Finite Group Databasebeta

← C3×#81653 #11887350

Subgroups — C3×#81653 #11887350

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5695C211yesmaximal, characteristic, complemented
2C3×#5676C211yesmaximal, characteristic, complemented
3C32×#488C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5057C211yesmaximal, characteristic, complemented
6C3×#4811C211yesmaximal, characteristic, complemented
7C3×#4810C211yesmaximal, characteristic, complemented
8C3×#4807C211yesmaximal, characteristic, complemented
9C3×#4804C211yesmaximal, characteristic, complemented
10C3×#4784C211yesmaximal, characteristic, complemented
11C3×#4775C211yesmaximal, characteristic, complemented
12C3×#4773C211yesmaximal, characteristic, complemented
13C3×D3×#102C211yesmaximal, characteristic, complemented
14C3×C4×D24C211yesmaximal, characteristic, complemented
15C3×C8×D12C211yesmaximal, characteristic, complemented
16C3×#3297—31nomaximal
17#81653C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×#125C2211yescharacteristic, complemented
21C32×#124C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic, complemented
24C3×#938C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic, complemented
29C3×#898—21no—
30C3×#895—21no—
31C3×#895C2211yescharacteristic
32C3×#895C2211yescharacteristic, complemented
33C3×#894—21no—
34C3×#893—21no—
35C3×#892C2211yescharacteristic, complemented
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×#884—21no—
38C3×#883—21no—
39C3×#882—21no—
40C3×D3×C22⋊C4—21no—
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C32×C4×C8C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic, complemented
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C3×#818C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#553—31no—
62C3×#546—31no—
63#5695C2×C311yescharacteristic, complemented
64#5676C2×C311yescharacteristic, complemented
65C3×#488—21no—
66C3×#488D311yescharacteristic, complemented
67C3×#488C2×C311yescharacteristic, complemented
68C3×#484—31no—
69C3×#482—31no—
70C3×#478—31no—
71C3×#466—31no—
72C3×#465—31no—
73C3×#463—31no—
74C3×#449—31no—
75C3×#447—31no—
76C3×C4×D8—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#102—31no—
80#5066C2×C311yescharacteristic, complemented
81#5057C2×C311yescharacteristic, complemented
82#4811C2×C311yescharacteristic, complemented
83#4810C2×C311yescharacteristic, complemented
84#4807C2×C311yescharacteristic, complemented
85#4804C2×C311yescharacteristic, complemented
86#4784C2×C311yescharacteristic, complemented
87#4775C2×C311yescharacteristic, complemented
88#4773C2×C311yescharacteristic, complemented
89D3×#102C2×C311yescharacteristic, complemented
90C4×D24C2×C311yescharacteristic, complemented
91C8×D12C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C3×#239—22no—
98C3×#239—41no—
99C3×D3×D4—22no—
100C3×D3×D4—41no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12D411yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4—21no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4—21no—
120C32×C22⋊C4—21no—
121C32×C42C2311yescharacteristic
122C3×#217—21no—
123C3×#215—41no—
124C3×#213—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×C4⋊Dic3D411yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×D3×C8—41no—
143C3×D3×C8—41no—
144#3297—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C22×C311yescharacteristic
148C2×D3×D4C22×C311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C2×C3×D8—31no—
152C22×C3×C8—31no—
153C22×C3×C8—31no—
154C3×#126—61no—
155C3×#125—21no—
156C3×#125C2×D311yescharacteristic, complemented
157C3×#125C22×C311yescharacteristic, complemented
158C3×#124—21no—
159C3×#124C2×D311yescharacteristic
160C3×#124C22×C311yescharacteristic
161C3×#123—61no—
162C3×#123—61no—
163C3×C22⋊Q8—31no—
164C3×#121—31no—
165C3×#121—31no—
166C3×#121—31no—
167C3×#121—61no—
168C3×#121—61no—
169C3×#120—61no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×C4×D4—31no—
173C3×C4×D4—61no—
174C3×#117—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C22⋊C4—61no—
177#946C22×C311yescharacteristic
178C2×#215C22×C311yescharacteristic, complemented
179#938C22×C311yescharacteristic
180C2×#213C22×C311yescharacteristic
181C2×D24C22×C311yescharacteristic
182C2×D3×C8C22×C311yescharacteristic
183C2×D3×C8C22×C311yescharacteristic, complemented
184#898—21no—
185#895—21no—
186#895C22×C311yescharacteristic
187#895C22×C311yescharacteristic, complemented
188#894—21no—
189#893—21no—
190#892C22×C311yescharacteristic, complemented
191D3×C4⋊C4C22×C311yescharacteristic
192#884—21no—
193#883—21no—
194#882—21no—
195D3×C22⋊C4—21no—
196C4×D12C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198C4×D12C22×C311yescharacteristic, complemented
199C3×#107—31no—
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—21no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic, complemented
207C3×#103C2×D311yescharacteristic, complemented
208C3×#103C22×C311yescharacteristic, complemented
209C3×#103C22×C311yescharacteristic, complemented
210C3×#102—21no—
211C3×#102—21no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102C2×D311yescharacteristic
218C3×#102C2×D311yescharacteristic
219C3×#102C22×C311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×C4×C8—21no—
224C3×C4×C8C2×D311yescharacteristic, complemented
225C3×C4×C8C22×C311yescharacteristic, complemented
226#835C22×C311yescharacteristic, complemented
227#832C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229#821C22×C311yescharacteristic, complemented
230(C2×D3)⋊C8C22×C311yescharacteristic
231(C2×D3)⋊C8C22×C311yescharacteristic, complemented
232#818C22×C311yescharacteristic, complemented
233#809C22×C311yescharacteristic
234#809C22×C311yescharacteristic
235#808C22×C311yescharacteristic, complemented
236#807C22×C311yescharacteristic, complemented
237C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67—42no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—22no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—42no—
267C3×D12—42no—
268C3×D12—81no—
269C3×D12#4112yes—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—42no—
275C3×C4×D3—81no—
276C3×C4×D3—81no—
277C3×C4×D3—81no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—31no—
283#546—31no—
284#488C3×D311yescharacteristic, complemented
285#484—31no—
286#482—31no—
287#478—31no—
288#466—31no—
289#465—31no—
290#463—31no—
291#449—31no—
292#447—31no—
293C4×D8—31no—
294C8×D4—31no—
295#416—31no—
296C2×#102—31no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—21no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—62no—
313C2×C3×D4—61no—
314C2×C3×D4—121no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C23×C311yescharacteristic
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C2×#67—21no—
324C2×#67—21no—
325#239—22no—
326#239—41no—
327D3×D4—22no—
328D3×D4—41no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12—21no—
332C2×D12C3×D411yescharacteristic
333C2×D12C23×C311yescharacteristic
334C2×D12C23×C311yescharacteristic
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3C23×C311yescharacteristic
340C2×C4×D3C23×C311yescharacteristic
341C3×SD16—121no—
342C3×D8—62no—
343C3×D8—121no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—121no—
349C2×C3×C8—121no—
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C23×C311yescharacteristic
353C2×C3×C8C23×C311yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—41no—
364C3×C4⋊C4—41no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C4⋊C4C23×C311yescharacteristic
370C3×C4⋊C4C23×C311yescharacteristic
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—41no—
378C3×C22⋊C4—41no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C42—21no—
387C3×C42—61no—
388C3×C42C22×D311yescharacteristic
389C3×C42C23×C311yescharacteristic
390#217—21no—
391#215—41no—
392#213—41no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4C3×D411yescharacteristic
400(C2×D3)⋊C4C3×D411yescharacteristic
401C4⋊Dic3C3×D411yescharacteristic
402C4⋊Dic3C23×C311yescharacteristic
403C4⋊Dic3C23×C311yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406C4×Dic3—21no—
407C2×C3⋊C8C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409D24—22no—
410D3×C8—41no—
411D3×C8—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—22no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—84no—
428C2×C3×D3#13512yes—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—31no—
441C22×D4—31no—
442C2×SD16—31no—
443C2×D8—31no—
444C2×D8—31no—
445C22×C8—31no—
446C22×C8—31no—
447#126—61no—
448#125C2×C3×D311yescharacteristic, complemented
449#124C2×C3×D311yescharacteristic
450#123—61no—
451#123—61no—
452C22⋊Q8—31no—
453#121—31no—
454#121—31no—
455#121—31no—
456#121—61no—
457#121—61no—
458#120—61no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—61no—
463#117—31no—
464C2×C4⋊C4—31no—
465C2×C22⋊C4—61no—
466#107—31no—
467#107—31no—
468#106—31no—
469C4⋊C8—31no—
470#103—31no—
471#103C2×C3×D311yescharacteristic, complemented
472#103C2×C3×D311yescharacteristic, complemented
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102C2×C3×D311yescharacteristic
479#102C2×C3×D311yescharacteristic
480C22⋊C8—31no—
481C22⋊C8—31no—
482C4×C8C2×C3×D311yescharacteristic, complemented
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—122no—
491C23×C3—122no—
492C23×C3—241no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3—81no—
498C22×D3C2×C3×D411yescharacteristic
499C22×D3C2×C3×D411yescharacteristic
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—32no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—62no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—122no—
518C3×D4—122no—
519C3×D4—122no—
520C3×D4—241no—
521C3×D4—241no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—122no—
543C2×C3×C4—241no—
544C2×C3×C4—241no—
545C2×C3×C4—241no—
546C2×C3×C4D3×D411yescharacteristic
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4C2×C3×D411yescharacteristic
549C2×C3×C4C2×C3×D411yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551C2×C3×C4C24×C311yescharacteristic
552#67—42no—
553#67—81no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3C2×C3×D411yescharacteristic
557C2×Dic3C2×C3×D411yescharacteristic
558D12—22no—
559D12—21no—
560D12—21no—
561D12—21no—
562D12—42no—
563D12—42no—
564D12—81no—
565D12C3×#4112yes—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—42no—
571C4×D3—81no—
572C4×D3—81no—
573C4×D3—81no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—41no—
579C3×C8—41no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C2×C32—81no—
585C2×C32#54611yescharacteristic
586C2×C32C2×#13511yescharacteristic
587C2×C32#57611yescharacteristic
588C3×D3—22no—
589C3×D3—41no—
590C3×D3—42no—
591C3×D3—81no—
592C24—61no—
593#41—62no—
594#41—121no—
595C2×Q8C22×C3×D311yescharacteristic
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—62no—
604C2×D4—61no—
605C2×D4—121no—
606C2×D4C22×C3×D311yescharacteristic
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613SD16—121no—
614D8—62no—
615D8—121no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—121no—
619C2×C8—121no—
620C2×C8C22×C3×D311yescharacteristic
621C2×C8C22×C3×D311yescharacteristic
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4C22×C3×D311yescharacteristic
630C4⋊C4C22×C3×D311yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—31no—
634C22⋊C4—31no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C42—61no—
643C42C22×C3×D311yescharacteristic
644C22×C3—21no—
645C22×C3—32no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—62no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—244no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C22×C3×D411yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—22no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—84no—
681C2×D3C3×#13512yes—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—81no—
699C3×C4—81no—
700C3×C4—81no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4D3×#4111yescharacteristic
704C3×C4#100911yescharacteristic
705C3×C4C2×C3×#4111yescharacteristic
706C3×C4C3×H(5,𝔽2)11yescharacteristic
707Dic3—21no—
708Dic3—21no—
709Dic3—41no—
710Dic3—41no—
711C32#329711yescharacteristic, complemented, Sylow
712C23—21no—
713C23—31no—
714C23—31no—
715C23—61no—
716C23—61no—
717C23—122no—
718C23—122no—
719C23—241no—
720Q8—21no—
721Q8—21no—
722D4—21no—
723D4—21no—
724D4—32no—
725D4—62no—
726D4—61no—
727D4—61no—
728D4—61no—
729D4—122no—
730D4—122no—
731D4—122no—
732D4—241no—
733D4—241no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—122no—
746C2×C4—241no—
747C2×C4—241no—
748C2×C4—241no—
749C2×C4C3×D3×D411yescharacteristic
750C2×C4C3×D3×D411yescharacteristic
751C2×C4C23×C3×D311yescharacteristic
752C8—21no—
753C8—21no—
754C8—61no—
755C8—61no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—62no—
760C2×C3—81no—
761C2×C3—81no—
762C2×C3—121no—
763C2×C3—122no—
764C2×C3—161no—
765C2×C3—241no—
766C2×C3#567611yescharacteristic
767C2×C3D3×#13511yescharacteristic
768C2×C3#576911yescharacteristic
769C2×C3C3×#54611yescharacteristic
770C2×C3C2×C3×#13511yescharacteristic
771C2×C3C3×#57611yescharacteristic
772D3—22no—
773D3—41no—
774D3—42no—
775D3—81no—
776C22—32no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—62no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—244no—
792C22C2×C3×D3×D411yescharacteristic
793C4—21no—
794C4—21no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—61no—
799C4—61no—
800C4—121no—
801C4—121no—
802C4C3×D3×#4111yescharacteristic
803C4C3×#100911yescharacteristic
804C3—21no—
805C3#8165311yescharacteristic, direct product factor
806C3C3×#329711yescharacteristic, complemented
807C2—62no—
808C2—81no—
809C2—121no—
810C2—122no—
811C2—241no—
812C2C3×#567611yescharacteristic
813C2C3×D3×#13511yescharacteristic
814C2C3×#576911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#488C2
socleC22×C32C22×D4
hypercenterC3×#488D3
hypocenterC3C3×#3297
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#488

Complements

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

NH ≅ G/Ntype
1. C3×#5695C2semidirect
2. C3×#5676C2semidirect
3. C32×#488C2semidirect
4. C3×#5066C2semidirect
5. C3×#5057C2semidirect
6. C3×#4811C2semidirect
7. C3×#4810C2semidirect
8. C3×#4807C2semidirect
9. C3×#4804C2semidirect
10. C3×#4784C2semidirect
11. C3×#4775C2semidirect
12. C3×#4773C2semidirect
13. C3×D3×#102C2semidirect
14. C3×C4×D24C2semidirect
15. C3×C8×D12C2semidirect
17. #81653C3direct (N × H)
20. C32×#125C22semidirect
23. C2×C3×#215C22semidirect
28. C2×C3×D3×C8C22semidirect
32. C3×#895C22semidirect
35. C3×#892C22semidirect
43. C3×C4×D12C22semidirect
44. C32×#103C22semidirect
45. C32×#103C22semidirect
48. C32×C4×C8C22semidirect
49. C3×#835C22semidirect
52. C3×#821C22semidirect
54. C3×(C2×D3)⋊C8C22semidirect
55. C3×#818C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×C4⋊(C3⋊C8)C22semidirect
63. #5695C2×C3semidirect
64. #5676C2×C3semidirect
66. C3×#488D3semidirect
67. C3×#488C2×C3semidirect
80. #5066C2×C3semidirect
81. #5057C2×C3semidirect
82. #4811C2×C3semidirect
83. #4810C2×C3semidirect
84. #4807C2×C3semidirect
85. #4804C2×C3semidirect
86. #4784C2×C3semidirect
87. #4775C2×C3semidirect
88. #4773C2×C3semidirect
89. D3×#102C2×C3semidirect
90. C4×D24C2×C3semidirect
91. C8×D12C2×C3semidirect
156. C3×#125C2×D3semidirect
157. C3×#125C22×C3semidirect
178. C2×#215C22×C3semidirect
183. C2×D3×C8C22×C3semidirect
187. #895C22×C3semidirect
190. #892C22×C3semidirect
198. C4×D12C22×C3semidirect
206. C3×#103C2×D3semidirect
207. C3×#103C2×D3semidirect
208. C3×#103C22×C3semidirect
209. C3×#103C22×C3semidirect
224. C3×C4×C8C2×D3semidirect
225. C3×C4×C8C22×C3semidirect
226. #835C22×C3semidirect
229. #821C22×C3semidirect
231. (C2×D3)⋊C8C22×C3semidirect
232. #818C22×C3semidirect
235. #808C22×C3semidirect
236. #807C22×C3semidirect
237. C4⋊(C3⋊C8)C22×C3semidirect
284. #488C3×D3semidirect
448. #125C2×C3×D3semidirect
471. #103C2×C3×D3semidirect
472. #103C2×C3×D3semidirect
482. C4×C8C2×C3×D3semidirect
711. C32#3297semidirect
805. C3#81653direct (N × H)
806. C3C3×#3297semidirect

Maximal subgroups

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

subgroupindex
C3×#56952
C3×#56762
C32×#4882
C3×#50662
C3×#50572
C3×#48112
C3×#48102
C3×#48072
C3×#48042
C3×#47842
C3×#47752
C3×#47732
C3×D3×#1022
C3×C4×D242
C3×C8×D122
C3×#32973
#816533