Finite Group Databasebeta

← C3×#80280 #11886558

Subgroups — C3×#80280 #11886558

Order 1152.

1012 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5836C211yesmaximal, characteristic, complemented
2C3×#5835C211yesmaximal, characteristic, complemented
3C3×#5775C211yesmaximal, characteristic, complemented
4C3×#5774C211yesmaximal, characteristic, complemented
5C32×#453C211yesmaximal, characteristic, complemented
6C3×#5200C211yesmaximal, characteristic, complemented
7C3×#5199C211yesmaximal, characteristic, complemented
8C3×#5077C211yesmaximal, characteristic, complemented
9C3×#5074C211yesmaximal, characteristic, complemented
10C3×#4827C211yesmaximal, characteristic, complemented
11C3×#4825C211yesmaximal, characteristic, complemented
12C3×#4823C211yesmaximal, characteristic, complemented
13C3×#4823C211yesmaximal, characteristic, complemented
14C3×#4749C211yesmaximal, characteristic, complemented
15C3×#4748C211yesmaximal, characteristic, complemented
16C3×#3288—31nomaximal
17#80280C311yesmaximal, characteristic, direct product factor
18C32×H(5,𝔽2)C2211yescharacteristic, complemented
19C3×#1010C2211yescharacteristic, complemented
20C3×#1009C2211yescharacteristic
21C3×#1004C2211yescharacteristic, complemented
22C32×AGL(1,ℤ/8)C2211yescharacteristic
23C32×AGL(1,ℤ/8)C2211yescharacteristic, complemented
24C32×#127C2211yescharacteristic, complemented
25C3×#951—21no—
26C3×#951C2211yescharacteristic, complemented
27C3×#950—21no—
28C3×#950—21no—
29C3×#950C2211yescharacteristic
30C3×#950C2211yescharacteristic
31C3×#949—21no—
32C3×#949C2211yescharacteristic, complemented
33C3×#948C2211yescharacteristic, complemented
34C3×#948C2211yescharacteristic, complemented
35C2×C3×#214—21no—
36C2×C3×#214C2211yescharacteristic, complemented
37C2×C3×#214C2211yescharacteristic, complemented
38C3×#932—21no—
39C3×#932—21no—
40C3×#932C2211yescharacteristic
41C3×#932C2211yescharacteristic, complemented
42C2×C3×#213—21no—
43C2×C3×#213C2211yescharacteristic, complemented
44C2×C3×#213C2211yescharacteristic, complemented
45C3×#916—21no—
46C3×#915—21no—
47C3×#914—21no—
48C3×D3×SD16—21no—
49C3×#912—21no—
50C3×#911—21no—
51C3×#911—21no—
52C3×D3×D8—21no—
53C3×#909C2211yescharacteristic, complemented
54C3×#908C2211yescharacteristic, complemented
55C3×#907C2211yescharacteristic, complemented
56C3×#907C2211yescharacteristic, complemented
57C3×#875C2211yescharacteristic, complemented
58C32×#104C2211yescharacteristic, complemented
59C32×#104C2211yescharacteristic, complemented
60C32×#100C2211yescharacteristic, complemented
61C3×#833C2211yescharacteristic, complemented
62C3×#824C2211yescharacteristic, complemented
63C3×#823C2211yescharacteristic, complemented
64C3×#822C2211yescharacteristic, complemented
65C3×#822C2211yescharacteristic, complemented
66C3×#805C2211yescharacteristic, complemented
67C3×#805C2211yescharacteristic, complemented
68C3×#803C2211yescharacteristic, complemented
69C3×#577—31no—
70C3×#577—31no—
71C3×#576—31no—
72C3×#576—31no—
73#5836C2×C311yescharacteristic, complemented
74#5835C2×C311yescharacteristic, complemented
75#5775C2×C311yescharacteristic, complemented
76#5774C2×C311yescharacteristic, complemented
77C3×#496—31no—
78C3×#472—31no—
79C3×#472—31no—
80C3×#471—31no—
81C3×#471—31no—
82C3×#455—31no—
83C3×#454—31no—
84C3×#453—21no—
85C3×#453—31no—
86C3×#453D311yescharacteristic, complemented
87C3×#453C2×C311yescharacteristic, complemented
88C3×#444—31no—
89C3×#444—31no—
90#5200C2×C311yescharacteristic, complemented
91#5199C2×C311yescharacteristic, complemented
92#5077C2×C311yescharacteristic, complemented
93#5074C2×C311yescharacteristic, complemented
94#4827C2×C311yescharacteristic, complemented
95#4825C2×C311yescharacteristic, complemented
96#4823C2×C311yescharacteristic, complemented
97#4823C2×C311yescharacteristic, complemented
98#4749C2×C311yescharacteristic, complemented
99#4748C2×C311yescharacteristic, complemented
100C32×#41—21no—
101C32×#41—21no—
102C32×#41C2311yescharacteristic
103C32×#41C2311yescharacteristic
104C2×C32×D4—21no—
105C2×C32×D4—21no—
106C2×C32×D4—41no—
107C2×C32×D4—41no—
108C2×C32×D4C2311yescharacteristic
109C2×C32×D4C2311yescharacteristic
110C2×C3×#67—41no—
111C3×#239—21no—
112C3×D3×Q8—21no—
113C3×#237—21no—
114C3×#237—21no—
115C3×#237—21no—
116C3×#237—41no—
117C3×D3×D4—21no—
118C3×D3×D4—21no—
119C3×D3×D4—21no—
120C3×D3×D4—41no—
121C3×#235—21no—
122C3×#235—21no—
123C3×#235C2311yescharacteristic
124C3×#235C2311yescharacteristic
125C2×C3×D12—21no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×Dic6—21no—
128C2×C3×Dic6C2311yescharacteristic
129C32×SD16—21no—
130C32×SD16—21no—
131C32×D8—21no—
132C32×D8—21no—
133C32×M16C2311yescharacteristic
134C32×M16C2311yescharacteristic
135C32×C42C2311yescharacteristic
136C3×#216—21no—
137C3×#216D411yescharacteristic, complemented
138C3×#216D411yescharacteristic, complemented
139C3×#215—21no—
140C3×#215D411yescharacteristic, complemented
141C3×#215D411yescharacteristic, complemented
142C3×#214—21no—
143C3×#214—21no—
144C3×#214—21no—
145C3×#214—21no—
146C3×#214—21no—
147C3×#214—21no—
148C3×#214—21no—
149C3×#214D411yescharacteristic, complemented
150C3×#214D411yescharacteristic, complemented
151C3×#213—21no—
152C3×#213—21no—
153C3×#213—21no—
154C3×#213—21no—
155C3×#213—21no—
156C3×#213—21no—
157C3×#213—21no—
158C3×#213D411yescharacteristic, complemented
159C3×#213D411yescharacteristic, complemented
160C3×(C2×D3)⋊C4—41no—
161C3×#208—21no—
162C3×#208—21no—
163C3×#208C2311yescharacteristic
164C3×#208C2311yescharacteristic
165C2×C3×C3⋊C8—21no—
166C2×C3×C3⋊C8—21no—
167C2×C3×C3⋊C8C2311yescharacteristic
168C2×C3×C3⋊C8C2311yescharacteristic
169C3×Dic12—21no—
170C3×D24—21no—
171C3×#204—21no—
172C3×#204—21no—
173C3×ΓL(1,𝔽25)—21no—
174C3×ΓL(1,𝔽25)—21no—
175C3×D3×C8—21no—
176C3×D3×C8—21no—
177#3288—31noSylow
178C3×2−1+4—31no—
179C3×H(5,𝔽2)—21no—
180C3×H(5,𝔽2)—31no—
181C3×H(5,𝔽2)—31no—
182C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
183C3×H(5,𝔽2)C22×C311yescharacteristic, complemented
184#1010C22×C311yescharacteristic, complemented
185#1009C22×C311yescharacteristic
186#1004C22×C311yescharacteristic, complemented
187C3×#137—31no—
188C3×#137—31no—
189C3×#137—61no—
190C3×#137—61no—
191C3×AGL(1,ℤ/8)—21no—
192C3×AGL(1,ℤ/8)—21no—
193C3×AGL(1,ℤ/8)—31no—
194C3×AGL(1,ℤ/8)—31no—
195C3×AGL(1,ℤ/8)—31no—
196C3×AGL(1,ℤ/8)—31no—
197C3×AGL(1,ℤ/8)—61no—
198C3×AGL(1,ℤ/8)—61no—
199C3×AGL(1,ℤ/8)—61no—
200C3×AGL(1,ℤ/8)—61no—
201C3×AGL(1,ℤ/8)—61no—
202C3×AGL(1,ℤ/8)—61no—
203C3×AGL(1,ℤ/8)C2×D311yescharacteristic
204C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
205C3×AGL(1,ℤ/8)C22×C311yescharacteristic
206C3×AGL(1,ℤ/8)C22×C311yescharacteristic, complemented
207C3×#135—31no—
208C3×#135—31no—
209C3×#135—61no—
210C3×#135—61no—
211C3×#135—61no—
212C3×#135—61no—
213C2×C3×SD16—31no—
214C2×C3×SD16—31no—
215C2×C3×SD16—61no—
216C2×C3×SD16—61no—
217C2×C3×D8—31no—
218C2×C3×D8—31no—
219C2×C3×D8—61no—
220C2×C3×D8—61no—
221C3×#131—31no—
222C3×#131—31no—
223C3×#131—31no—
224C3×#131—31no—
225C3×#127—21no—
226C3×#127C2×D311yescharacteristic, complemented
227C3×#127C22×C311yescharacteristic, complemented
228C3×#124—31no—
229#951—21no—
230#951C22×C311yescharacteristic, complemented
231#950—21no—
232#950—21no—
233#950C22×C311yescharacteristic
234#950C22×C311yescharacteristic
235#949—21no—
236#949C22×C311yescharacteristic, complemented
237#948C22×C311yescharacteristic, complemented
238#948C22×C311yescharacteristic, complemented
239C2×#214—21no—
240C2×#214C22×C311yescharacteristic, complemented
241C2×#214C22×C311yescharacteristic, complemented
242#932—21no—
243#932—21no—
244#932C22×C311yescharacteristic
245#932C22×C311yescharacteristic, complemented
246C2×#213—21no—
247C2×#213C22×C311yescharacteristic, complemented
248C2×#213C22×C311yescharacteristic, complemented
249#916—21no—
250#915—21no—
251#914—21no—
252D3×SD16—21no—
253#912—21no—
254#911—21no—
255#911—21no—
256D3×D8—21no—
257#909C22×C311yescharacteristic, complemented
258#908C22×C311yescharacteristic, complemented
259#907C22×C311yescharacteristic, complemented
260#907C22×C311yescharacteristic, complemented
261#875C22×C311yescharacteristic, complemented
262C3×#108—31no—
263C3×#108—31no—
264C3×#104—21no—
265C3×#104—21no—
266C3×#104—31no—
267C3×#104—31no—
268C3×#104C2×D311yescharacteristic, complemented
269C3×#104C2×D311yescharacteristic, complemented
270C3×#104C22×C311yescharacteristic, complemented
271C3×#104C22×C311yescharacteristic, complemented
272C3×#101—31no—
273C3×#100—21no—
274C3×#100—31no—
275C3×#100—31no—
276C3×#100C2×D311yescharacteristic, complemented
277C3×#100C22×C311yescharacteristic, complemented
278C3×#97—31no—
279#833C22×C311yescharacteristic, complemented
280#824C22×C311yescharacteristic, complemented
281#823C22×C311yescharacteristic, complemented
282#822C22×C311yescharacteristic, complemented
283#822C22×C311yescharacteristic, complemented
284#805C22×C311yescharacteristic, complemented
285#805C22×C311yescharacteristic, complemented
286#803C22×C311yescharacteristic, complemented
287C23×C32—21no—
288C23×C32—21no—
289C23×C32—41no—
290C22×C3×D3—21no—
291C22×C3×D3—41no—
292C22×C3×D3—41no—
293C32×Q8C2×D411yescharacteristic
294C32×Q8C2×D411yescharacteristic
295C32×D4—21no—
296C32×D4—21no—
297C32×D4—21no—
298C32×D4—21no—
299C32×D4—21no—
300C32×D4—21no—
301C32×D4—41no—
302C32×D4—41no—
303C32×D4—82no—
304C32×D4C2×D411yescharacteristic
305C32×D4C2×D411yescharacteristic
306C2×C32×C4—21no—
307C2×C32×C4—21no—
308C2×C32×C4—21no—
309C2×C32×C4—41no—
310C2×C32×C4C2411yescharacteristic
311C3×#67—21no—
312C3×#67—21no—
313C3×#67—41no—
314C3×#67—41no—
315C3×#67—41no—
316C3×#67—41no—
317C2×C3×Dic3—21no—
318C2×C3×Dic3—41no—
319C2×C3×Dic3—41no—
320C3×D12—21no—
321C3×D12—21no—
322C3×D12—41no—
323C3×D12C2×D411yescharacteristic
324C3×D12C2×D411yescharacteristic
325C3×C4×D3—21no—
326C3×C4×D3—21no—
327C3×C4×D3—41no—
328C3×C4×D3—41no—
329C3×Dic6—21no—
330C3×Dic6—21no—
331C3×Dic6—41no—
332C3×Dic6C2×D411yescharacteristic
333C3×Dic6C2×D411yescharacteristic
334C32×C8—21no—
335C32×C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341C3×C3⋊C8C2×D411yescharacteristic
342#577—31no—
343#577—31no—
344#576—31no—
345#576—31no—
346#496—31no—
347#472—31no—
348#472—31no—
349#471—31no—
350#471—31no—
351#455—31no—
352#454—31no—
353#453—31no—
354#453C3×D311yescharacteristic, complemented
355#444—31no—
356#444—31no—
357C3×#41—21no—
358C3×#41—21no—
359C3×#41—21no—
360C3×#41—21no—
361C3×#41—21no—
362C3×#41—21no—
363C3×#41—31no—
364C3×#41—31no—
365C3×#41—41no—
366C3×#41—41no—
367C3×#41—61no—
368C3×#41—61no—
369C3×#41—61no—
370C3×#41—61no—
371C3×#41—61no—
372C3×#41—61no—
373C3×#41—121no—
374C3×#41C22×D311yescharacteristic
375C3×#41C22×D311yescharacteristic
376C3×#41C23×C311yescharacteristic
377C3×#41C23×C311yescharacteristic
378C2×C3×Q8—31no—
379C2×C3×Q8—61no—
380C2×C3×Q8—61no—
381C2×C3×D4—21no—
382C2×C3×D4—21no—
383C2×C3×D4—21no—
384C2×C3×D4—21no—
385C2×C3×D4—21no—
386C2×C3×D4—21no—
387C2×C3×D4—31no—
388C2×C3×D4—41no—
389C2×C3×D4—41no—
390C2×C3×D4—41no—
391C2×C3×D4—41no—
392C2×C3×D4—41no—
393C2×C3×D4—41no—
394C2×C3×D4—42no—
395C2×C3×D4—42no—
396C2×C3×D4—61no—
397C2×C3×D4—61no—
398C2×C3×D4—61no—
399C2×C3×D4—61no—
400C2×C3×D4—121no—
401C2×C3×D4—121no—
402C2×C3×D4C22×D311yescharacteristic
403C2×C3×D4C22×D311yescharacteristic
404C2×C3×D4C23×C311yescharacteristic
405C2×C3×D4C23×C311yescharacteristic
406C2×#67—41no—
407#239—21no—
408D3×Q8—21no—
409#237—21no—
410#237—21no—
411#237—21no—
412#237—41no—
413D3×D4—21no—
414D3×D4—21no—
415D3×D4—21no—
416D3×D4—41no—
417#235—21no—
418#235—21no—
419#235C23×C311yescharacteristic
420#235C23×C311yescharacteristic
421C2×D12—21no—
422C2×D12C23×C311yescharacteristic
423C2×Dic6—21no—
424C2×Dic6C23×C311yescharacteristic
425C3×Q16—31no—
426C3×Q16—31no—
427C3×Q16—61no—
428C3×Q16—61no—
429C3×SD16—21no—
430C3×SD16—21no—
431C3×SD16—21no—
432C3×SD16—21no—
433C3×SD16—31no—
434C3×SD16—31no—
435C3×SD16—31no—
436C3×SD16—31no—
437C3×SD16—41no—
438C3×SD16—41no—
439C3×SD16—61no—
440C3×SD16—61no—
441C3×SD16—61no—
442C3×SD16—61no—
443C3×SD16—61no—
444C3×SD16—61no—
445C3×SD16—61no—
446C3×SD16—61no—
447C3×SD16—61no—
448C3×SD16—61no—
449C3×D8—21no—
450C3×D8—21no—
451C3×D8—21no—
452C3×D8—21no—
453C3×D8—31no—
454C3×D8—31no—
455C3×D8—41no—
456C3×D8—41no—
457C3×D8—61no—
458C3×D8—61no—
459C3×D8—61no—
460C3×D8—61no—
461C3×D8—61no—
462C3×D8—61no—
463C3×D8—61no—
464C3×D8—61no—
465C3×M16—21no—
466C3×M16—21no—
467C3×M16—31no—
468C3×M16—31no—
469C3×M16—61no—
470C3×M16—61no—
471C3×M16—61no—
472C3×M16—61no—
473C3×M16C22×D311yescharacteristic
474C3×M16C22×D311yescharacteristic
475C3×M16C23×C311yescharacteristic
476C3×M16C23×C311yescharacteristic
477C2×C3×C8—31no—
478C2×C3×C8—31no—
479C2×C3×C8—61no—
480C2×C3×C8—61no—
481C2×C3×C8—61no—
482C2×C3×C8—61no—
483C3×C22⋊C4—121no—
484C3×C42—21no—
485C3×C42C22×D311yescharacteristic
486C3×C42C23×C311yescharacteristic
487#216—21no—
488#216C3×D411yescharacteristic, complemented
489#216C3×D411yescharacteristic, complemented
490#215—21no—
491#215C3×D411yescharacteristic, complemented
492#215C3×D411yescharacteristic, complemented
493#214—21no—
494#214—21no—
495#214—21no—
496#214—21no—
497#214—21no—
498#214—21no—
499#214—21no—
500#214C3×D411yescharacteristic, complemented
501#214C3×D411yescharacteristic, complemented
502#213—21no—
503#213—21no—
504#213—21no—
505#213—21no—
506#213—21no—
507#213—21no—
508#213—21no—
509#213C3×D411yescharacteristic, complemented
510#213C3×D411yescharacteristic, complemented
511(C2×D3)⋊C4—41no—
512#208—21no—
513#208—21no—
514#208C23×C311yescharacteristic
515#208C23×C311yescharacteristic
516C2×C3⋊C8—21no—
517C2×C3⋊C8—21no—
518C2×C3⋊C8C23×C311yescharacteristic
519C2×C3⋊C8C23×C311yescharacteristic
520Dic12—21no—
521D24—21no—
522#204—21no—
523#204—21no—
524ΓL(1,𝔽25)—21no—
525ΓL(1,𝔽25)—21no—
526D3×C8—21no—
527D3×C8—21no—
528C22×C32—21no—
529C22×C32—21no—
530C22×C32—41no—
531C22×C32—41no—
532C22×C32—81no—
533C22×C32—81no—
534C22×C32—161no—
535C22×C32H(5,𝔽2)11yescharacteristic
536C2×C3×D3—21no—
537C2×C3×D3—21no—
538C2×C3×D3—41no—
539C2×C3×D3—81no—
540C2×C3×D3—161no—
541C2×C3×D3—161no—
542C32×C4—21no—
543C32×C4—21no—
544C32×C4—41no—
545C32×C4C22×D411yescharacteristic
546C32×C4C22×D411yescharacteristic
547C3×Dic3—21no—
548C3×Dic3—21no—
549C3×Dic3—41no—
5502−1+4—31no—
551H(5,𝔽2)—31no—
552H(5,𝔽2)—31no—
553H(5,𝔽2)C2×C3×D311yescharacteristic, complemented
554#137—31no—
555#137—31no—
556#137—61no—
557#137—61no—
558AGL(1,ℤ/8)—31no—
559AGL(1,ℤ/8)—31no—
560AGL(1,ℤ/8)—31no—
561AGL(1,ℤ/8)—31no—
562AGL(1,ℤ/8)—61no—
563AGL(1,ℤ/8)—61no—
564AGL(1,ℤ/8)—61no—
565AGL(1,ℤ/8)—61no—
566AGL(1,ℤ/8)—61no—
567AGL(1,ℤ/8)—61no—
568AGL(1,ℤ/8)C2×C3×D311yescharacteristic
569AGL(1,ℤ/8)C2×C3×D311yescharacteristic, complemented
570#135—31no—
571#135—31no—
572#135—61no—
573#135—61no—
574#135—61no—
575#135—61no—
576C2×SD16—31no—
577C2×SD16—31no—
578C2×SD16—61no—
579C2×SD16—61no—
580C2×D8—31no—
581C2×D8—31no—
582C2×D8—61no—
583C2×D8—61no—
584#131—31no—
585#131—31no—
586#131—31no—
587#131—31no—
588#127C2×C3×D311yescharacteristic, complemented
589#124—31no—
590#108—31no—
591#108—31no—
592#104—31no—
593#104—31no—
594#104C2×C3×D311yescharacteristic, complemented
595#104C2×C3×D311yescharacteristic, complemented
596#101—31no—
597#100—31no—
598#100—31no—
599#100C2×C3×D311yescharacteristic, complemented
600#97—31no—
601C23×C3—22no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—42no—
610C23×C3—61no—
611C23×C3—121no—
612C23×C3—121no—
613C22×D3—21no—
614C22×D3—41no—
615C22×D3—41no—
616C3×Q8—21no—
617C3×Q8—21no—
618C3×Q8—31no—
619C3×Q8—31no—
620C3×Q8—61no—
621C3×Q8—61no—
622C3×Q8—121no—
623C3×Q8D3×D411yescharacteristic
624C3×Q8D3×D411yescharacteristic
625C3×Q8C2×C3×D411yescharacteristic
626C3×Q8C2×C3×D411yescharacteristic
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—21no—
630C3×D4—21no—
631C3×D4—21no—
632C3×D4—21no—
633C3×D4—21no—
634C3×D4—21no—
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—21no—
638C3×D4—21no—
639C3×D4—21no—
640C3×D4—21no—
641C3×D4—31no—
642C3×D4—31no—
643C3×D4—41no—
644C3×D4—41no—
645C3×D4—41no—
646C3×D4—41no—
647C3×D4—41no—
648C3×D4—41no—
649C3×D4—41no—
650C3×D4—41no—
651C3×D4—41no—
652C3×D4—41no—
653C3×D4—42no—
654C3×D4—42no—
655C3×D4—61no—
656C3×D4—61no—
657C3×D4—61no—
658C3×D4—61no—
659C3×D4—82no—
660C3×D4—82no—
661C3×D4—84no—
662C3×D4—121no—
663C3×D4—121no—
664C3×D4—121no—
665C3×D4—121no—
666C3×D4—121no—
667C3×D4D3×D411yescharacteristic
668C3×D4D3×D411yescharacteristic
669C3×D4C2×C3×D411yescharacteristic
670C3×D4C2×C3×D411yescharacteristic
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—42no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—121no—
688C2×C3×C4—121no—
689C2×C3×C4—121no—
690C2×C3×C4—121no—
691C2×C3×C4C23×D311yescharacteristic
692C2×C3×C4C24×C311yescharacteristic
693#67—21no—
694#67—21no—
695#67—41no—
696#67—41no—
697#67—41no—
698#67—41no—
699C2×Dic3—21no—
700C2×Dic3—41no—
701C2×Dic3—41no—
702D12—21no—
703D12—21no—
704D12—41no—
705D12C2×C3×D411yescharacteristic
706D12C2×C3×D411yescharacteristic
707C4×D3—21no—
708C4×D3—21no—
709C4×D3—41no—
710C4×D3—41no—
711Dic6—21no—
712Dic6—21no—
713Dic6—41no—
714Dic6C2×C3×D411yescharacteristic
715Dic6C2×C3×D411yescharacteristic
716C3×C8—21no—
717C3×C8—21no—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—31no—
721C3×C8—31no—
722C3×C8—31no—
723C3×C8—31no—
724C3×C8—41no—
725C3×C8—41no—
726C3×C8—61no—
727C3×C8—61no—
728C3⋊C8—21no—
729C3⋊C8—21no—
730C3⋊C8C2×C3×D411yescharacteristic
731C3⋊C8C2×C3×D411yescharacteristic
732C3⋊C8C2×C3×D411yescharacteristic
733C3⋊C8C2×C3×D411yescharacteristic
734C2×C32—21no—
735C2×C32—41no—
736C2×C32—41no—
737C2×C32—81no—
738C2×C32—81no—
739C2×C32D4211yescharacteristic
740C3×D3—41no—
741C3×D3—41no—
742C3×D3—81no—
743#41—21no—
744#41—21no—
745#41—31no—
746#41—31no—
747#41—61no—
748#41—61no—
749#41—61no—
750#41—61no—
751#41—61no—
752#41—61no—
753#41—121no—
754#41C22×C3×D311yescharacteristic
755#41C22×C3×D311yescharacteristic
756C2×Q8—31no—
757C2×Q8—61no—
758C2×Q8—61no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—31no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4—61no—
765C2×D4—61no—
766C2×D4—61no—
767C2×D4—61no—
768C2×D4—121no—
769C2×D4—121no—
770C2×D4C22×C3×D311yescharacteristic
771C2×D4C22×C3×D311yescharacteristic
772Q16—31no—
773Q16—31no—
774Q16—61no—
775Q16—61no—
776SD16—21no—
777SD16—21no—
778SD16—31no—
779SD16—31no—
780SD16—31no—
781SD16—31no—
782SD16—61no—
783SD16—61no—
784SD16—61no—
785SD16—61no—
786SD16—61no—
787SD16—61no—
788SD16—61no—
789SD16—61no—
790SD16—61no—
791SD16—61no—
792D8—21no—
793D8—21no—
794D8—31no—
795D8—31no—
796D8—61no—
797D8—61no—
798D8—61no—
799D8—61no—
800D8—61no—
801D8—61no—
802D8—61no—
803D8—61no—
804M16—31no—
805M16—31no—
806M16—61no—
807M16—61no—
808M16—61no—
809M16—61no—
810M16C22×C3×D311yescharacteristic
811M16C22×C3×D311yescharacteristic
812C2×C8—31no—
813C2×C8—31no—
814C2×C8—61no—
815C2×C8—61no—
816C2×C8—61no—
817C2×C8—61no—
818C22⋊C4—121no—
819C42C22×C3×D311yescharacteristic
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—42no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—61no—
833C22×C3—61no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—82no—
840C22×C3—82no—
841C22×C3—121no—
842C22×C3—161no—
843C22×C3—161no—
844C22×C3—162no—
845C22×C3—241no—
846C22×C3—481no—
847C22×C3—481no—
848C22×C3#100411yescharacteristic
849C22×C3C3×H(5,𝔽2)11yescharacteristic
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—41no—
853C2×D3—81no—
854C2×D3—161no—
855C2×D3—161no—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—41no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—42no—
867C3×C4—61no—
868C3×C4—61no—
869C3×C4—121no—
870C3×C4C2×D3×D411yescharacteristic
871C3×C4C2×D3×D411yescharacteristic
872C3×C4C22×C3×D411yescharacteristic
873C3×C4C22×C3×D411yescharacteristic
874Dic3—21no—
875Dic3—21no—
876Dic3—41no—
877C32#328811yescharacteristic, complemented, Sylow
878C23—21no—
879C23—21no—
880C23—41no—
881C23—61no—
882C23—121no—
883C23—121no—
884Q8—31no—
885Q8—31no—
886Q8—61no—
887Q8—61no—
888Q8—121no—
889Q8C3×D3×D411yescharacteristic
890Q8C3×D3×D411yescharacteristic
891D4—21no—
892D4—21no—
893D4—21no—
894D4—21no—
895D4—21no—
896D4—21no—
897D4—31no—
898D4—31no—
899D4—41no—
900D4—41no—
901D4—61no—
902D4—61no—
903D4—61no—
904D4—61no—
905D4—82no—
906D4—121no—
907D4—121no—
908D4—121no—
909D4—121no—
910D4—121no—
911D4C3×D3×D411yescharacteristic
912D4C3×D3×D411yescharacteristic
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—41no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4C23×C3×D311yescharacteristic
925C8—21no—
926C8—21no—
927C8—31no—
928C8—31no—
929C8—31no—
930C8—31no—
931C8—61no—
932C8—61no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—41no—
937C2×C3—41no—
938C2×C3—41no—
939C2×C3—41no—
940C2×C3—41no—
941C2×C3—81no—
942C2×C3—81no—
943C2×C3—82no—
944C2×C3—81no—
945C2×C3—81no—
946C2×C3—81no—
947C2×C3—81no—
948C2×C3—121no—
949C2×C3—121no—
950C2×C3—161no—
951C2×C3—241no—
952C2×C3#559011yescharacteristic
953C2×C3C3×D4211yescharacteristic
954D3—41no—
955D3—41no—
956D3—81no—
957C22—21no—
958C22—21no—
959C22—41no—
960C22—41no—
961C22—61no—
962C22—61no—
963C22—81no—
964C22—81no—
965C22—121no—
966C22—161no—
967C22—241no—
968C22—481no—
969C22—481no—
970C22C3×#100411yescharacteristic
971C4—21no—
972C4—21no—
973C4—41no—
974C4—61no—
975C4—61no—
976C4—121no—
977C4C2×C3×D3×D411yescharacteristic
978C4C2×C3×D3×D411yescharacteristic
979C3—21no—
980C3#8028011yescharacteristic, direct product factor
981C3C3×#328811yescharacteristic, complemented
982C2—21no—
983C2—41no—
984C2—41no—
985C2—81no—
986C2—81no—
987C2—121no—
988C2—121no—
989C2—241no—
990C2C3×#559011yescharacteristic
subgroupG/H
centerC2×C3#5590
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#453C2
socleC2×C32D42
hypercenterC3×#453D3
hypocenterC3C3×#3288
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#453

Complements

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

NH ≅ G/Ntype
1. C3×#5836C2semidirect
2. C3×#5835C2semidirect
3. C3×#5775C2semidirect
4. C3×#5774C2semidirect
5. C32×#453C2semidirect
6. C3×#5200C2semidirect
7. C3×#5199C2semidirect
8. C3×#5077C2semidirect
9. C3×#5074C2semidirect
10. C3×#4827C2semidirect
11. C3×#4825C2semidirect
12. C3×#4823C2semidirect
13. C3×#4823C2semidirect
14. C3×#4749C2semidirect
15. C3×#4748C2semidirect
17. #80280C3direct (N × H)
18. C32×H(5,𝔽2)C22semidirect
19. C3×#1010C22semidirect
21. C3×#1004C22semidirect
23. C32×AGL(1,ℤ/8)C22semidirect
24. C32×#127C22semidirect
26. C3×#951C22semidirect
32. C3×#949C22semidirect
33. C3×#948C22semidirect
34. C3×#948C22semidirect
36. C2×C3×#214C22semidirect
37. C2×C3×#214C22semidirect
41. C3×#932C22semidirect
43. C2×C3×#213C22semidirect
44. C2×C3×#213C22semidirect
53. C3×#909C22semidirect
54. C3×#908C22semidirect
55. C3×#907C22semidirect
56. C3×#907C22semidirect
57. C3×#875C22semidirect
58. C32×#104C22semidirect
59. C32×#104C22semidirect
60. C32×#100C22semidirect
61. C3×#833C22semidirect
62. C3×#824C22semidirect
63. C3×#823C22semidirect
64. C3×#822C22semidirect
65. C3×#822C22semidirect
66. C3×#805C22semidirect
67. C3×#805C22semidirect
68. C3×#803C22semidirect
73. #5836C2×C3semidirect
74. #5835C2×C3semidirect
75. #5775C2×C3semidirect
76. #5774C2×C3semidirect
86. C3×#453D3semidirect
87. C3×#453C2×C3semidirect
90. #5200C2×C3semidirect
91. #5199C2×C3semidirect
92. #5077C2×C3semidirect
93. #5074C2×C3semidirect
94. #4827C2×C3semidirect
95. #4825C2×C3semidirect
96. #4823C2×C3semidirect
97. #4823C2×C3semidirect
98. #4749C2×C3semidirect
99. #4748C2×C3semidirect
137. C3×#216D4semidirect
138. C3×#216D4semidirect
140. C3×#215D4semidirect
141. C3×#215D4semidirect
149. C3×#214D4semidirect
150. C3×#214D4semidirect
158. C3×#213D4semidirect
159. C3×#213D4semidirect
182. C3×H(5,𝔽2)C2×D3semidirect
183. C3×H(5,𝔽2)C22×C3semidirect
184. #1010C22×C3semidirect
186. #1004C22×C3semidirect
204. C3×AGL(1,ℤ/8)C2×D3semidirect
206. C3×AGL(1,ℤ/8)C22×C3semidirect
226. C3×#127C2×D3semidirect
227. C3×#127C22×C3semidirect
230. #951C22×C3semidirect
236. #949C22×C3semidirect
237. #948C22×C3semidirect
238. #948C22×C3semidirect
240. C2×#214C22×C3semidirect
241. C2×#214C22×C3semidirect
245. #932C22×C3semidirect
247. C2×#213C22×C3semidirect
248. C2×#213C22×C3semidirect
257. #909C22×C3semidirect
258. #908C22×C3semidirect
259. #907C22×C3semidirect
260. #907C22×C3semidirect
261. #875C22×C3semidirect
268. C3×#104C2×D3semidirect
269. C3×#104C2×D3semidirect
270. C3×#104C22×C3semidirect
271. C3×#104C22×C3semidirect
276. C3×#100C2×D3semidirect
277. C3×#100C22×C3semidirect
279. #833C22×C3semidirect
280. #824C22×C3semidirect
281. #823C22×C3semidirect
282. #822C22×C3semidirect
283. #822C22×C3semidirect
284. #805C22×C3semidirect
285. #805C22×C3semidirect
286. #803C22×C3semidirect
354. #453C3×D3semidirect
488. #216C3×D4semidirect
489. #216C3×D4semidirect
491. #215C3×D4semidirect
492. #215C3×D4semidirect
500. #214C3×D4semidirect
501. #214C3×D4semidirect
509. #213C3×D4semidirect
510. #213C3×D4semidirect
553. H(5,𝔽2)C2×C3×D3semidirect
569. AGL(1,ℤ/8)C2×C3×D3semidirect
588. #127C2×C3×D3semidirect
594. #104C2×C3×D3semidirect
595. #104C2×C3×D3semidirect
599. #100C2×C3×D3semidirect
877. C32#3288semidirect
980. C3#80280direct (N × H)
981. C3C3×#3288semidirect

Maximal subgroups

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

subgroupindex
C3×#58362
C3×#58352
C3×#57752
C3×#57742
C32×#4532
C3×#52002
C3×#51992
C3×#50772
C3×#50742
C3×#48272
C3×#48252
C3×#48232
C3×#47492
C3×#47482
C3×#32883
#802803