Finite Group Databasebeta

← C3×#79649 #11860715

Subgroups — C3×#79649 #11860715

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic
2C3×#5572C211yesmaximal, characteristic, complemented
3C3×#5545C211yesmaximal, characteristic
4C32×C4×SD16C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6C3×#5026C211yesmaximal, characteristic, complemented
7C3×#5018C211yesmaximal, characteristic, complemented
8C3×#4860C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4817C211yesmaximal, characteristic, complemented
11C3×#4802C211yesmaximal, characteristic, complemented
12C3×#4770C211yesmaximal, characteristic
13C3×#4757C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×#4689C211yesmaximal, characteristic, complemented
16C3×#2949—31nomaximal
17#79649C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic, complemented
24C2×C3×#215C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×C4×#67—21no—
28C2×C3×(C2×D3)⋊C4—21no—
29C3×D3×SD16C418yescomplemented
30C2×C3×#204C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#892—21no—
35C3×#892C2211yescharacteristic
36C3×#892C2211yescharacteristic
37C3×#887—21no—
38C3×#887C2211yescharacteristic, complemented
39C3×#67⋊C4—21no—
40C3×D3×C22⋊C4—21no—
41C3×C4×D12C2211yescharacteristic
42C3×#872—21no—
43C3×#872C2211yescharacteristic
44C3×C4×Dic6—21no—
45C3×C4×Dic6C2211yescharacteristic, complemented
46C32×#106C2211yescharacteristic, complemented
47C32×#103C2211yescharacteristic, complemented
48C32×#102C2211yescharacteristic
49C32×C4×C8C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#832C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#817C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic
59C3×#807C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#803C2211yescharacteristic, complemented
62C22×C3×SD16—31no—
63C3×#519—31no—
64C3×#518—31no—
65C2×D3×SD16C2×C311yescharacteristic
66#5572C2×C311yescharacteristic, complemented
67#5545C2×C311yescharacteristic
68C3×#440—31no—
69C3×#440—31no—
70C3×#440—31no—
71C3×#440—31no—
72C3×C4×SD16—21no—
73C3×C4×SD16—31no—
74C3×C4×SD16—31no—
75C3×C4×SD16—31no—
76C3×C4×SD16D311yescharacteristic, complemented
77C3×C4×SD16C2×C311yescharacteristic, complemented
78C3×#427—31no—
79C3×#419—31no—
80C3×#418—31no—
81C3×#405—31no—
82Dic3×SD16C2×C311yescharacteristic, complemented
83#5026C2×C311yescharacteristic, complemented
84#5018C2×C311yescharacteristic, complemented
85#4860C2×C311yescharacteristic, complemented
86#4852C2×C311yescharacteristic, complemented
87#4817C2×C311yescharacteristic, complemented
88#4802C2×C311yescharacteristic, complemented
89#4770C2×C311yescharacteristic
90#4757C2×C311yescharacteristic, complemented
91C4×#204C2×C311yescharacteristic, complemented
92#4689C2×C311yescharacteristic, complemented
93C23×C3×D3—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×Q8—22no—
100C3×D3×Q8C2×C414yescomplemented
101C3×D3×D4—22no—
102C3×D3×D4C2×C414yes—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C32×SD16C2×C414yescomplemented
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C42—21no—
118C32×C42C2311yescharacteristic
119C3×#217—21no—
120C3×#215C2×C414yescomplemented
121C3×#214C2×C414yescomplemented
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204C2×C414yescomplemented
144C3×ΓL(1,𝔽25)—22no—
145C3×D3×C8C2×C414yescomplemented
146#2949—31noSylow
147C22×C3×Q8—31no—
148C22×C3×D4—31no—
149C2×D3×Q8C22×C311yescharacteristic
150C2×D3×D4C22×C311yescharacteristic
151C2×C3×SD16—21no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C2×C3×SD16—38no—
155C2×C3×SD16—31no—
156C2×C3×SD16C2×D311yescharacteristic
157C2×C3×SD16C22×C311yescharacteristic
158C2×C3×M16—31no—
159C22×C3×C8—31no—
160C3×C4×Q8—21no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—61no—
165C3×C4×Q8—61no—
166C3×C4×Q8C2×D311yescharacteristic, complemented
167C3×C4×Q8C22×C311yescharacteristic, complemented
168C3×C4×D4—21no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×C4×D4—61no—
173C3×C4×D4—61no—
174C3×C4×D4C2×D311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×#117—31no—
177C3×#117—31no—
178C3×#117—31no—
179C3×#117—61no—
180C3×#117—61no—
181C2×C3×C22⋊C4—61no—
182C2×C3×C22⋊C4—61no—
183Q8×Dic3C22×C311yescharacteristic, complemented
184C2×#215C22×C311yescharacteristic
185D4×Dic3C22×C311yescharacteristic
186C2×#214C22×C311yescharacteristic
187C4×#67—21no—
188C2×(C2×D3)⋊C4—21no—
189D3×SD16C3×C418yescomplemented
190C2×#204C22×C311yescharacteristic
191C2×ΓL(1,𝔽25)C22×C311yescharacteristic
192C2×D3×C8C22×C311yescharacteristic
193#893C22×C311yescharacteristic
194#892—21no—
195#892C22×C311yescharacteristic
196#892C22×C311yescharacteristic
197#887—21no—
198#887C22×C311yescharacteristic, complemented
199#67⋊C4—21no—
200D3×C22⋊C4—21no—
201C4×D12C22×C311yescharacteristic
202#872—21no—
203#872C22×C311yescharacteristic
204C4×Dic6—21no—
205C4×Dic6C22×C311yescharacteristic, complemented
206C3×#107—31no—
207C3×#107—31no—
208C3×#106—21no—
209C3×#106—31no—
210C3×#106C2×D311yescharacteristic, complemented
211C3×#106C22×C311yescharacteristic, complemented
212C3×#103—21no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103C2×D311yescharacteristic, complemented
217C3×#103C22×C311yescharacteristic, complemented
218C3×#102—21no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102—31no—
222C3×#102C2×D311yescharacteristic
223C3×#102C22×C311yescharacteristic
224C3×#97—31no—
225C3×#97—31no—
226C3×C4×C8—21no—
227C3×C4×C8—31no—
228C3×C4×C8C2×D311yescharacteristic, complemented
229C3×C4×C8C22×C311yescharacteristic, complemented
230#835C22×C311yescharacteristic, complemented
231#832C22×C311yescharacteristic
232#821C22×C311yescharacteristic
233#817C22×C311yescharacteristic, complemented
234#816C22×C311yescharacteristic, complemented
235#815C22×C311yescharacteristic, complemented
236C8×Dic3C22×C311yescharacteristic, complemented
237#810C22×C311yescharacteristic, complemented
238#809C22×C311yescharacteristic
239#807C22×C311yescharacteristic, complemented
240#807C22×C311yescharacteristic, complemented
241#803C22×C311yescharacteristic, complemented
242C23×C32—21no—
243C22×C3×D3—21no—
244C22×C3×D3—24no—
245C22×C3×D3—81no—
246C22×C3×D3—81no—
247C22×C3×D3C2×D411yescharacteristic
248C32×Q8—21no—
249C32×Q8C22×C412yes—
250C32×D4—21no—
251C32×D4C22×C412yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—81no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C3×#67—24no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12C22×C412yes—
269C3×C4×D3—24no—
270C3×C4×D3—81no—
271C3×C4×D3—81no—
272C3×C4×D3C22×C412yes—
273C3×C4×D3#4112yes—
274C3×Dic6—21no—
275C3×Dic6—24no—
276C3×Dic6C22×C412yes—
277C32×C8—21no—
278C32×C8C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C22×SD16—31no—
282#519—31no—
283#518—31no—
284#440—31no—
285#440—31no—
286#440—31no—
287#440—31no—
288C4×SD16—31no—
289C4×SD16—31no—
290C4×SD16—31no—
291C4×SD16C3×D311yescharacteristic, complemented
292#427—31no—
293#419—31no—
294#418—31no—
295#405—31no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—34no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×Q8—62no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C23×C311yescharacteristic
305C2×C3×D4—21no—
306C2×C3×D4—34no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C23×C311yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—41no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C2×#67—21no—
321C22×Dic3—21no—
322D3×Q8—22no—
323D3×Q8C2×C3×C414yescomplemented
324D3×D4—22no—
325D3×D4C2×C3×C414yes—
326C2×D12C23×C311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3C23×C311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6C23×C311yescharacteristic
333C3×SD16—24no—
334C3×SD16—34no—
335C3×SD16—34no—
336C3×SD16—34no—
337C3×SD16C4×D314yescomplemented
338C3×SD16C2×C3×C414yescomplemented
339C3×M16—62no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—34no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C23×C311yescharacteristic
364C3×C4⋊C4C23×C311yescharacteristic
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—41no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42—31no—
379C3×C42—41no—
380C3×C42—61no—
381C3×C42—61no—
382C3×C42—61no—
383C3×C42—61no—
384C3×C42—61no—
385C3×C42C22×D311yescharacteristic
386C3×C42C23×C311yescharacteristic
387#217—21no—
388#215C2×C3×C414yescomplemented
389#214C2×C3×C414yescomplemented
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4C3×D411yescharacteristic
395(C2×D3)⋊C4C3×D411yescharacteristic
396C4⋊Dic3—21no—
397C4⋊Dic3C23×C311yescharacteristic
398C4⋊Dic3C23×C311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4C3×D411yescharacteristic
402Dic3⋊C4C3×D411yescharacteristic
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3—21no—
406C4×Dic3—21no—
407C4×Dic3—21no—
408C4×Dic3C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410C2×C3⋊C8C23×C311yescharacteristic
411#204C2×C3×C414yescomplemented
412ΓL(1,𝔽25)—22no—
413D3×C8C2×C3×C414yescomplemented
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—84no—
424C2×C3×D3C4×D412yes—
425C32×C4—21no—
426C32×C4—22no—
427C32×C4—21no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4C23×C411yescharacteristic
431C32×C4C2×#4111yescharacteristic
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C4×D412yes—
438C22×Q8—31no—
439C22×D4—31no—
440C2×SD16—31no—
441C2×SD16—31no—
442C2×SD16—38no—
443C2×SD16—31no—
444C2×SD16C2×C3×D311yescharacteristic
445C2×M16—31no—
446C22×C8—31no—
447C4×Q8—31no—
448C4×Q8—31no—
449C4×Q8—31no—
450C4×Q8—61no—
451C4×Q8—61no—
452C4×Q8C2×C3×D311yescharacteristic, complemented
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—61no—
457C4×D4—61no—
458C4×D4C2×C3×D311yescharacteristic
459#117—31no—
460#117—31no—
461#117—31no—
462#117—61no—
463#117—61no—
464C2×C22⋊C4—61no—
465C2×C22⋊C4—61no—
466#107—31no—
467#107—31no—
468#106—31no—
469#106C2×C3×D311yescharacteristic, complemented
470#103—31no—
471#103—31no—
472#103—31no—
473#103C2×C3×D311yescharacteristic, complemented
474#102—31no—
475#102—31no—
476#102—31no—
477#102C2×C3×D311yescharacteristic
478#97—31no—
479#97—31no—
480C4×C8—31no—
481C4×C8C2×C3×D311yescharacteristic, complemented
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—64no—
487C23×C3—61no—
488C23×C3—241no—
489C23×C3—241no—
490C22×D3—21no—
491C22×D3—24no—
492C22×D3—81no—
493C22×D3—81no—
494C22×D3C2×C3×D411yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—22no—
498C3×Q8—32no—
499C3×Q8—41no—
500C3×Q8—64no—
501C3×Q8—61no—
502C3×Q8C2×C4×D312yes—
503C3×Q8C22×C3×C412yes—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—32no—
508C3×D4—41no—
509C3×D4—64no—
510C3×D4—61no—
511C3×D4C2×C4×D312yes—
512C3×D4C22×C3×C412yes—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—64no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—81no—
535C2×C3×C4—81no—
536C2×C3×C4—82no—
537C2×C3×C4—241no—
538C2×C3×C4—241no—
539C2×C3×C4—241no—
540C2×C3×C4D3×D411yescharacteristic
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×C3×D411yescharacteristic
543C2×C3×C4C2×C3×D411yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C24×C311yescharacteristic
546#67—24no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—81no—
551C2×Dic3C2×C3×D411yescharacteristic
552C2×Dic3C2×C3×D411yescharacteristic
553C2×Dic3C2×C3×D411yescharacteristic
554D12—21no—
555D12C22×C3×C412yes—
556C4×D3—24no—
557C4×D3—81no—
558C4×D3—81no—
559C4×D3C22×C3×C412yes—
560C4×D3C3×#4112yes—
561Dic6—21no—
562Dic6—24no—
563Dic6C22×C3×C412yes—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—22no—
567C3×C8—32no—
568C3×C8—41no—
569C3×C8—61no—
570C3×C8C2×C4×D312yes—
571C3×C8C22×C3×C412yes—
572C3⋊C8—21no—
573C3⋊C8C22×C3×C412yes—
574C2×C32—42no—
575C2×C32C2×C4×D411yescharacteristic
576C2×C32#57711yescharacteristic
577C2×C32#57711yescharacteristic
578C3×D3—22no—
579C3×D3—42no—
580C24—61no—
581C2×Q8—34no—
582C2×Q8—31no—
583C2×Q8—61no—
584C2×Q8—62no—
585C2×Q8C22×C3×D311yescharacteristic
586C2×D4—34no—
587C2×D4—31no—
588C2×D4—62no—
589C2×D4—61no—
590C2×D4C22×C3×D311yescharacteristic
591C22×C4—21no—
592C22×C4—31no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597SD16—34no—
598SD16—34no—
599SD16—34no—
600SD16C3×C4×D314yescomplemented
601M16—62no—
602C2×C8—31no—
603C2×C8—34no—
604C2×C8—31no—
605C2×C8C22×C3×D311yescharacteristic
606C2×C8C22×C3×D311yescharacteristic
607C4⋊C4—21no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4C22×C3×D311yescharacteristic
616C4⋊C4C22×C3×D311yescharacteristic
617C22⋊C4—21no—
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C42—21no—
626C42—31no—
627C42—61no—
628C42—61no—
629C42—61no—
630C42—61no—
631C42—61no—
632C42C22×C3×D311yescharacteristic
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—32no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—62no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—244no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C22×C3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—22no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—84no—
658C2×D3C3×C4×D412yes—
659C3×C4—22no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—32no—
669C3×C4—41no—
670C3×C4—42no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—62no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4C22×C4×D311yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4C23×C3×C411yescharacteristic
685C3×C4C2×C3×#4111yescharacteristic
686Dic3—21no—
687Dic3—21no—
688Dic3—22no—
689Dic3—41no—
690Dic3—41no—
691Dic3C3×C4×D412yes—
692C32#294911yescharacteristic, complemented, Sylow
693C23—21no—
694C23—31no—
695C23—64no—
696C23—61no—
697C23—241no—
698C23—241no—
699Q8—21no—
700Q8—32no—
701Q8—64no—
702Q8—61no—
703Q8C2×C3×C4×D312yes—
704D4—21no—
705D4—32no—
706D4—64no—
707D4—61no—
708D4C2×C3×C4×D312yes—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—31no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—64no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—81no—
722C2×C4—241no—
723C2×C4—241no—
724C2×C4—241no—
725C2×C4C3×D3×D411yescharacteristic
726C2×C4C3×D3×D411yescharacteristic
727C2×C4C23×C3×D311yescharacteristic
728C8—21no—
729C8—32no—
730C8—61no—
731C8C2×C3×C4×D312yes—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—42no—
736C2×C3—42no—
737C2×C3—62no—
738C2×C3—82no—
739C2×C3—122no—
740C2×C3C4×D3×D411yescharacteristic
741C2×C3#576211yescharacteristic
742C2×C3#577011yescharacteristic
743C2×C3C2×C3×C4×D411yescharacteristic
744C2×C3C3×#57711yescharacteristic
745C2×C3C3×#57711yescharacteristic
746D3—22no—
747D3—42no—
748C22—22no—
749C22—32no—
750C22—41no—
751C22—41no—
752C22—61no—
753C22—61no—
754C22—62no—
755C22—121no—
756C22—121no—
757C22—244no—
758C22C2×C3×D3×D411yescharacteristic
759C4—21no—
760C4—21no—
761C4—22no—
762C4—32no—
763C4—41no—
764C4—41no—
765C4—61no—
766C4—61no—
767C4—62no—
768C4—121no—
769C4—121no—
770C4C22×C3×C4×D311yescharacteristic
771C4C3×D3×#4111yescharacteristic
772C3—21no—
773C3#7964911yescharacteristic, direct product factor
774C3C3×#294911yescharacteristic, complemented
775C2—42no—
776C2—62no—
777C2—122no—
778C2C3×C4×D3×D411yescharacteristic
779C2C3×#576211yescharacteristic
780C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
cosocleC2×C3×C4C24×C3
hypercenterC3×C4×SD16D3
hypocenterC3C3×#2949
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C3×#5572C2semidirect
4. C32×C4×SD16C2semidirect
5. C3×Dic3×SD16C2semidirect
6. C3×#5026C2semidirect
7. C3×#5018C2semidirect
8. C3×#4860C2semidirect
9. C3×#4852C2semidirect
10. C3×#4817C2semidirect
11. C3×#4802C2semidirect
13. C3×#4757C2semidirect
14. C3×C4×#204C2semidirect
15. C3×#4689C2semidirect
17. #79649C3direct (N × H)
21. C32×C4×Q8C22semidirect
23. C3×Q8×Dic3C22semidirect
29. C3×D3×SD16C4semidirect
38. C3×#887C22semidirect
45. C3×C4×Dic6C22semidirect
46. C32×#106C22semidirect
47. C32×#103C22semidirect
49. C32×C4×C8C22semidirect
50. C3×#835C22semidirect
53. C3×#817C22semidirect
54. C3×#816C22semidirect
55. C3×#815C22semidirect
56. C3×C8×Dic3C22semidirect
57. C3×#810C22semidirect
59. C3×#807C22semidirect
60. C3×#807C22semidirect
61. C3×#803C22semidirect
66. #5572C2×C3semidirect
76. C3×C4×SD16D3semidirect
77. C3×C4×SD16C2×C3semidirect
82. Dic3×SD16C2×C3semidirect
83. #5026C2×C3semidirect
84. #5018C2×C3semidirect
85. #4860C2×C3semidirect
86. #4852C2×C3semidirect
87. #4817C2×C3semidirect
88. #4802C2×C3semidirect
90. #4757C2×C3semidirect
91. C4×#204C2×C3semidirect
92. #4689C2×C3semidirect
100. C3×D3×Q8C2×C4semidirect
110. C32×SD16C2×C4semidirect
120. C3×#215C2×C4semidirect
121. C3×#214C2×C4semidirect
143. C3×#204C2×C4semidirect
145. C3×D3×C8C2×C4semidirect
166. C3×C4×Q8C2×D3semidirect
167. C3×C4×Q8C22×C3semidirect
183. Q8×Dic3C22×C3semidirect
189. D3×SD16C3×C4semidirect
198. #887C22×C3semidirect
205. C4×Dic6C22×C3semidirect
210. C3×#106C2×D3semidirect
211. C3×#106C22×C3semidirect
216. C3×#103C2×D3semidirect
217. C3×#103C22×C3semidirect
228. C3×C4×C8C2×D3semidirect
229. C3×C4×C8C22×C3semidirect
230. #835C22×C3semidirect
233. #817C22×C3semidirect
234. #816C22×C3semidirect
235. #815C22×C3semidirect
236. C8×Dic3C22×C3semidirect
237. #810C22×C3semidirect
239. #807C22×C3semidirect
240. #807C22×C3semidirect
241. #803C22×C3semidirect
291. C4×SD16C3×D3semidirect
323. D3×Q8C2×C3×C4semidirect
337. C3×SD16C4×D3semidirect
338. C3×SD16C2×C3×C4semidirect
388. #215C2×C3×C4semidirect
389. #214C2×C3×C4semidirect
411. #204C2×C3×C4semidirect
413. D3×C8C2×C3×C4semidirect
452. C4×Q8C2×C3×D3semidirect
469. #106C2×C3×D3semidirect
473. #103C2×C3×D3semidirect
481. C4×C8C2×C3×D3semidirect
600. SD16C3×C4×D3semidirect
692. C32#2949semidirect
773. C3#79649direct (N × H)
774. C3C3×#2949semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
C3×#55722
C3×#55452
C32×C4×SD162
C3×Dic3×SD162
C3×#50262
C3×#50182
C3×#48602
C3×#48522
C3×#48172
C3×#48022
C3×#47702
C3×#47572
C3×C4×#2042
C3×#46892
C3×#29493
#796493