3×C4—68no—
292C22×C3×C4—61no—
293C22×C3×C4—61no—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C23×C311yescharacteristic
296C22×Dic3C3×D411yescharacteristic
297#239—28no—
298#239—28no—
299#239—24no—
300#239—24no—
301#239—24no—
302#239C3×D418yes—
303D3×Q8—24no—
304C2×D12—28no—
305C2×D12—22no—
306C2×D12—22no—
307C2×D12—21no—
308C2×D12—24no—
309C2×D12C23×C312yes—
310C2×C4×D3—28no—
311C2×C4×D3—22no—
312C2×C4×D3—22no—
313C2×C4×D3—24no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3C3×D411yescharacteristic
317C2×C4×D3C3×D411yescharacteristic
318C2×C4×D3C23×C311yescharacteristic
319C2×C4×D3C23×C311yescharacteristic
320C2×Dic6—21no—
321C2×Dic6C23×C311yescharacteristic
322C3×Q16—24no—
323C3×Q16—24no—
324C3×Q16—44no—
325C3×Q16—64no—
326C3×SD16—64no—
327C3×SD16—64no—
328C3×M16—64no—
329C2×C3×C8—22no—
330C2×C3×C8—32no—
331C2×C3×C8C22×D312yes—
332C2×C3×C8C23×C312yes—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—41no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—41no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350#217—21no—
351#216—24no—
352#215—24no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—21no—
355C4⋊Dic3—21no—
356C4⋊Dic3C23×C311yescharacteristic
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360C2×C3⋊C8C23×C312yes—
361#204—24no—
362ΓL(1,𝔽25)—24no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32#13712yescomplemented
366C22×C32C22×D411yescharacteristic
367C2×C3×D3—21no—
368C2×C3×D3—21no—
369C2×C3×D3—21no—
370C2×C3×D3—24no—
371C2×C3×D3—21no—
372C2×C3×D3—21no—
373C2×C3×D3—44no—
374C2×C3×D3—48no—
375C2×C3×D3—42no—
376C2×C3×D3—42no—
377C2×C3×D3#12012yes—
378C32×C4—24no—
379C32×C4—21no—
380C32×C4—41no—
381C32×C4—41no—
382C32×C4C22×D412yes—
383C3×Dic3—21no—
384C3×Dic3—41no—
385C3×Dic3—41no—
386C3×Dic3#12012yes—
387C2×#41—32no—
388C2×#41—32no—
389C2×#41—61no—
390C2×#41—61no—
391C2×#41—68no—
392C22×Q8—31no—
393C22×Q8C2×C3×D311yescharacteristic
394C22×D4—31no—
395C22×D4—61no—
396C23×C4—31no—
397C23×C4—61no—
398#137—68no—
399C2×Q16—32no—
400C2×Q16C2×C3×D312yescomplemented
401C2×SD16—32no—
402C2×SD16—32no—
403C2×M16—32no—
404C22⋊Q8—31no—
405C22⋊Q8—31no—
406C22⋊Q8—31no—
407C22⋊Q8—61no—
408C22⋊Q8—61no—
409C22⋊Q8C2×C3×D311yescharacteristic
410C2×C4⋊C4—31no—
411C2×C4⋊C4—61no—
412C2×C22⋊C4—61no—
413#103—32no—
414#103C2×C3×D312yescomplemented
415#102—32no—
416#102—32no—
417C22⋊C8—31no—
418C22⋊C8—32no—
419C22⋊C8C2×C3×D311yescharacteristic
420C23×C3—21no—
421C23×C3—31no—
422C23×C3—31no—
423C23×C3—62no—
424C23×C3—64no—
425C23×C3—62no—
426C23×C3—62no—
427C23×C3—121no—
428C23×C3—122no—
429C23×C3—122no—
430C23×C3D3×D411yescharacteristic
431C23×C3C2×C3×D411yescharacteristic
432C22×D3—24no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—41no—
437C22×D3—42no—
438C22×D3—42no—
439C22×D3C2×C3×D411yescharacteristic
440C22×D3C2×C3×D411yescharacteristic
441C3×Q8—24no—
442C3×Q8—24no—
443C3×Q8—22no—
444C3×Q8—22no—
445C3×Q8—22no—
446C3×Q8—22no—
447C3×Q8—24no—
448C3×Q8—42no—
449C3×Q8—42no—
450C3×Q8—44no—
451C3×Q8—62no—
452C3×Q8—122no—
453C3×Q8D3×D414yes—
454C3×Q8C2×C3×D414yes—
455C3×D4—34no—
456C3×D4—68no—
457C3×D4—68no—
458C3×D4—64no—
459C3×D4—62no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—31no—
473C2×C3×C4—34no—
474C2×C3×C4—31no—
475C2×C3×C4—42no—
476C2×C3×C4—42no—
477C2×C3×C4—44no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—62no—
481C2×C3×C4—68no—
482C2×C3×C4—62no—
483C2×C3×C4—68no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—122no—
489C2×C3×C4—122no—
490C2×C3×C4D3×D411yescharacteristic
491C2×C3×C4C2×C3×D411yescharacteristic
492C2×C3×C4C23×D311yescharacteristic
493C2×C3×C4C24×C311yescharacteristic
494C2×Dic3—22no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3C2×C3×D411yescharacteristic
498C2×Dic3C2×C3×D411yescharacteristic
499D12—28no—
500D12—24no—
501D12—28no—
502D12—22no—
503D12C2×C3×D414yes—
504C4×D3—28no—
505C4×D3—22no—
506C4×D3—22no—
507C4×D3—28no—
508C4×D3—22no—
509C4×D3—42no—
510C4×D3—42no—
511C4×D3C2×C3×D414yes—
512Dic6—22no—
513Dic6—42no—
514C3×C8—22no—
515C3×C8—22no—
516C3×C8—42no—
517C3×C8—62no—
518C3⋊C8—22no—
519C2×C32—22no—
520C2×C32C2×#12011yescharacteristic
521C2×C32C2×#13711yescharacteristic
522C2×C32#57511yescharacteristic
523C3×D3—22no—
524C3×D3—41no—
525C3×D3—44no—
526C24—31no—
527C24—61no—
528#41—38no—
529#41—64no—
530#41—64no—
531#41—68no—
532#41—68no—
533#41—64no—
534C2×Q8—24no—
535C2×Q8—21no—
536C2×Q8—31no—
537C2×Q8—61no—
538C2×Q8—64no—
539C2×Q8C22×C3×D311yescharacteristic
540C2×Q8C22×C3×D312yes—
541C2×D4—32no—
542C2×D4—64no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—68no—
546C2×D4—61no—
547C22×C4—21no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—64no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—68no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4C22×C3×D311yescharacteristic
560Q16—24no—
561Q16—64no—
562SD16—64no—
563SD16—64no—
564M16—64no—
565C2×C8—32no—
566C2×C8C22×C3×D312yes—
567C4⋊C4—21no—
568C4⋊C4—31no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4C22×C3×D311yescharacteristic
574C22⋊C4—21no—
575C22⋊C4—61no—
576C22⋊C4—61no—
577C22⋊C4—61no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—22no—
583C22×C3—21no—
584C22×C3—32no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—61no—
588C22×C3—61no—
589C22×C3—61no—
590C22×C3—61no—
591C22×C3—64no—
592C22×C3—61no—
593C22×C3—124no—
594C22×C3—128no—
595C22×C3—122no—
596C22×C3—122no—
597C22×C3#91812yescomplemented
598C22×C3C3×#13712yescomplemented
599C22×C3C2×D3×D411yescharacteristic
600C22×C3C22×C3×D411yescharacteristic
601C2×D3—21no—
602C2×D3—21no—
603C2×D3—21no—
604C2×D3—21no—
605C2×D3—21no—
606C2×D3—24no—
607C2×D3—44no—
608C2×D3—48no—
609C2×D3—42no—
610C2×D3—42no—
611C2×D3C3×#12012yes—
612C3×C4—24no—
613C3×C4—21no—
614C3×C4—24no—
615C3×C4—21no—
616C3×C4—22no—
617C3×C4—32no—
618C3×C4—41no—
619C3×C4—44no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—61no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—121no—
628C3×C4—121no—
629C3×C4C2×D3×D412yes—
630C3×C4C22×C3×D412yes—
631Dic3—21no—
632Dic3—41no—
633Dic3—41no—
634Dic3C3×#12012yes—
635C32#300711yescharacteristic, complemented, Sylow
636C23—31no—
637C23—31no—
638C23—62no—
639C23—64no—
640C23—62no—
641C23—62no—
642C23—121no—
643C23—122no—
644C23—122no—
645C23C3×D3×D411yescharacteristic
646Q8—24no—
647Q8—22no—
648Q8—22no—
649Q8—62no—
650Q8—122no—
651Q8C3×D3×D414yes—
652D4—34no—
653D4—68no—
654D4—68no—
655D4—64no—
656D4—62no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—31no—
663C2×C4—34no—
664C2×C4—31no—
665C2×C4—62no—
666C2×C4—68no—
667C2×C4—62no—
668C2×C4—68no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—122no—
674C2×C4—122no—
675C2×C4C3×D3×D411yescharacteristic
676C2×C4C23×C3×D311yescharacteristic
677C8—22no—
678C8—62no—
679C2×C3—22no—
680C2×C3—22no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—42no—
685C2×C3—62no—
686C2×C3—121no—
687C2×C3—124no—
688C2×C3D3×#12011yescharacteristic
689C2×C3C2×#91811yescharacteristic
690C2×C3#577711yescharacteristic
691C2×C3C2×C3×#12011yescharacteristic
692C2×C3C2×C3×#13711yescharacteristic
693C2×C3C3×#57511yescharacteristic
694D3—22no—
695D3—41no—
696D3—44no—
697C22—21no—
698C22—21no—
699C22—32no—
700C22—61no—
701C22—61no—
702C22—61no—
703C22—61no—
704C22—64no—
705C22—61no—
706C22—124no—
707C22—128no—
708C22—122no—
709C22—122no—
710C22C3×#91812yescomplemented
711C22C2×C3×D3×D411yescharacteristic
712C4—24no—
713C4—21no—
714C4—32no—
715C4—41no—
716C4—41no—
717C4—61no—
718C4—121no—
719C4—121no—
720C4C2×C3×D3×D412yes—
721C3—21no—
722C3#8018411yescharacteristic, direct product factor
723C3C3×#300711yescharacteristic, complemented
724C2—22no—
725C2—62no—
726C2—121no—
727C2—124no—
728C2C3×D3×#12011yescharacteristic
729C2C2×C3×#91811yescharacteristic
730C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC22×C3×#239C2
hypercenterC3×#451D3
hypocenterC3C3×#3007
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
2. C2×C3×#918C2semidirect
3. C3×D3×C22⋊Q8C2semidirect
4. C32×#451C2semidirect
5. C3×#5228C2semidirect
6. C3×#5187C2semidirect
7. C3×#5046C2semidirect
8. C3×#4808C2semidirect
9. C3×#4803C2semidirect
10. C3×#4731C2semidirect
11. C3×#4726C2semidirect
13. #80184C3direct (N × H)
20. C2×C3×D3×Q8C22semidirect
25. C2×C32×Q16C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#215C22semidirect
32. C2×C3×#204C22semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
34. C3×#897C22semidirect
37. C3×D3×C4⋊C4C22semidirect
40. C32×#103C22semidirect
42. C3×#835C22semidirect
44. C3×#821C22semidirect
45. C3×(C2×D3)⋊C8C22semidirect
46. C3×#809C22semidirect
51. C2×#918C2×C3semidirect
52. D3×C22⋊Q8C2×C3semidirect
57. C3×#451D3semidirect
58. C3×#451C2×C3semidirect
63. #5228C2×C3semidirect
64. #5187C2×C3semidirect
65. #5046C2×C3semidirect
66. #4808C2×C3semidirect
67. #4803C2×C3semidirect
68. #4731C2×C3semidirect
69. #4726C2×C3semidirect
141. C2×D3×Q8C22×C3semidirect
149. C2×C3×Q16C2×D3semidirect
150. C2×C3×Q16C22×C3semidirect
165. #946C22×C3semidirect
166. C2×#216C22×C3semidirect
167. C2×#215C22×C3semidirect
170. C2×#204C22×C3semidirect
171. C2×ΓL(1,𝔽25)C22×C3semidirect
172. #897C22×C3semidirect
175. D3×C4⋊C4C22×C3semidirect
180. C3×#103C2×D3semidirect
181. C3×#103C22×C3semidirect
189. #835C22×C3semidirect
191. #821C22×C3semidirect
192. (C2×D3)⋊C8C22×C3semidirect
193. #809C22×C3semidirect
243. #451C3×D3semidirect
365. C22×C32#137semidirect
400. C2×Q16C2×C3×D3semidirect
414. #103C2×C3×D3semidirect
597. C22×C3#918semidirect
598. C22×C3C3×#137semidirect
635. C32#3007semidirect
710. C22C3×#918semidirect
722. C3#80184direct (N × H)
723. C3C3×#3007semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×C3×#9182
C3×D3×C22⋊Q82
C32×#4512
C3×#52282
C3×#51872
C3×#50462
C3×#48082
C3×#48032
C3×#47312
C3×#47262
C3×#30073
#801843