Finite Group Databasebeta

← C3×#10594385 #13173950

Subgroups — C3×#10594385 #13173950

Order 1728.

1126 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64097C211yesmaximal, characteristic, complemented
2C32×#897C211yesmaximal, characteristic
3C32×#887C211yesmaximal, characteristic, complemented
4C3×#63896C212yesmaximal
5C3×#63877C212yesmaximal
6C3×C4×D3×Dic3C211yesmaximal, characteristic
7C3×#63873C211yesmaximal, characteristic, complemented
8C3×#63856C211yesmaximal, characteristic
9C3×#63847C212yesmaximal, complemented
10C3×#63844C212yesmaximal, complemented
11C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
12C3×#5622—31nomaximal
13C3×#5578—31nomaximal
14#10594385C311yesmaximal, characteristic, direct product factor
15C2×C3×#634C2212yes—
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×C32×Dic6C2211yescharacteristic
19C2×C3×D3×Dic3C2211yescharacteristic
20C2×C3×D3×Dic3C2211yescharacteristic
21C33×C4⋊C4C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#3750C2212yes—
24C3×C4×C3⋊Dic3C2211yescharacteristic
25C32×(C2×D3)⋊C4C2212yes—
26C32×C4⋊Dic3C2212yes—
27C32×Dic3⋊C4C2212yes—
28C32×C4×Dic3C2211yescharacteristic
29C32×C4×Dic3C2212yes—
30C3×#3724C2212yes—
31C3×#3724C2212yes—
32C3×#3724C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×(C2×D3)⋊Dic3C2212yes—
35C3×Dic32C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2211yescharacteristic
38C32×C22⋊Q8—31no—
39C32×C4×Q8—31no—
40#64097C2×C311yescharacteristic, complemented
41C3×#946—31no—
42C3×Q8×Dic3—31no—
43C3×#944—31no—
44C3×#944—31no—
45C3×#924—31no—
46C2×C3×C4×Dic3—31no—
47C3×#897—21no—
48C3×#897D311yescharacteristic
49C3×#897C2×C311yescharacteristic
50C3×#896—32no—
51C3×#889—32no—
52C3×#889—32no—
53C3×#888—31no—
54C3×#888—31no—
55C3×#888—61no—
56C3×#887—21no—
57C3×#887—32no—
58C3×#887D311yescharacteristic, complemented
59C3×#887C2×C311yescharacteristic, complemented
60C3×#878—32no—
61C3×#877—32no—
62C3×#872—32no—
63C3×C42×D3—31no—
64C3×C4×Dic6—31no—
65C3×C4×Dic6—32no—
66#63896C2×C312yes—
67#63877C2×C312yes—
68C4×D3×Dic3C2×C311yescharacteristic
69#63873C2×C311yescharacteristic, complemented
70#63856C2×C311yescharacteristic
71#63847C2×C312yescomplemented
72#63844C2×C312yescomplemented
73Dic3×Dic6C2×C311yescharacteristic, complemented
74C22×C32×D3C2311yescharacteristic
75C2×C33×C4C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3×C3⋊Dic3C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C3×#634—24no—
81C2×C32×Dic3C2311yescharacteristic
82C2×C32×Dic3C2311yescharacteristic
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C32×C4×D3—22no—
87C32×Dic6—22no—
88C32×Dic6—22no—
89C3×D3×Dic3—22no—
90C3×D3×Dic3Q814yescomplemented
91C3×#533—91no—
92#5622—31no—
93#5578—31no—
94C2×C32×Q8—31no—
95C2×C32×Q8—31no—
96C22×C32×C4—31no—
97C2×#634C22×C312yes—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3C2×D311yescharacteristic
104C2×C3×C4×D3C22×C311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6—32no—
108C2×C3×Dic6—32no—
109C2×C3×Dic6—62no—
110C2×C3×Dic6C2×D311yescharacteristic
111C2×C3×Dic6C2×D311yescharacteristic
112C2×C3×Dic6C22×C311yescharacteristic
113C2×C3×Dic6C22×C311yescharacteristic
114C2×D3×Dic3C22×C311yescharacteristic
115C2×D3×Dic3C22×C311yescharacteristic
116C32×C4⋊C4—21no—
117C32×C4⋊C4—21no—
118C32×C4⋊C4—21no—
119C32×C4⋊C4—32no—
120C32×C4⋊C4—32no—
121C32×C4⋊C4—41no—
122C32×C4⋊C4C2×D311yescharacteristic
123C32×C4⋊C4C2×D311yescharacteristic
124C32×C4⋊C4C22×C311yescharacteristic
125C32×C22⋊C4—32no—
126C32×C42—31no—
127C32×C42—32no—
128C4⋊(C3⋊Dic3)C22×C311yescharacteristic
129#3750C22×C312yes—
130C4×C3⋊Dic3C22×C311yescharacteristic
131C3×#217—32no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4C2×D312yes—
135C3×(C2×D3)⋊C4C22×C312yes—
136C3×C4⋊Dic3—22no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—32no—
140C3×C4⋊Dic3—61no—
141C3×C4⋊Dic3C2×D312yes—
142C3×C4⋊Dic3C22×C312yes—
143C3×Dic3⋊C4—22no—
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—62no—
154C3×Dic3⋊C4C2×D312yes—
155C3×Dic3⋊C4C22×C312yes—
156C3×C4×Dic3—22no—
157C3×C4×Dic3—21no—
158C3×C4×Dic3—31no—
159C3×C4×Dic3—31no—
160C3×C4×Dic3—32no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—31no—
165C3×C4×Dic3—32no—
166C3×C4×Dic3—61no—
167C3×C4×Dic3C2×D312yes—
168C3×C4×Dic3C2×D311yescharacteristic
169C3×C4×Dic3C22×C311yescharacteristic
170C3×C4×Dic3C22×C312yes—
171#3724C22×C312yes—
172#3724C22×C312yes—
173#3724C22×C312yes—
174Dic3⋊Dic3C22×C312yes—
175(C2×D3)⋊Dic3C22×C312yes—
176Dic32C22×C312yes—
177Dic32C22×C311yescharacteristic
178Dic32C22×C311yescharacteristic
179C22×C33C2411yescharacteristic
180C2×C32×D3—21no—
181C2×C32×D3—21no—
182C2×C32×D3C2×Q812yes—
183C33×C4—22no—
184C33×C4#4112yes—
185C3×C3⋊Dic3—22no—
186C3×C3⋊Dic3C2×Q812yes—
187C3×C3⋊Dic3#4112yes—
188C32×Dic3—22no—
189C32×Dic3—21no—
190C32×Dic3—22no—
191C32×Dic3—21no—
192C32×Dic3C2×Q812yes—
193C3×C4⋊Q8—91no—
194C3×C4⋊Q8—91no—
195C3×#125—92no—
196C3×C22⋊Q8—31no—
197C3×C22⋊Q8—31no—
198C3×C22⋊Q8—61no—
199C3×C22⋊Q8—92no—
200C3×C22⋊Q8—91no—
201C3×C4×Q8—31no—
202C3×C4×Q8—31no—
203C3×C4×Q8—61no—
204C3×C4×Q8—92no—
205C3×C4×Q8—91no—
206C3×#117—92no—
207C2×C3×C42—91no—
208#946—31no—
209Q8×Dic3—31no—
210#944—31no—
211#944—31no—
212#924—31no—
213C2×C4×Dic3—31no—
214#897C3×D311yescharacteristic
215#896—32no—
216#889—32no—
217#889—32no—
218#888—31no—
219#888—31no—
220#888—61no—
221#887—32no—
222#887C3×D311yescharacteristic, complemented
223#878—32no—
224#877—32no—
225#872—32no—
226C42×D3—31no—
227C4×Dic6—31no—
228C4×Dic6—32no—
229C23×C32—31no—
230C22×C3×D3—21no—
231C22×C3×D3C22×D311yescharacteristic
232C22×C3×D3C23×C311yescharacteristic
233C32×Q8—62no—
234C32×Q8—62no—
235C2×C32×C4—21no—
236C2×C32×C4—22no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—22no—
240C2×C32×C4—22no—
241C2×C32×C4—31no—
242C2×C32×C4—31no—
243C2×C32×C4—32no—
244C2×C32×C4—31no—
245C2×C32×C4—32no—
246C2×C32×C4—41no—
247C2×C32×C4—42no—
248C2×C32×C4—62no—
249C2×C32×C4C22×D312yes—
250C2×C32×C4C22×D312yes—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C23×C312yes—
254C2×C32×C4C23×C311yescharacteristic
255C2×C3⋊Dic3C23×C312yes—
256C2×C3⋊Dic3C23×C311yescharacteristic
257C2×C3⋊Dic3C23×C311yescharacteristic
258#634—24no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—34no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—62no—
274C2×C3×Dic3—62no—
275C2×C3×Dic3C22×D311yescharacteristic
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D312yes—
278C2×C3×Dic3C22×D312yes—
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C23×C311yescharacteristic
281C2×C3×Dic3C23×C311yescharacteristic
282C2×C3×Dic3C23×C312yes—
283C2×C3×Dic3C23×C312yes—
284C2×C3×Dic3C23×C311yescharacteristic
285C3×C4×D3—22no—
286C3×C4×D3—22no—
287C3×C4×D3—34no—
288C3×C4×D3—42no—
289C3×C4×D3—62no—
290C3×Dic6—24no—
291C3×Dic6—22no—
292C3×Dic6—22no—
293C3×Dic6—22no—
294C3×Dic6—22no—
295C3×Dic6—42no—
296C3×Dic6—64no—
297C3×Dic6—64no—
298C3×Dic6—124no—
299D3×Dic3—22no—
300D3×Dic3C3×Q814yescomplemented
301#533—91noSylow
302C2×C33C22×Q811yescharacteristic
303C2×C33C2×#4111yescharacteristic
304C2×C33C2×#4111yescharacteristic
305C32×D3—22no—
306C2×C3×Q8—31no—
307C2×C3×Q8—31no—
308C2×C3×Q8—31no—
309C2×C3×Q8—31no—
310C2×C3×Q8—61no—
311C2×C3×Q8—61no—
312C2×C3×Q8—92no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—61no—
316C22×C3×C4—91no—
317C22×C3×C4—91no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3C2×C3×D311yescharacteristic
323C2×Dic6—32no—
324C2×Dic6—32no—
325C2×Dic6—62no—
326C2×Dic6C2×C3×D311yescharacteristic
327C2×Dic6C2×C3×D311yescharacteristic
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—32no—
332C3×C4⋊C4—32no—
333C3×C4⋊C4—32no—
334C3×C4⋊C4—32no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—62no—
337C3×C4⋊C4—62no—
338C3×C4⋊C4—92no—
339C3×C4⋊C4—92no—
340C3×C4⋊C4—92no—
341C3×C4⋊C4—92no—
342C3×C4⋊C4—92no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4D3211yescharacteristic
345C3×C4⋊C4C2×C3×D311yescharacteristic
346C3×C4⋊C4C2×C3×D311yescharacteristic
347C3×C22⋊C4—32no—
348C3×C22⋊C4—32no—
349C3×C22⋊C4—62no—
350C3×C22⋊C4—92no—
351C3×C42—31no—
352C3×C42—32no—
353C3×C42—31no—
354C3×C42—32no—
355C3×C42—61no—
356C3×C42—62no—
357C3×C42—91no—
358C3×C42—91no—
359C3×C42—92no—
360C3×C42—91no—
361#217—32no—
362(C2×D3)⋊C4—32no—
363(C2×D3)⋊C4C2×C3×D312yes—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—32no—
367C4⋊Dic3—61no—
368C4⋊Dic3C2×C3×D312yes—
369Dic3⋊C4—32no—
370Dic3⋊C4—32no—
371Dic3⋊C4—32no—
372Dic3⋊C4—32no—
373Dic3⋊C4—32no—
374Dic3⋊C4—32no—
375Dic3⋊C4—32no—
376Dic3⋊C4—32no—
377Dic3⋊C4—32no—
378Dic3⋊C4—62no—
379Dic3⋊C4C2×C3×D312yes—
380C4×Dic3—31no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—32no—
384C4×Dic3—31no—
385C4×Dic3—32no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—61no—
389C4×Dic3C2×C3×D312yes—
390C4×Dic3C2×C3×D311yescharacteristic
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—32no—
395C22×C32—41no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32C23×D311yescharacteristic
399C22×C32C23×D311yescharacteristic
400C22×C32C24×C311yescharacteristic
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—22no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3D3×Q812yes—
409C2×C3×D3C2×C3×Q812yes—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—22no—
416C32×C4—32no—
417C32×C4—42no—
418C32×C4—42no—
419C32×C4—42no—
420C32×C4—42no—
421C32×C4—62no—
422C32×C4—61no—
423C32×C4—62no—
424C32×C4—61no—
425C32×C4—82no—
426C32×C4#23512yes—
427C32×C4#23712yes—
428C32×C4C3×#4112yes—
429C3⋊Dic3—22no—
430C3⋊Dic3C2×C3×Q812yes—
431C3⋊Dic3C3×#4112yes—
432C3×Dic3—24no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—21no—
441C3×Dic3—22no—
442C3×Dic3—32no—
443C3×Dic3—32no—
444C3×Dic3—32no—
445C3×Dic3—32no—
446C3×Dic3—42no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—62no—
450C3×Dic3—62no—
451C3×Dic3—62no—
452C3×Dic3—62no—
453C3×Dic3—122no—
454C3×Dic3D3×Q812yes—
455C3×Dic3C2×C3×Q812yes—
456C4⋊Q8—91no—
457C4⋊Q8—91no—
458#125—92no—
459C22⋊Q8—31no—
460C22⋊Q8—92no—
461C22⋊Q8—91no—
462C4×Q8—31no—
463C4×Q8—92no—
464C4×Q8—91no—
465#117—92no—
466C2×C42—91no—
467C33#53311yescharacteristic, complemented, Sylow
468C23×C3—31no—
469C23×C3—31no—
470C23×C3—61no—
471C22×D3C22×C3×D311yescharacteristic
472C3×Q8—64no—
473C3×Q8—62no—
474C3×Q8—62no—
475C3×Q8—62no—
476C3×Q8—62no—
477C3×Q8—122no—
478C3×Q8—184no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—32no—
489C2×C3×C4—31no—
490C2×C3×C4—32no—
491C2×C3×C4—31no—
492C2×C3×C4—32no—
493C2×C3×C4—31no—
494C2×C3×C4—32no—
495C2×C3×C4—41no—
496C2×C3×C4—42no—
497C2×C3×C4—61no—
498C2×C3×C4—62no—
499C2×C3×C4—61no—
500C2×C3×C4—62no—
501C2×C3×C4—61no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—94no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—92no—
508C2×C3×C4—122no—
509C2×C3×C4—182no—
510C2×C3×C4C2×D3212yes—
511C2×C3×C4C2×D3211yescharacteristic
512C2×C3×C4C22×C3×D312yes—
513C2×C3×C4C22×C3×D312yes—
514C2×C3×C4C22×C3×D311yescharacteristic
515C2×C3×C4C22×C3×D311yescharacteristic
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—34no—
521C2×Dic3—32no—
522C2×Dic3—32no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3C22×C3×D311yescharacteristic
528C2×Dic3C22×C3×D311yescharacteristic
529C2×Dic3C22×C3×D312yes—
530C2×Dic3C22×C3×D312yes—
531C2×Dic3C22×C3×D311yescharacteristic
532C4×D3—22no—
533C4×D3—34no—
534C4×D3—62no—
535Dic6—22no—
536Dic6—22no—
537Dic6—64no—
538Dic6—64no—
539Dic6—124no—
540C2×C32—21no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—41no—
550C2×C32—41no—
551C2×C32—41no—
552C2×C32—62no—
553C2×C32C2×#23511yescharacteristic
554C2×C32C2×#23711yescharacteristic
555C2×C32C2×D3×Q811yescharacteristic
556C2×C32C2×D3×Q811yescharacteristic
557C2×C32D3×#4111yescharacteristic
558C2×C32D3×#4111yescharacteristic
559C2×C32C22×C3×Q811yescharacteristic
560C2×C32C2×C3×#4111yescharacteristic
561C2×C32C2×C3×#4111yescharacteristic
562C3×D3—22no—
563C3×D3—22no—
564C3×D3—42no—
565C2×Q8—31no—
566C2×Q8—31no—
567C2×Q8—92no—
568C22×C4—31no—
569C22×C4—91no—
570C22×C4—91no—
571C4⋊C4—32no—
572C4⋊C4—32no—
573C4⋊C4—92no—
574C4⋊C4—92no—
575C4⋊C4—92no—
576C4⋊C4—92no—
577C4⋊C4—92no—
578C4⋊C4—91no—
579C4⋊C4C3×D3211yescharacteristic
580C22⋊C4—32no—
581C22⋊C4—92no—
582C42—31no—
583C42—32no—
584C42—91no—
585C42—91no—
586C42—92no—
587C42—91no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—32no—
592C22×C3—32no—
593C22×C3—41no—
594C22×C3—62no—
595C22×C3—61no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3—61no—
599C22×C3—121no—
600C22×C3—121no—
601C22×C3C22×D3211yescharacteristic
602C22×C3C23×C3×D311yescharacteristic
603C22×C3C23×C3×D311yescharacteristic
604C2×D3—21no—
605C2×D3—21no—
606C2×D3C3×D3×Q812yes—
607C3×C4—22no—
608C3×C4—22no—
609C3×C4—22no—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—32no—
614C3×C4—32no—
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—62no—
620C3×C4—64no—
621C3×C4—61no—
622C3×C4—62no—
623C3×C4—62no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—62no—
627C3×C4—62no—
628C3×C4—61no—
629C3×C4—82no—
630C3×C4—92no—
631C3×C4—92no—
632C3×C4—121no—
633C3×C4—122no—
634C3×C4—121no—
635C3×C4—182no—
636C3×C4#379512yes—
637C3×C4C3×#23512yes—
638C3×C4C3×#23712yes—
639Dic3—22no—
640Dic3—22no—
641Dic3—21no—
642Dic3—21no—
643Dic3—32no—
644Dic3—32no—
645Dic3—32no—
646Dic3—32no—
647Dic3—62no—
648Dic3—62no—
649Dic3—62no—
650Dic3—62no—
651Dic3—122no—
652Dic3C3×D3×Q812yes—
653C32—21no—
654C32—21no—
655C32—21no—
656C32—41no—
657C32#557811yescharacteristic, complemented
658C32#562211yescharacteristic, complemented
659C32C3×#53311yescharacteristic, complemented
660C23—31no—
661Q8—62no—
662Q8—62no—
663Q8—184no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—32no—
667C2×C4—31no—
668C2×C4—32no—
669C2×C4—62no—
670C2×C4—94no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—92no—
674C2×C4—182no—
675C2×C4C2×C3×D3212yes—
676C2×C4C2×C3×D3211yescharacteristic
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—41no—
687C2×C3—41no—
688C2×C3—41no—
689C2×C3—62no—
690C2×C3—62no—
691C2×C3—122no—
692C2×C3C2×#379511yescharacteristic
693C2×C3#6431211yescharacteristic
694C2×C3D32×Q811yescharacteristic
695C2×C3C2×C3×#23511yescharacteristic
696C2×C3C2×C3×#23711yescharacteristic
697C2×C3C2×C3×D3×Q811yescharacteristic
698C2×C3C2×C3×D3×Q811yescharacteristic
699C2×C3C3×D3×#4111yescharacteristic
700C2×C3C3×D3×#4111yescharacteristic
701D3—22no—
702C22—32no—
703C22—61no—
704C22—61no—
705C22C22×C3×D3211yescharacteristic
706C4—22no—
707C4—32no—
708C4—61no—
709C4—62no—
710C4—62no—
711C4—61no—
712C4—92no—
713C4—92no—
714C4—182no—
715C4C3×#379512yes—
716C3—21no—
717C3—21no—
718C3—21no—
719C3—41no—
720C3#1059438511yescharacteristic, direct product factor
721C3C3×#557811yescharacteristic, complemented
722C3C3×#562211yescharacteristic, complemented
723C2—62no—
724C2C2×C3×#379511yescharacteristic
725C2C3×#6431211yescharacteristic
726C2C3×D32×Q811yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC22×C32×D3C23
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#533
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×#64097C2semidirect
3. C32×#887C2semidirect
7. C3×#63873C2semidirect
9. C3×#63847C2semidirect
10. C3×#63844C2semidirect
11. C3×Dic3×Dic6C2semidirect
14. #10594385C3direct (N × H)
40. #64097C2×C3semidirect
58. C3×#887D3semidirect
59. C3×#887C2×C3semidirect
69. #63873C2×C3semidirect
71. #63847C2×C3semidirect
72. #63844C2×C3semidirect
73. Dic3×Dic6C2×C3semidirect
90. C3×D3×Dic3Q8semidirect
222. #887C3×D3semidirect
300. D3×Dic3C3×Q8semidirect
467. C33#533semidirect
657. C32#5578semidirect
658. C32#5622semidirect
659. C32C3×#533semidirect
720. C3#10594385direct (N × H)
721. C3C3×#5578semidirect
722. C3C3×#5622semidirect

Maximal subgroups

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

subgroupindex
C3×#640972
C32×#8972
C32×#8872
C3×#638962
C3×#638772
C3×C4×D3×Dic32
C3×#638732
C3×#638562
C3×#638472
C3×#638442
C3×Dic3×Dic62
C3×#56223
C3×#55783
#105943853