Finite Group Databasebeta

← C3×#80933 #11886652

Subgroups — C3×#80933 #11886652

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×#5779C211yesmaximal, characteristic, complemented
2C3×#5775C211yesmaximal, characteristic, complemented
3C3×#5762C211yesmaximal, characteristic, complemented
4C3×#5753C211yesmaximal, characteristic, complemented
5C32×#471C211yesmaximal, characteristic, complemented
6C3×#5205C211yesmaximal, characteristic, complemented
7C3×#5201C211yesmaximal, characteristic, complemented
8C3×#5167C211yesmaximal, characteristic, complemented
9C3×#5145C211yesmaximal, characteristic, complemented
10C3×#4896C211yesmaximal, characteristic, complemented
11C3×#4894C211yesmaximal, characteristic, complemented
12C3×#4755C211yesmaximal, characteristic, complemented
13C3×#4752C211yesmaximal, characteristic, complemented
14C3×#4748C211yesmaximal, characteristic, complemented
15C3×#4746C211yesmaximal, characteristic, complemented
16C3×#3289—31nomaximal
17#80933C311yesmaximal, characteristic, direct product factor
18C3×#1010C2211yescharacteristic
19C3×#1010C2211yescharacteristic, complemented
20C3×#1007C2211yescharacteristic
21C3×#1004C2211yescharacteristic
22C32×#137C2211yescharacteristic, complemented
23C32×AGL(1,ℤ/8)C2211yescharacteristic
24C2×C32×SD16C2211yescharacteristic
25C32×#131C2211yescharacteristic, complemented
26C3×#950C2211yescharacteristic
27C3×#944C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C3×#942C2211yescharacteristic
30C3×#936C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×#932C2211yescharacteristic
33C3×#918—21no—
34C3×D3×Q16—21no—
35C3×#916—21no—
36C3×#916—21no—
37C3×#915—21no—
38C3×#915—21no—
39C3×#915—21no—
40C3×#914—21no—
41C3×D3×SD16—21no—
42C3×D3×SD16—21no—
43C3×#912—21no—
44C3×#911—21no—
45C3×#909—21no—
46C3×#909—21no—
47C3×#909C2211yescharacteristic
48C3×#909C2211yescharacteristic
49C3×#909C2211yescharacteristic
50C3×#909C2211yescharacteristic, complemented
51C3×#907C2211yescharacteristic
52C3×#907C2211yescharacteristic, complemented
53C2×C3×Dic12—21no—
54C2×C3×Dic12C2211yescharacteristic, complemented
55C3×#904—21no—
56C3×#904C2211yescharacteristic
57C3×#901C2211yescharacteristic
58C32×#108C2211yescharacteristic, complemented
59C32×#101C2211yescharacteristic, complemented
60C32×#100C2211yescharacteristic
61C3×#837C2211yescharacteristic, complemented
62C3×#825C2211yescharacteristic
63C3×#825C2211yescharacteristic
64C3×#825C2211yescharacteristic, complemented
65C3×#824C2211yescharacteristic, complemented
66C3×#824C2211yescharacteristic, complemented
67C3×#822C2211yescharacteristic, complemented
68C3×#815C2211yescharacteristic, complemented
69C3×#578—31no—
70C3×#578—31no—
71C3×#577—31no—
72C3×#577—31no—
73#5779C2×C311yescharacteristic, complemented
74#5775C2×C311yescharacteristic, complemented
75#5762C2×C311yescharacteristic, complemented
76#5753C2×C311yescharacteristic, complemented
77C3×#497—31no—
78C3×#473—31no—
79C3×#473—31no—
80C3×#471—21no—
81C3×#471—31no—
82C3×#471D311yescharacteristic, complemented
83C3×#471C2×C311yescharacteristic, complemented
84C3×#456—31no—
85C3×#456—31no—
86C3×#455—31no—
87C3×#454—31no—
88C3×#444—31no—
89C3×#444—31no—
90#5205C2×C311yescharacteristic, complemented
91#5201C2×C311yescharacteristic, complemented
92#5167C2×C311yescharacteristic, complemented
93#5145C2×C311yescharacteristic, complemented
94#4896C2×C311yescharacteristic, complemented
95#4894C2×C311yescharacteristic, complemented
96#4755C2×C311yescharacteristic, complemented
97#4752C2×C311yescharacteristic, complemented
98#4748C2×C311yescharacteristic, complemented
99#4746C2×C311yescharacteristic, complemented
100C32×#41C2311yescharacteristic
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C2×C3×#67—41no—
104C3×#239—21no—
105C3×#239—21no—
106C3×D3×Q8—21no—
107C3×D3×Q8—21no—
108C3×D3×Q8—21no—
109C3×D3×Q8—21no—
110C3×#237—21no—
111C3×#237—21no—
112C3×#237—21no—
113C3×#237—21no—
114C3×#237—41no—
115C3×#237—41no—
116C3×D3×D4—21no—
117C3×D3×D4—21no—
118C3×#235—21no—
119C3×#235—21no—
120C3×#235—41no—
121C3×#235C2311yescharacteristic
122C3×#235C2311yescharacteristic
123C3×#235C2311yescharacteristic
124C2×C3×Dic6—21no—
125C2×C3×Dic6—21no—
126C2×C3×Dic6C2311yescharacteristic
127C2×C3×Dic6C2311yescharacteristic
128C32×Q16—21no—
129C32×SD16—21no—
130C32×SD16—21no—
131C32×SD16—21no—
132C32×SD16—21no—
133C32×D8—21no—
134C32×M16—21no—
135C32×M16C2311yescharacteristic
136C32×M16C2311yescharacteristic
137C32×M16C2311yescharacteristic
138C2×C32×C8—21no—
139C2×C32×C8C2311yescharacteristic
140C3×#217—41no—
141C3×#216—21no—
142C3×#216—21no—
143C3×#216—21no—
144C3×#216D411yescharacteristic
145C3×#215—21no—
146C3×#215D411yescharacteristic
147C3×#214—21no—
148C3×#214—21no—
149C3×#214—21no—
150C3×#214D411yescharacteristic
151C3×#213—21no—
152C3×#213D411yescharacteristic
153C3×Dic3⋊C4—41no—
154C3×C4×Dic3C2311yescharacteristic
155C3×#208C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157C3×Dic12—21no—
158C3×Dic12—21no—
159C3×Dic12—21no—
160C3×Dic12—21no—
161C3×Dic12—21no—
162C3×Dic12—21no—
163C3×Dic12D411yescharacteristic
164C3×D24D411yescharacteristic
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#1010C22×C311yescharacteristic, complemented
184#1007C22×C311yescharacteristic
185#1004C22×C311yescharacteristic
186C3×#137—21no—
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×#137C2×D311yescharacteristic, complemented
199C3×#137C22×C311yescharacteristic, complemented
200C3×AGL(1,ℤ/8)—21no—
201C3×AGL(1,ℤ/8)—31no—
202C3×AGL(1,ℤ/8)—61no—
203C3×AGL(1,ℤ/8)—61no—
204C3×AGL(1,ℤ/8)C2×D311yescharacteristic
205C3×AGL(1,ℤ/8)C22×C311yescharacteristic
206C3×#135—31no—
207C3×#135—31no—
208C3×#135—61no—
209C3×#135—61no—
210C3×#135—61no—
211C3×#135—61no—
212C2×C3×Q16—31no—
213C2×C3×Q16—31no—
214C2×C3×Q16—61no—
215C2×C3×Q16—61no—
216C2×C3×SD16—21no—
217C2×C3×SD16—31no—
218C2×C3×SD16—61no—
219C2×C3×SD16—61no—
220C2×C3×SD16C2×D311yescharacteristic
221C2×C3×SD16C22×C311yescharacteristic
222C3×#131—21no—
223C3×#131—31no—
224C3×#131—31no—
225C3×#131—31no—
226C3×#131C2×D311yescharacteristic, complemented
227C3×#131C22×C311yescharacteristic, complemented
228C3×C4⋊Q8—31no—
229C3×#124—31no—
230#950C22×C311yescharacteristic
231#944C22×C311yescharacteristic, complemented
232C2×#216C22×C311yescharacteristic, complemented
233#942C22×C311yescharacteristic
234#936C22×C311yescharacteristic
235C2×#214C22×C311yescharacteristic
236#932C22×C311yescharacteristic
237#918—21no—
238D3×Q16—21no—
239#916—21no—
240#916—21no—
241#915—21no—
242#915—21no—
243#915—21no—
244#914—21no—
245D3×SD16—21no—
246D3×SD16—21no—
247#912—21no—
248#911—21no—
249#909—21no—
250#909—21no—
251#909C22×C311yescharacteristic
252#909C22×C311yescharacteristic
253#909C22×C311yescharacteristic
254#909C22×C311yescharacteristic, complemented
255#907C22×C311yescharacteristic
256#907C22×C311yescharacteristic, complemented
257C2×Dic12—21no—
258C2×Dic12C22×C311yescharacteristic, complemented
259#904—21no—
260#904C22×C311yescharacteristic
261#901C22×C311yescharacteristic
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—31no—
272C3×#101—31no—
273C3×#101C2×D311yescharacteristic, complemented
274C3×#101C22×C311yescharacteristic, complemented
275C3×#100—21no—
276C3×#100C2×D311yescharacteristic
277C3×#100C22×C311yescharacteristic
278C3×#97—31no—
279#837C22×C311yescharacteristic, complemented
280#825C22×C311yescharacteristic
281#825C22×C311yescharacteristic
282#825C22×C311yescharacteristic, complemented
283#824C22×C311yescharacteristic, complemented
284#824C22×C311yescharacteristic, complemented
285#822C22×C311yescharacteristic, complemented
286#815C22×C311yescharacteristic, complemented
287C23×C32—21no—
288C22×C3×D3—41no—
289C32×Q8—21no—
290C32×Q8—21no—
291C32×Q8C2×D411yescharacteristic
292C32×D4—21no—
293C32×D4—21no—
294C32×D4—21no—
295C32×D4C2×D411yescharacteristic
296C2×C32×C4—21no—
297C2×C32×C4—21no—
298C2×C32×C4C2411yescharacteristic
299C3×#67—21no—
300C3×#67—21no—
301C3×#67—21no—
302C3×#67—41no—
303C3×#67—41no—
304C3×#67—41no—
305C3×#67—41no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—41no—
310C2×C3×Dic3—41no—
311C2×C3×Dic3—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×Dic6—21no—
324C3×Dic6—21no—
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#473—31no—
348#471—31no—
349#471C3×D311yescharacteristic, complemented
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—31no—
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×Q8C23×C311yescharacteristic
384C2×C3×D4—21no—
385C2×C3×D4—61no—
386C2×C3×D4—61no—
387C2×C3×D4—121no—
388C2×C3×D4C22×D311yescharacteristic
389C2×C3×D4C23×C311yescharacteristic
390C2×#67—41no—
391#239—21no—
392#239—21no—
393D3×Q8—21no—
394D3×Q8—21no—
395D3×Q8—21no—
396D3×Q8—21no—
397#237—21no—
398#237—21no—
399#237—21no—
400#237—21no—
401#237—41no—
402#237—41no—
403D3×D4—21no—
404D3×D4—21no—
405#235—21no—
406#235—21no—
407#235—41no—
408#235C23×C311yescharacteristic
409#235C23×C311yescharacteristic
410#235C23×C311yescharacteristic
411C2×Dic6—21no—
412C2×Dic6—21no—
413C2×Dic6C23×C311yescharacteristic
414C2×Dic6C23×C311yescharacteristic
415C3×Q16—21no—
416C3×Q16—21no—
417C3×Q16—31no—
418C3×Q16—31no—
419C3×Q16—41no—
420C3×Q16—61no—
421C3×Q16—61no—
422C3×Q16—61no—
423C3×Q16—61no—
424C3×Q16—61no—
425C3×Q16—61no—
426C3×Q16—61no—
427C3×Q16—61no—
428C3×Q16—61no—
429C3×SD16—21no—
430C3×SD16—21no—
431C3×SD16—21no—
432C3×SD16—21no—
433C3×SD16—21no—
434C3×SD16—21no—
435C3×SD16—21no—
436C3×SD16—21no—
437C3×SD16—31no—
438C3×SD16—31no—
439C3×SD16—31no—
440C3×SD16—31no—
441C3×SD16—41no—
442C3×SD16—41no—
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×D8—21no—
454C3×D8—21no—
455C3×D8—31no—
456C3×D8—31no—
457C3×D8—41no—
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#217—41no—
489#216—21no—
490#216—21no—
491#216—21no—
492#216C3×D411yescharacteristic
493#215—21no—
494#215C3×D411yescharacteristic
495#214—21no—
496#214—21no—
497#214—21no—
498#214C3×D411yescharacteristic
499#213—21no—
500#213C3×D411yescharacteristic
501Dic3⋊C4—41no—
502C4×Dic3C23×C311yescharacteristic
503#208C23×C311yescharacteristic
504C2×C3⋊C8C23×C311yescharacteristic
505Dic12—21no—
506Dic12—21no—
507Dic12—21no—
508Dic12—21no—
509Dic12—21no—
510Dic12—21no—
511Dic12C3×D411yescharacteristic
512D24C3×D411yescharacteristic
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×C32—41no—
527C22×C32—81no—
528C22×C32H(5,𝔽2)11yescharacteristic
529C2×C3×D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D3—161no—
533C32×C4—21no—
534C32×C4—41no—
535C32×C4C22×D411yescharacteristic
536C32×C4C22×D411yescharacteristic
537C3×Dic3—21no—
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—61no—
553#137—61no—
554#137—61no—
555#137—61no—
556#137—61no—
557#137—61no—
558#137C2×C3×D311yescharacteristic, complemented
559AGL(1,ℤ/8)—31no—
560AGL(1,ℤ/8)—61no—
561AGL(1,ℤ/8)—61no—
562AGL(1,ℤ/8)C2×C3×D311yescharacteristic
563#135—31no—
564#135—31no—
565#135—61no—
566#135—61no—
567#135—61no—
568#135—61no—
569C2×Q16—31no—
570C2×Q16—31no—
571C2×Q16—61no—
572C2×Q16—61no—
573C2×SD16—31no—
574C2×SD16—61no—
575C2×SD16—61no—
576C2×SD16C2×C3×D311yescharacteristic
577#131—31no—
578#131—31no—
579#131—31no—
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#104—31no—
588#104—31no—
589#101—31no—
590#101—31no—
591#101C2×C3×D311yescharacteristic, complemented
592#100C2×C3×D311yescharacteristic
593#97—31no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—41no—
597C23×C3—121no—
598C22×D3—41no—
599C3×Q8—21no—
600C3×Q8—21no—
601C3×Q8—21no—
602C3×Q8—21no—
603C3×Q8—21no—
604C3×Q8—31no—
605C3×Q8—31no—
606C3×Q8—31no—
607C3×Q8—41no—
608C3×Q8—41no—
609C3×Q8—61no—
610C3×Q8—61no—
611C3×Q8—61no—
612C3×Q8—61no—
613C3×Q8—121no—
614C3×Q8—121no—
615C3×Q8—121no—
616C3×Q8D3×D411yescharacteristic
617C3×Q8C2×C3×D411yescharacteristic
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—31no—
626C3×D4—31no—
627C3×D4—31no—
628C3×D4—41no—
629C3×D4—41no—
630C3×D4—41no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—121no—
635C3×D4—121no—
636C3×D4—121no—
637C3×D4—121no—
638C3×D4—121no—
639C3×D4D3×D411yescharacteristic
640C3×D4C2×C3×D411yescharacteristic
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
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—61no—
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×C4—121no—
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C24×C311yescharacteristic
663#67—21no—
664#67—21no—
665#67—21no—
666#67—41no—
667#67—41no—
668#67—41no—
669#67—41no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—41no—
674C2×Dic3—41no—
675C2×Dic3—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—
687Dic6—21no—
688Dic6—21no—
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×C32—81no—
721C2×C32D4211yescharacteristic
722C3×D3—41no—
723C3×D3—41no—
724C3×D3—41no—
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—31no—
742C2×Q8—61no—
743C2×Q8—61no—
744C2×Q8—61no—
745C2×Q8—61no—
746C2×Q8—61no—
747C2×Q8—61no—
748C2×Q8C22×C3×D311yescharacteristic
749C2×D4—61no—
750C2×D4—61no—
751C2×D4—121no—
752C2×D4C22×C3×D311yescharacteristic
753Q16—21no—
754Q16—31no—
755Q16—31no—
756Q16—61no—
757Q16—61no—
758Q16—61no—
759Q16—61no—
760Q16—61no—
761Q16—61no—
762Q16—61no—
763Q16—61no—
764Q16—61no—
765SD16—21no—
766SD16—21no—
767SD16—21no—
768SD16—21no—
769SD16—31no—
770SD16—31no—
771SD16—31no—
772SD16—31no—
773SD16—61no—
774SD16—61no—
775SD16—61no—
776SD16—61no—
777SD16—61no—
778SD16—61no—
779SD16—61no—
780SD16—61no—
781D8—21no—
782D8—31no—
783D8—31no—
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—41no—
807C22×C3—41no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—81no—
812C22×C3—81no—
813C22×C3—81no—
814C22×C3—161no—
815C22×C3—481no—
816C22×C3#100911yescharacteristic
817C22×C3C3×H(5,𝔽2)11yescharacteristic
818C2×D3—21no—
819C2×D3—21no—
820C2×D3—21no—
821C2×D3—161no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—41no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—61no—
832C3×C4—81no—
833C3×C4—121no—
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—
845Dic3—41no—
846C32#328911yescharacteristic, complemented, Sylow
847C23—21no—
848C23—121no—
849Q8—21no—
850Q8—21no—
851Q8—31no—
852Q8—31no—
853Q8—31no—
854Q8—61no—
855Q8—61no—
856Q8—61no—
857Q8—61no—
858Q8—121no—
859Q8—121no—
860Q8—121no—
861Q8C3×D3×D411yescharacteristic
862D4—21no—
863D4—21no—
864D4—21no—
865D4—31no—
866D4—31no—
867D4—31no—
868D4—61no—
869D4—61no—
870D4—61no—
871D4—121no—
872D4—121no—
873D4—121no—
874D4—121no—
875D4—121no—
876D4C3×D3×D411yescharacteristic
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—61no—
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—21no—
896C8—31no—
897C8—31no—
898C8—61no—
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—81no—
908C2×C3—81no—
909C2×C3—81no—
910C2×C3—121no—
911C2×C3—121no—
912C2×C3—121no—
913C2×C3—161no—
914C2×C3#560911yescharacteristic
915C2×C3C3×D4211yescharacteristic
916D3—41no—
917D3—41no—
918D3—41no—
919C22—21no—
920C22—41no—
921C22—61no—
922C22—61no—
923C22—61no—
924C22—81no—
925C22—481no—
926C22C3×#100911yescharacteristic
927C4—21no—
928C4—41no—
929C4—61no—
930C4—61no—
931C4—61no—
932C4—121no—
933C4—121no—
934C4—121no—
935C4C2×C3×D3×D411yescharacteristic
936C4C2×C3×D3×D411yescharacteristic
937C3—21no—
938C3#8093311yescharacteristic, direct product factor
939C3C3×#328911yescharacteristic, complemented
940C2—21no—
941C2—41no—
942C2—81no—
943C2—121no—
944C2—121no—
945C2—121no—
946C2C3×#560911yescharacteristic
subgroupG/H
centerC2×C3#5609
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#471C2
socleC2×C32D42
hypercenterC3×#471D3
hypocenterC3C3×#3289
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#471

Complements

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

NH ≅ G/Ntype
1. C3×#5779C2semidirect
2. C3×#5775C2semidirect
3. C3×#5762C2semidirect
4. C3×#5753C2semidirect
5. C32×#471C2semidirect
6. C3×#5205C2semidirect
7. C3×#5201C2semidirect
8. C3×#5167C2semidirect
9. C3×#5145C2semidirect
10. C3×#4896C2semidirect
11. C3×#4894C2semidirect
12. C3×#4755C2semidirect
13. C3×#4752C2semidirect
14. C3×#4748C2semidirect
15. C3×#4746C2semidirect
17. #80933C3direct (N × H)
19. C3×#1010C22semidirect
22. C32×#137C22semidirect
25. C32×#131C22semidirect
27. C3×#944C22semidirect
28. C2×C3×#216C22semidirect
50. C3×#909C22semidirect
52. C3×#907C22semidirect
54. C2×C3×Dic12C22semidirect
58. C32×#108C22semidirect
59. C32×#101C22semidirect
61. C3×#837C22semidirect
64. C3×#825C22semidirect
65. C3×#824C22semidirect
66. C3×#824C22semidirect
67. C3×#822C22semidirect
68. C3×#815C22semidirect
73. #5779C2×C3semidirect
74. #5775C2×C3semidirect
75. #5762C2×C3semidirect
76. #5753C2×C3semidirect
82. C3×#471D3semidirect
83. C3×#471C2×C3semidirect
90. #5205C2×C3semidirect
91. #5201C2×C3semidirect
92. #5167C2×C3semidirect
93. #5145C2×C3semidirect
94. #4896C2×C3semidirect
95. #4894C2×C3semidirect
96. #4755C2×C3semidirect
97. #4752C2×C3semidirect
98. #4748C2×C3semidirect
99. #4746C2×C3semidirect
183. #1010C22×C3semidirect
198. C3×#137C2×D3semidirect
199. C3×#137C22×C3semidirect
226. C3×#131C2×D3semidirect
227. C3×#131C22×C3semidirect
231. #944C22×C3semidirect
232. C2×#216C22×C3semidirect
254. #909C22×C3semidirect
256. #907C22×C3semidirect
258. C2×Dic12C22×C3semidirect
264. C3×#108C2×D3semidirect
265. C3×#108C22×C3semidirect
273. C3×#101C2×D3semidirect
274. C3×#101C22×C3semidirect
279. #837C22×C3semidirect
282. #825C22×C3semidirect
283. #824C22×C3semidirect
284. #824C22×C3semidirect
285. #822C22×C3semidirect
286. #815C22×C3semidirect
349. #471C3×D3semidirect
558. #137C2×C3×D3semidirect
580. #131C2×C3×D3semidirect
584. #108C2×C3×D3semidirect
591. #101C2×C3×D3semidirect
846. C32#3289semidirect
938. C3#80933direct (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×#57792
C3×#57752
C3×#57622
C3×#57532
C32×#4712
C3×#52052
C3×#52012
C3×#51672
C3×#51452
C3×#48962
C3×#48942
C3×#47552
C3×#47522
C3×#47482
C3×#47462
C3×#32893
#809333