Finite Group Databasebeta

← C3×#80478 #11866381

Subgroups — C3×#80478 #11866381

Order 1152.

970 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#918C211yesmaximal, characteristic
2C2×C3×D3×Q16C211yesmaximal, characteristic, complemented
3C3×#5724C211yesmaximal, characteristic
4C3×#5572C211yesmaximal, characteristic, complemented
5C32×#462C211yesmaximal, characteristic, complemented
6C3×#5185C211yesmaximal, characteristic, complemented
7C3×#5182C211yesmaximal, characteristic, complemented
8C3×#5090C211yesmaximal, characteristic, complemented
9C3×#5028C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4839C211yesmaximal, characteristic, complemented
12C3×#4804C211yesmaximal, characteristic
13C3×#4802C211yesmaximal, characteristic, complemented
14C3×#4798C211yesmaximal, characteristic, complemented
15C3×#4795C211yesmaximal, characteristic, complemented
16C3×#3044—31nomaximal
17#80478C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic
23C32×C4⋊Q8C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic
25C3×#947C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×#944C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×#918—24no—
33C3×D3×Q16—24no—
34C2×C3×Dic12C2211yescharacteristic
35C2×C3×#204C2211yescharacteristic
36C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic
38C3×#896—21no—
39C3×#896—21no—
40C3×#894—21no—
41C3×#894—21no—
42C3×#892—21no—
43C3×#892C2211yescharacteristic
44C3×#887—21no—
45C3×#887C2211yescharacteristic
46C3×#875C2211yescharacteristic
47C3×#872—21no—
48C3×#872C2211yescharacteristic
49C3×C4×Dic6—21no—
50C3×C4×Dic6C2211yescharacteristic
51C32×C4⋊C8C2211yescharacteristic
52C32×#103C2211yescharacteristic
53C32×#103C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#835C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×Dic3⋊C8C2211yescharacteristic
59C3×Dic3⋊C8C2211yescharacteristic
60C3×#810C2211yescharacteristic
61C3×#809C2211yescharacteristic
62C3×C4⋊(C3⋊C8)C2211yescharacteristic
63C2×C3×#137—31no—
64C22×C3×Q16—31no—
65C3×#536—31no—
66C3×#519—31no—
67C2×#918C2×C311yescharacteristic
68C2×D3×Q16C2×C311yescharacteristic, complemented
69#5724C2×C311yescharacteristic
70#5572C2×C311yescharacteristic, complemented
71C3×#464—31no—
72C3×#464—31no—
73C3×#464—31no—
74C3×#464—31no—
75C3×#462—21no—
76C3×#462—31no—
77C3×#462—31no—
78C3×#462—31no—
79C3×#462D311yescharacteristic, complemented
80C3×#462C2×C311yescharacteristic, complemented
81C3×#424—31no—
82C3×#419—31no—
83C3×#416—31no—
84#5185C2×C311yescharacteristic, complemented
85#5182C2×C311yescharacteristic, complemented
86#5090C2×C311yescharacteristic, complemented
87#5028C2×C311yescharacteristic, complemented
88#4845C2×C311yescharacteristic, complemented
89#4839C2×C311yescharacteristic, complemented
90#4804C2×C311yescharacteristic
91#4802C2×C311yescharacteristic, complemented
92#4798C2×C311yescharacteristic, complemented
93#4795C2×C311yescharacteristic, complemented
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C3×#239—22no—
98C3×#239—22no—
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C3×D3×Q8—22no—
102C3×D3×Q8D414yes—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C32×Q16—22no—
114C32×Q16—22no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4—21no—
118C32×C4⋊C4—21no—
119C32×C4⋊C4—21no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C42—21no—
122C32×C42C2311yescharacteristic
123C3×#216—22no—
124C3×#216—22no—
125C3×#216—22no—
126C3×#215—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4D411yescharacteristic
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3—21no—
143C3×C4×Dic3—21no—
144C3×C4×Dic3—21no—
145C3×C4×Dic3—21no—
146C3×C4×Dic3C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149C3×Dic12—22no—
150C3×#204—22no—
151C3×ΓL(1,𝔽25)—22no—
152C3×D3×C8—22no—
153#3044—31noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C22×C3×Q8—31no—
157C2×#239C22×C311yescharacteristic
158C2×D3×Q8C22×C311yescharacteristic
159C2×D3×Q8C22×C311yescharacteristic
160C3×#137—64no—
161C2×C3×Q16—21no—
162C2×C3×Q16—21no—
163C2×C3×Q16—31no—
164C2×C3×Q16—31no—
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C2×C3×Q16—64no—
168C2×C3×Q16C2×D311yescharacteristic
169C2×C3×Q16C2×D311yescharacteristic
170C2×C3×Q16C22×C311yescharacteristic
171C2×C3×Q16C22×C311yescharacteristic
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×M16—31no—
175C22×C3×C8—31no—
176C3×C4⋊Q8—21no—
177C3×C4⋊Q8—31no—
178C3×C4⋊Q8C2×D311yescharacteristic
179C3×C4⋊Q8C22×C311yescharacteristic
180C3×#124—31no—
181C3×#124—31no—
182C3×#123—61no—
183C3×#123—61no—
184C3×C22⋊Q8—61no—
185C3×C22⋊Q8—61no—
186C3×C4×Q8—21no—
187C3×C4×Q8—31no—
188C3×C4×Q8—31no—
189C3×C4×Q8—31no—
190C3×C4×Q8—61no—
191C3×C4×Q8—61no—
192C3×C4×Q8C2×D311yescharacteristic
193C3×C4×Q8C22×C311yescharacteristic
194C3×#117—31no—
195C3×#117—31no—
196C3×#117—61no—
197C3×#117—61no—
198#947C22×C311yescharacteristic
199Q8×Dic3C22×C311yescharacteristic
200#944C22×C311yescharacteristic
201C2×#216C22×C311yescharacteristic
202C2×#216C22×C311yescharacteristic
203C2×#216C22×C311yescharacteristic
204C2×#215C22×C311yescharacteristic
205#918—24no—
206D3×Q16—24no—
207C2×Dic12C22×C311yescharacteristic
208C2×#204C22×C311yescharacteristic
209C2×ΓL(1,𝔽25)C22×C311yescharacteristic
210C2×D3×C8C22×C311yescharacteristic
211#896—21no—
212#896—21no—
213#894—21no—
214#894—21no—
215#892—21no—
216#892C22×C311yescharacteristic
217#887—21no—
218#887C22×C311yescharacteristic
219#875C22×C311yescharacteristic
220#872—21no—
221#872C22×C311yescharacteristic
222C4×Dic6—21no—
223C4×Dic6C22×C311yescharacteristic
224C3×C4⋊C8—21no—
225C3×C4⋊C8—31no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8C2×D311yescharacteristic
229C3×C4⋊C8C22×C311yescharacteristic
230C3×#103—21no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#103C2×D311yescharacteristic
237C3×#103C2×D311yescharacteristic
238C3×#103C22×C311yescharacteristic
239C3×#103C22×C311yescharacteristic
240C3×#102—31no—
241C3×#102—31no—
242#835C22×C311yescharacteristic
243#835C22×C311yescharacteristic
244#821C22×C311yescharacteristic
245#816C22×C311yescharacteristic
246Dic3⋊C8C22×C311yescharacteristic
247Dic3⋊C8C22×C311yescharacteristic
248#810C22×C311yescharacteristic
249#809C22×C311yescharacteristic
250C4⋊(C3⋊C8)C22×C311yescharacteristic
251C22×C3×D3—21no—
252C22×C3×D3C2×D411yescharacteristic
253C32×Q8—21no—
254C32×Q8—21no—
255C32×Q8—21no—
256C32×Q8—21no—
257C32×Q8—21no—
258C32×Q8C2×D412yes—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—42no—
275C3×C4×D3—24no—
276C3×C4×D3—42no—
277C3×C4×D3—42no—
278C3×C4×D3C2×D412yes—
279C3×C4×D3#4112yes—
280C3×Dic6—21no—
281C3×Dic6—24no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6—42no—
285C3×Dic6C2×D412yes—
286C32×C8—21no—
287C32×C8—21no—
288C3×C3⋊C8—21no—
289C3×C3⋊C8—21no—
290C2×#137—31no—
291C22×Q16—31no—
292#536—31no—
293#519—31no—
294#464—31no—
295#464—31no—
296#464—31no—
297#464—31no—
298#462—31no—
299#462—31no—
300#462—31no—
301#462C3×D311yescharacteristic, complemented
302#424—31no—
303#419—31no—
304#416—31no—
305C3×#41—62no—
306C3×#41—62no—
307C2×C3×Q8—21no—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—34no—
311C2×C3×Q8—31no—
312C2×C3×Q8—31no—
313C2×C3×Q8—61no—
314C2×C3×Q8—61no—
315C2×C3×Q8—62no—
316C2×C3×Q8—62no—
317C2×C3×Q8—62no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×Q8C22×D311yescharacteristic
321C2×C3×Q8C23×C311yescharacteristic
322C2×C3×Q8C23×C311yescharacteristic
323C2×C3×Q8C23×C311yescharacteristic
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C22×C3×C4—31no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330#239—22no—
331#239—22no—
332D3×Q8—22no—
333D3×Q8—22no—
334D3×Q8—22no—
335D3×Q8C3×D414yes—
336C2×D12—21no—
337C2×D12C23×C311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—21no—
341C2×C4×D3C23×C311yescharacteristic
342C2×Dic6—21no—
343C2×Dic6—21no—
344C2×Dic6C23×C311yescharacteristic
345C2×Dic6C23×C311yescharacteristic
346C3×Q16—22no—
347C3×Q16—22no—
348C3×Q16—22no—
349C3×Q16—22no—
350C3×Q16—42no—
351C3×Q16—42no—
352C3×Q16—62no—
353C3×Q16—62no—
354C3×Q16—62no—
355C3×Q16—62no—
356C3×SD16—62no—
357C3×SD16—62no—
358C3×M16—62no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—62no—
364C2×C3×C8C22×D311yescharacteristic
365C2×C3×C8C22×D311yescharacteristic
366C2×C3×C8C23×C311yescharacteristic
367C2×C3×C8C23×C311yescharacteristic
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—41no—
379C3×C4⋊C4—41no—
380C3×C4⋊C4—41no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C4⋊C4C23×C311yescharacteristic
388C3×C22⋊C4—31no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C42—21no—
396C3×C42—21no—
397C3×C42—21no—
398C3×C42—31no—
399C3×C42—41no—
400C3×C42—61no—
401C3×C42—61no—
402C3×C42—61no—
403C3×C42—61no—
404C3×C42C22×D311yescharacteristic
405C3×C42C23×C311yescharacteristic
406#216—22no—
407#216—22no—
408#216—22no—
409#215—22no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4C3×D411yescharacteristic
416(C2×D3)⋊C4C3×D411yescharacteristic
417C4⋊Dic3—21no—
418C4⋊Dic3C23×C311yescharacteristic
419Dic3⋊C4—21no—
420Dic3⋊C4—21no—
421Dic3⋊C4—21no—
422Dic3⋊C4—21no—
423Dic3⋊C4C3×D411yescharacteristic
424Dic3⋊C4C3×D411yescharacteristic
425C4×Dic3—21no—
426C4×Dic3—21no—
427C4×Dic3—21no—
428C4×Dic3—21no—
429C4×Dic3C23×C311yescharacteristic
430C2×C3⋊C8C23×C311yescharacteristic
431C2×C3⋊C8C23×C311yescharacteristic
432Dic12—22no—
433#204—22no—
434ΓL(1,𝔽25)—22no—
435D3×C8—22no—
436C22×C32C22×D411yescharacteristic
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3#12112yes—
443C32×C4—21no—
444C32×C4—22no—
445C32×C4—21no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4—41no—
449C32×C4C22×D411yescharacteristic
450C32×C4C2×#4111yescharacteristic
451C3×Dic3—22no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3#12112yes—
457C2×#41—31no—
458C22×Q8—31no—
459C22×Q8—31no—
460#137—64no—
461C2×Q16—31no—
462C2×Q16—31no—
463C2×Q16—31no—
464C2×Q16—31no—
465C2×Q16—64no—
466C2×Q16C2×C3×D311yescharacteristic
467C2×Q16C2×C3×D311yescharacteristic
468C2×SD16—31no—
469C2×SD16—31no—
470C2×M16—31no—
471C22×C8—31no—
472C4⋊Q8—31no—
473C4⋊Q8C2×C3×D311yescharacteristic
474#124—31no—
475#124—31no—
476#123—61no—
477#123—61no—
478C22⋊Q8—61no—
479C22⋊Q8—61no—
480C4×Q8—31no—
481C4×Q8—31no—
482C4×Q8—31no—
483C4×Q8—61no—
484C4×Q8—61no—
485C4×Q8C2×C3×D311yescharacteristic
486#117—31no—
487#117—31no—
488#117—61no—
489#117—61no—
490C4⋊C8—31no—
491C4⋊C8—31no—
492C4⋊C8—31no—
493C4⋊C8C2×C3×D311yescharacteristic
494#103—31no—
495#103—31no—
496#103—31no—
497#103—31no—
498#103C2×C3×D311yescharacteristic
499#103C2×C3×D311yescharacteristic
500#102—31no—
501#102—31no—
502C23×C3—31no—
503C23×C3—61no—
504C22×D3—21no—
505C22×D3C2×C3×D411yescharacteristic
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—22no—
517C3×Q8—32no—
518C3×Q8—41no—
519C3×Q8—41no—
520C3×Q8—41no—
521C3×Q8—41no—
522C3×Q8—41no—
523C3×Q8—64no—
524C3×Q8—61no—
525C3×Q8—61no—
526C3×Q8—61no—
527C3×Q8—122no—
528C3×Q8D3×D412yes—
529C3×Q8C2×C3×D412yes—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—122no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—31no—
545C2×C3×C4—32no—
546C2×C3×C4—32no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—64no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—122no—
558C2×C3×C4—122no—
559C2×C3×C4D3×D411yescharacteristic
560C2×C3×C4D3×D411yescharacteristic
561C2×C3×C4C2×C3×D411yescharacteristic
562C2×C3×C4C2×C3×D411yescharacteristic
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C24×C311yescharacteristic
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3C2×C3×D411yescharacteristic
569C2×Dic3C2×C3×D411yescharacteristic
570C2×Dic3C2×C3×D411yescharacteristic
571D12—21no—
572D12—21no—
573D12—42no—
574C4×D3—24no—
575C4×D3—42no—
576C4×D3—42no—
577C4×D3C2×C3×D412yes—
578C4×D3C3×#4112yes—
579Dic6—21no—
580Dic6—24no—
581Dic6—21no—
582Dic6—21no—
583Dic6—42no—
584Dic6C2×C3×D412yes—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—41no—
590C3×C8—41no—
591C3×C8—61no—
592C3×C8—61no—
593C3⋊C8—21no—
594C3⋊C8—21no—
595C2×C32C2×#12111yescharacteristic
596C2×C32#57811yescharacteristic
597C2×C32#57811yescharacteristic
598C3×D3—22no—
599C3×D3—81no—
600#41—62no—
601#41—62no—
602C2×Q8—34no—
603C2×Q8—31no—
604C2×Q8—31no—
605C2×Q8—61no—
606C2×Q8—61no—
607C2×Q8—62no—
608C2×Q8—62no—
609C2×Q8—62no—
610C2×Q8C22×C3×D311yescharacteristic
611C2×Q8C22×C3×D311yescharacteristic
612C2×Q8C22×C3×D311yescharacteristic
613C2×D4—31no—
614C2×D4—61no—
615C22×C4—31no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619Q16—22no—
620Q16—22no—
621Q16—62no—
622Q16—62no—
623Q16—62no—
624Q16—62no—
625SD16—62no—
626SD16—62no—
627M16—62no—
628C2×C8—31no—
629C2×C8—31no—
630C2×C8—62no—
631C2×C8C22×C3×D311yescharacteristic
632C2×C8C22×C3×D311yescharacteristic
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4C22×C3×D311yescharacteristic
645C22⋊C4—31no—
646C22⋊C4—31no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C42—21no—
653C42—31no—
654C42—61no—
655C42—61no—
656C42—61no—
657C42—61no—
658C42C22×C3×D311yescharacteristic
659C22×C3—21no—
660C22×C3—32no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C22×C3×D411yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3C3×#12112yes—
674C3×C4—22no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—32no—
684C3×C4—41no—
685C3×C4—42no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—62no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—81no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C2×D3×D411yescharacteristic
701C3×C4D3×#4111yescharacteristic
702C3×C4C22×C3×D411yescharacteristic
703C3×C4C2×C3×#4111yescharacteristic
704Dic3—21no—
705Dic3—21no—
706Dic3—22no—
707Dic3—41no—
708Dic3—41no—
709Dic3C3×#12112yes—
710C32#304411yescharacteristic, complemented, Sylow
711C23—31no—
712C23—61no—
713Q8—21no—
714Q8—21no—
715Q8—21no—
716Q8—21no—
717Q8—21no—
718Q8—32no—
719Q8—64no—
720Q8—61no—
721Q8—61no—
722Q8—61no—
723Q8—122no—
724Q8C3×D3×D412yes—
725D4—61no—
726D4—61no—
727D4—122no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—31no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—64no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4C3×D3×D411yescharacteristic
744C2×C4C3×D3×D411yescharacteristic
745C2×C4C23×C3×D311yescharacteristic
746C8—21no—
747C8—21no—
748C8—61no—
749C8—61no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—62no—
754C2×C3—241no—
755C2×C3D3×#12111yescharacteristic
756C2×C3#576611yescharacteristic
757C2×C3#577911yescharacteristic
758C2×C3C2×C3×#12111yescharacteristic
759C2×C3C3×#57811yescharacteristic
760C2×C3C3×#57811yescharacteristic
761D3—22no—
762D3—81no—
763C22—32no—
764C22—61no—
765C22—61no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22C2×C3×D3×D411yescharacteristic
770C4—21no—
771C4—21no—
772C4—22no—
773C4—32no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—61no—
778C4—61no—
779C4—62no—
780C4—121no—
781C4—121no—
782C4C2×C3×D3×D411yescharacteristic
783C4C3×D3×#4111yescharacteristic
784C3—21no—
785C3#8047811yescharacteristic, direct product factor
786C3C3×#304411yescharacteristic, complemented
787C2—62no—
788C2—241no—
789C2C3×D3×#12111yescharacteristic
790C2C3×#576611yescharacteristic
791C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radicalC2×C3×#239C22
hypercenterC3×#462D3
hypocenterC3C3×#3044
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Q16C2semidirect
4. C3×#5572C2semidirect
5. C32×#462C2semidirect
6. C3×#5185C2semidirect
7. C3×#5182C2semidirect
8. C3×#5090C2semidirect
9. C3×#5028C2semidirect
10. C3×#4845C2semidirect
11. C3×#4839C2semidirect
13. C3×#4802C2semidirect
14. C3×#4798C2semidirect
15. C3×#4795C2semidirect
17. #80478C3direct (N × H)
68. C2×D3×Q16C2×C3semidirect
70. #5572C2×C3semidirect
79. C3×#462D3semidirect
80. C3×#462C2×C3semidirect
84. #5185C2×C3semidirect
85. #5182C2×C3semidirect
86. #5090C2×C3semidirect
87. #5028C2×C3semidirect
88. #4845C2×C3semidirect
89. #4839C2×C3semidirect
91. #4802C2×C3semidirect
92. #4798C2×C3semidirect
93. #4795C2×C3semidirect
301. #462C3×D3semidirect
710. C32#3044semidirect
785. C3#80478direct (N × H)
786. C3C3×#3044semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9182
C2×C3×D3×Q162
C3×#57242
C3×#55722
C32×#4622
C3×#51852
C3×#51822
C3×#50902
C3×#50282
C3×#48452
C3×#48392
C3×#48042
C3×#48022
C3×#47982
C3×#47952
C3×#30443
#804783