Finite Group Databasebeta

← #13168344

Subgroups — #13168344

Order 1728.

1138 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723668C211yesmaximal, characteristic, complemented
2#11723443C211yesmaximal, characteristic, complemented
3#11723426C211yesmaximal, characteristic
4#11723406C211yesmaximal, characteristic, complemented
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×C4×D3×Dic3C211yesmaximal, characteristic
7C3×#63857C211yesmaximal, characteristic
8#11723012C212yesmaximal, complemented
9#11722969C212yesmaximal
10#11722940C212yesmaximal, complemented
11#11722914C212yesmaximal
12#10594808—31nomaximal
13#10594387—31nomaximal
14#10593859—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×C3×#627C2212yes—
19C2×C3×D3×Dic3C2211yescharacteristic
20C2×C3×D3×Dic3C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4×C3⋊Dic3C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25#88815C2212yes—
26#88813C2212yes—
27#88807C2212yes—
28#88806C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31(C2×D3)⋊(C3⋊Dic3)C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2211yescharacteristic
38#64133—31no—
39#64096—31no—
40#64078—31no—
41C3×#924—31no—
42C2×C3×C4×Dic3—31no—
43C3×#897—31no—
44C3×#888—31no—
45C3×C42×D3—31no—
46C3×#869—31no—
47#63964—32no—
48#63955—32no—
49#63918D311yescharacteristic, complemented
50#63887—32no—
51#63878—32no—
52C4×D3×Dic3D311yescharacteristic
53#63869—32no—
54#63867—32no—
55#63866—31no—
56#63866—31no—
57#63866—61no—
58#63857—31no—
59#63857—31no—
60#63857—61no—
61#63857D311yescharacteristic
62#63856—32no—
63#63846—32no—
64#63844—31no—
65#63844—31no—
66#63844—31no—
67#63844—61no—
68#63843—31no—
69#63843—32no—
70Dic3×Dic6—31no—
71Dic3×Dic6—32no—
72#63841—32no—
73#63837—32no—
74C22×C32×D3C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2312yes—
77#6308—22no—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×#634—22no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3—22no—
88C3×#627—24no—
89C3×D3×Dic3—22no—
90C3×D3×Dic3Q814yescomplemented
91#5728—91no—
92#5622—91no—
93#5470—91no—
94C22×C32×C4—31no—
95C2×#634—31no—
96C2×#634—31no—
97C2×#634—31no—
98C2×#634—61no—
99C2×#634—61no—
100C2×#634—61no—
101C2×#634—121no—
102C2×#634C2×D311yescharacteristic
103C22×C3×Dic3—31no—
104C22×C3×Dic3—31no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3C2×D311yescharacteristic
109C2×C3×C4×D3C2×D311yescharacteristic
110C2×C3×Dic6—31no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—32no—
113C2×C3×Dic6—32no—
114C2×C3×Dic6—61no—
115C2×#627C2×D312yes—
116C2×D3×Dic3C2×D311yescharacteristic
117C2×D3×Dic3C2×D311yescharacteristic
118C32×C4⋊C4—31no—
119C32×C42—31no—
120#3757—32no—
121C4⋊(C3⋊Dic3)—32no—
122C4⋊(C3⋊Dic3)—32no—
123C4⋊(C3⋊Dic3)C2×D311yescharacteristic
124#3750—32no—
125#3750—32no—
126C4×C3⋊Dic3—32no—
127C4×C3⋊Dic3C2×D311yescharacteristic
128C3×#217—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3—32no—
135C3×C4⋊Dic3—61no—
136C3×C4⋊Dic3C2×D311yescharacteristic
137C3×C4⋊Dic3C2×D311yescharacteristic
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×C4×Dic3—21no—
141C3×C4×Dic3—31no—
142C3×C4×Dic3—31no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—31no—
145C3×C4×Dic3—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—61no—
148C3×C4×Dic3C2×D311yescharacteristic
149C3×C4×Dic3C2×D311yescharacteristic
150#3724—32no—
151#3724—32no—
152#3724—32no—
153#3724—62no—
154Dic3⋊Dic3—32no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—62no—
163Dic3⋊Dic3—62no—
164Dic3⋊Dic3—62no—
165Dic3⋊Dic3C2×D312yes—
166Dic3⋊Dic3C2×D312yes—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—62no—
170(C2×D3)⋊Dic3C2×D312yes—
171Dic32—32no—
172Dic32—32no—
173Dic32—32no—
174Dic32—32no—
175Dic32—32no—
176Dic32—62no—
177Dic32C2×D311yescharacteristic
178Dic32C2×D311yescharacteristic
179C22×C33C2411yescharacteristic
180C2×C32×D3—21no—
181C2×C32×D3—21no—
182C2×C32×D3C2×Q812yes—
183C33×C4#4112yes—
184C3⋊(C3⋊Dic3)—22no—
185C3×C3⋊Dic3—21no—
186C3×C3⋊Dic3—22no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3C2×Q812yes—
189C32×Dic3—22no—
190C32×Dic3—21no—
191C32×Dic3C2×Q812yes—
192C32×Dic3#4112yes—
193C3×C4⋊Q8—91no—
194C3×C22⋊Q8—91no—
195C2×C3×C42—91no—
196#946—92no—
197Q8×Dic3—92no—
198Q8×Dic3—91no—
199#944—91no—
200#926—92no—
201#924—31no—
202#924—91no—
203#924—91no—
204#924—92no—
205#924—181no—
206C2×C4×Dic3—31no—
207#897—31no—
208#897—91no—
209#892—92no—
210#890—92no—
211#889—92no—
212#888—31no—
213#887—91no—
214#887—91no—
215#887—92no—
216#887—91no—
217#887—181no—
218#878—92no—
219#877—92no—
220C42×D3—31no—
221#870—92no—
222#869—31no—
223#869—91no—
224#869—91no—
225#869—181no—
226C4×Dic6—92no—
227C4×Dic6—91no—
228C4×Dic6—91no—
229C23×C32—31no—
230C22×C3×D3—21no—
231C22×C3×D3C22×D311yescharacteristic
232C22×C3×D3C22×D311yescharacteristic
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—31no—
237C2×C32×C4—31no—
238C2×C32×C4—31no—
239C2×C32×C4—32no—
240C2×C32×C4—41no—
241C2×C32×C4—62no—
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C3⋊Dic3—32no—
246C2×C3⋊Dic3—32no—
247C2×C3⋊Dic3—32no—
248C2×C3⋊Dic3—62no—
249C2×C3⋊Dic3—62no—
250C2×C3⋊Dic3—62no—
251C2×C3⋊Dic3—122no—
252C2×C3⋊Dic3C22×D312yes—
253C2×C3⋊Dic3C22×D312yes—
254C2×C3⋊Dic3C22×D311yescharacteristic
255C2×C3⋊Dic3C22×D311yescharacteristic
256#634—22no—
257#634—62no—
258#634—64no—
259#634—62no—
260#634—62no—
261#634—122no—
262#634—122no—
263#634—124no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—22no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—34no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—62no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C3×C4×D3—22no—
291C3×C4×D3—22no—
292C3×C4×D3—34no—
293C3×C4×D3—42no—
294C3×C4×D3—62no—
295C3×Dic6—64no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298C3×Dic6—64no—
299C3×Dic6—122no—
300#627—24no—
301D3×Dic3—22no—
302D3×Dic3Dic614yescomplemented
303#533—271noSylow
304C2×C33C22×Q811yescharacteristic
305C2×C33C2×#4111yescharacteristic
306C2×C33C2×#4111yescharacteristic
307C32×D3—22no—
308C2×C3×Q8—92no—
309C2×C3×Q8—91no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—91no—
314C22×C3×C4—91no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3D3211yescharacteristic
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—32no—
323C2×Dic6—32no—
324C2×Dic6—61no—
325C2×Dic6—91no—
326C2×Dic6—91no—
327C2×Dic6—91no—
328C2×Dic6—181no—
329C2×Dic6—181no—
330C2×Dic6—181no—
331C2×Dic6—361no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—92no—
336C3×C4⋊C4—92no—
337C3×C4⋊C4—91no—
338C3×C22⋊C4—92no—
339C3×C42—31no—
340C3×C42—31no—
341C3×C42—61no—
342C3×C42—91no—
343C3×C42—91no—
344C3×C42—91no—
345#217—32no—
346#217—92no—
347#217—92no—
348#217—182no—
349(C2×D3)⋊C4—32no—
350(C2×D3)⋊C4—92no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—32no—
354C4⋊Dic3—32no—
355C4⋊Dic3—61no—
356C4⋊Dic3—92no—
357C4⋊Dic3—92no—
358C4⋊Dic3—92no—
359C4⋊Dic3—92no—
360C4⋊Dic3—92no—
361C4⋊Dic3—92no—
362C4⋊Dic3—182no—
363C4⋊Dic3—182no—
364C4⋊Dic3D3211yescharacteristic
365Dic3⋊C4—32no—
366Dic3⋊C4—32no—
367Dic3⋊C4—92no—
368Dic3⋊C4—92no—
369Dic3⋊C4—92no—
370Dic3⋊C4—92no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—182no—
377Dic3⋊C4—182no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—61no—
385C4×Dic3—92no—
386C4×Dic3—92no—
387C4×Dic3—92no—
388C4×Dic3—92no—
389C4×Dic3—92no—
390C4×Dic3—92no—
391C4×Dic3—182no—
392C4×Dic3D3211yescharacteristic
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—32no—
397C22×C32—41no—
398C22×C32—61no—
399C22×C32—61no—
400C22×C32C23×D311yescharacteristic
401C22×C32C23×D311yescharacteristic
402C22×C32C23×D311yescharacteristic
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3C2×Dic612yes—
411C2×C3×D3D3×Q812yes—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—32no—
416C32×C4—32no—
417C32×C4—42no—
418C32×C4—62no—
419C32×C4—61no—
420C32×C4#23512yes—
421C32×C4#23712yes—
422C32×C4#23912yes—
423C3⋊Dic3—21no—
424C3⋊Dic3—22no—
425C3⋊Dic3—22no—
426C3⋊Dic3—62no—
427C3⋊Dic3—64no—
428C3⋊Dic3—62no—
429C3⋊Dic3—62no—
430C3⋊Dic3—122no—
431C3⋊Dic3—122no—
432C3⋊Dic3—124no—
433C3⋊Dic3C2×Dic612yes—
434C3×Dic3—21no—
435C3×Dic3—22no—
436C3×Dic3—21no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—32no—
441C3×Dic3—32no—
442C3×Dic3—41no—
443C3×Dic3—42no—
444C3×Dic3—62no—
445C3×Dic3—62no—
446C3×Dic3—62no—
447C3×Dic3—61no—
448C3×Dic3—62no—
449C3×Dic3—62no—
450C3×Dic3—61no—
451C3×Dic3—122no—
452C3×Dic3—122no—
453C3×Dic3—121no—
454C3×Dic3C2×Dic612yes—
455C3×Dic3#23512yes—
456C3×Dic3#23712yes—
457C3×Dic3D3×Q812yes—
458C4⋊Q8—91no—
459C4⋊Q8—271no—
460#125—272no—
461C22⋊Q8—91no—
462C22⋊Q8—272no—
463C22⋊Q8—271no—
464C4×Q8—271no—
465C4×Q8—272no—
466C4×Q8—271no—
467#117—272no—
468C2×C42—91no—
469C33#53311yescharacteristic, complemented, Sylow
470C23×C3—31no—
471C23×C3—31no—
472C23×C3—61no—
473C22×D3C2×D3211yescharacteristic
474C3×Q8—184no—
475C3×Q8—182no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—31no—
487C2×C3×C4—41no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—62no—
491C2×C3×C4—61no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—94no—
495C2×C3×C4—91no—
496C2×C3×C4—92no—
497C2×C3×C4—92no—
498C2×C3×C4—91no—
499C2×C3×C4—122no—
500C2×C3×C4—182no—
501C2×C3×C4C2×D3211yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—34no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—32no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—62no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—92no—
519C2×Dic3—92no—
520C2×Dic3—92no—
521C2×Dic3—182no—
522C2×Dic3—182no—
523C2×Dic3—182no—
524C2×Dic3—362no—
525C2×Dic3C2×D3211yescharacteristic
526C2×Dic3C2×D3212yes—
527C2×Dic3C2×D3211yescharacteristic
528C2×Dic3C2×D3211yescharacteristic
529C4×D3—22no—
530C4×D3—34no—
531C4×D3—62no—
532Dic6—64no—
533Dic6—62no—
534Dic6—62no—
535Dic6—64no—
536Dic6—122no—
537Dic6—184no—
538Dic6—182no—
539Dic6—182no—
540Dic6—182no—
541Dic6—362no—
542Dic6—362no—
543Dic6—364no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—41no—
554C2×C32—41no—
555C2×C32—41no—
556C2×C32—62no—
557C2×C32C22×Dic611yescharacteristic
558C2×C32C2×#23511yescharacteristic
559C2×C32C2×#23511yescharacteristic
560C2×C32C2×#23711yescharacteristic
561C2×C32C2×#23711yescharacteristic
562C2×C32C2×D3×Q811yescharacteristic
563C2×C32C2×D3×Q811yescharacteristic
564C2×C32C2×#23911yescharacteristic
565C2×C32D3×#4111yescharacteristic
566C3×D3—22no—
567C3×D3—22no—
568C3×D3—42no—
569C2×Q8—92no—
570C2×Q8—91no—
571C2×Q8—271no—
572C22×C4—31no—
573C22×C4—91no—
574C22×C4—91no—
575C4⋊C4—31no—
576C4⋊C4—92no—
577C4⋊C4—92no—
578C4⋊C4—91no—
579C4⋊C4—272no—
580C4⋊C4—272no—
581C4⋊C4—272no—
582C4⋊C4—272no—
583C4⋊C4—272no—
584C22⋊C4—92no—
585C22⋊C4—272no—
586C42—31no—
587C42—91no—
588C42—91no—
589C42—91no—
590C42—272no—
591C42—272no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—32no—
596C22×C3—32no—
597C22×C3—41no—
598C22×C3—62no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3C22×D3211yescharacteristic
606C22×C3C22×D3211yescharacteristic
607C22×C3C22×D3211yescharacteristic
608C2×D3—21no—
609C2×D3—21no—
610C2×D3D3×Dic612yes—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—22no—
614C3×C4—32no—
615C3×C4—32no—
616C3×C4—32no—
617C3×C4—32no—
618C3×C4—42no—
619C3×C4—62no—
620C3×C4—62no—
621C3×C4—62no—
622C3×C4—61no—
623C3×C4—61no—
624C3×C4—62no—
625C3×C4—92no—
626C3×C4—121no—
627C3×C4—122no—
628C3×C4—182no—
629C3×C4—182no—
630C3×C4—181no—
631C3×C4#379612yes—
632C3×C4#379912yes—
633C3×C4#380412yes—
634Dic3—22no—
635Dic3—21no—
636Dic3—32no—
637Dic3—32no—
638Dic3—62no—
639Dic3—62no—
640Dic3—61no—
641Dic3—62no—
642Dic3—61no—
643Dic3—62no—
644Dic3—62no—
645Dic3—122no—
646Dic3—121no—
647Dic3—122no—
648Dic3—184no—
649Dic3—182no—
650Dic3—182no—
651Dic3—182no—
652Dic3—362no—
653Dic3—362no—
654Dic3—364no—
655Dic3D3×Dic612yes—
656Dic3#379512yes—
657C32—21no—
658C32—21no—
659C32—21no—
660C32—41no—
661C32#547011yescharacteristic, complemented
662C32#562211yescharacteristic, complemented
663C32#572811yescharacteristic, complemented
664C23—31no—
665Q8—184no—
666Q8—182no—
667Q8—542no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—32no—
672C2×C4—62no—
673C2×C4—94no—
674C2×C4—91no—
675C2×C4—91no—
676C2×C4—92no—
677C2×C4—92no—
678C2×C4—182no—
679C2×C4—272no—
680C2×C4D3311yescharacteristic
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—41no—
691C2×C3—41no—
692C2×C3—41no—
693C2×C3—62no—
694C2×C3—62no—
695C2×C3—122no—
696C2×C3C2×D3×Dic611yescharacteristic
697C2×C3C2×D3×Dic611yescharacteristic
698C2×C3C2×#379511yescharacteristic
699C2×C3C2×#379611yescharacteristic
700C2×C3C2×#379911yescharacteristic
701C2×C3D3×#23511yescharacteristic
702C2×C3D3×#23711yescharacteristic
703C2×C3D32×Q811yescharacteristic
704C2×C3C2×#380411yescharacteristic
705D3—22no—
706C22—32no—
707C22—61no—
708C22—61no—
709C22C2×D3311yescharacteristic
710C4—32no—
711C4—32no—
712C4—62no—
713C4—61no—
714C4—92no—
715C4—181no—
716C4—182no—
717C4—182no—
718C4—542no—
719C4#8896212yes—
720C3—21no—
721C3—21no—
722C3—21no—
723C3—41no—
724C3#1059385911yescharacteristic, complemented
725C3#1059438711yescharacteristic, complemented
726C3#1059480811yescharacteristic, complemented
727C2—62no—
728C2D32×Dic611yescharacteristic
729C2D3×#379511yescharacteristic
730C2C2×#8896211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×D3C23
hypercenterC2×C4D33
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723668C2semidirect
2. #11723443C2semidirect
4. #11723406C2semidirect
5. C3×#63918C2semidirect
8. #11723012C2semidirect
10. #11722940C2semidirect
49. #63918D3semidirect
90. C3×D3×Dic3Q8semidirect
302. D3×Dic3Dic6semidirect
469. C33#533semidirect
661. C32#5470semidirect
662. C32#5622semidirect
663. C32#5728semidirect
724. C3#10593859semidirect
725. C3#10594387semidirect
726. C3#10594808semidirect

Maximal subgroups

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

subgroupindex
#117236682
#117234432
#117234262
#117234062
C3×#639182
C3×C4×D3×Dic32
C3×#638572
#117230122
#117229692
#117229402
#117229142
#105948083
#105943873
#105938593