Finite Group Databasebeta

← #13141175

Subgroups — #13141175

Order 1728.

1133 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
1C22×#638⋊C3C211yesmaximal, characteristic
2C22×((C3⋊D3)⋊C3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#88552C211yesmaximal, characteristic, complemented
4C2×#3757⋊C3C211yesmaximal, characteristic, complemented
5C2×#88450C211yesmaximal, characteristic, complemented
6#11720334C211yesmaximal, characteristic, complemented
7#11720334C211yesmaximal, characteristic, complemented
8#10591722—31nomaximal
9#10591721—31nomaximal
10C24×H(3,𝔽3)C2211yescharacteristic
11C23×(C3⋊D3)⋊C3C2211yescharacteristic
12C22×#1084C2211yescharacteristic
13C22×#1084C2211yescharacteristic
14C2×#638⋊C3—22no—
15C2×#638⋊C3—22no—
16C2×#638⋊C3C414yescomplemented
17C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
18C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
19C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
20C2×((C3⋊D3)⋊C3)⋊C4—22no—
21C2×((C3⋊D3)⋊C3)⋊C4—22no—
22C2×((C3⋊D3)⋊C3)⋊C4—22no—
23#88552—22no—
24#3757⋊C3—22no—
25#88450—22no—
26C22×#638D311yescharacteristic
27C22×C3×#67—31no—
28C22×#624—31no—
29C22×D3×Dic3—31no—
30C2×#3757D311yescharacteristic, complemented
31C2×C3×#217—31no—
32C2×C3×#217—31no—
33C2×C3×#217—31no—
34C2×C3×#217—61no—
35C2×#3722—31no—
36C2×(C2×D3)⋊Dic3—31no—
37#63579—31no—
38#63579—31no—
39#63579—31no—
40#63579—31no—
41C23×H(3,𝔽3)—21no—
42C23×H(3,𝔽3)—21no—
43C23×H(3,𝔽3)—21no—
44C23×H(3,𝔽3)—21no—
45C23×H(3,𝔽3)—21no—
46C23×H(3,𝔽3)—21no—
47C23×H(3,𝔽3)C2×C412yescomplemented
48C23×H(3,𝔽3)C2311yescharacteristic
49C22×(C3⋊D3)⋊C3—21no—
50C22×(C3⋊D3)⋊C3—21no—
51C22×(C3⋊D3)⋊C3—21no—
52C22×(C3⋊D3)⋊C3—21no—
53C22×(C3⋊D3)⋊C3C2×C412yes—
54C22×(C3⋊D3)⋊C3D412yes—
55C22×(C3⋊D3)⋊C3D412yes—
56C2×#1084—21no—
57C2×#1084—21no—
58C2×#1084—21no—
59C2×#1084—21no—
60C2×#1084—21no—
61C2×#1084D412yescomplemented
62#638⋊C3—28no—
63C2×(C3⋊Dic3)⋊C3—21no—
64C2×(C3⋊Dic3)⋊C3—21no—
65C2×(C3⋊Dic3)⋊C3—21no—
66C2×(C3⋊Dic3)⋊C3—21no—
67C2×(C3⋊Dic3)⋊C3—21no—
68C2×(C3⋊Dic3)⋊C3—21no—
69C2×(C3⋊Dic3)⋊C3—21no—
70C2×(C3⋊Dic3)⋊C3C2×C412yescomplemented
71C2×(C3⋊Dic3)⋊C3D412yescomplemented
72((C3⋊D3)⋊C3)⋊C4—28no—
73#5220—91no—
74#4956—91no—
75#4956—91no—
76C24×C32—21no—
77C24×C32C2×D311yescharacteristic
78C24×C32C2×D311yescharacteristic
79C23×C3⋊D3C2×D311yescharacteristic
80C23×C3×D3—31no—
81C2×#638—22no—
82C2×#638—22no—
83C2×#638Dic314yescomplemented
84C22×C3⋊Dic3C2×D311yescharacteristic
85C22×C3⋊Dic3C2×D311yescharacteristic
86C22×C3⋊Dic3C2×D311yescharacteristic
87C2×C3×#67—34no—
88C2×C3×#67—62no—
89C2×C3×#67—62no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—61no—
98C22×C3×Dic3—61no—
99C2×#624—62no—
100C2×#624—62no—
101C2×#624—62no—
102C2×D3×Dic3—62no—
103C2×D3×Dic3—62no—
104C2×D3×Dic3—62no—
105#3757—22no—
106C3×#217—62no—
107C3×#217—62no—
108C3×#217—62no—
109C3×#217—64no—
110#3722—62no—
111(C2×D3)⋊Dic3—62no—
112C22×H(3,𝔽3)—22no—
113C22×H(3,𝔽3)—22no—
114C22×H(3,𝔽3)—22no—
115C22×H(3,𝔽3)—41no—
116C22×H(3,𝔽3)—41no—
117C22×H(3,𝔽3)—41no—
118C22×H(3,𝔽3)—41no—
119C22×H(3,𝔽3)C22×C411yescharacteristic
120C22×H(3,𝔽3)C2×D411yescharacteristic
121C22×H(3,𝔽3)C2×D411yescharacteristic
122C22×H(3,𝔽3)C2×D411yescharacteristic
123C22×H(3,𝔽3)C2×D411yescharacteristic
124C22×H(3,𝔽3)#4111yescharacteristic
125C22×H(3,𝔽3)#4111yescharacteristic
126C2×(C3⋊D3)⋊C3—22no—
127C2×(C3⋊D3)⋊C3—22no—
128C2×(C3⋊D3)⋊C3—22no—
129C2×(C3⋊D3)⋊C3—22no—
130C2×(C3⋊D3)⋊C3—22no—
131C2×(C3⋊D3)⋊C3—22no—
132C2×(C3⋊D3)⋊C3C22⋊C414yescomplemented
133#1084—22no—
134#1084—41no—
135(C3⋊Dic3)⋊C3—22no—
136(C3⋊Dic3)⋊C3—22no—
137(C3⋊Dic3)⋊C3—41no—
138C22×C3×D4—91no—
139C22×#67—31no—
140C22×#67—91no—
141C23×Dic3—91no—
142C22×C4×D3—91no—
143C22×C4×D3—91no—
144C2×C3×C22⋊C4—91no—
145C2×C3×C22⋊C4—91no—
146C2×#217—31no—
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—61no—
150C2×#217—91no—
151C2×#217—91no—
152C2×(C2×D3)⋊C4—91no—
153C2×(C2×D3)⋊C4—91no—
154C3⋊#95—91no—
155C3⋊#95—91no—
156C3⋊#95—91no—
157C3⋊#95—91no—
158C3⋊#95—91no—
159C3⋊#95—91no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—21no—
174C23×C32—22no—
175C23×C32—21no—
176C23×C32—41no—
177C23×C32—41no—
178C23×C32—41no—
179C23×C32—41no—
180C23×C32C4×D312yescomplemented
181C23×C32C2×Dic312yescomplemented
182C23×C32C22×D311yescharacteristic
183C23×C32C22×D311yescharacteristic
184C22×C3⋊D3—21no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3—21no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3C2×Dic312yes—
189C22×C3⋊D3#6712yes—
190C22×C3⋊D3#6712yes—
191C22×C3×D3—32no—
192C22×C3×D3—32no—
193C22×C3×D3—32no—
194C22×C3×D3—61no—
195C22×C3×D3—61no—
196C22×C3×D3—61no—
197C22×C3×D3—61no—
198#638—28no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3C2×Dic312yescomplemented
207C2×C3⋊Dic3#6712yescomplemented
208C3×#67—68no—
209C2×C3×Dic3—32no—
210C2×C3×Dic3—32no—
211C2×C3×Dic3—32no—
212C2×C3×Dic3—32no—
213C2×C3×Dic3—62no—
214C2×C3×Dic3—61no—
215C2×C3×Dic3—61no—
216C2×C3×Dic3—61no—
217C2×C3×Dic3—61no—
218C2×C3×Dic3—61no—
219C2×C3×Dic3—61no—
220C2×C3×Dic3—61no—
221C2×C3×Dic3—61no—
222C2×C3×Dic3—62no—
223C2×C3×Dic3—61no—
224C2×C3×Dic3—61no—
225C2×C3×Dic3—61no—
226C2×C3×Dic3—61no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3—61no—
229C2×C3×Dic3—61no—
230C2×C3×Dic3—61no—
231C2×C3×Dic3—61no—
232C2×C3×Dic3—121no—
233C2×C3×Dic3—121no—
234C2×C3×Dic3—121no—
235C2×C3×Dic3—121no—
236#624—68no—
237D3×Dic3—68no—
238#386—271noSylow
239C2×H(3,𝔽3)—42no—
240C2×H(3,𝔽3)C2×C22⋊C411yescharacteristic
241C2×H(3,𝔽3)C4×D411yescharacteristic
242C2×H(3,𝔽3)C4×D411yescharacteristic
243C2×H(3,𝔽3)#12011yescharacteristic
244C2×H(3,𝔽3)#12111yescharacteristic
245C2×H(3,𝔽3)#12111yescharacteristic
246C2×H(3,𝔽3)#12311yescharacteristic
247(C3⋊D3)⋊C3—24no—
248C24×C3—31no—
249C24×C3—31no—
250C24×C3—61no—
251C24×C3—91no—
252C24×C3D3211yescharacteristic
253C23×D3—31no—
254C23×D3—91no—
255C2×C3×D4—94no—
256C2×C3×D4—182no—
257C2×C3×D4—182no—
258C22×C3×C4—91no—
259C22×C3×C4—91no—
260C22×C3×C4—91no—
261C22×C3×C4—91no—
262C22×C3×C4—91no—
263C2×#67—34no—
264C2×#67—62no—
265C2×#67—62no—
266C2×#67—94no—
267C2×#67—182no—
268C2×#67—182no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—31no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—61no—
277C22×Dic3—61no—
278C22×Dic3—91no—
279C22×Dic3—91no—
280C22×Dic3—91no—
281C22×Dic3—182no—
282C22×Dic3—182no—
283C22×Dic3—182no—
284C2×C4×D3—182no—
285C2×C4×D3—182no—
286C2×C4×D3—182no—
287C2×C4×D3—182no—
288C2×C4×D3—182no—
289C2×C4×D3—182no—
290C3×C22⋊C4—182no—
291C3×C22⋊C4—182no—
292#217—62no—
293#217—62no—
294#217—62no—
295#217—64no—
296#217—182no—
297#217—182no—
298(C2×D3)⋊C4—182no—
299(C2×D3)⋊C4—182no—
300C22×C32—24no—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—22no—
304C22×C32—22no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—42no—
315C22×C32—42no—
316C22×C32—42no—
317C22×C32—42no—
318C22×C32—42no—
319C22×C32—42no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32—41no—
325C22×C32—41no—
326C22×C32—41no—
327C22×C32—41no—
328C22×C32C2×C4×D311yescharacteristic
329C22×C32#23511yescharacteristic
330C22×C32D3×D411yescharacteristic
331C22×C32D3×D411yescharacteristic
332C22×C32D3×D411yescharacteristic
333C22×C32D3×D411yescharacteristic
334C22×C32D3×D411yescharacteristic
335C22×C32#23711yescharacteristic
336C22×C32#23711yescharacteristic
337C22×C32#23711yescharacteristic
338C22×C32C22×Dic311yescharacteristic
339C22×C32C2×#6711yescharacteristic
340C22×C32C2×#6711yescharacteristic
341C22×C32C2×#6711yescharacteristic
342C2×C3⋊D3—22no—
343C2×C3⋊D3—22no—
344C2×C3⋊D3—22no—
345C2×C3⋊D3—22no—
346C2×C3⋊D3—22no—
347C2×C3⋊D3—22no—
348C2×C3⋊D3#21714yescomplemented
349C2×C3×D3—34no—
350C2×C3×D3—62no—
351C2×C3×D3—62no—
352C2×C3×D3—62no—
353C2×C3×D3—62no—
354C2×C3×D3—62no—
355C2×C3×D3—62no—
356C3⋊Dic3—22no—
357C3⋊Dic3—22no—
358C3⋊Dic3—41no—
359C3×Dic3—62no—
360C3×Dic3—62no—
361C3×Dic3—62no—
362C3×Dic3—62no—
363C3×Dic3—122no—
364C3×Dic3—122no—
365C3×Dic3—121no—
366C3×Dic3—121no—
367C3×Dic3—121no—
368C22×D4—91no—
369C23×C4—271no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—91no—
372C2×C22⋊C4—271no—
373#95—271no—
374#95—271no—
375H(3,𝔽3)#38611yescharacteristic, complemented, Sylow
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—32no—
383C23×C3—32no—
384C23×C3—31no—
385C23×C3—31no—
386C23×C3—61no—
387C23×C3—61no—
388C23×C3—61no—
389C23×C3—61no—
390C23×C3—61no—
391C23×C3—61no—
392C23×C3—61no—
393C23×C3—61no—
394C23×C3—61no—
395C23×C3—61no—
396C23×C3—61no—
397C23×C3—61no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3—62no—
401C23×C3—61no—
402C23×C3—92no—
403C23×C3—92no—
404C23×C3—92no—
405C23×C3—121no—
406C23×C3—121no—
407C23×C3—121no—
408C23×C3—121no—
409C23×C3—181no—
410C23×C3—181no—
411C23×C3—181no—
412C23×C3—181no—
413C23×C3D3×Dic312yes—
414C23×C3C2×D3211yescharacteristic
415C22×D3—32no—
416C22×D3—32no—
417C22×D3—32no—
418C22×D3—61no—
419C22×D3—61no—
420C22×D3—61no—
421C22×D3—61no—
422C22×D3—92no—
423C22×D3—92no—
424C22×D3—92no—
425C22×D3—181no—
426C22×D3—181no—
427C22×D3—181no—
428C22×D3—181no—
429C3×D4—188no—
430C2×C3×C4—92no—
431C2×C3×C4—92no—
432C2×C3×C4—92no—
433C2×C3×C4—181no—
434C2×C3×C4—181no—
435C2×C3×C4—181no—
436C2×C3×C4—181no—
437C2×C3×C4—181no—
438C2×C3×C4—181no—
439C2×C3×C4—181no—
440C2×C3×C4—181no—
441C2×C3×C4—181no—
442C2×C3×C4—181no—
443C2×C3×C4—181no—
444C2×C3×C4—181no—
445#67—68no—
446#67—188no—
447C2×Dic3—32no—
448C2×Dic3—32no—
449C2×Dic3—32no—
450C2×Dic3—32no—
451C2×Dic3—62no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—61no—
456C2×Dic3—61no—
457C2×Dic3—61no—
458C2×Dic3—61no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—61no—
464C2×Dic3—61no—
465C2×Dic3—61no—
466C2×Dic3—62no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—92no—
471C2×Dic3—92no—
472C2×Dic3—121no—
473C2×Dic3—121no—
474C2×Dic3—121no—
475C2×Dic3—121no—
476C2×Dic3—181no—
477C2×Dic3—181no—
478C2×Dic3—181no—
479C2×Dic3—181no—
480C2×Dic3—181no—
481C2×Dic3—181no—
482C2×Dic3—181no—
483C2×Dic3—188no—
484C4×D3—188no—
485C4×D3—188no—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32—21no—
490C2×C32—21no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—44no—
494C2×C32—42no—
495C2×C32—42no—
496C2×C32D3×C22⋊C411yescharacteristic
497C2×C32#67⋊C411yescharacteristic
498C2×C32#88311yescharacteristic
499C2×C32#88411yescharacteristic
500C2×C32C4×#6711yescharacteristic
501C2×C32D4×Dic311yescharacteristic
502C2×C32D4×Dic311yescharacteristic
503C2×C32#93511yescharacteristic
504C2×C32#93711yescharacteristic
505C2×C32#93711yescharacteristic
506C2×C32#93811yescharacteristic
507C2×C32#93911yescharacteristic
508C2×C32#93911yescharacteristic
509C2×C32C2×#21711yescharacteristic
510C3⋊D3—24no—
511C3×D3—64no—
512C24—91no—
513C24((C3⋊D3)⋊C3)⋊C211yescharacteristic
514C2×D4—94no—
515C2×D4—182no—
516C2×D4—182no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—542no—
523C22×C4—542no—
524C22×C4—542no—
525C22⋊C4—182no—
526C22⋊C4—182no—
527C22⋊C4—542no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—31no—
532C22×C3—31no—
533C22×C3—31no—
534C22×C3—31no—
535C22×C3—31no—
536C22×C3—31no—
537C22×C3—31no—
538C22×C3—31no—
539C22×C3—31no—
540C22×C3—31no—
541C22×C3—31no—
542C22×C3—31no—
543C22×C3—31no—
544C22×C3—31no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—62no—
550C22×C3—62no—
551C22×C3—62no—
552C22×C3—62no—
553C22×C3—62no—
554C22×C3—62no—
555C22×C3—64no—
556C22×C3—61no—
557C22×C3—61no—
558C22×C3—61no—
559C22×C3—61no—
560C22×C3—61no—
561C22×C3—61no—
562C22×C3—61no—
563C22×C3—94no—
564C22×C3—122no—
565C22×C3—122no—
566C22×C3—121no—
567C22×C3—121no—
568C22×C3—121no—
569C22×C3—121no—
570C22×C3—121no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3—121no—
574C22×C3—122no—
575C22×C3—122no—
576C22×C3—122no—
577C22×C3—122no—
578C22×C3—182no—
579C22×C3—182no—
580C22×C3—182no—
581C22×C3—182no—
582C22×C3—182no—
583C22×C3—182no—
584C22×C3C2×D3×Dic311yescharacteristic
585C22×C3#380411yescharacteristic
586C22×C3#380511yescharacteristic
587C22×C3D3×#6711yescharacteristic
588C22×C3D3×#6711yescharacteristic
589C22×C3D3×#6711yescharacteristic
590C22×C3#381111yescharacteristic
591C2×D3—34no—
592C2×D3—62no—
593C2×D3—62no—
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—94no—
599C2×D3—182no—
600C2×D3—182no—
601C2×D3—182no—
602C2×D3—182no—
603C2×D3—182no—
604C2×D3—182no—
605C3×C4—182no—
606C3×C4—182no—
607C3×C4—182no—
608C3×C4—361no—
609C3×C4—361no—
610Dic3—62no—
611Dic3—62no—
612Dic3—62no—
613Dic3—62no—
614Dic3—122no—
615Dic3—121no—
616Dic3—121no—
617Dic3—122no—
618Dic3—121no—
619Dic3—182no—
620Dic3—182no—
621Dic3—361no—
622C32—21no—
623C32#495611yescharacteristic, complemented
624C32#522011yescharacteristic, complemented
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—92no—
632C23—92no—
633C23—92no—
634C23—181no—
635C23—181no—
636C23—181no—
637C23—181no—
638C23((C3⋊D3)⋊C3)⋊C412yescomplemented
639C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
640D4—188no—
641C2×C4—92no—
642C2×C4—92no—
643C2×C4—92no—
644C2×C4—181no—
645C2×C4—181no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4—548no—
657C2×C3—31no—
658C2×C3—31no—
659C2×C3—31no—
660C2×C3—31no—
661C2×C3—31no—
662C2×C3—31no—
663C2×C3—31no—
664C2×C3—31no—
665C2×C3—31no—
666C2×C3—31no—
667C2×C3—31no—
668C2×C3—31no—
669C2×C3—31no—
670C2×C3—31no—
671C2×C3—42no—
672C2×C3—61no—
673C2×C3—61no—
674C2×C3—61no—
675C2×C3—61no—
676C2×C3—61no—
677C2×C3—61no—
678C2×C3—61no—
679C2×C3—122no—
680C2×C3—122no—
681C2×C3—124no—
682C2×C3—184no—
683C2×C3D3×#21711yescharacteristic
684C2×C3#6396911yescharacteristic
685C2×C3#6397011yescharacteristic
686C2×C3#6397111yescharacteristic
687C2×C3Dic3×#6711yescharacteristic
688C2×C3#67⋊Dic311yescharacteristic
689C2×C3#6398311yescharacteristic
690D3—64no—
691D3—184no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—94no—
700C22—182no—
701C22—182no—
702C22—182no—
703C22—182no—
704C22—182no—
705C22—182no—
706C22C2×((C3⋊D3)⋊C3)⋊C411yescharacteristic
707C22#8867111yescharacteristic
708C22#8867211yescharacteristic
709C22#8867611yescharacteristic
710C22#8867611yescharacteristic
711C22#8867611yescharacteristic
712C22#8867711yescharacteristic
713C4—182no—
714C4—182no—
715C4—182no—
716C4—361no—
717C4—361no—
718C3—31no—
719C3—31no—
720C3—61no—
721C3#1059172111yescharacteristic
722C2—42no—
723C2—184no—
724C2#1172131011yescharacteristic
725C2#1172131111yescharacteristic
726C2#1172131211yescharacteristic
727C2#1172131311yescharacteristic
728C2#1172131411yescharacteristic
729C2#1172131511yescharacteristic
730C2#1172132411yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutatorC22×H(3,𝔽3)C22×C4
Frattini, socleC23×C3C2×D32
FittingC24×H(3,𝔽3)C22
prime radicalC22×#638⋊C3C2
cosocleC23×H(3,𝔽3)C23
hypercenterC24((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#386
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×((C3⋊D3)⋊C3)⋊C4C2semidirect
3. C2×#88552C2semidirect
4. C2×#3757⋊C3C2semidirect
5. C2×#88450C2semidirect
6. #11720334C2semidirect
7. #11720334C2semidirect
16. C2×#638⋊C3C4semidirect
30. C2×#3757D3semidirect
47. C23×H(3,𝔽3)C2×C4semidirect
61. C2×#1084D4semidirect
70. C2×(C3⋊Dic3)⋊C3C2×C4semidirect
71. C2×(C3⋊Dic3)⋊C3D4semidirect
83. C2×#638Dic3semidirect
132. C2×(C3⋊D3)⋊C3C22⋊C4semidirect
180. C23×C32C4×D3semidirect
181. C23×C32C2×Dic3semidirect
206. C2×C3⋊Dic3C2×Dic3semidirect
207. C2×C3⋊Dic3#67semidirect
348. C2×C3⋊D3#217semidirect
375. H(3,𝔽3)#386semidirect
623. C32#4956semidirect
624. C32#5220semidirect
638. C23((C3⋊D3)⋊C3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#638⋊C32
C22×((C3⋊D3)⋊C3)⋊C42
C2×#885522
C2×#3757⋊C32
C2×#884502
#117203342
#105917223
#105917213