Finite Group Databasebeta

← C3×#80159 #11887211

Subgroups — C3×#80159 #11887211

Order 1152.

910 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic
2C3×#5642C211yesmaximal, characteristic, complemented
3C32×#450C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5C3×#5173C211yesmaximal, characteristic, complemented
6C3×#5171C211yesmaximal, characteristic, complemented
7C3×#5166C211yesmaximal, characteristic, complemented
8C3×Dic3×SD16C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×#4779C211yesmaximal, characteristic, complemented
11C3×#4772C211yesmaximal, characteristic, complemented
12C3×#4768C211yesmaximal, characteristic, complemented
13C3×#4763C211yesmaximal, characteristic, complemented
14C3×#67⋊C8C211yesmaximal, characteristic, complemented
15C3×#4721C211yesmaximal, characteristic, complemented
16C3×#3296—31nomaximal
17#80159C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C3×#953—21no—
24C2×C3×#217—21no—
25C3×#946C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C3×#939—21no—
29C3×#938C2211yescharacteristic
30C3×#936C2211yescharacteristic
31C3×#935—21no—
32C3×D4×Dic3C2211yescharacteristic
33C3×C4×#67C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C3×#924C2211yescharacteristic
36C22×C3×C3⋊C8C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#898—21no—
39C3×#892C2211yescharacteristic, complemented
40C3×#890—21no—
41C3×#890C2211yescharacteristic, complemented
42C3×#886—21no—
43C3×#877—21no—
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×#817C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C8×Dic3C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×#546—31no—
63#5806C2×C311yescharacteristic
64#5642C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#483—31no—
67C3×#482—31no—
68C3×#478—31no—
69C3×#467—31no—
70C3×#465—31no—
71C3×#464—31no—
72C3×#452—31no—
73C3×#450—21no—
74C3×#450D311yescharacteristic, complemented
75C3×#450C2×C311yescharacteristic, complemented
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#102—31no—
80C2×#832C2×C311yescharacteristic, complemented
81#5173C2×C311yescharacteristic, complemented
82#5171C2×C311yescharacteristic, complemented
83#5166C2×C311yescharacteristic, complemented
84Dic3×SD16C2×C311yescharacteristic, complemented
85#5051C2×C311yescharacteristic, complemented
86#4779C2×C311yescharacteristic, complemented
87#4772C2×C311yescharacteristic, complemented
88#4768C2×C311yescharacteristic, complemented
89#4763C2×C311yescharacteristic, complemented
90#67⋊C8C2×C311yescharacteristic, complemented
91#4721C2×C311yescharacteristic, complemented
92C24×C32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4—41no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#237—22no—
107C3×#237—41no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C32×SD16—22no—
111C32×SD16—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×#216—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
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#3296—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—21no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C22×C311yescharacteristic
149C2×#237C22×C311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×SD16—21no—
152C2×C3×SD16—21no—
153C2×C3×SD16C2×D311yescharacteristic
154C2×C3×SD16C2×D311yescharacteristic
155C2×C3×SD16C22×C311yescharacteristic
156C2×C3×SD16C22×C311yescharacteristic
157C22×C3×C8—31no—
158C22×C3×C8—31no—
159C3×#126—61no—
160C3×#125—31no—
161C3×#125—61no—
162C3×#124—31no—
163C3×#123—61no—
164C3×#123—61no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8C2×D311yescharacteristic
169C3×C22⋊Q8C22×C311yescharacteristic
170C3×#121—31no—
171C3×#121—61no—
172C3×#120—61no—
173C3×C4×Q8—31no—
174C3×C4×D4—31no—
175C3×C4×D4—31no—
176C3×#117—31no—
177C3×#117—61no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C22⋊C4—61no—
180#953—21no—
181C2×#217—21no—
182#946C22×C311yescharacteristic, complemented
183Q8×Dic3C22×C311yescharacteristic, complemented
184C2×#216C22×C311yescharacteristic, complemented
185#939—21no—
186#938C22×C311yescharacteristic
187#936C22×C311yescharacteristic
188#935—21no—
189D4×Dic3C22×C311yescharacteristic
190C4×#67C22×C311yescharacteristic
191C2×C4⋊Dic3C22×C311yescharacteristic
192#924C22×C311yescharacteristic
193C22×C3⋊C8C22×C311yescharacteristic
194C2×D3×C8C22×C311yescharacteristic, complemented
195#898—21no—
196#892C22×C311yescharacteristic, complemented
197#890—21no—
198#890C22×C311yescharacteristic, complemented
199#886—21no—
200#877—21no—
201C3×#107—31no—
202C3×#106—31no—
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—21no—
210C3×#102—21no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102C2×D311yescharacteristic
216C3×#102C2×D311yescharacteristic
217C3×#102C22×C311yescharacteristic
218C3×#102C22×C311yescharacteristic
219C3×C22⋊C8—21no—
220C3×C22⋊C8—31no—
221C3×C22⋊C8C2×D311yescharacteristic
222C3×C22⋊C8C22×C311yescharacteristic
223C3×C4×C8—31no—
224#835C22×C311yescharacteristic, complemented
225#832C22×C311yescharacteristic
226#832C22×C311yescharacteristic
227#832C22×C311yescharacteristic
228#832C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic, complemented
230#817C22×C311yescharacteristic, complemented
231#817C22×C311yescharacteristic, complemented
232#816C22×C311yescharacteristic, complemented
233#816C22×C311yescharacteristic, complemented
234Dic3⋊C8C22×C311yescharacteristic, complemented
235C8×Dic3C22×C311yescharacteristic, complemented
236#810C22×C311yescharacteristic, complemented
237#807C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—42no—
241C23×C32—42no—
242C23×C32—81no—
243C23×C32C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—21no—
249C32×D4—21no—
250C32×D4—42no—
251C32×D4#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258C3×#67—22no—
259C3×#67—42no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3—42no—
267C2×C3×Dic3—81no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—31no—
281#488—31no—
282#483—31no—
283#482—31no—
284#478—31no—
285#467—31no—
286#465—31no—
287#464—31no—
288#452—31no—
289#450C3×D311yescharacteristic, complemented
290C4×SD16—31no—
291C8×D4—31no—
292#416—31no—
293C2×#102—31no—
294C24×C3—21no—
295C24×C3—21no—
296C24×C3—41no—
297C3×#41—62no—
298C3×#41—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×D4—22no—
304C2×C3×D4—22no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—31no—
310C2×C3×D4—41no—
311C2×C3×D4—42no—
312C2×C3×D4—41no—
313C2×C3×D4—41no—
314C2×C3×D4—42no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C22×D311yescharacteristic
319C2×C3×D4C23×C311yescharacteristic
320C2×C3×D4C23×C311yescharacteristic
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C23×C311yescharacteristic
328C2×#67—21no—
329C2×#67—21no—
330C2×#67C3×D411yescharacteristic
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334#237—22no—
335#237—41no—
336C2×C4×D3C23×C311yescharacteristic
337C2×Dic6C23×C311yescharacteristic
338C3×Q16—121no—
339C3×SD16—22no—
340C3×SD16—22no—
341C3×SD16—42no—
342C3×SD16—41no—
343C3×SD16—41no—
344C3×SD16—42no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8—121no—
350C2×C3×C8—121no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C23×C311yescharacteristic
354C2×C3×C8C23×C311yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—41no—
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⋊C4C22×D311yescharacteristic
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×C22⋊C4—61no—
383C3×C42—31no—
384C3×C42—61no—
385C3×C42—61no—
386#217—21no—
387#217—21no—
388#217—21no—
389#217—21no—
390#217—21no—
391#217C3×D411yescharacteristic
392#216—41no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4C3×D411yescharacteristic
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
399C4⋊Dic3C23×C311yescharacteristic
400C4⋊Dic3C23×C311yescharacteristic
401C4⋊Dic3C23×C311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4C3×D411yescharacteristic
406C4×Dic3—21no—
407C4×Dic3—21no—
408C4×Dic3C23×C311yescharacteristic
409C2×C3⋊C8—41no—
410C2×C3⋊C8C23×C311yescharacteristic
411C2×C3⋊C8C23×C311yescharacteristic
412D3×C8—41no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—22no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—84no—
422C22×C32#13512yes—
423C22×C32C22×D411yescharacteristic
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C32×C4—21no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—31no—
440C22×D4C2×C3×D311yescharacteristic
441C2×Q16—31no—
442C2×SD16C2×C3×D311yescharacteristic
443C2×SD16C2×C3×D311yescharacteristic
444C22×C8—31no—
445C22×C8—31no—
446#126—61no—
447#125—31no—
448#125—61no—
449#124—31no—
450#123—61no—
451#123—61no—
452C22⋊Q8—31no—
453C22⋊Q8—31no—
454C22⋊Q8C2×C3×D311yescharacteristic
455#121—31no—
456#121—61no—
457#120—61no—
458C4×Q8—31no—
459C4×D4—31no—
460C4×D4—31no—
461#117—31no—
462#117—61no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—61no—
465#107—31no—
466#106—31no—
467#106—31no—
468C4⋊C8—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102C2×C3×D311yescharacteristic
478#102C2×C3×D311yescharacteristic
479C22⋊C8—31no—
480C22⋊C8C2×C3×D311yescharacteristic
481C4×C8—31no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—42no—
491C23×C3—42no—
492C23×C3—44no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—82no—
496C23×C3—81no—
497C23×C3—81no—
498C23×C3—82no—
499C23×C3D3×D411yescharacteristic
500C23×C3C2×C3×D411yescharacteristic
501C22×D3C2×C3×D411yescharacteristic
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—41no—
507C3×Q8—41no—
508C3×Q8—61no—
509C3×Q8—61no—
510C3×D4—22no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—22no—
518C3×D4—41no—
519C3×D4—41no—
520C3×D4—42no—
521C3×D4—42no—
522C3×D4—44no—
523C3×D4—62no—
524C3×D4—122no—
525C3×D4—241no—
526C3×D4#23712yes—
527C3×D4C3×#4112yes—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—122no—
552C2×C3×C4—122no—
553C2×C3×C4—241no—
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4C2×C3×D411yescharacteristic
556C2×C3×C4C23×D311yescharacteristic
557C2×C3×C4C24×C311yescharacteristic
558#67—22no—
559#67—42no—
560#67—81no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—42no—
566C2×Dic3—42no—
567C2×Dic3—81no—
568C2×Dic3C2×C3×D411yescharacteristic
569C2×Dic3C2×C3×D411yescharacteristic
570C2×Dic3C2×C3×D411yescharacteristic
571C4×D3—21no—
572C4×D3—21no—
573Dic6—21no—
574Dic6—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—41no—
580C3×C8—41no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C2×C32—22no—
586C2×C32—42no—
587C2×C32—81no—
588C2×C32#54611yescharacteristic
589C2×C32C2×#13511yescharacteristic
590C2×C32#57711yescharacteristic
591C3×D3—41no—
592C24—21no—
593#41—62no—
594#41—121no—
595C2×Q8—31no—
596C2×Q8C22×C3×D311yescharacteristic
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—31no—
600C2×D4—41no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4C22×C3×D311yescharacteristic
604C2×D4C22×C3×D311yescharacteristic
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4C22×C3×D311yescharacteristic
610Q16—121no—
611SD16—22no—
612SD16—41no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—121no—
616C2×C8—121no—
617C2×C8C22×C3×D311yescharacteristic
618C2×C8C22×C3×D311yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4C22×C3×D311yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C42—31no—
642C42—61no—
643C42—61no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—84no—
674C22×C3—84no—
675C22×C3—88no—
676C22×C3#91612yes—
677C22×C3C3×#13512yes—
678C22×C3C2×D3×D411yescharacteristic
679C22×C3C22×C3×D411yescharacteristic
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4C2×#23711yescharacteristic
702C3×C4#100411yescharacteristic
703C3×C4C2×C3×#4111yescharacteristic
704C3×C4C3×H(5,𝔽2)11yescharacteristic
705Dic3—21no—
706Dic3—21no—
707Dic3—21no—
708Dic3—41no—
709Dic3—41no—
710Dic3—41no—
711Dic3—41no—
712C32#329611yescharacteristic, complemented, Sylow
713C23—21no—
714C23—21no—
715C23—31no—
716C23—42no—
717C23—42no—
718C23—81no—
719C23C3×D3×D411yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—61no—
723Q8—61no—
724D4—21no—
725D4—21no—
726D4—21no—
727D4—42no—
728D4—62no—
729D4—122no—
730D4—241no—
731D4C3×#23712yes—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—31no—
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—122no—
747C2×C4—241no—
748C2×C4C3×D3×D411yescharacteristic
749C2×C4C23×C3×D311yescharacteristic
750C8—21no—
751C8—21no—
752C8—61no—
753C8—61no—
754C2×C3—22no—
755C2×C3—22no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—42no—
760C2×C3—42no—
761C2×C3—42no—
762C2×C3—82no—
763C2×C3—82no—
764C2×C3—81no—
765C2×C3—81no—
766C2×C3—121no—
767C2×C3#559111yescharacteristic
768C2×C3C2×#91611yescharacteristic
769C2×C3#577511yescharacteristic
770C2×C3C3×#54611yescharacteristic
771C2×C3C2×C3×#13511yescharacteristic
772C2×C3C3×#57711yescharacteristic
773D3—41no—
774C22—21no—
775C22—21no—
776C22—22no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—84no—
786C22C3×#91612yes—
787C22C2×C3×D3×D411yescharacteristic
788C4—21no—
789C4—41no—
790C4—41no—
791C4—61no—
792C4—61no—
793C4—61no—
794C4—121no—
795C4—121no—
796C4—121no—
797C4—121no—
798C4C2×C3×#23711yescharacteristic
799C4C3×#100411yescharacteristic
800C3—21no—
801C3#8015911yescharacteristic, direct product factor
802C3C3×#329611yescharacteristic, complemented
803C2—22no—
804C2—42no—
805C2—81no—
806C2—121no—
807C2C3×#559111yescharacteristic
808C2C2×C3×#91611yescharacteristic
809C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC3×#450D3
hypocenterC3C3×#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
2. C3×#5642C2semidirect
3. C32×#450C2semidirect
4. C2×C3×#832C2semidirect
5. C3×#5173C2semidirect
6. C3×#5171C2semidirect
7. C3×#5166C2semidirect
8. C3×Dic3×SD16C2semidirect
9. C3×#5051C2semidirect
10. C3×#4779C2semidirect
11. C3×#4772C2semidirect
12. C3×#4768C2semidirect
13. C3×#4763C2semidirect
14. C3×#67⋊C8C2semidirect
15. C3×#4721C2semidirect
17. #80159C3direct (N × H)
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
27. C2×C3×#216C22semidirect
37. C2×C3×D3×C8C22semidirect
39. C3×#892C22semidirect
41. C3×#890C22semidirect
47. C3×#835C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×#817C22semidirect
54. C3×#817C22semidirect
55. C3×#816C22semidirect
56. C3×#816C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C8×Dic3C22semidirect
59. C3×#810C22semidirect
60. C3×#807C22semidirect
64. #5642C2×C3semidirect
74. C3×#450D3semidirect
75. C3×#450C2×C3semidirect
80. C2×#832C2×C3semidirect
81. #5173C2×C3semidirect
82. #5171C2×C3semidirect
83. #5166C2×C3semidirect
84. Dic3×SD16C2×C3semidirect
85. #5051C2×C3semidirect
86. #4779C2×C3semidirect
87. #4772C2×C3semidirect
88. #4768C2×C3semidirect
89. #4763C2×C3semidirect
90. #67⋊C8C2×C3semidirect
91. #4721C2×C3semidirect
182. #946C22×C3semidirect
183. Q8×Dic3C22×C3semidirect
184. C2×#216C22×C3semidirect
194. C2×D3×C8C22×C3semidirect
196. #892C22×C3semidirect
198. #890C22×C3semidirect
224. #835C22×C3semidirect
229. (C2×D3)⋊C8C22×C3semidirect
230. #817C22×C3semidirect
231. #817C22×C3semidirect
232. #816C22×C3semidirect
233. #816C22×C3semidirect
234. Dic3⋊C8C22×C3semidirect
235. C8×Dic3C22×C3semidirect
236. #810C22×C3semidirect
237. #807C22×C3semidirect
289. #450C3×D3semidirect
712. C32#3296semidirect
801. C3#80159direct (N × H)
802. C3C3×#3296semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
C3×#56422
C32×#4502
C2×C3×#8322
C3×#51732
C3×#51712
C3×#51662
C3×Dic3×SD162
C3×#50512
C3×#47792
C3×#47722
C3×#47682
C3×#47632
C3×#67⋊C82
C3×#47212
C3×#32963
#801593