Finite Group Databasebeta

← C2×#11722822 #13170511

Subgroups — C2×#11722822 #13170511

Order 1728.

1298 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3798C211yesmaximal, characteristic
2C2×#88808C211yesmaximal, characteristic, complemented
3C2×#88787C211yesmaximal, characteristic, complemented
4C2×#88786C211yesmaximal, characteristic, complemented
5C2×D3×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×C3×#3711C211yesmaximal, characteristic, complemented
7C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
8#11722822C218yesmaximal, direct product factor
9C2×#63815—31nomaximal
10C2×#63814—31nomaximal
11C2×#63804—31nomaximal
12C2×C3×C4×C3⋊D3C2211yescharacteristic
13C2×C32×C4×D3C2211yescharacteristic
14C2×C32×C4×D3C2211yescharacteristic
15C2×C3×#627C411yescharacteristic
16C2×C3×#626C411yescharacteristic
17C2×C3×#626C411yescharacteristic
18C2×C3×#625C411yescharacteristic
19C3×#3798C414yes—
20C3×#3798C2214yes—
21C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
24C2×C32×C3⋊C8C2211yescharacteristic
25#88808C2214yescomplemented
26#88787C2214yescomplemented
27#88786C2214yescomplemented
28D3×C3⋊(C3⋊C8)C2214yescomplemented
29C3×#3711C2214yescomplemented
30C3×D3×C3⋊C8C2214yescomplemented
31C2×C3×#235—31no—
32C2×C3×#235—31no—
33C2×#3798D311yescharacteristic
34C2×#3748—31no—
35C22×C3⋊(C3⋊C8)—31no—
36C2×#3743—31no—
37C2×C3×#208—31no—
38C22×C3×C3⋊C8—31no—
39C2×C3×ΓL(1,𝔽25)—31no—
40C2×C3×D3×C8—31no—
41C2×#3711—31no—
42C2×#3711—31no—
43C2×#3711—31no—
44C2×#3711—31no—
45C2×#3711—61no—
46C2×#3711—61no—
47C2×#3711D311yescharacteristic, complemented
48C2×#3710—31no—
49#63815—38no—
50#63814—38no—
51C2×D3×C3⋊C8—31no—
52C2×D3×C3⋊C8—31no—
53C2×D3×C3⋊C8—31no—
54C2×D3×C3⋊C8—31no—
55C2×D3×C3⋊C8—61no—
56C2×D3×C3⋊C8D311yescharacteristic, complemented
57#63804—38no—
58C22×C3×C3⋊D3C2×C411yescharacteristic
59C22×C32×D3C2×C411yescharacteristic
60C22×C32×D3C2×C411yescharacteristic
61C2×C33×C4C2311yescharacteristic
62C2×C3×C3⋊Dic3C2×C411yescharacteristic
63C3×C4×C3⋊D3C2×C412yes—
64C3×C4×C3⋊D3C2312yes—
65C2×C32×Dic3C2×C411yescharacteristic
66C2×C32×Dic3C2×C411yescharacteristic
67C32×C4×D3C2×C412yes—
68C32×C4×D3C2×C412yes—
69C32×C4×D3C2312yes—
70C32×C4×D3C2312yes—
71C3×#627C2×C414yes—
72C3×#626C2×C414yes—
73C3×#626C2×C414yes—
74C3×#625C2×C414yes—
75C3⋊(C3⋊(C3⋊C8))C2312yes—
76C3×C3⋊(C3⋊C8)C2312yes—
77C3×C3⋊(C3⋊C8)C2312yes—
78C32×C3⋊C8C2312yes—
79C2×#948—91no—
80C2×#907—91no—
81C2×#901—91no—
82C22×C32×C4—31no—
83C22×C32×C4—31no—
84C2×C4×C3⋊D3C2×D311yescharacteristic
85C2×C3×#67—31no—
86C2×C3×#67—31no—
87C2×C3×#67—31no—
88C2×C3×#67—31no—
89C3×#235—34no—
90C3×#235—34no—
91C3×#235—34no—
92C3×#235—34no—
93C2×C3×D12—31no—
94C2×C3×D12—31no—
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—31no—
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—61no—
100C2×C3×C4×D3C2×D311yescharacteristic
101C2×C3×C4×D3C2×D311yescharacteristic
102C2×C3×C4×D3C2×D311yescharacteristic
103C2×C3×C4×D3C2×D311yescharacteristic
104C2×C3×Dic6—31no—
105C2×C3×Dic6—31no—
106C2×#627Dic311yescharacteristic
107C2×#626Dic311yescharacteristic
108C2×#626Dic311yescharacteristic
109C2×#625Dic311yescharacteristic
110#3798Dic314yes—
111#3798C2×D314yes—
112C2×C32×C8—31no—
113#3748—34no—
114C2×C3⋊(C3⋊C8)—31no—
115C2×C3⋊(C3⋊C8)—31no—
116C2×C3⋊(C3⋊C8)—31no—
117C2×C3⋊(C3⋊C8)—34no—
118C2×C3⋊(C3⋊C8)—61no—
119C2×C3⋊(C3⋊C8)—61no—
120C2×C3⋊(C3⋊C8)—61no—
121C2×C3⋊(C3⋊C8)—121no—
122C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
123C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
124#3743—34no—
125C3×#208—34no—
126C2×C3×C3⋊C8—21no—
127C2×C3×C3⋊C8—31no—
128C2×C3×C3⋊C8—31no—
129C2×C3×C3⋊C8—31no—
130C2×C3×C3⋊C8—31no—
131C2×C3×C3⋊C8—34no—
132C2×C3×C3⋊C8—61no—
133C2×C3×C3⋊C8—61no—
134C2×C3×C3⋊C8C2×D311yescharacteristic
135C2×C3×C3⋊C8C2×D311yescharacteristic
136C3×ΓL(1,𝔽25)—34no—
137C3×D3×C8—34no—
138#3711—34no—
139#3711—34no—
140#3711—34no—
141#3711—34no—
142#3711—64no—
143#3711—64no—
144#3711C2×D314yescomplemented
145#3710—34no—
146D3×C3⋊C8—34no—
147D3×C3⋊C8—34no—
148D3×C3⋊C8—34no—
149D3×C3⋊C8—34no—
150D3×C3⋊C8—64no—
151D3×C3⋊C8C2×D314yescomplemented
152C22×C33C22×C411yescharacteristic
153C2×C3×C3⋊D3—22no—
154C2×C3×C3⋊D3C22×C412yes—
155C2×C32×D3—22no—
156C2×C32×D3—22no—
157C2×C32×D3C22×C412yes—
158C2×C32×D3C22×C412yes—
159C33×C4C22×C411yescharacteristic
160C33×C4C2411yescharacteristic
161C3×C3⋊Dic3C22×C412yes—
162C32×Dic3C22×C412yes—
163C32×Dic3C22×C412yes—
164C2×C3×#41—91no—
165C2×#235—31no—
166C2×#235—31no—
167C2×C3×M16—91no—
168C22×C3×C8—91no—
169#948—98no—
170C2×#208—31no—
171C2×#208—91no—
172C2×#208—91no—
173C2×#208—91no—
174C2×#208—181no—
175C22×C3⋊C8—31no—
176C22×C3⋊C8—91no—
177C22×C3⋊C8—91no—
178C22×C3⋊C8—91no—
179C22×C3⋊C8—181no—
180#907—98no—
181#901—98no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—91no—
184C2×ΓL(1,𝔽25)—91no—
185C2×ΓL(1,𝔽25)—91no—
186C2×ΓL(1,𝔽25)—181no—
187C2×D3×C8—31no—
188C2×D3×C8—91no—
189C2×D3×C8—91no—
190C2×D3×C8—91no—
191C23×C32—31no—
192C23×C32—31no—
193C22×C3⋊D3C2×Dic311yescharacteristic
194C22×C3×D3—21no—
195C22×C3×D3—21no—
196C22×C3×D3—31no—
197C22×C3×D3—31no—
198C22×C3×D3—61no—
199C22×C3×D3C4×D311yescharacteristic
200C22×C3×D3C4×D311yescharacteristic
201C22×C3×D3C2×Dic311yescharacteristic
202C22×C3×D3C2×Dic311yescharacteristic
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—31no—
207C2×C32×C4—31no—
208C2×C32×C4—32no—
209C2×C32×C4—32no—
210C2×C32×C4—32no—
211C2×C32×C4—32no—
212C2×C32×C4—41no—
213C2×C32×C4C22×D311yescharacteristic
214C2×C32×C4C22×D311yescharacteristic
215C2×C32×C4C22×D311yescharacteristic
216C2×C3⋊Dic3C2×Dic311yescharacteristic
217C4×C3⋊D3C2×Dic312yes—
218C4×C3⋊D3C22×D312yes—
219C3×#67—34no—
220C3×#67—34no—
221C3×#67—34no—
222C3×#67—34no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—31no—
226C2×C3×Dic3—31no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3C4×D311yescharacteristic
229C2×C3×Dic3C4×D311yescharacteristic
230C2×C3×Dic3C2×Dic311yescharacteristic
231C2×C3×Dic3C2×Dic311yescharacteristic
232C3×D12—34no—
233C3×D12—34no—
234C3×C4×D3—22no—
235C3×C4×D3—22no—
236C3×C4×D3—22no—
237C3×C4×D3—22no—
238C3×C4×D3—32no—
239C3×C4×D3—32no—
240C3×C4×D3—32no—
241C3×C4×D3—32no—
242C3×C4×D3—62no—
243C3×C4×D3—62no—
244C3×C4×D3C4×D312yes—
245C3×C4×D3C4×D312yes—
246C3×C4×D3C2×Dic312yes—
247C3×C4×D3C2×Dic312yes—
248C3×C4×D3C22×D312yes—
249C3×C4×D3C22×D312yes—
250C3×C4×D3C22×D312yes—
251C3×C4×D3C22×D312yes—
252C3×Dic6—34no—
253C3×Dic6—34no—
254#627C2×Dic314yes—
255#626C2×Dic314yes—
256#626C2×Dic314yes—
257#625C2×Dic314yes—
258C32×C8—32no—
259C3⋊(C3⋊C8)—32no—
260C3⋊(C3⋊C8)—32no—
261C3⋊(C3⋊C8)—32no—
262C3⋊(C3⋊C8)—62no—
263C3⋊(C3⋊C8)—62no—
264C3⋊(C3⋊C8)—62no—
265C3⋊(C3⋊C8)—122no—
266C3⋊(C3⋊C8)C22×D312yes—
267C3⋊(C3⋊C8)C22×D312yes—
268C3×C3⋊C8—22no—
269C3×C3⋊C8—32no—
270C3×C3⋊C8—32no—
271C3×C3⋊C8—32no—
272C3×C3⋊C8—32no—
273C3×C3⋊C8—62no—
274C3×C3⋊C8—62no—
275C3×C3⋊C8C22×D312yes—
276C3×C3⋊C8C22×D312yes—
277C2×#131—271noSylow
278C2×C33#13112yescomplemented
279C2×C33C23×C411yescharacteristic
280C3×C3⋊D3—22no—
281C32×D3—22no—
282C32×D3—22no—
283C3×#41—94no—
284C3×#41—94no—
285C2×C3×Q8—91no—
286C2×C3×D4—91no—
287C2×C3×D4—91no—
288C2×C3×D4—91no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—61no—
294C22×C3×C4—61no—
295C22×C3×C4—91no—
296C2×#67—31no—
297C2×#67—31no—
298C2×#67—31no—
299C2×#67—31no—
300#235—34no—
301#235—34no—
302#235—34no—
303#235—34no—
304C2×D12—31no—
305C2×D12—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—61no—
309C2×C4×D3D3211yescharacteristic
310C2×C4×D3D3211yescharacteristic
311C2×Dic6—31no—
312C2×Dic6—31no—
313C3×M16—94no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8—61no—
317C2×C3×C8—94no—
318C2×C3×C8—91no—
319C2×C3×C8—91no—
320#208—34no—
321#208—94no—
322#208—94no—
323#208—94no—
324#208—184no—
325C2×C3⋊C8—31no—
326C2×C3⋊C8—31no—
327C2×C3⋊C8—31no—
328C2×C3⋊C8—31no—
329C2×C3⋊C8—34no—
330C2×C3⋊C8—61no—
331C2×C3⋊C8—61no—
332C2×C3⋊C8—94no—
333C2×C3⋊C8—94no—
334C2×C3⋊C8—94no—
335C2×C3⋊C8—91no—
336C2×C3⋊C8—91no—
337C2×C3⋊C8—91no—
338C2×C3⋊C8—184no—
339C2×C3⋊C8—181no—
340C2×C3⋊C8—181no—
341C2×C3⋊C8—181no—
342C2×C3⋊C8—361no—
343C2×C3⋊C8D3211yescharacteristic
344ΓL(1,𝔽25)—34no—
345ΓL(1,𝔽25)—94no—
346ΓL(1,𝔽25)—94no—
347ΓL(1,𝔽25)—94no—
348ΓL(1,𝔽25)—184no—
349D3×C8—34no—
350D3×C8—94no—
351D3×C8—94no—
352D3×C8—94no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—21no—
356C22×C32—32no—
357C22×C32—32no—
358C22×C32—41no—
359C22×C32—62no—
360C22×C32—62no—
361C22×C32C2×C4×D311yescharacteristic
362C22×C32C2×C4×D311yescharacteristic
363C22×C32C22×Dic311yescharacteristic
364C2×C3⋊D3—22no—
365C2×C3⋊D3C22×Dic312yes—
366C2×C3×D3—24no—
367C2×C3×D3—22no—
368C2×C3×D3—22no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—32no—
374C2×C3×D3—32no—
375C2×C3×D3—42no—
376C2×C3×D3—62no—
377C2×C3×D3—62no—
378C2×C3×D3—62no—
379C2×C3×D3—122no—
380C2×C3×D3C2×C4×D312yes—
381C2×C3×D3C2×C4×D312yes—
382C2×C3×D3C22×Dic312yes—
383C2×C3×D3C22×Dic312yes—
384C32×C4—21no—
385C32×C4—21no—
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—32no—
391C32×C4—32no—
392C32×C4—41no—
393C32×C4—41no—
394C32×C4C2×C4×D311yescharacteristic
395C32×C4C2×C4×D311yescharacteristic
396C32×C4C22×Dic311yescharacteristic
397C32×C4C23×D311yescharacteristic
398C32×C4C23×D311yescharacteristic
399C32×C4C23×D311yescharacteristic
400C3⋊Dic3C22×Dic312yes—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—32no—
404C3×Dic3—32no—
405C3×Dic3—62no—
406C3×Dic3C2×C4×D312yes—
407C3×Dic3C2×C4×D312yes—
408C3×Dic3C22×Dic312yes—
409C3×Dic3C22×Dic312yes—
410C2×#41—91no—
411#131—278no—
412C2×M16—91no—
413C2×M16—271no—
414C2×M16—271no—
415C22×C8—91no—
416C22×C8—271no—
417C22×C8—271no—
418C33C2×#13111yescharacteristic, complemented, Sylow
419C23×C3—31no—
420C23×C3—31no—
421C23×C3—31no—
422C23×C3—31no—
423C23×C3—61no—
424C23×C3—61no—
425C23×C3—91no—
426C22×D3—31no—
427C22×D3—31no—
428C22×D3—61no—
429C22×D3D3×Dic311yescharacteristic
430C22×D3D3×Dic311yescharacteristic
431C3×Q8—94no—
432C3×D4—94no—
433C3×D4—94no—
434C3×D4—94no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—31no—
439C2×C3×C4—31no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—32no—
443C2×C3×C4—32no—
444C2×C3×C4—32no—
445C2×C3×C4—32no—
446C2×C3×C4—32no—
447C2×C3×C4—32no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—41no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—91no—
458C2×C3×C4—92no—
459C2×C3×C4—92no—
460C2×C3×C4C2×D3211yescharacteristic
461C2×C3×C4C2×D3211yescharacteristic
462C2×C3×C4C2×D3211yescharacteristic
463#67—34no—
464#67—34no—
465#67—34no—
466#67—34no—
467C2×Dic3—31no—
468C2×Dic3—31no—
469C2×Dic3—61no—
470C2×Dic3D3×Dic311yescharacteristic
471C2×Dic3D3×Dic311yescharacteristic
472D12—34no—
473D12—34no—
474C4×D3—32no—
475C4×D3—32no—
476C4×D3—32no—
477C4×D3—32no—
478C4×D3—62no—
479C4×D3—62no—
480C4×D3D3×Dic312yes—
481C4×D3D3×Dic312yes—
482C4×D3C2×D3212yes—
483C4×D3C2×D3212yes—
484Dic6—34no—
485Dic6—34no—
486C3×C8—32no—
487C3×C8—32no—
488C3×C8—62no—
489C3×C8—92no—
490C3×C8—92no—
491C3⋊C8—32no—
492C3⋊C8—32no—
493C3⋊C8—32no—
494C3⋊C8—32no—
495C3⋊C8—62no—
496C3⋊C8—62no—
497C3⋊C8—92no—
498C3⋊C8—92no—
499C3⋊C8—92no—
500C3⋊C8—182no—
501C3⋊C8—182no—
502C3⋊C8—182no—
503C3⋊C8—362no—
504C3⋊C8C2×D3212yes—
505C2×C32—21no—
506C2×C32—22no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—22no—
510C2×C32—22no—
511C2×C32—42no—
512C2×C32—41no—
513C2×C32—62no—
514C2×C32—62no—
515C2×C32#90112yescomplemented
516C2×C32#90712yescomplemented
517C2×C32#94812yescomplemented
518C2×C32C22×C4×D311yescharacteristic
519C2×C32C22×C4×D311yescharacteristic
520C2×C32C23×Dic311yescharacteristic
521C3⋊D3—22no—
522C3×D3—24no—
523C3×D3—22no—
524C3×D3—22no—
525C3×D3—22no—
526C3×D3—22no—
527C3×D3—42no—
528C3×D3—62no—
529C3×D3—62no—
530C3×D3—122no—
531#41—94no—
532#41—94no—
533C2×Q8—91no—
534C2×D4—91no—
535C2×D4—91no—
536C2×D4—91no—
537C22×C4—31no—
538C22×C4—31no—
539C22×C4—91no—
540M16—94no—
541M16—274no—
542M16—274no—
543C2×C8—31no—
544C2×C8—94no—
545C2×C8—91no—
546C2×C8—91no—
547C2×C8—274no—
548C2×C8—274no—
549C2×C8—271no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—32no—
554C22×C3—32no—
555C22×C3—32no—
556C22×C3—32no—
557C22×C3—41no—
558C22×C3—62no—
559C22×C3—62no—
560C22×C3—64no—
561C22×C3—62no—
562C22×C3—62no—
563C22×C3—62no—
564C22×C3—62no—
565C22×C3—92no—
566C22×C3—122no—
567C22×C3—182no—
568C22×C3C4×D3211yescharacteristic
569C22×C3C2×D3×Dic311yescharacteristic
570C22×C3C2×D3×Dic311yescharacteristic
571C2×D3—22no—
572C2×D3—22no—
573C2×D3—32no—
574C2×D3—32no—
575C2×D3—62no—
576C2×D3—62no—
577C2×D3—62no—
578C2×D3—122no—
579C2×D3C2×D3×Dic312yes—
580C2×D3C2×D3×Dic312yes—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—32no—
588C3×C4—32no—
589C3×C4—32no—
590C3×C4—32no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—62no—
594C3×C4—62no—
595C3×C4—92no—
596C3×C4C4×D3211yescharacteristic
597C3×C4C2×D3×Dic311yescharacteristic
598C3×C4C2×D3×Dic311yescharacteristic
599C3×C4C22×D3211yescharacteristic
600C3×C4C22×D3211yescharacteristic
601C3×C4C22×D3211yescharacteristic
602Dic3—32no—
603Dic3—32no—
604Dic3—62no—
605Dic3C2×D3×Dic312yes—
606Dic3C2×D3×Dic312yes—
607C32—21no—
608C32—21no—
609C32—21no—
610C32—41no—
611C32C2×#90111yescharacteristic, complemented
612C32C2×#90711yescharacteristic, complemented
613C32C2×#94811yescharacteristic, complemented
614C23—31no—
615C23—31no—
616C23—91no—
617Q8—94no—
618D4—94no—
619D4—94no—
620D4—94no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—32no—
624C2×C4—32no—
625C2×C4—32no—
626C2×C4—32no—
627C2×C4—91no—
628C2×C4—92no—
629C2×C4—92no—
630C2×C4D3311yescharacteristic
631C8—32no—
632C8—92no—
633C8—92no—
634C8—272no—
635C2×C3—22no—
636C2×C3—22no—
637C2×C3—22no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—42no—
642C2×C3—41no—
643C2×C3—64no—
644C2×C3—62no—
645C2×C3—62no—
646C2×C3—62no—
647C2×C3—62no—
648C2×C3—122no—
649C2×C3—182no—
650C2×C3#6380412yescomplemented
651C2×C3#6381412yescomplemented
652C2×C3#6381512yescomplemented
653C2×C3C2×C4×D3211yescharacteristic
654C2×C3C22×D3×Dic311yescharacteristic
655C2×C3C22×D3×Dic311yescharacteristic
656D3—22no—
657D3—22no—
658D3—62no—
659D3—62no—
660D3—122no—
661C22—32no—
662C22—32no—
663C22—62no—
664C22—62no—
665C22—92no—
666C22—182no—
667C22D32×Dic311yescharacteristic
668C4—32no—
669C4—32no—
670C4—92no—
671C4D32×Dic311yescharacteristic
672C4C2×D3311yescharacteristic
673C3—21no—
674C3—21no—
675C3—21no—
676C3—41no—
677C3C2×#6380411yescharacteristic, complemented
678C3C2×#6381411yescharacteristic, complemented
679C3C2×#6381511yescharacteristic, complemented
680C2—62no—
681C2—62no—
682C2—182no—
683C2#1172282212yesdirect product factor
684C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, hypercenterC2×C4D33
commutatorC2×C33C23×C4
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C22×C4
prime radicalC2×C3×#3798C2
cosocleC33×C4C24
hypocenterC33C2×#131
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×#88808C2semidirect
3. C2×#88787C2semidirect
4. C2×#88786C2semidirect
5. C2×D3×C3⋊(C3⋊C8)C2semidirect
6. C2×C3×#3711C2semidirect
7. C2×C3×D3×C3⋊C8C2semidirect
8. #11722822C2direct (N × H)
25. #88808C22semidirect
26. #88787C22semidirect
27. #88786C22semidirect
28. D3×C3⋊(C3⋊C8)C22semidirect
29. C3×#3711C22semidirect
30. C3×D3×C3⋊C8C22semidirect
47. C2×#3711D3semidirect
56. C2×D3×C3⋊C8D3semidirect
144. #3711C2×D3semidirect
151. D3×C3⋊C8C2×D3semidirect
278. C2×C33#131semidirect
418. C33C2×#131semidirect
515. C2×C32#901semidirect
516. C2×C32#907semidirect
517. C2×C32#948semidirect
611. C32C2×#901semidirect
612. C32C2×#907semidirect
613. C32C2×#948semidirect
650. C2×C3#63804semidirect
651. C2×C3#63814semidirect
652. C2×C3#63815semidirect
677. C3C2×#63804semidirect
678. C3C2×#63814semidirect
679. C3C2×#63815semidirect
683. C2#11722822direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#37982
C2×#888082
C2×#887872
C2×#887862
C2×D3×C3⋊(C3⋊C8)2
C2×C3×#37112
C2×C3×D3×C3⋊C82
#117228222
C2×#638153
C2×#638143
C2×#638043