Finite Group Databasebeta

← #13140258

Subgroups — #13140258

Order 1728.

1035 conjugacy classes of subgroups.

The subgroup lattice has 725 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6200C211yesmaximal, characteristic
2C2×#88542C211yesmaximal, characteristic, complemented
3C2×#3752⋊C3C211yesmaximal, characteristic, complemented
4C2×C4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
5C2×#88451C211yesmaximal, characteristic, complemented
6C2×#88450C211yesmaximal, characteristic, complemented
7C2×#88448C211yesmaximal, characteristic, complemented
8#10591385—31nomaximal
9#10591383—31nomaximal
10C23×#272C2211yescharacteristic
11C23×(C3⋊D3)⋊C3C2211yescharacteristic
12C22×C4×H(3,𝔽3)C2211yescharacteristic
13C22×#1084C2211yescharacteristic
14C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
15C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
16C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
17C2×#6200—22no—
18C2×#6200—22no—
19C2×#6200C414yescomplemented
20#88542—22no—
21#3752⋊C3—22no—
22C4×(C3⋊Dic3)⋊C3—22no—
23#88451—22no—
24#88450—22no—
25#88448—22no—
26C22×#626—31no—
27C22×#625—31no—
28C2×#3752D311yescharacteristic, complemented
29C2×C4×C3⋊Dic3D311yescharacteristic, complemented
30C2×C3×(C2×D3)⋊C4—31no—
31C2×C3×(C2×D3)⋊C4—31no—
32C2×C3×(C2×D3)⋊C4—31no—
33C2×C3×(C2×D3)⋊C4—61no—
34C2×C3×C4×Dic3—31no—
35C2×#3724—31no—
36C2×Dic3⋊Dic3—31no—
37C2×#3722—31no—
38C2×(C2×D3)⋊Dic3—31no—
39C2×(C2×D3)⋊Dic3—31no—
40C2×(C2×D3)⋊Dic3—31no—
41C23×H(3,𝔽3)C2311yescharacteristic
42C22×#272—21no—
43C22×#272—21no—
44C22×#272—21no—
45C22×#272—21no—
46C22×#272—21no—
47C22×#272—21no—
48C22×#272C2×C412yes—
49C22×(C3⋊D3)⋊C3—21no—
50C22×(C3⋊D3)⋊C3—21no—
51C22×(C3⋊D3)⋊C3—21no—
52C22×(C3⋊D3)⋊C3—21no—
53C22×(C3⋊D3)⋊C3—21no—
54C22×(C3⋊D3)⋊C3—21no—
55C22×(C3⋊D3)⋊C3C2×C412yes—
56C2×C4×H(3,𝔽3)—21no—
57C2×C4×H(3,𝔽3)—21no—
58C2×C4×H(3,𝔽3)D412yescomplemented
59C2×#1084—21no—
60C2×#1084—21no—
61C2×#1084—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)⋊C3C2×C412yes—
68C2×(C3⋊Dic3)⋊C3D412yes—
69C2×(C3⋊Dic3)⋊C3D412yes—
70C2×(C3⋊Dic3)⋊C3D412yescomplemented
71#6200—28no—
72#4957—91no—
73#4957—91no—
74#4939—91no—
75C23×C3⋊D3C2×D311yescharacteristic
76C23×C3×D3—31no—
77C23×C3×D3—31no—
78C23×C3×D3—31no—
79C23×C3×D3—61no—
80C22×C32×C4—21no—
81C22×C32×C4C2×D311yescharacteristic
82C22×C32×C4C2×D311yescharacteristic
83C22×C3⋊Dic3C2×D311yescharacteristic
84C22×C3⋊Dic3C2×D311yescharacteristic
85C22×C3⋊Dic3C2×D311yescharacteristic
86C22×C3×Dic3—31no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—61no—
92C2×#626—34no—
93C2×#626—62no—
94C2×#626—62no—
95C2×#625—34no—
96C2×#625—62no—
97C2×#625—62no—
98#3752—22no—
99C4×C3⋊Dic3—22no—
100C3×(C2×D3)⋊C4—64no—
101C3×(C2×D3)⋊C4—62no—
102C3×(C2×D3)⋊C4—62no—
103C3×(C2×D3)⋊C4—62no—
104C3×C4×Dic3—62no—
105#3724—62no—
106Dic3⋊Dic3—62no—
107#3722—62no—
108(C2×D3)⋊Dic3—62no—
109(C2×D3)⋊Dic3—62no—
110(C2×D3)⋊Dic3—62no—
111C22×H(3,𝔽3)C22×C411yescharacteristic
112C22×H(3,𝔽3)C2×D411yescharacteristic
113C22×H(3,𝔽3)C2×D411yescharacteristic
114C22×H(3,𝔽3)C2×D411yescharacteristic
115C22×H(3,𝔽3)C2×D411yescharacteristic
116C22×H(3,𝔽3)#4111yescharacteristic
117C22×H(3,𝔽3)#4111yescharacteristic
118C2×#272—22no—
119C2×#272—22no—
120C2×#272—22no—
121C2×#272—41no—
122C2×#272—41no—
123C2×#272—41no—
124C2×#272—41no—
125C2×(C3⋊D3)⋊C3—22no—
126C2×(C3⋊D3)⋊C3—22no—
127C2×(C3⋊D3)⋊C3—22no—
128C2×(C3⋊D3)⋊C3—41no—
129C2×(C3⋊D3)⋊C3—41no—
130C2×(C3⋊D3)⋊C3—41no—
131C2×(C3⋊D3)⋊C3—41no—
132C4×H(3,𝔽3)—22no—
133#1084—41no—
134(C3⋊Dic3)⋊C3—22no—
135(C3⋊Dic3)⋊C3—41no—
136(C3⋊Dic3)⋊C3C22⋊C414yescomplemented
137C22×#67—91no—
138C22×#67—91no—
139C22×D12—91no—
140C2×C3×C22⋊C4—91no—
141C2×C3×C22⋊C4—91no—
142C2×C3×C42—91no—
143C2×#217—91no—
144C2×#217—91no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—61no—
149C2×(C2×D3)⋊C4—91no—
150C2×(C2×D3)⋊C4—91no—
151C2×(C2×D3)⋊C4—91no—
152C2×(C2×D3)⋊C4—91no—
153C2×(C2×D3)⋊C4—91no—
154C2×C4⋊Dic3—91no—
155C2×Dic3⋊C4—91no—
156C2×Dic3⋊C4—91no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—91no—
159C23×C32—21no—
160C23×C32C22×D311yescharacteristic
161C23×C32C22×D311yescharacteristic
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3C4×D312yes—
169C22×C3×D3—32no—
170C22×C3×D3—32no—
171C22×C3×D3—32no—
172C22×C3×D3—62no—
173C22×C3×D3—62no—
174C22×C3×D3—62no—
175C22×C3×D3—61no—
176C22×C3×D3—61no—
177C22×C3×D3—61no—
178C22×C3×D3—61no—
179C22×C3×D3—61no—
180C22×C3×D3—61no—
181C22×C3×D3—61no—
182C22×C3×D3—61no—
183C22×C3×D3—61no—
184C22×C3×D3—61no—
185C22×C3×D3—61no—
186C22×C3×D3—61no—
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—121no—
194C22×C3×D3—121no—
195C22×C3×D3—121no—
196C22×C3×D3—121no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—22no—
202C2×C32×C4—41no—
203C2×C32×C4—41no—
204C2×C32×C4D1212yescomplemented
205C2×C32×C4#6712yescomplemented
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3C4×D312yes—
212C2×C3⋊Dic3D1212yes—
213C2×C3⋊Dic3D1212yescomplemented
214C2×C3⋊Dic3#6712yes—
215C2×C3×Dic3—32no—
216C2×C3×Dic3—32no—
217C2×C3×Dic3—32no—
218C2×C3×Dic3—32no—
219C2×C3×Dic3—61no—
220C2×C3×Dic3—61no—
221C2×C3×Dic3—62no—
222C2×C3×Dic3—61no—
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—121no—
232C2×C3×Dic3—121no—
233#626—68no—
234#625—68no—
235#390—271noSylow
236C2×H(3,𝔽3)C2×C22⋊C411yescharacteristic
237C2×H(3,𝔽3)C4×D411yescharacteristic
238C2×H(3,𝔽3)C4×D411yescharacteristic
239C2×H(3,𝔽3)#12111yescharacteristic
240C2×H(3,𝔽3)#12111yescharacteristic
241C2×H(3,𝔽3)#12411yescharacteristic
242C2×H(3,𝔽3)#12711yescharacteristic
243#272—42no—
244(C3⋊D3)⋊C3—42no—
245C24×C3—91no—
246C24×C3—91no—
247C23×D3—31no—
248C23×D3—31no—
249C23×D3—31no—
250C23×D3—61no—
251C23×D3—91no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—61no—
255C22×C3×C4—91no—
256C22×C3×C4—91no—
257C22×C3×C4—91no—
258C22×C3×C4—91no—
259C22×C3×C4D3211yescharacteristic
260C2×#67—94no—
261C2×#67—94no—
262C2×#67—182no—
263C2×#67—182no—
264C2×#67—182no—
265C2×#67—182no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—61no—
272C22×Dic3—91no—
273C22×Dic3—91no—
274C22×Dic3—91no—
275C2×D12—94no—
276C2×D12—182no—
277C2×D12—182no—
278C3×C22⋊C4—182no—
279C3×C22⋊C4—182no—
280C3×C42—182no—
281#217—182no—
282#217—182no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—64no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—182no—
288(C2×D3)⋊C4—182no—
289(C2×D3)⋊C4—182no—
290(C2×D3)⋊C4—182no—
291(C2×D3)⋊C4—182no—
292C4⋊Dic3—182no—
293Dic3⋊C4—182no—
294Dic3⋊C4—182no—
295C4×Dic3—62no—
296C4×Dic3—182no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32C2×C4×D311yescharacteristic
305C22×C32C2×C4×D311yescharacteristic
306C22×C32C2×D1211yescharacteristic
307C22×C32C2×D1211yescharacteristic
308C22×C32C2×D1211yescharacteristic
309C22×C32#23511yescharacteristic
310C22×C32#23511yescharacteristic
311C22×C32#23511yescharacteristic
312C22×C32D3×D411yescharacteristic
313C22×C32D3×D411yescharacteristic
314C22×C32D3×D411yescharacteristic
315C22×C32#23711yescharacteristic
316C22×C32C2×#6711yescharacteristic
317C22×C32C2×#6711yescharacteristic
318C2×C3⋊D3—22no—
319C2×C3⋊D3—22no—
320C2×C3⋊D3—22no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3×D3—64no—
326C2×C3×D3—62no—
327C2×C3×D3—62no—
328C2×C3×D3—62no—
329C2×C3×D3—62no—
330C2×C3×D3—62no—
331C2×C3×D3—62no—
332C2×C3×D3—62no—
333C2×C3×D3—62no—
334C2×C3×D3—62no—
335C2×C3×D3—122no—
336C2×C3×D3—122no—
337C2×C3×D3—122no—
338C2×C3×D3—122no—
339C2×C3×D3—122no—
340C2×C3×D3—122no—
341C2×C3×D3—121no—
342C2×C3×D3—121no—
343C2×C3×D3—121no—
344C2×C3×D3—121no—
345C2×C3×D3—121no—
346C2×C3×D3—121no—
347C2×C3×D3—121no—
348C2×C3×D3—121no—
349C2×C3×D3—121no—
350C2×C3×D3—121no—
351C2×C3×D3—121no—
352C2×C3×D3—121no—
353C32×C4—22no—
354C32×C4—22no—
355C32×C4—42no—
356C3⋊Dic3—22no—
357C3⋊Dic3—41no—
358C3⋊Dic3(C2×D3)⋊C414yescomplemented
359C3×Dic3—34no—
360C3×Dic3—62no—
361C3×Dic3—122no—
362C3×Dic3—121no—
363C3×Dic3—121no—
364C3×Dic3—121no—
365C22×D4—271no—
366C2×C4⋊C4—271no—
367C2×C22⋊C4—91no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4—271no—
370C2×C22⋊C4—271no—
371C2×C42—91no—
372H(3,𝔽3)#39011yescharacteristic, complemented, Sylow
373C23×C3—31no—
374C23×C3—31no—
375C23×C3—61no—
376C23×C3—92no—
377C23×C3—92no—
378C23×C3—181no—
379C23×C3—181no—
380C23×C3—181no—
381C23×C3—181no—
382C23×C3—181no—
383C23×C3—181no—
384C23×C3—181no—
385C23×C3—181no—
386C23×C3—181no—
387C23×C3—181no—
388C23×C3—181no—
389C23×C3—181no—
390C23×C3C2×D3211yescharacteristic
391C22×D3—32no—
392C22×D3—32no—
393C22×D3—32no—
394C22×D3—62no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—61no—
400C22×D3—61no—
401C22×D3—61no—
402C22×D3—61no—
403C22×D3—61no—
404C22×D3—61no—
405C22×D3—61no—
406C22×D3—61no—
407C22×D3—62no—
408C22×D3—62no—
409C22×D3—61no—
410C22×D3—61no—
411C22×D3—61no—
412C22×D3—61no—
413C22×D3—61no—
414C22×D3—61no—
415C22×D3—92no—
416C22×D3—121no—
417C22×D3—121no—
418C22×D3—121no—
419C22×D3—121no—
420C22×D3—181no—
421C22×D3—181no—
422C22×D3—181no—
423C22×D3—181no—
424C22×D3—181no—
425C22×D3—181no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—32no—
429C2×C3×C4—32no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—61no—
433C2×C3×C4—61no—
434C2×C3×C4—62no—
435C2×C3×C4—92no—
436C2×C3×C4—92no—
437C2×C3×C4—92no—
438C2×C3×C4—92no—
439C2×C3×C4—121no—
440C2×C3×C4—121no—
441C2×C3×C4—181no—
442C2×C3×C4—181no—
443C2×C3×C4—181no—
444C2×C3×C4—181no—
445C2×C3×C4—181no—
446C2×C3×C4—181no—
447C2×C3×C4—181no—
448C2×C3×C4—181no—
449C2×C3×C4#62612yes—
450#67—188no—
451#67—188no—
452C2×Dic3—32no—
453C2×Dic3—32no—
454C2×Dic3—32no—
455C2×Dic3—32no—
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—62no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—92no—
469C2×Dic3—92no—
470C2×Dic3—92no—
471C2×Dic3—92no—
472C2×Dic3—121no—
473C2×Dic3—121no—
474C2×Dic3—181no—
475C2×Dic3—181no—
476C2×Dic3—181no—
477C2×Dic3—181no—
478C2×Dic3—181no—
479D12—188no—
480C2×C32—21no—
481C2×C32—21no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32C4×D1211yescharacteristic
488C2×C32C4×D1211yescharacteristic
489C2×C32#87411yescharacteristic
490C2×C32#87511yescharacteristic
491C2×C32D3×C22⋊C411yescharacteristic
492C2×C32#67⋊C411yescharacteristic
493C2×C32#88411yescharacteristic
494C2×C32#88511yescharacteristic
495C2×C32C2×(C2×D3)⋊C411yescharacteristic
496C2×C32C4×#6711yescharacteristic
497C2×C32#93011yescharacteristic
498C2×C32#93011yescharacteristic
499C2×C32#93911yescharacteristic
500C2×C32#94011yescharacteristic
501C3⋊D3—42no—
502C3×D3—124no—
503C3×D3—122no—
504C3×D3—122no—
505C3×D3—122no—
506C24—91no—
507C24—91no—
508C2×D4—274no—
509C2×D4—542no—
510C2×D4—542no—
511C22×C4—91no—
512C22×C4—91no—
513C22×C4—91no—
514C22×C4—91no—
515C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
516C4⋊C4—542no—
517C22⋊C4—182no—
518C22⋊C4—182no—
519C22⋊C4—542no—
520C22⋊C4—542no—
521C42—182no—
522C22×C3—31no—
523C22×C3—31no—
524C22×C3—31no—
525C22×C3—31no—
526C22×C3—31no—
527C22×C3—31no—
528C22×C3—31no—
529C22×C3—31no—
530C22×C3—31no—
531C22×C3—31no—
532C22×C3—31no—
533C22×C3—31no—
534C22×C3—31no—
535C22×C3—31no—
536C22×C3—61no—
537C22×C3—61no—
538C22×C3—61no—
539C22×C3—61no—
540C22×C3—61no—
541C22×C3—61no—
542C22×C3—61no—
543C22×C3—182no—
544C22×C3—182no—
545C22×C3—182no—
546C22×C3—182no—
547C22×C3—182no—
548C22×C3—182no—
549C22×C3—361no—
550C22×C3—361no—
551C22×C3—361no—
552C22×C3—361no—
553C22×C3—361no—
554C22×C3—361no—
555C22×C3—361no—
556C22×C3—361no—
557C22×C3#379811yescharacteristic
558C22×C3C4×D3211yescharacteristic
559C22×C3D3×D1211yescharacteristic
560C22×C3D3×D1211yescharacteristic
561C22×C3#380411yescharacteristic
562C22×C3C2×#62611yescharacteristic
563C22×C3D3×#6711yescharacteristic
564C2×D3—62no—
565C2×D3—62no—
566C2×D3—62no—
567C2×D3—62no—
568C2×D3—62no—
569C2×D3—62no—
570C2×D3—64no—
571C2×D3—62no—
572C2×D3—62no—
573C2×D3—62no—
574C2×D3—122no—
575C2×D3—122no—
576C2×D3—121no—
577C2×D3—121no—
578C2×D3—121no—
579C2×D3—121no—
580C2×D3—121no—
581C2×D3—121no—
582C2×D3—121no—
583C2×D3—121no—
584C2×D3—122no—
585C2×D3—122no—
586C2×D3—122no—
587C2×D3—122no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—182no—
593C2×D3—182no—
594C2×D3—182no—
595C2×D3—361no—
596C2×D3—361no—
597C2×D3—361no—
598C2×D3—361no—
599C3×C4—22no—
600C3×C4—62no—
601C3×C4—62no—
602C3×C4—94no—
603C3×C4—122no—
604C3×C4—182no—
605C3×C4—361no—
606C3×C4—361no—
607Dic3—34no—
608Dic3—62no—
609Dic3—94no—
610Dic3—121no—
611Dic3—121no—
612Dic3—122no—
613Dic3—121no—
614Dic3—182no—
615Dic3—361no—
616C32—21no—
617C32#493911yescharacteristic, complemented
618C32#495711yescharacteristic, complemented
619C23—92no—
620C23—92no—
621C23—181no—
622C23—181no—
623C23—181no—
624C23—181no—
625C23—181no—
626C23—181no—
627C23—181no—
628C23—181no—
629C23—181no—
630C23—181no—
631C23—181no—
632C23—181no—
633C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
634D4—548no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—92no—
638C2×C4—92no—
639C2×C4—92no—
640C2×C4—92no—
641C2×C4—181no—
642C2×C4—181no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4—181no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4#620012yescomplemented
650C2×C3—31no—
651C2×C3—31no—
652C2×C3—31no—
653C2×C3—31no—
654C2×C3—31no—
655C2×C3—31no—
656C2×C3—31no—
657C2×C3—31no—
658C2×C3—31no—
659C2×C3—31no—
660C2×C3—31no—
661C2×C3—31no—
662C2×C3—31no—
663C2×C3—31no—
664C2×C3—61no—
665C2×C3—61no—
666C2×C3—61no—
667C2×C3—61no—
668C2×C3—61no—
669C2×C3—61no—
670C2×C3—61no—
671C2×C3—362no—
672C2×C3—362no—
673C2×C3#6385211yescharacteristic
674C2×C3#6388011yescharacteristic
675C2×C3C4×#62611yescharacteristic
676C2×C3#6390611yescharacteristic
677C2×C3#6391111yescharacteristic
678C2×C3D3×(C2×D3)⋊C411yescharacteristic
679C2×C3#6397811yescharacteristic
680D3—122no—
681D3—122no—
682D3—124no—
683D3—122no—
684D3—362no—
685C22—182no—
686C22—182no—
687C22—182no—
688C22—182no—
689C22—182no—
690C22—182no—
691C22—361no—
692C22—361no—
693C22—361no—
694C22—361no—
695C22—361no—
696C22—361no—
697C22—361no—
698C22—361no—
699C22#8865011yescharacteristic
700C22C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
701C22#8865411yescharacteristic
702C22#8865411yescharacteristic
703C22#8867111yescharacteristic
704C22C2×#620011yescharacteristic
705C22#8867611yescharacteristic
706C4—22no—
707C4—94no—
708C4—182no—
709C4—361no—
710C4—361no—
711C3—31no—
712C3—31no—
713C3—61no—
714C3#1059138311yescharacteristic
715C2—362no—
716C2—362no—
717C2#1172110311yescharacteristic
718C2#1172112311yescharacteristic
719C2#1172114011yescharacteristic
720C2C4×#620011yescharacteristic
721C2#1172115811yescharacteristic
722C2#1172116011yescharacteristic
723C2#1172132211yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutatorC22×H(3,𝔽3)C22×C4
Frattini, socleC23×C3C2×D32
FittingC22×C4×H(3,𝔽3)C22
prime radicalC22×#6200C2
cosocleC23×H(3,𝔽3)C23
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#390
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#88542C2semidirect
3. C2×#3752⋊C3C2semidirect
4. C2×C4×(C3⋊Dic3)⋊C3C2semidirect
5. C2×#88451C2semidirect
6. C2×#88450C2semidirect
7. C2×#88448C2semidirect
19. C2×#6200C4semidirect
28. C2×#3752D3semidirect
29. C2×C4×C3⋊Dic3D3semidirect
58. C2×C4×H(3,𝔽3)D4semidirect
70. C2×(C3⋊Dic3)⋊C3D4semidirect
136. (C3⋊Dic3)⋊C3C22⋊C4semidirect
204. C2×C32×C4D12semidirect
205. C2×C32×C4#67semidirect
213. C2×C3⋊Dic3D12semidirect
358. C3⋊Dic3(C2×D3)⋊C4semidirect
372. H(3,𝔽3)#390semidirect
617. C32#4939semidirect
618. C32#4957semidirect
649. C2×C4#6200semidirect

Maximal subgroups

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

subgroupindex
C22×#62002
C2×#885422
C2×#3752⋊C32
C2×C4×(C3⋊Dic3)⋊C32
C2×#884512
C2×#884502
C2×#884482
#105913853
#105913833