Finite Group Databasebeta

← C3×#79901 #11886664

Subgroups — C3×#79901 #11886664

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5771C211yesmaximal, characteristic, complemented
2C3×#5770C211yesmaximal, characteristic, complemented
3C3×#5753C211yesmaximal, characteristic, complemented
4C3×#5751C211yesmaximal, characteristic, complemented
5C32×#444C211yesmaximal, characteristic, complemented
6C3×#5143C211yesmaximal, characteristic, complemented
7C3×#5141C211yesmaximal, characteristic, complemented
8C3×#4898C211yesmaximal, characteristic, complemented
9C3×#4896C211yesmaximal, characteristic, complemented
10C3×#4827C211yesmaximal, characteristic, complemented
11C3×#4826C211yesmaximal, characteristic, complemented
12C3×#4826C211yesmaximal, characteristic, complemented
13C3×#4825C211yesmaximal, characteristic, complemented
14C3×#4717C211yesmaximal, characteristic, complemented
15C3×#4715C211yesmaximal, characteristic, complemented
16C3×#3289—31nomaximal
17#79901C311yesmaximal, characteristic, direct product factor
18C3×#1010C2211yescharacteristic
19C3×#1010C2211yescharacteristic
20C3×#1010C2211yescharacteristic, complemented
21C3×#1009C2211yescharacteristic
22C32×#135C2211yescharacteristic
23C32×#131C2211yescharacteristic
24C32×#131C2211yescharacteristic, complemented
25C3×#951C2211yescharacteristic
26C3×#951C2211yescharacteristic
27C3×#951C2211yescharacteristic, complemented
28C3×#949C2211yescharacteristic
29C3×#918—21no—
30C3×D3×Q16—21no—
31C3×#916—21no—
32C3×#915—21no—
33C3×#915—21no—
34C3×D3×SD16—21no—
35C3×#912—21no—
36C3×#911—21no—
37C3×#909—21no—
38C3×#909—21no—
39C3×#909—21no—
40C3×#909C2211yescharacteristic
41C3×#909C2211yescharacteristic
42C3×#909C2211yescharacteristic, complemented
43C3×#908—21no—
44C3×#908C2211yescharacteristic
45C2×C3×Dic12—21no—
46C2×C3×Dic12C2211yescharacteristic, complemented
47C2×C3×Dic12C2211yescharacteristic, complemented
48C3×#904—21no—
49C3×#904—21no—
50C3×#904C2211yescharacteristic
51C2×C3×#204—21no—
52C2×C3×#204C2211yescharacteristic
53C2×C3×#204C2211yescharacteristic
54C3×#901C2211yescharacteristic
55C3×#901C2211yescharacteristic, complemented
56C3×#875C2211yescharacteristic
57C3×#869C2211yescharacteristic, complemented
58C32×#108C2211yescharacteristic, complemented
59C32×#104C2211yescharacteristic
60C32×#104C2211yescharacteristic, complemented
61C32×#97C2211yescharacteristic, complemented
62C3×#824C2211yescharacteristic, complemented
63C3×#824C2211yescharacteristic, complemented
64C3×#824C2211yescharacteristic, complemented
65C3×#823C2211yescharacteristic
66C3×#819C2211yescharacteristic, complemented
67C3×#805C2211yescharacteristic
68C3×#805C2211yescharacteristic, complemented
69C3×#578—31no—
70C3×#578—31no—
71C3×#577—31no—
72C3×#577—31no—
73#5771C2×C311yescharacteristic, complemented
74#5770C2×C311yescharacteristic, complemented
75#5753C2×C311yescharacteristic, complemented
76#5751C2×C311yescharacteristic, complemented
77C3×#497—31no—
78C3×#473—31no—
79C3×#473—31no—
80C3×#471—31no—
81C3×#471—31no—
82C3×#456—31no—
83C3×#456—31no—
84C3×#455—31no—
85C3×#454—31no—
86C3×#444—21no—
87C3×#444—31no—
88C3×#444D311yescharacteristic, complemented
89C3×#444C2×C311yescharacteristic, complemented
90#5143C2×C311yescharacteristic, complemented
91#5141C2×C311yescharacteristic, complemented
92#4898C2×C311yescharacteristic, complemented
93#4896C2×C311yescharacteristic, complemented
94#4827C2×C311yescharacteristic, complemented
95#4826C2×C311yescharacteristic, complemented
96#4826C2×C311yescharacteristic, complemented
97#4825C2×C311yescharacteristic, complemented
98#4717C2×C311yescharacteristic, complemented
99#4715C2×C311yescharacteristic, complemented
100C32×#41C2311yescharacteristic
101C32×#41C2311yescharacteristic
102C3×#239—21no—
103C3×D3×Q8—21no—
104C3×D3×Q8—21no—
105C3×D3×Q8—21no—
106C3×#237—21no—
107C3×#237—21no—
108C3×#237—21no—
109C3×#237—41no—
110C3×#237—41no—
111C3×#237—41no—
112C3×D3×D4—21no—
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×D12C2311yescharacteristic
122C2×C3×Dic6—21no—
123C2×C3×Dic6—21no—
124C2×C3×Dic6—21no—
125C2×C3×Dic6C2311yescharacteristic
126C2×C3×Dic6C2311yescharacteristic
127C2×C3×Dic6C2311yescharacteristic
128C32×Q16D411yescharacteristic
129C32×SD16D411yescharacteristic
130C32×SD16D411yescharacteristic
131C32×D8D411yescharacteristic
132C32×M16—21no—
133C32×M16—21no—
134C32×M16C2311yescharacteristic
135C32×M16C2311yescharacteristic
136C2×C32×C8—21no—
137C2×C32×C8—21no—
138C2×C32×C8C2311yescharacteristic
139C2×C32×C8C2311yescharacteristic
140C32×C42C2311yescharacteristic
141C3×#216—21no—
142C3×#216—21no—
143C3×#216—21no—
144C3×#215—21no—
145C3×#214—21no—
146C3×#214—21no—
147C3×#214—21no—
148C3×#213—21no—
149C3×(C2×D3)⋊C4—41no—
150C3×C4⋊Dic3—41no—
151C3×#208C2311yescharacteristic
152C3×#208C2311yescharacteristic
153C3×Dic12—21no—
154C3×Dic12—21no—
155C3×Dic12—21no—
156C3×Dic12—21no—
157C3×Dic12—21no—
158C3×Dic12—21no—
159C3×Dic12—21no—
160C3×Dic12D411yescharacteristic
161C3×D24—21no—
162C3×D24D411yescharacteristic
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
172C3×#204D411yescharacteristic
173C3×ΓL(1,𝔽25)—21no—
174C3×ΓL(1,𝔽25)—21no—
175C3×D3×C8—21no—
176C3×D3×C8—21no—
177#3289—31noSylow
178C3×2−1+4—31no—
179C3×2−1+4—31no—
180C3×2−1+4—31no—
181C3×H(5,𝔽2)—31no—
182#1010C22×C311yescharacteristic
183#1010C22×C311yescharacteristic
184#1010C22×C311yescharacteristic, complemented
185#1009C22×C311yescharacteristic
186C3×#137—31no—
187C3×#137—31no—
188C3×#137—31no—
189C3×#137—31no—
190C3×#137—31no—
191C3×#137—31no—
192C3×#137—61no—
193C3×#137—61no—
194C3×#137—61no—
195C3×#137—61no—
196C3×#137—61no—
197C3×#137—61no—
198C3×AGL(1,ℤ/8)—31no—
199C3×AGL(1,ℤ/8)—31no—
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×Q16—31no—
211C2×C3×Q16—31no—
212C2×C3×Q16—61no—
213C2×C3×Q16—61no—
214C2×C3×SD16—31no—
215C2×C3×SD16—31no—
216C2×C3×SD16—61no—
217C2×C3×SD16—61no—
218C3×#131—21no—
219C3×#131—21no—
220C3×#131—31no—
221C3×#131—31no—
222C3×#131C2×D311yescharacteristic
223C3×#131C2×D311yescharacteristic, complemented
224C3×#131C22×C311yescharacteristic
225C3×#131C22×C311yescharacteristic, complemented
226C3×C4⋊Q8—31no—
227C3×#124—31no—
228#951C22×C311yescharacteristic
229#951C22×C311yescharacteristic
230#951C22×C311yescharacteristic, complemented
231#949C22×C311yescharacteristic
232#918—21no—
233D3×Q16—21no—
234#916—21no—
235#915—21no—
236#915—21no—
237D3×SD16—21no—
238#912—21no—
239#911—21no—
240#909—21no—
241#909—21no—
242#909—21no—
243#909C22×C311yescharacteristic
244#909C22×C311yescharacteristic
245#909C22×C311yescharacteristic, complemented
246#908—21no—
247#908C22×C311yescharacteristic
248C2×Dic12—21no—
249C2×Dic12C22×C311yescharacteristic, complemented
250C2×Dic12C22×C311yescharacteristic, complemented
251#904—21no—
252#904—21no—
253#904C22×C311yescharacteristic
254C2×#204—21no—
255C2×#204C22×C311yescharacteristic
256C2×#204C22×C311yescharacteristic
257#901C22×C311yescharacteristic
258#901C22×C311yescharacteristic, complemented
259#875C22×C311yescharacteristic
260#869C22×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
270C3×#104C2×D311yescharacteristic, complemented
271C3×#104C22×C311yescharacteristic
272C3×#104C22×C311yescharacteristic, complemented
273C3×#101—31no—
274C3×#101—31no—
275C3×#101—31no—
276C3×#100—31no—
277C3×#97—21no—
278C3×#97C2×D311yescharacteristic, complemented
279C3×#97C22×C311yescharacteristic, complemented
280#824C22×C311yescharacteristic, complemented
281#824C22×C311yescharacteristic, complemented
282#824C22×C311yescharacteristic, complemented
283#823C22×C311yescharacteristic
284#819C22×C311yescharacteristic, complemented
285#805C22×C311yescharacteristic
286#805C22×C311yescharacteristic, complemented
287C22×C3×D3—21no—
288C22×C3×D3—41no—
289C32×Q8C2×D411yescharacteristic
290C32×Q8C2×D411yescharacteristic
291C32×D4—21no—
292C32×D4—21no—
293C32×D4C2×D411yescharacteristic
294C32×D4C2×D411yescharacteristic
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4—21no—
298C2×C32×C4C2411yescharacteristic
299C3×#67—21no—
300C3×#67—21no—
301C3×#67—41no—
302C3×#67—41no—
303C3×#67—41no—
304C3×#67—41no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—41no—
309C2×C3×Dic3—41no—
310C2×C3×Dic3—41no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—41no—
314C3×D12C2×D411yescharacteristic
315C3×D12C2×D411yescharacteristic
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—41no—
319C3×C4×D3—41no—
320C3×C4×D3—41no—
321C3×C4×D3—41no—
322C3×Dic6—21no—
323C3×Dic6—21no—
324C3×Dic6—21no—
325C3×Dic6—21no—
326C3×Dic6—21no—
327C3×Dic6—21no—
328C3×Dic6—41no—
329C3×Dic6—41no—
330C3×Dic6—41no—
331C3×Dic6C2×D411yescharacteristic
332C3×Dic6C2×D411yescharacteristic
333C32×C8—21no—
334C32×C8—21no—
335C32×C8C2×D411yescharacteristic
336C32×C8C2×D411yescharacteristic
337C32×C8C2×D411yescharacteristic
338C32×C8C2×D411yescharacteristic
339C3×C3⋊C8—21no—
340C3×C3⋊C8—21no—
341#578—31no—
342#578—31no—
343#577—31no—
344#577—31no—
345#497—31no—
346#473—31no—
347#473—31no—
348#471—31no—
349#471—31no—
350#456—31no—
351#456—31no—
352#455—31no—
353#454—31no—
354#444—31no—
355#444C3×D311yescharacteristic, complemented
356C3×#41—21no—
357C3×#41—21no—
358C3×#41—31no—
359C3×#41—31no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41—61no—
366C3×#41—61no—
367C3×#41—61no—
368C3×#41—121no—
369C3×#41—121no—
370C3×#41—121no—
371C3×#41C22×D311yescharacteristic
372C3×#41C22×D311yescharacteristic
373C3×#41C23×C311yescharacteristic
374C3×#41C23×C311yescharacteristic
375C2×C3×Q8—31no—
376C2×C3×Q8—31no—
377C2×C3×Q8—31no—
378C2×C3×Q8—61no—
379C2×C3×Q8—61no—
380C2×C3×Q8—61no—
381C2×C3×Q8—61no—
382C2×C3×Q8—61no—
383C2×C3×Q8—61no—
384C2×C3×D4—31no—
385C2×C3×D4—61no—
386C2×C3×D4—61no—
387C2×C3×D4—121no—
388#239—21no—
389D3×Q8—21no—
390D3×Q8—21no—
391D3×Q8—21no—
392#237—21no—
393#237—21no—
394#237—21no—
395#237—41no—
396#237—41no—
397#237—41no—
398D3×D4—21no—
399D3×D4—41no—
400#235—21no—
401#235—21no—
402#235—21no—
403#235—21no—
404#235C23×C311yescharacteristic
405#235C23×C311yescharacteristic
406C2×D12—21no—
407C2×D12C23×C311yescharacteristic
408C2×Dic6—21no—
409C2×Dic6—21no—
410C2×Dic6—21no—
411C2×Dic6C23×C311yescharacteristic
412C2×Dic6C23×C311yescharacteristic
413C2×Dic6C23×C311yescharacteristic
414C3×Q16—21no—
415C3×Q16—31no—
416C3×Q16—61no—
417C3×Q16—61no—
418C3×Q16—61no—
419C3×Q16—61no—
420C3×Q16—61no—
421C3×Q16—61no—
422C3×Q16—61no—
423C3×Q16—61no—
424C3×Q16—61no—
425C3×Q16—61no—
426C3×Q16D1211yescharacteristic
427C3×Q16C3×D411yescharacteristic
428C3×SD16—21no—
429C3×SD16—21no—
430C3×SD16—31no—
431C3×SD16—31no—
432C3×SD16—61no—
433C3×SD16—61no—
434C3×SD16—61no—
435C3×SD16—61no—
436C3×SD16—61no—
437C3×SD16—61no—
438C3×SD16—61no—
439C3×SD16—61no—
440C3×SD16—61no—
441C3×SD16—61no—
442C3×SD16—61no—
443C3×SD16—61no—
444C3×SD16D1211yescharacteristic
445C3×SD16D1211yescharacteristic
446C3×SD16C3×D411yescharacteristic
447C3×SD16C3×D411yescharacteristic
448C3×D8—21no—
449C3×D8—31no—
450C3×D8—61no—
451C3×D8—61no—
452C3×D8D1211yescharacteristic
453C3×D8C3×D411yescharacteristic
454C3×M16—21no—
455C3×M16—21no—
456C3×M16—21no—
457C3×M16—21no—
458C3×M16—21no—
459C3×M16—21no—
460C3×M16—31no—
461C3×M16—31no—
462C3×M16—41no—
463C3×M16—41no—
464C3×M16—61no—
465C3×M16—61no—
466C3×M16C22×D311yescharacteristic
467C3×M16C22×D311yescharacteristic
468C3×M16C23×C311yescharacteristic
469C3×M16C23×C311yescharacteristic
470C2×C3×C8—21no—
471C2×C3×C8—21no—
472C2×C3×C8—21no—
473C2×C3×C8—21no—
474C2×C3×C8—21no—
475C2×C3×C8—21no—
476C2×C3×C8—41no—
477C2×C3×C8—41no—
478C2×C3×C8—61no—
479C2×C3×C8—61no—
480C2×C3×C8C22×D311yescharacteristic
481C2×C3×C8C22×D311yescharacteristic
482C2×C3×C8C23×C311yescharacteristic
483C2×C3×C8C23×C311yescharacteristic
484C3×C4⋊C4—121no—
485C3×C22⋊C4—121no—
486C3×C42—21no—
487C3×C42C22×D311yescharacteristic
488C3×C42C23×C311yescharacteristic
489#216—21no—
490#216—21no—
491#216—21no—
492#215—21no—
493#214—21no—
494#214—21no—
495#214—21no—
496#213—21no—
497(C2×D3)⋊C4—41no—
498C4⋊Dic3—41no—
499#208C23×C311yescharacteristic
500#208C23×C311yescharacteristic
501Dic12—21no—
502Dic12—21no—
503Dic12—21no—
504Dic12—21no—
505Dic12—21no—
506Dic12—21no—
507Dic12—21no—
508Dic12C3×D411yescharacteristic
509D24—21no—
510D24C3×D411yescharacteristic
511#204—21no—
512#204—21no—
513#204—21no—
514#204—21no—
515#204—21no—
516#204—21no—
517#204—21no—
518#204—21no—
519#204C3×D411yescharacteristic
520#204C3×D411yescharacteristic
521ΓL(1,𝔽25)—21no—
522ΓL(1,𝔽25)—21no—
523D3×C8—21no—
524D3×C8—21no—
525C22×C32—21no—
526C22×C32—21no—
527C22×C32H(5,𝔽2)11yescharacteristic
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—81no—
532C2×C3×D3—161no—
533C32×C4—21no—
534C32×C4—21no—
535C32×C4—41no—
536C32×C4C22×D411yescharacteristic
537C32×C4C22×D411yescharacteristic
538C3×Dic3—21no—
539C3×Dic3—21no—
540C3×Dic3—41no—
541C3×Dic3—41no—
542C3×Dic3—41no—
5432−1+4—31no—
5442−1+4—31no—
5452−1+4—31no—
546H(5,𝔽2)—31no—
547#137—31no—
548#137—31no—
549#137—31no—
550#137—31no—
551#137—31no—
552#137—31no—
553#137—61no—
554#137—61no—
555#137—61no—
556#137—61no—
557#137—61no—
558#137—61no—
559AGL(1,ℤ/8)—31no—
560AGL(1,ℤ/8)—31no—
561AGL(1,ℤ/8)—61no—
562AGL(1,ℤ/8)—61no—
563#135—31no—
564#135—61no—
565#135—61no—
566#135—61no—
567#135—61no—
568#135C2×C3×D311yescharacteristic
569C2×Q16—31no—
570C2×Q16—31no—
571C2×Q16—61no—
572C2×Q16—61no—
573C2×SD16—31no—
574C2×SD16—31no—
575C2×SD16—61no—
576C2×SD16—61no—
577#131—31no—
578#131—31no—
579#131C2×C3×D311yescharacteristic
580#131C2×C3×D311yescharacteristic, complemented
581C4⋊Q8—31no—
582#124—31no—
583#108—31no—
584#108C2×C3×D311yescharacteristic, complemented
585#104—31no—
586#104—31no—
587#104C2×C3×D311yescharacteristic
588#104C2×C3×D311yescharacteristic, complemented
589#101—31no—
590#101—31no—
591#101—31no—
592#100—31no—
593#97C2×C3×D311yescharacteristic, complemented
594C23×C3—61no—
595C23×C3—121no—
596C22×D3—21no—
597C22×D3—41no—
598C3×Q8—21no—
599C3×Q8—21no—
600C3×Q8—31no—
601C3×Q8—31no—
602C3×Q8—61no—
603C3×Q8—61no—
604C3×Q8—61no—
605C3×Q8—61no—
606C3×Q8—61no—
607C3×Q8—61no—
608C3×Q8—121no—
609C3×Q8—121no—
610C3×Q8—121no—
611C3×Q8C2×D1211yescharacteristic
612C3×Q8C2×D1211yescharacteristic
613C3×Q8C2×C3×D411yescharacteristic
614C3×Q8C2×C3×D411yescharacteristic
615C3×D4—21no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—31no—
622C3×D4—31no—
623C3×D4—41no—
624C3×D4—41no—
625C3×D4—61no—
626C3×D4—61no—
627C3×D4—61no—
628C3×D4—61no—
629C3×D4—121no—
630C3×D4—121no—
631C3×D4—121no—
632C3×D4—121no—
633C3×D4—121no—
634C3×D4C2×D1211yescharacteristic
635C3×D4C2×D1211yescharacteristic
636C3×D4C2×C3×D411yescharacteristic
637C3×D4C2×C3×D411yescharacteristic
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—121no—
654C2×C3×C4—121no—
655C2×C3×C4—121no—
656C2×C3×C4—121no—
657C2×C3×C4—121no—
658C2×C3×C4—121no—
659C2×C3×C4—121no—
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C24×C311yescharacteristic
662#67—21no—
663#67—21no—
664#67—41no—
665#67—41no—
666#67—41no—
667#67—41no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3—41no—
674D12—21no—
675D12—21no—
676D12—41no—
677D12C2×C3×D411yescharacteristic
678D12C2×C3×D411yescharacteristic
679C4×D3—21no—
680C4×D3—21no—
681C4×D3—41no—
682C4×D3—41no—
683C4×D3—41no—
684C4×D3—41no—
685Dic6—21no—
686Dic6—21no—
687Dic6—21no—
688Dic6—21no—
689Dic6—21no—
690Dic6—21no—
691Dic6—41no—
692Dic6—41no—
693Dic6—41no—
694Dic6C2×C3×D411yescharacteristic
695Dic6C2×C3×D411yescharacteristic
696C3×C8—21no—
697C3×C8—21no—
698C3×C8—21no—
699C3×C8—21no—
700C3×C8—21no—
701C3×C8—21no—
702C3×C8—21no—
703C3×C8—21no—
704C3×C8—41no—
705C3×C8—41no—
706C3×C8—61no—
707C3×C8—61no—
708C3×C8C2×D1211yescharacteristic
709C3×C8C2×D1211yescharacteristic
710C3×C8D3×D411yescharacteristic
711C3×C8D3×D411yescharacteristic
712C3×C8C2×C3×D411yescharacteristic
713C3×C8C2×C3×D411yescharacteristic
714C3×C8C2×C3×D411yescharacteristic
715C3×C8C2×C3×D411yescharacteristic
716C3⋊C8—21no—
717C3⋊C8—21no—
718C2×C32—21no—
719C2×C32—41no—
720C2×C32—41no—
721C2×C32D4211yescharacteristic
722C3×D3—41no—
723C3×D3—41no—
724C3×D3—81no—
725#41—31no—
726#41—31no—
727#41—61no—
728#41—61no—
729#41—61no—
730#41—61no—
731#41—61no—
732#41—61no—
733#41—61no—
734#41—61no—
735#41—121no—
736#41—121no—
737#41—121no—
738#41C22×C3×D311yescharacteristic
739#41C22×C3×D311yescharacteristic
740C2×Q8—31no—
741C2×Q8—31no—
742C2×Q8—31no—
743C2×Q8—61no—
744C2×Q8—61no—
745C2×Q8—61no—
746C2×Q8—61no—
747C2×Q8—61no—
748C2×Q8—61no—
749C2×D4—31no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—121no—
753Q16—31no—
754Q16—61no—
755Q16—61no—
756Q16—61no—
757Q16—61no—
758Q16—61no—
759Q16—61no—
760Q16—61no—
761Q16—61no—
762Q16—61no—
763Q16—61no—
764Q16C3×D1211yescharacteristic
765SD16—31no—
766SD16—31no—
767SD16—61no—
768SD16—61no—
769SD16—61no—
770SD16—61no—
771SD16—61no—
772SD16—61no—
773SD16—61no—
774SD16—61no—
775SD16—61no—
776SD16—61no—
777SD16—61no—
778SD16—61no—
779SD16C3×D1211yescharacteristic
780SD16C3×D1211yescharacteristic
781D8—31no—
782D8—61no—
783D8—61no—
784D8C3×D1211yescharacteristic
785M16—21no—
786M16—21no—
787M16—31no—
788M16—31no—
789M16—61no—
790M16—61no—
791M16C22×C3×D311yescharacteristic
792M16C22×C3×D311yescharacteristic
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—61no—
796C2×C8—61no—
797C2×C8C22×C3×D311yescharacteristic
798C2×C8C22×C3×D311yescharacteristic
799C4⋊C4—121no—
800C22⋊C4—121no—
801C42C22×C3×D311yescharacteristic
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—121no—
812C22×C3—241no—
813C22×C3—481no—
814C22×C3#100911yescharacteristic
815C22×C3C3×H(5,𝔽2)11yescharacteristic
816C2×D3—21no—
817C2×D3—21no—
818C2×D3—41no—
819C2×D3—81no—
820C2×D3—161no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—41no—
830C3×C4—41no—
831C3×C4—61no—
832C3×C4—61no—
833C3×C4—81no—
834C3×C4—121no—
835C3×C4—121no—
836C3×C4—121no—
837C3×C4C22×D1211yescharacteristic
838C3×C4C2×D3×D411yescharacteristic
839C3×C4C22×C3×D411yescharacteristic
840C3×C4C22×C3×D411yescharacteristic
841Dic3—21no—
842Dic3—21no—
843Dic3—41no—
844Dic3—41no—
845Dic3—41no—
846C32#328911yescharacteristic, complemented, Sylow
847C23—61no—
848C23—121no—
849Q8—31no—
850Q8—31no—
851Q8—61no—
852Q8—61no—
853Q8—61no—
854Q8—61no—
855Q8—61no—
856Q8—61no—
857Q8—121no—
858Q8—121no—
859Q8—121no—
860Q8C2×C3×D1211yescharacteristic
861Q8C2×C3×D1211yescharacteristic
862D4—21no—
863D4—21no—
864D4—31no—
865D4—31no—
866D4—61no—
867D4—61no—
868D4—61no—
869D4—61no—
870D4—121no—
871D4—121no—
872D4—121no—
873D4—121no—
874D4—121no—
875D4C2×C3×D1211yescharacteristic
876D4C2×C3×D1211yescharacteristic
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—121no—
888C2×C4—121no—
889C2×C4—121no—
890C2×C4—121no—
891C2×C4—121no—
892C2×C4C23×C3×D311yescharacteristic
893C8—21no—
894C8—21no—
895C8—61no—
896C8—61no—
897C8C2×C3×D1211yescharacteristic
898C8C2×C3×D1211yescharacteristic
899C8C3×D3×D411yescharacteristic
900C8C3×D3×D411yescharacteristic
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—41no—
907C2×C3—41no—
908C2×C3—41no—
909C2×C3—81no—
910C2×C3—81no—
911C2×C3—121no—
912C2×C3—121no—
913C2×C3—241no—
914C2×C3D4×D1211yescharacteristic
915C2×C3C3×D4211yescharacteristic
916D3—41no—
917D3—41no—
918D3—81no—
919C22—21no—
920C22—21no—
921C22—61no—
922C22—61no—
923C22—121no—
924C22—241no—
925C22—481no—
926C22C3×#100911yescharacteristic
927C4—21no—
928C4—21no—
929C4—41no—
930C4—61no—
931C4—61no—
932C4—121no—
933C4—121no—
934C4—121no—
935C4C22×C3×D1211yescharacteristic
936C4C2×C3×D3×D411yescharacteristic
937C3—21no—
938C3#7990111yescharacteristic, direct product factor
939C3C3×#328911yescharacteristic, complemented
940C2—21no—
941C2—41no—
942C2—41no—
943C2—121no—
944C2—121no—
945C2—241no—
946C2C3×D4×D1211yescharacteristic
subgroupG/H
centerC2×C3D4×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#444C2
socleC2×C32D42
hypercenterC3×#444D3
hypocenterC3C3×#3289
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×#5771C2semidirect
2. C3×#5770C2semidirect
3. C3×#5753C2semidirect
4. C3×#5751C2semidirect
5. C32×#444C2semidirect
6. C3×#5143C2semidirect
7. C3×#5141C2semidirect
8. C3×#4898C2semidirect
9. C3×#4896C2semidirect
10. C3×#4827C2semidirect
11. C3×#4826C2semidirect
12. C3×#4826C2semidirect
13. C3×#4825C2semidirect
14. C3×#4717C2semidirect
15. C3×#4715C2semidirect
17. #79901C3direct (N × H)
20. C3×#1010C22semidirect
24. C32×#131C22semidirect
27. C3×#951C22semidirect
42. C3×#909C22semidirect
46. C2×C3×Dic12C22semidirect
47. C2×C3×Dic12C22semidirect
55. C3×#901C22semidirect
57. C3×#869C22semidirect
58. C32×#108C22semidirect
60. C32×#104C22semidirect
61. C32×#97C22semidirect
62. C3×#824C22semidirect
63. C3×#824C22semidirect
64. C3×#824C22semidirect
66. C3×#819C22semidirect
68. C3×#805C22semidirect
73. #5771C2×C3semidirect
74. #5770C2×C3semidirect
75. #5753C2×C3semidirect
76. #5751C2×C3semidirect
88. C3×#444D3semidirect
89. C3×#444C2×C3semidirect
90. #5143C2×C3semidirect
91. #5141C2×C3semidirect
92. #4898C2×C3semidirect
93. #4896C2×C3semidirect
94. #4827C2×C3semidirect
95. #4826C2×C3semidirect
96. #4826C2×C3semidirect
97. #4825C2×C3semidirect
98. #4717C2×C3semidirect
99. #4715C2×C3semidirect
184. #1010C22×C3semidirect
223. C3×#131C2×D3semidirect
225. C3×#131C22×C3semidirect
230. #951C22×C3semidirect
245. #909C22×C3semidirect
249. C2×Dic12C22×C3semidirect
250. C2×Dic12C22×C3semidirect
258. #901C22×C3semidirect
260. #869C22×C3semidirect
263. C3×#108C2×D3semidirect
264. C3×#108C22×C3semidirect
270. C3×#104C2×D3semidirect
272. C3×#104C22×C3semidirect
278. C3×#97C2×D3semidirect
279. C3×#97C22×C3semidirect
280. #824C22×C3semidirect
281. #824C22×C3semidirect
282. #824C22×C3semidirect
284. #819C22×C3semidirect
286. #805C22×C3semidirect
355. #444C3×D3semidirect
580. #131C2×C3×D3semidirect
584. #108C2×C3×D3semidirect
588. #104C2×C3×D3semidirect
593. #97C2×C3×D3semidirect
846. C32#3289semidirect
938. C3#79901direct (N × H)
939. C3C3×#3289semidirect

Maximal subgroups

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

subgroupindex
C3×#57712
C3×#57702
C3×#57532
C3×#57512
C32×#4442
C3×#51432
C3×#51412
C3×#48982
C3×#48962
C3×#48272
C3×#48262
C3×#48252
C3×#47172
C3×#47152
C3×#32893
#799013