Finite Group Databasebeta

← #13140256

Subgroups — #13140256

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×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
2C22×#6200C211yesmaximal, characteristic
3C2×#88542C211yesmaximal, characteristic, complemented
4C2×#88451C211yesmaximal, characteristic, complemented
5C2×#88450C211yesmaximal, characteristic, complemented
6#63658⋊C3C211yesmaximal, characteristic, complemented
7#11720334C211yesmaximal, characteristic, complemented
8#10591387—31nomaximal
9#10591381—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×C4×(C3⋊D3)⋊C3—22no—
18C2×C4×(C3⋊D3)⋊C3—22no—
19C2×C4×(C3⋊D3)⋊C3—22no—
20C2×#6200—22no—
21C2×#6200—22no—
22C2×#6200C414yescomplemented
23#88542—22no—
24#88451—22no—
25#88450—22no—
26C22×C4×C3⋊D3D311yescharacteristic, complemented
27C22×C3×C4×D3—31no—
28C22×#626—31no—
29C22×#625—31no—
30C2×C3×(C2×D3)⋊C4—31no—
31C2×C3×(C2×D3)⋊C4—31no—
32C2×C3×(C2×D3)⋊C4—61no—
33C2×#3722—31no—
34C2×(C2×D3)⋊Dic3—31no—
35C2×(C2×D3)⋊Dic3—31no—
36C2×(C2×D3)⋊Dic3—31no—
37#63658D311yescharacteristic, complemented
38C3×C3⋊#95—31no—
39#63579—31no—
40#63579—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×C412yescomplemented
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×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)⋊C3—21no—
68C2×(C3⋊Dic3)⋊C3—21no—
69C2×(C3⋊Dic3)⋊C3C2×C412yescomplemented
70C2×(C3⋊Dic3)⋊C3D412yescomplemented
71C4×(C3⋊D3)⋊C3—28no—
72#6200—28no—
73#5213—91no—
74#4956—91no—
75#4665—91no—
76C23×C3⋊D3C2×D311yescharacteristic
77C23×C3×D3—31no—
78C23×C3×D3—31no—
79C23×C3×D3—31no—
80C23×C3×D3—61no—
81C22×C32×C4—21no—
82C22×C32×C4C2×D311yescharacteristic
83C22×C32×C4C2×D311yescharacteristic
84C22×C3⋊Dic3C2×D311yescharacteristic
85C22×C3⋊Dic3C2×D311yescharacteristic
86C22×C3⋊Dic3C2×D311yescharacteristic
87C2×C4×C3⋊D3—22no—
88C2×C4×C3⋊D3—22no—
89C2×C4×C3⋊D3—22no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—61no—
96C2×C3×C4×D3—62no—
97C2×C3×C4×D3—62no—
98C2×C3×C4×D3—62no—
99C2×#626—34no—
100C2×#626—62no—
101C2×#626—62no—
102C2×#625—34no—
103C2×#625—62no—
104C2×#625—62no—
105C3×(C2×D3)⋊C4—64no—
106C3×(C2×D3)⋊C4—62no—
107C3×(C2×D3)⋊C4—62no—
108#3722—62no—
109(C2×D3)⋊Dic3—62no—
110(C2×D3)⋊Dic3—62no—
111(C2×D3)⋊Dic3—62no—
112C22×H(3,𝔽3)C22×C411yescharacteristic
113C22×H(3,𝔽3)C2×D411yescharacteristic
114C22×H(3,𝔽3)C2×D411yescharacteristic
115C22×H(3,𝔽3)C2×D411yescharacteristic
116C22×H(3,𝔽3)C2×D411yescharacteristic
117C22×H(3,𝔽3)#4111yescharacteristic
118C22×H(3,𝔽3)#4111yescharacteristic
119C2×#272—22no—
120C2×#272—22no—
121C2×#272—22no—
122C2×#272—41no—
123C2×#272—41no—
124C2×#272—41no—
125C2×#272—41no—
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
133C4×H(3,𝔽3)—22no—
134#1084—41no—
135(C3⋊Dic3)⋊C3—22no—
136(C3⋊Dic3)⋊C3—22no—
137(C3⋊Dic3)⋊C3—41no—
138C23×C3×C4—91no—
139C22×#67—91no—
140C22×#67—91no—
141C22×D12—91no—
142C22×C4×D3—31no—
143C22×C4×D3—91no—
144C2×C3×C22⋊C4—91no—
145C2×#217—91no—
146C2×#217—91no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—61no—
150C2×(C2×D3)⋊C4—91no—
151C2×(C2×D3)⋊C4—91no—
152C2×(C2×D3)⋊C4—91no—
153C2×(C2×D3)⋊C4—91no—
154C3×#95—91no—
155C3⋊#95—31no—
156C3⋊#95—91no—
157C3⋊#95—91no—
158C3⋊#95—91no—
159C3⋊#95—91no—
160C23×C32—21no—
161C23×C32C22×D311yescharacteristic
162C23×C32C22×D311yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3C4×D312yes—
168C22×C3⋊D3D1212yes—
169C22×C3⋊D3#6712yes—
170C22×C3×D3—32no—
171C22×C3×D3—32no—
172C22×C3×D3—32no—
173C22×C3×D3—32no—
174C22×C3×D3—32no—
175C22×C3×D3—62no—
176C22×C3×D3—61no—
177C22×C3×D3—61no—
178C22×C3×D3—61no—
179C22×C3×D3—61no—
180C22×C3×D3—62no—
181C22×C3×D3—62no—
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—61no—
194C22×C3×D3—121no—
195C22×C3×D3—121no—
196C22×C3×D3—121no—
197C22×C3×D3—121no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—22no—
203C2×C32×C4—41no—
204C2×C32×C4—41no—
205C2×C32×C4D1212yescomplemented
206C2×C32×C4#6712yescomplemented
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⋊Dic3C4×D312yescomplemented
215C2×C3⋊Dic3#6712yescomplemented
216C4×C3⋊D3—28no—
217C2×C3×Dic3—32no—
218C2×C3×Dic3—32no—
219C2×C3×Dic3—61no—
220C2×C3×Dic3—61no—
221C2×C3×Dic3—61no—
222C2×C3×Dic3—61no—
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—121no—
234C2×C3×Dic3—121no—
235C3×C4×D3—68no—
236#626—68no—
237#625—68no—
238#386—271noSylow
239C2×H(3,𝔽3)C2×C22⋊C411yescharacteristic
240C2×H(3,𝔽3)C4×D411yescharacteristic
241C2×H(3,𝔽3)C4×D411yescharacteristic
242C2×H(3,𝔽3)#12011yescharacteristic
243C2×H(3,𝔽3)#12111yescharacteristic
244C2×H(3,𝔽3)#12111yescharacteristic
245C2×H(3,𝔽3)#12311yescharacteristic
246#272—42no—
247(C3⋊D3)⋊C3—24no—
248C24×C3—91no—
249C24×C3—91no—
250C23×D3—31no—
251C23×D3—31no—
252C23×D3—31no—
253C23×D3—61no—
254C23×D3—91no—
255C22×C3×C4—31no—
256C22×C3×C4—31no—
257C22×C3×C4—61no—
258C22×C3×C4—91no—
259C22×C3×C4—91no—
260C22×C3×C4—91no—
261C22×C3×C4—91no—
262C22×C3×C4—182no—
263C22×C3×C4—182no—
264C22×C3×C4—182no—
265C22×C3×C4D3211yescharacteristic
266C2×#67—94no—
267C2×#67—94no—
268C2×#67—182no—
269C2×#67—182no—
270C2×#67—182no—
271C2×#67—182no—
272C22×Dic3—31no—
273C22×Dic3—31no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—61no—
278C22×Dic3—91no—
279C22×Dic3—91no—
280C22×Dic3—91no—
281C2×D12—94no—
282C2×D12—182no—
283C2×D12—182no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×C4×D3—182no—
288C2×C4×D3—182no—
289C2×C4×D3—182no—
290C3×C22⋊C4—182no—
291#217—182no—
292#217—182no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—182no—
297(C2×D3)⋊C4—182no—
298(C2×D3)⋊C4—182no—
299(C2×D3)⋊C4—182no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32C2×C4×D311yescharacteristic
308C22×C32C2×C4×D311yescharacteristic
309C22×C32C2×D1211yescharacteristic
310C22×C32C2×D1211yescharacteristic
311C22×C32#23511yescharacteristic
312C22×C32#23511yescharacteristic
313C22×C32#23511yescharacteristic
314C22×C32D3×D411yescharacteristic
315C22×C32D3×D411yescharacteristic
316C22×C32D3×D411yescharacteristic
317C22×C32#23911yescharacteristic
318C22×C32C2×#6711yescharacteristic
319C22×C32C2×#6711yescharacteristic
320C22×C32C2×#6711yescharacteristic
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—22no—
324C2×C3⋊D3—22no—
325C2×C3⋊D3—22no—
326C2×C3⋊D3—22no—
327C2×C3⋊D3(C2×D3)⋊C414yescomplemented
328C2×C3×D3—34no—
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—64no—
336C2×C3×D3—62no—
337C2×C3×D3—62no—
338C2×C3×D3—62no—
339C2×C3×D3—62no—
340C2×C3×D3—62no—
341C2×C3×D3—62no—
342C2×C3×D3—122no—
343C2×C3×D3—122no—
344C2×C3×D3—122no—
345C2×C3×D3—122no—
346C2×C3×D3—122no—
347C2×C3×D3—122no—
348C2×C3×D3—121no—
349C2×C3×D3—121no—
350C2×C3×D3—121no—
351C2×C3×D3—121no—
352C2×C3×D3—121no—
353C2×C3×D3—121no—
354C2×C3×D3—121no—
355C2×C3×D3—121no—
356C32×C4—22no—
357C32×C4—22no—
358C32×C4—42no—
359C3⋊Dic3—22no—
360C3⋊Dic3—22no—
361C3⋊Dic3—41no—
362C3×Dic3—62no—
363C3×Dic3—62no—
364C3×Dic3—122no—
365C3×Dic3—121no—
366C3×Dic3—121no—
367C3×Dic3—121no—
368C22×D4—271no—
369C23×C4—91no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—271no—
372C2×C22⋊C4—271no—
373#95—91no—
374#95—271no—
375H(3,𝔽3)#38611yescharacteristic, complemented, Sylow
376C23×C3—31no—
377C23×C3—31no—
378C23×C3—61no—
379C23×C3—92no—
380C23×C3—92no—
381C23×C3—92no—
382C23×C3—92no—
383C23×C3—181no—
384C23×C3—181no—
385C23×C3—181no—
386C23×C3—181no—
387C23×C3—181no—
388C23×C3—181no—
389C23×C3—181no—
390C23×C3—181no—
391C23×C3—181no—
392C23×C3—181no—
393C23×C3C2×D3211yescharacteristic
394C22×D3—32no—
395C22×D3—32no—
396C22×D3—32no—
397C22×D3—32no—
398C22×D3—32no—
399C22×D3—62no—
400C22×D3—61no—
401C22×D3—61no—
402C22×D3—61no—
403C22×D3—61no—
404C22×D3—61no—
405C22×D3—61no—
406C22×D3—61no—
407C22×D3—61no—
408C22×D3—61no—
409C22×D3—61no—
410C22×D3—61no—
411C22×D3—61no—
412C22×D3—61no—
413C22×D3—61no—
414C22×D3—61no—
415C22×D3—61no—
416C22×D3—62no—
417C22×D3—62no—
418C22×D3—92no—
419C22×D3—92no—
420C22×D3—92no—
421C22×D3—121no—
422C22×D3—121no—
423C22×D3—121no—
424C22×D3—121no—
425C22×D3—181no—
426C22×D3—181no—
427C22×D3—181no—
428C22×D3—181no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4—62no—
438C2×C3×C4—92no—
439C2×C3×C4—92no—
440C2×C3×C4—121no—
441C2×C3×C4—121no—
442C2×C3×C4—188no—
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—181no—
450C2×C3×C4—181no—
451C2×C3×C4—181no—
452C2×C3×C4—181no—
453C2×C3×C4#62612yes—
454#67—188no—
455#67—188no—
456C2×Dic3—32no—
457C2×Dic3—32no—
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—61no—
467C2×Dic3—61no—
468C2×Dic3—62no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—92no—
473C2×Dic3—92no—
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—
483D12—188no—
484C4×D3—68no—
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×C32C4×D1211yescharacteristic
494C2×C32D3×C22⋊C411yescharacteristic
495C2×C32#88211yescharacteristic
496C2×C32#88411yescharacteristic
497C2×C32#89311yescharacteristic
498C2×C32#89411yescharacteristic
499C2×C32#89511yescharacteristic
500C2×C32C2×(C2×D3)⋊C411yescharacteristic
501C2×C32C4×#6711yescharacteristic
502C2×C32C4×#6711yescharacteristic
503C2×C32#92911yescharacteristic
504C2×C32#93011yescharacteristic
505C2×C32#93011yescharacteristic
506C2×C32#95311yescharacteristic
507C3⋊D3—24no—
508C3×D3—64no—
509C3×D3—124no—
510C3×D3—122no—
511C3×D3—122no—
512C24—91no—
513C24—91no—
514C2×D4—274no—
515C2×D4—542no—
516C2×D4—542no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—91no—
521C22×C4—182no—
522C22×C4—182no—
523C22×C4—182no—
524C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
525C22⋊C4—182no—
526C22⋊C4—542no—
527C22⋊C4—542no—
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—31no—
537C22×C3—31no—
538C22×C3—31no—
539C22×C3—31no—
540C22×C3—31no—
541C22×C3—31no—
542C22×C3—61no—
543C22×C3—61no—
544C22×C3—61no—
545C22×C3—61no—
546C22×C3—61no—
547C22×C3—61no—
548C22×C3—61no—
549C22×C3—94no—
550C22×C3—182no—
551C22×C3—182no—
552C22×C3—182no—
553C22×C3—182no—
554C22×C3—182no—
555C22×C3—182no—
556C22×C3—182no—
557C22×C3—182no—
558C22×C3—182no—
559C22×C3—361no—
560C22×C3—361no—
561C22×C3—361no—
562C22×C3—361no—
563C22×C3#379811yescharacteristic
564C22×C3#379911yescharacteristic
565C22×C3C4×D3211yescharacteristic
566C22×C3D3×D1211yescharacteristic
567C22×C3C2×#62611yescharacteristic
568C22×C3D3×#6711yescharacteristic
569C22×C3D3×#6711yescharacteristic
570C2×D3—34no—
571C2×D3—62no—
572C2×D3—62no—
573C2×D3—62no—
574C2×D3—62no—
575C2×D3—62no—
576C2×D3—62no—
577C2×D3—62no—
578C2×D3—62no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—62no—
583C2×D3—64no—
584C2×D3—94no—
585C2×D3—122no—
586C2×D3—122no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—122no—
596C2×D3—122no—
597C2×D3—122no—
598C2×D3—122no—
599C2×D3—182no—
600C2×D3—182no—
601C2×D3—182no—
602C2×D3—182no—
603C2×D3—182no—
604C2×D3—182no—
605C3×C4—22no—
606C3×C4—62no—
607C3×C4—62no—
608C3×C4—122no—
609C3×C4—182no—
610C3×C4—182no—
611C3×C4—361no—
612C3×C4—361no—
613Dic3—62no—
614Dic3—62no—
615Dic3—121no—
616Dic3—121no—
617Dic3—122no—
618Dic3—121no—
619Dic3—182no—
620Dic3—182no—
621Dic3—361no—
622C32—21no—
623C32#466511yescharacteristic, complemented
624C32#521311yescharacteristic, complemented
625C23—92no—
626C23—92no—
627C23—92no—
628C23—92no—
629C23—181no—
630C23—181no—
631C23—181no—
632C23—181no—
633C23—181no—
634C23—181no—
635C23—181no—
636C23—181no—
637C23—181no—
638C23—181no—
639C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
640D4—548no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—92no—
644C2×C4—92no—
645C2×C4—188no—
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#620012yescomplemented
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—61no—
672C2×C3—61no—
673C2×C3—61no—
674C2×C3—61no—
675C2×C3—61no—
676C2×C3—61no—
677C2×C3—61no—
678C2×C3—184no—
679C2×C3—362no—
680C2×C3#6385011yescharacteristic
681C2×C3C4×#62611yescharacteristic
682C2×C3#6390411yescharacteristic
683C2×C3#6390611yescharacteristic
684C2×C3#6390911yescharacteristic
685C2×C3D3×(C2×D3)⋊C411yescharacteristic
686C2×C3#6397711yescharacteristic
687D3—64no—
688D3—122no—
689D3—122no—
690D3—124no—
691D3—184no—
692C22—94no—
693C22—182no—
694C22—182no—
695C22—182no—
696C22—182no—
697C22—182no—
698C22—182no—
699C22—182no—
700C22—182no—
701C22—182no—
702C22—361no—
703C22—361no—
704C22—361no—
705C22—361no—
706C22#8865011yescharacteristic
707C22#8865211yescharacteristic
708C22C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
709C22#8865411yescharacteristic
710C22C2×#620011yescharacteristic
711C22#8867611yescharacteristic
712C22#8867611yescharacteristic
713C4—22no—
714C4—182no—
715C4—182no—
716C4—361no—
717C4—361no—
718C3—31no—
719C3—31no—
720C3—61no—
721C3#1059138211yescharacteristic
722C2—184no—
723C2—362no—
724C2#1172110011yescharacteristic
725C2#1172114011yescharacteristic
726C2C4×#620011yescharacteristic
727C2#1172115411yescharacteristic
728C2#1172115611yescharacteristic
729C2#1172116011yescharacteristic
730C2#1172132111yescharacteristic
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)#386
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
1. C22×C4×(C3⋊D3)⋊C3C2semidirect
3. C2×#88542C2semidirect
4. C2×#88451C2semidirect
5. C2×#88450C2semidirect
6. #63658⋊C3C2semidirect
7. #11720334C2semidirect
22. C2×#6200C4semidirect
26. C22×C4×C3⋊D3D3semidirect
37. #63658D3semidirect
48. C22×#272C2×C4semidirect
58. C2×C4×H(3,𝔽3)D4semidirect
69. C2×(C3⋊Dic3)⋊C3C2×C4semidirect
70. C2×(C3⋊Dic3)⋊C3D4semidirect
132. C2×(C3⋊D3)⋊C3C22⋊C4semidirect
205. C2×C32×C4D12semidirect
206. C2×C32×C4#67semidirect
214. C2×C3⋊Dic3C4×D3semidirect
215. C2×C3⋊Dic3#67semidirect
327. C2×C3⋊D3(C2×D3)⋊C4semidirect
375. H(3,𝔽3)#386semidirect
623. C32#4665semidirect
624. C32#5213semidirect
656. C2×C4#6200semidirect

Maximal subgroups

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

subgroupindex
C22×C4×(C3⋊D3)⋊C32
C22×#62002
C2×#885422
C2×#884512
C2×#884502
#63658⋊C32
#117203342
#105913873
#105913813