Finite Group Databasebeta

← C3×#81188 #11888567

Subgroups — C3×#81188 #11888567

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5695C211yesmaximal, characteristic, complemented
2C3×#5555C211yesmaximal, characteristic, complemented
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5069C211yesmaximal, characteristic, complemented
5C3×#5014C211yesmaximal, characteristic, complemented
6C3×#4888C211yesmaximal, characteristic, complemented
7C3×#4886C211yesmaximal, characteristic, complemented
8C3×#4864C211yesmaximal, characteristic, complemented
9C3×#4862C211yesmaximal, characteristic, complemented
10C3×#4841C211yesmaximal, characteristic, complemented
11C3×#4836C211yesmaximal, characteristic, complemented
12C3×#4781C211yesmaximal, characteristic, complemented
13C3×#4781C211yesmaximal, characteristic, complemented
14C3×#4772C211yesmaximal, characteristic, complemented
15C3×#4771C211yesmaximal, characteristic, complemented
16C3×#3307—31nomaximal
17#81188C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C32×#125C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C2×C3×#213C2211yescharacteristic
23C3×#930—21no—
24C2×C3×C4⋊Dic3—21no—
25C2×C3×#204C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#898—21no—
30C3×#897C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#895—21no—
33C3×#895C2211yescharacteristic
34C3×#895C2211yescharacteristic
35C3×#894—21no—
36C3×#893—21no—
37C3×#892C2211yescharacteristic
38C3×D3×C4⋊C4C2211yescharacteristic
39C3×#886—21no—
40C3×#886—21no—
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C32×#107C2211yescharacteristic
45C32×#106C2211yescharacteristic
46C32×C4⋊C8C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C32×#102C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#553—31no—
62C3×#547—31no—
63#5695C2×C311yescharacteristic, complemented
64#5555C2×C311yescharacteristic, complemented
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#478—21no—
69C3×#478D311yescharacteristic, complemented
70C3×#478C2×C311yescharacteristic, complemented
71C3×#468—31no—
72C3×#465—31no—
73C3×#461—31no—
74C3×#449—31no—
75C3×#449—31no—
76C3×#442—31no—
77C3×#435—31no—
78C3×#417—31no—
79C3×#416—31no—
80#5069C2×C311yescharacteristic, complemented
81#5014C2×C311yescharacteristic, complemented
82#4888C2×C311yescharacteristic, complemented
83#4886C2×C311yescharacteristic, complemented
84#4864C2×C311yescharacteristic, complemented
85#4862C2×C311yescharacteristic, complemented
86#4841C2×C311yescharacteristic, complemented
87#4836C2×C311yescharacteristic, complemented
88#4781C2×C311yescharacteristic, complemented
89#4781C2×C311yescharacteristic, complemented
90#4772C2×C311yescharacteristic, complemented
91#4771C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C3×#237—22no—
99C3×#237—22no—
100C3×#237—41no—
101C3×#237—41no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12D411yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4—21no—
120C32×C42C2311yescharacteristic
121C3×#213—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3D411yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3—21no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—41no—
141C3×#204—41no—
142C3×ΓL(1,𝔽25)—41no—
143C3×D3×C8—41no—
144#3307—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#237C22×C311yescharacteristic
148C2×#237C22×C311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×D8—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×#126—61no—
156C3×#125—21no—
157C3×#125C2×D311yescharacteristic
158C3×#125C22×C311yescharacteristic
159C3×#123—61no—
160C3×#123—61no—
161C3×#123—61no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×#121—31no—
165C3×#121—31no—
166C3×#121—61no—
167C3×#121—61no—
168C3×C4×D4—21no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171C3×C4×D4—61no—
172C3×C4×D4C2×D311yescharacteristic
173C3×C4×D4C22×C311yescharacteristic
174C3×#117—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—61no—
177C2×#213C22×C311yescharacteristic
178#930—21no—
179C2×C4⋊Dic3—21no—
180C2×#204C22×C311yescharacteristic
181C2×#204C22×C311yescharacteristic
182C2×ΓL(1,𝔽25)C22×C311yescharacteristic
183C2×D3×C8C22×C311yescharacteristic
184#898—21no—
185#897C22×C311yescharacteristic
186#897C22×C311yescharacteristic
187#895—21no—
188#895C22×C311yescharacteristic
189#895C22×C311yescharacteristic
190#894—21no—
191#893—21no—
192#892C22×C311yescharacteristic
193D3×C4⋊C4C22×C311yescharacteristic
194#886—21no—
195#886—21no—
196C4×D12C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198#869C22×C311yescharacteristic
199C3×#107—21no—
200C3×#107C2×D311yescharacteristic
201C3×#107C22×C311yescharacteristic
202C3×#106—21no—
203C3×#106—31no—
204C3×#106C2×D311yescharacteristic
205C3×#106C22×C311yescharacteristic
206C3×C4⋊C8—21no—
207C3×C4⋊C8C2×D311yescharacteristic
208C3×C4⋊C8C22×C311yescharacteristic
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#102—21no—
216C3×#102—21no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102C2×D311yescharacteristic
220C3×#102C2×D311yescharacteristic
221C3×#102C22×C311yescharacteristic
222C3×#102C22×C311yescharacteristic
223C3×C22⋊C8—31no—
224C3×C22⋊C8—31no—
225C3×#97—31no—
226#832C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#808C22×C311yescharacteristic
237#803C22×C311yescharacteristic
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—42no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C3×#67—42no—
252C3×#67—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—41no—
263C3×D12—42no—
264C3×D12—81no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#547—31no—
281#491—31no—
282#485—31no—
283#483—31no—
284#478C3×D311yescharacteristic, complemented
285#468—31no—
286#465—31no—
287#461—31no—
288#449—31no—
289#449—31no—
290#442—31no—
291#435—31no—
292#417—31no—
293#416—31no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—121no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C23×C311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—41no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C2×#67—21no—
319C2×#67—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322#237—22no—
323#237—22no—
324#237—41no—
325#237—41no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12C3×D411yescharacteristic
329C2×D12C23×C311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3C23×C311yescharacteristic
333C2×C4×D3C23×C311yescharacteristic
334C2×Dic6C23×C311yescharacteristic
335C2×Dic6C23×C311yescharacteristic
336C3×SD16—121no—
337C3×SD16—121no—
338C3×D8—62no—
339C3×M16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
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—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—41no—
359C3×C4⋊C4—41no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C23×C311yescharacteristic
369C3×C4⋊C4C23×C311yescharacteristic
370C3×C4⋊C4C23×C311yescharacteristic
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—41no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C42—21no—
383C3×C42—61no—
384C3×C42C22×D311yescharacteristic
385C3×C42C23×C311yescharacteristic
386#213—22no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4C3×D411yescharacteristic
394(C2×D3)⋊C4C3×D411yescharacteristic
395C4⋊Dic3—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
399C4⋊Dic3C3×D411yescharacteristic
400C4⋊Dic3C23×C311yescharacteristic
401Dic3⋊C4—21no—
402C4×Dic3—21no—
403C2×C3⋊C8C23×C311yescharacteristic
404C2×C3⋊C8C23×C311yescharacteristic
405#204—41no—
406#204—41no—
407ΓL(1,𝔽25)—41no—
408D3×C8—41no—
409C22×C32—22no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—31no—
435C2×#41—31no—
436C2×SD16—31no—
437C2×SD16—31no—
438C2×D8—31no—
439C2×M16—31no—
440C22×C8—31no—
441C4⋊Q8—31no—
442#126—61no—
443#125C2×C3×D311yescharacteristic
444#123—61no—
445#123—61no—
446#123—61no—
447C22⋊Q8—31no—
448C22⋊Q8—31no—
449#121—31no—
450#121—31no—
451#121—61no—
452#121—61no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—61no—
456C4×D4C2×C3×D311yescharacteristic
457#117—31no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—61no—
460#107C2×C3×D311yescharacteristic
461#106—31no—
462#106C2×C3×D311yescharacteristic
463C4⋊C8C2×C3×D311yescharacteristic
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#102—31no—
471#102—31no—
472#102C2×C3×D311yescharacteristic
473#102C2×C3×D311yescharacteristic
474C22⋊C8—31no—
475C22⋊C8—31no—
476#97—31no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—41no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3C2×C3×D411yescharacteristic
485C22×D3C2×C3×D411yescharacteristic
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—41no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—121no—
497C3×D4—122no—
498C3×D4—122no—
499C3×D4—122no—
500C3×D4—241no—
501C3×D4#23912yes—
502C3×D4C3×#4112yes—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—82no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—241no—
530C2×C3×C4—241no—
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C2×C3×D411yescharacteristic
534C2×C3×C4C2×C3×D411yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C24×C311yescharacteristic
537#67—42no—
538#67—42no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—42no—
543C2×Dic3—42no—
544C2×Dic3C2×C3×D411yescharacteristic
545C2×Dic3C2×C3×D411yescharacteristic
546D12—21no—
547D12—21no—
548D12—41no—
549D12—42no—
550D12—81no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—81no—
556C4×D3—81no—
557Dic6—21no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C2×C32—42no—
572C2×C32#54611yescharacteristic
573C2×C32#57511yescharacteristic
574C2×C32#57711yescharacteristic
575C3×D3—41no—
576C3×D3—41no—
577C3×D3—81no—
578#41—62no—
579#41—62no—
580#41—121no—
581#41—121no—
582C2×Q8—31no—
583C2×Q8—31no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4C22×C3×D311yescharacteristic
591C22×C4—21no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598SD16—121no—
599SD16—121no—
600D8—62no—
601M16—121no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—121no—
605C2×C8C22×C3×D311yescharacteristic
606C2×C8C22×C3×D311yescharacteristic
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4C22×C3×D311yescharacteristic
617C4⋊C4C22×C3×D311yescharacteristic
618C4⋊C4C22×C3×D311yescharacteristic
619C22⋊C4—21no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C42—61no—
629C42C22×C3×D311yescharacteristic
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C22×C3×D411yescharacteristic
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—81no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4C2×#23911yescharacteristic
683C3×C4#100911yescharacteristic
684C3×C4C2×C3×#4111yescharacteristic
685C3×C4C3×H(5,𝔽2)11yescharacteristic
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691C32#330711yescharacteristic, complemented, Sylow
692C23—21no—
693C23—31no—
694C23—31no—
695C23—61no—
696Q8—61no—
697Q8—61no—
698Q8—61no—
699Q8—61no—
700D4—21no—
701D4—61no—
702D4—61no—
703D4—121no—
704D4—122no—
705D4—122no—
706D4—122no—
707D4—241no—
708D4C3×#23912yes—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—42no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—241no—
725C2×C4—241no—
726C2×C4C3×D3×D411yescharacteristic
727C2×C4C3×D3×D411yescharacteristic
728C2×C4C23×C3×D311yescharacteristic
729C8—21no—
730C8—21no—
731C8—61no—
732C8—61no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—42no—
737C2×C3—42no—
738C2×C3—82no—
739C2×C3—121no—
740C2×C3—121no—
741C2×C3—241no—
742C2×C3#563011yescharacteristic
743C2×C3#577011yescharacteristic
744C2×C3#577311yescharacteristic
745C2×C3C3×#54611yescharacteristic
746C2×C3C3×#57511yescharacteristic
747C2×C3C3×#57711yescharacteristic
748D3—41no—
749D3—41no—
750D3—81no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—61no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22C2×C3×D3×D411yescharacteristic
764C4—21no—
765C4—21no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—61no—
770C4—61no—
771C4—121no—
772C4—121no—
773C4—121no—
774C4C2×C3×#23911yescharacteristic
775C4C3×#100911yescharacteristic
776C3—21no—
777C3#8118811yescharacteristic, direct product factor
778C3C3×#330711yescharacteristic, complemented
779C2—42no—
780C2—121no—
781C2—121no—
782C2—241no—
783C2C3×#563011yescharacteristic
784C2C3×#577011yescharacteristic
785C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
hypercenterC3×#478D3
hypocenterC3C3×#3307
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5695C2semidirect
2. C3×#5555C2semidirect
3. C32×#478C2semidirect
4. C3×#5069C2semidirect
5. C3×#5014C2semidirect
6. C3×#4888C2semidirect
7. C3×#4886C2semidirect
8. C3×#4864C2semidirect
9. C3×#4862C2semidirect
10. C3×#4841C2semidirect
11. C3×#4836C2semidirect
12. C3×#4781C2semidirect
13. C3×#4781C2semidirect
14. C3×#4772C2semidirect
15. C3×#4771C2semidirect
17. #81188C3direct (N × H)
63. #5695C2×C3semidirect
64. #5555C2×C3semidirect
69. C3×#478D3semidirect
70. C3×#478C2×C3semidirect
80. #5069C2×C3semidirect
81. #5014C2×C3semidirect
82. #4888C2×C3semidirect
83. #4886C2×C3semidirect
84. #4864C2×C3semidirect
85. #4862C2×C3semidirect
86. #4841C2×C3semidirect
87. #4836C2×C3semidirect
88. #4781C2×C3semidirect
89. #4781C2×C3semidirect
90. #4772C2×C3semidirect
91. #4771C2×C3semidirect
284. #478C3×D3semidirect
691. C32#3307semidirect
777. C3#81188direct (N × H)
778. C3C3×#3307semidirect

Maximal subgroups

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

subgroupindex
C3×#56952
C3×#55552
C32×#4782
C3×#50692
C3×#50142
C3×#48882
C3×#48862
C3×#48642
C3×#48622
C3×#48412
C3×#48362
C3×#47812
C3×#47722
C3×#47712
C3×#33073
#811883