Finite Group Databasebeta

← C3×#80939 #11886564

Subgroups — C3×#80939 #11886564

Order 1152.

982 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5775C211yesmaximal, characteristic, complemented
2C3×#5774C211yesmaximal, characteristic, complemented
3C3×#5757C211yesmaximal, characteristic, complemented
4C3×#5751C211yesmaximal, characteristic, complemented
5C32×#472C211yesmaximal, characteristic, complemented
6C3×#5201C211yesmaximal, characteristic, complemented
7C3×#5198C211yesmaximal, characteristic, complemented
8C3×#5154C211yesmaximal, characteristic, complemented
9C3×#5145C211yesmaximal, characteristic, complemented
10C3×#4898C211yesmaximal, characteristic, complemented
11C3×#4894C211yesmaximal, characteristic, complemented
12C3×#4749C211yesmaximal, characteristic, complemented
13C3×#4748C211yesmaximal, characteristic, complemented
14C3×#4747C211yesmaximal, characteristic, complemented
15C3×#4746C211yesmaximal, characteristic, complemented
16C3×#3288—31nomaximal
17#80939C311yesmaximal, characteristic, direct product factor
18C3×#1010C2211yescharacteristic, complemented
19C3×#1009C2211yescharacteristic, complemented
20C3×#1004C2211yescharacteristic
21C3×#1004C2211yescharacteristic, complemented
22C32×AGL(1,ℤ/8)C2211yescharacteristic, complemented
23C32×AGL(1,ℤ/8)C2211yescharacteristic, complemented
24C2×C32×D8C2211yescharacteristic, complemented
25C32×#131C2211yescharacteristic, complemented
26C3×#950C2211yescharacteristic
27C3×#940C2211yescharacteristic, complemented
28C3×#936C2211yescharacteristic, complemented
29C2×C3×#214C2211yescharacteristic, complemented
30C3×#932C2211yescharacteristic
31C3×#932C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic, complemented
33C3×#916—21no—
34C3×#915—21no—
35C3×#914—21no—
36C3×D3×SD16—21no—
37C3×#912—21no—
38C3×#912—21no—
39C3×#911—21no—
40C3×#911—21no—
41C3×#911—21no—
42C3×#911—21no—
43C3×D3×D8—21no—
44C3×D3×D8—21no—
45C3×#909—21no—
46C3×#909C2211yescharacteristic, complemented
47C3×#909C2211yescharacteristic, complemented
48C3×#908—21no—
49C3×#908C2211yescharacteristic
50C3×#908C2211yescharacteristic, complemented
51C3×#907C2211yescharacteristic, complemented
52C3×#907C2211yescharacteristic, complemented
53C3×#904—21no—
54C3×#904C2211yescharacteristic
55C2×C3×#204—21no—
56C2×C3×#204C2211yescharacteristic, complemented
57C3×#901C2211yescharacteristic, complemented
58C32×#108C2211yescharacteristic, complemented
59C32×#100C2211yescharacteristic, complemented
60C32×#100C2211yescharacteristic, complemented
61C3×#837C2211yescharacteristic, complemented
62C3×#825C2211yescharacteristic, complemented
63C3×#825C2211yescharacteristic, complemented
64C3×#825C2211yescharacteristic, complemented
65C3×#824C2211yescharacteristic, complemented
66C3×#823C2211yescharacteristic, complemented
67C3×#822C2211yescharacteristic, complemented
68C3×#815C2211yescharacteristic, complemented
69C3×#577—31no—
70C3×#577—31no—
71C3×#576—31no—
72C3×#576—31no—
73#5775C2×C311yescharacteristic, complemented
74#5774C2×C311yescharacteristic, complemented
75#5757C2×C311yescharacteristic, complemented
76#5751C2×C311yescharacteristic, complemented
77C3×#496—31no—
78C3×#472—21no—
79C3×#472—31no—
80C3×#472D311yescharacteristic, complemented
81C3×#472C2×C311yescharacteristic, complemented
82C3×#471—31no—
83C3×#471—31no—
84C3×#455—31no—
85C3×#454—31no—
86C3×#453—31no—
87C3×#453—31no—
88C3×#444—31no—
89C3×#444—31no—
90#5201C2×C311yescharacteristic, complemented
91#5198C2×C311yescharacteristic, complemented
92#5154C2×C311yescharacteristic, complemented
93#5145C2×C311yescharacteristic, complemented
94#4898C2×C311yescharacteristic, complemented
95#4894C2×C311yescharacteristic, complemented
96#4749C2×C311yescharacteristic, complemented
97#4748C2×C311yescharacteristic, complemented
98#4747C2×C311yescharacteristic, complemented
99#4746C2×C311yescharacteristic, complemented
100C32×#41C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C2×C3×#67—41no—
104C2×C3×#67—41no—
105C2×C3×#67—41no—
106C3×#239—21no—
107C3×D3×Q8—21no—
108C3×#237—21no—
109C3×#237—21no—
110C3×#237—21no—
111C3×#237—21no—
112C3×#237—21no—
113C3×#237—41no—
114C3×D3×D4—21no—
115C3×D3×D4—21no—
116C3×D3×D4—21no—
117C3×D3×D4—21no—
118C3×D3×D4—21no—
119C3×D3×D4—41no—
120C3×#235—21no—
121C3×#235—21no—
122C3×#235C2311yescharacteristic
123C3×#235C2311yescharacteristic
124C3×#235C2311yescharacteristic
125C2×C3×D12—21no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×Dic6—21no—
128C2×C3×Dic6C2311yescharacteristic
129C32×SD16—21no—
130C32×SD16—21no—
131C32×D8—21no—
132C32×D8—21no—
133C32×D8—21no—
134C32×D8—21no—
135C32×M16—21no—
136C32×M16C2311yescharacteristic
137C32×M16C2311yescharacteristic
138C32×M16C2311yescharacteristic
139C2×C32×C8—21no—
140C2×C32×C8C2311yescharacteristic
141C3×#217—41no—
142C3×#216D411yescharacteristic, complemented
143C3×#215D411yescharacteristic, complemented
144C3×#214—21no—
145C3×#214—21no—
146C3×#214—21no—
147C3×#214—21no—
148C3×#214D411yescharacteristic, complemented
149C3×#213—21no—
150C3×#213—21no—
151C3×#213—21no—
152C3×#213—21no—
153C3×#213D411yescharacteristic, complemented
154C3×C4×Dic3C2311yescharacteristic
155C3×#208C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157C3×Dic12—21no—
158C3×Dic12—21no—
159C3×Dic12D411yescharacteristic, complemented
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×#204D411yescharacteristic, complemented
170C3×#204D411yescharacteristic, complemented
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#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, complemented
184#1004C22×C311yescharacteristic
185#1004C22×C311yescharacteristic, complemented
186C3×#137—31no—
187C3×#137—31no—
188C3×#137—61no—
189C3×#137—61no—
190C3×AGL(1,ℤ/8)—21no—
191C3×AGL(1,ℤ/8)—21no—
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×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
203C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
204C3×AGL(1,ℤ/8)C22×C311yescharacteristic, complemented
205C3×AGL(1,ℤ/8)C22×C311yescharacteristic, complemented
206C3×#135—31no—
207C3×#135—31no—
208C3×#135—61no—
209C3×#135—61no—
210C3×#135—61no—
211C3×#135—61no—
212C2×C3×SD16—31no—
213C2×C3×SD16—31no—
214C2×C3×SD16—61no—
215C2×C3×SD16—61no—
216C2×C3×D8—21no—
217C2×C3×D8—31no—
218C2×C3×D8—61no—
219C2×C3×D8—61no—
220C2×C3×D8C2×D311yescharacteristic, complemented
221C2×C3×D8C22×C311yescharacteristic, complemented
222C3×#131—21no—
223C3×#131—31no—
224C3×#131—31no—
225C3×#131—31no—
226C3×#131C2×D311yescharacteristic, complemented
227C3×#131C22×C311yescharacteristic, complemented
228C3×#127—31no—
229C3×#124—31no—
230#950C22×C311yescharacteristic
231#940C22×C311yescharacteristic, complemented
232#936C22×C311yescharacteristic, complemented
233C2×#214C22×C311yescharacteristic, complemented
234#932C22×C311yescharacteristic
235#932C22×C311yescharacteristic, complemented
236C2×#213C22×C311yescharacteristic, complemented
237#916—21no—
238#915—21no—
239#914—21no—
240D3×SD16—21no—
241#912—21no—
242#912—21no—
243#911—21no—
244#911—21no—
245#911—21no—
246#911—21no—
247D3×D8—21no—
248D3×D8—21no—
249#909—21no—
250#909C22×C311yescharacteristic, complemented
251#909C22×C311yescharacteristic, complemented
252#908—21no—
253#908C22×C311yescharacteristic
254#908C22×C311yescharacteristic, complemented
255#907C22×C311yescharacteristic, complemented
256#907C22×C311yescharacteristic, complemented
257#904—21no—
258#904C22×C311yescharacteristic
259C2×#204—21no—
260C2×#204C22×C311yescharacteristic, complemented
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—31no—
271C3×#100—21no—
272C3×#100—21no—
273C3×#100—31no—
274C3×#100C2×D311yescharacteristic, complemented
275C3×#100C2×D311yescharacteristic, complemented
276C3×#100C22×C311yescharacteristic, complemented
277C3×#100C22×C311yescharacteristic, complemented
278C3×#97—31no—
279#837C22×C311yescharacteristic, complemented
280#825C22×C311yescharacteristic, complemented
281#825C22×C311yescharacteristic, complemented
282#825C22×C311yescharacteristic, complemented
283#824C22×C311yescharacteristic, complemented
284#823C22×C311yescharacteristic, complemented
285#822C22×C311yescharacteristic, complemented
286#815C22×C311yescharacteristic, complemented
287C23×C32—21no—
288C23×C32—21no—
289C22×C3×D3—21no—
290C22×C3×D3—41no—
291C22×C3×D3—41no—
292C22×C3×D3—41no—
293C32×Q8C2×D411yescharacteristic
294C32×D4—21no—
295C32×D4—21no—
296C32×D4—21no—
297C32×D4—21no—
298C32×D4—21no—
299C32×D4C2×D411yescharacteristic
300C2×C32×C4—21no—
301C2×C32×C4C2411yescharacteristic
302C3×#67—21no—
303C3×#67—21no—
304C3×#67—21no—
305C3×#67—41no—
306C3×#67—41no—
307C3×#67—41no—
308C3×#67—41no—
309C3×#67—41no—
310C3×#67—41no—
311C3×#67—82no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3—41no—
315C2×C3×Dic3—41no—
316C2×C3×Dic3—41no—
317C3×D12—21no—
318C3×D12—21no—
319C3×D12—41no—
320C3×D12C2×D411yescharacteristic
321C3×D12C2×D411yescharacteristic
322C3×D12C2×D411yescharacteristic
323C3×C4×D3—21no—
324C3×C4×D3—21no—
325C3×C4×D3—21no—
326C3×C4×D3—41no—
327C3×C4×D3—41no—
328C3×Dic6—21no—
329C3×Dic6—21no—
330C3×Dic6—41no—
331C3×Dic6C2×D411yescharacteristic
332C3×Dic6C2×D411yescharacteristic
333C3×Dic6C2×D411yescharacteristic
334C32×C8—21no—
335C32×C8—21no—
336C32×C8—21no—
337C32×C8C2×D411yescharacteristic
338C32×C8C2×D411yescharacteristic
339C3×C3⋊C8—21no—
340C3×C3⋊C8C2×D411yescharacteristic
341C3×C3⋊C8C2×D411yescharacteristic
342#577—31no—
343#577—31no—
344#576—31no—
345#576—31no—
346#496—31no—
347#472—31no—
348#472C3×D311yescharacteristic, complemented
349#471—31no—
350#471—31no—
351#455—31no—
352#454—31no—
353#453—31no—
354#453—31no—
355#444—31no—
356#444—31no—
357C3×#41—21no—
358C3×#41—31no—
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×#41C23×C311yescharacteristic
372C2×C3×Q8—31no—
373C2×C3×Q8—61no—
374C2×C3×Q8—61no—
375C2×C3×D4—21no—
376C2×C3×D4—21no—
377C2×C3×D4—31no—
378C2×C3×D4—61no—
379C2×C3×D4—61no—
380C2×C3×D4—61no—
381C2×C3×D4—61no—
382C2×C3×D4—61no—
383C2×C3×D4—61no—
384C2×C3×D4—121no—
385C2×C3×D4—121no—
386C2×C3×D4—121no—
387C2×C3×D4—121no—
388C2×C3×D4C22×D311yescharacteristic
389C2×C3×D4C22×D311yescharacteristic
390C2×C3×D4C23×C311yescharacteristic
391C2×C3×D4C23×C311yescharacteristic
392C2×#67—41no—
393C2×#67—41no—
394C2×#67—41no—
395#239—21no—
396D3×Q8—21no—
397#237—21no—
398#237—21no—
399#237—21no—
400#237—21no—
401#237—21no—
402#237—41no—
403D3×D4—21no—
404D3×D4—21no—
405D3×D4—21no—
406D3×D4—21no—
407D3×D4—21no—
408D3×D4—41no—
409#235—21no—
410#235—21no—
411#235C23×C311yescharacteristic
412#235C23×C311yescharacteristic
413#235C23×C311yescharacteristic
414C2×D12—21no—
415C2×D12C23×C311yescharacteristic
416C2×Dic6—21no—
417C2×Dic6C23×C311yescharacteristic
418C3×Q16—31no—
419C3×Q16—31no—
420C3×Q16—61no—
421C3×Q16—61no—
422C3×SD16—21no—
423C3×SD16—21no—
424C3×SD16—21no—
425C3×SD16—21no—
426C3×SD16—31no—
427C3×SD16—31no—
428C3×SD16—31no—
429C3×SD16—31no—
430C3×SD16—41no—
431C3×SD16—41no—
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×D8—21no—
443C3×D8—21no—
444C3×D8—21no—
445C3×D8—21no—
446C3×D8—21no—
447C3×D8—21no—
448C3×D8—21no—
449C3×D8—21no—
450C3×D8—31no—
451C3×D8—31no—
452C3×D8—41no—
453C3×D8—41no—
454C3×D8—41no—
455C3×D8—41no—
456C3×D8—61no—
457C3×D8—61no—
458C3×D8—61no—
459C3×D8—61no—
460C3×D8—61no—
461C3×D8—61no—
462C3×M16—21no—
463C3×M16—21no—
464C3×M16—21no—
465C3×M16—21no—
466C3×M16—21no—
467C3×M16—31no—
468C3×M16—41no—
469C3×M16—61no—
470C3×M16—61no—
471C3×M16—61no—
472C3×M16C22×D311yescharacteristic
473C3×M16C22×D311yescharacteristic
474C3×M16C22×D311yescharacteristic
475C3×M16C23×C311yescharacteristic
476C3×M16C23×C311yescharacteristic
477C3×M16C23×C311yescharacteristic
478C2×C3×C8—21no—
479C2×C3×C8—21no—
480C2×C3×C8—21no—
481C2×C3×C8—31no—
482C2×C3×C8—41no—
483C2×C3×C8—61no—
484C2×C3×C8—61no—
485C2×C3×C8—61no—
486C2×C3×C8C22×D311yescharacteristic
487C2×C3×C8C23×C311yescharacteristic
488C3×C22⋊C4—121no—
489C3×C42—31no—
490#217—41no—
491#216C3×D411yescharacteristic, complemented
492#215C3×D411yescharacteristic, complemented
493#214—21no—
494#214—21no—
495#214—21no—
496#214—21no—
497#214C3×D411yescharacteristic, complemented
498#213—21no—
499#213—21no—
500#213—21no—
501#213—21no—
502#213C3×D411yescharacteristic, complemented
503C4×Dic3C23×C311yescharacteristic
504#208C23×C311yescharacteristic
505C2×C3⋊C8C23×C311yescharacteristic
506Dic12—21no—
507Dic12—21no—
508Dic12C3×D411yescharacteristic, complemented
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#204C3×D411yescharacteristic, complemented
519#204C3×D411yescharacteristic, complemented
520ΓL(1,𝔽25)—21no—
521ΓL(1,𝔽25)—21no—
522ΓL(1,𝔽25)—21no—
523D3×C8—21no—
524D3×C8—21no—
525D3×C8—21no—
526C22×C32—21no—
527C22×C32—41no—
528C22×C32—41no—
529C22×C32—81no—
530C22×C32—81no—
531C22×C32H(5,𝔽2)11yescharacteristic
532C2×C3×D3—21no—
533C2×C3×D3—21no—
534C2×C3×D3—21no—
535C2×C3×D3—41no—
536C2×C3×D3—81no—
537C2×C3×D3—161no—
538C2×C3×D3—161no—
539C2×C3×D3—161no—
540C32×C4—21no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3×Dic3—21no—
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—41no—
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)—61no—
561AGL(1,ℤ/8)—61no—
562AGL(1,ℤ/8)—61no—
563AGL(1,ℤ/8)—61no—
564AGL(1,ℤ/8)—61no—
565AGL(1,ℤ/8)—61no—
566AGL(1,ℤ/8)C2×C3×D311yescharacteristic, complemented
567AGL(1,ℤ/8)C2×C3×D311yescharacteristic, complemented
568#135—31no—
569#135—31no—
570#135—61no—
571#135—61no—
572#135—61no—
573#135—61no—
574C2×SD16—31no—
575C2×SD16—31no—
576C2×SD16—61no—
577C2×SD16—61no—
578C2×D8—31no—
579C2×D8—61no—
580C2×D8—61no—
581C2×D8C2×C3×D311yescharacteristic, complemented
582#131—31no—
583#131—31no—
584#131—31no—
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#104—31no—
593#104—31no—
594#101—31no—
595#100—31no—
596#100C2×C3×D311yescharacteristic, complemented
597#100C2×C3×D311yescharacteristic, complemented
598#97—31no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—61no—
606C23×C3—121no—
607C23×C3—121no—
608C23×C3—121no—
609C22×D3—21no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—41no—
613C3×Q8—21no—
614C3×Q8—31no—
615C3×Q8—31no—
616C3×Q8—31no—
617C3×Q8—61no—
618C3×Q8—61no—
619C3×Q8—121no—
620C3×Q8D3×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—21no—
629C3×D4—21no—
630C3×D4—21no—
631C3×D4—21no—
632C3×D4—21no—
633C3×D4—31no—
634C3×D4—31no—
635C3×D4—31no—
636C3×D4—41no—
637C3×D4—41no—
638C3×D4—41no—
639C3×D4—41no—
640C3×D4—41no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—121no—
647C3×D4—121no—
648C3×D4—121no—
649C3×D4—121no—
650C3×D4—121no—
651C3×D4—121no—
652C3×D4—121no—
653C3×D4—242no—
654C3×D4D3×D411yescharacteristic
655C3×D4C2×C3×D411yescharacteristic
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—41no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
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—21no—
675#67—41no—
676#67—41no—
677#67—41no—
678#67—41no—
679#67—41no—
680#67—41no—
681#67—82no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—41no—
685C2×Dic3—41no—
686C2×Dic3—41no—
687D12—21no—
688D12—21no—
689D12—41no—
690D12C2×C3×D411yescharacteristic
691D12C2×C3×D411yescharacteristic
692D12C2×C3×D411yescharacteristic
693C4×D3—21no—
694C4×D3—21no—
695C4×D3—21no—
696C4×D3—41no—
697C4×D3—41no—
698Dic6—21no—
699Dic6—21no—
700Dic6—41no—
701Dic6C2×C3×D411yescharacteristic
702Dic6C2×C3×D411yescharacteristic
703Dic6C2×C3×D411yescharacteristic
704C3×C8—21no—
705C3×C8—21no—
706C3×C8—21no—
707C3×C8—21no—
708C3×C8—21no—
709C3×C8—21no—
710C3×C8—21no—
711C3×C8—21no—
712C3×C8—31no—
713C3×C8—31no—
714C3×C8—41no—
715C3×C8—41no—
716C3×C8—41no—
717C3×C8—61no—
718C3×C8D3×D411yescharacteristic
719C3×C8D3×D411yescharacteristic
720C3×C8C2×C3×D411yescharacteristic
721C3×C8C2×C3×D411yescharacteristic
722C3⋊C8—21no—
723C3⋊C8C2×C3×D411yescharacteristic
724C3⋊C8C2×C3×D411yescharacteristic
725C2×C32—21no—
726C2×C32—41no—
727C2×C32—81no—
728C2×C32—81no—
729C2×C32D4211yescharacteristic
730C3×D3—41no—
731C3×D3—41no—
732C3×D3—41no—
733C3×D3—81no—
734#41—31no—
735#41—31no—
736#41—31no—
737#41—61no—
738#41—61no—
739#41—61no—
740#41—61no—
741#41—61no—
742#41—61no—
743#41—61no—
744#41—61no—
745#41—121no—
746#41C22×C3×D311yescharacteristic
747C2×Q8—31no—
748C2×Q8—61no—
749C2×Q8—61no—
750C2×D4—31no—
751C2×D4—61no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—121no—
758C2×D4—121no—
759C2×D4—121no—
760C2×D4—121no—
761C2×D4C22×C3×D311yescharacteristic
762C2×D4C22×C3×D311yescharacteristic
763Q16—31no—
764Q16—31no—
765Q16—61no—
766Q16—61no—
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—
781SD16—61no—
782SD16—61no—
783D8—21no—
784D8—21no—
785D8—21no—
786D8—21no—
787D8—31no—
788D8—31no—
789D8—61no—
790D8—61no—
791D8—61no—
792D8—61no—
793D8—61no—
794D8—61no—
795M16—21no—
796M16—31no—
797M16—61no—
798M16—61no—
799M16—61no—
800M16C22×C3×D311yescharacteristic
801M16C22×C3×D311yescharacteristic
802M16C22×C3×D311yescharacteristic
803C2×C8—21no—
804C2×C8—31no—
805C2×C8—61no—
806C2×C8—61no—
807C2×C8—61no—
808C2×C8C22×C3×D311yescharacteristic
809C22⋊C4—121no—
810C42—31no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—81no—
823C22×C3—81no—
824C22×C3—81no—
825C22×C3—81no—
826C22×C3—81no—
827C22×C3—81no—
828C22×C3—121no—
829C22×C3—161no—
830C22×C3—161no—
831C22×C3—241no—
832C22×C3—481no—
833C22×C3—481no—
834C22×C3—481no—
835C22×C3#100911yescharacteristic
836C22×C3C3×H(5,𝔽2)11yescharacteristic
837C2×D3—21no—
838C2×D3—21no—
839C2×D3—21no—
840C2×D3—41no—
841C2×D3—81no—
842C2×D3—161no—
843C2×D3—161no—
844C2×D3—161no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—21no—
849C3×C4—41no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—121no—
854C3×C4—121no—
855C3×C4C2×D3×D411yescharacteristic
856C3×C4C2×D3×D411yescharacteristic
857C3×C4C22×C3×D411yescharacteristic
858C3×C4C22×C3×D411yescharacteristic
859Dic3—21no—
860Dic3—21no—
861Dic3—21no—
862Dic3—41no—
863Dic3—41no—
864C32#328811yescharacteristic, complemented, Sylow
865C23—21no—
866C23—21no—
867C23—61no—
868C23—121no—
869C23—121no—
870C23—121no—
871Q8—31no—
872Q8—31no—
873Q8—31no—
874Q8—61no—
875Q8—61no—
876Q8—121no—
877Q8C3×D3×D411yescharacteristic
878D4—21no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—21no—
883D4—31no—
884D4—31no—
885D4—31no—
886D4—61no—
887D4—61no—
888D4—61no—
889D4—61no—
890D4—61no—
891D4—121no—
892D4—121no—
893D4—121no—
894D4—121no—
895D4—121no—
896D4—121no—
897D4—121no—
898D4—242no—
899D4C3×D3×D411yescharacteristic
900C2×C4—21no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—121no—
907C2×C4—121no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4—121no—
911C2×C4C23×C3×D311yescharacteristic
912C8—21no—
913C8—21no—
914C8—21no—
915C8—31no—
916C8—31no—
917C8—61no—
918C8C3×D3×D411yescharacteristic
919C8C3×D3×D411yescharacteristic
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—41no—
926C2×C3—81no—
927C2×C3—81no—
928C2×C3—81no—
929C2×C3—81no—
930C2×C3—81no—
931C2×C3—121no—
932C2×C3—121no—
933C2×C3—121no—
934C2×C3—161no—
935C2×C3—161no—
936C2×C3—241no—
937C2×C3#560911yescharacteristic
938C2×C3C3×D4211yescharacteristic
939D3—41no—
940D3—41no—
941D3—41no—
942D3—81no—
943C22—21no—
944C22—41no—
945C22—41no—
946C22—61no—
947C22—61no—
948C22—61no—
949C22—81no—
950C22—81no—
951C22—121no—
952C22—241no—
953C22—481no—
954C22—481no—
955C22—481no—
956C22C3×#100911yescharacteristic
957C4—21no—
958C4—61no—
959C4—61no—
960C4—61no—
961C4—121no—
962C4—121no—
963C4C2×C3×D3×D411yescharacteristic
964C4C2×C3×D3×D411yescharacteristic
965C3—21no—
966C3#8093911yescharacteristic, direct product factor
967C3C3×#328811yescharacteristic, complemented
968C2—21no—
969C2—41no—
970C2—81no—
971C2—81no—
972C2—121no—
973C2—121no—
974C2—121no—
975C2—241no—
976C2C3×#560911yescharacteristic
subgroupG/H
centerC2×C3#5609
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#472C2
socleC2×C32D42
hypercenterC3×#472D3
hypocenterC3C3×#3288
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#472

Complements

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

NH ≅ G/Ntype
1. C3×#5775C2semidirect
2. C3×#5774C2semidirect
3. C3×#5757C2semidirect
4. C3×#5751C2semidirect
5. C32×#472C2semidirect
6. C3×#5201C2semidirect
7. C3×#5198C2semidirect
8. C3×#5154C2semidirect
9. C3×#5145C2semidirect
10. C3×#4898C2semidirect
11. C3×#4894C2semidirect
12. C3×#4749C2semidirect
13. C3×#4748C2semidirect
14. C3×#4747C2semidirect
15. C3×#4746C2semidirect
17. #80939C3direct (N × H)
18. C3×#1010C22semidirect
19. C3×#1009C22semidirect
21. C3×#1004C22semidirect
22. C32×AGL(1,ℤ/8)C22semidirect
23. C32×AGL(1,ℤ/8)C22semidirect
24. C2×C32×D8C22semidirect
25. C32×#131C22semidirect
27. C3×#940C22semidirect
28. C3×#936C22semidirect
29. C2×C3×#214C22semidirect
31. C3×#932C22semidirect
32. C2×C3×#213C22semidirect
46. C3×#909C22semidirect
47. C3×#909C22semidirect
50. C3×#908C22semidirect
51. C3×#907C22semidirect
52. C3×#907C22semidirect
56. C2×C3×#204C22semidirect
57. C3×#901C22semidirect
58. C32×#108C22semidirect
59. C32×#100C22semidirect
60. C32×#100C22semidirect
61. C3×#837C22semidirect
62. C3×#825C22semidirect
63. C3×#825C22semidirect
64. C3×#825C22semidirect
65. C3×#824C22semidirect
66. C3×#823C22semidirect
67. C3×#822C22semidirect
68. C3×#815C22semidirect
73. #5775C2×C3semidirect
74. #5774C2×C3semidirect
75. #5757C2×C3semidirect
76. #5751C2×C3semidirect
80. C3×#472D3semidirect
81. C3×#472C2×C3semidirect
90. #5201C2×C3semidirect
91. #5198C2×C3semidirect
92. #5154C2×C3semidirect
93. #5145C2×C3semidirect
94. #4898C2×C3semidirect
95. #4894C2×C3semidirect
96. #4749C2×C3semidirect
97. #4748C2×C3semidirect
98. #4747C2×C3semidirect
99. #4746C2×C3semidirect
142. C3×#216D4semidirect
143. C3×#215D4semidirect
148. C3×#214D4semidirect
153. C3×#213D4semidirect
159. C3×Dic12D4semidirect
162. C3×D24D4semidirect
169. C3×#204D4semidirect
170. C3×#204D4semidirect
182. #1010C22×C3semidirect
183. #1009C22×C3semidirect
185. #1004C22×C3semidirect
202. C3×AGL(1,ℤ/8)C2×D3semidirect
203. C3×AGL(1,ℤ/8)C2×D3semidirect
204. C3×AGL(1,ℤ/8)C22×C3semidirect
205. C3×AGL(1,ℤ/8)C22×C3semidirect
220. C2×C3×D8C2×D3semidirect
221. C2×C3×D8C22×C3semidirect
226. C3×#131C2×D3semidirect
227. C3×#131C22×C3semidirect
231. #940C22×C3semidirect
232. #936C22×C3semidirect
233. C2×#214C22×C3semidirect
235. #932C22×C3semidirect
236. C2×#213C22×C3semidirect
250. #909C22×C3semidirect
251. #909C22×C3semidirect
254. #908C22×C3semidirect
255. #907C22×C3semidirect
256. #907C22×C3semidirect
260. C2×#204C22×C3semidirect
261. #901C22×C3semidirect
264. C3×#108C2×D3semidirect
265. C3×#108C22×C3semidirect
274. C3×#100C2×D3semidirect
275. C3×#100C2×D3semidirect
276. C3×#100C22×C3semidirect
277. C3×#100C22×C3semidirect
279. #837C22×C3semidirect
280. #825C22×C3semidirect
281. #825C22×C3semidirect
282. #825C22×C3semidirect
283. #824C22×C3semidirect
284. #823C22×C3semidirect
285. #822C22×C3semidirect
286. #815C22×C3semidirect
348. #472C3×D3semidirect
491. #216C3×D4semidirect
492. #215C3×D4semidirect
497. #214C3×D4semidirect
502. #213C3×D4semidirect
508. Dic12C3×D4semidirect
511. D24C3×D4semidirect
518. #204C3×D4semidirect
519. #204C3×D4semidirect
566. AGL(1,ℤ/8)C2×C3×D3semidirect
567. AGL(1,ℤ/8)C2×C3×D3semidirect
581. C2×D8C2×C3×D3semidirect
585. #131C2×C3×D3semidirect
589. #108C2×C3×D3semidirect
596. #100C2×C3×D3semidirect
597. #100C2×C3×D3semidirect
864. C32#3288semidirect
966. C3#80939direct (N × H)
967. C3C3×#3288semidirect

Maximal subgroups

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

subgroupindex
C3×#57752
C3×#57742
C3×#57572
C3×#57512
C32×#4722
C3×#52012
C3×#51982
C3×#51542
C3×#51452
C3×#48982
C3×#48942
C3×#47492
C3×#47482
C3×#47472
C3×#47462
C3×#32883
#809393