Finite Group Databasebeta

← C3×#10594397 #13173957

Subgroups — C3×#10594397 #13173957

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×#64106C211yesmaximal, characteristic
2C32×#888C211yesmaximal, characteristic, complemented
3C32×#887C211yesmaximal, characteristic, complemented
4C3×#63888C212yesmaximal
5C3×C4×#624C211yesmaximal, characteristic
6C3×#63871C211yesmaximal, characteristic
7C3×#63866C211yesmaximal, characteristic, complemented
8C3×#63845C212yesmaximal, complemented
9C3×#63844C211yesmaximal, characteristic, complemented
10C3×Dic3×Dic6C212yesmaximal, complemented
11C3×#63836C212yesmaximal
12C3×#5728—31nomaximal
13C3×#5578—31nomaximal
14#10594397C311yesmaximal, characteristic, direct product factor
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×Dic6C2212yes—
18C2×C32×Dic6C2211yescharacteristic
19C2×C3×#624C2211yescharacteristic
20C2×C3×#624C2211yescharacteristic
21C33×C4⋊C4C2211yescharacteristic
22C3×#3752C2212yes—
23C3×C4⋊(C3⋊Dic3)C2212yes—
24C32×C4⋊Dic3C2211yescharacteristic
25C32×Dic3⋊C4C2212yes—
26C32×Dic3⋊C4C2212yes—
27C32×C4×Dic3C2212yes—
28C32×C4×Dic3C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30C3×#3724C2212yes—
31C3×Dic3⋊Dic3C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×#3722C2212yes—
35C3×Dic32C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2211yescharacteristic
38C32×C4⋊Q8—31no—
39C32×C4×Q8—31no—
40#64106C2×C311yescharacteristic
41C3×#946—31no—
42C3×#946—32no—
43C3×Q8×Dic3—32no—
44C3×#944—31no—
45C3×#897—31no—
46C3×#897—31no—
47C3×#897—31no—
48C3×#897—61no—
49C3×#896—32no—
50C3×#892—32no—
51C3×#890—32no—
52C3×#889—32no—
53C3×#888—21no—
54C3×#888D311yescharacteristic, complemented
55C3×#888C2×C311yescharacteristic, complemented
56C3×#887—21no—
57C3×#887—31no—
58C3×#887D311yescharacteristic, complemented
59C3×#887C2×C311yescharacteristic, complemented
60C3×#872—32no—
61C3×C42×D3—31no—
62C3×C42×D3—31no—
63C3×#869—31no—
64C3×C4×Dic6—32no—
65C3×C4×Dic6—31no—
66#63888C2×C312yes—
67C4×#624C2×C311yescharacteristic
68#63871C2×C311yescharacteristic
69#63866C2×C311yescharacteristic, complemented
70#63845C2×C312yescomplemented
71#63844C2×C311yescharacteristic, complemented
72Dic3×Dic6C2×C312yescomplemented
73#63836C2×C312yes—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2312yes—
79C3×C4×C3⋊D3—22no—
80C3×#634—22no—
81C2×C32×Dic3C2311yescharacteristic
82C2×C32×Dic3C2312yes—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×Dic6—22no—
88C32×Dic6—24no—
89C3×#624—22no—
90C3×#624Q814yescomplemented
91C3×#533—91no—
92#5728—31no—
93#5578—31no—
94C2×C32×Q8—31no—
95C2×C32×Q8—32no—
96C2×C4×C3⋊D3C22×C311yescharacteristic
97C2×#634C22×C311yescharacteristic
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—61no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6—22no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—31no—
109C2×C3×Dic6—61no—
110C2×C3×Dic6C2×D311yescharacteristic
111C2×C3×Dic6C2×D312yes—
112C2×C3×Dic6C22×C311yescharacteristic
113C2×C3×Dic6C22×C312yes—
114C2×#624C22×C311yescharacteristic
115C2×#624C22×C311yescharacteristic
116C32×C4⋊C4—21no—
117C32×C4⋊C4—21no—
118C32×C4⋊C4—21no—
119C32×C4⋊C4—31no—
120C32×C4⋊C4—32no—
121C32×C4⋊C4—32no—
122C32×C4⋊C4—41no—
123C32×C4⋊C4C2×D311yescharacteristic
124C32×C4⋊C4C2×D311yescharacteristic
125C32×C4⋊C4C22×C311yescharacteristic
126C32×C42—31no—
127C32×C42—32no—
128C32×C42—31no—
129#3752C22×C312yes—
130C4⋊(C3⋊Dic3)C22×C312yes—
131C3×(C2×D3)⋊C4—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×(C2×D3)⋊C4—62no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—32no—
140C3×C4⋊Dic3—32no—
141C3×C4⋊Dic3—32no—
142C3×C4⋊Dic3—62no—
143C3×C4⋊Dic3C2×D311yescharacteristic
144C3×C4⋊Dic3C22×C311yescharacteristic
145C3×Dic3⋊C4—22no—
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4C2×D312yes—
153C3×Dic3⋊C4C2×D312yes—
154C3×Dic3⋊C4C22×C312yes—
155C3×Dic3⋊C4C22×C312yes—
156C3×C4×Dic3—22no—
157C3×C4×Dic3—21no—
158C3×C4×Dic3—21no—
159C3×C4×Dic3—32no—
160C3×C4×Dic3—31no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—32no—
165C3×C4×Dic3C2×D311yescharacteristic
166C3×C4×Dic3C2×D312yes—
167C3×C4×Dic3C2×D311yescharacteristic
168C3×C4×Dic3C22×C312yes—
169C3×C4×Dic3C22×C311yescharacteristic
170C3×C4×Dic3C22×C311yescharacteristic
171#3724C22×C312yes—
172Dic3⋊Dic3C22×C312yes—
173Dic3⋊Dic3C22×C312yes—
174Dic3⋊Dic3C22×C312yes—
175#3722C22×C312yes—
176Dic32C22×C312yes—
177Dic32C22×C311yescharacteristic
178Dic32C22×C311yescharacteristic
179C22×C33C2411yescharacteristic
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3C2×Q812yes—
183C33×C4—22no—
184C33×C4#4112yes—
185C3×C3⋊Dic3—22no—
186C3×C3⋊Dic3—21no—
187C32×Dic3—22no—
188C32×Dic3—21no—
189C32×Dic3—22no—
190C32×Dic3C2×Q812yes—
191C32×Dic3C2×Q812yes—
192C32×Dic3#4112yes—
193C3×C4⋊Q8—31no—
194C3×C4⋊Q8—31no—
195C3×C4⋊Q8—61no—
196C3×C4⋊Q8—91no—
197C3×#125—92no—
198C3×C22⋊Q8—92no—
199C3×C22⋊Q8—91no—
200C3×C22⋊Q8—91no—
201C3×C4×Q8—31no—
202C3×C4×Q8—31no—
203C3×C4×Q8—61no—
204C3×C4×Q8—91no—
205C3×C4×Q8—92no—
206C3×#117—92no—
207C2×C3×C42—91no—
208#946—31no—
209#946—32no—
210Q8×Dic3—32no—
211#944—31no—
212#897—31no—
213#897—31no—
214#897—31no—
215#897—61no—
216#896—32no—
217#892—32no—
218#890—32no—
219#889—32no—
220#888C3×D311yescharacteristic, complemented
221#887—31no—
222#887C3×D311yescharacteristic, complemented
223#872—32no—
224C42×D3—31no—
225C42×D3—31no—
226#869—31no—
227C4×Dic6—32no—
228C4×Dic6—31no—
229C22×C3⋊D3C23×C311yescharacteristic
230C22×C3×D3—31no—
231C22×C3×D3—31no—
232C22×C3×D3—61no—
233C32×Q8—62no—
234C32×Q8—64no—
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—31no—
244C2×C32×C4—31no—
245C2×C32×C4—32no—
246C2×C32×C4—32no—
247C2×C32×C4—41no—
248C2×C32×C4—42no—
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×C311yescharacteristic
256C2×C3⋊Dic3C23×C312yes—
257C4×C3⋊D3—22no—
258#634—22no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—22no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D312yes—
273C2×C3×Dic3C22×D312yes—
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C23×C312yes—
278C2×C3×Dic3C23×C311yescharacteristic
279C2×C3×Dic3C23×C312yes—
280C2×C3×Dic3C23×C311yescharacteristic
281C2×C3×Dic3C23×C311yescharacteristic
282C2×C3×Dic3C23×C311yescharacteristic
283C3×C4×D3—34no—
284C3×C4×D3—34no—
285C3×C4×D3—62no—
286C3×C4×D3—62no—
287C3×C4×D3—62no—
288C3×C4×D3—62no—
289C3×C4×D3—122no—
290C3×Dic6—24no—
291C3×Dic6—22no—
292C3×Dic6—22no—
293C3×Dic6—24no—
294C3×Dic6—24no—
295C3×Dic6—44no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298C3×Dic6—122no—
299#624—22no—
300#624C3×Q814yescomplemented
301#533—91noSylow
302C2×C33C22×Q811yescharacteristic
303C2×C33C2×#4111yescharacteristic
304C2×C33C2×#4111yescharacteristic
305C3×C3⋊D3—22no—
306C2×C3×Q8—31no—
307C2×C3×Q8—32no—
308C2×C3×Q8—31no—
309C2×C3×Q8—32no—
310C2×C3×Q8—61no—
311C2×C3×Q8—62no—
312C2×C3×Q8—91no—
313C22×C3×C4—91no—
314C22×C3×C4—91no—
315C22×C3×C4—91no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×Dic6—31no—
324C2×Dic6—31no—
325C2×Dic6—61no—
326C2×Dic6C2×C3×D312yes—
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—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—32no—
336C3×C4⋊C4—32no—
337C3×C4⋊C4—41no—
338C3×C4⋊C4—62no—
339C3×C4⋊C4—62no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—92no—
342C3×C4⋊C4—92no—
343C3×C4⋊C4—92no—
344C3×C4⋊C4—92no—
345C3×C4⋊C4—92no—
346C3×C4⋊C4D3211yescharacteristic
347C3×C4⋊C4C2×C3×D311yescharacteristic
348C3×C4⋊C4C2×C3×D311yescharacteristic
349C3×C22⋊C4—92no—
350C3×C22⋊C4—92no—
351C3×C42—31no—
352C3×C42—31no—
353C3×C42—32no—
354C3×C42—31no—
355C3×C42—32no—
356C3×C42—31no—
357C3×C42—61no—
358C3×C42—62no—
359C3×C42—61no—
360C3×C42—91no—
361C3×C42—91no—
362C3×C42—92no—
363(C2×D3)⋊C4—32no—
364(C2×D3)⋊C4—32no—
365(C2×D3)⋊C4—32no—
366(C2×D3)⋊C4—32no—
367(C2×D3)⋊C4—62no—
368C4⋊Dic3—32no—
369C4⋊Dic3—32no—
370C4⋊Dic3—32no—
371C4⋊Dic3—32no—
372C4⋊Dic3—32no—
373C4⋊Dic3—62no—
374C4⋊Dic3C2×C3×D311yescharacteristic
375Dic3⋊C4—32no—
376Dic3⋊C4—32no—
377Dic3⋊C4—32no—
378Dic3⋊C4—32no—
379Dic3⋊C4—32no—
380Dic3⋊C4C2×C3×D312yes—
381Dic3⋊C4C2×C3×D312yes—
382C4×Dic3—31no—
383C4×Dic3—32no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—32no—
388C4×Dic3C2×C3×D311yescharacteristic
389C4×Dic3C2×C3×D311yescharacteristic
390C4×Dic3C2×C3×D312yes—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—41no—
395C22×C32C23×D311yescharacteristic
396C22×C32C23×D311yescharacteristic
397C22×C32C24×C311yescharacteristic
398C2×C3⋊D3—21no—
399C2×C3⋊D3—21no—
400C2×C3⋊D3C2×C3×Q812yes—
401C2×C3×D3—32no—
402C2×C3×D3—32no—
403C2×C3×D3—62no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3—61no—
407C2×C3×D3—61no—
408C2×C3×D3—121no—
409C2×C3×D3—121no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—22no—
416C32×C4—32no—
417C32×C4—32no—
418C32×C4—32no—
419C32×C4—42no—
420C32×C4—42no—
421C32×C4—42no—
422C32×C4—42no—
423C32×C4—62no—
424C32×C4—61no—
425C32×C4—62no—
426C32×C4—82no—
427C32×C4#23512yes—
428C32×C4#23912yes—
429C32×C4C3×#4112yes—
430C3⋊Dic3—22no—
431C3⋊Dic3—21no—
432C3×Dic3—24no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—22no—
442C3×Dic3—42no—
443C3×Dic3—41no—
444C3×Dic3—62no—
445C3×Dic3—61no—
446C3×Dic3—62no—
447C3×Dic3—61no—
448C3×Dic3—122no—
449C3×Dic3—121no—
450C3×Dic3#23712yes—
451C3×Dic3D3×Q812yes—
452C3×Dic3D3×Q812yes—
453C3×Dic3C2×C3×Q812yes—
454C3×Dic3C2×C3×Q812yes—
455C3×Dic3C3×#4112yes—
456C4⋊Q8—31no—
457C4⋊Q8—91no—
458#125—92no—
459C22⋊Q8—92no—
460C22⋊Q8—91no—
461C22⋊Q8—91no—
462C4×Q8—31no—
463C4×Q8—91no—
464C4×Q8—92no—
465#117—92no—
466C2×C42—91no—
467C33#53311yescharacteristic, complemented, Sylow
468C23×C3—91no—
469C22×D3—31no—
470C22×D3—31no—
471C22×D3—61no—
472C3×Q8—64no—
473C3×Q8—64no—
474C3×Q8—64no—
475C3×Q8—62no—
476C3×Q8—62no—
477C3×Q8—124no—
478C3×Q8—182no—
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—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—31no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—41no—
498C2×C3×C4—42no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—62no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—62no—
505C2×C3×C4—94no—
506C2×C3×C4—91no—
507C2×C3×C4—92no—
508C2×C3×C4—182no—
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—32no—
519C2×Dic3—32no—
520C2×Dic3—61no—
521C2×Dic3—62no—
522C2×Dic3C22×C3×D311yescharacteristic
523C2×Dic3C22×C3×D312yes—
524C2×Dic3C22×C3×D312yes—
525C2×Dic3C22×C3×D311yescharacteristic
526C2×Dic3C22×C3×D311yescharacteristic
527C2×Dic3C22×C3×D311yescharacteristic
528C4×D3—34no—
529C4×D3—34no—
530C4×D3—62no—
531C4×D3—62no—
532C4×D3—62no—
533C4×D3—62no—
534C4×D3—122no—
535Dic6—22no—
536Dic6—24no—
537Dic6—62no—
538Dic6—62no—
539Dic6—122no—
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×C32C2×#23511yescharacteristic
553C2×C32C2×#23711yescharacteristic
554C2×C32C2×D3×Q811yescharacteristic
555C2×C32C2×D3×Q811yescharacteristic
556C2×C32C2×#23911yescharacteristic
557C2×C32D3×#4111yescharacteristic
558C2×C32C22×C3×Q811yescharacteristic
559C2×C32C2×C3×#4111yescharacteristic
560C2×C32C2×C3×#4111yescharacteristic
561C3⋊D3—22no—
562C3×D3—62no—
563C3×D3—62no—
564C3×D3—122no—
565C2×Q8—31no—
566C2×Q8—32no—
567C2×Q8—91no—
568C22×C4—91no—
569C22×C4—91no—
570C22×C4—91no—
571C4⋊C4—32no—
572C4⋊C4—32no—
573C4⋊C4—31no—
574C4⋊C4—92no—
575C4⋊C4—92no—
576C4⋊C4—92no—
577C4⋊C4—92no—
578C4⋊C4—92no—
579C4⋊C4C3×D3211yescharacteristic
580C22⋊C4—92no—
581C22⋊C4—92no—
582C42—31no—
583C42—31no—
584C42—32no—
585C42—91no—
586C42—91no—
587C42—92no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—41no—
592C22×C3—92no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3C22×D3211yescharacteristic
596C22×C3C23×C3×D311yescharacteristic
597C22×C3C23×C3×D311yescharacteristic
598C2×D3—32no—
599C2×D3—32no—
600C2×D3—62no—
601C2×D3—61no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—61no—
605C2×D3—121no—
606C2×D3—121no—
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—32no—
616C3×C4—32no—
617C3×C4—32no—
618C3×C4—32no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4—64no—
627C3×C4—62no—
628C3×C4—61no—
629C3×C4—62no—
630C3×C4—61no—
631C3×C4—62no—
632C3×C4—62no—
633C3×C4—82no—
634C3×C4—122no—
635C3×C4—121no—
636C3×C4—181no—
637C3×C4—182no—
638C3×C4#379912yes—
639C3×C4C3×#23512yes—
640C3×C4C3×#23912yes—
641Dic3—22no—
642Dic3—22no—
643Dic3—21no—
644Dic3—62no—
645Dic3—61no—
646Dic3—62no—
647Dic3—61no—
648Dic3—122no—
649Dic3—121no—
650Dic3C3×#23712yes—
651Dic3C3×D3×Q812yes—
652Dic3C3×D3×Q812yes—
653C32—21no—
654C32—21no—
655C32—21no—
656C32—41no—
657C32#557811yescharacteristic, complemented
658C32#572811yescharacteristic, complemented
659C32C3×#53311yescharacteristic, complemented
660C23—91no—
661Q8—64no—
662Q8—62no—
663Q8—182no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—94no—
671C2×C4—91no—
672C2×C4—92no—
673C2×C4—182no—
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—182no—
690C2×C3C2×#379911yescharacteristic
691C2×C3D3×#23711yescharacteristic
692C2×C3D32×Q811yescharacteristic
693C2×C3C2×C3×#23511yescharacteristic
694C2×C3C2×C3×#23711yescharacteristic
695C2×C3C2×C3×D3×Q811yescharacteristic
696C2×C3C2×C3×D3×Q811yescharacteristic
697C2×C3C2×C3×#23911yescharacteristic
698C2×C3C3×D3×#4111yescharacteristic
699D3—62no—
700D3—62no—
701D3—122no—
702C22—92no—
703C22—181no—
704C22—181no—
705C22C22×C3×D3211yescharacteristic
706C4—22no—
707C4—32no—
708C4—32no—
709C4—32no—
710C4—62no—
711C4—61no—
712C4—62no—
713C4—181no—
714C4—182no—
715C4C3×#379912yes—
716C3—21no—
717C3—21no—
718C3—21no—
719C3—41no—
720C3#1059439711yescharacteristic, direct product factor
721C3C3×#557811yescharacteristic, complemented
722C3C3×#572811yescharacteristic, complemented
723C2—182no—
724C2C2×C3×#379911yescharacteristic
725C2C3×D3×#23711yescharacteristic
726C2C3×D32×Q811yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC22×C3×C3⋊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
2. C32×#888C2semidirect
3. C32×#887C2semidirect
7. C3×#63866C2semidirect
8. C3×#63845C2semidirect
9. C3×#63844C2semidirect
10. C3×Dic3×Dic6C2semidirect
14. #10594397C3direct (N × H)
54. C3×#888D3semidirect
55. C3×#888C2×C3semidirect
58. C3×#887D3semidirect
59. C3×#887C2×C3semidirect
69. #63866C2×C3semidirect
70. #63845C2×C3semidirect
71. #63844C2×C3semidirect
72. Dic3×Dic6C2×C3semidirect
90. C3×#624Q8semidirect
220. #888C3×D3semidirect
222. #887C3×D3semidirect
300. #624C3×Q8semidirect
467. C33#533semidirect
657. C32#5578semidirect
658. C32#5728semidirect
659. C32C3×#533semidirect
720. C3#10594397direct (N × H)
721. C3C3×#5578semidirect
722. C3C3×#5728semidirect

Maximal subgroups

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

subgroupindex
C3×#641062
C32×#8882
C32×#8872
C3×#638882
C3×C4×#6242
C3×#638712
C3×#638662
C3×#638452
C3×#638442
C3×Dic3×Dic62
C3×#638362
C3×#57283
C3×#55783
#105943973