Finite Group Databasebeta

← #13178340

Subgroups — #13178340

Order 1728.

1156 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64102C211yesmaximal, characteristic
2C3×#64099C211yesmaximal, characteristic, complemented
3C3×#64097C211yesmaximal, characteristic, complemented
4C4×#6296C211yesmaximal, characteristic, complemented
5#11723692C212yesmaximal, complemented
6#11723691C211yesmaximal, characteristic
7#11723691C211yesmaximal, characteristic
8#11723688C212yesmaximal, complemented
9#11723682C212yesmaximal, complemented
10#11723680C211yesmaximal, characteristic, complemented
11#11723674C212yesmaximal, complemented
12#10594485—31nomaximal
13#10594470—31nomaximal
14#10594460—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2212yes—
17C2×C3×#634C2212yes—
18C2×#6296C2211yescharacteristic
19C2×#6294C2212yes—
20C2×#6294C2212yes—
21C33×C4⋊C4C2211yescharacteristic
22C3×#3752C2212yes—
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4⋊(C3⋊Dic3)C2212yes—
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×#3750C2212yes—
27C3×#3750C2212yes—
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2211yescharacteristic
30C3×C4×C3⋊Dic3C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2212yes—
33#88815C2212yes—
34#88815C2211yescharacteristic
35#88815C2211yescharacteristic
36#88814C2212yes—
37#88814C2212yes—
38#64102D311yescharacteristic
39#64099D311yescharacteristic, complemented
40#64097D311yescharacteristic, complemented
41C3×#893—31no—
42C3×#893—31no—
43C3×#893—61no—
44C3×#890—31no—
45C3×#890—31no—
46C3×#890—61no—
47C3×#888—31no—
48C3×#888—31no—
49C3×#888—61no—
50C4×#627—31no—
51C4×#627—31no—
52C4×#627—31no—
53#63899—32no—
54#63898—31no—
55#63898—31no—
56#63896—32no—
57#63895—32no—
58#63894—31no—
59#63894—31no—
60#63893—32no—
61Dic3×D12—31no—
62Dic3×D12—31no—
63#63888—32no—
64#63887—32no—
65#63883—32no—
66D3×Dic3⋊C4—32no—
67D3×Dic3⋊C4—32no—
68#63872—31no—
69#63871—32no—
70#63869—31no—
71#63869—31no—
72#63857—32no—
73#63856—32no—
74C22×C3×C3⋊D3C2312yes—
75C2×C33×C4C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4⋊(C3⋊D3)Q814yescomplemented
86C3×C4×C3⋊D3—42no—
87C3×#634—42no—
88#6296—22no—
89#6294—24no—
90#6294—42no—
91#5730—91no—
92#5690—91no—
93#5539—91no—
94C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
95C2×C4×C3⋊D3C2×D312yes—
96C2×#634C2×D312yes—
97C2×C3×D12—31no—
98C2×C3×D12—31no—
99C2×C3×D12—61no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3—32no—
102C2×C3×C4×D3—62no—
103C2×C3×Dic6—32no—
104C2×C3×Dic6—32no—
105C2×C3×Dic6—62no—
106C2×#627—31no—
107C2×#627—31no—
108C2×#627—31no—
109C2×#624—32no—
110C2×#624—32no—
111C2×D3×Dic3—32no—
112C2×D3×Dic3—32no—
113C2×D3×Dic3—32no—
114C2×D3×Dic3—32no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4—21no—
118C32×C4⋊C4—41no—
119C32×C4⋊C4C2×D311yescharacteristic
120C32×C4⋊C4C2×D311yescharacteristic
121C32×C4⋊C4C2×D311yescharacteristic
122#3752C2×D312yes—
123C4⋊(C3⋊Dic3)C2×D311yescharacteristic
124C4⋊(C3⋊Dic3)C2×D312yes—
125C4⋊(C3⋊Dic3)C2×D311yescharacteristic
126#3750C2×D312yes—
127#3750C2×D312yes—
128C4×C3⋊Dic3C2×D311yescharacteristic
129C4×C3⋊Dic3C2×D311yescharacteristic
130C4×C3⋊Dic3C2×D311yescharacteristic
131C3×(C2×D3)⋊C4—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—62no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—32no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—61no—
141C3×C4⋊Dic3—62no—
142C3×C4⋊Dic3—61no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—62no—
148C3×Dic3⋊C4—62no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—61no—
156C3×C4×Dic3—61no—
157C3×C4×Dic3—61no—
158#3724—31no—
159#3724—32no—
160#3724—32no—
161#3724—31no—
162#3724—31no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—32no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—31no—
173#3722—32no—
174#3722—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—32no—
179C22×C33C2411yescharacteristic
180C2×C3×C3⋊D3—22no—
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3C2×Q814yes—
183C33×C4—22no—
184C33×C4C2×Q812yes—
185C3×C3⋊Dic3—22no—
186C3×C3⋊Dic3—21no—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3#4112yes—
193C3×C4⋊Q8—91no—
194C3×#125—91no—
195C3×C4×D4—91no—
196#946—92no—
197#946—92no—
198D4×Dic3—91no—
199D4×Dic3—91no—
200#924—92no—
201C2×Dic3⋊C4—92no—
202#897—92no—
203#897—92no—
204#896—92no—
205#896—92no—
206#893—31no—
207#893—31no—
208#893—61no—
209#893—91no—
210#893—91no—
211D3×C4⋊C4—92no—
212D3×C4⋊C4—92no—
213#890—31no—
214#890—31no—
215#890—61no—
216#890—91no—
217#890—91no—
218#888—31no—
219#888—31no—
220#888—61no—
221#878—92no—
222#878—92no—
223C4×D12—91no—
224C4×D12—91no—
225#870—91no—
226C4×Dic6—91no—
227C4×Dic6—91no—
228C4×Dic6—91no—
229C22×C3⋊D3C22×D312yes—
230C22×C3×D3—32no—
231C22×C3×D3—32no—
232C22×C3×D3—62no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—22no—
237C2×C32×C4—22no—
238C2×C32×C4—22no—
239C2×C32×C4—41no—
240C2×C32×C4—42no—
241C2×C32×C4C22×D312yes—
242C2×C32×C4C22×D312yes—
243C2×C32×C4C22×D312yes—
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C3⋊Dic3C22×D311yescharacteristic
248C2×C3⋊Dic3C22×D311yescharacteristic
249C2×C3⋊Dic3C22×D312yes—
250C2×C3⋊Dic3C22×D312yes—
251C2×C3⋊Dic3C22×D311yescharacteristic
252C2×C3⋊Dic3C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D311yescharacteristic
255C4⋊(C3⋊D3)Dic614yescomplemented
256C4×C3⋊D3—42no—
257#634—42no—
258C2×C3×Dic3—31no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—62no—
282C3×D12—34no—
283C3×D12—34no—
284C3×D12—64no—
285C3×C4×D3—122no—
286C3×C4×D3—122no—
287C3×C4×D3—124no—
288C3×Dic6—122no—
289C3×Dic6—122no—
290C3×Dic6—124no—
291#627—62no—
292#627—62no—
293#627—62no—
294#624—64no—
295#624—122no—
296D3×Dic3—64no—
297D3×Dic3—64no—
298D3×Dic3—122no—
299D3×Dic3—122no—
300#554—271noSylow
301C2×C33C22×Q811yescharacteristic
302C2×C33C2×#4111yescharacteristic
303C2×C33H(5,𝔽2)11yescharacteristic
304C3×C3⋊D3—24no—
305C2×C3×Q8—92no—
306C2×C3×D4—91no—
307C22×C3×C4—92no—
308C22×Dic3—92no—
309C22×Dic3—92no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—61no—
313C2×C4×D3—32no—
314C2×C4×D3—32no—
315C2×C4×D3—62no—
316C2×C4×D3—92no—
317C2×C4×D3—92no—
318C2×C4×D3—92no—
319C2×C4×D3—92no—
320C2×Dic6—32no—
321C2×Dic6—32no—
322C2×Dic6—62no—
323C2×Dic6—91no—
324C2×Dic6—91no—
325C2×Dic6—91no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—41no—
330C3×C4⋊C4—91no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—92no—
333C3×C4⋊C4—92no—
334C3×C4⋊C4—92no—
335C3×C4⋊C4D3211yescharacteristic
336C3×C4⋊C4D3211yescharacteristic
337C3×C4⋊C4D3211yescharacteristic
338C3×C22⋊C4—92no—
339C3×C42—91no—
340C3×C42—91no—
341C3×C42—91no—
342#217—92no—
343#217—92no—
344(C2×D3)⋊C4—32no—
345(C2×D3)⋊C4—32no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—92no—
348(C2×D3)⋊C4—92no—
349(C2×D3)⋊C4—92no—
350(C2×D3)⋊C4—92no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—32no—
356C4⋊Dic3—32no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—62no—
360C4⋊Dic3—91no—
361C4⋊Dic3—91no—
362C4⋊Dic3—91no—
363C4⋊Dic3—92no—
364C4⋊Dic3—92no—
365Dic3⋊C4—32no—
366Dic3⋊C4—32no—
367Dic3⋊C4—32no—
368Dic3⋊C4—32no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—41no—
394C22×C32C23×D311yescharacteristic
395C22×C32C23×D311yescharacteristic
396C22×C32C23×D311yescharacteristic
397C2×C3⋊D3—22no—
398C2×C3⋊D3—22no—
399C2×C3⋊D3C2×Dic614yes—
400C2×C3×D3—34no—
401C2×C3×D3—34no—
402C2×C3×D3—64no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—122no—
408C2×C3×D3—122no—
409C32×C4—22no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—42no—
416C32×C4—42no—
417C32×C4—42no—
418C32×C4—42no—
419C32×C4—82no—
420C32×C4C2×Dic612yes—
421C32×C4D3×Q812yes—
422C32×C4D3×Q812yes—
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3⋊Dic3—22no—
426C3⋊Dic3—22no—
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3#23912yes—
431C3×Dic3—32no—
432C3×Dic3—32no—
433C3×Dic3—62no—
434C3×Dic3—62no—
435C3×Dic3—62no—
436C3×Dic3—61no—
437C3×Dic3—61no—
438C3×Dic3—62no—
439C3×Dic3—61no—
440C3×Dic3—61no—
441C3×Dic3—62no—
442C3×Dic3—61no—
443C3×Dic3—61no—
444C3×Dic3—62no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C3×Dic3—62no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—122no—
451C3×Dic3—121no—
452C3×Dic3—121no—
453C3×Dic3—121no—
454C3×Dic3—122no—
455C4⋊Q8—91no—
456#125—91no—
457#125—271no—
458C22⋊Q8—272no—
459C22⋊Q8—272no—
460C22⋊Q8—272no—
461C4×Q8—271no—
462C4×D4—91no—
463C4×D4—271no—
464C4×D4—271no—
465C2×C4⋊C4—272no—
466C33#55411yescharacteristic, complemented, Sylow
467C23×C3—92no—
468C22×D3—32no—
469C22×D3—32no—
470C22×D3—62no—
471C3×Q8—362no—
472C3×D4—94no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—41no—
480C2×C3×C4—42no—
481C2×C3×C4—91no—
482C2×C3×C4—91no—
483C2×C3×C4—91no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—92no—
487C2×C3×C4—92no—
488C2×C3×C4—91no—
489C2×C3×C4—362no—
490C2×C3×C4C2×D3212yes—
491C2×C3×C4C2×D3212yes—
492C2×C3×C4C2×D3212yes—
493C2×C3×C4C2×D3211yescharacteristic
494C2×C3×C4C2×D3211yescharacteristic
495C2×C3×C4C2×D3211yescharacteristic
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—32no—
509C2×Dic3—32no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—184no—
521C2×Dic3—362no—
522D12—34no—
523D12—34no—
524D12—64no—
525C4×D3—122no—
526C4×D3—122no—
527C4×D3—124no—
528C4×D3—184no—
529C4×D3—184no—
530C4×D3—362no—
531C4×D3—362no—
532Dic6—122no—
533Dic6—122no—
534Dic6—124no—
535Dic6—182no—
536Dic6—182no—
537Dic6—182no—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32—21no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—41no—
548C2×C32—41no—
549C2×C32—41no—
550C2×C32C22×Dic611yescharacteristic
551C2×C32#100411yescharacteristic
552C2×C32#100411yescharacteristic
553C2×C32C2×D3×Q811yescharacteristic
554C2×C32C2×D3×Q811yescharacteristic
555C2×C32C2×#23911yescharacteristic
556C2×C32D3×#4111yescharacteristic
557C2×C32D3×#4111yescharacteristic
558C2×C32#100911yescharacteristic
559C3⋊D3—24no—
560C3×D3—64no—
561C3×D3—64no—
562C3×D3—124no—
563C2×Q8—92no—
564C2×Q8—271no—
565C2×D4—91no—
566C22×C4—92no—
567C22×C4—272no—
568C22×C4—272no—
569C4⋊C4—92no—
570C4⋊C4—92no—
571C4⋊C4—91no—
572C4⋊C4—91no—
573C4⋊C4—92no—
574C4⋊C4—271no—
575C4⋊C4—272no—
576C4⋊C4—271no—
577C4⋊C4—271no—
578C4⋊C4—272no—
579C4⋊C4#111311yescharacteristic
580C22⋊C4—92no—
581C22⋊C4—272no—
582C22⋊C4—272no—
583C42—91no—
584C42—91no—
585C42—91no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—41no—
590C22×C3—94no—
591C22×C3—182no—
592C22×C3—182no—
593C22×C3C22×D3211yescharacteristic
594C22×C3C22×D3211yescharacteristic
595C22×C3C22×D3211yescharacteristic
596C2×D3—34no—
597C2×D3—34no—
598C2×D3—64no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—62no—
602C2×D3—62no—
603C2×D3—122no—
604C2×D3—122no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—22no—
609C3×C4—22no—
610C3×C4—22no—
611C3×C4—42no—
612C3×C4—42no—
613C3×C4—42no—
614C3×C4—42no—
615C3×C4—82no—
616C3×C4—92no—
617C3×C4—181no—
618C3×C4—182no—
619C3×C4—181no—
620C3×C4—181no—
621C3×C4—181no—
622C3×C4—181no—
623C3×C4—182no—
624C3×C4D3×Dic612yes—
625C3×C4D3×Dic612yes—
626C3×C4#379712yes—
627Dic3—32no—
628Dic3—32no—
629Dic3—62no—
630Dic3—62no—
631Dic3—62no—
632Dic3—61no—
633Dic3—62no—
634Dic3—61no—
635Dic3—61no—
636Dic3—62no—
637Dic3—61no—
638Dic3—61no—
639Dic3—61no—
640Dic3—61no—
641Dic3—61no—
642Dic3—62no—
643Dic3—61no—
644Dic3—61no—
645Dic3—62no—
646Dic3—122no—
647Dic3—121no—
648Dic3—122no—
649Dic3—121no—
650Dic3—121no—
651C32—21no—
652C32—21no—
653C32—21no—
654C32—41no—
655C32#553911yescharacteristic, complemented
656C32#569011yescharacteristic, complemented
657C32#573011yescharacteristic, complemented
658C23—92no—
659Q8—362no—
660Q8—542no—
661D4—94no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—92no—
669C2×C4—92no—
670C2×C4—362no—
671C2×C4—544no—
672C2×C4—1082no—
673C2×C4C2×#111312yes—
674C2×C4C2×#111311yescharacteristic
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—41no—
685C2×C3—41no—
686C2×C3—41no—
687C2×C3—184no—
688C2×C3C2×D3×Dic611yescharacteristic
689C2×C3C2×D3×Dic611yescharacteristic
690C2×C3C2×#379711yescharacteristic
691C2×C3#6431311yescharacteristic
692C2×C3#6431411yescharacteristic
693C2×C3#6431411yescharacteristic
694C2×C3D3×#23911yescharacteristic
695C2×C3D3×#23911yescharacteristic
696C2×C3#6431911yescharacteristic
697D3—64no—
698D3—64no—
699D3—124no—
700C22—94no—
701C22—182no—
702C22—182no—
703C22C22×#111311yescharacteristic
704C4—22no—
705C4—92no—
706C4—181no—
707C4—181no—
708C4—182no—
709C4—181no—
710C4—182no—
711C4—181no—
712C4—181no—
713C4#8904012yes—
714C3—21no—
715C3—21no—
716C3—21no—
717C3—41no—
718C3#1059446011yescharacteristic, complemented
719C3#1059447011yescharacteristic, complemented
720C3#1059448511yescharacteristic, complemented
721C2—184no—
722C2C2×#8904011yescharacteristic
723C2#1172462311yescharacteristic
724C2#1172462611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC2×C3×C4⋊(C3⋊D3)C22
hypercenterC4⋊C4#1113
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#64099C2semidirect
3. C3×#64097C2semidirect
4. C4×#6296C2semidirect
5. #11723692C2semidirect
8. #11723688C2semidirect
9. #11723682C2semidirect
10. #11723680C2semidirect
11. #11723674C2semidirect
39. #64099D3semidirect
40. #64097D3semidirect
85. C3×C4⋊(C3⋊D3)Q8semidirect
255. C4⋊(C3⋊D3)Dic6semidirect
466. C33#554semidirect
655. C32#5539semidirect
656. C32#5690semidirect
657. C32#5730semidirect
718. C3#10594460semidirect
719. C3#10594470semidirect
720. C3#10594485semidirect

Maximal subgroups

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

subgroupindex
C3×#641022
C3×#640992
C3×#640972
C4×#62962
#117236922
#117236912
#117236882
#117236822
#117236802
#117236742
#105944853
#105944703
#105944603