Finite Group Databasebeta

← C3×#80938 #11868081

Subgroups — C3×#80938 #11868081

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5773C211yesmaximal, characteristic, complemented
2C3×D3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C2×C3×#911C211yesmaximal, characteristic, complemented
4C3×#5750C211yesmaximal, characteristic, complemented
5C32×#472C211yesmaximal, characteristic, complemented
6C3×#5200C211yesmaximal, characteristic, complemented
7C3×#5199C211yesmaximal, characteristic, complemented
8C3×#5160C211yesmaximal, characteristic, complemented
9C3×#5141C211yesmaximal, characteristic, complemented
10C3×#4898C211yesmaximal, characteristic, complemented
11C3×#4893C211yesmaximal, characteristic, complemented
12C3×#4749C211yesmaximal, characteristic, complemented
13C3×#4748C211yesmaximal, characteristic, complemented
14C3×#4745C211yesmaximal, characteristic, complemented
15C3×D3×#100C211yesmaximal, characteristic, complemented
16C3×#3068—31nomaximal
17#80938C311yesmaximal, characteristic, direct product factor
18C3×D3×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C32×AGL(1,ℤ/8)C2211yescharacteristic
22C32×AGL(1,ℤ/8)C2211yescharacteristic, complemented
23C2×C32×D8C2211yescharacteristic, complemented
24C32×#131C2211yescharacteristic, complemented
25C3×#951C2211yescharacteristic, complemented
26C3×#949C2211yescharacteristic
27C3×#948C2211yescharacteristic, complemented
28C2×C3×#214C2211yescharacteristic, complemented
29C3×#932C2211yescharacteristic
30C3×#932C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic, complemented
32C3×#916—21no—
33C3×#915—21no—
34C3×#914—21no—
35C3×D3×SD16—21no—
36C3×#912—21no—
37C3×#911—21no—
38C3×#911—21no—
39C3×#911—21no—
40C3×#911—21no—
41C3×#911—21no—
42C3×#911—21no—
43C3×D3×D8—21no—
44C3×#909C2211yescharacteristic, complemented
45C3×#908C2211yescharacteristic
46C3×#907—21no—
47C3×#907C2211yescharacteristic, complemented
48C3×D3×M16—21no—
49C3×D3×M16C2211yescharacteristic
50C3×D3×M16C2211yescharacteristic
51C3×D3×M16C2211yescharacteristic
52C2×C3×#204C2211yescharacteristic, complemented
53C3×#901—21no—
54C3×#901C2211yescharacteristic, complemented
55C2×C3×ΓL(1,𝔽25)—21no—
56C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
57C32×#108C2211yescharacteristic, complemented
58C32×#100C2211yescharacteristic, complemented
59C32×#100C2211yescharacteristic, complemented
60C3×#833C2211yescharacteristic, complemented
61C3×#833C2211yescharacteristic, complemented
62C3×#824C2211yescharacteristic, complemented
63C3×#824C2211yescharacteristic, complemented
64C3×#823C2211yescharacteristic, complemented
65C3×#823C2211yescharacteristic, complemented
66C3×#822C2211yescharacteristic, complemented
67C3×#822C2211yescharacteristic, complemented
68C3×#819C2211yescharacteristic, complemented
69C3×#575—31no—
70C2×C3×AGL(1,ℤ/8)—31no—
71C2×C3×AGL(1,ℤ/8)—31no—
72C3×#568—31no—
73#5773C2×C311yescharacteristic, complemented
74D3×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
75C2×#911C2×C311yescharacteristic, complemented
76#5750C2×C311yescharacteristic, complemented
77C3×#472—21no—
78C3×#472—31no—
79C3×#472—31no—
80C3×#472—31no—
81C3×#472D311yescharacteristic, complemented
82C3×#472C2×C311yescharacteristic, complemented
83C3×#471—31no—
84C3×#471—31no—
85C3×#471—31no—
86C3×#471—31no—
87C3×#430—31no—
88C3×#413—31no—
89C2×C3×#100—31no—
90#5200C2×C311yescharacteristic, complemented
91#5199C2×C311yescharacteristic, complemented
92#5160C2×C311yescharacteristic, complemented
93#5141C2×C311yescharacteristic, complemented
94#4898C2×C311yescharacteristic, complemented
95#4893C2×C311yescharacteristic, complemented
96#4749C2×C311yescharacteristic, complemented
97#4748C2×C311yescharacteristic, complemented
98#4745C2×C311yescharacteristic, complemented
99D3×#100C2×C311yescharacteristic, complemented
100C23×C3×D3—21no—
101C32×#41C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C2×C32×D4C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C22×C3×Dic3—21no—
107C3×#239D411yescharacteristic
108C3×D3×Q8D411yescharacteristic
109C3×#237—21no—
110C3×#237—21no—
111C3×#237—21no—
112C3×#237—21no—
113C3×#237—21no—
114C3×#237D411yescharacteristic
115C3×D3×D4—21no—
116C3×D3×D4—21no—
117C3×D3×D4—21no—
118C3×D3×D4—21no—
119C3×D3×D4—21no—
120C3×D3×D4D411yescharacteristic
121C3×#235—21no—
122C3×#235C2311yescharacteristic
123C2×C3×D12C2311yescharacteristic
124C2×C3×C4×D3—21no—
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×Dic6C2311yescharacteristic
127C32×SD16—21no—
128C32×SD16—21no—
129C32×D8—21no—
130C32×D8—21no—
131C32×D8—21no—
132C32×D8—21no—
133C32×M16—21no—
134C32×M16C2311yescharacteristic
135C32×M16C2311yescharacteristic
136C32×M16C2311yescharacteristic
137C2×C32×C8—21no—
138C2×C32×C8C2311yescharacteristic
139C3×#216—21no—
140C3×#215—21no—
141C3×#214—21no—
142C3×#214—21no—
143C3×#214—21no—
144C3×#214—21no—
145C3×#214—21no—
146C3×#213—21no—
147C3×#213—21no—
148C3×#213—21no—
149C3×#213—21no—
150C3×#213—21no—
151C3×#208—21no—
152C3×#208C2311yescharacteristic
153C3×#208C2311yescharacteristic
154C3×#208C2311yescharacteristic
155C2×C3×C3⋊C8—21no—
156C2×C3×C3⋊C8C2311yescharacteristic
157C3×Dic12—21no—
158C3×D24—21no—
159C3×#204—21no—
160C3×#204—21no—
161C3×#204—21no—
162C3×#204—21no—
163C3×ΓL(1,𝔽25)—21no—
164C3×ΓL(1,𝔽25)—21no—
165C3×ΓL(1,𝔽25)—21no—
166C3×ΓL(1,𝔽25)—21no—
167C3×ΓL(1,𝔽25)—21no—
168C3×ΓL(1,𝔽25)D411yescharacteristic
169C3×ΓL(1,𝔽25)D411yescharacteristic
170C3×ΓL(1,𝔽25)D411yescharacteristic
171C3×ΓL(1,𝔽25)D411yescharacteristic
172C3×D3×C8—21no—
173C3×D3×C8—21no—
174C3×D3×C8—21no—
175C3×D3×C8—21no—
176C3×D3×C8—21no—
177#3068—31noSylow
178C2×C3×#41—31no—
179C2×C3×#41—31no—
180C22×C3×D4—31no—
181D3×#41C22×C311yescharacteristic
182C2×#237C22×C311yescharacteristic
183C2×D3×D4C22×C311yescharacteristic
184C3×#137—31no—
185C3×#137—31no—
186C3×#137—61no—
187C3×AGL(1,ℤ/8)—21no—
188C3×AGL(1,ℤ/8)—21no—
189C3×AGL(1,ℤ/8)—31no—
190C3×AGL(1,ℤ/8)—31no—
191C3×AGL(1,ℤ/8)—31no—
192C3×AGL(1,ℤ/8)—31no—
193C3×AGL(1,ℤ/8)—61no—
194C3×AGL(1,ℤ/8)—61no—
195C3×AGL(1,ℤ/8)—61no—
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)C2×D311yescharacteristic
201C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
202C3×AGL(1,ℤ/8)C22×C311yescharacteristic
203C3×AGL(1,ℤ/8)C22×C311yescharacteristic, complemented
204C3×#135—61no—
205C3×#135—61no—
206C2×C3×SD16—31no—
207C2×C3×SD16—31no—
208C2×C3×SD16—61no—
209C2×C3×D8—21no—
210C2×C3×D8—31no—
211C2×C3×D8—61no—
212C2×C3×D8C2×D311yescharacteristic, complemented
213C2×C3×D8C22×C311yescharacteristic, complemented
214C3×#131—21no—
215C3×#131—31no—
216C3×#131—31no—
217C3×#131—31no—
218C3×#131—61no—
219C3×#131—61no—
220C3×#131C2×D311yescharacteristic, complemented
221C3×#131C22×C311yescharacteristic, complemented
222C2×C3×M16—31no—
223C2×C3×M16—31no—
224C2×C3×M16—31no—
225C2×C3×M16—31no—
226C2×C3×M16—61no—
227C2×C3×M16—61no—
228#951C22×C311yescharacteristic, complemented
229#949C22×C311yescharacteristic
230#948C22×C311yescharacteristic, complemented
231C2×#214C22×C311yescharacteristic, complemented
232#932C22×C311yescharacteristic
233#932C22×C311yescharacteristic, complemented
234C2×#213C22×C311yescharacteristic, complemented
235#916—21no—
236#915—21no—
237#914—21no—
238D3×SD16—21no—
239#912—21no—
240#911—21no—
241#911—21no—
242#911—21no—
243#911—21no—
244#911—21no—
245#911—21no—
246D3×D8—21no—
247#909C22×C311yescharacteristic, complemented
248#908C22×C311yescharacteristic
249#907—21no—
250#907C22×C311yescharacteristic, complemented
251D3×M16—21no—
252D3×M16C22×C311yescharacteristic
253D3×M16C22×C311yescharacteristic
254D3×M16C22×C311yescharacteristic
255C2×#204C22×C311yescharacteristic, complemented
256#901—21no—
257#901C22×C311yescharacteristic, complemented
258C2×ΓL(1,𝔽25)—21no—
259C2×ΓL(1,𝔽25)C22×C311yescharacteristic
260C3×#108—21no—
261C3×#108—31no—
262C3×#108—31no—
263C3×#108—31no—
264C3×#108C2×D311yescharacteristic, complemented
265C3×#108C22×C311yescharacteristic, complemented
266C3×#101—31no—
267C3×#101—31no—
268C3×#100—21no—
269C3×#100—21no—
270C3×#100—31no—
271C3×#100—31no—
272C3×#100—31no—
273C3×#100—31no—
274C3×#100C2×D311yescharacteristic, complemented
275C3×#100C2×D311yescharacteristic, complemented
276C3×#100C22×C311yescharacteristic, complemented
277C3×#100C22×C311yescharacteristic, complemented
278#833C22×C311yescharacteristic, complemented
279#833C22×C311yescharacteristic, complemented
280#824C22×C311yescharacteristic, complemented
281#824C22×C311yescharacteristic, complemented
282#823C22×C311yescharacteristic, complemented
283#823C22×C311yescharacteristic, complemented
284#822C22×C311yescharacteristic, complemented
285#822C22×C311yescharacteristic, complemented
286#819C22×C311yescharacteristic, complemented
287C23×C32—21no—
288C23×C32—21no—
289C22×C3×D3—21no—
290C22×C3×D3—21no—
291C22×C3×D3—41no—
292C22×C3×D3—41no—
293C22×C3×D3—82no—
294C22×C3×D3#4111yescharacteristic
295C32×Q8C2×D411yescharacteristic
296C32×D4—21no—
297C32×D4—21no—
298C32×D4—21no—
299C32×D4—21no—
300C32×D4—21no—
301C32×D4C2×D411yescharacteristic
302C2×C32×C4—21no—
303C2×C32×C4C2411yescharacteristic
304C3×#67—21no—
305C3×#67—21no—
306C3×#67—21no—
307C3×#67—41no—
308C3×#67—41no—
309C3×#67—41no—
310C3×#67—41no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—41no—
314C2×C3×Dic3—41no—
315C2×C3×Dic3#4111yescharacteristic
316C3×D12—21no—
317C3×D12—21no—
318C3×D12—21no—
319C3×D12C2×D411yescharacteristic
320C3×C4×D3—21no—
321C3×C4×D3—21no—
322C3×C4×D3—21no—
323C3×C4×D3C2×D411yescharacteristic
324C3×C4×D3C2×D411yescharacteristic
325C3×C4×D3C2×D411yescharacteristic
326C3×C4×D3C2×D411yescharacteristic
327C3×Dic6—21no—
328C3×Dic6—21no—
329C3×Dic6—21no—
330C3×Dic6C2×D411yescharacteristic
331C32×C8—21no—
332C32×C8—21no—
333C32×C8—21no—
334C32×C8C2×D411yescharacteristic
335C32×C8C2×D411yescharacteristic
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8—21no—
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341#575—31no—
342C2×AGL(1,ℤ/8)—31no—
343C2×AGL(1,ℤ/8)—31no—
344#568—31no—
345#472—31no—
346#472—31no—
347#472—31no—
348#472C3×D311yescharacteristic, complemented
349#471—31no—
350#471—31no—
351#471—31no—
352#471—31no—
353#430—31no—
354#413—31no—
355C2×#100—31no—
356C24×C3—61no—
357C23×D3—21no—
358C3×#41—21no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—31no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41—61no—
366C3×#41—61no—
367C3×#41—61no—
368C3×#41C22×D311yescharacteristic
369C3×#41C23×C311yescharacteristic
370C2×C3×Q8—31no—
371C2×C3×Q8—31no—
372C2×C3×D4—21no—
373C2×C3×D4—21no—
374C2×C3×D4—31no—
375C2×C3×D4—31no—
376C2×C3×D4—61no—
377C2×C3×D4—61no—
378C2×C3×D4—61no—
379C2×C3×D4—61no—
380C2×C3×D4—61no—
381C2×C3×D4—61no—
382C2×C3×D4—61no—
383C2×C3×D4C22×D311yescharacteristic
384C2×C3×D4C22×D311yescharacteristic
385C2×C3×D4C23×C311yescharacteristic
386C2×C3×D4C23×C311yescharacteristic
387C22×C3×C4—31no—
388C22×C3×C4—61no—
389C22×C3×C4—61no—
390C2×#67—21no—
391C2×#67—21no—
392C22×Dic3—21no—
393#239C3×D411yescharacteristic
394D3×Q8C3×D411yescharacteristic
395#237—21no—
396#237—21no—
397#237—21no—
398#237—21no—
399#237—21no—
400#237C3×D411yescharacteristic
401D3×D4—21no—
402D3×D4—21no—
403D3×D4—21no—
404D3×D4—21no—
405D3×D4—21no—
406D3×D4C3×D411yescharacteristic
407#235—21no—
408#235C23×C311yescharacteristic
409C2×D12C23×C311yescharacteristic
410C2×C4×D3—21no—
411C2×C4×D3C23×C311yescharacteristic
412C2×Dic6C23×C311yescharacteristic
413C3×Q16—61no—
414C3×Q16—61no—
415C3×SD16—21no—
416C3×SD16—21no—
417C3×SD16—21no—
418C3×SD16—21no—
419C3×SD16—41no—
420C3×SD16—41no—
421C3×SD16—61no—
422C3×SD16—61no—
423C3×SD16—61no—
424C3×SD16—61no—
425C3×SD16—61no—
426C3×SD16—61no—
427C3×SD16—61no—
428C3×SD16—61no—
429C3×SD16—61no—
430C3×SD16—61no—
431C3×D8—21no—
432C3×D8—21no—
433C3×D8—21no—
434C3×D8—21no—
435C3×D8—21no—
436C3×D8—21no—
437C3×D8—21no—
438C3×D8—21no—
439C3×D8—41no—
440C3×D8—41no—
441C3×D8—41no—
442C3×D8—41no—
443C3×D8—61no—
444C3×D8—61no—
445C3×D8—61no—
446C3×D8—61no—
447C3×D8—61no—
448C3×D8—61no—
449C3×M16—21no—
450C3×M16—21no—
451C3×M16—21no—
452C3×M16—21no—
453C3×M16—21no—
454C3×M16—31no—
455C3×M16—31no—
456C3×M16—31no—
457C3×M16—31no—
458C3×M16—31no—
459C3×M16—31no—
460C3×M16—31no—
461C3×M16—41no—
462C3×M16—61no—
463C3×M16—61no—
464C3×M16—61no—
465C3×M16—61no—
466C3×M16—61no—
467C3×M16—61no—
468C3×M16C22×D311yescharacteristic
469C3×M16C22×D311yescharacteristic
470C3×M16C22×D311yescharacteristic
471C3×M16C23×C311yescharacteristic
472C3×M16C23×C311yescharacteristic
473C3×M16C23×C311yescharacteristic
474C2×C3×C8—21no—
475C2×C3×C8—21no—
476C2×C3×C8—21no—
477C2×C3×C8—31no—
478C2×C3×C8—41no—
479C2×C3×C8—61no—
480C2×C3×C8—61no—
481C2×C3×C8—61no—
482C2×C3×C8—61no—
483C2×C3×C8—61no—
484C2×C3×C8—61no—
485C2×C3×C8C22×D311yescharacteristic
486C2×C3×C8C23×C311yescharacteristic
487#216—21no—
488#215—21no—
489#214—21no—
490#214—21no—
491#214—21no—
492#214—21no—
493#214—21no—
494#213—21no—
495#213—21no—
496#213—21no—
497#213—21no—
498#213—21no—
499#208—21no—
500#208C23×C311yescharacteristic
501#208C23×C311yescharacteristic
502#208C23×C311yescharacteristic
503C2×C3⋊C8—21no—
504C2×C3⋊C8C23×C311yescharacteristic
505Dic12—21no—
506D24—21no—
507#204—21no—
508#204—21no—
509#204—21no—
510#204—21no—
511ΓL(1,𝔽25)—21no—
512ΓL(1,𝔽25)—21no—
513ΓL(1,𝔽25)—21no—
514ΓL(1,𝔽25)—21no—
515ΓL(1,𝔽25)—21no—
516ΓL(1,𝔽25)C3×D411yescharacteristic
517ΓL(1,𝔽25)C3×D411yescharacteristic
518ΓL(1,𝔽25)C3×D411yescharacteristic
519ΓL(1,𝔽25)C3×D411yescharacteristic
520D3×C8—21no—
521D3×C8—21no—
522D3×C8—21no—
523D3×C8—21no—
524D3×C8—21no—
525C22×C32—21no—
526C22×C32—41no—
527C22×C32—41no—
528C22×C32—81no—
529C22×C32—81no—
530C22×C32C2×#4111yescharacteristic
531C2×C3×D3—21no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—81no—
535C2×C3×D3—82no—
536C2×C3×D3—82no—
537C2×C3×D3—81no—
538C2×C3×D3#12111yescharacteristic
539C2×C3×D3#12111yescharacteristic
540C32×C4—21no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3×Dic3—21no—
544C3×Dic3—41no—
545C3×Dic3#12111yescharacteristic
546C3×Dic3#12111yescharacteristic
547C2×#41—31no—
548C2×#41—31no—
549C22×D4—31no—
550#137—31no—
551#137—31no—
552#137—61no—
553AGL(1,ℤ/8)—31no—
554AGL(1,ℤ/8)—31no—
555AGL(1,ℤ/8)—31no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—61no—
558AGL(1,ℤ/8)—61no—
559AGL(1,ℤ/8)—61no—
560AGL(1,ℤ/8)—61no—
561AGL(1,ℤ/8)—61no—
562AGL(1,ℤ/8)—61no—
563AGL(1,ℤ/8)—61no—
564AGL(1,ℤ/8)C2×C3×D311yescharacteristic
565AGL(1,ℤ/8)C2×C3×D311yescharacteristic, complemented
566#135—61no—
567#135—61no—
568C2×SD16—31no—
569C2×SD16—31no—
570C2×SD16—61no—
571C2×D8—31no—
572C2×D8—61no—
573C2×D8C2×C3×D311yescharacteristic, complemented
574#131—31no—
575#131—31no—
576#131—31no—
577#131—61no—
578#131—61no—
579#131C2×C3×D311yescharacteristic, complemented
580C2×M16—31no—
581C2×M16—31no—
582C2×M16—31no—
583C2×M16—31no—
584C2×M16—61no—
585C2×M16—61no—
586#108—31no—
587#108—31no—
588#108—31no—
589#108C2×C3×D311yescharacteristic, complemented
590#101—31no—
591#101—31no—
592#100—31no—
593#100—31no—
594#100—31no—
595#100—31no—
596#100C2×C3×D311yescharacteristic, complemented
597#100C2×C3×D311yescharacteristic, complemented
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—31no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—121no—
608C23×C3—121no—
609C23×C3—242no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—41no—
613C22×D3—41no—
614C22×D3—82no—
615C22×D3C3×#4111yescharacteristic
616C3×Q8—21no—
617C3×Q8—31no—
618C3×Q8—61no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×Q8D3×D411yescharacteristic
622C3×Q8C2×C3×D411yescharacteristic
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—21no—
634C3×D4—31no—
635C3×D4—41no—
636C3×D4—41no—
637C3×D4—41no—
638C3×D4—41no—
639C3×D4—41no—
640C3×D4—61no—
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×D4D3×D411yescharacteristic
651C3×D4C2×C3×D411yescharacteristic
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—31no—
656C2×C3×C4—31no—
657C2×C3×C4—31no—
658C2×C3×C4—31no—
659C2×C3×C4—31no—
660C2×C3×C4—41no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—121no—
667C2×C3×C4—121no—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C24×C311yescharacteristic
670#67—21no—
671#67—21no—
672#67—21no—
673#67—41no—
674#67—41no—
675#67—41no—
676#67—41no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—41no—
680C2×Dic3—41no—
681C2×Dic3C3×#4111yescharacteristic
682D12—21no—
683D12—21no—
684D12—21no—
685D12C2×C3×D411yescharacteristic
686C4×D3—21no—
687C4×D3—21no—
688C4×D3—21no—
689C4×D3C2×C3×D411yescharacteristic
690C4×D3C2×C3×D411yescharacteristic
691C4×D3C2×C3×D411yescharacteristic
692C4×D3C2×C3×D411yescharacteristic
693Dic6—21no—
694Dic6—21no—
695Dic6—21no—
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×C8—61no—
712C3×C8—61no—
713C3×C8D3×D411yescharacteristic
714C3×C8D3×D411yescharacteristic
715C3×C8C2×C3×D411yescharacteristic
716C3×C8C2×C3×D411yescharacteristic
717C3⋊C8—21no—
718C3⋊C8—21no—
719C3⋊C8—21no—
720C3⋊C8C2×C3×D411yescharacteristic
721C3⋊C8C2×C3×D411yescharacteristic
722C2×C32—21no—
723C2×C32—41no—
724C2×C32—81no—
725C2×C32—81no—
726C2×C32C2×#12111yescharacteristic
727C3×D3—21no—
728C3×D3—21no—
729C3×D3—41no—
730C3×D3—81no—
731C24—61no—
732#41—31no—
733#41—31no—
734#41—31no—
735#41—61no—
736#41—61no—
737#41—61no—
738#41—61no—
739#41—61no—
740#41—61no—
741#41C22×C3×D311yescharacteristic
742C2×Q8—31no—
743C2×Q8—31no—
744C2×D4—31no—
745C2×D4—31no—
746C2×D4—61no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—61no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—61no—
753C2×D4C22×C3×D311yescharacteristic
754C2×D4C22×C3×D311yescharacteristic
755C22×C4—31no—
756C22×C4—61no—
757C22×C4—61no—
758Q16—61no—
759Q16—61no—
760SD16—21no—
761SD16—21no—
762SD16—61no—
763SD16—61no—
764SD16—61no—
765SD16—61no—
766SD16—61no—
767SD16—61no—
768SD16—61no—
769SD16—61no—
770SD16—61no—
771SD16—61no—
772D8—21no—
773D8—21no—
774D8—21no—
775D8—21no—
776D8—61no—
777D8—61no—
778D8—61no—
779D8—61no—
780D8—61no—
781D8—61no—
782M16—21no—
783M16—31no—
784M16—31no—
785M16—31no—
786M16—31no—
787M16—31no—
788M16—31no—
789M16—31no—
790M16—61no—
791M16—61no—
792M16—61no—
793M16—61no—
794M16—61no—
795M16—61no—
796M16C22×C3×D311yescharacteristic
797M16C22×C3×D311yescharacteristic
798M16C22×C3×D311yescharacteristic
799C2×C8—21no—
800C2×C8—31no—
801C2×C8—61no—
802C2×C8—61no—
803C2×C8—61no—
804C2×C8—61no—
805C2×C8—61no—
806C2×C8—61no—
807C2×C8C22×C3×D311yescharacteristic
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—31no—
812C22×C3—31no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—61no—
819C22×C3—81no—
820C22×C3—81no—
821C22×C3—81no—
822C22×C3—81no—
823C22×C3—81no—
824C22×C3—81no—
825C22×C3—121no—
826C22×C3—121no—
827C22×C3—161no—
828C22×C3—161no—
829C22×C3—241no—
830C22×C3—241no—
831C22×C3—242no—
832C22×C3—242no—
833C22×C3D3×#4111yescharacteristic
834C22×C3C2×C3×#4111yescharacteristic
835C2×D3—21no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—81no—
839C2×D3—82no—
840C2×D3—82no—
841C2×D3—81no—
842C2×D3C3×#12111yescharacteristic
843C2×D3C3×#12111yescharacteristic
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—31no—
849C3×C4—31no—
850C3×C4—41no—
851C3×C4—61no—
852C3×C4—121no—
853C3×C4C2×D3×D411yescharacteristic
854C3×C4C2×D3×D411yescharacteristic
855C3×C4C22×C3×D411yescharacteristic
856C3×C4C22×C3×D411yescharacteristic
857Dic3—21no—
858Dic3—41no—
859Dic3C3×#12111yescharacteristic
860Dic3C3×#12111yescharacteristic
861C32#306811yescharacteristic, complemented, Sylow
862C23—21no—
863C23—21no—
864C23—31no—
865C23—61no—
866C23—61no—
867C23—121no—
868C23—121no—
869C23—242no—
870Q8—31no—
871Q8—61no—
872Q8—61no—
873Q8—61no—
874Q8C3×D3×D411yescharacteristic
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—31no—
881D4—61no—
882D4—61no—
883D4—61no—
884D4—61no—
885D4—61no—
886D4—61no—
887D4—121no—
888D4—121no—
889D4—121no—
890D4—121no—
891D4C3×D3×D411yescharacteristic
892C2×C4—21no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—31no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—121no—
904C2×C4—121no—
905C2×C4C23×C3×D311yescharacteristic
906C8—21no—
907C8—21no—
908C8—21no—
909C8—31no—
910C8—31no—
911C8—61no—
912C8—61no—
913C8—61no—
914C8C3×D3×D411yescharacteristic
915C8C3×D3×D411yescharacteristic
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—41no—
922C2×C3—61no—
923C2×C3—61no—
924C2×C3—81no—
925C2×C3—81no—
926C2×C3—81no—
927C2×C3—81no—
928C2×C3—81no—
929C2×C3—121no—
930C2×C3—161no—
931C2×C3—161no—
932C2×C3—241no—
933C2×C3D3×#12111yescharacteristic
934C2×C3C2×C3×#12111yescharacteristic
935D3—21no—
936D3—21no—
937D3—41no—
938D3—81no—
939C22—21no—
940C22—31no—
941C22—31no—
942C22—41no—
943C22—41no—
944C22—61no—
945C22—81no—
946C22—81no—
947C22—121no—
948C22—121no—
949C22—241no—
950C22—241no—
951C22—242no—
952C22—242no—
953C22C3×D3×#4111yescharacteristic
954C4—21no—
955C4—31no—
956C4—31no—
957C4—61no—
958C4—121no—
959C4C2×C3×D3×D411yescharacteristic
960C4C2×C3×D3×D411yescharacteristic
961C3—21no—
962C3#8093811yescharacteristic, direct product factor
963C3C3×#306811yescharacteristic, complemented
964C2—21no—
965C2—41no—
966C2—61no—
967C2—61no—
968C2—81no—
969C2—81no—
970C2—121no—
971C2—241no—
972C2C3×D3×#12111yescharacteristic
subgroupG/H
centerC2×C3D3×#121
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#472C2
socleC2×C32C2×#121
hypercenterC3×#472D3
hypocenterC3C3×#3068
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×#5773C2semidirect
2. C3×D3×AGL(1,ℤ/8)C2semidirect
3. C2×C3×#911C2semidirect
4. C3×#5750C2semidirect
5. C32×#472C2semidirect
6. C3×#5200C2semidirect
7. C3×#5199C2semidirect
8. C3×#5160C2semidirect
9. C3×#5141C2semidirect
10. C3×#4898C2semidirect
11. C3×#4893C2semidirect
12. C3×#4749C2semidirect
13. C3×#4748C2semidirect
14. C3×#4745C2semidirect
15. C3×D3×#100C2semidirect
17. #80938C3direct (N × H)
22. C32×AGL(1,ℤ/8)C22semidirect
23. C2×C32×D8C22semidirect
24. C32×#131C22semidirect
25. C3×#951C22semidirect
27. C3×#948C22semidirect
28. C2×C3×#214C22semidirect
30. C3×#932C22semidirect
31. C2×C3×#213C22semidirect
44. C3×#909C22semidirect
47. C3×#907C22semidirect
52. C2×C3×#204C22semidirect
54. C3×#901C22semidirect
57. C32×#108C22semidirect
58. C32×#100C22semidirect
59. C32×#100C22semidirect
60. C3×#833C22semidirect
61. C3×#833C22semidirect
62. C3×#824C22semidirect
63. C3×#824C22semidirect
64. C3×#823C22semidirect
65. C3×#823C22semidirect
66. C3×#822C22semidirect
67. C3×#822C22semidirect
68. C3×#819C22semidirect
73. #5773C2×C3semidirect
74. D3×AGL(1,ℤ/8)C2×C3semidirect
75. C2×#911C2×C3semidirect
76. #5750C2×C3semidirect
81. C3×#472D3semidirect
82. C3×#472C2×C3semidirect
90. #5200C2×C3semidirect
91. #5199C2×C3semidirect
92. #5160C2×C3semidirect
93. #5141C2×C3semidirect
94. #4898C2×C3semidirect
95. #4893C2×C3semidirect
96. #4749C2×C3semidirect
97. #4748C2×C3semidirect
98. #4745C2×C3semidirect
99. D3×#100C2×C3semidirect
201. C3×AGL(1,ℤ/8)C2×D3semidirect
203. C3×AGL(1,ℤ/8)C22×C3semidirect
212. C2×C3×D8C2×D3semidirect
213. C2×C3×D8C22×C3semidirect
220. C3×#131C2×D3semidirect
221. C3×#131C22×C3semidirect
228. #951C22×C3semidirect
230. #948C22×C3semidirect
231. C2×#214C22×C3semidirect
233. #932C22×C3semidirect
234. C2×#213C22×C3semidirect
247. #909C22×C3semidirect
250. #907C22×C3semidirect
255. C2×#204C22×C3semidirect
257. #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
278. #833C22×C3semidirect
279. #833C22×C3semidirect
280. #824C22×C3semidirect
281. #824C22×C3semidirect
282. #823C22×C3semidirect
283. #823C22×C3semidirect
284. #822C22×C3semidirect
285. #822C22×C3semidirect
286. #819C22×C3semidirect
348. #472C3×D3semidirect
565. AGL(1,ℤ/8)C2×C3×D3semidirect
573. C2×D8C2×C3×D3semidirect
579. #131C2×C3×D3semidirect
589. #108C2×C3×D3semidirect
596. #100C2×C3×D3semidirect
597. #100C2×C3×D3semidirect
861. C32#3068semidirect
962. C3#80938direct (N × H)
963. C3C3×#3068semidirect

Maximal subgroups

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

subgroupindex
C3×#57732
C3×D3×AGL(1,ℤ/8)2
C2×C3×#9112
C3×#57502
C32×#4722
C3×#52002
C3×#51992
C3×#51602
C3×#51412
C3×#48982
C3×#48932
C3×#47492
C3×#47482
C3×#47452
C3×D3×#1002
C3×#30683
#809383