Finite Group Databasebeta

← C3×#79881 #11888591

Subgroups — C3×#79881 #11888591

Order 1152.

854 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5558C211yesmaximal, characteristic, complemented
2C3×#5555C211yesmaximal, characteristic, complemented
3C32×#442C211yesmaximal, characteristic, complemented
4C3×#5158C211yesmaximal, characteristic, complemented
5C3×#5158C211yesmaximal, characteristic, complemented
6C3×#5019C211yesmaximal, characteristic, complemented
7C3×#5009C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic, complemented
9C3×#4862C211yesmaximal, characteristic, complemented
10C3×#4780C211yesmaximal, characteristic, complemented
11C3×#4778C211yesmaximal, characteristic, complemented
12C3×#4772C211yesmaximal, characteristic, complemented
13C3×#4771C211yesmaximal, characteristic, complemented
14C3×#4706C211yesmaximal, characteristic, complemented
15C3×#4703C211yesmaximal, characteristic, complemented
16C3×#3307—31nomaximal
17#79881C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×#930—21no—
28C3×#929—21no—
29C3×C4×#67—21no—
30C2×C3×C4⋊Dic3—21no—
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33C3×#897C2211yescharacteristic
34C3×#897C2211yescharacteristic
35C3×#892C2211yescharacteristic
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×#886—21no—
38C3×#886—21no—
39C3×#884—21no—
40C3×#879—21no—
41C3×C4×D12C2211yescharacteristic
42C3×#870C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×#97C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#553—31no—
62C3×#547—31no—
63#5558C2×C311yescharacteristic, complemented
64#5555C2×C311yescharacteristic, complemented
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#478—31no—
69C3×#468—31no—
70C3×#465—31no—
71C3×#461—31no—
72C3×#449—31no—
73C3×#449—31no—
74C3×#442—21no—
75C3×#442D311yescharacteristic, complemented
76C3×#442C2×C311yescharacteristic, complemented
77C3×#435—31no—
78C3×#417—31no—
79C3×#416—31no—
80#5158C2×C311yescharacteristic, complemented
81#5158C2×C311yescharacteristic, complemented
82#5019C2×C311yescharacteristic, complemented
83#5009C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic, complemented
85#4862C2×C311yescharacteristic, complemented
86#4780C2×C311yescharacteristic, complemented
87#4778C2×C311yescharacteristic, complemented
88#4772C2×C311yescharacteristic, complemented
89#4771C2×C311yescharacteristic, complemented
90#4706C2×C311yescharacteristic, complemented
91#4703C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#237—22no—
103C3×#237—22no—
104C3×#237—41no—
105C3×#237—41no—
106C2×C3×D12D411yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C32×D8—22no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C22⋊C4—21no—
119C32×C42C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×#214—41no—
123C3×#214—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3D411yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×ΓL(1,𝔽25)—41no—
143C3×D3×C8—41no—
144#3307—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#237C22×C311yescharacteristic
148C2×#237C22×C311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×D8—21no—
152C2×C3×D8C2×D311yescharacteristic
153C2×C3×D8C22×C311yescharacteristic
154C2×C3×M16—31no—
155C22×C3×C8—31no—
156C3×C4⋊Q8—31no—
157C3×#126—61no—
158C3×#125—31no—
159C3×#123—61no—
160C3×#123—61no—
161C3×#123—61no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×#121—31no—
165C3×#121—31no—
166C3×#121—61no—
167C3×#121—61no—
168C3×C4×D4—21no—
169C3×C4×D4—21no—
170C3×C4×D4—31no—
171C3×C4×D4—61no—
172C3×C4×D4C2×D311yescharacteristic
173C3×C4×D4C2×D311yescharacteristic
174C3×C4×D4C22×C311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×#117—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—61no—
179#938C22×C311yescharacteristic
180#938C22×C311yescharacteristic
181C2×#214C22×C311yescharacteristic
182C2×#214C22×C311yescharacteristic
183#930—21no—
184#929—21no—
185C4×#67—21no—
186C2×C4⋊Dic3—21no—
187C2×ΓL(1,𝔽25)C22×C311yescharacteristic
188C2×D3×C8C22×C311yescharacteristic
189#897C22×C311yescharacteristic
190#897C22×C311yescharacteristic
191#892C22×C311yescharacteristic
192D3×C4⋊C4C22×C311yescharacteristic
193#886—21no—
194#886—21no—
195#884—21no—
196#879—21no—
197C4×D12C22×C311yescharacteristic
198#870C22×C311yescharacteristic
199#869C22×C311yescharacteristic
200C3×#107—31no—
201C3×#106—21no—
202C3×#106—31no—
203C3×#106C2×D311yescharacteristic
204C3×#106C22×C311yescharacteristic
205C3×C4⋊C8—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—21no—
213C3×#102—21no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102C2×D311yescharacteristic
217C3×#102C2×D311yescharacteristic
218C3×#102C22×C311yescharacteristic
219C3×#102C22×C311yescharacteristic
220C3×C22⋊C8—31no—
221C3×C22⋊C8—31no—
222C3×#97—21no—
223C3×#97C2×D311yescharacteristic
224C3×#97C22×C311yescharacteristic
225#832C22×C311yescharacteristic
226#832C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#808C22×C311yescharacteristic
236#807C22×C311yescharacteristic
237C4⋊(C3⋊C8)C22×C311yescharacteristic
238C23×C32—21no—
239C23×C32—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4#4112yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—42no—
249C2×C32×C4—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C3×#67—42no—
254C3×#67—42no—
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—41no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—81no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#547—31no—
281#491—31no—
282#485—31no—
283#483—31no—
284#478—31no—
285#468—31no—
286#465—31no—
287#461—31no—
288#449—31no—
289#449—31no—
290#442C3×D311yescharacteristic, complemented
291#435—31no—
292#417—31no—
293#416—31no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—121no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C23×C311yescharacteristic
310C2×C3×D4C23×C311yescharacteristic
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—41no—
318C22×C3×C4—41no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C2×#67—21no—
323C2×#67—21no—
324C2×#67—21no—
325C2×#67—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328#237—22no—
329#237—22no—
330#237—41no—
331#237—41no—
332C2×D12C3×D411yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3C23×C311yescharacteristic
335C2×C4×D3C23×C311yescharacteristic
336C2×Dic6C23×C311yescharacteristic
337C2×Dic6C23×C311yescharacteristic
338C3×SD16—121no—
339C3×SD16—121no—
340C3×D8—24no—
341C3×D8—22no—
342C3×D8—22no—
343C3×M16—121no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
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—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
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⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C23×C311yescharacteristic
368C3×C4⋊C4C23×C311yescharacteristic
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—41no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C42—21no—
383C3×C42—61no—
384C3×C42C22×D311yescharacteristic
385C3×C42C23×C311yescharacteristic
386#217—21no—
387#217—21no—
388#214—41no—
389#214—41no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4C3×D411yescharacteristic
394(C2×D3)⋊C4C3×D411yescharacteristic
395C4⋊Dic3—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
399C4⋊Dic3C3×D411yescharacteristic
400C4⋊Dic3C23×C311yescharacteristic
401C4⋊Dic3C23×C311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405C4×Dic3—21no—
406C2×C3⋊C8C23×C311yescharacteristic
407C2×C3⋊C8C23×C311yescharacteristic
408ΓL(1,𝔽25)—41no—
409D3×C8—41no—
410C22×C32—22no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C2×#41—31no—
437C2×SD16—31no—
438C2×SD16—31no—
439C2×D8C2×C3×D311yescharacteristic
440C2×M16—31no—
441C22×C8—31no—
442C4⋊Q8—31no—
443#126—61no—
444#125—31no—
445#123—61no—
446#123—61no—
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450#121—31no—
451#121—31no—
452#121—61no—
453#121—61no—
454C4×D4—31no—
455C4×D4—61no—
456C4×D4C2×C3×D311yescharacteristic
457C4×D4C2×C3×D311yescharacteristic
458#117—31no—
459C2×C4⋊C4—31no—
460C2×C4⋊C4—61no—
461#107—31no—
462#106—31no—
463#106C2×C3×D311yescharacteristic
464C4⋊C8—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#102—31no—
472#102—31no—
473#102C2×C3×D311yescharacteristic
474#102C2×C3×D311yescharacteristic
475C22⋊C8—31no—
476C22⋊C8—31no—
477#97C2×C3×D311yescharacteristic
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—41no—
486C22×D3C2×C3×D411yescharacteristic
487C22×D3C2×C3×D411yescharacteristic
488C3×Q8—61no—
489C3×Q8—61no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—22no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—121no—
503C3×D4—122no—
504C3×D4—122no—
505C3×D4—122no—
506C3×D4—241no—
507C3×D4#23512yes—
508C3×D4C3×#4112yes—
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—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—42no—
521C2×C3×C4—42no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—82no—
531C2×C3×C4—81no—
532C2×C3×C4—81no—
533C2×C3×C4—82no—
534C2×C3×C4—122no—
535C2×C3×C4—122no—
536C2×C3×C4—241no—
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C2×C3×D411yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C24×C311yescharacteristic
543#67—42no—
544#67—42no—
545#67—42no—
546#67—81no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—42no—
552C2×Dic3—42no—
553C2×Dic3C2×C3×D411yescharacteristic
554C2×Dic3C2×C3×D411yescharacteristic
555D12—41no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—81no—
561Dic6—21no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565C3×C8—22no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—41no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C2×C32—42no—
576C2×C32—81no—
577C2×C32#54611yescharacteristic
578C2×C32#57511yescharacteristic
579C2×C32#57711yescharacteristic
580C3×D3—41no—
581C3×D3—41no—
582#41—62no—
583#41—62no—
584#41—121no—
585#41—121no—
586C2×Q8—31no—
587C2×Q8—31no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4C22×C3×D311yescharacteristic
594C2×D4C22×C3×D311yescharacteristic
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602SD16—121no—
603SD16—121no—
604D8—22no—
605M16—121no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—121no—
609C2×C8C22×C3×D311yescharacteristic
610C2×C8C22×C3×D311yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4C22×C3×D311yescharacteristic
622C4⋊C4C22×C3×D311yescharacteristic
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—31no—
626C22⋊C4—31no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C42—61no—
633C42C22×C3×D311yescharacteristic
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—21no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C22×C3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4C2×#23511yescharacteristic
688C3×C4#100911yescharacteristic
689C3×C4C2×C3×#4111yescharacteristic
690C3×C4C3×H(5,𝔽2)11yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697C32#330711yescharacteristic, complemented, Sylow
698C23—21no—
699C23—21no—
700C23—31no—
701C23—31no—
702Q8—61no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—121no—
710D4—122no—
711D4—122no—
712D4—122no—
713D4—241no—
714D4C3×#23512yes—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—42no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—81no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—241no—
732C2×C4C3×D3×D411yescharacteristic
733C2×C4C3×D3×D411yescharacteristic
734C2×C4C23×C3×D311yescharacteristic
735C8—21no—
736C8—21no—
737C8—61no—
738C8—61no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—82no—
745C2×C3—82no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—121no—
749C2×C3—121no—
750C2×C3#555011yescharacteristic
751C2×C3#577311yescharacteristic
752C2×C3#577511yescharacteristic
753C2×C3C3×#54611yescharacteristic
754C2×C3C3×#57511yescharacteristic
755C2×C3C3×#57711yescharacteristic
756D3—41no—
757D3—41no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22C2×C3×D3×D411yescharacteristic
771C4—21no—
772C4—21no—
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4C2×C3×#23511yescharacteristic
782C4C3×#100911yescharacteristic
783C3—21no—
784C3#7988111yescharacteristic, direct product factor
785C3C3×#330711yescharacteristic, complemented
786C2—42no—
787C2—81no—
788C2—121no—
789C2—121no—
790C2C3×#555011yescharacteristic
791C2C3×#577311yescharacteristic
792C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#442C2
socleC22×C32C22×D4
hypercenterC3×#442D3
hypocenterC3C3×#3307
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#442

Complements

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

NH ≅ G/Ntype
1. C3×#5558C2semidirect
2. C3×#5555C2semidirect
3. C32×#442C2semidirect
4. C3×#5158C2semidirect
5. C3×#5158C2semidirect
6. C3×#5019C2semidirect
7. C3×#5009C2semidirect
8. C3×#4868C2semidirect
9. C3×#4862C2semidirect
10. C3×#4780C2semidirect
11. C3×#4778C2semidirect
12. C3×#4772C2semidirect
13. C3×#4771C2semidirect
14. C3×#4706C2semidirect
15. C3×#4703C2semidirect
17. #79881C3direct (N × H)
63. #5558C2×C3semidirect
64. #5555C2×C3semidirect
75. C3×#442D3semidirect
76. C3×#442C2×C3semidirect
80. #5158C2×C3semidirect
81. #5158C2×C3semidirect
82. #5019C2×C3semidirect
83. #5009C2×C3semidirect
84. #4868C2×C3semidirect
85. #4862C2×C3semidirect
86. #4780C2×C3semidirect
87. #4778C2×C3semidirect
88. #4772C2×C3semidirect
89. #4771C2×C3semidirect
90. #4706C2×C3semidirect
91. #4703C2×C3semidirect
290. #442C3×D3semidirect
697. C32#3307semidirect
784. C3#79881direct (N × H)
785. C3C3×#3307semidirect

Maximal subgroups

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

subgroupindex
C3×#55582
C3×#55552
C32×#4422
C3×#51582
C3×#50192
C3×#50092
C3×#48682
C3×#48622
C3×#47802
C3×#47782
C3×#47722
C3×#47712
C3×#47062
C3×#47032
C3×#33073
#798813