Finite Group Databasebeta

← C3×#80096 #11878555

Subgroups — C3×#80096 #11878555

Order 1152.

885 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic, complemented
2C3×#5608C211yesmaximal, characteristic, complemented
3C32×#449C211yesmaximal, characteristic, complemented
4C3×#5239C211yesmaximal, characteristic, complemented
5C3×#5173C211yesmaximal, characteristic, complemented
6C3×#5171C211yesmaximal, characteristic, complemented
7C3×#5159C211yesmaximal, characteristic, complemented
8C3×#5158C211yesmaximal, characteristic, complemented
9C3×#5034C211yesmaximal, characteristic, complemented
10C3×#4816C211yesmaximal, characteristic, complemented
11C3×#4805C211yesmaximal, characteristic, complemented
12C3×#4778C211yesmaximal, characteristic, complemented
13C3×#4777C211yesmaximal, characteristic, complemented
14C3×#4727C211yesmaximal, characteristic, complemented
15C3×#4721C211yesmaximal, characteristic, complemented
16C3×#3204—31nomaximal
17#80096C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic
23C32×#121C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#939—21no—
28C3×#939—21no—
29C3×#939—21no—
30C3×#938—21no—
31C3×#938C2211yescharacteristic
32C3×#938C2211yescharacteristic
33C3×#938C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic
35C3×#930—21no—
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C3×#924—21no—
38C3×#924C2211yescharacteristic
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
40C2×C3×D3×C8C2211yescharacteristic
41C3×#897C2211yescharacteristic
42C3×D3×C4⋊C4C2211yescharacteristic
43C3×#884—21no—
44C3×#878—21no—
45C32×#103C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#830C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×#817C2211yescharacteristic
56C3×#817C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×#816C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#537—31no—
62C3×#537—31no—
63#5833C2×C311yescharacteristic, complemented
64#5608C2×C311yescharacteristic, complemented
65C3×#483—31no—
66C3×#483—31no—
67C3×#481—31no—
68C3×#481—31no—
69C3×#470—31no—
70C3×#469—31no—
71C3×#465—31no—
72C3×#465—31no—
73C3×#452—31no—
74C3×#452—31no—
75C3×#449—21no—
76C3×#449—31no—
77C3×#449D311yescharacteristic, complemented
78C3×#449C2×C311yescharacteristic, complemented
79C3×#408—31no—
80#5239C2×C311yescharacteristic, complemented
81#5173C2×C311yescharacteristic, complemented
82#5171C2×C311yescharacteristic, complemented
83#5159C2×C311yescharacteristic, complemented
84#5158C2×C311yescharacteristic, complemented
85#5034C2×C311yescharacteristic, complemented
86#4816C2×C311yescharacteristic, complemented
87#4805C2×C311yescharacteristic, complemented
88#4778C2×C311yescharacteristic, complemented
89#4777C2×C311yescharacteristic, complemented
90#4727C2×C311yescharacteristic, complemented
91#4721C2×C311yescharacteristic, complemented
92C32×#41—41no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C22×C32×C4C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C2×C3×#67D411yescharacteristic
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C3×#237—41no—
110C3×#237—41no—
111C3×#235—41no—
112C3×#235—41no—
113C2×C3×D12D411yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6D411yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C32×SD16—41no—
120C32×D8—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125C3×#217—21no—
126C3×#217—21no—
127C3×#217—21no—
128C3×#217—21no—
129C3×#216—41no—
130C3×#214—41no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C3×ΓL(1,𝔽25)—41no—
146C3×D3×C8—41no—
147#3204—31noSylow
148C2×C3×#41—21no—
149C2×C3×#41—31no—
150C2×C3×#41—31no—
151C2×C3×#41C2×D311yescharacteristic
152C2×C3×#41C22×C311yescharacteristic
153C2×#237C22×C311yescharacteristic
154C2×#235C22×C311yescharacteristic
155C2×C3×Q16—31no—
156C2×C3×SD16—21no—
157C2×C3×SD16—31no—
158C2×C3×SD16C2×D311yescharacteristic
159C2×C3×SD16C22×C311yescharacteristic
160C2×C3×D8—21no—
161C2×C3×D8C2×D311yescharacteristic
162C2×C3×D8C22×C311yescharacteristic
163C2×C3×M16—31no—
164C22×C3×C8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—61no—
170C3×C22⋊Q8—61no—
171C3×#121—21no—
172C3×#121—31no—
173C3×#121—31no—
174C3×#121—31no—
175C3×#121—61no—
176C3×#121—61no—
177C3×#121—61no—
178C3×#121—61no—
179C3×#121—61no—
180C3×#121—61no—
181C3×#121C2×D311yescharacteristic
182C3×#121C22×C311yescharacteristic
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185#946C22×C311yescharacteristic
186#946C22×C311yescharacteristic
187C2×#216C22×C311yescharacteristic
188#939—21no—
189#939—21no—
190#939—21no—
191#938—21no—
192#938C22×C311yescharacteristic
193#938C22×C311yescharacteristic
194#938C22×C311yescharacteristic
195C2×#214C22×C311yescharacteristic
196#930—21no—
197C2×C4⋊Dic3C22×C311yescharacteristic
198#924—21no—
199#924C22×C311yescharacteristic
200C2×ΓL(1,𝔽25)C22×C311yescharacteristic
201C2×D3×C8C22×C311yescharacteristic
202#897C22×C311yescharacteristic
203D3×C4⋊C4C22×C311yescharacteristic
204#884—21no—
205#878—21no—
206C3×#106—31no—
207C3×#106—31no—
208C3×#106—31no—
209C3×#106—31no—
210C3×#103—21no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103C2×D311yescharacteristic
215C3×#103C22×C311yescharacteristic
216C3×#102—21no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102C2×D311yescharacteristic
221C3×#102C22×C311yescharacteristic
222C3×C22⋊C8—21no—
223C3×C22⋊C8—31no—
224C3×C22⋊C8—31no—
225C3×C22⋊C8—31no—
226C3×C22⋊C8C2×D311yescharacteristic
227C3×C22⋊C8C22×C311yescharacteristic
228#835C22×C311yescharacteristic
229#832C22×C311yescharacteristic
230#832C22×C311yescharacteristic
231#832C22×C311yescharacteristic
232#830C22×C311yescharacteristic
233(C2×D3)⋊C8C22×C311yescharacteristic
234(C2×D3)⋊C8C22×C311yescharacteristic
235#817C22×C311yescharacteristic
236#817C22×C311yescharacteristic
237#816C22×C311yescharacteristic
238#816C22×C311yescharacteristic
239#808C22×C311yescharacteristic
240#808C22×C311yescharacteristic
241C23×C32—21no—
242C23×C32—21no—
243C23×C32C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—21no—
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—42no—
253C32×D4—81no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—42no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C3×#67—41no—
262C3×#67—41no—
263C3×#67—42no—
264C3×#67—81no—
265C3×#67—81no—
266C3×#67—81no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—42no—
272C2×C3×Dic3—81no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—41no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×C4×D3—81no—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—41no—
284C32×C8—21no—
285C32×C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—31no—
289#537—31no—
290#483—31no—
291#483—31no—
292#481—31no—
293#481—31no—
294#470—31no—
295#469—31no—
296#465—31no—
297#465—31no—
298#452—31no—
299#452—31no—
300#449—31no—
301#449C3×D311yescharacteristic, complemented
302#408—31no—
303C3×#41—41no—
304C3×#41—41no—
305C3×#41—41no—
306C3×#41—41no—
307C3×#41—42no—
308C3×#41—42no—
309C3×#41—121no—
310C3×#41—121no—
311C3×#41—121no—
312C3×#41—121no—
313C2×C3×Q8—21no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C23×C311yescharacteristic
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—41no—
328C2×C3×D4—41no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C23×C311yescharacteristic
336C2×C3×D4C23×C311yescharacteristic
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—41no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C23×C311yescharacteristic
348C2×#67—21no—
349C2×#67—21no—
350C2×#67—21no—
351C2×#67—21no—
352C2×#67C3×D411yescharacteristic
353C2×#67C3×D411yescharacteristic
354C22×Dic3—21no—
355C22×Dic3—21no—
356#237—41no—
357#237—41no—
358#235—41no—
359#235—41no—
360C2×D12C3×D411yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3C23×C311yescharacteristic
363C2×C4×D3C23×C311yescharacteristic
364C2×Dic6C3×D411yescharacteristic
365C2×Dic6C23×C311yescharacteristic
366C3×Q16—121no—
367C3×SD16—41no—
368C3×SD16—41no—
369C3×SD16—42no—
370C3×SD16—121no—
371C3×D8—41no—
372C3×D8—41no—
373C3×D8—42no—
374C3×M16—121no—
375C2×C3×C8—21no—
376C2×C3×C8—21no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C2×C3×C8—121no—
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C23×C311yescharacteristic
383C2×C3×C8C23×C311yescharacteristic
384C3×C4⋊C4—21no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C4⋊C4C23×C311yescharacteristic
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—41no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406#217—21no—
407#217—21no—
408#217—21no—
409#217—21no—
410#216—41no—
411#214—41no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415C4⋊Dic3—21no—
416C4⋊Dic3—21no—
417C4⋊Dic3C23×C311yescharacteristic
418C4⋊Dic3C23×C311yescharacteristic
419C4⋊Dic3C23×C311yescharacteristic
420Dic3⋊C4—21no—
421Dic3⋊C4—21no—
422Dic3⋊C4—21no—
423Dic3⋊C4—21no—
424C2×C3⋊C8C23×C311yescharacteristic
425C2×C3⋊C8C23×C311yescharacteristic
426ΓL(1,𝔽25)—41no—
427D3×C8—41no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32C22×D411yescharacteristic
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C2×C3×D3—21no—
443C2×C3×D3—21no—
444C32×C4—21no—
445C32×C4—41no—
446C32×C4—41no—
447C32×C4H(5,𝔽2)11yescharacteristic
448C32×C4H(5,𝔽2)11yescharacteristic
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—31no—
456C2×#41—31no—
457C2×#41C2×C3×D311yescharacteristic
458C2×Q16—31no—
459C2×SD16—31no—
460C2×SD16C2×C3×D311yescharacteristic
461C2×D8C2×C3×D311yescharacteristic
462C2×M16—31no—
463C22×C8—31no—
464C22⋊Q8—31no—
465C22⋊Q8—31no—
466C22⋊Q8—31no—
467C22⋊Q8—31no—
468C22⋊Q8—61no—
469C22⋊Q8—61no—
470#121—31no—
471#121—31no—
472#121—31no—
473#121—61no—
474#121—61no—
475#121—61no—
476#121—61no—
477#121—61no—
478#121—61no—
479#121C2×C3×D311yescharacteristic
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482#106—31no—
483#106—31no—
484#106—31no—
485#106—31no—
486#103—31no—
487#103—31no—
488#103—31no—
489#103C2×C3×D311yescharacteristic
490#102—31no—
491#102—31no—
492#102—31no—
493#102C2×C3×D311yescharacteristic
494C22⋊C8—31no—
495C22⋊C8—31no—
496C22⋊C8—31no—
497C22⋊C8C2×C3×D311yescharacteristic
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—31no—
504C23×C3—31no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3D3×D411yescharacteristic
508C23×C3C2×C3×D411yescharacteristic
509C22×D3C2×C3×D411yescharacteristic
510C22×D3C2×C3×D411yescharacteristic
511C3×Q8—22no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—41no—
517C3×Q8—61no—
518C3×Q8—61no—
519C3×Q8—121no—
520C3×D4—22no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—41no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—42no—
533C3×D4—42no—
534C3×D4—44no—
535C3×D4—81no—
536C3×D4—81no—
537C3×D4—82no—
538C3×D4—121no—
539C3×D4—121no—
540C3×D4—121no—
541C3×D4—122no—
542C3×D4—241no—
543C3×D4—241no—
544C3×D4—241no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—42no—
562C2×C3×C4—42no—
563C2×C3×C4—44no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—122no—
573C2×C3×C4—241no—
574C2×C3×C4—241no—
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4C2×C3×D411yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C24×C311yescharacteristic
579#67—41no—
580#67—41no—
581#67—42no—
582#67—81no—
583#67—81no—
584#67—81no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—42no—
590C2×Dic3—81no—
591C2×Dic3C2×C3×D411yescharacteristic
592C2×Dic3C2×C3×D411yescharacteristic
593D12—41no—
594C4×D3—21no—
595C4×D3—21no—
596C4×D3—21no—
597C4×D3—21no—
598C4×D3—81no—
599Dic6—21no—
600Dic6—21no—
601Dic6—41no—
602C3×C8—21no—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—41no—
607C3×C8—41no—
608C3×C8—61no—
609C3×C8—61no—
610C3⋊C8—21no—
611C3⋊C8—21no—
612C2×C32—41no—
613C2×C32—81no—
614C2×C32—81no—
615C2×C32#53411yescharacteristic
616C2×C32#57711yescharacteristic
617C2×C32#57711yescharacteristic
618C3×D3—41no—
619C3×D3—41no—
620#41—41no—
621#41—41no—
622#41—121no—
623#41—121no—
624#41—121no—
625#41—121no—
626C2×Q8—31no—
627C2×Q8—31no—
628C2×Q8C22×C3×D311yescharacteristic
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—31no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4C22×C3×D311yescharacteristic
639C2×D4C22×C3×D311yescharacteristic
640C22×C4—21no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4C22×C3×D311yescharacteristic
647Q16—121no—
648SD16—41no—
649SD16—121no—
650D8—41no—
651M16—121no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—121no—
655C2×C8C22×C3×D311yescharacteristic
656C2×C8C22×C3×D311yescharacteristic
657C4⋊C4—31no—
658C4⋊C4—31no—
659C4⋊C4—31no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4—61no—
666C4⋊C4C22×C3×D311yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—42no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—81no—
709C22×C3C2×D3×D411yescharacteristic
710C22×C3C22×C3×D411yescharacteristic
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—41no—
722C3×C4—42no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—61no—
728C3×C4—61no—
729C3×C4—81no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4—121no—
733C3×C4—121no—
734C3×C4#100411yescharacteristic
735C3×C4#100411yescharacteristic
736C3×C4C3×H(5,𝔽2)11yescharacteristic
737C3×C4C3×H(5,𝔽2)11yescharacteristic
738Dic3—21no—
739Dic3—21no—
740Dic3—41no—
741Dic3—41no—
742Dic3—41no—
743Dic3—41no—
744C32#320411yescharacteristic, complemented, Sylow
745C23—21no—
746C23—21no—
747C23—31no—
748C23—31no—
749C23C3×D3×D411yescharacteristic
750Q8—21no—
751Q8—21no—
752Q8—61no—
753Q8—61no—
754Q8—121no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—42no—
760D4—81no—
761D4—121no—
762D4—121no—
763D4—121no—
764D4—122no—
765D4—241no—
766D4—241no—
767D4—241no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—42no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—122no—
784C2×C4—241no—
785C2×C4—241no—
786C2×C4C3×D3×D411yescharacteristic
787C2×C4C23×C3×D311yescharacteristic
788C8—21no—
789C8—21no—
790C8—61no—
791C8—61no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—41no—
796C2×C3—41no—
797C2×C3—81no—
798C2×C3—82no—
799C2×C3—81no—
800C2×C3—81no—
801C2×C3—81no—
802C2×C3—81no—
803C2×C3—121no—
804C2×C3—121no—
805C2×C3—161no—
806C2×C3#558911yescharacteristic
807C2×C3#577011yescharacteristic
808C2×C3#577511yescharacteristic
809C2×C3C3×#53411yescharacteristic
810C2×C3C3×#57711yescharacteristic
811C2×C3C3×#57711yescharacteristic
812D3—41no—
813D3—41no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22C2×C3×D3×D411yescharacteristic
830C4—21no—
831C4—41no—
832C4—41no—
833C4—61no—
834C4—61no—
835C4—121no—
836C4—121no—
837C4—121no—
838C4—121no—
839C4C3×#100411yescharacteristic
840C4C3×#100411yescharacteristic
841C3—21no—
842C3#8009611yescharacteristic, direct product factor
843C3C3×#320411yescharacteristic, complemented
844C2—41no—
845C2—81no—
846C2—81no—
847C2—121no—
848C2—121no—
849C2C3×#558911yescharacteristic
850C2C3×#577011yescharacteristic
851C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenterC3×#449D3
hypocenterC3C3×#3204
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C3×#5833C2semidirect
2. C3×#5608C2semidirect
3. C32×#449C2semidirect
4. C3×#5239C2semidirect
5. C3×#5173C2semidirect
6. C3×#5171C2semidirect
7. C3×#5159C2semidirect
8. C3×#5158C2semidirect
9. C3×#5034C2semidirect
10. C3×#4816C2semidirect
11. C3×#4805C2semidirect
12. C3×#4778C2semidirect
13. C3×#4777C2semidirect
14. C3×#4727C2semidirect
15. C3×#4721C2semidirect
17. #80096C3direct (N × H)
63. #5833C2×C3semidirect
64. #5608C2×C3semidirect
77. C3×#449D3semidirect
78. C3×#449C2×C3semidirect
80. #5239C2×C3semidirect
81. #5173C2×C3semidirect
82. #5171C2×C3semidirect
83. #5159C2×C3semidirect
84. #5158C2×C3semidirect
85. #5034C2×C3semidirect
86. #4816C2×C3semidirect
87. #4805C2×C3semidirect
88. #4778C2×C3semidirect
89. #4777C2×C3semidirect
90. #4727C2×C3semidirect
91. #4721C2×C3semidirect
301. #449C3×D3semidirect
744. C32#3204semidirect
842. C3#80096direct (N × H)
843. C3C3×#3204semidirect

Maximal subgroups

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

subgroupindex
C3×#58332
C3×#56082
C32×#4492
C3×#52392
C3×#51732
C3×#51712
C3×#51592
C3×#51582
C3×#50342
C3×#48162
C3×#48052
C3×#47782
C3×#47772
C3×#47272
C3×#47212
C3×#32043
#800963