Finite Group Databasebeta

← C3×#80193 #11887588

Subgroups — C3×#80193 #11887588

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic
2C3×#5635C211yesmaximal, characteristic
3C32×#451C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5C3×#5188C211yesmaximal, characteristic, complemented
6C3×#5186C211yesmaximal, characteristic, complemented
7C3×#5182C211yesmaximal, characteristic, complemented
8C3×Dic3×Q16C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×#4811C211yesmaximal, characteristic, complemented
11C3×D3×#103C211yesmaximal, characteristic, complemented
12C3×#4793C211yesmaximal, characteristic, complemented
13C3×#4792C211yesmaximal, characteristic, complemented
14C3×#67⋊C8C211yesmaximal, characteristic
15C3×#4722C211yesmaximal, characteristic, complemented
16C3×#3299—31nomaximal
17#80193C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C3×#946—21no—
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C3×#944—21no—
29C3×#944C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C3×C4×#67—21no—
32C3×C4×#67C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C3×#924—21no—
35C3×#924C2211yescharacteristic
36C22×C3×C3⋊C8C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic
38C3×#897—21no—
39C3×D3×C4⋊C4C2211yescharacteristic
40C3×#889—21no—
41C3×#888C2211yescharacteristic
42C3×#67⋊C4—21no—
43C3×#878—21no—
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#818C2211yescharacteristic
54C3×#818C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#816C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic
58C3×C8×Dic3C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#554—31no—
62C3×D4×Q8—31no—
63Q8×#67C2×C311yescharacteristic
64#5635C2×C311yescharacteristic
65C3×#487—31no—
66C3×#484—31no—
67C3×#484—31no—
68C3×#477—31no—
69C3×#467—31no—
70C3×#467—31no—
71C3×#462—31no—
72C3×#451—21no—
73C3×#451—31no—
74C3×#451D311yescharacteristic, complemented
75C3×#451C2×C311yescharacteristic, complemented
76C3×C4×Q16—31no—
77C3×C8×D4—31no—
78C2×C3×#103—31no—
79C2×C3×#103—31no—
80C2×#835C2×C311yescharacteristic, complemented
81#5188C2×C311yescharacteristic, complemented
82#5186C2×C311yescharacteristic, complemented
83#5182C2×C311yescharacteristic, complemented
84Dic3×Q16C2×C311yescharacteristic, complemented
85#5051C2×C311yescharacteristic, complemented
86#4811C2×C311yescharacteristic, complemented
87D3×#103C2×C311yescharacteristic, complemented
88#4793C2×C311yescharacteristic, complemented
89#4792C2×C311yescharacteristic, complemented
90#67⋊C8C2×C311yescharacteristic
91#4722C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C32×Q16—22no—
111C32×Q16—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8—41no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3299—31noSylow
145C22×C3×Q8—21no—
146C22×C3×Q8—31no—
147C22×C3×Q8C2×D311yescharacteristic
148C22×C3×Q8C22×C311yescharacteristic
149C2×D3×Q8C22×C311yescharacteristic
150C2×C3×Q16—21no—
151C2×C3×Q16—21no—
152C2×C3×Q16—31no—
153C2×C3×Q16C2×D311yescharacteristic
154C2×C3×Q16C2×D311yescharacteristic
155C2×C3×Q16C22×C311yescharacteristic
156C2×C3×Q16C22×C311yescharacteristic
157C22×C3×C8—31no—
158C22×C3×C8—31no—
159C3×C4⋊Q8—31no—
160C3×C4⋊Q8—31no—
161C3×C4⋊Q8—61no—
162C3×#125—61no—
163C3×C22⋊Q8—21no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—61no—
168C3×C22⋊Q8—61no—
169C3×C22⋊Q8—61no—
170C3×C22⋊Q8—61no—
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×C22⋊Q8C22×C311yescharacteristic
173C3×C4×Q8—31no—
174C3×C4×Q8—31no—
175C3×C4×D4—31no—
176C3×C4×D4—61no—
177C3×C4×D4—61no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180#946—21no—
181#946C22×C311yescharacteristic
182#946C22×C311yescharacteristic
183Q8×Dic3C22×C311yescharacteristic
184Q8×Dic3C22×C311yescharacteristic
185#944—21no—
186#944C22×C311yescharacteristic
187C2×#216C22×C311yescharacteristic
188C4×#67—21no—
189C4×#67C22×C311yescharacteristic
190C2×C4⋊Dic3C22×C311yescharacteristic
191#924—21no—
192#924C22×C311yescharacteristic
193C22×C3⋊C8C22×C311yescharacteristic
194C2×D3×C8C22×C311yescharacteristic
195#897—21no—
196D3×C4⋊C4C22×C311yescharacteristic
197#889—21no—
198#888C22×C311yescharacteristic
199#67⋊C4—21no—
200#878—21no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#107—31no—
204C3×C4⋊C8—31no—
205C3×#103—21no—
206C3×#103—21no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103C2×D311yescharacteristic
216C3×#103C2×D311yescharacteristic
217C3×#103C22×C311yescharacteristic
218C3×#103C22×C311yescharacteristic
219C3×C22⋊C8—21no—
220C3×C22⋊C8—31no—
221C3×C22⋊C8C2×D311yescharacteristic
222C3×C22⋊C8C22×C311yescharacteristic
223C3×C4×C8—31no—
224#835C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#835C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230#818C22×C311yescharacteristic
231#818C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234Dic3⋊C8C22×C311yescharacteristic
235C8×Dic3C22×C311yescharacteristic
236#810C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×Q8—42no—
246C32×Q8#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67Q1614yescomplemented
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C3×Dic6—81no—
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#467—31no—
285#462—31no—
286#451—31no—
287#451C3×D311yescharacteristic, complemented
288C4×Q16—31no—
289C8×D4—31no—
290C2×#103—31no—
291C2×#103—31no—
292C2×C3×Q8—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8—22no—
295C2×C3×Q8—22no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8—41no—
301C2×C3×Q8—42no—
302C2×C3×Q8—41no—
303C2×C3×Q8—41no—
304C2×C3×Q8—42no—
305C2×C3×Q8—61no—
306C2×C3×Q8—61no—
307C2×C3×Q8—62no—
308C2×C3×Q8—121no—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×Q8C23×C311yescharacteristic
313C2×C3×Q8C23×C311yescharacteristic
314C2×C3×Q8C23×C311yescharacteristic
315C2×C3×D4—31no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—41no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C23×C311yescharacteristic
326C2×#67C3×D411yescharacteristic
327C22×Dic3—21no—
328D3×Q8—22no—
329D3×Q8—41no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3C23×C311yescharacteristic
333C2×Dic6—21no—
334C2×Dic6—21no—
335C2×Dic6C23×C311yescharacteristic
336C3×Q16—22no—
337C3×Q16—22no—
338C3×Q16—42no—
339C3×Q16—41no—
340C3×Q16—41no—
341C3×Q16—42no—
342C3×Q16—121no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—121no—
348C2×C3×C8—121no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C23×C311yescharacteristic
352C2×C3×C8C23×C311yescharacteristic
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—41no—
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⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C23×C311yescharacteristic
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—41no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C42—31no—
382C3×C42—61no—
383C3×C42—61no—
384#217—21no—
385#217C3×D411yescharacteristic
386#216—41no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4C3×D411yescharacteristic
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3C23×C311yescharacteristic
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⋊C4—21no—
403Dic3⋊C4C3×D411yescharacteristic
404C4×Dic3—21no—
405C4×Dic3—21no—
406C4×Dic3C23×C311yescharacteristic
407C2×C3⋊C8—41no—
408C2×C3⋊C8C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410D3×C8—41no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32C2×Q1612yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C2×Q1612yes—
418C32×C4—22no—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4H(5,𝔽2)11yescharacteristic
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3C2×Q1612yes—
432C22×Q8—31no—
433C22×Q8C2×C3×D311yescharacteristic
434C2×Q16—31no—
435C2×Q16C2×C3×D311yescharacteristic
436C2×Q16C2×C3×D311yescharacteristic
437C22×C8—31no—
438C22×C8—31no—
439C4⋊Q8—31no—
440C4⋊Q8—31no—
441C4⋊Q8—61no—
442#125—61no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—31no—
446C22⋊Q8—61no—
447C22⋊Q8—61no—
448C22⋊Q8—61no—
449C22⋊Q8—61no—
450C22⋊Q8C2×C3×D311yescharacteristic
451C4×Q8—31no—
452C4×Q8—31no—
453C4×D4—31no—
454C4×D4—61no—
455C4×D4—61no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—31no—
458#107—31no—
459#107—31no—
460#107—31no—
461C4⋊C8—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103C2×C3×D311yescharacteristic
471#103C2×C3×D311yescharacteristic
472C22⋊C8—31no—
473C22⋊C8C2×C3×D311yescharacteristic
474C4×C8—31no—
475C23×C3—21no—
476C23×C3—31no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×C3×D411yescharacteristic
479C22×D3C2×C3×D411yescharacteristic
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—22no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—22no—
492C3×Q8—41no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8—41no—
496C3×Q8—42no—
497C3×Q8—42no—
498C3×Q8—44no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—122no—
502C3×Q8—241no—
503C3×Q8#23712yes—
504C3×Q8C3×#4112yes—
505C3×D4—34no—
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—21no—
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—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—42no—
530C2×C3×C4—42no—
531C2×C3×C4—44no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—122no—
539C2×C3×C4—241no—
540C2×C3×C4—241no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×C3×D411yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C24×C311yescharacteristic
545#67C3×Q1614yescomplemented
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—81no—
551C2×Dic3C2×C3×D411yescharacteristic
552C2×Dic3C2×C3×D411yescharacteristic
553C2×Dic3C2×C3×D411yescharacteristic
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—42no—
557C4×D3—81no—
558Dic6—21no—
559Dic6—21no—
560Dic6—42no—
561Dic6—81no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C2×C32—22no—
573C2×C32#54611yescharacteristic
574C2×C32C22×Q1611yescharacteristic
575C2×C32#57711yescharacteristic
576C3×D3—22no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—31no—
580C2×Q8—41no—
581C2×Q8—61no—
582C2×Q8—61no—
583C2×Q8—62no—
584C2×Q8—121no—
585C2×Q8C22×C3×D311yescharacteristic
586C2×Q8C22×C3×D311yescharacteristic
587C2×Q8C22×C3×D311yescharacteristic
588C2×D4—31no—
589C22×C4—21no—
590C22×C4—31no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4C22×C3×D311yescharacteristic
595Q16—22no—
596Q16—41no—
597Q16—121no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—121no—
601C2×C8—121no—
602C2×C8C22×C3×D311yescharacteristic
603C2×C8C22×C3×D311yescharacteristic
604C4⋊C4—21no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4C22×C3×D311yescharacteristic
620C22⋊C4—21no—
621C22⋊C4—31no—
622C22⋊C4—31no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C42—31no—
627C42—61no—
628C42—61no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3D3×Q1612yes—
641C22×C3C2×C3×Q1612yes—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C22×C3×D411yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3C2×C3×Q1612yes—
647C3×C4—21no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—81no—
666C3×C4—81no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4C2×#23711yescharacteristic
672C3×C4#100411yescharacteristic
673C3×C4C2×C3×#4111yescharacteristic
674C3×C4C3×H(5,𝔽2)11yescharacteristic
675Dic3—21no—
676Dic3—21no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3C2×C3×Q1612yes—
682C32#329911yescharacteristic, complemented, Sylow
683C23—31no—
684C23C3×D3×D411yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—42no—
691Q8—61no—
692Q8—61no—
693Q8—122no—
694Q8—241no—
695Q8C3×#23712yes—
696D4—34no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—42no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—122no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4C3×D3×D411yescharacteristic
717C2×C4C23×C3×D311yescharacteristic
718C8—21no—
719C8—21no—
720C8—61no—
721C8—61no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—62no—
729C2×C3#559111yescharacteristic
730C2×C3C2×D3×Q1611yescharacteristic
731C2×C3#577811yescharacteristic
732C2×C3C3×#54611yescharacteristic
733C2×C3C22×C3×Q1611yescharacteristic
734C2×C3C3×#57711yescharacteristic
735D3—22no—
736C22—21no—
737C22—21no—
738C22—32no—
739C22—61no—
740C22—61no—
741C22C3×D3×Q1612yes—
742C22C2×C3×D3×D411yescharacteristic
743C4—21no—
744C4—22no—
745C4—32no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—61no—
750C4—61no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—121no—
755C4C2×C3×#23711yescharacteristic
756C4C3×#100411yescharacteristic
757C3—21no—
758C3#8019311yescharacteristic, direct product factor
759C3C3×#329911yescharacteristic, complemented
760C2—22no—
761C2—62no—
762C2C3×#559111yescharacteristic
763C2C2×C3×D3×Q1611yescharacteristic
764C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC3×#451D3
hypocenterC3C3×#3299
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
3. C32×#451C2semidirect
4. C2×C3×#835C2semidirect
5. C3×#5188C2semidirect
6. C3×#5186C2semidirect
7. C3×#5182C2semidirect
8. C3×Dic3×Q16C2semidirect
9. C3×#5051C2semidirect
10. C3×#4811C2semidirect
11. C3×D3×#103C2semidirect
12. C3×#4793C2semidirect
13. C3×#4792C2semidirect
15. C3×#4722C2semidirect
17. #80193C3direct (N × H)
74. C3×#451D3semidirect
75. C3×#451C2×C3semidirect
80. C2×#835C2×C3semidirect
81. #5188C2×C3semidirect
82. #5186C2×C3semidirect
83. #5182C2×C3semidirect
84. Dic3×Q16C2×C3semidirect
85. #5051C2×C3semidirect
86. #4811C2×C3semidirect
87. D3×#103C2×C3semidirect
88. #4793C2×C3semidirect
89. #4792C2×C3semidirect
91. #4722C2×C3semidirect
256. C3×#67Q16semidirect
287. #451C3×D3semidirect
545. #67C3×Q16semidirect
682. C32#3299semidirect
758. C3#80193direct (N × H)
759. C3C3×#3299semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
C3×#56352
C32×#4512
C2×C3×#8352
C3×#51882
C3×#51862
C3×#51822
C3×Dic3×Q162
C3×#50512
C3×#48112
C3×D3×#1032
C3×#47932
C3×#47922
C3×#67⋊C82
C3×#47222
C3×#32993
#801933