Finite Group Databasebeta

← C4×#89029 #13176906

Subgroups — C4×#89029 #13176906

Order 1728.

2292 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89029C211yesmaximal, characteristic
2C2×C4×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C3×C4×#638C211yesmaximal, characteristic, complemented
4C32×C4×#67C211yesmaximal, characteristic, complemented
5#11723626C211yesmaximal, characteristic, complemented
6#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7#11723598C211yesmaximal, characteristic, complemented
8C4×#6293C211yesmaximal, characteristic, complemented
9#11723508C211yesmaximal, characteristic, complemented
10C4×#6290C211yesmaximal, characteristic, complemented
11#11723466C211yesmaximal, characteristic, complemented
12C4×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
13#11723460C211yesmaximal, characteristic, complemented
14C4×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
15#11723391C211yesmaximal, characteristic, complemented
16C4×#3830—31nomaximal
17C4×#3805—34nomaximal
18C22×C33×C4C2211yescharacteristic
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29#89029C418yesdirect product factor
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C2×D3×C3⋊Dic3C2211yescharacteristic
32C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
33C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
34C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
35C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
36C3×#3757C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×C4×C3⋊Dic3C2211yescharacteristic
40C32×#217C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C32×C4×Dic3C2211yescharacteristic
44#88807C2211yescharacteristic
45#88806C2211yescharacteristic
46#88806C2211yescharacteristic
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic
48#88803C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50Dic3×C3⋊Dic3C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53Dic3×C3⋊Dic3C2211yescharacteristic
54C2×#3830—31no—
55C2×#3805—34no—
56C32×C4×D4—31no—
57D4×C3⋊Dic3—31no—
58C4×#638—31no—
59C4×#638D311yescharacteristic, complemented
60C2×C4×C3⋊Dic3—31no—
61C2×C4×C3⋊Dic3—31no—
62C2×C4×C3⋊Dic3—34no—
63C2×C4×C3⋊Dic3—64no—
64#64101—31no—
65#64096—31no—
66#64090—31no—
67#64090—31no—
68#64086—31no—
69#64086—31no—
70C42×C3⋊D3—31no—
71C4×#634—31no—
72C3×C4×#67—34no—
73C3×C4×#67D314yescomplemented
74#67⋊Dic3—34no—
75#67⋊Dic3—34no—
76#63957—34no—
77C4×#627—34no—
78#63902—34no—
79C4×#625—34no—
80#63878—34no—
81#63878—34no—
82C4×D3×Dic3—34no—
83C4×D3×Dic3—34no—
84#63838—34no—
85C23×C33C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×C33×C4—22no—
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)—22no—
92C2×C3⋊(C3⋊Dic3)C2×C414yescomplemented
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C3×#638C2×C414yescomplemented
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×C4×C3⋊D3—22no—
102C32×#67C2×C414yescomplemented
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C32×C4×D3—22no—
107#6293C2×C414yescomplemented
108#6290C2×C414yescomplemented
109Dic3×C3⋊D3—22no—
110Dic3×C3⋊D3C2×C414yescomplemented
111D3×C3⋊Dic3—22no—
112D3×C3⋊Dic3C2×C414yescomplemented
113C4×#237—94no—
114C4×#237—91no—
115C2×C32×D4—31no—
116C22×C32×C4—24no—
117C22×C32×C4—31no—
118C22×C32×C4C2×D314yes—
119C22×C32×C4C2×D311yescharacteristic
120C2×#638—31no—
121C2×#638C2×D311yescharacteristic
122C22×C3⋊Dic3—31no—
123C22×C3⋊Dic3—34no—
124C22×C3⋊Dic3—31no—
125C22×C3⋊Dic3—31no—
126C22×C3⋊Dic3—34no—
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—64no—
129C22×C3⋊Dic3—64no—
130#3830—38no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3C2×D311yescharacteristic
134C2×#634—31no—
135C2×C3×#67—34no—
136C2×C3×#67C2×D314yes—
137C2×C3×C4×D3—34no—
138C2×C3×C4×D3C2×D314yes—
139C2×#627—34no—
140C2×#625—34no—
141#3805—332no—
142C2×D3×Dic3—34no—
143C2×D3×Dic3—34no—
144C2×D3×Dic3—34no—
145C2×D3×Dic3—34no—
146C32×C4⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C42—31no—
150#3757—31no—
151#3757C2×D311yescharacteristic
152#3752—31no—
153#3752C2×D311yescharacteristic
154C4⋊(C3⋊Dic3)—31no—
155#3750—31no—
156#3750—31no—
157#3750—31no—
158#3750C2×D311yescharacteristic
159C4×C3⋊Dic3—31no—
160C4×C3⋊Dic3—31no—
161C4×C3⋊Dic3—31no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—34no—
164C4×C3⋊Dic3—34no—
165C4×C3⋊Dic3—34no—
166C4×C3⋊Dic3—34no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3—31no—
170C4×C3⋊Dic3—31no—
171C4×C3⋊Dic3—64no—
172C4×C3⋊Dic3—64no—
173C4×C3⋊Dic3—64no—
174C4×C3⋊Dic3—64no—
175C4×C3⋊Dic3C2×D311yescharacteristic
176C3×#217—34no—
177C3×#217C2×D314yes—
178C3×(C2×D3)⋊C4—34no—
179C3×(C2×D3)⋊C4C2×D314yes—
180C3×Dic3⋊C4—34no—
181C3×Dic3⋊C4C2×D314yes—
182C3×C4×Dic3—34no—
183C3×C4×Dic3C2×D314yes—
184#3724—34no—
185#3724—34no—
186Dic3⋊Dic3—34no—
187Dic3⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190Dic32—34no—
191Dic32—34no—
192Dic32—34no—
193Dic32—34no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33C22×C412yes—
197C22×C33C2411yescharacteristic
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C3×C3⋊D3C22×C412yes—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C2×C32×D3C22×C412yes—
204C33×C4—21no—
205C33×C4#4112yescomplemented
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)C22×C412yes—
208C3⋊(C3⋊Dic3)C22×C412yes—
209C3⋊(C3⋊Dic3)#4112yescomplemented
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3C22×C412yes—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C32×Dic3C22×C412yes—
216C2×#237—94no—
217C2×#237—91no—
218C3×C4×D4—34no—
219C3×C4×D4—91no—
220D4×Dic3—94no—
221D4×Dic3—91no—
222C4×#67—34no—
223C4×#67—94no—
224C4×#67—91no—
225C4×#67C3⋊D311yescharacteristic, complemented
226C2×C4×Dic3—94no—
227C2×C4×Dic3—94no—
228C2×C4×Dic3—91no—
229C2×C4×Dic3—91no—
230C2×C4×Dic3—184no—
231#892—94no—
232#892—91no—
233#887—94no—
234#887—91no—
235#67⋊C4—94no—
236#67⋊C4—94no—
237#67⋊C4—91no—
238#67⋊C4—91no—
239#877—94no—
240#877—94no—
241#877—91no—
242#877—91no—
243C42×D3—94no—
244C42×D3—91no—
245C4×Dic6—94no—
246C4×Dic6—91no—
247C23×C32—24no—
248C23×C32—31no—
249C23×C32C22×D314yes—
250C23×C32C22×D311yescharacteristic
251C22×C3⋊D3C22×D311yescharacteristic
252C22×C3×D3—34no—
253C22×C3×D3C22×D314yes—
254C32×D4—34no—
255C2×C32×C4—216no—
256C2×C32×C4—28no—
257C2×C32×C4—22no—
258C2×C32×C4—24no—
259C2×C32×C4—24no—
260C2×C32×C4—31no—
261C2×C32×C4—31no—
262C2×C32×C4—31no—
263C2×C32×C4—62no—
264C2×C32×C4C22×D314yes—
265C2×C32×C4C22×D314yes—
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268#638—34no—
269#638C4×D314yescomplemented
270C2×C3⋊Dic3—34no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—316no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—34no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3—64no—
284C2×C3⋊Dic3—64no—
285C2×C3⋊Dic3—616no—
286C2×C3⋊Dic3—62no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—68no—
289C2×C3⋊Dic3—616no—
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C4×C3⋊D3—22no—
294C4×C3⋊D3—34no—
295C4×C3⋊D3—62no—
296#634—34no—
297C3×#67—316no—
298C3×#67C4×D3116yescomplemented
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3C22×D314yes—
303C2×C3×Dic3C22×D314yes—
304C2×C3×Dic3C22×D314yes—
305C3×C4×D3—28no—
306C3×C4×D3—68no—
307#627—316no—
308#625—316no—
309D3×Dic3—316no—
310D3×Dic3—316no—
311D3×Dic3—68no—
312D3×Dic3—68no—
313C4×#41—271noSylow
314C2×C33—22no—
315C2×C33C23×C411yescharacteristic
316C2×C33C2×#4111yescharacteristic
317C2×C33C2×#4111yescharacteristic
318C3×C3⋊D3—22no—
319C32×D3—22no—
320C2×C3×D4—34no—
321C2×C3×D4—91no—
322C22×C3×C4—24no—
323C22×C3×C4—34no—
324C22×C3×C4—91no—
325C22×C3×C4D3214yes—
326C22×C3×C4C2×C3⋊D311yescharacteristic
327C2×#67—34no—
328C2×#67—94no—
329C2×#67—91no—
330C2×#67C2×C3⋊D311yescharacteristic
331C22×Dic3—94no—
332C22×Dic3—94no—
333C22×Dic3—94no—
334C22×Dic3—91no—
335C22×Dic3—91no—
336C22×Dic3—94no—
337C22×Dic3—91no—
338C22×Dic3—91no—
339C22×Dic3—184no—
340C22×Dic3—184no—
341#237—932no—
342#237—98no—
343C2×C4×D3—34no—
344C2×C4×D3—94no—
345C2×C4×D3—91no—
346C2×C4×D3—94no—
347C2×C4×D3—91no—
348C2×C4×D3C2×C3⋊D311yescharacteristic
349C2×Dic6—94no—
350C2×Dic6—91no—
351C3×C4⋊C4—34no—
352C3×C4⋊C4—91no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4—34no—
355C3×C22⋊C4—91no—
356C3×C22⋊C4—91no—
357C3×C42—34no—
358C3×C42—91no—
359#217—34no—
360#217—94no—
361#217—91no—
362#217C2×C3⋊D311yescharacteristic
363(C2×D3)⋊C4—34no—
364(C2×D3)⋊C4—94no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
367C4⋊Dic3—94no—
368C4⋊Dic3—91no—
369Dic3⋊C4—34no—
370Dic3⋊C4—94no—
371Dic3⋊C4—94no—
372Dic3⋊C4—94no—
373Dic3⋊C4—91no—
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
376Dic3⋊C4C2×C3⋊D311yescharacteristic
377C4×Dic3—34no—
378C4×Dic3—94no—
379C4×Dic3—94no—
380C4×Dic3—94no—
381C4×Dic3—94no—
382C4×Dic3—94no—
383C4×Dic3—94no—
384C4×Dic3—94no—
385C4×Dic3—94no—
386C4×Dic3—91no—
387C4×Dic3—91no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—184no—
395C4×Dic3—184no—
396C4×Dic3—184no—
397C4×Dic3—184no—
398C4×Dic3C2×C3⋊D311yescharacteristic
399C22×C32—28no—
400C22×C32—28no—
401C22×C32—24no—
402C22×C32—21no—
403C22×C32—24no—
404C22×C32—21no—
405C22×C32—24no—
406C22×C32—28no—
407C22×C32—32no—
408C22×C32—61no—
409C22×C32—61no—
410C22×C32C2×C4×D318yes—
411C22×C32C2×C4×D312yes—
412C22×C32C23×D314yes—
413C22×C32C23×D311yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3C2×C4×D312yes—
417C2×C3×D3—24no—
418C2×C3×D3—24no—
419C2×C3×D3—38no—
420C2×C3×D3—64no—
421C2×C3×D3—64no—
422C2×C3×D3C2×C4×D318yes—
423C32×C4—28no—
424C32×C4—24no—
425C32×C4—21no—
426C32×C4—28no—
427C32×C4—32no—
428C32×C4—61no—
429C32×C4—61no—
430C32×C4#23718yescomplemented
431C32×C4#23712yescomplemented
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
434C3⋊Dic3—32no—
435C3⋊Dic3—32no—
436C3⋊Dic3—32no—
437C3⋊Dic3—38no—
438C3⋊Dic3—38no—
439C3⋊Dic3—38no—
440C3⋊Dic3—68no—
441C3⋊Dic3—68no—
442C3⋊Dic3—68no—
443C3⋊Dic3—68no—
444C3⋊Dic3—64no—
445C3⋊Dic3—61no—
446C3⋊Dic3C2×C4×D312yes—
447C3×Dic3—24no—
448C3×Dic3—24no—
449C3×Dic3—38no—
450C3×Dic3—64no—
451C3×Dic3—64no—
452C3×Dic3C2×C4×D318yes—
453C2×#41—271no—
454C4×Q8—271no—
455C4×Q8—271no—
456C4×D4—31no—
457C4×D4—91no—
458C4×D4—271no—
459C4×D4—271no—
460C4×D4—271no—
461C4×D4—271no—
462#117—271no—
463#117—271no—
464#117—271no—
465C2×C42—271no—
466C2×C42—271no—
467C2×C42—271no—
468C33C4×#4111yescharacteristic, complemented, Sylow
469C23×C3—24no—
470C23×C3—34no—
471C23×C3—91no—
472C23×C3C2×D3214yes—
473C23×C3C22×C3⋊D311yescharacteristic
474C22×D3—34no—
475C22×D3C22×C3⋊D311yescharacteristic
476C3×D4—316no—
477C3×D4—94no—
478C2×C3×C4—216no—
479C2×C3×C4—28no—
480C2×C3×C4—22no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—34no—
484C2×C3×C4—34no—
485C2×C3×C4—34no—
486C2×C3×C4—68no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—182no—
491C2×C3×C4C2×D3214yes—
492C2×C3×C4C2×D3214yes—
493C2×C3×C4C22×C3⋊D311yescharacteristic
494C2×C3×C4C22×C3⋊D311yescharacteristic
495#67—316no—
496#67—916no—
497#67—94no—
498#67C4×C3⋊D314yescomplemented
499C2×Dic3—34no—
500C2×Dic3—34no—
501C2×Dic3—34no—
502C2×Dic3—916no—
503C2×Dic3—94no—
504C2×Dic3—94no—
505C2×Dic3—94no—
506C2×Dic3—91no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—916no—
510C2×Dic3—94no—
511C2×Dic3—94no—
512C2×Dic3—94no—
513C2×Dic3—91no—
514C2×Dic3—184no—
515C2×Dic3—184no—
516C2×Dic3—184no—
517C2×Dic3—184no—
518C2×Dic3—1816no—
519C2×Dic3—182no—
520C2×Dic3—188no—
521C2×Dic3—188no—
522C2×Dic3—182no—
523C2×Dic3—1816no—
524C2×Dic3C22×C3⋊D311yescharacteristic
525C2×Dic3C22×C3⋊D311yescharacteristic
526C2×Dic3C22×C3⋊D311yescharacteristic
527C4×D3—22no—
528C4×D3—68no—
529C4×D3—916no—
530C4×D3—94no—
531C4×D3—188no—
532C4×D3—182no—
533Dic6—916no—
534Dic6—94no—
535C2×C32—216no—
536C2×C32—28no—
537C2×C32—22no—
538C2×C32—24no—
539C2×C32—24no—
540C2×C32—24no—
541C2×C32—62no—
542C2×C32C22×C4×D314yes—
543C2×C32C22×C4×D311yescharacteristic
544C2×C32C2×#23714yes—
545C2×C32C2×#23711yescharacteristic
546C2×C32D3×#4114yes—
547C2×C32D3×#4111yescharacteristic
548C3⋊D3—22no—
549C3×D3—28no—
550C3×D3—68no—
551#41—278no—
552C2×Q8—271no—
553C2×D4—31no—
554C2×D4—91no—
555C2×D4—271no—
556C22×C4—31no—
557C22×C4—91no—
558C22×C4—271no—
559C22×C4—271no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4D3×C3⋊D311yescharacteristic
565C4⋊C4—31no—
566C4⋊C4—91no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C22⋊C4—31no—
572C22⋊C4—31no—
573C22⋊C4—91no—
574C22⋊C4—91no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C42—31no—
578C42—91no—
579C42—271no—
580C42—271no—
581C42—271no—
582C42—271no—
583C42—271no—
584C42—271no—
585C42—271no—
586C42—271no—
587C22×C3—28no—
588C22×C3—28no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—24no—
594C22×C3—28no—
595C22×C3—38no—
596C22×C3—64no—
597C22×C3—64no—
598C22×C3—92no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3C4×D3218yes—
602C22×C3C2×C4×C3⋊D312yes—
603C22×C3C22×D3214yes—
604C22×C3C23×C3⋊D311yescharacteristic
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—38no—
608C2×D3—64no—
609C2×D3—64no—
610C2×D3C2×C4×C3⋊D312yes—
611C3×C4—28no—
612C3×C4—24no—
613C3×C4—21no—
614C3×C4—28no—
615C3×C4—38no—
616C3×C4—64no—
617C3×C4—64no—
618C3×C4—92no—
619C3×C4—181no—
620C3×C4—181no—
621C3×C4#380518yescomplemented
622C3×C4#383012yescomplemented
623Dic3—21no—
624Dic3—21no—
625Dic3—38no—
626Dic3—64no—
627Dic3—64no—
628Dic3—98no—
629Dic3—98no—
630Dic3—98no—
631Dic3—92no—
632Dic3—92no—
633Dic3—92no—
634Dic3—188no—
635Dic3—188no—
636Dic3—188no—
637Dic3—188no—
638Dic3—184no—
639Dic3—181no—
640Dic3C2×C4×C3⋊D312yes—
641C32—24no—
642C32C4×#23714yescomplemented
643C32C4×#23711yescharacteristic, complemented
644C23—31no—
645C23—91no—
646C23C2×D3×C3⋊D311yescharacteristic
647Q8—274no—
648D4—34no—
649D4—94no—
650D4—274no—
651C2×C4—22no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—62no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—91no—
659C2×C4—182no—
660C2×C4—274no—
661C2×C4—274no—
662C2×C4—271no—
663C2×C4—271no—
664C2×C4—271no—
665C2×C4—274no—
666C2×C4—271no—
667C2×C4—542no—
668C2×C4—542no—
669C2×C4—542no—
670C2×C4C2×D3×C3⋊D311yescharacteristic
671C2×C4C2×D3×C3⋊D311yescharacteristic
672C2×C3—216no—
673C2×C3—28no—
674C2×C3—22no—
675C2×C3—24no—
676C2×C3—24no—
677C2×C3—24no—
678C2×C3—68no—
679C2×C3—182no—
680C2×C3C2×C4×D3214yes—
681C2×C3#6430614yes—
682C2×C3C2×#380514yes—
683C2×C3C22×C4×C3⋊D311yescharacteristic
684C2×C3C2×#383011yescharacteristic
685C2×C3#41×C3⋊D311yescharacteristic
686D3—22no—
687D3—68no—
688C22—21no—
689C22—21no—
690C22—32no—
691C22—61no—
692C22—61no—
693C22—92no—
694C22—181no—
695C22—181no—
696C22C4×D3×C3⋊D312yes—
697C22C22×D3×C3⋊D311yescharacteristic
698C4—21no—
699C4—32no—
700C4—61no—
701C4—61no—
702C4—92no—
703C4—181no—
704C4—181no—
705C4—272no—
706C4—272no—
707C4—272no—
708C4—541no—
709C4#8902912yesdirect product factor
710C3—24no—
711C3C4×#380514yescomplemented
712C3C4×#383011yescharacteristic, complemented
713C2—22no—
714C2—62no—
715C2—182no—
716C2C2×C4×D3×C3⋊D311yescharacteristic
717C2#1172457811yescharacteristic
718C2C2×#8902911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutatorC2×C33C23×C4
FrattiniC22C22×D3×C3⋊D3
FittingC22×C33×C4C22
socle, cosocleC22×C33C24
prime radicalC2×#89029C2
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C4×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C3⋊(C3⋊Dic3)C2semidirect
3. C3×C4×#638C2semidirect
4. C32×C4×#67C2semidirect
5. #11723626C2semidirect
6. #67⋊(C3⋊Dic3)C2semidirect
7. #11723598C2semidirect
8. C4×#6293C2semidirect
9. #11723508C2semidirect
10. C4×#6290C2semidirect
11. #11723466C2semidirect
12. C4×Dic3×C3⋊D3C2semidirect
13. #11723460C2semidirect
14. C4×D3×C3⋊Dic3C2semidirect
15. #11723391C2semidirect
29. #89029C4direct (N × H)
59. C4×#638D3semidirect
73. C3×C4×#67D3semidirect
92. C2×C3⋊(C3⋊Dic3)C2×C4semidirect
97. C3×#638C2×C4semidirect
102. C32×#67C2×C4semidirect
107. #6293C2×C4semidirect
108. #6290C2×C4semidirect
110. Dic3×C3⋊D3C2×C4semidirect
112. D3×C3⋊Dic3C2×C4semidirect
205. C33×C4#41semidirect
209. C3⋊(C3⋊Dic3)#41semidirect
225. C4×#67C3⋊D3semidirect
269. #638C4×D3semidirect
298. C3×#67C4×D3semidirect
430. C32×C4#237semidirect
431. C32×C4#237semidirect
468. C33C4×#41semidirect
498. #67C4×C3⋊D3semidirect
621. C3×C4#3805semidirect
622. C3×C4#3830semidirect
642. C32C4×#237semidirect
643. C32C4×#237semidirect
709. C4#89029direct (N × H)
711. C3C4×#3805semidirect
712. C3C4×#3830semidirect

Maximal subgroups

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

subgroupindex
C2×#890292
C2×C4×C3⋊(C3⋊Dic3)2
C3×C4×#6382
C32×C4×#672
#117236262
#67⋊(C3⋊Dic3)2
#117235982
C4×#62932
#117235082
C4×#62902
#117234662
C4×Dic3×C3⋊D32
#117234602
C4×D3×C3⋊Dic32
#117233912
C4×#38303
C4×#38053