Finite Group Databasebeta

← C3×#80781 #11887594

Subgroups — C3×#80781 #11887594

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5635C211yesmaximal, characteristic
2C3×#5632C211yesmaximal, characteristic
3C32×#467C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic, complemented
5C3×#5182C211yesmaximal, characteristic, complemented
6C3×C8×#67C211yesmaximal, characteristic
7C2×C3×#816C211yesmaximal, characteristic, complemented
8C3×#5050C211yesmaximal, characteristic, complemented
9C3×#5044C211yesmaximal, characteristic, complemented
10C3×#4884C211yesmaximal, characteristic, complemented
11C3×#4875C211yesmaximal, characteristic, complemented
12C3×#4813C211yesmaximal, characteristic, complemented
13C3×D3×#103C211yesmaximal, characteristic, complemented
14C3×#4792C211yesmaximal, characteristic, complemented
15C3×#4790C211yesmaximal, characteristic, complemented
16C3×#3299—31nomaximal
17#80781C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×D3×C8C2211yescharacteristic
32C3×#897—21no—
33C3×#897C2211yescharacteristic
34C3×#896—21no—
35C3×D3×C4⋊C4C2211yescharacteristic
36C3×#889—21no—
37C3×#888—21no—
38C3×#888C2211yescharacteristic
39C3×#887C2211yescharacteristic
40C3×#67⋊C4—21no—
41C3×#67⋊C4—21no—
42C3×#878—21no—
43C3×#878—21no—
44C32×#107C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#830C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#554—31no—
62C3×D4×Q8—31no—
63#5635C2×C311yescharacteristic
64#5632C2×C311yescharacteristic
65C3×#487—31no—
66C3×#484—31no—
67C3×#484—31no—
68C3×#477—31no—
69C3×#467—21no—
70C3×#467—31no—
71C3×#467D311yescharacteristic, complemented
72C3×#467C2×C311yescharacteristic, complemented
73C3×#462—31no—
74C3×#451—31no—
75C3×#451—31no—
76C3×C4×Q16—31no—
77C3×C8×D4—31no—
78C2×C3×#103—31no—
79C2×C3×#103—31no—
80#5186C2×C311yescharacteristic, complemented
81#5182C2×C311yescharacteristic, complemented
82C8×#67C2×C311yescharacteristic
83C2×#816C2×C311yescharacteristic, complemented
84#5050C2×C311yescharacteristic, complemented
85#5044C2×C311yescharacteristic, complemented
86#4884C2×C311yescharacteristic, complemented
87#4875C2×C311yescharacteristic, complemented
88#4813C2×C311yescharacteristic, complemented
89D3×#103C2×C311yescharacteristic, complemented
90#4792C2×C311yescharacteristic, complemented
91#4790C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—41no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—22no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6—41no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C32×Q16—41no—
111C2×C32×C8—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C22⋊C4—21no—
120C3×#217D411yescharacteristic
121C3×#216—22no—
122C3×#216—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3299—31noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C22×C311yescharacteristic
148C22×Dic6C22×C311yescharacteristic
149C2×C3×Q16—21no—
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C22×C311yescharacteristic
154C22×C3×C8—21no—
155C22×C3×C8—31no—
156C22×C3×C8C2×D311yescharacteristic
157C22×C3×C8C22×C311yescharacteristic
158C3×C4⋊Q8—31no—
159C3×C4⋊Q8—31no—
160C3×C4⋊Q8—61no—
161C3×#125—61no—
162C3×C22⋊Q8—21no—
163C3×C22⋊Q8—21no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—61no—
167C3×C22⋊Q8—61no—
168C3×C22⋊Q8—61no—
169C3×C22⋊Q8—61no—
170C3×C22⋊Q8C2×D311yescharacteristic
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×C22⋊Q8C22×C311yescharacteristic
173C3×C22⋊Q8C22×C311yescharacteristic
174C3×C4×Q8—31no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178C3×C4×D4—61no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181#946C22×C311yescharacteristic
182Q8×Dic3C22×C311yescharacteristic
183#944C22×C311yescharacteristic
184C2×#216C22×C311yescharacteristic
185C2×#216C22×C311yescharacteristic
186C4×#67C22×C311yescharacteristic
187C2×C4⋊Dic3C22×C311yescharacteristic
188C2×D3×C8C22×C311yescharacteristic
189#897—21no—
190#897C22×C311yescharacteristic
191#896—21no—
192D3×C4⋊C4C22×C311yescharacteristic
193#889—21no—
194#888—21no—
195#888C22×C311yescharacteristic
196#887C22×C311yescharacteristic
197#67⋊C4—21no—
198#67⋊C4—21no—
199#878—21no—
200#878—21no—
201C3×#107—21no—
202C3×#107—31no—
203C3×#107—31no—
204C3×#107C2×D311yescharacteristic
205C3×#107C22×C311yescharacteristic
206C3×C4⋊C8—31no—
207C3×#103—21no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103C2×D311yescharacteristic
218C3×#103C2×D311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×#103C22×C311yescharacteristic
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×C4×C8—31no—
224#835C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#830C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232Dic3⋊C8C22×C311yescharacteristic
233C8×Dic3C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#807C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67Q1614yescomplemented
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6—42no—
271C3×Dic6—81no—
272C3×Dic6#4112yes—
273C32×C8—21no—
274C32×C8—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—31no—
278D4×Q8—31no—
279#487—31no—
280#484—31no—
281#484—31no—
282#477—31no—
283#467—31no—
284#467C3×D311yescharacteristic, complemented
285#462—31no—
286#451—31no—
287#451—31no—
288C4×Q16—31no—
289C8×D4—31no—
290C2×#103—31no—
291C2×#103—31no—
292C2×C3×Q8—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×Q8—61no—
297C2×C3×Q8—61no—
298C2×C3×Q8—62no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8—121no—
302C2×C3×Q8—121no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C23×C311yescharacteristic
306C2×C3×Q8C23×C311yescharacteristic
307C2×C3×D4—31no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C23×C311yescharacteristic
316C2×#67C3×D411yescharacteristic
317C22×Dic3—21no—
318C22×Dic3—21no—
319D3×Q8—22no—
320D3×Q8—41no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3C23×C311yescharacteristic
324C2×Dic6—22no—
325C2×Dic6—21no—
326C2×Dic6—21no—
327C2×Dic6—21no—
328C2×Dic6—41no—
329C2×Dic6C23×C311yescharacteristic
330C2×Dic6C23×C311yescharacteristic
331C3×Q16—41no—
332C3×Q16—41no—
333C3×Q16—42no—
334C3×Q16—62no—
335C3×Q16—121no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—41no—
341C2×C3×C8—41no—
342C2×C3×C8—42no—
343C2×C3×C8—121no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C23×C311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—41no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C23×C311yescharacteristic
371C3×C4⋊C4C23×C311yescharacteristic
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—41no—
379C3×C22⋊C4—41no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C42—31no—
383C3×C42—61no—
384C3×C42—61no—
385#217C3×D411yescharacteristic
386#216—22no—
387#216—41no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4C3×D411yescharacteristic
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4C3×D411yescharacteristic
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3C23×C311yescharacteristic
406C2×C3⋊C8C23×C311yescharacteristic
407C2×C3⋊C8C23×C311yescharacteristic
408D3×C8—41no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32C2×Q1612yes—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3C2×Q1612yes—
416C32×C4—21no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4C2×#4111yescharacteristic
422C32×C4H(5,𝔽2)11yescharacteristic
423C3×Dic3—22no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3C2×Q1612yes—
430C22×Q8—31no—
431C22×Q8—31no—
432C2×Q16—31no—
433C2×Q16—31no—
434C2×Q16C2×C3×D311yescharacteristic
435C22×C8—31no—
436C22×C8C2×C3×D311yescharacteristic
437C4⋊Q8—31no—
438C4⋊Q8—31no—
439C4⋊Q8—61no—
440#125—61no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—61no—
444C22⋊Q8—61no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C22⋊Q8C2×C3×D311yescharacteristic
448C22⋊Q8C2×C3×D311yescharacteristic
449C4×Q8—31no—
450C4×Q8—31no—
451C4×D4—31no—
452C4×D4—61no—
453C4×D4—61no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—31no—
456#107—31no—
457#107—31no—
458#107C2×C3×D311yescharacteristic
459C4⋊C8—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103C2×C3×D311yescharacteristic
469#103C2×C3×D311yescharacteristic
470C22⋊C8—31no—
471C22⋊C8—31no—
472C4×C8—31no—
473C23×C3—21no—
474C23×C3—31no—
475C23×C3D3×D411yescharacteristic
476C23×C3C2×C3×D411yescharacteristic
477C22×D3C2×C3×D411yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—32no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—122no—
495C3×Q8—122no—
496C3×Q8—241no—
497C3×D4—34no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
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—31no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—241no—
530C2×C3×C4—241no—
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4C2×C3×D411yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C24×C311yescharacteristic
535#67C3×Q1614yescomplemented
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—42no—
541C2×Dic3—81no—
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544C2×Dic3C2×C3×D411yescharacteristic
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—42no—
548C4×D3—81no—
549Dic6—21no—
550Dic6—21no—
551Dic6—21no—
552Dic6—42no—
553Dic6—42no—
554Dic6—81no—
555Dic6C3×#4112yes—
556C3×C8—22no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—41no—
562C3×C8—61no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C2×C32—22no—
567C2×C32#54611yescharacteristic
568C2×C32C22×Q1611yescharacteristic
569C2×C32#57711yescharacteristic
570C3×D3—22no—
571C2×Q8—31no—
572C2×Q8—31no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×Q8—62no—
576C2×Q8—61no—
577C2×Q8—62no—
578C2×Q8—121no—
579C2×Q8—121no—
580C2×Q8C22×C3×D311yescharacteristic
581C2×Q8C22×C3×D311yescharacteristic
582C2×D4—31no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4C22×C3×D311yescharacteristic
589Q16—41no—
590Q16—62no—
591Q16—121no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—41no—
595C2×C8—121no—
596C2×C8C22×C3×D311yescharacteristic
597C2×C8C22×C3×D311yescharacteristic
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4C22×C3×D311yescharacteristic
613C4⋊C4C22×C3×D311yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—31no—
617C22⋊C4—31no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C42—31no—
621C42—61no—
622C42—61no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—32no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3D3×Q1612yes—
635C22×C3C2×C3×Q1612yes—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C22×C3×D411yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3C2×C3×Q1612yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—32no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—62no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4#100411yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4C2×C3×#4111yescharacteristic
668C3×C4C3×H(5,𝔽2)11yescharacteristic
669Dic3—21no—
670Dic3—22no—
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3C2×C3×Q1612yes—
676C32#329911yescharacteristic, complemented, Sylow
677C23—31no—
678C23C3×D3×D411yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—21no—
683Q8—32no—
684Q8—61no—
685Q8—61no—
686Q8—61no—
687Q8—122no—
688Q8—122no—
689Q8—241no—
690D4—34no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—241no—
709C2×C4—241no—
710C2×C4C3×D3×D411yescharacteristic
711C2×C4C23×C3×D311yescharacteristic
712C8—21no—
713C8—21no—
714C8—61no—
715C8—61no—
716C2×C3—22no—
717C2×C3—22no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—42no—
722C2×C3—62no—
723C2×C3#561011yescharacteristic
724C2×C3C2×D3×Q1611yescharacteristic
725C2×C3#577011yescharacteristic
726C2×C3C3×#54611yescharacteristic
727C2×C3C22×C3×Q1611yescharacteristic
728C2×C3C3×#57711yescharacteristic
729D3—22no—
730C22—21no—
731C22—21no—
732C22—32no—
733C22—61no—
734C22—61no—
735C22C3×D3×Q1612yes—
736C22C2×C3×D3×D411yescharacteristic
737C4—21no—
738C4—32no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—61no—
744C4—61no—
745C4—62no—
746C4—121no—
747C4—121no—
748C4—121no—
749C4C3×#100411yescharacteristic
750C4C3×D3×#4111yescharacteristic
751C3—21no—
752C3#8078111yescharacteristic, direct product factor
753C3C3×#329911yescharacteristic, complemented
754C2—22no—
755C2—62no—
756C2C3×#561011yescharacteristic
757C2C2×C3×D3×Q1611yescharacteristic
758C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#467C2
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC3×#467D3
hypocenterC3C3×#3299
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#467

Complements

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

NH ≅ G/Ntype
3. C32×#467C2semidirect
4. C3×#5186C2semidirect
5. C3×#5182C2semidirect
7. C2×C3×#816C2semidirect
8. C3×#5050C2semidirect
9. C3×#5044C2semidirect
10. C3×#4884C2semidirect
11. C3×#4875C2semidirect
12. C3×#4813C2semidirect
13. C3×D3×#103C2semidirect
14. C3×#4792C2semidirect
15. C3×#4790C2semidirect
17. #80781C3direct (N × H)
71. C3×#467D3semidirect
72. C3×#467C2×C3semidirect
80. #5186C2×C3semidirect
81. #5182C2×C3semidirect
83. C2×#816C2×C3semidirect
84. #5050C2×C3semidirect
85. #5044C2×C3semidirect
86. #4884C2×C3semidirect
87. #4875C2×C3semidirect
88. #4813C2×C3semidirect
89. D3×#103C2×C3semidirect
90. #4792C2×C3semidirect
91. #4790C2×C3semidirect
252. C3×#67Q16semidirect
284. #467C3×D3semidirect
535. #67C3×Q16semidirect
676. C32#3299semidirect
752. C3#80781direct (N × H)
753. C3C3×#3299semidirect

Maximal subgroups

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

subgroupindex
C3×#56352
C3×#56322
C32×#4672
C3×#51862
C3×#51822
C3×C8×#672
C2×C3×#8162
C3×#50502
C3×#50442
C3×#48842
C3×#48752
C3×#48132
C3×D3×#1032
C3×#47922
C3×#47902
C3×#32993
#807813