Finite Group Databasebeta

← C3×#10590408 #13157425

Subgroups — C3×#10590408 #13157425

Order 1728.

856 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64330C211yesmaximal, characteristic
2C32×#886C211yesmaximal, characteristic, complemented
3C3×#63966C211yesmaximal, characteristic, complemented
4C3×#63961C211yesmaximal, characteristic, complemented
5C3×#63633C211yesmaximal, characteristic, complemented
6C32×#806C211yesmaximal, characteristic, complemented
7C3×#63580C211yesmaximal, characteristic, complemented
8C3×#5053—31nomaximal
9C3×#4742—31nomaximal
10#10590408C311yesmaximal, characteristic, direct product factor
11C2×C3×#638C2211yescharacteristic
12C2×C32×#67C2211yescharacteristic
13C2×C32×#67C2211yescharacteristic
14C22×C32×Dic3C2211yescharacteristic, complemented
15C3×#3811—21no—
16C3×D3×#67—21no—
17C3×D3×#67—21no—
18C3×#3805—21no—
19C3×#3804—21no—
20C3×#3804—21no—
21C33×C22⋊C4C2211yescharacteristic, complemented
22C3×#3757C2211yescharacteristic, complemented
23C32×#217C2211yescharacteristic, complemented
24C32×(C2×D3)⋊C4—21no—
25C32×C4⋊Dic3—21no—
26C3×#3724—21no—
27C3×Dic3⋊Dic3—21no—
28C3×#3722—21no—
29C3×(C2×D3)⋊Dic3—21no—
30C3×#1004—31no—
31C3×#1004—31no—
32#64330C2×C311yescharacteristic
33C32×#123—31no—
34C3×#935—31no—
35C3×#929—31no—
36C3×#929—31no—
37C3×#886—21no—
38C3×#886—31no—
39C3×#886D311yescharacteristic, complemented
40C3×#886C2×C311yescharacteristic, complemented
41#63966C2×C311yescharacteristic, complemented
42#63961C2×C311yescharacteristic, complemented
43C32×#99—31no—
44#63633C2×C311yescharacteristic, complemented
45C3×#834—31no—
46C3×#806—21no—
47C3×#806—31no—
48C3×#806—31no—
49C3×#806—31no—
50C3×#806—61no—
51C3×#806D311yescharacteristic, complemented
52C3×#806C2×C311yescharacteristic, complemented
53#63580C2×C311yescharacteristic, complemented
54C23×C33C2311yescharacteristic
55C22×C3×C3⋊D3D411yescharacteristic
56C22×C32×D3D411yescharacteristic
57C22×C32×D3D411yescharacteristic
58C2×C3×D32—21no—
59C2×C33×C4—21no—
60C3×#638—21no—
61C3×#638—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3D411yescharacteristic
64C32×#67—21no—
65C32×#67—21no—
66C32×#67—21no—
67C32×#67—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3—21no—
72C2×C32×Dic3D411yescharacteristic
73C2×C32×Dic3D411yescharacteristic
74C3×#627—21no—
75C3×#626—21no—
76C3×#626—21no—
77C3×#625—21no—
78C3×#624—21no—
79C3×D3×Dic3—21no—
80C3×D3×Dic3—21no—
81C3×#458—91no—
82#5053—31no—
83#4742—31no—
84C2×C32×D4—31no—
85C2×C32×D4—31no—
86C22×C32×C4—31no—
87C2×#638C22×C311yescharacteristic
88C2×C3×#67—21no—
89C2×C3×#67—21no—
90C2×C3×#67—31no—
91C2×C3×#67—31no—
92C2×C3×#67—61no—
93C2×C3×#67—61no—
94C2×C3×#67—61no—
95C2×C3×#67C2×D311yescharacteristic
96C2×C3×#67C2×D311yescharacteristic
97C2×C3×#67C22×C311yescharacteristic
98C2×C3×#67C22×C311yescharacteristic
99C22×C3×Dic3—21no—
100C22×C3×Dic3C2×D311yescharacteristic, complemented
101C22×C3×Dic3C22×C311yescharacteristic, complemented
102C3×#237—61no—
103C3×#237—61no—
104C3×#237—61no—
105C3×#237—61no—
106C3×D3×D4—61no—
107C3×D3×D4—61no—
108C3×D3×D4—61no—
109C3×D3×D4—61no—
110C3×#235—61no—
111C3×#235—61no—
112#3811—21no—
113D3×#67—21no—
114D3×#67—21no—
115#3805—21no—
116#3804—21no—
117#3804—21no—
118C32×C4⋊C4—61no—
119C32×C22⋊C4—21no—
120C32×C22⋊C4—21no—
121C32×C22⋊C4—21no—
122C32×C22⋊C4—31no—
123C32×C22⋊C4—41no—
124C32×C22⋊C4—61no—
125C32×C22⋊C4C2×D311yescharacteristic, complemented
126C32×C22⋊C4C2×D311yescharacteristic, complemented
127C32×C22⋊C4C22×C311yescharacteristic, complemented
128#3757C22×C311yescharacteristic, complemented
129C3×#217—21no—
130C3×#217—31no—
131C3×#217—31no—
132C3×#217—61no—
133C3×#217—61no—
134C3×#217C2×D311yescharacteristic, complemented
135C3×#217C22×C311yescharacteristic, complemented
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—61no—
140C3×(C2×D3)⋊C4—61no—
141C3×(C2×D3)⋊C4—61no—
142C3×C4⋊Dic3—22no—
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3—21no—
145C3×C4⋊Dic3—61no—
146C3×Dic3⋊C4—61no—
147C3×Dic3⋊C4—61no—
148C3×Dic3⋊C4—61no—
149#3724—21no—
150Dic3⋊Dic3—21no—
151#3722—21no—
152(C2×D3)⋊Dic3—21no—
153C22×C33—41no—
154C22×C33C2×D411yescharacteristic
155C22×C33C2×D411yescharacteristic
156C22×C33C2×D411yescharacteristic
157C2×C3×C3⋊D3—21no—
158C2×C3×C3⋊D3—41no—
159C2×C32×D3—21no—
160C2×C32×D3—21no—
161C2×C32×D3—41no—
162C2×C32×D3—41no—
163C3×D32—81no—
164C33×C4—41no—
165C3×C3⋊Dic3—21no—
166C3×C3⋊Dic3—41no—
167C32×Dic3—21no—
168C32×Dic3—21no—
169C32×Dic3—41no—
170C32×Dic3—41no—
171C3×H(5,𝔽2)—91no—
172#1004—31no—
173#1004—31no—
174C3×#123—31no—
175C3×#123—31no—
176C3×#123—61no—
177C3×#123—91no—
178C3×#123—91no—
179#935—31no—
180#929—31no—
181#929—31no—
182#886—31no—
183#886C3×D311yescharacteristic, complemented
184C3×#99—31no—
185C3×#99—31no—
186C3×#99—61no—
187C3×#99—91no—
188C3×#99—91no—
189#834—31no—
190#806—31no—
191#806—31no—
192#806—31no—
193#806—61no—
194#806C3×D311yescharacteristic, complemented
195C23×C32—21no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32—31no—
199C23×C32—31no—
200C23×C32—41no—
201C23×C32C22×D311yescharacteristic
202C23×C32C22×D311yescharacteristic
203C23×C32C23×C311yescharacteristic
204C22×C3⋊D3C3×D411yescharacteristic
205C22×C3×D3—21no—
206C22×C3×D3—21no—
207C22×C3×D3—31no—
208C22×C3×D3—31no—
209C22×C3×D3—61no—
210C22×C3×D3—61no—
211C22×C3×D3—61no—
212C22×C3×D3D1211yescharacteristic
213C22×C3×D3#6711yescharacteristic
214C22×C3×D3C3×D411yescharacteristic
215C22×C3×D3C3×D411yescharacteristic
216C2×D32—21no—
217C32×D4—61no—
218C32×D4—61no—
219C32×D4—61no—
220C32×D4—61no—
221C2×C32×C4—21no—
222C2×C32×C4—22no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—31no—
226C2×C32×C4—31no—
227C2×C32×C4—41no—
228C2×C32×C4—41no—
229C2×C32×C4—42no—
230C2×C32×C4—61no—
231C2×C32×C4—61no—
232C2×C32×C4—61no—
233C2×C32×C4—61no—
234#638—21no—
235#638—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3C3×D411yescharacteristic
238C3×#67—21no—
239C3×#67—21no—
240C3×#67—21no—
241C3×#67—21no—
242C3×#67—21no—
243C3×#67—21no—
244C3×#67—21no—
245C3×#67—21no—
246C3×#67—41no—
247C3×#67—41no—
248C3×#67—41no—
249C3×#67—41no—
250C3×#67—61no—
251C3×#67—61no—
252C3×#67—61no—
253C3×#67—61no—
254C3×#67—61no—
255C3×#67—61no—
256C3×#67—61no—
257C3×#67—61no—
258C3×#67—121no—
259C3×#67—121no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—41no—
274C2×C3×Dic3—41no—
275C2×C3×Dic3—41no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—121no—
282C2×C3×Dic3D1211yescharacteristic
283C2×C3×Dic3#6711yescharacteristic
284C2×C3×Dic3C3×D411yescharacteristic
285C2×C3×Dic3C3×D411yescharacteristic
286C3×D12—61no—
287C3×D12—61no—
288C3×C4×D3—61no—
289C3×C4×D3—61no—
290C3×C4×D3—61no—
291C3×C4×D3—61no—
292C3×Dic6—61no—
293C3×Dic6—61no—
294#627—21no—
295#626—21no—
296#626—21no—
297#625—21no—
298#624—21no—
299D3×Dic3—21no—
300D3×Dic3—21no—
301#458—91noSylow
302C2×C33—21no—
303C2×C33—21no—
304C2×C33—21no—
305C2×C33#12011yescharacteristic
306C3×C3⋊D3—41no—
307C32×D3—41no—
308C32×D3—41no—
309C3×#41—181no—
310C3×#41—181no—
311C3×#41—181no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4—91no—
319C2×C3×D4—181no—
320C2×C3×D4—181no—
321C2×C3×D4—181no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—61no—
325C2×#67—31no—
326C2×#67—31no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67C2×C3×D311yescharacteristic
331C2×#67C2×C3×D311yescharacteristic
332C22×Dic3C2×C3×D311yescharacteristic, complemented
333#237—61no—
334#237—61no—
335#237—61no—
336#237—61no—
337D3×D4—61no—
338D3×D4—61no—
339D3×D4—61no—
340D3×D4—61no—
341#235—61no—
342#235—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—62no—
346C3×C4⋊C4—181no—
347C3×C4⋊C4—181no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—62no—
358C3×C22⋊C4—91no—
359C3×C22⋊C4—181no—
360C3×C22⋊C4—181no—
361C3×C22⋊C4D3211yescharacteristic, complemented
362C3×C22⋊C4C2×C3×D311yescharacteristic, complemented
363C3×C22⋊C4C2×C3×D311yescharacteristic, complemented
364#217—31no—
365#217—31no—
366#217—61no—
367#217—61no—
368#217C2×C3×D311yescharacteristic, complemented
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373C4⋊Dic3—21no—
374C4⋊Dic3—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—42no—
394C22×C32—61no—
395C22×C32—61no—
396C22×C32—81no—
397C22×C32—81no—
398C22×C32—82no—
399C22×C32—121no—
400C22×C32—121no—
401C22×C32C2×D1211yescharacteristic
402C22×C32D3×D411yescharacteristic
403C22×C32D3×D411yescharacteristic
404C22×C32D3×D411yescharacteristic
405C22×C32D3×D411yescharacteristic
406C22×C32C2×#6711yescharacteristic
407C22×C32C2×C3×D411yescharacteristic
408C22×C32C2×C3×D411yescharacteristic
409C22×C32C2×C3×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—41no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—42no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—81no—
426C2×C3×D3—121no—
427C2×C3×D3—121no—
428C2×C3×D3—121no—
429C2×C3×D3—241no—
430C2×C3×D3—241no—
431C2×C3×D3—241no—
432D32—81no—
433C32×C4—41no—
434C32×C4—42no—
435C32×C4—41no—
436C32×C4—41no—
437C32×C4—61no—
438C32×C4—61no—
439C32×C4—81no—
440C32×C4—81no—
441C32×C4—82no—
442C32×C4—121no—
443C32×C4—121no—
444C3⋊Dic3—21no—
445C3⋊Dic3—41no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—21no—
449C3×Dic3—21no—
450C3×Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—42no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3—81no—
460C3×Dic3—121no—
461C3×Dic3—121no—
462C3×Dic3—121no—
463C3×Dic3—241no—
464H(5,𝔽2)—91no—
465#123—31no—
466#123—91no—
467#123—91no—
468#99—31no—
469#99—91no—
470#99—91no—
471C33#45811yescharacteristic, complemented, Sylow
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—31no—
477C23×C3—31no—
478C23×C3—31no—
479C23×C3—41no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—91no—
483C23×C3—181no—
484C23×C3C2×D3211yescharacteristic
485C23×C3C22×C3×D311yescharacteristic
486C23×C3C22×C3×D311yescharacteristic
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3C3×D1211yescharacteristic
493C22×D3C3×#6711yescharacteristic
494C3×Q8—181no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—121no—
504C3×D4—121no—
505C3×D4—121no—
506C3×D4—121no—
507C3×D4—181no—
508C3×D4—181no—
509C3×D4—181no—
510C3×D4—181no—
511C3×D4—181no—
512C2×C3×C4—22no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—42no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—62no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—91no—
535C2×C3×C4—121no—
536C2×C3×C4—121no—
537C2×C3×C4—121no—
538C2×C3×C4—181no—
539C2×C3×C4—181no—
540C2×C3×C4—181no—
541C2×C3×C4—181no—
542#67—21no—
543#67—21no—
544#67—21no—
545#67—21no—
546#67—61no—
547#67—61no—
548#67—61no—
549#67—61no—
550#67—61no—
551#67—61no—
552#67—61no—
553#67—61no—
554#67—121no—
555#67—121no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—121no—
568C2×Dic3C3×D1211yescharacteristic
569C2×Dic3C3×#6711yescharacteristic
570D12—61no—
571D12—61no—
572C4×D3—61no—
573C4×D3—61no—
574C4×D3—61no—
575C4×D3—61no—
576Dic6—61no—
577Dic6—61no—
578C2×C32—21no—
579C2×C32—22no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—21no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32—42no—
595C2×C32—41no—
596C2×C32—41no—
597C2×C32—41no—
598C2×C32—41no—
599C2×C32—41no—
600C2×C32—41no—
601C2×C32—81no—
602C2×C32—81no—
603C2×C32—121no—
604C2×C32—121no—
605C2×C32#88211yescharacteristic
606C2×C32#93711yescharacteristic
607C2×C32C3×#12011yescharacteristic
608C3⋊D3—41no—
609C3×D3—41no—
610C3×D3—41no—
611C3×D3—41no—
612C3×D3—41no—
613C3×D3—81no—
614C3×D3—81no—
615C3×D3—121no—
616C3×D3—121no—
617C3×D3—241no—
618#41—181no—
619#41—181no—
620#41—181no—
621C2×D4—31no—
622C2×D4—31no—
623C2×D4—91no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—181no—
627C22×C4—31no—
628C4⋊C4—61no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—31no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4C3×D3211yescharacteristic, complemented
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—42no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—82no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—122no—
667C22×C3—181no—
668C22×C3—241no—
669C22×C3—361no—
670C22×C3—721no—
671C22×C3D3×D1211yescharacteristic
672C22×C3#380211yescharacteristic
673C22×C3D3×#6711yescharacteristic
674C22×C3C2×C3×D1211yescharacteristic
675C22×C3C3×D3×D411yescharacteristic
676C22×C3C3×D3×D411yescharacteristic
677C22×C3C3×D3×D411yescharacteristic
678C22×C3C3×D3×D411yescharacteristic
679C22×C3C2×C3×#6711yescharacteristic
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—241no—
690C2×D3—241no—
691C2×D3—241no—
692C3×C4—41no—
693C3×C4—42no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—81no—
701C3×C4—81no—
702C3×C4—82no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4—122no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4—181no—
711C3×C4—241no—
712C3×C4—361no—
713Dic3—21no—
714Dic3—21no—
715Dic3—41no—
716Dic3—41no—
717Dic3—61no—
718Dic3—61no—
719Dic3—121no—
720Dic3—121no—
721Dic3—121no—
722Dic3—241no—
723C32—21no—
724C32—21no—
725C32—21no—
726C32—41no—
727C32#474211yescharacteristic, complemented
728C32#505311yescharacteristic, complemented
729C32C3×#45811yescharacteristic, complemented
730C23—31no—
731C23—31no—
732C23—91no—
733C23—181no—
734C23C2×C3×D3211yescharacteristic
735Q8—181no—
736D4—61no—
737D4—61no—
738D4—61no—
739D4—61no—
740D4—181no—
741D4—181no—
742D4—181no—
743D4—181no—
744D4—181no—
745C2×C4—21no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—91no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C3—22no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—41no—
774C2×C3—41no—
775C2×C3—41no—
776C2×C3—41no—
777C2×C3—41no—
778C2×C3—42no—
779C2×C3—41no—
780C2×C3—81no—
781C2×C3—81no—
782C2×C3—121no—
783C2×C3—121no—
784C2×C3—121no—
785C2×C3—121no—
786C2×C3—241no—
787C2×C3—241no—
788C2×C3—361no—
789C2×C3#6392211yescharacteristic
790C2×C3C3×#88211yescharacteristic
791C2×C3C3×#93711yescharacteristic
792D3—41no—
793D3—41no—
794D3—121no—
795D3—121no—
796D3—241no—
797C22—41no—
798C22—61no—
799C22—61no—
800C22—121no—
801C22—121no—
802C22—181no—
803C22—361no—
804C22—721no—
805C22C3×D3×D1211yescharacteristic
806C22C3×#380211yescharacteristic
807C22C3×D3×#6711yescharacteristic
808C4—41no—
809C4—61no—
810C4—61no—
811C4—121no—
812C4—121no—
813C4—181no—
814C4—361no—
815C3—21no—
816C3—21no—
817C3—21no—
818C3—41no—
819C3#1059040811yescharacteristic, direct product factor
820C3C3×#474211yescharacteristic, complemented
821C3C3×#505311yescharacteristic, complemented
822C2—21no—
823C2—21no—
824C2—21no—
825C2—121no—
826C2—121no—
827C2—361no—
828C2C3×#6392211yescharacteristic
subgroupG/H
centerC2×C3#63922
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC33×C22⋊C4C22
socleC2×C33#120
prime radicalC3×#64330C2
hypercenterC3×C22⋊C4D32
hypocenterC32C3×#458
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×#886C2semidirect
3. C3×#63966C2semidirect
4. C3×#63961C2semidirect
5. C3×#63633C2semidirect
6. C32×#806C2semidirect
7. C3×#63580C2semidirect
10. #10590408C3direct (N × H)
14. C22×C32×Dic3C22semidirect
21. C33×C22⋊C4C22semidirect
22. C3×#3757C22semidirect
23. C32×#217C22semidirect
39. C3×#886D3semidirect
40. C3×#886C2×C3semidirect
41. #63966C2×C3semidirect
42. #63961C2×C3semidirect
44. #63633C2×C3semidirect
51. C3×#806D3semidirect
52. C3×#806C2×C3semidirect
53. #63580C2×C3semidirect
100. C22×C3×Dic3C2×D3semidirect
101. C22×C3×Dic3C22×C3semidirect
125. C32×C22⋊C4C2×D3semidirect
126. C32×C22⋊C4C2×D3semidirect
127. C32×C22⋊C4C22×C3semidirect
128. #3757C22×C3semidirect
134. C3×#217C2×D3semidirect
135. C3×#217C22×C3semidirect
183. #886C3×D3semidirect
194. #806C3×D3semidirect
332. C22×Dic3C2×C3×D3semidirect
361. C3×C22⋊C4D32semidirect
362. C3×C22⋊C4C2×C3×D3semidirect
363. C3×C22⋊C4C2×C3×D3semidirect
368. #217C2×C3×D3semidirect
471. C33#458semidirect
636. C22⋊C4C3×D32semidirect
727. C32#4742semidirect
728. C32#5053semidirect
729. C32C3×#458semidirect
819. C3#10590408direct (N × H)
820. C3C3×#4742semidirect
821. C3C3×#5053semidirect

Maximal subgroups

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

subgroupindex
C3×#643302
C32×#8862
C3×#639662
C3×#639612
C3×#636332
C32×#8062
C3×#635802
C3×#50533
C3×#47423
#105904083