Finite Group Databasebeta

← #13140260

Subgroups — #13140260

Order 1728.

1237 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#272C211yesmaximal, characteristic, complemented
2C22×#6200C211yesmaximal, characteristic
3C2×#3752⋊C3C211yesmaximal, characteristic, complemented
4C2×#88451C211yesmaximal, characteristic, complemented
5C2×#88450C211yesmaximal, characteristic, complemented
6#63658⋊C3C211yesmaximal, characteristic, complemented
7#11720334C211yesmaximal, characteristic, complemented
8#10591382—31nomaximal
9#10591381—31nomaximal
10C23×#272C2211yescharacteristic
11C23×(C3⋊D3)⋊C3C2211yescharacteristic
12C22×C4×H(3,𝔽3)C2211yescharacteristic
13C22×#1084C2211yescharacteristic
14C2×C4×#272—22no—
15C2×C4×#272—22no—
16C2×C4×#272—22no—
17C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
18C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
19C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
20C2×#6200—22no—
21C2×#6200—22no—
22C2×#6200C414yescomplemented
23#3752⋊C3—22no—
24#88451—22no—
25#88450—22no—
26C22×C3×C4×D3—31no—
27C22×C3×C4×D3—31no—
28C22×C3×C4×D3—61no—
29C22×#626—31no—
30C22×#625—31no—
31C2×#3752D311yescharacteristic, complemented
32C2×C3×(C2×D3)⋊C4—31no—
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×#272C2×C412yes—
47C22×#272D412yes—
48C22×#272D412yes—
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×C412yescomplemented
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×#1084D412yescomplemented
62C4×#272—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)⋊C3—21no—
71C2×(C3⋊Dic3)⋊C3C2×C412yescomplemented
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
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—61no—
93C2×C3×C4×D3—62no—
94C2×C3×C4×D3—62no—
95C2×C3×C4×D3—62no—
96C2×C3×C4×D3—62no—
97C2×C3×C4×D3—64no—
98C2×C3×C4×D3—64no—
99C2×C3×C4×D3—64no—
100C2×C3×C4×D3—62no—
101C2×C3×C4×D3—62no—
102C2×#626—34no—
103C2×#626—62no—
104C2×#626—62no—
105C2×#625—34no—
106C2×#625—62no—
107C2×#625—62no—
108#3752—22no—
109C3×(C2×D3)⋊C4—62no—
110#3722—62no—
111(C2×D3)⋊Dic3—62no—
112(C2×D3)⋊Dic3—62no—
113(C2×D3)⋊Dic3—62no—
114C22×H(3,𝔽3)C22×C411yescharacteristic
115C22×H(3,𝔽3)C2×D411yescharacteristic
116C22×H(3,𝔽3)C2×D411yescharacteristic
117C22×H(3,𝔽3)C2×D411yescharacteristic
118C22×H(3,𝔽3)C2×D411yescharacteristic
119C22×H(3,𝔽3)#4111yescharacteristic
120C22×H(3,𝔽3)#4111yescharacteristic
121C2×#272—22no—
122C2×#272—22no—
123C2×#272—22no—
124C2×#272—22no—
125C2×#272—22no—
126C2×#272—22no—
127C2×#272C22⋊C414yescomplemented
128C2×(C3⋊D3)⋊C3—22no—
129C2×(C3⋊D3)⋊C3—22no—
130C2×(C3⋊D3)⋊C3—22no—
131C2×(C3⋊D3)⋊C3—41no—
132C2×(C3⋊D3)⋊C3—41no—
133C2×(C3⋊D3)⋊C3—41no—
134C2×(C3⋊D3)⋊C3—41no—
135C4×H(3,𝔽3)—22no—
136#1084—22no—
137(C3⋊Dic3)⋊C3—22no—
138(C3⋊Dic3)⋊C3—41no—
139(C3⋊Dic3)⋊C3—41no—
140C23×C3×C4—91no—
141C22×#67—91no—
142C22×#67—91no—
143C22×D12—91no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—61no—
147C2×C3×C22⋊C4—91no—
148C2×#217—91no—
149C2×#217—91no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—91no—
152C2×(C2×D3)⋊C4—91no—
153C2×(C2×D3)⋊C4—91no—
154C2×(C2×D3)⋊C4—91no—
155C2×(C2×D3)⋊C4—91no—
156C3×#95—91no—
157C3⋊#95—31no—
158C3⋊#95—91no—
159C3⋊#95—91no—
160C3⋊#95—91no—
161C3⋊#95—91no—
162C23×C32—21no—
163C23×C32C22×D311yescharacteristic
164C23×C32C22×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3C4×D312yescomplemented
172C22×C3×D3—32no—
173C22×C3×D3—32no—
174C22×C3×D3—32no—
175C22×C3×D3—32no—
176C22×C3×D3—32no—
177C22×C3×D3—32no—
178C22×C3×D3—32no—
179C22×C3×D3—62no—
180C22×C3×D3—62no—
181C22×C3×D3—62no—
182C22×C3×D3—62no—
183C22×C3×D3—62no—
184C22×C3×D3—62no—
185C22×C3×D3—62no—
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—61no—
195C22×C3×D3—61no—
196C22×C3×D3—61no—
197C22×C3×D3—61no—
198C22×C3×D3—61no—
199C22×C3×D3—61no—
200C2×C32×C4—22no—
201C2×C32×C4—22no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—22no—
207C2×C32×C4D1212yescomplemented
208C2×C32×C4#6712yescomplemented
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3C4×D312yescomplemented
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—
236C3×C4×D3—616no—
237C3×C4×D3—68no—
238C3×C4×D3—68no—
239#626—68no—
240#625—68no—
241#386—271noSylow
242C2×H(3,𝔽3)C2×C22⋊C411yescharacteristic
243C2×H(3,𝔽3)C4×D411yescharacteristic
244C2×H(3,𝔽3)C4×D411yescharacteristic
245C2×H(3,𝔽3)#12011yescharacteristic
246C2×H(3,𝔽3)#12111yescharacteristic
247C2×H(3,𝔽3)#12111yescharacteristic
248C2×H(3,𝔽3)#12311yescharacteristic
249#272—24no—
250(C3⋊D3)⋊C3—42no—
251C24×C3—91no—
252C24×C3—91no—
253C23×D3—31no—
254C23×D3—31no—
255C23×D3—31no—
256C23×D3—61no—
257C23×D3—91no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—61no—
261C22×C3×C4—91no—
262C22×C3×C4—91no—
263C22×C3×C4—91no—
264C22×C3×C4—91no—
265C22×C3×C4—182no—
266C22×C3×C4—182no—
267C22×C3×C4—182no—
268C22×C3×C4D3211yescharacteristic
269C2×#67—94no—
270C2×#67—94no—
271C2×#67—182no—
272C2×#67—182no—
273C2×#67—182no—
274C2×#67—182no—
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—
284C2×D12—94no—
285C2×D12—182no—
286C2×D12—182no—
287C2×C4×D3—62no—
288C2×C4×D3—62no—
289C2×C4×D3—62no—
290C2×C4×D3—62no—
291C2×C4×D3—62no—
292C2×C4×D3—62no—
293C2×C4×D3—64no—
294C2×C4×D3—64no—
295C2×C4×D3—64no—
296C3×C22⋊C4—182no—
297#217—182no—
298#217—182no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—182no—
301(C2×D3)⋊C4—182no—
302(C2×D3)⋊C4—182no—
303(C2×D3)⋊C4—182no—
304(C2×D3)⋊C4—182no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32C2×C4×D311yescharacteristic
313C22×C32C2×C4×D311yescharacteristic
314C22×C32C2×D1211yescharacteristic
315C22×C32#23511yescharacteristic
316C22×C32#23511yescharacteristic
317C22×C32D3×D411yescharacteristic
318C22×C32D3×D411yescharacteristic
319C22×C32D3×D411yescharacteristic
320C22×C32D3×D411yescharacteristic
321C22×C32D3×D411yescharacteristic
322C22×C32D3×D411yescharacteristic
323C22×C32#23711yescharacteristic
324C22×C32#23911yescharacteristic
325C22×C32C2×#6711yescharacteristic
326C2×C3⋊D3—22no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—22no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3⋊D3—41no—
332C2×C3⋊D3—41no—
333C2×C3×D3—34no—
334C2×C3×D3—34no—
335C2×C3×D3—64no—
336C2×C3×D3—64no—
337C2×C3×D3—64no—
338C2×C3×D3—64no—
339C2×C3×D3—64no—
340C2×C3×D3—64no—
341C2×C3×D3—64no—
342C2×C3×D3—62no—
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—62no—
350C2×C3×D3—62no—
351C2×C3×D3—62no—
352C2×C3×D3—62no—
353C2×C3×D3—62no—
354C2×C3×D3—62no—
355C2×C3×D3—62no—
356C2×C3×D3—62no—
357C2×C3×D3—121no—
358C2×C3×D3—121no—
359C2×C3×D3—121no—
360C2×C3×D3—121no—
361C32×C4—24no—
362C32×C4—22no—
363C32×C4—22no—
364C3⋊Dic3—22no—
365C3⋊Dic3—41no—
366C3⋊Dic3—41no—
367C3×Dic3—64no—
368C3×Dic3—62no—
369C3×Dic3—62no—
370C3×Dic3—62no—
371C3×Dic3—121no—
372C3×Dic3—121no—
373C22×D4—271no—
374C23×C4—91no—
375C2×C22⋊C4—91no—
376C2×C22⋊C4—271no—
377C2×C22⋊C4—271no—
378#95—91no—
379#95—271no—
380H(3,𝔽3)#38611yescharacteristic, complemented, Sylow
381C23×C3—31no—
382C23×C3—31no—
383C23×C3—61no—
384C23×C3—92no—
385C23×C3—92no—
386C23×C3—92no—
387C23×C3—92no—
388C23×C3—181no—
389C23×C3—181no—
390C23×C3—181no—
391C23×C3—181no—
392C23×C3—181no—
393C23×C3—181no—
394C23×C3—181no—
395C23×C3—181no—
396C23×C3—181no—
397C23×C3—181no—
398C23×C3C2×D3211yescharacteristic
399C22×D3—32no—
400C22×D3—32no—
401C22×D3—32no—
402C22×D3—32no—
403C22×D3—32no—
404C22×D3—32no—
405C22×D3—32no—
406C22×D3—62no—
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—61no—
416C22×D3—61no—
417C22×D3—62no—
418C22×D3—62no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—61no—
422C22×D3—61no—
423C22×D3—61no—
424C22×D3—61no—
425C22×D3—61no—
426C22×D3—61no—
427C22×D3—92no—
428C22×D3—181no—
429C22×D3—181no—
430C22×D3—181no—
431C22×D3—181no—
432C22×D3—181no—
433C22×D3—181no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—32no—
437C2×C3×C4—32no—
438C2×C3×C4—61no—
439C2×C3×C4—61no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—62no—
443C2×C3×C4—62no—
444C2×C3×C4—62no—
445C2×C3×C4—92no—
446C2×C3×C4—92no—
447C2×C3×C4—188no—
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—
458C2×C3×C4#62612yes—
459#67—188no—
460#67—188no—
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—92no—
480C2×Dic3—181no—
481C2×Dic3—181no—
482C2×Dic3—181no—
483C2×Dic3—181no—
484C2×Dic3—181no—
485C2×Dic3—181no—
486C2×Dic3—181no—
487C2×Dic3—181no—
488D12—188no—
489C4×D3—68no—
490C4×D3—68no—
491C4×D3—616no—
492C2×C32—21no—
493C2×C32—21no—
494C2×C32—21no—
495C2×C32—21no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32C4×D1211yescharacteristic
500C2×C32D3×C22⋊C411yescharacteristic
501C2×C32D3×C22⋊C411yescharacteristic
502C2×C32#67⋊C411yescharacteristic
503C2×C32#88211yescharacteristic
504C2×C32#88311yescharacteristic
505C2×C32#88411yescharacteristic
506C2×C32#88411yescharacteristic
507C2×C32#89311yescharacteristic
508C2×C32#89411yescharacteristic
509C2×C32#89511yescharacteristic
510C2×C32C4×#6711yescharacteristic
511C2×C32#93711yescharacteristic
512C2×C32#93811yescharacteristic
513C3⋊D3—42no—
514C3×D3—68no—
515C3×D3—64no—
516C3×D3—64no—
517C3×D3—122no—
518C24—91no—
519C24—91no—
520C2×D4—274no—
521C2×D4—542no—
522C2×D4—542no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4—91no—
527C22×C4—182no—
528C22×C4—182no—
529C22×C4—182no—
530C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
531C22⋊C4—182no—
532C22⋊C4—542no—
533C22⋊C4—542no—
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—31no—
546C22×C3—31no—
547C22×C3—31no—
548C22×C3—61no—
549C22×C3—61no—
550C22×C3—61no—
551C22×C3—61no—
552C22×C3—61no—
553C22×C3—61no—
554C22×C3—61no—
555C22×C3—94no—
556C22×C3—182no—
557C22×C3—182no—
558C22×C3—182no—
559C22×C3—182no—
560C22×C3—182no—
561C22×C3—182no—
562C22×C3—182no—
563C22×C3—182no—
564C22×C3—182no—
565C22×C3—361no—
566C22×C3—361no—
567C22×C3—361no—
568C22×C3—361no—
569C22×C3#379611yescharacteristic
570C22×C3#379811yescharacteristic
571C22×C3C4×D3211yescharacteristic
572C22×C3#380211yescharacteristic
573C22×C3C2×#62611yescharacteristic
574C22×C3#381111yescharacteristic
575C22×C3#381111yescharacteristic
576C2×D3—34no—
577C2×D3—34no—
578C2×D3—64no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—62no—
583C2×D3—62no—
584C2×D3—62no—
585C2×D3—62no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—62no—
589C2×D3—62no—
590C2×D3—62no—
591C2×D3—64no—
592C2×D3—64no—
593C2×D3—64no—
594C2×D3—64no—
595C2×D3—64no—
596C2×D3—64no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—121no—
601C2×D3—121no—
602C2×D3—121no—
603C2×D3—121no—
604C2×D3—182no—
605C2×D3—182no—
606C2×D3—182no—
607C2×D3—361no—
608C2×D3—361no—
609C2×D3—361no—
610C2×D3—361no—
611C3×C4—22no—
612C3×C4—62no—
613C3×C4—62no—
614C3×C4—64no—
615C3×C4—182no—
616C3×C4—182no—
617C3×C4—361no—
618C3×C4—361no—
619Dic3—62no—
620Dic3—62no—
621Dic3—64no—
622Dic3—62no—
623Dic3—121no—
624Dic3—121no—
625Dic3—182no—
626Dic3—361no—
627Dic3—361no—
628C32—21no—
629C32#466511yescharacteristic, complemented
630C32#495611yescharacteristic, complemented
631C23—92no—
632C23—92no—
633C23—92no—
634C23—92no—
635C23—181no—
636C23—181no—
637C23—181no—
638C23—181no—
639C23—181no—
640C23—181no—
641C23—181no—
642C23—181no—
643C23—181no—
644C23—181no—
645C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
646D4—548no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—92no—
650C2×C4—92no—
651C2×C4—188no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4—181no—
659C2×C4—181no—
660C2×C4—181no—
661C2×C4—181no—
662C2×C4#620012yescomplemented
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—31no—
672C2×C3—31no—
673C2×C3—31no—
674C2×C3—31no—
675C2×C3—31no—
676C2×C3—31no—
677C2×C3—61no—
678C2×C3—61no—
679C2×C3—61no—
680C2×C3—61no—
681C2×C3—61no—
682C2×C3—61no—
683C2×C3—61no—
684C2×C3—184no—
685C2×C3—362no—
686C2×C3#6385311yescharacteristic
687C2×C3#6388111yescharacteristic
688C2×C3C4×#62611yescharacteristic
689C2×C3#6391211yescharacteristic
690C2×C3#6391611yescharacteristic
691C2×C3#6392111yescharacteristic
692C2×C3#6398111yescharacteristic
693D3—64no—
694D3—64no—
695D3—68no—
696D3—122no—
697D3—362no—
698C22—94no—
699C22—182no—
700C22—182no—
701C22—182no—
702C22—182no—
703C22—182no—
704C22—182no—
705C22—182no—
706C22—182no—
707C22—182no—
708C22—361no—
709C22—361no—
710C22—361no—
711C22—361no—
712C22#8864911yescharacteristic
713C22#8865011yescharacteristic
714C22C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
715C22#8865511yescharacteristic
716C22C2×#620011yescharacteristic
717C22#8867711yescharacteristic
718C22#8867711yescharacteristic
719C4—22no—
720C4—182no—
721C4—182no—
722C4—361no—
723C4—361no—
724C3—31no—
725C3—31no—
726C3—61no—
727C3#1059138711yescharacteristic
728C2—184no—
729C2—362no—
730C2#1172110411yescharacteristic
731C2#1172112411yescharacteristic
732C2#1172114211yescharacteristic
733C2C4×#620011yescharacteristic
734C2#1172115911yescharacteristic
735C2#1172116111yescharacteristic
736C2#1172132311yescharacteristic
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×#272C2semidirect
3. C2×#3752⋊C3C2semidirect
4. C2×#88451C2semidirect
5. C2×#88450C2semidirect
6. #63658⋊C3C2semidirect
7. #11720334C2semidirect
22. C2×#6200C4semidirect
31. C2×#3752D3semidirect
37. #63658D3semidirect
55. C22×(C3⋊D3)⋊C3C2×C4semidirect
58. C2×C4×H(3,𝔽3)D4semidirect
61. C2×#1084D4semidirect
71. C2×(C3⋊Dic3)⋊C3C2×C4semidirect
127. C2×#272C22⋊C4semidirect
171. C22×C3⋊D3C4×D3semidirect
207. C2×C32×C4D12semidirect
208. C2×C32×C4#67semidirect
217. C2×C3⋊Dic3C4×D3semidirect
380. H(3,𝔽3)#386semidirect
629. C32#4665semidirect
630. C32#4956semidirect
662. 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×#2722
C22×#62002
C2×#3752⋊C32
C2×#884512
C2×#884502
#63658⋊C32
#117203342
#105913823
#105913813