Finite Group Databasebeta

← C3×#79787 #11872798

Subgroups — C3×#79787 #11872798

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5583C211yesmaximal, characteristic, complemented
2C3×#5545C211yesmaximal, characteristic
3C32×#440C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic
5C3×#5162C211yesmaximal, characteristic, complemented
6C3×C4×#215C211yesmaximal, characteristic, complemented
7C3×C4×#214C211yesmaximal, characteristic, complemented
8C3×#4891C211yesmaximal, characteristic, complemented
9C3×#4888C211yesmaximal, characteristic, complemented
10C3×#4818C211yesmaximal, characteristic, complemented
11C3×#4814C211yesmaximal, characteristic, complemented
12C3×#4776C211yesmaximal, characteristic
13C3×#4766C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4709C211yesmaximal, characteristic, complemented
16C3×#3123—31nomaximal
17#79787C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic, complemented
21C32×C4×D4C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#944C2211yescharacteristic, complemented
24C2×C3×#215C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×C4×#67—21no—
28C2×C3×(C2×D3)⋊C4—21no—
29C2×C3×#204C2211yescharacteristic
30C3×#898—21no—
31C3×#897C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#892C2211yescharacteristic
34C3×#890C2211yescharacteristic, complemented
35C3×#889—21no—
36C3×#67⋊C4—21no—
37C3×D3×C22⋊C4—21no—
38C3×#876—21no—
39C3×C4×D12C2211yescharacteristic
40C3×#872C2211yescharacteristic
41C3×#870—21no—
42C3×C4×Dic6C2211yescharacteristic, complemented
43C32×#107C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic
46C32×#97C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic, complemented
59C3×#808C2211yescharacteristic, complemented
60C3×C4×C3⋊C8C2211yescharacteristic, complemented
61C3×#541—31no—
62C3×#518—31no—
63#5583C2×C311yescharacteristic, complemented
64#5545C2×C311yescharacteristic
65C3×#485—31no—
66C3×#485—31no—
67C3×#478—31no—
68C3×#478—31no—
69C3×#461—31no—
70C3×#461—31no—
71C3×#450—31no—
72C3×#450—31no—
73C3×#440—21no—
74C3×#440—31no—
75C3×#440D311yescharacteristic, complemented
76C3×#440C2×C311yescharacteristic, complemented
77C3×C4×SD16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5169C2×C311yescharacteristic
81#5162C2×C311yescharacteristic, complemented
82C4×#215C2×C311yescharacteristic, complemented
83C4×#214C2×C311yescharacteristic, complemented
84#4891C2×C311yescharacteristic, complemented
85#4888C2×C311yescharacteristic, complemented
86#4818C2×C311yescharacteristic, complemented
87#4814C2×C311yescharacteristic, complemented
88#4776C2×C311yescharacteristic
89#4766C2×C311yescharacteristic, complemented
90#4710C2×C311yescharacteristic, complemented
91#4709C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C32×SD16—22no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114C3×#217—21no—
115C3×#215—22no—
116C3×#214—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141#3123—31noSylow
142C22×C3×D4—31no—
143C2×D3×D4C22×C311yescharacteristic
144C2×C3×SD16—21no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C2×C3×SD16C2×D311yescharacteristic
149C2×C3×SD16C22×C311yescharacteristic
150C3×C4⋊Q8—31no—
151C3×#126—61no—
152C3×#126—61no—
153C3×#125—31no—
154C3×#125—61no—
155C3×#125—61no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—21no—
159C3×C4×Q8—31no—
160C3×C4×Q8C2×D311yescharacteristic, complemented
161C3×C4×Q8C22×C311yescharacteristic, complemented
162C3×C4×D4—21no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—61no—
167C3×C4×D4—61no—
168C3×C4×D4C2×D311yescharacteristic
169C3×C4×D4C22×C311yescharacteristic
170C3×#117—31no—
171C3×#117—31no—
172C2×C3×C22⋊C4—61no—
173C2×C3×C22⋊C4—61no—
174#946C22×C311yescharacteristic
175#944C22×C311yescharacteristic, complemented
176C2×#215C22×C311yescharacteristic
177D4×Dic3C22×C311yescharacteristic
178C2×#214C22×C311yescharacteristic
179C4×#67—21no—
180C2×(C2×D3)⋊C4—21no—
181C2×#204C22×C311yescharacteristic
182#898—21no—
183#897C22×C311yescharacteristic
184#893C22×C311yescharacteristic
185#892C22×C311yescharacteristic
186#890C22×C311yescharacteristic, complemented
187#889—21no—
188#67⋊C4—21no—
189D3×C22⋊C4—21no—
190#876—21no—
191C4×D12C22×C311yescharacteristic
192#872C22×C311yescharacteristic
193#870—21no—
194C4×Dic6C22×C311yescharacteristic, complemented
195C3×#107—21no—
196C3×#107—31no—
197C3×#107C2×D311yescharacteristic, complemented
198C3×#107C22×C311yescharacteristic, complemented
199C3×#106—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103C2×D311yescharacteristic, complemented
208C3×#103C22×C311yescharacteristic, complemented
209C3×#102—21no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102C2×D311yescharacteristic
214C3×#102C22×C311yescharacteristic
215C3×C22⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×#97—21no—
218C3×#97C2×D311yescharacteristic, complemented
219C3×#97C22×C311yescharacteristic, complemented
220C3×C4×C8—31no—
221#835C22×C311yescharacteristic, complemented
222#832C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226#818C22×C311yescharacteristic, complemented
227#816C22×C311yescharacteristic, complemented
228Dic3⋊C8C22×C311yescharacteristic, complemented
229Dic3⋊C8C22×C311yescharacteristic, complemented
230#810C22×C311yescharacteristic, complemented
231#809C22×C311yescharacteristic
232#808C22×C311yescharacteristic, complemented
233#808C22×C311yescharacteristic, complemented
234C4×C3⋊C8C22×C311yescharacteristic, complemented
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—81no—
239C22×C3×D3—81no—
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—81no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67—24no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—31no—
273#518—31no—
274#485—31no—
275#485—31no—
276#478—31no—
277#478—31no—
278#461—31no—
279#461—31no—
280#450—31no—
281#450—31no—
282#440—31no—
283#440C3×D311yescharacteristic, complemented
284C4×SD16—31no—
285C4×SD16—31no—
286#433—31no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C23×C311yescharacteristic
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—62no—
297C2×C3×D4—62no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C23×C311yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—31no—
303C22×C3×C4—41no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C2×#67—21no—
308C22×Dic3—21no—
309D3×D4—22no—
310D3×D4—22no—
311C2×D12C23×C311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3C23×C311yescharacteristic
315C2×Dic6C23×C311yescharacteristic
316C3×SD16—24no—
317C3×SD16—22no—
318C3×SD16—22no—
319C3×SD16—62no—
320C3×SD16—62no—
321C3×SD16—62no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8C22×D311yescharacteristic
327C2×C3×C8C22×D311yescharacteristic
328C2×C3×C8C23×C311yescharacteristic
329C2×C3×C8C23×C311yescharacteristic
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—41no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C23×C311yescharacteristic
349C3×C4⋊C4C23×C311yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—21no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—31no—
365C3×C42—41no—
366C3×C42—61no—
367C3×C42—61no—
368C3×C42C22×D311yescharacteristic
369C3×C42C23×C311yescharacteristic
370#217—21no—
371#215—22no—
372#214—22no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4C3×D411yescharacteristic
379(C2×D3)⋊C4C3×D411yescharacteristic
380C4⋊Dic3—21no—
381C4⋊Dic3—21no—
382C4⋊Dic3C23×C311yescharacteristic
383C4⋊Dic3C23×C311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4C3×D411yescharacteristic
390Dic3⋊C4C3×D411yescharacteristic
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3C23×C311yescharacteristic
394C2×C3⋊C8C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396#204—22no—
397C22×C32—22no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C2×C3×D3—21no—
402C2×C3×D3—22no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—84no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4—41no—
413C32×C4C2×#4111yescharacteristic
414C32×C4C2×#4111yescharacteristic
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C22×D4—31no—
422C2×SD16—31no—
423C2×SD16—31no—
424C2×SD16—31no—
425C2×SD16C2×C3×D311yescharacteristic
426C4⋊Q8—31no—
427#126—61no—
428#126—61no—
429#125—31no—
430#125—61no—
431#125—61no—
432C22⋊Q8—31no—
433C22⋊Q8—31no—
434C4×Q8—31no—
435C4×Q8C2×C3×D311yescharacteristic, complemented
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—61no—
440C4×D4—61no—
441C4×D4C2×C3×D311yescharacteristic
442#117—31no—
443#117—31no—
444C2×C22⋊C4—61no—
445C2×C22⋊C4—61no—
446#107—31no—
447#107C2×C3×D311yescharacteristic, complemented
448#106—31no—
449#106—31no—
450C4⋊C8—31no—
451C4⋊C8—31no—
452#103—31no—
453#103—31no—
454#103—31no—
455#103C2×C3×D311yescharacteristic, complemented
456#102—31no—
457#102—31no—
458#102—31no—
459#102C2×C3×D311yescharacteristic
460C22⋊C8—31no—
461C22⋊C8—31no—
462#97C2×C3×D311yescharacteristic, complemented
463C4×C8—31no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—31no—
467C23×C3—41no—
468C23×C3—64no—
469C23×C3—61no—
470C23×C3—241no—
471C23×C3—241no—
472C22×D3—21no—
473C22×D3—24no—
474C22×D3—81no—
475C22×D3—81no—
476C22×D3C2×C3×D411yescharacteristic
477C3×Q8—22no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—41no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—22no—
488C3×D4—32no—
489C3×D4—41no—
490C3×D4—64no—
491C3×D4—61no—
492C3×D4#23512yes—
493C3×D4C3×#4112yes—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—81no—
515C2×C3×C4—81no—
516C2×C3×C4—82no—
517C2×C3×C4—241no—
518C2×C3×C4—241no—
519C2×C3×C4—241no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×C3×D411yescharacteristic
523C2×C3×C4C2×C3×D411yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C24×C311yescharacteristic
526#67—24no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—81no—
531C2×Dic3C2×C3×D411yescharacteristic
532C2×Dic3C2×C3×D411yescharacteristic
533C2×Dic3C2×C3×D411yescharacteristic
534D12—21no—
535D12C3×#4112yes—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—81no—
539C4×D3—81no—
540Dic6—21no—
541Dic6—21no—
542C3×C8—22no—
543C3×C8—21no—
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—21no—
547C3×C8—41no—
548C3×C8—61no—
549C3×C8—61no—
550C3⋊C8—21no—
551C3⋊C8—21no—
552C2×C32—42no—
553C2×C32#52511yescharacteristic
554C2×C32#57711yescharacteristic
555C2×C32#57711yescharacteristic
556C3×D3—41no—
557C3×D3—42no—
558C24—61no—
559C2×Q8—31no—
560C2×Q8C22×C3×D311yescharacteristic
561C2×D4—31no—
562C2×D4—61no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4C22×C3×D311yescharacteristic
566C22×C4—21no—
567C22×C4—31no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571SD16—22no—
572SD16—62no—
573SD16—62no—
574SD16—62no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8C22×C3×D311yescharacteristic
578C2×C8C22×C3×D311yescharacteristic
579C4⋊C4—21no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4C22×C3×D311yescharacteristic
592C4⋊C4C22×C3×D311yescharacteristic
593C22⋊C4—21no—
594C22⋊C4—31no—
595C22⋊C4—31no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C22⋊C4—61no—
601C22⋊C4—61no—
602C42—21no—
603C42—31no—
604C42—61no—
605C42—61no—
606C42C22×C3×D311yescharacteristic
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—42no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—62no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—244no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C22×C3×D411yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—22no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—84no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—42no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4C2×#23511yescharacteristic
657C3×C4D3×#4111yescharacteristic
658C3×C4C2×C3×#4111yescharacteristic
659C3×C4C2×C3×#4111yescharacteristic
660Dic3—21no—
661Dic3—21no—
662Dic3—21no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666C32#312311yescharacteristic, complemented, Sylow
667C23—21no—
668C23—31no—
669C23—64no—
670C23—61no—
671C23—241no—
672C23—241no—
673Q8—21no—
674Q8—21no—
675Q8—61no—
676Q8—61no—
677D4—21no—
678D4—32no—
679D4—64no—
680D4—61no—
681D4C3×#23512yes—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—81no—
694C2×C4—241no—
695C2×C4—241no—
696C2×C4—241no—
697C2×C4C3×D3×D411yescharacteristic
698C2×C4C3×D3×D411yescharacteristic
699C2×C4C23×C3×D311yescharacteristic
700C8—21no—
701C8—21no—
702C8—61no—
703C8—61no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—42no—
708C2×C3—42no—
709C2×C3—82no—
710C2×C3—121no—
711C2×C3—122no—
712C2×C3#554711yescharacteristic
713C2×C3#577511yescharacteristic
714C2×C3#577811yescharacteristic
715C2×C3C3×#52511yescharacteristic
716C2×C3C3×#57711yescharacteristic
717C2×C3C3×#57711yescharacteristic
718D3—41no—
719D3—42no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—61no—
724C22—61no—
725C22—61no—
726C22—62no—
727C22—121no—
728C22—121no—
729C22—244no—
730C22C2×C3×D3×D411yescharacteristic
731C4—21no—
732C4—21no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—61no—
737C4—61no—
738C4—61no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4C2×C3×#23511yescharacteristic
743C4C3×D3×#4111yescharacteristic
744C3—21no—
745C3#7978711yescharacteristic, direct product factor
746C3C3×#312311yescharacteristic, complemented
747C2—42no—
748C2—121no—
749C2—122no—
750C2C3×#554711yescharacteristic
751C2C3×#577511yescharacteristic
752C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC3×#440D3
hypocenterC3C3×#3123
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
1. C3×#5583C2semidirect
3. C32×#440C2semidirect
5. C3×#5162C2semidirect
6. C3×C4×#215C2semidirect
7. C3×C4×#214C2semidirect
8. C3×#4891C2semidirect
9. C3×#4888C2semidirect
10. C3×#4818C2semidirect
11. C3×#4814C2semidirect
13. C3×#4766C2semidirect
14. C3×#4710C2semidirect
15. C3×#4709C2semidirect
17. #79787C3direct (N × H)
20. C32×C4×Q8C22semidirect
23. C3×#944C22semidirect
34. C3×#890C22semidirect
42. C3×C4×Dic6C22semidirect
43. C32×#107C22semidirect
44. C32×#103C22semidirect
46. C32×#97C22semidirect
47. C3×#835C22semidirect
52. C3×#818C22semidirect
53. C3×#816C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×#810C22semidirect
58. C3×#808C22semidirect
59. C3×#808C22semidirect
60. C3×C4×C3⋊C8C22semidirect
63. #5583C2×C3semidirect
75. C3×#440D3semidirect
76. C3×#440C2×C3semidirect
81. #5162C2×C3semidirect
82. C4×#215C2×C3semidirect
83. C4×#214C2×C3semidirect
84. #4891C2×C3semidirect
85. #4888C2×C3semidirect
86. #4818C2×C3semidirect
87. #4814C2×C3semidirect
89. #4766C2×C3semidirect
90. #4710C2×C3semidirect
91. #4709C2×C3semidirect
160. C3×C4×Q8C2×D3semidirect
161. C3×C4×Q8C22×C3semidirect
175. #944C22×C3semidirect
186. #890C22×C3semidirect
194. C4×Dic6C22×C3semidirect
197. C3×#107C2×D3semidirect
198. C3×#107C22×C3semidirect
207. C3×#103C2×D3semidirect
208. C3×#103C22×C3semidirect
218. C3×#97C2×D3semidirect
219. C3×#97C22×C3semidirect
221. #835C22×C3semidirect
226. #818C22×C3semidirect
227. #816C22×C3semidirect
228. Dic3⋊C8C22×C3semidirect
229. Dic3⋊C8C22×C3semidirect
230. #810C22×C3semidirect
232. #808C22×C3semidirect
233. #808C22×C3semidirect
234. C4×C3⋊C8C22×C3semidirect
283. #440C3×D3semidirect
435. C4×Q8C2×C3×D3semidirect
447. #107C2×C3×D3semidirect
455. #103C2×C3×D3semidirect
462. #97C2×C3×D3semidirect
666. C32#3123semidirect
745. C3#79787direct (N × H)
746. C3C3×#3123semidirect

Maximal subgroups

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

subgroupindex
C3×#55832
C3×#55452
C32×#4402
C3×#51692
C3×#51622
C3×C4×#2152
C3×C4×#2142
C3×#48912
C3×#48882
C3×#48182
C3×#48142
C3×#47762
C3×#47662
C3×#47102
C3×#47092
C3×#31233
#797873