Finite Group Databasebeta

← #13168351

Subgroups — #13168351

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#11723674C211yesmaximal, characteristic
2#11723443C211yesmaximal, characteristic, complemented
3#11723431C211yesmaximal, characteristic
4#11723399C211yesmaximal, characteristic, complemented
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×C4×#624C211yesmaximal, characteristic
7C3×#63844C211yesmaximal, characteristic, complemented
8#11723011C212yesmaximal, complemented
9#11722970C212yesmaximal
10Dic3×#627C212yesmaximal, complemented
11#11722915C212yesmaximal
12#10594397—31nomaximal
13#10593873—31nomaximal
14#10593859—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×C3×#627C2212yes—
19C2×C3×#624C2211yescharacteristic
20C2×C3×#624C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C32×C4⋊Dic3C2211yescharacteristic
23C32×C4×Dic3C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25#88815C2212yes—
26#88814C2212yes—
27#88806C2212yes—
28Dic3⋊(C3⋊Dic3)C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31#88803C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic32C2211yescharacteristic
36C3×Dic32C2212yes—
37C3×Dic32C2211yescharacteristic
38#64106—31no—
39#64078—31no—
40C4×#634—31no—
41C3×#888—31no—
42C3×#887—31no—
43C3×C42×D3—31no—
44C3×C42×D3—31no—
45C3×#869—31no—
46C3×C4×Dic6—31no—
47#63918D311yescharacteristic, complemented
48C4×#627—32no—
49#63888—32no—
50C4×#624D311yescharacteristic
51#63871—31no—
52#63869—32no—
53#63867—32no—
54#63866—31no—
55#63866—31no—
56#63866—61no—
57#63857—31no—
58#63857—31no—
59#63857—31no—
60#63857—61no—
61#63856—31no—
62#63856—32no—
63#63855—32no—
64#63851—32no—
65#63845—32no—
66#63844—31no—
67#63844—31no—
68#63844—61no—
69#63844D311yescharacteristic, complemented
70Dic3×Dic6—32no—
71Dic3×Dic6—32no—
72#63841—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2312yes—
77#6308—22no—
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C3×C4×C3⋊D3—22no—
82C3×#634—22no—
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C3×#627—24no—
89C3×#624—22no—
90C3×#624Q814yescomplemented
91#5728—91no—
92#5578—91no—
93#5470—91no—
94C2×C4×C3⋊D3C2×D311yescharacteristic
95C2×#634—31no—
96C2×#634—31no—
97C2×#634—31no—
98C2×#634—61no—
99C2×#634—61no—
100C2×#634—61no—
101C2×#634—121no—
102C2×#634C2×D311yescharacteristic
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—61no—
110C2×C3×Dic6—31no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—32no—
113C2×C3×Dic6—32no—
114C2×C3×Dic6—61no—
115C2×#627C2×D312yes—
116C2×#624C2×D311yescharacteristic
117C2×#624C2×D311yescharacteristic
118C32×C4⋊C4—31no—
119C32×C42—31no—
120C32×C42—31no—
121#3752—32no—
122C4⋊(C3⋊Dic3)—32no—
123C4⋊(C3⋊Dic3)—32no—
124C4⋊(C3⋊Dic3)—32no—
125C4⋊(C3⋊Dic3)C2×D311yescharacteristic
126#3750—32no—
127C4×C3⋊Dic3—32no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—31no—
130C3×C4⋊Dic3—31no—
131C3×C4⋊Dic3—32no—
132C3×C4⋊Dic3—61no—
133C3×C4⋊Dic3C2×D311yescharacteristic
134C3×C4⋊Dic3C2×D311yescharacteristic
135C3×Dic3⋊C4—32no—
136C3×Dic3⋊C4—32no—
137C3×Dic3⋊C4—32no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3—32no—
141C3×C4×Dic3—31no—
142C3×C4×Dic3—32no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—31no—
145C3×C4×Dic3—31no—
146C3×C4×Dic3C2×D311yescharacteristic
147C3×C4×Dic3C2×D311yescharacteristic
148C3×C4×Dic3C2×D311yescharacteristic
149C3×C4×Dic3C2×D311yescharacteristic
150#3724—32no—
151#3724—32no—
152#3724—32no—
153#3724—62no—
154#3724C2×D312yes—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—62no—
164Dic3⋊Dic3—62no—
165Dic3⋊Dic3—62no—
166Dic3⋊Dic3C2×D312yes—
167#3722—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—62no—
173Dic32—32no—
174Dic32—32no—
175Dic32—62no—
176Dic32C2×D312yes—
177Dic32C2×D311yescharacteristic
178Dic32C2×D311yescharacteristic
179C22×C33C2411yescharacteristic
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3C2×Q812yes—
183C33×C4#4112yes—
184C3⋊(C3⋊Dic3)—22no—
185C3×C3⋊Dic3—22no—
186C3×C3⋊Dic3—22no—
187C3×C3⋊Dic3—21no—
188C32×Dic3—21no—
189C32×Dic3—22no—
190C32×Dic3C2×Q812yes—
191C32×Dic3C2×Q812yes—
192C32×Dic3#4112yes—
193C3×C4⋊Q8—91no—
194C3×C4×Q8—91no—
195C2×C3×C42—91no—
196#946—92no—
197#946—91no—
198Q8×Dic3—92no—
199#944—91no—
200#926—92no—
201#924—92no—
202#924—91no—
203#924—91no—
204#897—91no—
205#897—91no—
206#897—91no—
207#897—181no—
208#896—92no—
209#892—92no—
210#890—92no—
211#889—92no—
212#888—31no—
213#887—31no—
214#887—91no—
215#872—92no—
216C42×D3—31no—
217C42×D3—31no—
218#870—92no—
219#869—31no—
220#869—91no—
221#869—91no—
222#869—181no—
223C4×Dic6—31no—
224C4×Dic6—92no—
225C4×Dic6—92no—
226C4×Dic6—91no—
227C4×Dic6—91no—
228C4×Dic6—181no—
229C22×C3⋊D3C22×D311yescharacteristic
230C22×C3×D3—31no—
231C22×C3×D3—31no—
232C22×C3×D3—61no—
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—31no—
240C2×C32×C4—32no—
241C2×C32×C4—41no—
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×D311yescharacteristic
253C2×C3⋊Dic3C22×D312yes—
254C2×C3⋊Dic3C22×D312yes—
255C4×C3⋊D3—22no—
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—21no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—62no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3C22×D312yes—
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D312yes—
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C3×C4×D3—34no—
289C3×C4×D3—34no—
290C3×C4×D3—62no—
291C3×C4×D3—62no—
292C3×C4×D3—62no—
293C3×C4×D3—62no—
294C3×C4×D3—122no—
295C3×Dic6—64no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298C3×Dic6—64no—
299C3×Dic6—122no—
300#627—24no—
301#624—22no—
302#624Dic614yescomplemented
303#533—271noSylow
304C2×C33C22×Q811yescharacteristic
305C2×C33C2×#4111yescharacteristic
306C2×C33C2×#4111yescharacteristic
307C3×C3⋊D3—22no—
308C2×C3×Q8—92no—
309C2×C3×Q8—91no—
310C22×C3×C4—91no—
311C22×C3×C4—91no—
312C22×C3×C4—91no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
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×C42—31no—
339C3×C42—31no—
340C3×C42—31no—
341C3×C42—31no—
342C3×C42—61no—
343C3×C42—61no—
344C3×C42—91no—
345C3×C42—92no—
346C3×C42—91no—
347#217—92no—
348#217—92no—
349(C2×D3)⋊C4—92no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—92no—
352(C2×D3)⋊C4—92no—
353(C2×D3)⋊C4—182no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—32no—
357C4⋊Dic3—61no—
358C4⋊Dic3—92no—
359C4⋊Dic3—92no—
360C4⋊Dic3—92no—
361C4⋊Dic3—92no—
362C4⋊Dic3—92no—
363C4⋊Dic3—92no—
364C4⋊Dic3—92no—
365C4⋊Dic3—182no—
366C4⋊Dic3—182no—
367C4⋊Dic3—182no—
368C4⋊Dic3D3211yescharacteristic
369Dic3⋊C4—32no—
370Dic3⋊C4—32no—
371Dic3⋊C4—32no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—182no—
381C4×Dic3—32no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—32no—
387C4×Dic3—92no—
388C4×Dic3—92no—
389C4×Dic3—92no—
390C4×Dic3—182no—
391C4×Dic3D3211yescharacteristic
392C4×Dic3D3211yescharacteristic
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—41no—
397C22×C32C23×D311yescharacteristic
398C22×C32C23×D311yescharacteristic
399C22×C32C23×D311yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3C2×Dic612yes—
403C2×C3×D3—32no—
404C2×C3×D3—32no—
405C2×C3×D3—62no—
406C2×C3×D3—61no—
407C2×C3×D3—61no—
408C2×C3×D3—61no—
409C2×C3×D3—61no—
410C2×C3×D3—121no—
411C2×C3×D3—121no—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—32no—
416C32×C4—32no—
417C32×C4—32no—
418C32×C4—42no—
419C32×C4—62no—
420C32×C4—61no—
421C32×C4#23512yes—
422C32×C4#23512yes—
423C32×C4#23912yes—
424C3⋊Dic3—22no—
425C3⋊Dic3—21no—
426C3⋊Dic3—22no—
427C3⋊Dic3—62no—
428C3⋊Dic3—64no—
429C3⋊Dic3—62no—
430C3⋊Dic3—62no—
431C3⋊Dic3—122no—
432C3⋊Dic3—122no—
433C3⋊Dic3—124no—
434C3×Dic3—21no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—21no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—41no—
442C3×Dic3—42no—
443C3×Dic3—62no—
444C3×Dic3—62no—
445C3×Dic3—61no—
446C3×Dic3—62no—
447C3×Dic3—61no—
448C3×Dic3—62no—
449C3×Dic3—122no—
450C3×Dic3—121no—
451C3×Dic3—122no—
452C3×Dic3C2×Dic612yes—
453C3×Dic3C2×Dic612yes—
454C3×Dic3#23512yes—
455C3×Dic3#23712yes—
456C3×Dic3D3×Q812yes—
457C3×Dic3D3×Q812yes—
458C4⋊Q8—91no—
459C4⋊Q8—271no—
460#125—272no—
461C22⋊Q8—271no—
462C22⋊Q8—272no—
463C22⋊Q8—271no—
464C4×Q8—91no—
465C4×Q8—271no—
466C4×Q8—272no—
467#117—272no—
468C2×C42—91no—
469C33#53311yescharacteristic, complemented, Sylow
470C23×C3—91no—
471C22×D3—31no—
472C22×D3—31no—
473C22×D3—61no—
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—31no—
485C2×C3×C4—32no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—32no—
489C2×C3×C4—41no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—62no—
495C2×C3×C4—94no—
496C2×C3×C4—92no—
497C2×C3×C4—91no—
498C2×C3×C4—92no—
499C2×C3×C4—182no—
500C2×C3×C4—182no—
501C2×C3×C4C2×D3211yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—32no—
509C2×Dic3—32no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—61no—
513C2×Dic3—92no—
514C2×Dic3—92no—
515C2×Dic3—92no—
516C2×Dic3—182no—
517C2×Dic3—182no—
518C2×Dic3—182no—
519C2×Dic3—362no—
520C2×Dic3C2×D3211yescharacteristic
521C2×Dic3C2×D3212yes—
522C2×Dic3C2×D3211yescharacteristic
523C2×Dic3C2×D3211yescharacteristic
524C2×Dic3C2×D3211yescharacteristic
525C4×D3—34no—
526C4×D3—34no—
527C4×D3—62no—
528C4×D3—62no—
529C4×D3—62no—
530C4×D3—62no—
531C4×D3—122no—
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×C32C22×Dic611yescharacteristic
557C2×C32C2×#23511yescharacteristic
558C2×C32C2×#23511yescharacteristic
559C2×C32C2×#23511yescharacteristic
560C2×C32C2×#23711yescharacteristic
561C2×C32C2×D3×Q811yescharacteristic
562C2×C32C2×D3×Q811yescharacteristic
563C2×C32C2×#23911yescharacteristic
564C2×C32D3×#4111yescharacteristic
565C3⋊D3—22no—
566C3×D3—62no—
567C3×D3—62no—
568C3×D3—122no—
569C2×Q8—92no—
570C2×Q8—91no—
571C2×Q8—271no—
572C22×C4—91no—
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—272no—
585C22⋊C4—272no—
586C42—31no—
587C42—31no—
588C42—91no—
589C42—91no—
590C42—92no—
591C42—272no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—41no—
596C22×C3—92no—
597C22×C3—181no—
598C22×C3—181no—
599C22×C3C22×D3211yescharacteristic
600C22×C3C22×D3211yescharacteristic
601C22×C3C22×D3211yescharacteristic
602C2×D3—32no—
603C2×D3—32no—
604C2×D3—62no—
605C2×D3—61no—
606C2×D3—61no—
607C2×D3—61no—
608C2×D3—61no—
609C2×D3—121no—
610C2×D3—121no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—22no—
614C3×C4—32no—
615C3×C4—32no—
616C3×C4—32no—
617C3×C4—32no—
618C3×C4—32no—
619C3×C4—32no—
620C3×C4—42no—
621C3×C4—62no—
622C3×C4—62no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4—61no—
626C3×C4—62no—
627C3×C4—61no—
628C3×C4—121no—
629C3×C4—122no—
630C3×C4—181no—
631C3×C4—182no—
632C3×C4—182no—
633C3×C4#379812yes—
634C3×C4#379912yes—
635C3×C4#379912yes—
636Dic3—21no—
637Dic3—22no—
638Dic3—62no—
639Dic3—62no—
640Dic3—61no—
641Dic3—62no—
642Dic3—61no—
643Dic3—62no—
644Dic3—122no—
645Dic3—121no—
646Dic3—122no—
647Dic3—184no—
648Dic3—182no—
649Dic3—182no—
650Dic3—182no—
651Dic3—362no—
652Dic3—362no—
653Dic3—364no—
654Dic3D3×Dic612yes—
655Dic3D3×Dic612yes—
656Dic3#379512yes—
657C32—21no—
658C32—21no—
659C32—21no—
660C32—41no—
661C32#547011yescharacteristic, complemented
662C32#557811yescharacteristic, complemented
663C32#572811yescharacteristic, complemented
664C23—91no—
665Q8—184no—
666Q8—182no—
667Q8—542no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—32no—
673C2×C4—94no—
674C2×C4—91no—
675C2×C4—92no—
676C2×C4—92no—
677C2×C4—182no—
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—182no—
694C2×C3C2×D3×Dic611yescharacteristic
695C2×C3C2×D3×Dic611yescharacteristic
696C2×C3C2×#379511yescharacteristic
697C2×C3C2×#379811yescharacteristic
698C2×C3C2×#379911yescharacteristic
699C2×C3C2×#379911yescharacteristic
700C2×C3D3×#23511yescharacteristic
701C2×C3D3×#23711yescharacteristic
702C2×C3D32×Q811yescharacteristic
703D3—62no—
704D3—62no—
705D3—122no—
706C22—92no—
707C22—181no—
708C22—181no—
709C22C2×D3311yescharacteristic
710C4—32no—
711C4—32no—
712C4—32no—
713C4—61no—
714C4—62no—
715C4—182no—
716C4—181no—
717C4—182no—
718C4—542no—
719C4#8896512yes—
720C3—21no—
721C3—21no—
722C3—21no—
723C3—41no—
724C3#1059385911yescharacteristic, complemented
725C3#1059387311yescharacteristic, complemented
726C3#1059439711yescharacteristic, complemented
727C2—182no—
728C2D32×Dic611yescharacteristic
729C2D3×#379511yescharacteristic
730C2C2×#8896511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×C3⋊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
2. #11723443C2semidirect
4. #11723399C2semidirect
5. C3×#63918C2semidirect
7. C3×#63844C2semidirect
8. #11723011C2semidirect
10. Dic3×#627C2semidirect
47. #63918D3semidirect
69. #63844D3semidirect
90. C3×#624Q8semidirect
302. #624Dic6semidirect
469. C33#533semidirect
661. C32#5470semidirect
662. C32#5578semidirect
663. C32#5728semidirect
724. C3#10593859semidirect
725. C3#10593873semidirect
726. C3#10594397semidirect

Maximal subgroups

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

subgroupindex
#117236742
#117234432
#117234312
#117233992
C3×#639182
C3×C4×#6242
C3×#638442
#117230112
#117229702
Dic3×#6272
#117229152
#105943973
#105938733
#105938593