Finite Group Databasebeta

← #13141171

Subgroups — #13141171

Order 1728.

1069 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6235C211yesmaximal, characteristic
2C2×#3757⋊C3C211yesmaximal, characteristic, complemented
3C2×#3757⋊C3C211yesmaximal, characteristic, complemented
4C2×#88451C211yesmaximal, characteristic, complemented
5C2×#88451C211yesmaximal, characteristic, complemented
6C2×#88448C211yesmaximal, characteristic, complemented
7#11720334C211yesmaximal, characteristic, complemented
8#10591709—31nomaximal
9#10591708—31nomaximal
10C24×H(3,𝔽3)C2211yescharacteristic
11C23×#272C2211yescharacteristic
12C2×#6235—22no—
13C2×#6235—22no—
14C2×#6235—22no—
15C22×#1084C2211yescharacteristic
16C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
17C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
18C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
19C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
20#3757⋊C3—22no—
21#3757⋊C3—22no—
22#88451—22no—
23#88451—22no—
24#88448—22no—
25C22×C3×#67—31no—
26C22×C3×#67—31no—
27C22×C3×#67—61no—
28C2×#3757D311yescharacteristic, complemented
29C2×#3757D311yescharacteristic, complemented
30C2×C3×#217—31no—
31C2×C3×#217—31no—
32C2×#3724—31no—
33C2×Dic3⋊Dic3—31no—
34C2×(C2×D3)⋊Dic3—31no—
35C2×(C2×D3)⋊Dic3—31no—
36C2×(C2×D3)⋊Dic3—31no—
37C2×(C2×D3)⋊Dic3—31no—
38#63579—31no—
39#63579—31no—
40C23×H(3,𝔽3)—21no—
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)D412yes—
47C23×H(3,𝔽3)C2311yescharacteristic
48C22×#272—21no—
49C22×#272—21no—
50C22×#272—21no—
51C22×#272—21no—
52C22×#272—21no—
53C22×#272—21no—
54C22×#272D412yes—
55#6235—28no—
56C2×#1084—21no—
57C2×#1084—21no—
58C2×#1084D412yes—
59C2×(C3⋊Dic3)⋊C3—21no—
60C2×(C3⋊Dic3)⋊C3—21no—
61C2×(C3⋊Dic3)⋊C3—21no—
62C2×(C3⋊Dic3)⋊C3—21no—
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)⋊C3D412yescomplemented
71#5222—91no—
72#4961—91no—
73#4959—91no—
74C24×C32—21no—
75C24×C32C2×D311yescharacteristic
76C24×C32C2×D311yescharacteristic
77C23×C3×D3—31no—
78C23×C3×D3—31no—
79C23×C3×D3—61no—
80C22×C3⋊Dic3C2×D311yescharacteristic
81C22×C3⋊Dic3C2×D311yescharacteristic
82C22×C3⋊Dic3C2×D311yescharacteristic
83C22×C3⋊Dic3C2×D311yescharacteristic
84C2×C3×#67—62no—
85C2×C3×#67—62no—
86C2×C3×#67—62no—
87C2×C3×#67—62no—
88C2×C3×#67—64no—
89C2×C3×#67—64no—
90C2×C3×#67—64no—
91C2×C3×#67—62no—
92C2×C3×#67—62no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—61no—
100#3757—22no—
101#3757—22no—
102C3×#217—62no—
103C3×#217—62no—
104#3724—62no—
105Dic3⋊Dic3—62no—
106(C2×D3)⋊Dic3—62no—
107(C2×D3)⋊Dic3—62no—
108(C2×D3)⋊Dic3—62no—
109(C2×D3)⋊Dic3—62no—
110C22×H(3,𝔽3)—22no—
111C22×H(3,𝔽3)—22no—
112C22×H(3,𝔽3)—22no—
113C22×H(3,𝔽3)—41no—
114C22×H(3,𝔽3)—41no—
115C22×H(3,𝔽3)—41no—
116C22×H(3,𝔽3)—41no—
117C22×H(3,𝔽3)C2×D411yescharacteristic
118C22×H(3,𝔽3)C2×D411yescharacteristic
119C22×H(3,𝔽3)C2×D411yescharacteristic
120C22×H(3,𝔽3)C2×D411yescharacteristic
121C22×H(3,𝔽3)#4111yescharacteristic
122C22×H(3,𝔽3)#4111yescharacteristic
123C22×H(3,𝔽3)#4111yescharacteristic
124C2×#272—22no—
125C2×#272—22no—
126C2×#272—22no—
127C2×#272—41no—
128C2×#272—41no—
129C2×#272—41no—
130C2×#272—41no—
131#1084—22no—
132(C3⋊Dic3)⋊C3—22no—
133(C3⋊Dic3)⋊C3—41no—
134(C3⋊Dic3)⋊C3—41no—
135(C3⋊Dic3)⋊C3—41no—
136C22×C3×D4—91no—
137C22×#67—31no—
138C22×#67—31no—
139C22×#67—61no—
140C2×C3×C22⋊C4—91no—
141C2×C3×C22⋊C4—91no—
142C2×#217—31no—
143C2×#217—31no—
144C2×#217—91no—
145C2×#217—91no—
146C2×#217—91no—
147C2×#217—91no—
148C2×(C2×D3)⋊C4—91no—
149C2×(C2×D3)⋊C4—91no—
150C2×(C2×D3)⋊C4—91no—
151C2×(C2×D3)⋊C4—91no—
152C2×C4⋊Dic3—91no—
153C2×Dic3⋊C4—91no—
154C2×Dic3⋊C4—91no—
155C3⋊#95—91no—
156C3⋊#95—91no—
157C3⋊#95—91no—
158C23×C32—22no—
159C23×C32—22no—
160C23×C32—21no—
161C23×C32—21no—
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—22no—
173C23×C32—21no—
174C23×C32—41no—
175C23×C32—41no—
176C23×C32—41no—
177C23×C32—41no—
178C23×C32D1212yes—
179C23×C32#6712yes—
180C23×C32C22×D311yescharacteristic
181C23×C32C22×D311yescharacteristic
182C22×C3×D3—32no—
183C22×C3×D3—32no—
184C22×C3×D3—62no—
185C22×C3×D3—62no—
186C22×C3×D3—62no—
187C22×C3×D3—61no—
188C22×C3×D3—61no—
189C22×C3×D3—61no—
190C22×C3×D3—61no—
191C22×C3×D3—61no—
192C22×C3×D3—61no—
193C22×C3×D3—61no—
194C22×C3×D3—61no—
195C22×C3×D3—61no—
196C22×C3×D3—61no—
197C22×C3×D3—61no—
198C22×C3×D3—61no—
199C22×C3×D3—121no—
200C22×C3×D3—121no—
201C22×C3×D3—121no—
202C22×C3×D3—121no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3#6712yescomplemented
215C3×#67—616no—
216C3×#67—68no—
217C3×#67—68no—
218C2×C3×Dic3—32no—
219C2×C3×Dic3—32no—
220C2×C3×Dic3—32no—
221C2×C3×Dic3—62no—
222C2×C3×Dic3—62no—
223C2×C3×Dic3—62no—
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—61no—
233C2×C3×Dic3—61no—
234C2×C3×Dic3—61no—
235C2×C3×Dic3—61no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—61no—
239#394—271noSylow
240C2×H(3,𝔽3)—42no—
241C2×H(3,𝔽3)#12011yescharacteristic
242C2×H(3,𝔽3)#12111yescharacteristic
243C2×H(3,𝔽3)#12111yescharacteristic
244C2×H(3,𝔽3)#12111yescharacteristic
245C2×H(3,𝔽3)#12311yescharacteristic
246C2×H(3,𝔽3)#12311yescharacteristic
247C2×H(3,𝔽3)#12411yescharacteristic
248#272—42no—
249C24×C3—31no—
250C24×C3—31no—
251C24×C3—61no—
252C24×C3—91no—
253C24×C3D3211yescharacteristic
254C23×D3—31no—
255C23×D3—31no—
256C23×D3—61no—
257C2×C3×D4—182no—
258C2×C3×D4—182no—
259C2×C3×D4—182no—
260C22×C3×C4—91no—
261C22×C3×C4—91no—
262C22×C3×C4—91no—
263C22×C3×C4—91no—
264C22×C3×C4—91no—
265C2×#67—62no—
266C2×#67—62no—
267C2×#67—62no—
268C2×#67—62no—
269C2×#67—62no—
270C2×#67—62no—
271C2×#67—64no—
272C2×#67—64no—
273C2×#67—64no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—31no—
279C22×Dic3—31no—
280C22×Dic3—61no—
281C22×Dic3—91no—
282C22×Dic3—91no—
283C22×Dic3—91no—
284C22×Dic3—91no—
285C3×C22⋊C4—182no—
286C3×C22⋊C4—182no—
287#217—62no—
288#217—62no—
289#217—182no—
290#217—182no—
291#217—182no—
292#217—182no—
293(C2×D3)⋊C4—182no—
294(C2×D3)⋊C4—182no—
295(C2×D3)⋊C4—182no—
296(C2×D3)⋊C4—182no—
297C4⋊Dic3—182no—
298Dic3⋊C4—182no—
299Dic3⋊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×D1211yescharacteristic
329C22×C32#23511yescharacteristic
330C22×C32#23511yescharacteristic
331C22×C32#23511yescharacteristic
332C22×C32D3×D411yescharacteristic
333C22×C32D3×D411yescharacteristic
334C22×C32D3×D411yescharacteristic
335C22×C32D3×D411yescharacteristic
336C22×C32D3×D411yescharacteristic
337C22×C32#23711yescharacteristic
338C22×C32#23711yescharacteristic
339C22×C32#23711yescharacteristic
340C22×C32C2×#6711yescharacteristic
341C22×C32C2×#6711yescharacteristic
342C2×C3×D3—64no—
343C2×C3×D3—62no—
344C2×C3×D3—62no—
345C2×C3×D3—62no—
346C2×C3×D3—62no—
347C2×C3×D3—62no—
348C2×C3×D3—62no—
349C2×C3×D3—122no—
350C2×C3×D3—122no—
351C2×C3×D3—122no—
352C2×C3×D3—122no—
353C2×C3×D3—122no—
354C2×C3×D3—122no—
355C2×C3×D3—121no—
356C2×C3×D3—121no—
357C2×C3×D3—121no—
358C2×C3×D3—121no—
359C2×C3×D3—121no—
360C2×C3×D3—121no—
361C2×C3×D3—121no—
362C2×C3×D3—121no—
363C3⋊Dic3—22no—
364C3⋊Dic3—41no—
365C3⋊Dic3—41no—
366C3⋊Dic3—41no—
367C3×Dic3—64no—
368C3×Dic3—62no—
369C3×Dic3—62no—
370C3×Dic3—62no—
371C3×Dic3—121no—
372C3×Dic3—121no—
373C3×Dic3—121no—
374C22×D4—91no—
375C2×C4⋊C4—271no—
376C2×C22⋊C4—91no—
377C2×C22⋊C4—91no—
378C2×C22⋊C4—271no—
379C2×C22⋊C4—271no—
380#95—271no—
381H(3,𝔽3)#39411yescharacteristic, complemented, Sylow
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—32no—
389C23×C3—32no—
390C23×C3—31no—
391C23×C3—31no—
392C23×C3—61no—
393C23×C3—61no—
394C23×C3—61no—
395C23×C3—61no—
396C23×C3—61no—
397C23×C3—61no—
398C23×C3—61no—
399C23×C3—61no—
400C23×C3—61no—
401C23×C3—61no—
402C23×C3—61no—
403C23×C3—61no—
404C23×C3—62no—
405C23×C3—62no—
406C23×C3—62no—
407C23×C3—61no—
408C23×C3—92no—
409C23×C3—121no—
410C23×C3—121no—
411C23×C3—121no—
412C23×C3—121no—
413C23×C3—181no—
414C23×C3—181no—
415C23×C3—181no—
416C23×C3—181no—
417C23×C3—181no—
418C23×C3—181no—
419C23×C3#62612yes—
420C23×C3C2×D3211yescharacteristic
421C22×D3—32no—
422C22×D3—32no—
423C22×D3—62no—
424C22×D3—61no—
425C22×D3—61no—
426C22×D3—61no—
427C22×D3—61no—
428C22×D3—61no—
429C22×D3—61no—
430C22×D3—61no—
431C22×D3—61no—
432C22×D3—61no—
433C22×D3—61no—
434C22×D3—61no—
435C22×D3—61no—
436C22×D3—62no—
437C22×D3—62no—
438C22×D3—121no—
439C22×D3—121no—
440C22×D3—121no—
441C22×D3—121no—
442C3×D4—188no—
443C2×C3×C4—92no—
444C2×C3×C4—92no—
445C2×C3×C4—181no—
446C2×C3×C4—181no—
447C2×C3×C4—181no—
448C2×C3×C4—181no—
449C2×C3×C4—181no—
450C2×C3×C4—181no—
451C2×C3×C4—181no—
452C2×C3×C4—181no—
453C2×C3×C4—181no—
454C2×C3×C4—181no—
455C2×C3×C4—181no—
456C2×C3×C4—181no—
457C2×C3×C4—181no—
458#67—68no—
459#67—68no—
460#67—616no—
461C2×Dic3—32no—
462C2×Dic3—32no—
463C2×Dic3—32no—
464C2×Dic3—62no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—92no—
483C2×Dic3—181no—
484C2×Dic3—181no—
485C2×Dic3—181no—
486C2×Dic3—181no—
487C2×Dic3—181no—
488C2×Dic3—181no—
489C2×Dic3—181no—
490C2×Dic3—181no—
491C2×Dic3—181no—
492C2×Dic3—181no—
493C2×Dic3—181no—
494C2×C32—21no—
495C2×C32—21no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—44no—
502C2×C32—42no—
503C2×C32—42no—
504C2×C32#88211yescharacteristic
505C2×C32#88311yescharacteristic
506C2×C32#88311yescharacteristic
507C2×C32#88411yescharacteristic
508C2×C32#88411yescharacteristic
509C2×C32#88511yescharacteristic
510C2×C32#88511yescharacteristic
511C2×C32#88611yescharacteristic
512C2×C32#92911yescharacteristic
513C2×C32#93011yescharacteristic
514C2×C32#93711yescharacteristic
515C2×C32#93811yescharacteristic
516C2×C32#93911yescharacteristic
517C2×C32#93911yescharacteristic
518C3×D3—124no—
519C3×D3—122no—
520C3×D3—122no—
521C24—91no—
522C24((C3⋊D3)⋊C3)⋊C211yescharacteristic
523C2×D4—182no—
524C2×D4—182no—
525C2×D4—182no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—91no—
529C22×C4—91no—
530C22×C4—91no—
531C4⋊C4—542no—
532C22⋊C4—182no—
533C22⋊C4—182no—
534C22⋊C4—542no—
535C22⋊C4—542no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—31no—
540C22×C3—31no—
541C22×C3—31no—
542C22×C3—31no—
543C22×C3—31no—
544C22×C3—31no—
545C22×C3—31no—
546C22×C3—31no—
547C22×C3—31no—
548C22×C3—31no—
549C22×C3—31no—
550C22×C3—31no—
551C22×C3—31no—
552C22×C3—31no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—41no—
557C22×C3—62no—
558C22×C3—62no—
559C22×C3—62no—
560C22×C3—62no—
561C22×C3—62no—
562C22×C3—62no—
563C22×C3—64no—
564C22×C3—61no—
565C22×C3—61no—
566C22×C3—61no—
567C22×C3—61no—
568C22×C3—61no—
569C22×C3—61no—
570C22×C3—61no—
571C22×C3—122no—
572C22×C3—122no—
573C22×C3—121no—
574C22×C3—121no—
575C22×C3—121no—
576C22×C3—121no—
577C22×C3—121no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3—122no—
582C22×C3—122no—
583C22×C3—122no—
584C22×C3—122no—
585C22×C3—182no—
586C22×C3—182no—
587C22×C3—182no—
588C22×C3—361no—
589C22×C3—361no—
590C22×C3—361no—
591C22×C3—361no—
592C22×C3#380411yescharacteristic
593C22×C3#380411yescharacteristic
594C22×C3#380411yescharacteristic
595C22×C3C2×#62611yescharacteristic
596C22×C3D3×#6711yescharacteristic
597C22×C3#381111yescharacteristic
598C22×C3#381111yescharacteristic
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—62no—
602C2×D3—62no—
603C2×D3—62no—
604C2×D3—62no—
605C2×D3—64no—
606C2×D3—122no—
607C2×D3—122no—
608C2×D3—121no—
609C2×D3—121no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—121no—
614C2×D3—121no—
615C2×D3—121no—
616C2×D3—122no—
617C2×D3—122no—
618C2×D3—122no—
619C2×D3—122no—
620C3×C4—182no—
621C3×C4—182no—
622C3×C4—361no—
623C3×C4—361no—
624C3×C4—361no—
625Dic3—62no—
626Dic3—62no—
627Dic3—64no—
628Dic3—62no—
629Dic3—121no—
630Dic3—121no—
631Dic3—121no—
632Dic3—182no—
633Dic3—361no—
634Dic3—361no—
635Dic3—361no—
636C32—21no—
637C32#495911yescharacteristic, complemented
638C32#496111yescharacteristic, complemented
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—92no—
646C23—181no—
647C23—181no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—181no—
652C23#620012yes—
653C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
654D4—188no—
655C2×C4—92no—
656C2×C4—92no—
657C2×C4—181no—
658C2×C4—181no—
659C2×C4—181no—
660C2×C4—181no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C3—31no—
671C2×C3—31no—
672C2×C3—31no—
673C2×C3—31no—
674C2×C3—31no—
675C2×C3—31no—
676C2×C3—31no—
677C2×C3—31no—
678C2×C3—31no—
679C2×C3—31no—
680C2×C3—31no—
681C2×C3—31no—
682C2×C3—31no—
683C2×C3—31no—
684C2×C3—42no—
685C2×C3—61no—
686C2×C3—61no—
687C2×C3—61no—
688C2×C3—61no—
689C2×C3—61no—
690C2×C3—61no—
691C2×C3—61no—
692C2×C3—122no—
693C2×C3—122no—
694C2×C3—124no—
695C2×C3—362no—
696C2×C3#6395311yescharacteristic
697C2×C3#6395811yescharacteristic
698C2×C3#6396611yescharacteristic
699C2×C3#6397111yescharacteristic
700C2×C3#6397511yescharacteristic
701C2×C3#6397811yescharacteristic
702C2×C3#6398111yescharacteristic
703D3—122no—
704D3—122no—
705D3—124no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—182no—
714C22—182no—
715C22—182no—
716C22—361no—
717C22—361no—
718C22—361no—
719C22—361no—
720C22#8867111yescharacteristic
721C22#8867111yescharacteristic
722C22#8867111yescharacteristic
723C22C2×#620011yescharacteristic
724C22#8867611yescharacteristic
725C22#8867711yescharacteristic
726C22#8867711yescharacteristic
727C4—182no—
728C4—182no—
729C4—361no—
730C4—361no—
731C4—361no—
732C3—31no—
733C3—31no—
734C3—61no—
735C3#1059171211yescharacteristic
736C2—42no—
737C2—362no—
738C2#1172129411yescharacteristic
739C2#1172130111yescharacteristic
740C2#1172130311yescharacteristic
741C2#1172131211yescharacteristic
742C2#1172131911yescharacteristic
743C2#1172132211yescharacteristic
744C2#1172132311yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC23×H(3,𝔽3)C23
Frattini, socleC23×C3C2×D32
FittingC24×H(3,𝔽3)C22
prime radicalC22×#6235C2
hypercenterC24((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#394
LCSG ▷ C23×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×#3757⋊C3C2semidirect
3. C2×#3757⋊C3C2semidirect
4. C2×#88451C2semidirect
5. C2×#88451C2semidirect
6. C2×#88448C2semidirect
7. #11720334C2semidirect
28. C2×#3757D3semidirect
29. C2×#3757D3semidirect
70. C2×(C3⋊Dic3)⋊C3D4semidirect
214. C2×C3⋊Dic3#67semidirect
381. H(3,𝔽3)#394semidirect
637. C32#4959semidirect
638. C32#4961semidirect

Maximal subgroups

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

subgroupindex
C22×#62352
C2×#3757⋊C32
C2×#884512
C2×#884482
#117203342
#105917093
#105917083