Finite Group Databasebeta

← #13169441

Subgroups — #13169441

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
1C4×#6294C211yesmaximal, characteristic
2#11723455C211yesmaximal, characteristic, complemented
3#11723431C211yesmaximal, characteristic
4#11723406C211yesmaximal, characteristic, complemented
5C3×#63919C211yesmaximal, characteristic, complemented
6C3×#63871C211yesmaximal, characteristic
7C3×#63843C211yesmaximal, characteristic, complemented
8#11723017C212yesmaximal, complemented
9#11722979C212yesmaximal
10#11722940C212yesmaximal, complemented
11#11722922C212yesmaximal
12#10595367—31nomaximal
13#10594397—31nomaximal
14#10594387—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6294C2211yescharacteristic
19C2×#6294C2211yescharacteristic
20C2×C3×#627C2212yes—
21C3×C4×C3⋊Dic3C2211yescharacteristic
22C3×C4×C3⋊Dic3C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25#88813C2211yescharacteristic
26#88813C2211yescharacteristic
27#88807C2212yes—
28#88807C2212yes—
29#88806C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31#88803C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×Dic32C2212yes—
38#64153—31no—
39#64106—31no—
40#64096—31no—
41C3×#946—31no—
42C3×Q8×Dic3—31no—
43C3×#897—31no—
44C3×#888—31no—
45C3×#888—31no—
46C3×#887—31no—
47#63919D311yescharacteristic, complemented
48#63899—32no—
49#63888—32no—
50#63887—32no—
51C4×#624—31no—
52#63878—32no—
53#63877—32no—
54C4×D3×Dic3—31no—
55C4×D3×Dic3—31no—
56#63871D311yescharacteristic
57#63866—31no—
58#63866—31no—
59#63866—61no—
60#63857—31no—
61#63857—31no—
62#63857—61no—
63#63847—32no—
64#63846—32no—
65#63845—32no—
66#63844—31no—
67#63844—31no—
68#63844—61no—
69#63843—32no—
70#63843D311yescharacteristic, complemented
71Dic3×Dic6—32no—
72#63837—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2312yes—
77#6308—22no—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C32×Dic6—22no—
88#6294—22no—
89#6294Q814yescomplemented
90C3×#627—24no—
91#5728—91no—
92#5622—91no—
93#5578—91no—
94C2×C32×Q8—31no—
95C2×C4×C3⋊D3C2×D311yescharacteristic
96C2×#634—31no—
97C2×#634—31no—
98C2×#634—31no—
99C2×#634—61no—
100C2×#634—61no—
101C2×#634—61no—
102C2×#634—121no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—61no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6—32no—
108C2×C3×Dic6—32no—
109C2×C3×Dic6C2×D311yescharacteristic
110C2×C3×Dic6C2×D311yescharacteristic
111C2×#627C2×D312yes—
112C2×#624—31no—
113C2×#624—31no—
114C2×D3×Dic3—31no—
115C2×D3×Dic3—31no—
116C2×D3×Dic3—31no—
117C2×D3×Dic3—31no—
118C32×C4⋊C4—31no—
119C32×C4⋊C4—31no—
120#3752—32no—
121C4⋊(C3⋊Dic3)—32no—
122#3750—32no—
123#3750—32no—
124#3750—32no—
125C4×C3⋊Dic3—32no—
126C4×C3⋊Dic3C2×D311yescharacteristic
127C4×C3⋊Dic3C2×D311yescharacteristic
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3—32no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3C2×D311yescharacteristic
135C3×C4⋊Dic3C2×D311yescharacteristic
136C3×C4⋊Dic3C2×D311yescharacteristic
137C3×C4⋊Dic3C2×D311yescharacteristic
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×Dic3⋊C4—32no—
141C3×Dic3⋊C4—32no—
142C3×C4×Dic3—31no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—31no—
145C3×C4×Dic3—31no—
146C3×C4×Dic3—32no—
147C3×C4×Dic3—32no—
148C3×C4×Dic3—61no—
149C3×C4×Dic3—61no—
150#3724—32no—
151#3724—32no—
152#3724—62no—
153#3724C2×D312yes—
154Dic3⋊Dic3—32no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—62no—
161Dic3⋊Dic3—62no—
162Dic3⋊Dic3—62no—
163Dic3⋊Dic3C2×D312yes—
164Dic3⋊Dic3C2×D312yes—
165#3722C2×D312yes—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—62no—
169Dic32—31no—
170Dic32—31no—
171Dic32—31no—
172Dic32—31no—
173Dic32—31no—
174Dic32—31no—
175Dic32—32no—
176Dic32—32no—
177Dic32—62no—
178Dic32C2×D312yes—
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—21no—
186C3×C3⋊Dic3—21no—
187C3×C3⋊Dic3C2×Q812yes—
188C3×C3⋊Dic3C2×Q812yes—
189C3×C3⋊Dic3#4112yes—
190C32×Dic3—22no—
191C32×Dic3—22no—
192C32×Dic3—22no—
193C3×C4⋊Q8—91no—
194C3×C22⋊Q8—91no—
195C3×C4×Q8—91no—
196#946—31no—
197#946—92no—
198Q8×Dic3—31no—
199Q8×Dic3—92no—
200#944—91no—
201#944—91no—
202#944—181no—
203#924—91no—
204C2×C4×Dic3—91no—
205#897—31no—
206#897—91no—
207#897—91no—
208#897—181no—
209#896—92no—
210#892—92no—
211#890—92no—
212#889—92no—
213#889—92no—
214#888—31no—
215#888—31no—
216#887—31no—
217#887—91no—
218#887—91no—
219#887—92no—
220#887—181no—
221#878—92no—
222#877—92no—
223#872—92no—
224C42×D3—91no—
225C42×D3—91no—
226#869—91no—
227C4×Dic6—92no—
228C4×Dic6—91no—
229C22×C3⋊D3C22×D311yescharacteristic
230C22×C3×D3—31no—
231C22×C3×D3—31no—
232C22×C3×D3—61no—
233C32×Q8—62no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—32no—
238C2×C32×C4—32no—
239C2×C32×C4—32no—
240C2×C32×C4—41no—
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244C2×C3⋊Dic3—32no—
245C2×C3⋊Dic3—32no—
246C2×C3⋊Dic3—32no—
247C2×C3⋊Dic3—62no—
248C2×C3⋊Dic3—62no—
249C2×C3⋊Dic3—62no—
250C2×C3⋊Dic3—122no—
251C2×C3⋊Dic3C22×D311yescharacteristic
252C2×C3⋊Dic3C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D311yescharacteristic
255C2×C3⋊Dic3C22×D311yescharacteristic
256C4×C3⋊D3—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—22no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—22no—
267C2×C3×Dic3—31no—
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—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D312yes—
288C3×C4×D3—62no—
289C3×C4×D3—62no—
290C3×C4×D3—122no—
291C3×Dic6—22no—
292C3×Dic6—22no—
293C3×Dic6—42no—
294C3×Dic6—64no—
295C3×Dic6—64no—
296#627—24no—
297#624—34no—
298#624—62no—
299D3×Dic3—34no—
300D3×Dic3—34no—
301D3×Dic3—62no—
302D3×Dic3—62no—
303#533—271noSylow
304C2×C33C22×Q811yescharacteristic
305C2×C33C2×#4111yescharacteristic
306C2×C33C2×#4111yescharacteristic
307C3×C3⋊D3—22no—
308C2×C3×Q8—31no—
309C2×C3×Q8—31no—
310C2×C3×Q8—61no—
311C2×C3×Q8—92no—
312C22×C3×C4—91no—
313C22×Dic3—91no—
314C22×Dic3—91no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—61no—
318C2×C4×D3—91no—
319C2×C4×D3—91no—
320C2×C4×D3—91no—
321C2×C4×D3—91no—
322C2×Dic6—32no—
323C2×Dic6—32no—
324C2×Dic6—91no—
325C2×Dic6—91no—
326C2×Dic6—91no—
327C2×Dic6—181no—
328C2×Dic6—181no—
329C2×Dic6—181no—
330C2×Dic6—361no—
331C2×Dic6D3211yescharacteristic
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—92no—
339C3×C4⋊C4—92no—
340C3×C4⋊C4—92no—
341C3×C22⋊C4—92no—
342C3×C42—92no—
343C3×C42—91no—
344C3×C42—91no—
345#217—92no—
346(C2×D3)⋊C4—32no—
347(C2×D3)⋊C4—32no—
348(C2×D3)⋊C4—92no—
349(C2×D3)⋊C4—92no—
350(C2×D3)⋊C4—182no—
351C4⋊Dic3—32no—
352C4⋊Dic3—32no—
353C4⋊Dic3—92no—
354C4⋊Dic3—92no—
355C4⋊Dic3—92no—
356C4⋊Dic3—92no—
357C4⋊Dic3—182no—
358C4⋊Dic3D3211yescharacteristic
359C4⋊Dic3D3211yescharacteristic
360Dic3⋊C4—32no—
361Dic3⋊C4—32no—
362Dic3⋊C4—32no—
363Dic3⋊C4—32no—
364Dic3⋊C4—92no—
365Dic3⋊C4—92no—
366Dic3⋊C4—92no—
367Dic3⋊C4—92no—
368Dic3⋊C4—92no—
369Dic3⋊C4—92no—
370Dic3⋊C4—92no—
371Dic3⋊C4—92no—
372Dic3⋊C4—182no—
373Dic3⋊C4—182no—
374Dic3⋊C4—182no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—32no—
380C4×Dic3—32no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—91no—
384C4×Dic3—91no—
385C4×Dic3—91no—
386C4×Dic3—91no—
387C4×Dic3—91no—
388C4×Dic3—91no—
389C4×Dic3—92no—
390C4×Dic3—92no—
391C4×Dic3—92no—
392C4×Dic3—182no—
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⋊D3D3×Q812yes—
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—42no—
416C32×C4—62no—
417C32×C4—62no—
418C32×C4—62no—
419C32×C4#23512yes—
420C32×C4#23712yes—
421C32×C4#23912yes—
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—62no—
425C3⋊Dic3—64no—
426C3⋊Dic3—62no—
427C3⋊Dic3—62no—
428C3⋊Dic3—122no—
429C3⋊Dic3—122no—
430C3⋊Dic3—124no—
431C3⋊Dic3#23712yes—
432C3⋊Dic3D3×Q812yes—
433C3⋊Dic3D3×Q812yes—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—32no—
441C3×Dic3—32no—
442C3×Dic3—32no—
443C3×Dic3—32no—
444C3×Dic3—32no—
445C3×Dic3—32no—
446C3×Dic3—42no—
447C3×Dic3—42no—
448C3×Dic3—42no—
449C3×Dic3—62no—
450C3×Dic3—62no—
451C3×Dic3—62no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—121no—
457C3×Dic3—121no—
458C4⋊Q8—91no—
459C4⋊Q8—271no—
460#125—272no—
461C22⋊Q8—91no—
462C22⋊Q8—272no—
463C22⋊Q8—271no—
464C4×Q8—91no—
465C4×Q8—271no—
466C4×Q8—272no—
467#117—272no—
468C2×C42—271no—
469C33#53311yescharacteristic, complemented, Sylow
470C23×C3—91no—
471C22×D3—31no—
472C22×D3—31no—
473C22×D3—61no—
474C3×Q8—62no—
475C3×Q8—62no—
476C3×Q8—122no—
477C3×Q8—184no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—41no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4—91no—
496C2×C3×C4—182no—
497C2×C3×C4C2×D3211yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
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—31no—
509C2×Dic3—31no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—94no—
516C2×Dic3—92no—
517C2×Dic3—92no—
518C2×Dic3—92no—
519C2×Dic3—182no—
520C2×Dic3—182no—
521C2×Dic3—182no—
522C2×Dic3—182no—
523C2×Dic3—362no—
524C2×Dic3C2×D3212yes—
525C2×Dic3C2×D3212yes—
526C2×Dic3C2×D3212yes—
527C4×D3—62no—
528C4×D3—62no—
529C4×D3—94no—
530C4×D3—94no—
531C4×D3—122no—
532C4×D3—182no—
533C4×D3—182no—
534Dic6—22no—
535Dic6—64no—
536Dic6—64no—
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×C32C2×#23511yescharacteristic
557C2×C32C2×#23711yescharacteristic
558C2×C32C2×#23711yescharacteristic
559C2×C32C2×D3×Q811yescharacteristic
560C2×C32C2×D3×Q811yescharacteristic
561C2×C32C2×D3×Q811yescharacteristic
562C2×C32C2×#23911yescharacteristic
563C2×C32D3×#4111yescharacteristic
564C2×C32D3×#4111yescharacteristic
565C3⋊D3—22no—
566C3×D3—62no—
567C3×D3—62no—
568C3×D3—122no—
569C2×Q8—31no—
570C2×Q8—92no—
571C2×Q8—271no—
572C22×C4—91no—
573C22×C4—271no—
574C22×C4—271no—
575C4⋊C4—31no—
576C4⋊C4—31no—
577C4⋊C4—92no—
578C4⋊C4—92no—
579C4⋊C4—92no—
580C4⋊C4—272no—
581C4⋊C4—272no—
582C4⋊C4—272no—
583C4⋊C4—272no—
584C22⋊C4—92no—
585C22⋊C4—272no—
586C42—92no—
587C42—91no—
588C42—91no—
589C42—272no—
590C42—271no—
591C42—271no—
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—42no—
615C3×C4—62no—
616C3×C4—62no—
617C3×C4—62no—
618C3×C4—62no—
619C3×C4—62no—
620C3×C4—62no—
621C3×C4—92no—
622C3×C4—92no—
623C3×C4—92no—
624C3×C4—122no—
625C3×C4—122no—
626C3×C4—122no—
627C3×C4—181no—
628C3×C4—181no—
629C3×C4#379612yes—
630C3×C4#379912yes—
631C3×C4#380412yes—
632Dic3—22no—
633Dic3—22no—
634Dic3—22no—
635Dic3—32no—
636Dic3—32no—
637Dic3—32no—
638Dic3—32no—
639Dic3—32no—
640Dic3—32no—
641Dic3—62no—
642Dic3—62no—
643Dic3—62no—
644Dic3—61no—
645Dic3—61no—
646Dic3—61no—
647Dic3—61no—
648Dic3—121no—
649Dic3—121no—
650Dic3—184no—
651Dic3—182no—
652Dic3—182no—
653Dic3—182no—
654Dic3—362no—
655Dic3—362no—
656Dic3—364no—
657C32—21no—
658C32—21no—
659C32—21no—
660C32—41no—
661C32#557811yescharacteristic, complemented
662C32#562211yescharacteristic, complemented
663C32#572811yescharacteristic, complemented
664C23—91no—
665Q8—62no—
666Q8—184no—
667Q8—542no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—91no—
674C2×C4—91no—
675C2×C4—91no—
676C2×C4—182no—
677C2×C4—274no—
678C2×C4—272no—
679C2×C4—542no—
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×#379611yescharacteristic
695C2×C3C2×#379911yescharacteristic
696C2×C3D3×#23711yescharacteristic
697C2×C3D3×#23711yescharacteristic
698C2×C3D32×Q811yescharacteristic
699C2×C3D32×Q811yescharacteristic
700C2×C3D32×Q811yescharacteristic
701C2×C3#6431911yescharacteristic
702C2×C3C2×#380411yescharacteristic
703D3—62no—
704D3—62no—
705D3—122no—
706C22—92no—
707C22—181no—
708C22—181no—
709C22C2×D3311yescharacteristic
710C4—62no—
711C4—62no—
712C4—62no—
713C4—92no—
714C4—92no—
715C4—92no—
716C4—181no—
717C4—181no—
718C4—542no—
719C4#8896212yes—
720C3—21no—
721C3—21no—
722C3—21no—
723C3—41no—
724C3#1059438711yescharacteristic, complemented
725C3#1059439711yescharacteristic, complemented
726C3#1059536711yescharacteristic, complemented
727C2—182no—
728C2#1172437411yescharacteristic
729C2#1172437811yescharacteristic
730C2C2×#8896211yescharacteristic
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. #11723455C2semidirect
4. #11723406C2semidirect
5. C3×#63919C2semidirect
7. C3×#63843C2semidirect
8. #11723017C2semidirect
10. #11722940C2semidirect
47. #63919D3semidirect
70. #63843D3semidirect
89. #6294Q8semidirect
469. C33#533semidirect
661. C32#5578semidirect
662. C32#5622semidirect
663. C32#5728semidirect
724. C3#10594387semidirect
725. C3#10594397semidirect
726. C3#10595367semidirect

Maximal subgroups

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

subgroupindex
C4×#62942
#117234552
#117234312
#117234062
C3×#639192
C3×#638712
C3×#638432
#117230172
#117229792
#117229402
#117229222
#105953673
#105943973
#105943873