Finite Group Databasebeta

← C3×#10594447 #13173994

Subgroups — C3×#10594447 #13173994

Order 1728.

1186 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64106C211yesmaximal, characteristic, complemented
2C32×#893C211yesmaximal, characteristic, complemented
3C32×#890C211yesmaximal, characteristic, complemented
4C3×#63916C211yesmaximal, characteristic
5C3×#63904C212yesmaximal, complemented
6C3×C4×#624C211yesmaximal, characteristic, complemented
7C3×#63861C212yesmaximal, complemented
8C3×#63860C211yesmaximal, characteristic, complemented
9C3×#63854C212yesmaximal, complemented
10C3×#63844C211yesmaximal, characteristic, complemented
11C3×#63841C212yesmaximal, complemented
12C3×#5691—31nomaximal
13C3×#5557—31nomaximal
14#10594447C311yesmaximal, characteristic, direct product factor
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×C32×C4×D3C2212yes—
19C2×C3×#626C2212yes—
20C2×C3×#624C2211yescharacteristic
21C2×C3×#624C2211yescharacteristic
22C33×C4⋊C4C2211yescharacteristic
23C3×#3752C2212yes—
24C3×C4⋊(C3⋊Dic3)C2212yes—
25C32×(C2×D3)⋊C4C2212yes—
26C32×C4⋊Dic3C2212yes—
27C32×C4⋊Dic3C2211yescharacteristic
28C32×Dic3⋊C4C2212yes—
29C32×C4×Dic3C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31C3×#3724C2212yes—
32C3×(C2×D3)⋊Dic3C2212yes—
33C3×(C2×D3)⋊Dic3C2212yes—
34C3×(C2×D3)⋊Dic3C2212yes—
35C3×Dic32C2211yescharacteristic
36C3×Dic32C2212yes—
37C3×Dic32C2211yescharacteristic
38C32×#125—31no—
39C32×C4×D4—31no—
40#64106C2×C311yescharacteristic, complemented
41C3×#938—31no—
42C3×#936—31no—
43C3×C4×#67—32no—
44C3×#926—32no—
45C3×#898—32no—
46C3×#897—31no—
47C3×#897—31no—
48C3×#897—61no—
49C3×#895—31no—
50C3×#894—32no—
51C3×#893—21no—
52C3×#893—32no—
53C3×#893D311yescharacteristic, complemented
54C3×#893C2×C311yescharacteristic, complemented
55C3×#892—32no—
56C3×#890—21no—
57C3×#890D311yescharacteristic, complemented
58C3×#890C2×C311yescharacteristic, complemented
59C3×#887—31no—
60C3×#883—32no—
61C3×#879—32no—
62C3×#875—31no—
63C3×C42×D3—31no—
64C3×C42×D3—31no—
65C3×C4×Dic6—31no—
66#63916C2×C311yescharacteristic
67#63904C2×C312yescomplemented
68C4×#624C2×C311yescharacteristic, complemented
69#63861C2×C312yescomplemented
70#63860C2×C311yescharacteristic, complemented
71#63854C2×C312yescomplemented
72#63844C2×C311yescharacteristic, complemented
73#63841C2×C312yescomplemented
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C32×D3C2312yes—
76C2×C33×C4C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C3×C4×C3⋊D3—22no—
81C3×#634—22no—
82C2×C32×Dic3C2311yescharacteristic
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C32×D12—22no—
88C32×C4×D3—24no—
89C3×#626—24no—
90C3×#624—22no—
91C3×#624—22no—
92C3×#529—91no—
93#5691—31no—
94#5557—31no—
95C2×C32×D4—31no—
96C22×C32×C4—32no—
97C2×C4×C3⋊D3C22×C311yescharacteristic
98C2×#634C22×C311yescharacteristic
99C2×C3×#67—32no—
100C2×C3×D12—21no—
101C2×C3×D12—32no—
102C2×C3×D12C2×D311yescharacteristic
103C2×C3×D12C22×C311yescharacteristic
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—31no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—61no—
112C2×C3×C4×D3C2×D312yes—
113C2×C3×C4×D3C22×C312yes—
114C2×C3×Dic6—31no—
115C2×C3×Dic6—31no—
116C2×C3×Dic6—61no—
117C2×#626C22×C312yes—
118C2×#624C22×C311yescharacteristic
119C2×#624C22×C311yescharacteristic
120C32×C4⋊C4—21no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4—31no—
124C32×C4⋊C4—32no—
125C32×C4⋊C4—32no—
126C32×C4⋊C4—41no—
127C32×C4⋊C4C2×D311yescharacteristic
128C32×C4⋊C4C2×D311yescharacteristic
129C32×C4⋊C4C22×C311yescharacteristic
130C32×C22⋊C4—32no—
131C32×C42—31no—
132C32×C42—31no—
133#3752C22×C312yes—
134C4⋊(C3⋊Dic3)C22×C312yes—
135C3×#217—32no—
136C3×#217—32no—
137C3×#217—32no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×(C2×D3)⋊C4—32no—
144C3×(C2×D3)⋊C4—62no—
145C3×(C2×D3)⋊C4C2×D312yes—
146C3×(C2×D3)⋊C4C22×C312yes—
147C3×C4⋊Dic3—22no—
148C3×C4⋊Dic3—21no—
149C3×C4⋊Dic3—32no—
150C3×C4⋊Dic3—32no—
151C3×C4⋊Dic3—62no—
152C3×C4⋊Dic3C2×D312yes—
153C3×C4⋊Dic3C2×D311yescharacteristic
154C3×C4⋊Dic3C22×C312yes—
155C3×C4⋊Dic3C22×C311yescharacteristic
156C3×Dic3⋊C4—22no—
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—32no—
159C3×Dic3⋊C4C2×D312yes—
160C3×Dic3⋊C4C22×C312yes—
161C3×C4×Dic3—21no—
162C3×C4×Dic3—21no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—32no—
165C3×C4×Dic3—31no—
166C3×C4×Dic3—31no—
167C3×C4×Dic3—31no—
168C3×C4×Dic3—32no—
169C3×C4×Dic3C2×D311yescharacteristic
170C3×C4×Dic3C2×D311yescharacteristic
171C3×C4×Dic3C22×C311yescharacteristic
172C3×C4×Dic3C22×C311yescharacteristic
173#3724C22×C312yes—
174(C2×D3)⋊Dic3C22×C312yes—
175(C2×D3)⋊Dic3C22×C312yes—
176(C2×D3)⋊Dic3C22×C312yes—
177Dic32C22×C311yescharacteristic
178Dic32C22×C312yes—
179Dic32C22×C311yescharacteristic
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3#4112yes—
184C2×C32×D3—22no—
185C2×C32×D3—22no—
186C2×C32×D3—22no—
187C33×C4—22no—
188C33×C4#4112yes—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C32×Dic3—21no—
192C32×Dic3—21no—
193C32×Dic3—21no—
194C32×Dic3—22no—
195C32×Dic3#4112yes—
196C3×#126—92no—
197C3×#125—31no—
198C3×#125—31no—
199C3×#125—61no—
200C3×#124—91no—
201C3×#123—92no—
202C3×C22⋊Q8—91no—
203C3×#121—91no—
204C3×C4×Q8—91no—
205C3×C4×D4—31no—
206C3×C4×D4—31no—
207C3×C4×D4—61no—
208C3×C4×D4—92no—
209C3×#117—92no—
210C2×C3×C42—91no—
211#938—31no—
212#936—31no—
213C4×#67—32no—
214#926—32no—
215#898—32no—
216#897—31no—
217#897—31no—
218#897—61no—
219#895—31no—
220#894—32no—
221#893—32no—
222#893C3×D311yescharacteristic, complemented
223#892—32no—
224#890C3×D311yescharacteristic, complemented
225#887—31no—
226#883—32no—
227#879—32no—
228#875—31no—
229C42×D3—31no—
230C42×D3—31no—
231C4×Dic6—31no—
232C23×C32—32no—
233C22×C3⋊D3C23×C311yescharacteristic
234C22×C3×D3—22no—
235C22×C3×D3—31no—
236C22×C3×D3—31no—
237C22×C3×D3—61no—
238C22×C3×D3C22×D312yes—
239C22×C3×D3C23×C312yes—
240C32×D4—62no—
241C2×C32×C4—21no—
242C2×C32×C4—22no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—22no—
246C2×C32×C4—22no—
247C2×C32×C4—31no—
248C2×C32×C4—31no—
249C2×C32×C4—32no—
250C2×C32×C4—31no—
251C2×C32×C4—31no—
252C2×C32×C4—41no—
253C2×C32×C4—42no—
254C2×C32×C4—64no—
255C2×C32×C4C22×D312yes—
256C2×C32×C4C22×D312yes—
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C23×C312yes—
260C2×C32×C4C23×C311yescharacteristic
261C2×C3⋊Dic3C23×C311yescharacteristic
262C2×C3⋊Dic3C23×C312yes—
263C4×C3⋊D3—22no—
264#634—22no—
265C3×#67—64no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—62no—
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D312yes—
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C23×C311yescharacteristic
283C2×C3×Dic3C23×C311yescharacteristic
284C2×C3×Dic3C23×C312yes—
285C2×C3×Dic3C23×C311yescharacteristic
286C2×C3×Dic3C23×C311yescharacteristic
287C3×D12—24no—
288C3×D12—22no—
289C3×D12—22no—
290C3×D12—64no—
291C3×C4×D3—24no—
292C3×C4×D3—24no—
293C3×C4×D3—44no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×C4×D3—62no—
297C3×C4×D3—62no—
298C3×C4×D3—62no—
299C3×C4×D3—62no—
300C3×C4×D3—122no—
301C3×Dic6—62no—
302C3×Dic6—62no—
303C3×Dic6—122no—
304#626—24no—
305#624—22no—
306#624—22no—
307#529—91noSylow
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C3×C3⋊D3—22no—
312C32×D3—42no—
313C2×C3×Q8—91no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—61no—
317C2×C3×D4—92no—
318C22×C3×C4—32no—
319C22×C3×C4—32no—
320C22×C3×C4—62no—
321C22×C3×C4—91no—
322C22×C3×C4—91no—
323C22×C3×C4—91no—
324C2×#67—32no—
325C2×D12—32no—
326C2×D12C2×C3×D311yescharacteristic
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—61no—
334C2×C4×D3C2×C3×D312yes—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—32no—
342C3×C4⋊C4—32no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—32no—
346C3×C4⋊C4—32no—
347C3×C4⋊C4—41no—
348C3×C4⋊C4—62no—
349C3×C4⋊C4—62no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—92no—
352C3×C4⋊C4—92no—
353C3×C4⋊C4D3211yescharacteristic
354C3×C4⋊C4C2×C3×D311yescharacteristic
355C3×C4⋊C4C2×C3×D311yescharacteristic
356C3×C22⋊C4—32no—
357C3×C22⋊C4—32no—
358C3×C22⋊C4—62no—
359C3×C22⋊C4—92no—
360C3×C22⋊C4—92no—
361C3×C22⋊C4—92no—
362C3×C22⋊C4—92no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42—91no—
370C3×C42—91no—
371C3×C42—92no—
372#217—32no—
373#217—32no—
374#217—32no—
375(C2×D3)⋊C4—32no—
376(C2×D3)⋊C4—32no—
377(C2×D3)⋊C4—32no—
378(C2×D3)⋊C4—32no—
379(C2×D3)⋊C4—32no—
380(C2×D3)⋊C4—62no—
381(C2×D3)⋊C4C2×C3×D312yes—
382C4⋊Dic3—32no—
383C4⋊Dic3—32no—
384C4⋊Dic3—62no—
385C4⋊Dic3C2×C3×D311yescharacteristic
386C4⋊Dic3C2×C3×D312yes—
387Dic3⋊C4—32no—
388Dic3⋊C4—32no—
389Dic3⋊C4C2×C3×D312yes—
390C4×Dic3—32no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—32no—
396C4×Dic3C2×C3×D311yescharacteristic
397C4×Dic3C2×C3×D311yescharacteristic
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—41no—
402C22×C32—62no—
403C22×C32—62no—
404C22×C32—62no—
405C22×C32C23×D311yescharacteristic
406C22×C32C23×D311yescharacteristic
407C22×C32C24×C311yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
410C2×C3⋊D3C3×#4112yes—
411C2×C3×D3—24no—
412C2×C3×D3—22no—
413C2×C3×D3—22no—
414C2×C3×D3—22no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—32no—
419C2×C3×D3—32no—
420C2×C3×D3—42no—
421C2×C3×D3—42no—
422C2×C3×D3—62no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—121no—
428C2×C3×D3—121no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—22no—
433C32×C4—22no—
434C32×C4—22no—
435C32×C4—32no—
436C32×C4—42no—
437C32×C4—42no—
438C32×C4—42no—
439C32×C4—42no—
440C32×C4—61no—
441C32×C4—61no—
442C32×C4—61no—
443C32×C4—62no—
444C32×C4—82no—
445C32×C4#23512yes—
446C32×C4#23912yes—
447C32×C4C3×#4112yes—
448C3⋊Dic3—22no—
449C3⋊Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—21no—
453C3×Dic3—22no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—21no—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—41no—
460C3×Dic3—41no—
461C3×Dic3—41no—
462C3×Dic3—42no—
463C3×Dic3—62no—
464C3×Dic3—61no—
465C3×Dic3—62no—
466C3×Dic3—61no—
467C3×Dic3—122no—
468C3×Dic3—121no—
469C3×Dic3#23712yes—
470C3×Dic3C3×#4112yes—
471#126—92no—
472#125—31no—
473#124—91no—
474#123—92no—
475C22⋊Q8—91no—
476#121—91no—
477C4×Q8—91no—
478C4×D4—31no—
479C4×D4—92no—
480#117—92no—
481C2×C42—91no—
482C33#52911yescharacteristic, complemented, Sylow
483C23×C3—32no—
484C23×C3—32no—
485C23×C3—62no—
486C23×C3—91no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—61no—
490C22×D3C22×C3×D312yes—
491C3×Q8—182no—
492C3×D4—64no—
493C3×D4—62no—
494C3×D4—62no—
495C3×D4—184no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—32no—
508C2×C3×C4—31no—
509C2×C3×C4—32no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—42no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—62no—
519C2×C3×C4—64no—
520C2×C3×C4—64no—
521C2×C3×C4—91no—
522C2×C3×C4—92no—
523C2×C3×C4—124no—
524C2×C3×C4—182no—
525C2×C3×C4—182no—
526C2×C3×C4—182no—
527C2×C3×C4C2×D3212yes—
528C2×C3×C4C2×D3211yescharacteristic
529C2×C3×C4C22×C3×D312yes—
530C2×C3×C4C22×C3×D312yes—
531C2×C3×C4C22×C3×D311yescharacteristic
532C2×C3×C4C22×C3×D311yescharacteristic
533#67—64no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—61no—
539C2×Dic3—62no—
540C2×Dic3C22×C3×D311yescharacteristic
541C2×Dic3C22×C3×D311yescharacteristic
542C2×Dic3C22×C3×D311yescharacteristic
543C2×Dic3C22×C3×D312yes—
544C2×Dic3C22×C3×D311yescharacteristic
545D12—22no—
546D12—64no—
547C4×D3—24no—
548C4×D3—62no—
549C4×D3—62no—
550C4×D3—62no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—62no—
554C4×D3—122no—
555Dic6—62no—
556Dic6—62no—
557Dic6—122no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—41no—
568C2×C32—41no—
569C2×C32—41no—
570C2×C32—122no—
571C2×C32C2×#23511yescharacteristic
572C2×C32C2×#23711yescharacteristic
573C2×C32C2×#23911yescharacteristic
574C2×C32D3×#4111yescharacteristic
575C2×C32D3×#4111yescharacteristic
576C2×C32D3×#4111yescharacteristic
577C2×C32C2×C3×#4111yescharacteristic
578C2×C32C2×C3×#4111yescharacteristic
579C2×C32C2×C3×#4111yescharacteristic
580C3⋊D3—22no—
581C3×D3—44no—
582C3×D3—42no—
583C3×D3—42no—
584C3×D3—62no—
585C3×D3—62no—
586C3×D3—122no—
587C2×Q8—91no—
588C2×D4—31no—
589C2×D4—92no—
590C22×C4—32no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—91no—
594C4⋊C4—32no—
595C4⋊C4—32no—
596C4⋊C4—31no—
597C4⋊C4—92no—
598C4⋊C4—92no—
599C4⋊C4C3×D3211yescharacteristic
600C22⋊C4—32no—
601C22⋊C4—92no—
602C22⋊C4—92no—
603C22⋊C4—92no—
604C22⋊C4—92no—
605C42—31no—
606C42—31no—
607C42—91no—
608C42—91no—
609C42—92no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—41no—
614C22×C3—64no—
615C22×C3—62no—
616C22×C3—62no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—62no—
620C22×C3—62no—
621C22×C3—92no—
622C22×C3—122no—
623C22×C3—122no—
624C22×C3—181no—
625C22×C3—181no—
626C22×C3C22×D3211yescharacteristic
627C22×C3C23×C3×D311yescharacteristic
628C22×C3C23×C3×D311yescharacteristic
629C2×D3—22no—
630C2×D3—22no—
631C2×D3—22no—
632C2×D3—32no—
633C2×D3—32no—
634C2×D3—62no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—121no—
640C2×D3—121no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—32no—
648C3×C4—32no—
649C3×C4—42no—
650C3×C4—42no—
651C3×C4—42no—
652C3×C4—42no—
653C3×C4—62no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—62no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—62no—
662C3×C4—82no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—122no—
666C3×C4—121no—
667C3×C4—181no—
668C3×C4—182no—
669C3×C4#379912yes—
670C3×C4C3×#23512yes—
671C3×C4C3×#23912yes—
672Dic3—21no—
673Dic3—21no—
674Dic3—21no—
675Dic3—22no—
676Dic3—62no—
677Dic3—61no—
678Dic3—62no—
679Dic3—61no—
680Dic3—122no—
681Dic3—121no—
682Dic3C3×#23712yes—
683C32—21no—
684C32—21no—
685C32—21no—
686C32—41no—
687C32#555711yescharacteristic, complemented
688C32#569111yescharacteristic, complemented
689C32C3×#52911yescharacteristic, complemented
690C23—32no—
691C23—91no—
692Q8—182no—
693D4—62no—
694D4—184no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—32no—
700C2×C4—64no—
701C2×C4—91no—
702C2×C4—92no—
703C2×C4—182no—
704C2×C4—182no—
705C2×C4—182no—
706C2×C4C2×C3×D3212yes—
707C2×C4C2×C3×D3211yescharacteristic
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—41no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—124no—
721C2×C3—122no—
722C2×C3—122no—
723C2×C3—182no—
724C2×C3C2×#379911yescharacteristic
725C2×C3D3×#23711yescharacteristic
726C2×C3#6431911yescharacteristic
727C2×C3C2×C3×#23511yescharacteristic
728C2×C3C2×C3×#23711yescharacteristic
729C2×C3C2×C3×#23911yescharacteristic
730C2×C3C3×D3×#4111yescharacteristic
731C2×C3C3×D3×#4111yescharacteristic
732C2×C3C3×D3×#4111yescharacteristic
733D3—42no—
734D3—62no—
735D3—62no—
736D3—122no—
737C22—62no—
738C22—62no—
739C22—62no—
740C22—92no—
741C22—181no—
742C22—181no—
743C22C22×C3×D3211yescharacteristic
744C4—22no—
745C4—32no—
746C4—61no—
747C4—61no—
748C4—62no—
749C4—61no—
750C4—181no—
751C4—182no—
752C4C3×#379912yes—
753C3—21no—
754C3—21no—
755C3—21no—
756C3—41no—
757C3#1059444711yescharacteristic, direct product factor
758C3C3×#555711yescharacteristic, complemented
759C3C3×#569111yescharacteristic, complemented
760C2—122no—
761C2—182no—
762C2C2×C3×#379911yescharacteristic
763C2C3×D3×#23711yescharacteristic
764C2C3×#6431911yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC3×#63916C2
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64106C2semidirect
2. C32×#893C2semidirect
3. C32×#890C2semidirect
5. C3×#63904C2semidirect
6. C3×C4×#624C2semidirect
7. C3×#63861C2semidirect
8. C3×#63860C2semidirect
9. C3×#63854C2semidirect
10. C3×#63844C2semidirect
11. C3×#63841C2semidirect
14. #10594447C3direct (N × H)
40. #64106C2×C3semidirect
53. C3×#893D3semidirect
54. C3×#893C2×C3semidirect
57. C3×#890D3semidirect
58. C3×#890C2×C3semidirect
67. #63904C2×C3semidirect
68. C4×#624C2×C3semidirect
69. #63861C2×C3semidirect
70. #63860C2×C3semidirect
71. #63854C2×C3semidirect
72. #63844C2×C3semidirect
73. #63841C2×C3semidirect
222. #893C3×D3semidirect
224. #890C3×D3semidirect
482. C33#529semidirect
687. C32#5557semidirect
688. C32#5691semidirect
689. C32C3×#529semidirect
757. C3#10594447direct (N × H)
758. C3C3×#5557semidirect
759. C3C3×#5691semidirect

Maximal subgroups

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

subgroupindex
C3×#641062
C32×#8932
C32×#8902
C3×#639162
C3×#639042
C3×C4×#6242
C3×#638612
C3×#638602
C3×#638542
C3×#638442
C3×#638412
C3×#56913
C3×#55573
#105944473