Finite Group Databasebeta

← C3×D3×#468 #11866883

Subgroups — C3×D3×#468 #11866883

Order 1152.

1148 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2C2×C3×D3×M16C211yesmaximal, characteristic, complemented
3C3×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
4C3×D3×#121C211yesmaximal, characteristic
5C32×#468C211yesmaximal, characteristic, complemented
6C3×#5174C211yesmaximal, characteristic, complemented
7C3×#5134C211yesmaximal, characteristic, complemented
8C3×#5049C211yesmaximal, characteristic, complemented
9C3×#5042C211yesmaximal, characteristic, complemented
10C3×#4886C211yesmaximal, characteristic, complemented
11C3×D3×#107C211yesmaximal, characteristic, complemented
12C3×#4812C211yesmaximal, characteristic, complemented
13C3×D3×#103C211yesmaximal, characteristic, complemented
14C3×#4780C211yesmaximal, characteristic, complemented
15C3×D3×#102C211yesmaximal, characteristic, complemented
16C2×C3×#468—31nomaximal
17D3×#468C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23C2×C32×M16C2211yescharacteristic, complemented
24C32×C22⋊Q8C2211yescharacteristic, complemented
25C32×#121C2211yescharacteristic
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#939—21no—
29C3×#938C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic, complemented
31C3×#930C2211yescharacteristic
32C3×#924C2211yescharacteristic, complemented
33C2×C3×#208C2211yescharacteristic, complemented
34C3×D3×SD16—24no—
35C3×D3×M16—24no—
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
39C2×C3×D3×C8C2211yescharacteristic
40C2×C3×D3×C8C2211yescharacteristic
41C3×#897C2211yescharacteristic, complemented
42C3×#896—21no—
43C3×#895C2211yescharacteristic
44C3×D3×C4⋊C4—21no—
45C3×D3×C4⋊C4C2211yescharacteristic
46C3×D3×C4⋊C4C2211yescharacteristic
47C3×#884—21no—
48C3×D3×C22⋊C4—21no—
49C3×D3×C22⋊C4—21no—
50C3×#878—21no—
51C32×#107C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#818C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61C3×#807C2211yescharacteristic, complemented
62C3×#807C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64C22×C3×M16—31no—
65C2×C3×C22⋊Q8—31no—
66C2×C3×#121—31no—
67C2×D3×SD16C2×C311yescharacteristic, complemented
68C2×D3×M16C2×C311yescharacteristic, complemented
69D3×C22⋊Q8C2×C311yescharacteristic, complemented
70D3×#121C2×C311yescharacteristic
71C3×#468—21no—
72C3×#468—31no—
73C3×#468—31no—
74C3×#468—31no—
75C3×#468—31no—
76C3×#468—31no—
77C3×#468—31no—
78C3×#468—31no—
79C3×#468D311yescharacteristic, direct product factor
80C3×#468C2×C311yescharacteristic, complemented
81C2×C3×#107—31no—
82C2×C3×#103—31no—
83C2×C3×#102—31no—
84#5174C2×C311yescharacteristic, complemented
85#5134C2×C311yescharacteristic, complemented
86#5049C2×C311yescharacteristic, complemented
87#5042C2×C311yescharacteristic, complemented
88#4886C2×C311yescharacteristic, complemented
89D3×#107C2×C311yescharacteristic, complemented
90#4812C2×C311yescharacteristic, complemented
91D3×#103C2×C311yescharacteristic, complemented
92#4780C2×C311yescharacteristic, complemented
93D3×#102C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C23×C3×D3D411yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3D411yescharacteristic
104C3×D3×Q8—22no—
105C3×D3×Q8—22no—
106C3×D3×D4—22no—
107C3×D3×D4—22no—
108C3×D3×D4—44no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3D411yescharacteristic
117C2×C3×C4×D3D411yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6—21no—
121C2×C3×Dic6C2311yescharacteristic
122C32×SD16—22no—
123C32×M16—22no—
124C2×C32×C8C2311yescharacteristic
125C2×C32×C8C2311yescharacteristic
126C32×C4⋊C4—21no—
127C32×C4⋊C4C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#215—22no—
134C3×#214—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×#208—22no—
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149C3×#204—22no—
150C3×ΓL(1,𝔽25)—22no—
151C3×ΓL(1,𝔽25)—22no—
152C3×D3×C8—22no—
153C3×D3×C8D414yescomplemented
154C2×#468—31noSylow
155C22×C3×Q8—31no—
156C22×C3×D4—31no—
157C22×C3×D4—61no—
158C23×C3×C4—31no—
159C2×D3×Q8C22×C311yescharacteristic
160C2×D3×D4—21no—
161C2×D3×D4C22×C311yescharacteristic
162C22×C4×D3C22×C311yescharacteristic
163C2×C3×SD16—21no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—64no—
168C2×C3×SD16C2×D311yescharacteristic, complemented
169C2×C3×SD16C22×C311yescharacteristic, complemented
170C2×C3×M16—21no—
171C2×C3×M16—31no—
172C2×C3×M16—31no—
173C2×C3×M16—31no—
174C2×C3×M16—64no—
175C2×C3×M16C2×D311yescharacteristic, complemented
176C2×C3×M16C22×C311yescharacteristic, complemented
177C22×C3×C8—31no—
178C22×C3×C8—31no—
179C3×C22⋊Q8—21no—
180C3×C22⋊Q8—31no—
181C3×C22⋊Q8—31no—
182C3×C22⋊Q8—31no—
183C3×C22⋊Q8—61no—
184C3×C22⋊Q8—61no—
185C3×C22⋊Q8C2×D311yescharacteristic, complemented
186C3×C22⋊Q8C22×C311yescharacteristic, complemented
187C3×#121—21no—
188C3×#121—31no—
189C3×#121—31no—
190C3×#121—31no—
191C3×#121—61no—
192C3×#121—61no—
193C3×#121C2×D311yescharacteristic
194C3×#121C22×C311yescharacteristic
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4—31no—
197C2×C3×C4⋊C4—61no—
198C2×C3×C22⋊C4—61no—
199C2×C3×C22⋊C4—61no—
200#946C22×C311yescharacteristic, complemented
201C2×#215C22×C311yescharacteristic, complemented
202#939—21no—
203#938C22×C311yescharacteristic
204C2×#214C22×C311yescharacteristic, complemented
205#930C22×C311yescharacteristic
206#924C22×C311yescharacteristic, complemented
207C2×#208C22×C311yescharacteristic, complemented
208D3×SD16—24no—
209D3×M16—24no—
210C2×#204C22×C311yescharacteristic, complemented
211C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
212C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
213C2×D3×C8C22×C311yescharacteristic
214C2×D3×C8C22×C311yescharacteristic
215#897C22×C311yescharacteristic, complemented
216#896—21no—
217#895C22×C311yescharacteristic
218D3×C4⋊C4—21no—
219D3×C4⋊C4C22×C311yescharacteristic
220D3×C4⋊C4C22×C311yescharacteristic
221#884—21no—
222D3×C22⋊C4—21no—
223D3×C22⋊C4—21no—
224#878—21no—
225C3×#107—21no—
226C3×#107—31no—
227C3×#107—31no—
228C3×#107—31no—
229C3×#107C2×D311yescharacteristic, complemented
230C3×#107C22×C311yescharacteristic, complemented
231C3×#103—21no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103C2×D311yescharacteristic, complemented
236C3×#103C22×C311yescharacteristic, complemented
237C3×#102—21no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102C2×D311yescharacteristic, complemented
242C3×#102C22×C311yescharacteristic, complemented
243#835C22×C311yescharacteristic, complemented
244#832C22×C311yescharacteristic, complemented
245#821C22×C311yescharacteristic, complemented
246#818C22×C311yescharacteristic, complemented
247#816C22×C311yescharacteristic, complemented
248#810C22×C311yescharacteristic, complemented
249#809C22×C311yescharacteristic, complemented
250#807C22×C311yescharacteristic, complemented
251#807C22×C311yescharacteristic, complemented
252C23×C32—21no—
253C23×C32C2×D411yescharacteristic
254C22×C3×D3—22no—
255C22×C3×D3—22no—
256C22×C3×D3—22no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—42no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275C3×#67—42no—
276C3×#67—42no—
277C3×#67—42no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×C4×D3—22no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—22no—
291C3×C4×D3—42no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×C4×D3C2×D412yes—
295C3×C4×D3#4112yes—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—42no—
299C32×C8—21no—
300C32×C8C2×D412yescomplemented
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yescomplemented
303C22×SD16—31no—
304C22×M16—31no—
305C2×C22⋊Q8—31no—
306C2×#121—31no—
307#468—31no—
308#468—31no—
309#468—31no—
310#468—31no—
311#468—31no—
312#468—31no—
313#468—31no—
314#468C3×D311yescharacteristic, direct product factor
315C2×#107—31no—
316C2×#103—31no—
317C2×#102—31no—
318C24×C3—31no—
319C24×C3—61no—
320C23×D3—21no—
321C23×D3C3×D411yescharacteristic
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—61no—
325C2×C3×Q8—62no—
326C2×C3×Q8—62no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C23×C311yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—41no—
334C2×C3×D4—61no—
335C2×C3×D4—62no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—124no—
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C23×C311yescharacteristic
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—62no—
350C22×C3×C4—62no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C23×C311yescharacteristic
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—21no—
359C22×Dic3C3×D411yescharacteristic
360D3×Q8—22no—
361D3×Q8—22no—
362D3×D4—22no—
363D3×D4—22no—
364D3×D4—44no—
365C2×D12—21no—
366C2×D12C23×C311yescharacteristic
367C2×C4×D3—22no—
368C2×C4×D3—22no—
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—21no—
372C2×C4×D3C3×D411yescharacteristic
373C2×C4×D3C3×D411yescharacteristic
374C2×C4×D3C23×C311yescharacteristic
375C2×C4×D3C23×C311yescharacteristic
376C2×Dic6—21no—
377C2×Dic6C23×C311yescharacteristic
378C3×SD16—22no—
379C3×SD16—22no—
380C3×SD16—42no—
381C3×SD16—62no—
382C3×SD16—62no—
383C3×SD16—62no—
384C3×M16—22no—
385C3×M16—22no—
386C3×M16—42no—
387C3×M16—62no—
388C3×M16—62no—
389C3×M16—62no—
390C2×C3×C8—21no—
391C2×C3×C8—21no—
392C2×C3×C8—31no—
393C2×C3×C8—34no—
394C2×C3×C8—31no—
395C2×C3×C8—62no—
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C23×C311yescharacteristic
399C2×C3×C8C23×C311yescharacteristic
400C3×C4⋊C4—21no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—21no—
403C3×C4⋊C4—21no—
404C3×C4⋊C4—31no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—41no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4C22×D311yescharacteristic
413C3×C4⋊C4C22×D311yescharacteristic
414C3×C4⋊C4C23×C311yescharacteristic
415C3×C4⋊C4C23×C311yescharacteristic
416C3×C22⋊C4—21no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—21no—
420C3×C22⋊C4—41no—
421C3×C22⋊C4—41no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428#217—21no—
429#217—21no—
430#215—22no—
431#214—22no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436C4⋊Dic3—21no—
437C4⋊Dic3C23×C311yescharacteristic
438C4⋊Dic3C23×C311yescharacteristic
439Dic3⋊C4—21no—
440Dic3⋊C4—21no—
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443#208—22no—
444C2×C3⋊C8C23×C311yescharacteristic
445C2×C3⋊C8C23×C311yescharacteristic
446#204—22no—
447ΓL(1,𝔽25)—22no—
448ΓL(1,𝔽25)—22no—
449D3×C8—22no—
450D3×C8C3×D414yescomplemented
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—44no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—84no—
466C2×C3×D3#12112yes—
467C2×C3×D3AGL(1,ℤ/8)12yes—
468C2×C3×D3#13712yes—
469C32×C4—21no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4C2×#4111yescharacteristic
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3#12112yes—
480C22×Q8—31no—
481C22×D4—31no—
482C22×D4—61no—
483C23×C4—31no—
484C2×SD16—31no—
485C2×SD16—31no—
486C2×SD16—31no—
487C2×SD16—64no—
488C2×SD16C2×C3×D311yescharacteristic, complemented
489C2×M16—31no—
490C2×M16—31no—
491C2×M16—31no—
492C2×M16—64no—
493C2×M16C2×C3×D311yescharacteristic, complemented
494C22×C8—31no—
495C22×C8—31no—
496C22⋊Q8—31no—
497C22⋊Q8—31no—
498C22⋊Q8—31no—
499C22⋊Q8—61no—
500C22⋊Q8—61no—
501C22⋊Q8C2×C3×D311yescharacteristic, complemented
502#121—31no—
503#121—31no—
504#121—31no—
505#121—61no—
506#121—61no—
507#121C2×C3×D311yescharacteristic
508C2×C4⋊C4—31no—
509C2×C4⋊C4—31no—
510C2×C4⋊C4—61no—
511C2×C22⋊C4—61no—
512C2×C22⋊C4—61no—
513#107—31no—
514#107—31no—
515#107—31no—
516#107C2×C3×D311yescharacteristic, complemented
517#103—31no—
518#103—31no—
519#103—31no—
520#103C2×C3×D311yescharacteristic, complemented
521#102—31no—
522#102—31no—
523#102—31no—
524#102C2×C3×D311yescharacteristic, complemented
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—31no—
530C23×C3—41no—
531C23×C3—62no—
532C23×C3—62no—
533C23×C3—62no—
534C23×C3—61no—
535C23×C3—122no—
536C23×C3—122no—
537C23×C3—122no—
538C23×C3D3×D411yescharacteristic
539C23×C3C2×C3×D411yescharacteristic
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—21no—
544C22×D3—42no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3C2×C3×D411yescharacteristic
548C22×D3C2×C3×D411yescharacteristic
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—122no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—42no—
565C3×D4—42no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—82no—
569C3×D4—122no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—122no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—31no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—31no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—62no—
595C2×C3×C4—62no—
596C2×C3×C4—62no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—122no—
603C2×C3×C4—122no—
604C2×C3×C4—122no—
605C2×C3×C4D3×D411yescharacteristic
606C2×C3×C4C2×C3×D411yescharacteristic
607C2×C3×C4C23×D311yescharacteristic
608C2×C3×C4C24×C311yescharacteristic
609#67—42no—
610#67—42no—
611#67—42no—
612C2×Dic3—22no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3C2×C3×D411yescharacteristic
617C2×Dic3C2×C3×D411yescharacteristic
618D12—21no—
619D12—21no—
620D12—42no—
621C4×D3—22no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—22no—
625C4×D3—42no—
626C4×D3—42no—
627C4×D3—42no—
628C4×D3C2×C3×D412yes—
629C4×D3C3×#4112yes—
630Dic6—21no—
631Dic6—21no—
632Dic6—42no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—22no—
636C3×C8—32no—
637C3×C8—41no—
638C3×C8—61no—
639C3×C8D3×D412yescomplemented
640C3×C8C2×C3×D412yescomplemented
641C3⋊C8—21no—
642C3⋊C8C2×C3×D412yescomplemented
643C2×C32—41no—
644C2×C32—81no—
645C2×C32C2×#12111yescharacteristic
646C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
647C2×C32C2×#13711yescharacteristic
648C3×D3—41no—
649C3×D3—81no—
650C3×D3#46814yesdirect product factor
651C24—31no—
652C24—61no—
653C2×Q8—31no—
654C2×Q8—61no—
655C2×Q8—62no—
656C2×Q8—62no—
657C2×Q8C22×C3×D311yescharacteristic
658C2×D4—21no—
659C2×D4—31no—
660C2×D4—61no—
661C2×D4—62no—
662C2×D4—62no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—124no—
667C2×D4C22×C3×D311yescharacteristic
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4C22×C3×D311yescharacteristic
679SD16—22no—
680SD16—62no—
681SD16—62no—
682SD16—62no—
683M16—22no—
684M16—62no—
685M16—62no—
686M16—62no—
687C2×C8—31no—
688C2×C8—34no—
689C2×C8—31no—
690C2×C8—62no—
691C2×C8C22×C3×D311yescharacteristic
692C2×C8C22×C3×D311yescharacteristic
693C4⋊C4—21no—
694C4⋊C4—31no—
695C4⋊C4—31no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4—61no—
701C4⋊C4C22×C3×D311yescharacteristic
702C4⋊C4C22×C3×D311yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—32no—
719C22×C3—32no—
720C22×C3—32no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—124no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—244no—
741C22×C3C2×D3×D411yescharacteristic
742C22×C3C22×C3×D411yescharacteristic
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—44no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—84no—
751C2×D3C3×#12112yes—
752C2×D3C3×AGL(1,ℤ/8)12yes—
753C2×D3C3×#13712yes—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—32no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—61no—
767C3×C4—81no—
768C3×C4—81no—
769C3×C4—81no—
770C3×C4—121no—
771C3×C4—121no—
772C3×C4—121no—
773C3×C4C2×D3×D411yescharacteristic
774C3×C4D3×#4111yescharacteristic
775C3×C4C22×C3×D411yescharacteristic
776C3×C4C2×C3×#4111yescharacteristic
777Dic3—21no—
778Dic3—41no—
779Dic3—41no—
780Dic3—41no—
781Dic3C3×#12112yes—
782C32C2×#46811yescharacteristic, complemented, Sylow
783C23—21no—
784C23—31no—
785C23—31no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—61no—
790C23—122no—
791C23—122no—
792C23—122no—
793C23C3×D3×D411yescharacteristic
794Q8—21no—
795Q8—21no—
796Q8—61no—
797Q8—61no—
798Q8—122no—
799D4—21no—
800D4—21no—
801D4—42no—
802D4—61no—
803D4—61no—
804D4—122no—
805D4—122no—
806D4—122no—
807D4—122no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—31no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—31no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—122no—
826C2×C4—122no—
827C2×C4—122no—
828C2×C4C3×D3×D411yescharacteristic
829C2×C4C23×C3×D311yescharacteristic
830C8—21no—
831C8—32no—
832C8—61no—
833C8C3×D3×D412yescomplemented
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—34no—
838C2×C3—41no—
839C2×C3—41no—
840C2×C3—81no—
841C2×C3—81no—
842C2×C3—81no—
843C2×C3—121no—
844C2×C3—161no—
845C2×C3—241no—
846C2×C3D3×#12111yescharacteristic
847C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
848C2×C3D3×#13711yescharacteristic
849C2×C3C2×C3×#12111yescharacteristic
850C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
851C2×C3C2×C3×#13711yescharacteristic
852D3—41no—
853D3—81no—
854D3C3×#46814yesdirect product factor
855C22—21no—
856C22—21no—
857C22—21no—
858C22—32no—
859C22—32no—
860C22—32no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—61no—
865C22—61no—
866C22—61no—
867C22—124no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—244no—
872C22C2×C3×D3×D411yescharacteristic
873C4—21no—
874C4—32no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—61no—
879C4—121no—
880C4—121no—
881C4—121no—
882C4C2×C3×D3×D411yescharacteristic
883C4C3×D3×#4111yescharacteristic
884C3—21no—
885C3D3×#46811yescharacteristic, direct product factor
886C3C2×C3×#46811yescharacteristic, complemented
887C2—34no—
888C2—41no—
889C2—81no—
890C2—121no—
891C2—241no—
892C2C3×D3×#12111yescharacteristic
893C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
894C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#468C2
socleC22×C32C22×D4
prime radicalC3×D3×#121C2
hypercenterC3×#468D3
hypocenterC3C2×C3×#468
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#468

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×SD16C2semidirect
2. C2×C3×D3×M16C2semidirect
3. C3×D3×C22⋊Q8C2semidirect
5. C32×#468C2semidirect
6. C3×#5174C2semidirect
7. C3×#5134C2semidirect
8. C3×#5049C2semidirect
9. C3×#5042C2semidirect
10. C3×#4886C2semidirect
11. C3×D3×#107C2semidirect
12. C3×#4812C2semidirect
13. C3×D3×#103C2semidirect
14. C3×#4780C2semidirect
15. C3×D3×#102C2semidirect
17. D3×#468C3direct (N × H)
22. C2×C32×SD16C22semidirect
23. C2×C32×M16C22semidirect
24. C32×C22⋊Q8C22semidirect
26. C3×#946C22semidirect
27. C2×C3×#215C22semidirect
30. C2×C3×#214C22semidirect
32. C3×#924C22semidirect
33. C2×C3×#208C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
38. C2×C3×ΓL(1,𝔽25)C22semidirect
41. C3×#897C22semidirect
51. C32×#107C22semidirect
52. C32×#103C22semidirect
53. C32×#102C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×#818C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. C3×#807C22semidirect
62. C3×#807C22semidirect
67. C2×D3×SD16C2×C3semidirect
68. C2×D3×M16C2×C3semidirect
69. D3×C22⋊Q8C2×C3semidirect
79. C3×#468D3direct (N × H)
80. C3×#468C2×C3semidirect
84. #5174C2×C3semidirect
85. #5134C2×C3semidirect
86. #5049C2×C3semidirect
87. #5042C2×C3semidirect
88. #4886C2×C3semidirect
89. D3×#107C2×C3semidirect
90. #4812C2×C3semidirect
91. D3×#103C2×C3semidirect
92. #4780C2×C3semidirect
93. D3×#102C2×C3semidirect
153. C3×D3×C8D4semidirect
168. C2×C3×SD16C2×D3semidirect
169. C2×C3×SD16C22×C3semidirect
175. C2×C3×M16C2×D3semidirect
176. C2×C3×M16C22×C3semidirect
185. C3×C22⋊Q8C2×D3semidirect
186. C3×C22⋊Q8C22×C3semidirect
200. #946C22×C3semidirect
201. C2×#215C22×C3semidirect
204. C2×#214C22×C3semidirect
206. #924C22×C3semidirect
207. C2×#208C22×C3semidirect
210. C2×#204C22×C3semidirect
211. C2×ΓL(1,𝔽25)C22×C3semidirect
212. C2×ΓL(1,𝔽25)C22×C3semidirect
215. #897C22×C3semidirect
229. C3×#107C2×D3semidirect
230. C3×#107C22×C3semidirect
235. C3×#103C2×D3semidirect
236. C3×#103C22×C3semidirect
241. C3×#102C2×D3semidirect
242. C3×#102C22×C3semidirect
243. #835C22×C3semidirect
244. #832C22×C3semidirect
245. #821C22×C3semidirect
246. #818C22×C3semidirect
247. #816C22×C3semidirect
248. #810C22×C3semidirect
249. #809C22×C3semidirect
250. #807C22×C3semidirect
251. #807C22×C3semidirect
300. C32×C8C2×D4semidirect
302. C3×C3⋊C8C2×D4semidirect
314. #468C3×D3direct (N × H)
450. D3×C8C3×D4semidirect
488. C2×SD16C2×C3×D3semidirect
493. C2×M16C2×C3×D3semidirect
501. C22⋊Q8C2×C3×D3semidirect
516. #107C2×C3×D3semidirect
520. #103C2×C3×D3semidirect
524. #102C2×C3×D3semidirect
639. C3×C8D3×D4semidirect
640. C3×C8C2×C3×D4semidirect
642. C3⋊C8C2×C3×D4semidirect
650. C3×D3#468direct (N × H)
782. C32C2×#468semidirect
833. C8C3×D3×D4semidirect
854. D3C3×#468direct (N × H)
885. C3D3×#468direct (N × H)
886. C3C2×C3×#468semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
C2×C3×D3×M162
C3×D3×C22⋊Q82
C3×D3×#1212
C32×#4682
C3×#51742
C3×#51342
C3×#50492
C3×#50422
C3×#48862
C3×D3×#1072
C3×#48122
C3×D3×#1032
C3×#47802
C3×D3×#1022
C2×C3×#4683
D3×#4683