Finite Group Databasebeta

← C3×#79900 #11886576

Subgroups — C3×#79900 #11886576

Order 1152.

980 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5770C211yesmaximal, characteristic, complemented
2C3×#5769C211yesmaximal, characteristic, complemented
3C3×#5752C211yesmaximal, characteristic, complemented
4C3×#5751C211yesmaximal, characteristic, complemented
5C32×#444C211yesmaximal, characteristic, complemented
6C3×#5142C211yesmaximal, characteristic, complemented
7C3×#5141C211yesmaximal, characteristic, complemented
8C3×#4898C211yesmaximal, characteristic, complemented
9C3×#4897C211yesmaximal, characteristic, complemented
10C3×#4827C211yesmaximal, characteristic, complemented
11C3×#4825C211yesmaximal, characteristic, complemented
12C3×#4822C211yesmaximal, characteristic, complemented
13C3×#4822C211yesmaximal, characteristic, complemented
14C3×#4717C211yesmaximal, characteristic, complemented
15C3×#4712C211yesmaximal, characteristic, complemented
16C3×#3288—31nomaximal
17#79900C311yesmaximal, characteristic, direct product factor
18C3×#1010C2211yescharacteristic, complemented
19C3×#1009C2211yescharacteristic
20C3×#1009C2211yescharacteristic, complemented
21C3×#1009C2211yescharacteristic, complemented
22C32×#135C2211yescharacteristic
23C32×#131C2211yescharacteristic, complemented
24C32×#131C2211yescharacteristic, complemented
25C3×#951C2211yescharacteristic, complemented
26C3×#949C2211yescharacteristic
27C3×#949C2211yescharacteristic, complemented
28C3×#949C2211yescharacteristic, complemented
29C3×#919—21no—
30C3×#918—21no—
31C3×#916—21no—
32C3×#914—21no—
33C3×#914—21no—
34C3×D3×SD16—21no—
35C3×#911—21no—
36C3×D3×D8—21no—
37C3×#909—21no—
38C3×#909C2211yescharacteristic, complemented
39C3×#908—21no—
40C3×#908—21no—
41C3×#908—21no—
42C3×#908C2211yescharacteristic
43C3×#908C2211yescharacteristic, complemented
44C3×#908C2211yescharacteristic, complemented
45C3×#904—21no—
46C3×#904—21no—
47C3×#904C2211yescharacteristic
48C2×C3×D24—21no—
49C2×C3×D24C2211yescharacteristic, complemented
50C2×C3×D24C2211yescharacteristic, complemented
51C2×C3×#204—21no—
52C2×C3×#204C2211yescharacteristic, complemented
53C2×C3×#204C2211yescharacteristic, complemented
54C3×#901C2211yescharacteristic, complemented
55C3×#901C2211yescharacteristic, complemented
56C3×#875C2211yescharacteristic, complemented
57C3×#874C2211yescharacteristic, complemented
58C32×#108C2211yescharacteristic, complemented
59C32×#104C2211yescharacteristic, complemented
60C32×#104C2211yescharacteristic, complemented
61C32×#97C2211yescharacteristic, complemented
62C3×#824C2211yescharacteristic, complemented
63C3×#823C2211yescharacteristic, complemented
64C3×#823C2211yescharacteristic, complemented
65C3×#823C2211yescharacteristic, complemented
66C3×#819C2211yescharacteristic, complemented
67C3×#805C2211yescharacteristic, complemented
68C3×#805C2211yescharacteristic, complemented
69C3×#577—31no—
70C3×#577—31no—
71C3×#576—31no—
72C3×#576—31no—
73#5770C2×C311yescharacteristic, complemented
74#5769C2×C311yescharacteristic, complemented
75#5752C2×C311yescharacteristic, complemented
76#5751C2×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—31no—
85C3×#453—31no—
86C3×#444—21no—
87C3×#444—31no—
88C3×#444D311yescharacteristic, complemented
89C3×#444C2×C311yescharacteristic, complemented
90#5142C2×C311yescharacteristic, complemented
91#5141C2×C311yescharacteristic, complemented
92#4898C2×C311yescharacteristic, complemented
93#4897C2×C311yescharacteristic, complemented
94#4827C2×C311yescharacteristic, complemented
95#4825C2×C311yescharacteristic, complemented
96#4822C2×C311yescharacteristic, complemented
97#4822C2×C311yescharacteristic, complemented
98#4717C2×C311yescharacteristic, complemented
99#4712C2×C311yescharacteristic, complemented
100C32×#41C2311yescharacteristic
101C32×#41C2311yescharacteristic
102C3×#239—21no—
103C3×#239—21no—
104C3×#239—21no—
105C3×D3×Q8—21no—
106C3×#237—21no—
107C3×#237—41no—
108C3×D3×D4—21no—
109C3×D3×D4—21no—
110C3×D3×D4—21no—
111C3×D3×D4—41no—
112C3×D3×D4—41no—
113C3×D3×D4—41no—
114C3×#235—21no—
115C3×#235—21no—
116C3×#235—21no—
117C3×#235—21no—
118C3×#235C2311yescharacteristic
119C3×#235C2311yescharacteristic
120C2×C3×D12—21no—
121C2×C3×D12—21no—
122C2×C3×D12—21no—
123C2×C3×D12—41no—
124C2×C3×D12C2311yescharacteristic
125C2×C3×D12C2311yescharacteristic
126C2×C3×D12C2311yescharacteristic
127C2×C3×Dic6—21no—
128C2×C3×Dic6C2311yescharacteristic
129C32×Q16D411yescharacteristic, complemented
130C32×SD16D411yescharacteristic, complemented
131C32×SD16D411yescharacteristic, complemented
132C32×D8D411yescharacteristic, complemented
133C32×M16—21no—
134C32×M16—21no—
135C32×M16C2311yescharacteristic
136C32×M16C2311yescharacteristic
137C2×C32×C8—21no—
138C2×C32×C8—21no—
139C2×C32×C8C2311yescharacteristic
140C2×C32×C8C2311yescharacteristic
141C32×C42C2311yescharacteristic
142C3×#216—21no—
143C3×#215—21no—
144C3×#215—21no—
145C3×#215—21no—
146C3×#214—21no—
147C3×#213—21no—
148C3×#213—21no—
149C3×#213—21no—
150C3×(C2×D3)⋊C4—41no—
151C3×#208C2311yescharacteristic
152C3×#208C2311yescharacteristic
153C3×Dic12—21no—
154C3×Dic12D411yescharacteristic, complemented
155C3×D24—21no—
156C3×D24—21no—
157C3×D24—21no—
158C3×D24—21no—
159C3×D24—21no—
160C3×D24—21no—
161C3×D24—21no—
162C3×D24D411yescharacteristic, complemented
163C3×#204—21no—
164C3×#204—21no—
165C3×#204—21no—
166C3×#204—21no—
167C3×#204—21no—
168C3×#204—21no—
169C3×#204—21no—
170C3×#204—21no—
171C3×#204D411yescharacteristic, complemented
172C3×#204D411yescharacteristic, complemented
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)—31no—
180C3×H(5,𝔽2)—31no—
181C3×H(5,𝔽2)—31no—
182#1010C22×C311yescharacteristic, complemented
183#1009C22×C311yescharacteristic
184#1009C22×C311yescharacteristic, complemented
185#1009C22×C311yescharacteristic, complemented
186C3×#137—31no—
187C3×#137—31no—
188C3×#137—61no—
189C3×#137—61no—
190C3×AGL(1,ℤ/8)—31no—
191C3×AGL(1,ℤ/8)—31no—
192C3×AGL(1,ℤ/8)—31no—
193C3×AGL(1,ℤ/8)—31no—
194C3×AGL(1,ℤ/8)—31no—
195C3×AGL(1,ℤ/8)—31no—
196C3×AGL(1,ℤ/8)—61no—
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×#135—21no—
203C3×#135—31no—
204C3×#135—61no—
205C3×#135—61no—
206C3×#135—61no—
207C3×#135—61no—
208C3×#135C2×D311yescharacteristic
209C3×#135C22×C311yescharacteristic
210C2×C3×SD16—31no—
211C2×C3×SD16—31no—
212C2×C3×SD16—61no—
213C2×C3×SD16—61no—
214C2×C3×D8—31no—
215C2×C3×D8—31no—
216C2×C3×D8—61no—
217C2×C3×D8—61no—
218C3×#131—21no—
219C3×#131—21no—
220C3×#131—31no—
221C3×#131—31no—
222C3×#131C2×D311yescharacteristic, complemented
223C3×#131C2×D311yescharacteristic, complemented
224C3×#131C22×C311yescharacteristic, complemented
225C3×#131C22×C311yescharacteristic, complemented
226C3×#127—31no—
227C3×#124—31no—
228#951C22×C311yescharacteristic, complemented
229#949C22×C311yescharacteristic
230#949C22×C311yescharacteristic, complemented
231#949C22×C311yescharacteristic, complemented
232#919—21no—
233#918—21no—
234#916—21no—
235#914—21no—
236#914—21no—
237D3×SD16—21no—
238#911—21no—
239D3×D8—21no—
240#909—21no—
241#909C22×C311yescharacteristic, complemented
242#908—21no—
243#908—21no—
244#908—21no—
245#908C22×C311yescharacteristic
246#908C22×C311yescharacteristic, complemented
247#908C22×C311yescharacteristic, complemented
248#904—21no—
249#904—21no—
250#904C22×C311yescharacteristic
251C2×D24—21no—
252C2×D24C22×C311yescharacteristic, complemented
253C2×D24C22×C311yescharacteristic, complemented
254C2×#204—21no—
255C2×#204C22×C311yescharacteristic, complemented
256C2×#204C22×C311yescharacteristic, complemented
257#901C22×C311yescharacteristic, complemented
258#901C22×C311yescharacteristic, complemented
259#875C22×C311yescharacteristic, complemented
260#874C22×C311yescharacteristic, complemented
261C3×#108—21no—
262C3×#108—31no—
263C3×#108C2×D311yescharacteristic, complemented
264C3×#108C22×C311yescharacteristic, complemented
265C3×#104—21no—
266C3×#104—21no—
267C3×#104—31no—
268C3×#104—31no—
269C3×#104C2×D311yescharacteristic, complemented
270C3×#104C2×D311yescharacteristic, complemented
271C3×#104C22×C311yescharacteristic, complemented
272C3×#104C22×C311yescharacteristic, complemented
273C3×#101—31no—
274C3×#100—31no—
275C3×#100—31no—
276C3×#100—31no—
277C3×#97—21no—
278C3×#97C2×D311yescharacteristic, complemented
279C3×#97C22×C311yescharacteristic, complemented
280#824C22×C311yescharacteristic, complemented
281#823C22×C311yescharacteristic, complemented
282#823C22×C311yescharacteristic, complemented
283#823C22×C311yescharacteristic, complemented
284#819C22×C311yescharacteristic, complemented
285#805C22×C311yescharacteristic, complemented
286#805C22×C311yescharacteristic, complemented
287C22×C3×D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3—41no—
291C22×C3×D3—41no—
292C22×C3×D3—41no—
293C32×Q8C2×D411yescharacteristic
294C32×Q8C2×D411yescharacteristic
295C32×D4—21no—
296C32×D4—21no—
297C32×D4C2×D411yescharacteristic
298C32×D4C2×D411yescharacteristic
299C2×C32×C4—21no—
300C2×C32×C4—21no—
301C2×C32×C4—21no—
302C2×C32×C4C2411yescharacteristic
303C3×#67—21no—
304C3×#67—21no—
305C3×#67—41no—
306C3×#67—41no—
307C3×#67—41no—
308C3×#67—41no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—41no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—41no—
318C3×D12—41no—
319C3×D12—41no—
320C3×D12—82no—
321C3×D12C2×D411yescharacteristic
322C3×D12C2×D411yescharacteristic
323C3×C4×D3—21no—
324C3×C4×D3—21no—
325C3×C4×D3—41no—
326C3×C4×D3—41no—
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—
336C32×C8C2×D411yescharacteristic
337C32×C8C2×D411yescharacteristic
338C32×C8C2×D411yescharacteristic
339C32×C8C2×D411yescharacteristic
340C3×C3⋊C8—21no—
341C3×C3⋊C8—21no—
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#453—31no—
355#444—31no—
356#444C3×D311yescharacteristic, complemented
357C3×#41—21no—
358C3×#41—21no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41—61no—
366C3×#41—61no—
367C3×#41—61no—
368C3×#41—61no—
369C3×#41—121no—
370C3×#41C22×D311yescharacteristic
371C3×#41C22×D311yescharacteristic
372C3×#41C23×C311yescharacteristic
373C3×#41C23×C311yescharacteristic
374C2×C3×Q8—31no—
375C2×C3×Q8—61no—
376C2×C3×Q8—61no—
377C2×C3×D4—31no—
378C2×C3×D4—31no—
379C2×C3×D4—31no—
380C2×C3×D4—61no—
381C2×C3×D4—61no—
382C2×C3×D4—61no—
383C2×C3×D4—61no—
384C2×C3×D4—61no—
385C2×C3×D4—61no—
386C2×C3×D4—121no—
387C2×C3×D4—121no—
388C2×C3×D4—121no—
389C2×C3×D4—121no—
390#239—21no—
391#239—21no—
392#239—21no—
393D3×Q8—21no—
394#237—21no—
395#237—41no—
396D3×D4—21no—
397D3×D4—21no—
398D3×D4—21no—
399D3×D4—41no—
400D3×D4—41no—
401D3×D4—41no—
402#235—21no—
403#235—21no—
404#235—21no—
405#235—21no—
406#235C23×C311yescharacteristic
407#235C23×C311yescharacteristic
408C2×D12—21no—
409C2×D12—21no—
410C2×D12—21no—
411C2×D12—41no—
412C2×D12C23×C311yescharacteristic
413C2×D12C23×C311yescharacteristic
414C2×D12C23×C311yescharacteristic
415C2×Dic6—21no—
416C2×Dic6C23×C311yescharacteristic
417C3×Q16—21no—
418C3×Q16—31no—
419C3×Q16—61no—
420C3×Q16—61no—
421C3×Q16D1211yescharacteristic, complemented
422C3×Q16C3×D411yescharacteristic, complemented
423C3×SD16—21no—
424C3×SD16—21no—
425C3×SD16—31no—
426C3×SD16—31no—
427C3×SD16—61no—
428C3×SD16—61no—
429C3×SD16—61no—
430C3×SD16—61no—
431C3×SD16—61no—
432C3×SD16—61no—
433C3×SD16—61no—
434C3×SD16—61no—
435C3×SD16—61no—
436C3×SD16—61no—
437C3×SD16—61no—
438C3×SD16—61no—
439C3×SD16D1211yescharacteristic, complemented
440C3×SD16D1211yescharacteristic, complemented
441C3×SD16C3×D411yescharacteristic, complemented
442C3×SD16C3×D411yescharacteristic, complemented
443C3×D8—21no—
444C3×D8—31no—
445C3×D8—61no—
446C3×D8—61no—
447C3×D8—61no—
448C3×D8—61no—
449C3×D8—61no—
450C3×D8—61no—
451C3×D8—61no—
452C3×D8—61no—
453C3×D8—61no—
454C3×D8—61no—
455C3×D8D1211yescharacteristic, complemented
456C3×D8C3×D411yescharacteristic, complemented
457C3×M16—21no—
458C3×M16—21no—
459C3×M16—21no—
460C3×M16—21no—
461C3×M16—21no—
462C3×M16—21no—
463C3×M16—31no—
464C3×M16—31no—
465C3×M16—41no—
466C3×M16—41no—
467C3×M16—61no—
468C3×M16—61no—
469C3×M16C22×D311yescharacteristic
470C3×M16C22×D311yescharacteristic
471C3×M16C23×C311yescharacteristic
472C3×M16C23×C311yescharacteristic
473C2×C3×C8—21no—
474C2×C3×C8—21no—
475C2×C3×C8—21no—
476C2×C3×C8—21no—
477C2×C3×C8—21no—
478C2×C3×C8—21no—
479C2×C3×C8—41no—
480C2×C3×C8—41no—
481C2×C3×C8—61no—
482C2×C3×C8—61no—
483C2×C3×C8C22×D311yescharacteristic
484C2×C3×C8C22×D311yescharacteristic
485C2×C3×C8C23×C311yescharacteristic
486C2×C3×C8C23×C311yescharacteristic
487C3×C22⋊C4—121no—
488C3×C42—21no—
489C3×C42C22×D311yescharacteristic
490C3×C42C23×C311yescharacteristic
491#216—21no—
492#215—21no—
493#215—21no—
494#215—21no—
495#214—21no—
496#213—21no—
497#213—21no—
498#213—21no—
499(C2×D3)⋊C4—41no—
500#208C23×C311yescharacteristic
501#208C23×C311yescharacteristic
502Dic12—21no—
503Dic12C3×D411yescharacteristic, complemented
504D24—21no—
505D24—21no—
506D24—21no—
507D24—21no—
508D24—21no—
509D24—21no—
510D24—21no—
511D24C3×D411yescharacteristic, complemented
512#204—21no—
513#204—21no—
514#204—21no—
515#204—21no—
516#204—21no—
517#204—21no—
518#204—21no—
519#204—21no—
520#204C3×D411yescharacteristic, complemented
521#204C3×D411yescharacteristic, complemented
522ΓL(1,𝔽25)—21no—
523ΓL(1,𝔽25)—21no—
524D3×C8—21no—
525D3×C8—21no—
526C22×C32—21no—
527C22×C32—21no—
528C22×C32H(5,𝔽2)11yescharacteristic
529C2×C3×D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—81no—
535C2×C3×D3—81no—
536C2×C3×D3—81no—
537C2×C3×D3—161no—
538C2×C3×D3—161no—
539C2×C3×D3—161no—
540C32×C4—21no—
541C32×C4—21no—
542C32×C4—41no—
543C32×C4C22×D411yescharacteristic
544C32×C4C22×D411yescharacteristic
545C3×Dic3—21no—
546C3×Dic3—21no—
547C3×Dic3—41no—
5482−1+4—31no—
549H(5,𝔽2)—31no—
550H(5,𝔽2)—31no—
551H(5,𝔽2)—31no—
552#137—31no—
553#137—31no—
554#137—61no—
555#137—61no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—31no—
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—
568#135—31no—
569#135—61no—
570#135—61no—
571#135—61no—
572#135—61no—
573#135C2×C3×D311yescharacteristic
574C2×SD16—31no—
575C2×SD16—31no—
576C2×SD16—61no—
577C2×SD16—61no—
578C2×D8—31no—
579C2×D8—31no—
580C2×D8—61no—
581C2×D8—61no—
582#131—31no—
583#131—31no—
584#131C2×C3×D311yescharacteristic, complemented
585#131C2×C3×D311yescharacteristic, complemented
586#127—31no—
587#124—31no—
588#108—31no—
589#108C2×C3×D311yescharacteristic, complemented
590#104—31no—
591#104—31no—
592#104C2×C3×D311yescharacteristic, complemented
593#104C2×C3×D311yescharacteristic, complemented
594#101—31no—
595#100—31no—
596#100—31no—
597#100—31no—
598#97C2×C3×D311yescharacteristic, complemented
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—121no—
603C23×C3—121no—
604C23×C3—121no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C3×Q8—21no—
612C3×Q8—21no—
613C3×Q8—31no—
614C3×Q8—31no—
615C3×Q8—61no—
616C3×Q8—61no—
617C3×Q8—121no—
618C3×Q8C2×D1211yescharacteristic
619C3×Q8C2×D1211yescharacteristic
620C3×Q8C2×C3×D411yescharacteristic
621C3×Q8C2×C3×D411yescharacteristic
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—31no—
629C3×D4—31no—
630C3×D4—41no—
631C3×D4—41no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—121no—
641C3×D4—121no—
642C3×D4—121no—
643C3×D4—121no—
644C3×D4—121no—
645C3×D4—121no—
646C3×D4—121no—
647C3×D4—242no—
648C3×D4C2×D1211yescharacteristic
649C3×D4C2×D1211yescharacteristic
650C3×D4C2×C3×D411yescharacteristic
651C3×D4C2×C3×D411yescharacteristic
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—121no—
666C2×C3×C4—121no—
667C2×C3×C4—121no—
668C2×C3×C4—121no—
669C2×C3×C4—121no—
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C24×C311yescharacteristic
672#67—21no—
673#67—21no—
674#67—41no—
675#67—41no—
676#67—41no—
677#67—41no—
678C2×Dic3—21no—
679C2×Dic3—41no—
680D12—21no—
681D12—21no—
682D12—21no—
683D12—21no—
684D12—21no—
685D12—21no—
686D12—41no—
687D12—41no—
688D12—41no—
689D12—82no—
690D12C2×C3×D411yescharacteristic
691D12C2×C3×D411yescharacteristic
692C4×D3—21no—
693C4×D3—21no—
694C4×D3—41no—
695C4×D3—41no—
696C4×D3—41no—
697C4×D3—41no—
698Dic6—21no—
699Dic6—21no—
700Dic6—41no—
701Dic6C2×C3×D411yescharacteristic
702Dic6C2×C3×D411yescharacteristic
703C3×C8—21no—
704C3×C8—21no—
705C3×C8—21no—
706C3×C8—21no—
707C3×C8—21no—
708C3×C8—21no—
709C3×C8—21no—
710C3×C8—21no—
711C3×C8—41no—
712C3×C8—41no—
713C3×C8—61no—
714C3×C8—61no—
715C3×C8C2×D1211yescharacteristic
716C3×C8C2×D1211yescharacteristic
717C3×C8D3×D411yescharacteristic
718C3×C8D3×D411yescharacteristic
719C3×C8C2×C3×D411yescharacteristic
720C3×C8C2×C3×D411yescharacteristic
721C3×C8C2×C3×D411yescharacteristic
722C3×C8C2×C3×D411yescharacteristic
723C3⋊C8—21no—
724C3⋊C8—21no—
725C2×C32—21no—
726C2×C32—41no—
727C2×C32—41no—
728C2×C32D4211yescharacteristic
729C3×D3—41no—
730C3×D3—41no—
731C3×D3—81no—
732C3×D3—81no—
733C3×D3—81no—
734#41—31no—
735#41—31no—
736#41—61no—
737#41—61no—
738#41—61no—
739#41—61no—
740#41—61no—
741#41—61no—
742#41—61no—
743#41—61no—
744#41—121no—
745#41C22×C3×D311yescharacteristic
746#41C22×C3×D311yescharacteristic
747C2×Q8—31no—
748C2×Q8—61no—
749C2×Q8—61no—
750C2×D4—31no—
751C2×D4—31no—
752C2×D4—31no—
753C2×D4—61no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—61no—
758C2×D4—61no—
759C2×D4—121no—
760C2×D4—121no—
761C2×D4—121no—
762C2×D4—121no—
763Q16—31no—
764Q16—61no—
765Q16—61no—
766Q16C3×D1211yescharacteristic, complemented
767SD16—31no—
768SD16—31no—
769SD16—61no—
770SD16—61no—
771SD16—61no—
772SD16—61no—
773SD16—61no—
774SD16—61no—
775SD16—61no—
776SD16—61no—
777SD16—61no—
778SD16—61no—
779SD16—61no—
780SD16—61no—
781SD16C3×D1211yescharacteristic, complemented
782SD16C3×D1211yescharacteristic, complemented
783D8—31no—
784D8—61no—
785D8—61no—
786D8—61no—
787D8—61no—
788D8—61no—
789D8—61no—
790D8—61no—
791D8—61no—
792D8—61no—
793D8—61no—
794D8C3×D1211yescharacteristic, complemented
795M16—21no—
796M16—21no—
797M16—31no—
798M16—31no—
799M16—61no—
800M16—61no—
801M16C22×C3×D311yescharacteristic
802M16C22×C3×D311yescharacteristic
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—61no—
806C2×C8—61no—
807C2×C8C22×C3×D311yescharacteristic
808C2×C8C22×C3×D311yescharacteristic
809C22⋊C4—121no—
810C42C22×C3×D311yescharacteristic
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—241no—
824C22×C3—241no—
825C22×C3—241no—
826C22×C3—481no—
827C22×C3—481no—
828C22×C3—481no—
829C22×C3#100911yescharacteristic
830C22×C3C3×H(5,𝔽2)11yescharacteristic
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—81no—
837C2×D3—81no—
838C2×D3—81no—
839C2×D3—161no—
840C2×D3—161no—
841C2×D3—161no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—41no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—41no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—81no—
855C3×C4—121no—
856C3×C4C22×D1211yescharacteristic
857C3×C4C2×D3×D411yescharacteristic
858C3×C4C22×C3×D411yescharacteristic
859C3×C4C22×C3×D411yescharacteristic
860Dic3—21no—
861Dic3—21no—
862Dic3—41no—
863C32#328811yescharacteristic, complemented, Sylow
864C23—61no—
865C23—61no—
866C23—61no—
867C23—121no—
868C23—121no—
869C23—121no—
870Q8—31no—
871Q8—31no—
872Q8—61no—
873Q8—61no—
874Q8—121no—
875Q8C2×C3×D1211yescharacteristic
876Q8C2×C3×D1211yescharacteristic
877D4—21no—
878D4—21no—
879D4—31no—
880D4—31no—
881D4—61no—
882D4—61no—
883D4—61no—
884D4—61no—
885D4—61no—
886D4—61no—
887D4—61no—
888D4—61no—
889D4—121no—
890D4—121no—
891D4—121no—
892D4—121no—
893D4—121no—
894D4—121no—
895D4—121no—
896D4—242no—
897D4C2×C3×D1211yescharacteristic
898D4C2×C3×D1211yescharacteristic
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—121no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4C23×C3×D311yescharacteristic
911C8—21no—
912C8—21no—
913C8—61no—
914C8—61no—
915C8C2×C3×D1211yescharacteristic
916C8C2×C3×D1211yescharacteristic
917C8C3×D3×D411yescharacteristic
918C8C3×D3×D411yescharacteristic
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—41no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—41no—
926C2×C3—41no—
927C2×C3—81no—
928C2×C3—81no—
929C2×C3—121no—
930C2×C3—121no—
931C2×C3—241no—
932C2×C3—241no—
933C2×C3—241no—
934C2×C3D4×D1211yescharacteristic
935C2×C3C3×D4211yescharacteristic
936D3—41no—
937D3—41no—
938D3—81no—
939D3—81no—
940D3—81no—
941C22—21no—
942C22—21no—
943C22—61no—
944C22—61no—
945C22—121no—
946C22—121no—
947C22—121no—
948C22—241no—
949C22—241no—
950C22—241no—
951C22—481no—
952C22—481no—
953C22—481no—
954C22C3×#100911yescharacteristic
955C4—21no—
956C4—21no—
957C4—41no—
958C4—61no—
959C4—61no—
960C4—121no—
961C4C22×C3×D1211yescharacteristic
962C4C2×C3×D3×D411yescharacteristic
963C3—21no—
964C3#7990011yescharacteristic, direct product factor
965C3C3×#328811yescharacteristic, complemented
966C2—21no—
967C2—41no—
968C2—41no—
969C2—121no—
970C2—121no—
971C2—241no—
972C2—241no—
973C2—241no—
974C2C3×D4×D1211yescharacteristic
subgroupG/H
centerC2×C3D4×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#444C2
socleC2×C32D42
hypercenterC3×#444D3
hypocenterC3C3×#3288
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#444

Complements

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

NH ≅ G/Ntype
1. C3×#5770C2semidirect
2. C3×#5769C2semidirect
3. C3×#5752C2semidirect
4. C3×#5751C2semidirect
5. C32×#444C2semidirect
6. C3×#5142C2semidirect
7. C3×#5141C2semidirect
8. C3×#4898C2semidirect
9. C3×#4897C2semidirect
10. C3×#4827C2semidirect
11. C3×#4825C2semidirect
12. C3×#4822C2semidirect
13. C3×#4822C2semidirect
14. C3×#4717C2semidirect
15. C3×#4712C2semidirect
17. #79900C3direct (N × H)
18. C3×#1010C22semidirect
20. C3×#1009C22semidirect
21. C3×#1009C22semidirect
23. C32×#131C22semidirect
24. C32×#131C22semidirect
25. C3×#951C22semidirect
27. C3×#949C22semidirect
28. C3×#949C22semidirect
38. C3×#909C22semidirect
43. C3×#908C22semidirect
44. C3×#908C22semidirect
49. C2×C3×D24C22semidirect
50. C2×C3×D24C22semidirect
52. C2×C3×#204C22semidirect
53. C2×C3×#204C22semidirect
54. C3×#901C22semidirect
55. C3×#901C22semidirect
56. C3×#875C22semidirect
57. C3×#874C22semidirect
58. C32×#108C22semidirect
59. C32×#104C22semidirect
60. C32×#104C22semidirect
61. C32×#97C22semidirect
62. C3×#824C22semidirect
63. C3×#823C22semidirect
64. C3×#823C22semidirect
65. C3×#823C22semidirect
66. C3×#819C22semidirect
67. C3×#805C22semidirect
68. C3×#805C22semidirect
73. #5770C2×C3semidirect
74. #5769C2×C3semidirect
75. #5752C2×C3semidirect
76. #5751C2×C3semidirect
88. C3×#444D3semidirect
89. C3×#444C2×C3semidirect
90. #5142C2×C3semidirect
91. #5141C2×C3semidirect
92. #4898C2×C3semidirect
93. #4897C2×C3semidirect
94. #4827C2×C3semidirect
95. #4825C2×C3semidirect
96. #4822C2×C3semidirect
97. #4822C2×C3semidirect
98. #4717C2×C3semidirect
99. #4712C2×C3semidirect
129. C32×Q16D4semidirect
130. C32×SD16D4semidirect
131. C32×SD16D4semidirect
132. C32×D8D4semidirect
154. C3×Dic12D4semidirect
162. C3×D24D4semidirect
171. C3×#204D4semidirect
172. C3×#204D4semidirect
182. #1010C22×C3semidirect
184. #1009C22×C3semidirect
185. #1009C22×C3semidirect
222. C3×#131C2×D3semidirect
223. C3×#131C2×D3semidirect
224. C3×#131C22×C3semidirect
225. C3×#131C22×C3semidirect
228. #951C22×C3semidirect
230. #949C22×C3semidirect
231. #949C22×C3semidirect
241. #909C22×C3semidirect
246. #908C22×C3semidirect
247. #908C22×C3semidirect
252. C2×D24C22×C3semidirect
253. C2×D24C22×C3semidirect
255. C2×#204C22×C3semidirect
256. C2×#204C22×C3semidirect
257. #901C22×C3semidirect
258. #901C22×C3semidirect
259. #875C22×C3semidirect
260. #874C22×C3semidirect
263. C3×#108C2×D3semidirect
264. C3×#108C22×C3semidirect
269. C3×#104C2×D3semidirect
270. C3×#104C2×D3semidirect
271. C3×#104C22×C3semidirect
272. C3×#104C22×C3semidirect
278. C3×#97C2×D3semidirect
279. C3×#97C22×C3semidirect
280. #824C22×C3semidirect
281. #823C22×C3semidirect
282. #823C22×C3semidirect
283. #823C22×C3semidirect
284. #819C22×C3semidirect
285. #805C22×C3semidirect
286. #805C22×C3semidirect
356. #444C3×D3semidirect
421. C3×Q16D12semidirect
422. C3×Q16C3×D4semidirect
439. C3×SD16D12semidirect
440. C3×SD16D12semidirect
441. C3×SD16C3×D4semidirect
442. C3×SD16C3×D4semidirect
455. C3×D8D12semidirect
456. C3×D8C3×D4semidirect
503. Dic12C3×D4semidirect
511. D24C3×D4semidirect
520. #204C3×D4semidirect
521. #204C3×D4semidirect
584. #131C2×C3×D3semidirect
585. #131C2×C3×D3semidirect
589. #108C2×C3×D3semidirect
592. #104C2×C3×D3semidirect
593. #104C2×C3×D3semidirect
598. #97C2×C3×D3semidirect
766. Q16C3×D12semidirect
781. SD16C3×D12semidirect
782. SD16C3×D12semidirect
794. D8C3×D12semidirect
863. C32#3288semidirect
964. C3#79900direct (N × H)
965. C3C3×#3288semidirect

Maximal subgroups

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

subgroupindex
C3×#57702
C3×#57692
C3×#57522
C3×#57512
C32×#4442
C3×#51422
C3×#51412
C3×#48982
C3×#48972
C3×#48272
C3×#48252
C3×#48222
C3×#47172
C3×#47122
C3×#32883
#799003