Finite Group Databasebeta

← C3×#80945 #11886658

Subgroups — C3×#80945 #11886658

Order 1152.

946 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5779C211yesmaximal, characteristic, complemented
2C3×#5778C211yesmaximal, characteristic, complemented
3C3×#5766C211yesmaximal, characteristic, complemented
4C3×#5751C211yesmaximal, characteristic, complemented
5C32×#473C211yesmaximal, characteristic, complemented
6C3×#5205C211yesmaximal, characteristic, complemented
7C3×#5202C211yesmaximal, characteristic, complemented
8C3×#5190C211yesmaximal, characteristic, complemented
9C3×#5145C211yesmaximal, characteristic, complemented
10C3×#4898C211yesmaximal, characteristic, complemented
11C3×#4894C211yesmaximal, characteristic, complemented
12C3×#4755C211yesmaximal, characteristic, complemented
13C3×#4754C211yesmaximal, characteristic, complemented
14C3×#4753C211yesmaximal, characteristic, complemented
15C3×#4752C211yesmaximal, characteristic, complemented
16C3×#3289—31nomaximal
17#80945C311yesmaximal, characteristic, direct product factor
18C3×#1010C2211yescharacteristic
19C3×#1009C2211yescharacteristic
20C3×#1007C2211yescharacteristic
21C3×#1007C2211yescharacteristic, complemented
22C32×#137C2211yescharacteristic
23C32×#137C2211yescharacteristic
24C2×C32×Q16C2211yescharacteristic, complemented
25C32×#131C2211yescharacteristic
26C3×#950C2211yescharacteristic
27C3×#947C2211yescharacteristic
28C3×#944C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C3×#942C2211yescharacteristic
31C3×#942C2211yescharacteristic, complemented
32C2×C3×#215C2211yescharacteristic
33C3×#919—21no—
34C3×#919—21no—
35C3×#918—21no—
36C3×#918—21no—
37C3×#918—21no—
38C3×#918—21no—
39C3×D3×Q16—21no—
40C3×D3×Q16—21no—
41C3×#916—21no—
42C3×#915—21no—
43C3×#914—21no—
44C3×D3×SD16—21no—
45C3×#909—21no—
46C3×#909C2211yescharacteristic
47C3×#909C2211yescharacteristic, complemented
48C3×#908—21no—
49C3×#908C2211yescharacteristic
50C3×#908C2211yescharacteristic
51C3×#907C2211yescharacteristic
52C3×#907C2211yescharacteristic, complemented
53C3×#904—21no—
54C3×#904C2211yescharacteristic
55C2×C3×#204—21no—
56C2×C3×#204C2211yescharacteristic
57C3×#901C2211yescharacteristic, complemented
58C32×#108C2211yescharacteristic, complemented
59C32×#101C2211yescharacteristic, complemented
60C32×#101C2211yescharacteristic, complemented
61C3×#837C2211yescharacteristic
62C3×#825C2211yescharacteristic
63C3×#825C2211yescharacteristic, complemented
64C3×#825C2211yescharacteristic, complemented
65C3×#824C2211yescharacteristic, complemented
66C3×#823C2211yescharacteristic
67C3×#822C2211yescharacteristic, complemented
68C3×#815C2211yescharacteristic, complemented
69C3×#578—31no—
70C3×#578—31no—
71C3×#577—31no—
72C3×#577—31no—
73#5779C2×C311yescharacteristic, complemented
74#5778C2×C311yescharacteristic, complemented
75#5766C2×C311yescharacteristic, complemented
76#5751C2×C311yescharacteristic, complemented
77C3×#497—31no—
78C3×#473—21no—
79C3×#473—31no—
80C3×#473D311yescharacteristic, complemented
81C3×#473C2×C311yescharacteristic, complemented
82C3×#471—31no—
83C3×#471—31no—
84C3×#456—31no—
85C3×#456—31no—
86C3×#455—31no—
87C3×#454—31no—
88C3×#444—31no—
89C3×#444—31no—
90#5205C2×C311yescharacteristic, complemented
91#5202C2×C311yescharacteristic, complemented
92#5190C2×C311yescharacteristic, complemented
93#5145C2×C311yescharacteristic, complemented
94#4898C2×C311yescharacteristic, complemented
95#4894C2×C311yescharacteristic, complemented
96#4755C2×C311yescharacteristic, complemented
97#4754C2×C311yescharacteristic, complemented
98#4753C2×C311yescharacteristic, complemented
99#4752C2×C311yescharacteristic, complemented
100C32×#41C2311yescharacteristic
101C2×C32×Q8C2311yescharacteristic
102C2×C32×Q8C2311yescharacteristic
103C3×#239—21no—
104C3×#239—21no—
105C3×#239—21no—
106C3×#239—21no—
107C3×#239—21no—
108C3×D3×Q8—21no—
109C3×D3×Q8—21no—
110C3×D3×Q8—21no—
111C3×D3×Q8—21no—
112C3×D3×Q8—21no—
113C3×#237—21no—
114C3×#237—41no—
115C3×D3×D4—21no—
116C3×D3×D4—41no—
117C3×#235—21no—
118C3×#235—21no—
119C3×#235—41no—
120C3×#235—41no—
121C3×#235C2311yescharacteristic
122C3×#235C2311yescharacteristic
123C3×#235C2311yescharacteristic
124C2×C3×D12—21no—
125C2×C3×D12C2311yescharacteristic
126C2×C3×Dic6—21no—
127C2×C3×Dic6C2311yescharacteristic
128C32×Q16—21no—
129C32×Q16—21no—
130C32×Q16—21no—
131C32×Q16—21no—
132C32×SD16—21no—
133C32×SD16—21no—
134C32×M16—21no—
135C32×M16C2311yescharacteristic
136C32×M16C2311yescharacteristic
137C32×M16C2311yescharacteristic
138C2×C32×C8—21no—
139C2×C32×C8C2311yescharacteristic
140C3×#216—21no—
141C3×#216—21no—
142C3×#216—21no—
143C3×#216—21no—
144C3×#216D411yescharacteristic
145C3×#215—21no—
146C3×#215—21no—
147C3×#215—21no—
148C3×#215—21no—
149C3×#215D411yescharacteristic
150C3×#214D411yescharacteristic
151C3×#213D411yescharacteristic
152C3×(C2×D3)⋊C4—41no—
153C3×Dic3⋊C4—41no—
154C3×C4×Dic3C2311yescharacteristic
155C3×#208C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157C3×Dic12—21no—
158C3×Dic12—21no—
159C3×Dic12D411yescharacteristic
160C3×D24—21no—
161C3×D24—21no—
162C3×D24D411yescharacteristic
163C3×#204—21no—
164C3×#204—21no—
165C3×#204—21no—
166C3×#204—21no—
167C3×#204—21no—
168C3×#204—21no—
169C3×#204D411yescharacteristic
170C3×#204D411yescharacteristic
171C3×ΓL(1,𝔽25)—21no—
172C3×ΓL(1,𝔽25)—21no—
173C3×ΓL(1,𝔽25)—21no—
174C3×D3×C8—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#1009C22×C311yescharacteristic
184#1007C22×C311yescharacteristic
185#1007C22×C311yescharacteristic, complemented
186C3×#137—21no—
187C3×#137—21no—
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×#137C2×D311yescharacteristic
199C3×#137C2×D311yescharacteristic
200C3×#137C22×C311yescharacteristic
201C3×#137C22×C311yescharacteristic
202C3×AGL(1,ℤ/8)—31no—
203C3×AGL(1,ℤ/8)—31no—
204C3×AGL(1,ℤ/8)—61no—
205C3×AGL(1,ℤ/8)—61no—
206C3×#135—31no—
207C3×#135—31no—
208C3×#135—61no—
209C3×#135—61no—
210C3×#135—61no—
211C3×#135—61no—
212C2×C3×Q16—21no—
213C2×C3×Q16—31no—
214C2×C3×Q16—61no—
215C2×C3×Q16—61no—
216C2×C3×Q16C2×D311yescharacteristic, complemented
217C2×C3×Q16C22×C311yescharacteristic, complemented
218C2×C3×SD16—31no—
219C2×C3×SD16—31no—
220C2×C3×SD16—61no—
221C2×C3×SD16—61no—
222C3×#131—21no—
223C3×#131—31no—
224C3×#131—31no—
225C3×#131—31no—
226C3×#131C2×D311yescharacteristic
227C3×#131C22×C311yescharacteristic
228C3×C4⋊Q8—31no—
229C3×#124—31no—
230#950C22×C311yescharacteristic
231#947C22×C311yescharacteristic
232#944C22×C311yescharacteristic, complemented
233C2×#216C22×C311yescharacteristic, complemented
234#942C22×C311yescharacteristic
235#942C22×C311yescharacteristic, complemented
236C2×#215C22×C311yescharacteristic
237#919—21no—
238#919—21no—
239#918—21no—
240#918—21no—
241#918—21no—
242#918—21no—
243D3×Q16—21no—
244D3×Q16—21no—
245#916—21no—
246#915—21no—
247#914—21no—
248D3×SD16—21no—
249#909—21no—
250#909C22×C311yescharacteristic
251#909C22×C311yescharacteristic, complemented
252#908—21no—
253#908C22×C311yescharacteristic
254#908C22×C311yescharacteristic
255#907C22×C311yescharacteristic
256#907C22×C311yescharacteristic, complemented
257#904—21no—
258#904C22×C311yescharacteristic
259C2×#204—21no—
260C2×#204C22×C311yescharacteristic
261#901C22×C311yescharacteristic, complemented
262C3×#108—21no—
263C3×#108—31no—
264C3×#108C2×D311yescharacteristic, complemented
265C3×#108C22×C311yescharacteristic, complemented
266C3×#104—31no—
267C3×#104—31no—
268C3×#104—31no—
269C3×#104—31no—
270C3×#101—21no—
271C3×#101—21no—
272C3×#101—31no—
273C3×#101C2×D311yescharacteristic, complemented
274C3×#101C2×D311yescharacteristic, complemented
275C3×#101C22×C311yescharacteristic, complemented
276C3×#101C22×C311yescharacteristic, complemented
277C3×#100—31no—
278C3×#97—31no—
279#837C22×C311yescharacteristic
280#825C22×C311yescharacteristic
281#825C22×C311yescharacteristic, complemented
282#825C22×C311yescharacteristic, complemented
283#824C22×C311yescharacteristic, complemented
284#823C22×C311yescharacteristic
285#822C22×C311yescharacteristic, complemented
286#815C22×C311yescharacteristic, complemented
287C22×C3×D3—21no—
288C22×C3×D3—41no—
289C32×Q8—21no—
290C32×Q8—21no—
291C32×Q8—21no—
292C32×Q8—21no—
293C32×Q8C2×D411yescharacteristic
294C32×D4—21no—
295C32×D4C2×D411yescharacteristic
296C2×C32×C4—21no—
297C2×C32×C4—21no—
298C2×C32×C4—21no—
299C2×C32×C4C2411yescharacteristic
300C3×#67—21no—
301C3×#67—21no—
302C3×#67—21no—
303C3×#67—41no—
304C3×#67—41no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—41no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—41no—
311C3×D12—41no—
312C3×D12—41no—
313C3×D12C2×D411yescharacteristic
314C3×D12C2×D411yescharacteristic
315C3×D12C2×D411yescharacteristic
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—41no—
320C3×C4×D3—41no—
321C3×C4×D3—41no—
322C3×C4×D3—41no—
323C3×C4×D3—41no—
324C3×C4×D3—41no—
325C3×Dic6—21no—
326C3×Dic6—21no—
327C3×Dic6—41no—
328C3×Dic6—41no—
329C3×Dic6—41no—
330C3×Dic6C2×D411yescharacteristic
331C3×Dic6C2×D411yescharacteristic
332C3×Dic6C2×D411yescharacteristic
333C32×C8—21no—
334C32×C8—21no—
335C32×C8—21no—
336C32×C8C2×D411yescharacteristic
337C32×C8C2×D411yescharacteristic
338C3×C3⋊C8—21no—
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341#578—31no—
342#578—31no—
343#577—31no—
344#577—31no—
345#497—31no—
346#473—31no—
347#473C3×D311yescharacteristic, complemented
348#471—31no—
349#471—31no—
350#456—31no—
351#456—31no—
352#455—31no—
353#454—31no—
354#444—31no—
355#444—31no—
356C3×#41—21no—
357C3×#41—31no—
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×#41C23×C311yescharacteristic
373C2×C3×Q8—21no—
374C2×C3×Q8—21no—
375C2×C3×Q8—31no—
376C2×C3×Q8—61no—
377C2×C3×Q8—61no—
378C2×C3×Q8—61no—
379C2×C3×Q8—61no—
380C2×C3×Q8—61no—
381C2×C3×Q8—61no—
382C2×C3×Q8C22×D311yescharacteristic
383C2×C3×Q8C22×D311yescharacteristic
384C2×C3×Q8C23×C311yescharacteristic
385C2×C3×Q8C23×C311yescharacteristic
386C2×C3×D4—31no—
387C2×C3×D4—61no—
388C2×C3×D4—61no—
389C2×C3×D4—121no—
390#239—21no—
391#239—21no—
392#239—21no—
393#239—21no—
394#239—21no—
395D3×Q8—21no—
396D3×Q8—21no—
397D3×Q8—21no—
398D3×Q8—21no—
399D3×Q8—21no—
400#237—21no—
401#237—41no—
402D3×D4—21no—
403D3×D4—41no—
404#235—21no—
405#235—21no—
406#235—41no—
407#235—41no—
408#235C23×C311yescharacteristic
409#235C23×C311yescharacteristic
410#235C23×C311yescharacteristic
411C2×D12—21no—
412C2×D12C23×C311yescharacteristic
413C2×Dic6—21no—
414C2×Dic6C23×C311yescharacteristic
415C3×Q16—21no—
416C3×Q16—21no—
417C3×Q16—21no—
418C3×Q16—21no—
419C3×Q16—21no—
420C3×Q16—21no—
421C3×Q16—21no—
422C3×Q16—21no—
423C3×Q16—31no—
424C3×Q16—31no—
425C3×Q16—41no—
426C3×Q16—41no—
427C3×Q16—41no—
428C3×Q16—41no—
429C3×Q16—61no—
430C3×Q16—61no—
431C3×Q16—61no—
432C3×Q16—61no—
433C3×Q16—61no—
434C3×Q16—61no—
435C3×SD16—21no—
436C3×SD16—21no—
437C3×SD16—21no—
438C3×SD16—21no—
439C3×SD16—31no—
440C3×SD16—31no—
441C3×SD16—31no—
442C3×SD16—31no—
443C3×SD16—41no—
444C3×SD16—41no—
445C3×SD16—61no—
446C3×SD16—61no—
447C3×SD16—61no—
448C3×SD16—61no—
449C3×SD16—61no—
450C3×SD16—61no—
451C3×SD16—61no—
452C3×SD16—61no—
453C3×SD16—61no—
454C3×SD16—61no—
455C3×D8—31no—
456C3×D8—31no—
457C3×D8—61no—
458C3×D8—61no—
459C3×M16—21no—
460C3×M16—21no—
461C3×M16—21no—
462C3×M16—21no—
463C3×M16—21no—
464C3×M16—31no—
465C3×M16—41no—
466C3×M16—61no—
467C3×M16—61no—
468C3×M16—61no—
469C3×M16C22×D311yescharacteristic
470C3×M16C22×D311yescharacteristic
471C3×M16C22×D311yescharacteristic
472C3×M16C23×C311yescharacteristic
473C3×M16C23×C311yescharacteristic
474C3×M16C23×C311yescharacteristic
475C2×C3×C8—21no—
476C2×C3×C8—21no—
477C2×C3×C8—21no—
478C2×C3×C8—31no—
479C2×C3×C8—41no—
480C2×C3×C8—61no—
481C2×C3×C8—61no—
482C2×C3×C8—61no—
483C2×C3×C8C22×D311yescharacteristic
484C2×C3×C8C23×C311yescharacteristic
485C3×C4⋊C4—121no—
486C3×C22⋊C4—121no—
487C3×C42—31no—
488#216—21no—
489#216—21no—
490#216—21no—
491#216—21no—
492#216C3×D411yescharacteristic
493#215—21no—
494#215—21no—
495#215—21no—
496#215—21no—
497#215C3×D411yescharacteristic
498#214C3×D411yescharacteristic
499#213C3×D411yescharacteristic
500(C2×D3)⋊C4—41no—
501Dic3⋊C4—41no—
502C4×Dic3C23×C311yescharacteristic
503#208C23×C311yescharacteristic
504C2×C3⋊C8C23×C311yescharacteristic
505Dic12—21no—
506Dic12—21no—
507Dic12C3×D411yescharacteristic
508D24—21no—
509D24—21no—
510D24C3×D411yescharacteristic
511#204—21no—
512#204—21no—
513#204—21no—
514#204—21no—
515#204—21no—
516#204—21no—
517#204C3×D411yescharacteristic
518#204C3×D411yescharacteristic
519ΓL(1,𝔽25)—21no—
520ΓL(1,𝔽25)—21no—
521ΓL(1,𝔽25)—21no—
522D3×C8—21no—
523D3×C8—21no—
524D3×C8—21no—
525C22×C32—21no—
526C22×C32H(5,𝔽2)11yescharacteristic
527C2×C3×D3—21no—
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—41no—
535C32×C4—41no—
536C32×C4C22×D411yescharacteristic
537C32×C4C22×D411yescharacteristic
538C3×Dic3—21no—
539C3×Dic3—21no—
540C3×Dic3—21no—
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—61no—
552#137—61no—
553#137—61no—
554#137—61no—
555#137—61no—
556#137—61no—
557#137C2×C3×D311yescharacteristic
558#137C2×C3×D311yescharacteristic
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—31no—
565#135—61no—
566#135—61no—
567#135—61no—
568#135—61no—
569C2×Q16—31no—
570C2×Q16—61no—
571C2×Q16—61no—
572C2×Q16C2×C3×D311yescharacteristic, complemented
573C2×SD16—31no—
574C2×SD16—31no—
575C2×SD16—61no—
576C2×SD16—61no—
577#131—31no—
578#131—31no—
579#131—31no—
580#131C2×C3×D311yescharacteristic
581C4⋊Q8—31no—
582#124—31no—
583#108—31no—
584#108C2×C3×D311yescharacteristic, complemented
585#104—31no—
586#104—31no—
587#104—31no—
588#104—31no—
589#101—31no—
590#101C2×C3×D311yescharacteristic, complemented
591#101C2×C3×D311yescharacteristic, complemented
592#100—31no—
593#97—31no—
594C23×C3—61no—
595C23×C3—121no—
596C22×D3—21no—
597C22×D3—41no—
598C3×Q8—21no—
599C3×Q8—21no—
600C3×Q8—21no—
601C3×Q8—21no—
602C3×Q8—21no—
603C3×Q8—21no—
604C3×Q8—21no—
605C3×Q8—21no—
606C3×Q8—21no—
607C3×Q8—31no—
608C3×Q8—31no—
609C3×Q8—31no—
610C3×Q8—41no—
611C3×Q8—41no—
612C3×Q8—41no—
613C3×Q8—41no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8—121no—
617C3×Q8—121no—
618C3×Q8—121no—
619C3×Q8D3×D411yescharacteristic
620C3×Q8C2×C3×D411yescharacteristic
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—31no—
625C3×D4—31no—
626C3×D4—31no—
627C3×D4—41no—
628C3×D4—61no—
629C3×D4—61no—
630C3×D4—61no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—121no—
634C3×D4—121no—
635C3×D4—121no—
636C3×D4—121no—
637C3×D4—121no—
638C3×D4D3×D411yescharacteristic
639C3×D4C2×C3×D411yescharacteristic
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—121no—
656C2×C3×C4—121no—
657C2×C3×C4—121no—
658C2×C3×C4—121no—
659C2×C3×C4—121no—
660C2×C3×C4—121no—
661C2×C3×C4—121no—
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C24×C311yescharacteristic
664#67—21no—
665#67—21no—
666#67—21no—
667#67—41no—
668#67—41no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—41no—
672D12—21no—
673D12—21no—
674D12—41no—
675D12—41no—
676D12—41no—
677D12C2×C3×D411yescharacteristic
678D12C2×C3×D411yescharacteristic
679D12C2×C3×D411yescharacteristic
680C4×D3—21no—
681C4×D3—21no—
682C4×D3—21no—
683C4×D3—41no—
684C4×D3—41no—
685C4×D3—41no—
686C4×D3—41no—
687C4×D3—41no—
688C4×D3—41no—
689Dic6—21no—
690Dic6—21no—
691Dic6—41no—
692Dic6—41no—
693Dic6—41no—
694Dic6C2×C3×D411yescharacteristic
695Dic6C2×C3×D411yescharacteristic
696Dic6C2×C3×D411yescharacteristic
697C3×C8—21no—
698C3×C8—21no—
699C3×C8—21no—
700C3×C8—21no—
701C3×C8—21no—
702C3×C8—21no—
703C3×C8—21no—
704C3×C8—21no—
705C3×C8—31no—
706C3×C8—31no—
707C3×C8—41no—
708C3×C8—41no—
709C3×C8—41no—
710C3×C8—61no—
711C3×C8D3×D411yescharacteristic
712C3×C8D3×D411yescharacteristic
713C3×C8C2×C3×D411yescharacteristic
714C3×C8C2×C3×D411yescharacteristic
715C3⋊C8—21no—
716C3⋊C8C2×C3×D411yescharacteristic
717C3⋊C8C2×C3×D411yescharacteristic
718C2×C32—21no—
719C2×C32—41no—
720C2×C32D4211yescharacteristic
721C3×D3—41no—
722C3×D3—41no—
723C3×D3—41no—
724C3×D3—81no—
725#41—31no—
726#41—31no—
727#41—31no—
728#41—61no—
729#41—61no—
730#41—61no—
731#41—61no—
732#41—61no—
733#41—61no—
734#41—61no—
735#41—61no—
736#41—121no—
737#41—121no—
738#41—121no—
739#41C22×C3×D311yescharacteristic
740C2×Q8—31no—
741C2×Q8—61no—
742C2×Q8—61no—
743C2×Q8—61no—
744C2×Q8—61no—
745C2×Q8—61no—
746C2×Q8—61no—
747C2×Q8C22×C3×D311yescharacteristic
748C2×Q8C22×C3×D311yescharacteristic
749C2×D4—31no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—121no—
753Q16—21no—
754Q16—21no—
755Q16—21no—
756Q16—21no—
757Q16—31no—
758Q16—31no—
759Q16—61no—
760Q16—61no—
761Q16—61no—
762Q16—61no—
763Q16—61no—
764Q16—61no—
765SD16—21no—
766SD16—21no—
767SD16—31no—
768SD16—31no—
769SD16—31no—
770SD16—31no—
771SD16—61no—
772SD16—61no—
773SD16—61no—
774SD16—61no—
775SD16—61no—
776SD16—61no—
777SD16—61no—
778SD16—61no—
779SD16—61no—
780SD16—61no—
781D8—31no—
782D8—31no—
783D8—61no—
784D8—61no—
785M16—21no—
786M16—31no—
787M16—61no—
788M16—61no—
789M16—61no—
790M16C22×C3×D311yescharacteristic
791M16C22×C3×D311yescharacteristic
792M16C22×C3×D311yescharacteristic
793C2×C8—21no—
794C2×C8—31no—
795C2×C8—61no—
796C2×C8—61no—
797C2×C8—61no—
798C2×C8C22×C3×D311yescharacteristic
799C4⋊C4—121no—
800C22⋊C4—121no—
801C42—31no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—41no—
806C22×C3—61no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—121no—
810C22×C3—241no—
811C22×C3—481no—
812C22×C3#100911yescharacteristic
813C22×C3C3×H(5,𝔽2)11yescharacteristic
814C2×D3—21no—
815C2×D3—21no—
816C2×D3—21no—
817C2×D3—41no—
818C2×D3—81no—
819C2×D3—161no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—41no—
825C3×C4—41no—
826C3×C4—41no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—61no—
832C3×C4—81no—
833C3×C4—81no—
834C3×C4—121no—
835C3×C4—121no—
836C3×C4C2×D3×D411yescharacteristic
837C3×C4C2×D3×D411yescharacteristic
838C3×C4C22×C3×D411yescharacteristic
839C3×C4C22×C3×D411yescharacteristic
840Dic3—21no—
841Dic3—21no—
842Dic3—21no—
843Dic3—41no—
844Dic3—41no—
845C32#328911yescharacteristic, complemented, Sylow
846C23—61no—
847C23—121no—
848Q8—21no—
849Q8—21no—
850Q8—21no—
851Q8—21no—
852Q8—31no—
853Q8—31no—
854Q8—31no—
855Q8—61no—
856Q8—61no—
857Q8—121no—
858Q8—121no—
859Q8—121no—
860Q8C3×D3×D411yescharacteristic
861D4—21no—
862D4—31no—
863D4—31no—
864D4—31no—
865D4—61no—
866D4—61no—
867D4—61no—
868D4—61no—
869D4—61no—
870D4—121no—
871D4—121no—
872D4—121no—
873D4—121no—
874D4—121no—
875D4C3×D3×D411yescharacteristic
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—121no—
888C2×C4—121no—
889C2×C4—121no—
890C2×C4—121no—
891C2×C4C23×C3×D311yescharacteristic
892C8—21no—
893C8—21no—
894C8—21no—
895C8—31no—
896C8—31no—
897C8—61no—
898C8C3×D3×D411yescharacteristic
899C8C3×D3×D411yescharacteristic
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—41no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—81no—
907C2×C3—121no—
908C2×C3—121no—
909C2×C3—121no—
910C2×C3—241no—
911C2×C3#560911yescharacteristic
912C2×C3C3×D4211yescharacteristic
913D3—41no—
914D3—41no—
915D3—41no—
916D3—81no—
917C22—21no—
918C22—61no—
919C22—61no—
920C22—61no—
921C22—121no—
922C22—241no—
923C22—481no—
924C22C3×#100911yescharacteristic
925C4—21no—
926C4—41no—
927C4—41no—
928C4—61no—
929C4—61no—
930C4—61no—
931C4—121no—
932C4—121no—
933C4C2×C3×D3×D411yescharacteristic
934C4C2×C3×D3×D411yescharacteristic
935C3—21no—
936C3#8094511yescharacteristic, direct product factor
937C3C3×#328911yescharacteristic, complemented
938C2—21no—
939C2—41no—
940C2—121no—
941C2—121no—
942C2—121no—
943C2—241no—
944C2C3×#560911yescharacteristic
subgroupG/H
centerC2×C3#5609
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#473C2
socleC2×C32D42
hypercenterC3×#473D3
hypocenterC3C3×#3289
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#473

Complements

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

NH ≅ G/Ntype
1. C3×#5779C2semidirect
2. C3×#5778C2semidirect
3. C3×#5766C2semidirect
4. C3×#5751C2semidirect
5. C32×#473C2semidirect
6. C3×#5205C2semidirect
7. C3×#5202C2semidirect
8. C3×#5190C2semidirect
9. C3×#5145C2semidirect
10. C3×#4898C2semidirect
11. C3×#4894C2semidirect
12. C3×#4755C2semidirect
13. C3×#4754C2semidirect
14. C3×#4753C2semidirect
15. C3×#4752C2semidirect
17. #80945C3direct (N × H)
21. C3×#1007C22semidirect
24. C2×C32×Q16C22semidirect
28. C3×#944C22semidirect
29. C2×C3×#216C22semidirect
31. C3×#942C22semidirect
47. C3×#909C22semidirect
52. C3×#907C22semidirect
57. C3×#901C22semidirect
58. C32×#108C22semidirect
59. C32×#101C22semidirect
60. C32×#101C22semidirect
63. C3×#825C22semidirect
64. C3×#825C22semidirect
65. C3×#824C22semidirect
67. C3×#822C22semidirect
68. C3×#815C22semidirect
73. #5779C2×C3semidirect
74. #5778C2×C3semidirect
75. #5766C2×C3semidirect
76. #5751C2×C3semidirect
80. C3×#473D3semidirect
81. C3×#473C2×C3semidirect
90. #5205C2×C3semidirect
91. #5202C2×C3semidirect
92. #5190C2×C3semidirect
93. #5145C2×C3semidirect
94. #4898C2×C3semidirect
95. #4894C2×C3semidirect
96. #4755C2×C3semidirect
97. #4754C2×C3semidirect
98. #4753C2×C3semidirect
99. #4752C2×C3semidirect
185. #1007C22×C3semidirect
216. C2×C3×Q16C2×D3semidirect
217. C2×C3×Q16C22×C3semidirect
232. #944C22×C3semidirect
233. C2×#216C22×C3semidirect
235. #942C22×C3semidirect
251. #909C22×C3semidirect
256. #907C22×C3semidirect
261. #901C22×C3semidirect
264. C3×#108C2×D3semidirect
265. C3×#108C22×C3semidirect
273. C3×#101C2×D3semidirect
274. C3×#101C2×D3semidirect
275. C3×#101C22×C3semidirect
276. C3×#101C22×C3semidirect
281. #825C22×C3semidirect
282. #825C22×C3semidirect
283. #824C22×C3semidirect
285. #822C22×C3semidirect
286. #815C22×C3semidirect
347. #473C3×D3semidirect
572. C2×Q16C2×C3×D3semidirect
584. #108C2×C3×D3semidirect
590. #101C2×C3×D3semidirect
591. #101C2×C3×D3semidirect
845. C32#3289semidirect
936. C3#80945direct (N × H)
937. C3C3×#3289semidirect

Maximal subgroups

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

subgroupindex
C3×#57792
C3×#57782
C3×#57662
C3×#57512
C32×#4732
C3×#52052
C3×#52022
C3×#51902
C3×#51452
C3×#48982
C3×#48942
C3×#47552
C3×#47542
C3×#47532
C3×#47522
C3×#32893
#809453