Finite Group Databasebeta

← C2×C3⋊D3×#235 #13181601

Subgroups — C2×C3⋊D3×#235 #13181601

Order 1728.

5996 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×#89076C211yesmaximal, characteristic, complemented
2C22×C3×C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C32×#235C211yesmaximal, characteristic, complemented
4C2×C3⋊D3×#67C212yesmaximal, complemented
5C2×#89028C212yesmaximal, complemented
6C3⋊D3×#235C2116yesmaximal, direct product factor
7C2×C3⋊D3×D12C211yesmaximal, characteristic, complemented
8C2×C4×D3×C3⋊D3C212yesmaximal, complemented
9C2×#89020C212yesmaximal, complemented
10C2×#89018C211yesmaximal, characteristic, complemented
11C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
12C2×#89014C211yesmaximal, characteristic, complemented
13C2×#41×C3⋊D3—31nomaximal
14C2×D3×#235—34nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C22×D3×C3⋊D3C2212yes—
17C22×C33×C4C2211yescharacteristic, complemented
18C2×#6312C2212yescomplemented
19#89076C2218yescomplemented
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
21C2×C4×C3⋊(C3⋊D3)C2212yescomplemented
22C2×#6308C2211yescharacteristic, complemented
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C3×C4×C3⋊D3C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2218yescomplemented
27C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
28C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
29C2×C32×#67C2212yescomplemented
30C32×#235C2218yescomplemented
31C2×C32×D12C2211yescharacteristic, complemented
32C2×C32×C4×D3C2212yescomplemented
33C2×C32×Dic6C2211yescharacteristic, complemented
34C3⋊D3×#67C22116yescomplemented
35C2×#6293C2212yescomplemented
36C2×#6292C2212yescomplemented
37C2×#6291C2212yescomplemented
38C2×#6290C2212yescomplemented
39C2×#6289C2212yescomplemented
40C2×Dic3×C3⋊D3C2212yes—
41#89028C22116yescomplemented
42C2×D3×C3⋊Dic3C2212yescomplemented
43C3⋊D3×D12C2218yescomplemented
44C4×D3×C3⋊D3C22116yescomplemented
45#89020C22116yescomplemented
46#89018C2218yescomplemented
47C3⋊D3×Dic6C2218yescomplemented
48#89014C2218yescomplemented
49C2×C32×#41—31no—
50#41×C3⋊D3—316no—
51C2×#3832—31no—
52C2×Q8×C3⋊D3—31no—
53C2×#3830—32no—
54C2×#3830—31no—
55C2×D4×C3⋊D3—31no—
56C2×D4×C3⋊D3—32no—
57C2×#3828—31no—
58C2×#3828—32no—
59C2×#3828—34no—
60C2×#3828—64no—
61C22×C4×C3⋊D3—32no—
62C22×C4×C3⋊D3D311yescharacteristic, complemented
63C2×C3×#235D314yescomplemented
64C22×C3×C4×D3—34no—
65C2×D3×#67—38no—
66C2×#3804—38no—
67D3×#235—364no—
68C2×D3×D12—34no—
69C2×C4×D32—38no—
70C2×#3799—34no—
71C2×#3798—38no—
72C2×#3795—34no—
73C2×D3×Dic6—34no—
74C23×C33C2311yescharacteristic
75C22×C3⋊(C3⋊D3)C2312yes—
76C22×C3×C3⋊D3—24no—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C3×C3⋊D3C2314yes—
79C22×C3×C3⋊D3C2311yescharacteristic
80C22×C32×D3C2312yes—
81C2×D3×C3⋊D3—28no—
82C2×D3×C3⋊D3C2318yes—
83C2×C33×C4C2311yescharacteristic
84C2×C33×C4C2311yescharacteristic
85C2×C33×C4C2314yescomplemented
86#6312C2318yescomplemented
87C2×C3⋊(C3⋊Dic3)C2312yes—
88C4⋊(C3⋊(C3⋊D3))C2314yescomplemented
89C4×C3⋊(C3⋊D3)C2318yescomplemented
90#6308C2314yescomplemented
91C2×C3×C3⋊Dic3C2311yescharacteristic
92C2×C3×C3⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊Dic3C2314yescomplemented
94C3×C4×C3⋊D3C2314yes—
95C3×C4×C3⋊D3C2314yes—
96C3×C4×C3⋊D3C2314yescomplemented
97C3×C4×C3⋊D3C2314yescomplemented
98C32×#67C2318yescomplemented
99C2×C32×Dic3C2312yes—
100C32×D12C2314yescomplemented
101C32×C4×D3C2318yescomplemented
102C32×Dic6C2314yescomplemented
103#6293C2318yescomplemented
104#6292C2318yescomplemented
105#6291C2318yescomplemented
106#6290C2318yescomplemented
107#6289C2318yescomplemented
108Dic3×C3⋊D3C2318yes—
109D3×C3⋊Dic3C2318yescomplemented
110C2×D3×#41—94no—
111C22×#235—91no—
112C23×C3⋊D3—32no—
113C23×C3⋊D3C2×D311yescharacteristic
114C23×C3×D3—34no—
115C22×D32—38no—
116C32×#41—38no—
117C2×C32×Q8—31no—
118C2×C32×D4—32no—
119C2×C32×D4—31no—
120C22×C32×C4—24no—
121C22×C32×C4—32no—
122C22×C32×C4C2×D314yescomplemented
123C22×C32×C4C2×D311yescharacteristic, complemented
124C2×#638—32no—
125C2×#638—38no—
126C2×#638—32no—
127C2×#638—32no—
128C2×#638—68no—
129C22×C3⋊Dic3—32no—
130C22×C3⋊Dic3C2×D311yescharacteristic, complemented
131#3832—38no—
132Q8×C3⋊D3—38no—
133#3830—316no—
134#3830—38no—
135D4×C3⋊D3—316no—
136D4×C3⋊D3—38no—
137#3828—38no—
138#3828—332no—
139#3828—316no—
140#3828—632no—
141C2×C4⋊(C3⋊D3)—32no—
142C2×C4⋊(C3⋊D3)—31no—
143C2×C4⋊(C3⋊D3)—34no—
144C2×C4⋊(C3⋊D3)—64no—
145C2×C4×C3⋊D3—32no—
146C2×C4×C3⋊D3—32no—
147C2×C4×C3⋊D3—38no—
148C2×C4×C3⋊D3—32no—
149C2×C4×C3⋊D3—316no—
150C2×C4×C3⋊D3—68no—
151C2×C4×C3⋊D3C2×D311yescharacteristic
152C2×C4×C3⋊D3C2×D311yescharacteristic
153C2×C4×C3⋊D3C2×D318yescomplemented
154C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
155C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
156C2×#634—31no—
157C2×#634—34no—
158C2×#634—32no—
159C2×#634—64no—
160C2×C3×#67C2×D318yescomplemented
161C22×C3×Dic3—34no—
162C3×#235C2×D3132yescomplemented
163C2×C3×D12C2×D314yescomplemented
164C2×C3×C4×D3—34no—
165C2×C3×C4×D3—34no—
166C2×C3×C4×D3—34no—
167C2×C3×C4×D3—34no—
168C2×C3×C4×D3—332no—
169C2×C3×C4×D3C2×D318yescomplemented
170C2×C3×Dic6C2×D314yescomplemented
171D3×#67—364no—
172C2×#627—38no—
173C2×#626—38no—
174C2×#626—38no—
175C2×#625—38no—
176C2×#624—38no—
177#3804—364no—
178C2×D3×Dic3—38no—
179C2×D3×Dic3—38no—
180D3×D12—332no—
181C4×D32—364no—
182#3799—332no—
183#3798—364no—
184#3795—332no—
185D3×Dic6—332no—
186C22×C33—22no—
187C22×C33C2412yes—
188C22×C33C2411yescharacteristic
189C2×C3⋊(C3⋊D3)—24no—
190C2×C3⋊(C3⋊D3)C2414yes—
191C2×C3×C3⋊D3—22no—
192C2×C3×C3⋊D3—28no—
193C2×C3×C3⋊D3#4114yescomplemented
194C2×C3×C3⋊D3C2412yes—
195C2×C3×C3⋊D3C2412yes—
196C2×C32×D3—24no—
197C2×C32×D3C2414yes—
198D3×C3⋊D3—216no—
199C33×C4C2412yes—
200C33×C4C2412yes—
201C3⋊(C3⋊Dic3)C2414yes—
202C3×C3⋊Dic3C2412yes—
203C3×C3⋊Dic3C2412yes—
204C32×Dic3C2414yes—
205C2×C3×#41—34no—
206C23×C3×C4—91no—
207C22×#67—92no—
208D3×#41—964no—
209C2×#239—94no—
210C2×D3×Q8—94no—
211C2×#237—94no—
212C2×#237—98no—
213C2×D3×D4—94no—
214C2×D3×D4—98no—
215C2×#235—98no—
216C2×#235—94no—
217C2×#235—91no—
218C2×#235—92no—
219C2×#235—916no—
220C2×#235—91no—
221C2×#235—92no—
222C2×#235—91no—
223C2×#235—184no—
224C2×#235C3⋊D311yescharacteristic, direct product factor
225C22×D12—91no—
226C22×C4×D3—34no—
227C22×C4×D3—98no—
228C22×C4×D3—92no—
229C22×Dic6—91no—
230C23×C32—24no—
231C23×C32—32no—
232C23×C32C22×D314yes—
233C23×C32C22×D311yescharacteristic
234C22×C3⋊D3—24no—
235C22×C3⋊D3—32no—
236C22×C3⋊D3—38no—
237C22×C3⋊D3—38no—
238C22×C3⋊D3—68no—
239C22×C3⋊D3—68no—
240C22×C3⋊D3C22×D311yescharacteristic
241C22×C3⋊D3C22×D314yes—
242C22×C3⋊D3C22×D311yescharacteristic
243C22×C3×D3—34no—
244C22×C3×D3—34no—
245C22×C3×D3—316no—
246C22×C3×D3—616no—
247C22×C3×D3C22×D318yes—
248C2×D32—332no—
249C2×D32—632no—
250C32×Q8—34no—
251C32×D4—38no—
252C32×D4—34no—
253C2×C32×C4—24no—
254C2×C32×C4—24no—
255C2×C32×C4—216no—
256C2×C32×C4—32no—
257C2×C32×C4—38no—
258C2×C32×C4C22×D314yes—
259C2×C32×C4C22×D314yes—
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D3116yescomplemented
263C2×C32×C4C22×D314yescomplemented
264#638—38no—
265#638—38no—
266#638—38no—
267#638—332no—
268#638—632no—
269C2×C3⋊Dic3—32no—
270C2×C3⋊Dic3—38no—
271C2×C3⋊Dic3—38no—
272C2×C3⋊Dic3—68no—
273C2×C3⋊Dic3C22×D311yescharacteristic
274C2×C3⋊Dic3C22×D311yescharacteristic
275C2×C3⋊Dic3C22×D314yescomplemented
276C4⋊(C3⋊D3)—38no—
277C4⋊(C3⋊D3)—34no—
278C4⋊(C3⋊D3)—316no—
279C4⋊(C3⋊D3)—616no—
280C4×C3⋊D3—38no—
281C4×C3⋊D3—38no—
282C4×C3⋊D3—38no—
283C4×C3⋊D3—332no—
284C4×C3⋊D3—632no—
285C4×C3⋊D3C22×D314yes—
286C4×C3⋊D3C22×D314yes—
287C4×C3⋊D3C22×D314yescomplemented
288C4×C3⋊D3C22×D314yescomplemented
289#634—34no—
290#634—38no—
291#634—316no—
292#634—616no—
293C3×#67C22×D3132yescomplemented
294C2×C3×Dic3—34no—
295C2×C3×Dic3—34no—
296C2×C3×Dic3—316no—
297C2×C3×Dic3C22×D318yes—
298C3×D12C22×D3116yescomplemented
299C3×C4×D3—316no—
300C3×C4×D3—316no—
301C3×C4×D3—316no—
302C3×C4×D3—316no—
303C3×C4×D3C22×D3132yescomplemented
304C3×Dic6C22×D3116yescomplemented
305#627—332no—
306#626—332no—
307#626—332no—
308#625—332no—
309#624—332no—
310D3×Dic3—332no—
311D3×Dic3—332no—
312C22×#41—271noSylow
313C2×C33—22no—
314C2×C33C2×#4112yescomplemented
315C2×C33C2511yescharacteristic
316C3⋊(C3⋊D3)—24no—
317C3×C3⋊D3—22no—
318C3×C3⋊D3C2×#4114yescomplemented
319C32×D3—24no—
320C24×C3—91no—
321C23×D3—34no—
322C23×D3—98no—
323C23×D3—92no—
324C3×#41—332no—
325C2×C3×Q8—34no—
326C2×C3×D4—38no—
327C2×C3×D4—34no—
328C22×C3×C4—24no—
329C22×C3×C4—38no—
330C22×C3×C4—91no—
331C22×C3×C4—91no—
332C22×C3×C4—91no—
333C22×C3×C4—91no—
334C22×C3×C4—91no—
335C22×C3×C4—98no—
336C22×C3×C4D3214yescomplemented
337C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
338C2×#67—98no—
339C2×#67—98no—
340C2×#67—98no—
341C2×#67—92no—
342C2×#67—92no—
343C2×#67—916no—
344C2×#67—92no—
345C2×#67—188no—
346C2×#67C2×C3⋊D312yescomplemented
347C22×Dic3—34no—
348C22×Dic3—98no—
349C22×Dic3—92no—
350#239—932no—
351D3×Q8—932no—
352#237—932no—
353#237—964no—
354D3×D4—932no—
355D3×D4—964no—
356#235—964no—
357#235—932no—
358#235—98no—
359#235—916no—
360#235—98no—
361#235—916no—
362#235—98no—
363#235—1832no—
364#235C2×C3⋊D318yesdirect product factor
365C2×D12—98no—
366C2×D12—92no—
367C2×D12—94no—
368C2×D12—91no—
369C2×D12—98no—
370C2×D12—184no—
371C2×D12C2×C3⋊D311yescharacteristic, complemented
372C2×C4×D3—34no—
373C2×C4×D3—34no—
374C2×C4×D3—34no—
375C2×C4×D3—34no—
376C2×C4×D3—332no—
377C2×C4×D3—964no—
378C2×C4×D3—98no—
379C2×C4×D3—98no—
380C2×C4×D3—92no—
381C2×C4×D3—98no—
382C2×C4×D3—92no—
383C2×C4×D3—92no—
384C2×C4×D3—916no—
385C2×C4×D3—188no—
386C2×C4×D3C2×C3⋊D312yescomplemented
387C2×Dic6—98no—
388C2×Dic6—94no—
389C2×Dic6—91no—
390C2×Dic6—92no—
391C2×Dic6—98no—
392C2×Dic6—184no—
393C2×Dic6C2×C3⋊D311yescharacteristic, complemented
394C22×C32—22no—
395C22×C32—24no—
396C22×C32—28no—
397C22×C32—28no—
398C22×C32—34no—
399C22×C32—48no—
400C22×C32—64no—
401C22×C32C23×D318yes—
402C22×C32C23×D314yes—
403C22×C32C23×D312yes—
404C22×C32C23×D311yescharacteristic
405C2×C3⋊D3—22no—
406C2×C3⋊D3—28no—
407C2×C3⋊D3—34no—
408C2×C3⋊D3—316no—
409C2×C3⋊D3—616no—
410C2×C3⋊D3—64no—
411C2×C3⋊D3—616no—
412C2×C3⋊D3—616no—
413C2×C3⋊D3—1216no—
414C2×C3⋊D3#23514yesdirect product factor
415C2×C3⋊D3C23×D312yes—
416C2×C3⋊D3C23×D312yes—
417C2×C3×D3—216no—
418C2×C3×D3—316no—
419C2×C3×D3—38no—
420C2×C3×D3—38no—
421C2×C3×D3—632no—
422C2×C3×D3—68no—
423C2×C3×D3C23×D3116yes—
424D32—664no—
425C32×C4—28no—
426C32×C4—28no—
427C32×C4—34no—
428C32×C4C23×D318yes—
429C32×C4C23×D318yes—
430C32×C4C23×D312yes—
431C32×C4C23×D312yes—
432C3⋊Dic3—34no—
433C3⋊Dic3—316no—
434C3⋊Dic3—616no—
435C3⋊Dic3C23×D312yes—
436C3⋊Dic3C23×D312yes—
437C3×Dic3—38no—
438C3×Dic3—38no—
439C3×Dic3C23×D3116yes—
440C2×#41—31no—
441C2×#41—272no—
442C2×#41—272no—
443C2×#41—271no—
444C2×#41—271no—
445C2×#41—2716no—
446C2×#41—271no—
447C22×Q8—271no—
448C22×D4—271no—
449C22×D4—272no—
450C23×C4—91no—
451C23×C4—272no—
452C33C22×#4111yescharacteristic, complemented, Sylow
453C23×C3—24no—
454C23×C3—38no—
455C23×C3—91no—
456C23×C3—94no—
457C23×C3—91no—
458C23×C3—184no—
459C23×C3C2×D3214yes—
460C23×C3C22×C3⋊D311yescharacteristic
461C22×D3—34no—
462C22×D3—34no—
463C22×D3—316no—
464C22×D3—616no—
465C22×D3—932no—
466C22×D3—98no—
467C22×D3—92no—
468C22×D3—98no—
469C22×D3—188no—
470C22×D3—188no—
471C22×D3—1832no—
472C22×D3C22×C3⋊D312yes—
473C3×Q8—316no—
474C3×D4—332no—
475C3×D4—316no—
476C2×C3×C4—24no—
477C2×C3×C4—24no—
478C2×C3×C4—216no—
479C2×C3×C4—38no—
480C2×C3×C4—332no—
481C2×C3×C4—91no—
482C2×C3×C4—91no—
483C2×C3×C4—94no—
484C2×C3×C4—94no—
485C2×C3×C4—94no—
486C2×C3×C4—94no—
487C2×C3×C4—94no—
488C2×C3×C4C2×D3214yes—
489C2×C3×C4C2×D3214yes—
490C2×C3×C4C2×D32116yescomplemented
491C2×C3×C4C22×C3⋊D311yescharacteristic
492C2×C3×C4C22×C3⋊D311yescharacteristic
493C2×C3×C4C22×C3⋊D314yescomplemented
494#67—932no—
495#67—932no—
496#67—932no—
497#67—98no—
498#67—98no—
499#67—98no—
500#67—1832no—
501#67C22×C3⋊D318yescomplemented
502C2×Dic3—34no—
503C2×Dic3—34no—
504C2×Dic3—316no—
505C2×Dic3—932no—
506C2×Dic3—98no—
507C2×Dic3—92no—
508C2×Dic3—98no—
509C2×Dic3—188no—
510C2×Dic3C22×C3⋊D312yes—
511D12—932no—
512D12—98no—
513D12—916no—
514D12—94no—
515D12—1816no—
516D12C22×C3⋊D314yescomplemented
517C4×D3—316no—
518C4×D3—316no—
519C4×D3—316no—
520C4×D3—316no—
521C4×D3—932no—
522C4×D3—932no—
523C4×D3—98no—
524C4×D3—932no—
525C4×D3—98no—
526C4×D3—98no—
527C4×D3—1832no—
528C4×D3C22×C3⋊D318yescomplemented
529Dic6—932no—
530Dic6—916no—
531Dic6—94no—
532Dic6—98no—
533Dic6—1816no—
534Dic6C22×C3⋊D314yescomplemented
535C2×C32—22no—
536C2×C32—28no—
537C2×C32—24no—
538C2×C32—28no—
539C2×C32—48no—
540C2×C32—64no—
541C2×C32C2×#23512yescomplemented
542C2×C32D3×#4118yescomplemented
543C2×C32C24×D314yes—
544C2×C32C24×D311yescharacteristic
545C3⋊D3—22no—
546C3⋊D3—64no—
547C3⋊D3—616no—
548C3⋊D3—1216no—
549C3⋊D3C2×#23514yesdirect product factor
550C3×D3—216no—
551C3×D3—316no—
552C3×D3—68no—
553C24—91no—
554C24—272no—
555#41—38no—
556#41—2716no—
557#41—2716no—
558#41—278no—
559#41—278no—
560#41—278no—
561C2×Q8—31no—
562C2×Q8—272no—
563C2×Q8—278no—
564C2×Q8—271no—
565C2×D4—32no—
566C2×D4—31no—
567C2×D4—272no—
568C2×D4—278no—
569C2×D4—272no—
570C2×D4—2716no—
571C2×D4—272no—
572C2×D4—272no—
573C2×D4—271no—
574C22×C4—32no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—91no—
580C22×C4—98no—
581C22×C4—272no—
582C22×C4—2716no—
583C22×C4—272no—
584C22×C4—272no—
585C22×C4—272no—
586C22×C4D3×C3⋊D311yescharacteristic, complemented
587C22×C3—28no—
588C22×C3—22no—
589C22×C3—24no—
590C22×C3—28no—
591C22×C3—316no—
592C22×C3—48no—
593C22×C3—616no—
594C22×C3—94no—
595C22×C3—92no—
596C22×C3—92no—
597C22×C3—188no—
598C22×C3—182no—
599C22×C3C22×D3218yes—
600C22×C3C22×D3214yes—
601C22×C3C23×C3⋊D312yes—
602C22×C3C23×C3⋊D311yescharacteristic
603C2×D3—24no—
604C2×D3—316no—
605C2×D3—38no—
606C2×D3—38no—
607C2×D3—632no—
608C2×D3—68no—
609C2×D3—916no—
610C2×D3—94no—
611C2×D3—1816no—
612C2×D3—1816no—
613C2×D3—1864no—
614C2×D3—1816no—
615C2×D3—184no—
616C2×D3—3616no—
617C2×D3C23×C3⋊D314yes—
618C3×C4—28no—
619C3×C4—28no—
620C3×C4—316no—
621C3×C4—92no—
622C3×C4—92no—
623C3×C4C22×D3218yes—
624C3×C4C22×D3218yes—
625C3×C4C23×C3⋊D312yes—
626C3×C4C23×C3⋊D312yes—
627Dic3—38no—
628Dic3—38no—
629Dic3—916no—
630Dic3—94no—
631Dic3—1816no—
632Dic3C23×C3⋊D314yes—
633C32—24no—
634C32C22×#23511yescharacteristic, complemented
635C32C2×D3×#4114yescomplemented
636C23—32no—
637C23—91no—
638C23—94no—
639C23—91no—
640C23—184no—
641C23—278no—
642C23—272no—
643C23—548no—
644C23C2×D3×C3⋊D311yescharacteristic
645Q8—34no—
646Q8—278no—
647Q8—274no—
648D4—38no—
649D4—34no—
650D4—278no—
651D4—278no—
652D4—278no—
653D4—278no—
654D4—274no—
655C2×C4—32no—
656C2×C4—38no—
657C2×C4—91no—
658C2×C4—91no—
659C2×C4—94no—
660C2×C4—94no—
661C2×C4—94no—
662C2×C4—94no—
663C2×C4—94no—
664C2×C4—278no—
665C2×C4—278no—
666C2×C4—278no—
667C2×C4—272no—
668C2×C4—278no—
669C2×C4C2×D3×C3⋊D311yescharacteristic
670C2×C4C2×D3×C3⋊D311yescharacteristic
671C2×C4C2×D3×C3⋊D314yescomplemented
672C2×C3—28no—
673C2×C3—22no—
674C2×C3—28no—
675C2×C3—24no—
676C2×C3—48no—
677C2×C3—616no—
678C2×C3—94no—
679C2×C3—182no—
680C2×C3D3×#23518yescomplemented
681C2×C3#41×C3⋊D312yescomplemented
682C2×C3C23×D3214yes—
683C2×C3C24×C3⋊D311yescharacteristic
684D3—24no—
685D3—316no—
686D3—68no—
687D3—1816no—
688D3—184no—
689D3—3616no—
690C22—22no—
691C22—34no—
692C22—64no—
693C22—94no—
694C22—92no—
695C22—92no—
696C22—188no—
697C22—182no—
698C22—274no—
699C22—5416no—
700C22—544no—
701C22C22×D3×C3⋊D312yes—
702C22C22×D3×C3⋊D311yescharacteristic
703C4—34no—
704C4—92no—
705C4—92no—
706C4—274no—
707C4C22×D3×C3⋊D312yes—
708C4C22×D3×C3⋊D312yes—
709C3—24no—
710C3C2×D3×#23514yescomplemented
711C3C2×#41×C3⋊D311yescharacteristic, complemented
712C2—22no—
713C2—64no—
714C2—94no—
715C2—182no—
716C2—544no—
717C2C3⋊D3×#23512yesdirect product factor
718C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutator, cosocleC2×C33C25
FrattiniC2C23×D3×C3⋊D3
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C22×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89076C2semidirect
2. C22×C3×C4×C3⋊D3C2semidirect
3. C2×C32×#235C2semidirect
4. C2×C3⋊D3×#67C2semidirect
5. C2×#89028C2semidirect
6. C3⋊D3×#235C2direct (N × H)
7. C2×C3⋊D3×D12C2semidirect
8. C2×C4×D3×C3⋊D3C2semidirect
9. C2×#89020C2semidirect
10. C2×#89018C2semidirect
11. C2×C3⋊D3×Dic6C2semidirect
12. C2×#89014C2semidirect
17. C22×C33×C4C22semidirect
18. C2×#6312C22semidirect
19. #89076C22semidirect
20. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
22. C2×#6308C22semidirect
23. C22×C3×C3⋊Dic3C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C3×C4×C3⋊D3C22semidirect
29. C2×C32×#67C22semidirect
30. C32×#235C22semidirect
31. C2×C32×D12C22semidirect
32. C2×C32×C4×D3C22semidirect
33. C2×C32×Dic6C22semidirect
34. C3⋊D3×#67C22semidirect
35. C2×#6293C22semidirect
36. C2×#6292C22semidirect
37. C2×#6291C22semidirect
38. C2×#6290C22semidirect
39. C2×#6289C22semidirect
41. #89028C22semidirect
42. C2×D3×C3⋊Dic3C22semidirect
43. C3⋊D3×D12C22semidirect
44. C4×D3×C3⋊D3C22semidirect
45. #89020C22semidirect
46. #89018C22semidirect
47. C3⋊D3×Dic6C22semidirect
48. #89014C22semidirect
62. C22×C4×C3⋊D3D3semidirect
63. C2×C3×#235D3semidirect
85. C2×C33×C4C23semidirect
86. #6312C23semidirect
88. C4⋊(C3⋊(C3⋊D3))C23semidirect
89. C4×C3⋊(C3⋊D3)C23semidirect
90. #6308C23semidirect
93. C2×C3×C3⋊Dic3C23semidirect
96. C3×C4×C3⋊D3C23semidirect
97. C3×C4×C3⋊D3C23semidirect
98. C32×#67C23semidirect
100. C32×D12C23semidirect
101. C32×C4×D3C23semidirect
102. C32×Dic6C23semidirect
103. #6293C23semidirect
104. #6292C23semidirect
105. #6291C23semidirect
106. #6290C23semidirect
107. #6289C23semidirect
109. D3×C3⋊Dic3C23semidirect
122. C22×C32×C4C2×D3semidirect
123. C22×C32×C4C2×D3semidirect
130. C22×C3⋊Dic3C2×D3semidirect
153. C2×C4×C3⋊D3C2×D3semidirect
154. C2×C4×C3⋊D3C2×D3semidirect
155. C2×C4×C3⋊D3C2×D3semidirect
160. C2×C3×#67C2×D3semidirect
162. C3×#235C2×D3semidirect
163. C2×C3×D12C2×D3semidirect
169. C2×C3×C4×D3C2×D3semidirect
170. C2×C3×Dic6C2×D3semidirect
193. C2×C3×C3⋊D3#41semidirect
224. C2×#235C3⋊D3direct (N × H)
262. C2×C32×C4C22×D3semidirect
263. C2×C32×C4C22×D3semidirect
275. C2×C3⋊Dic3C22×D3semidirect
287. C4×C3⋊D3C22×D3semidirect
288. C4×C3⋊D3C22×D3semidirect
293. C3×#67C22×D3semidirect
298. C3×D12C22×D3semidirect
303. C3×C4×D3C22×D3semidirect
304. C3×Dic6C22×D3semidirect
314. C2×C33C2×#41semidirect
318. C3×C3⋊D3C2×#41semidirect
336. C22×C3×C4D32semidirect
337. C22×C3×C4C2×C3⋊D3semidirect
346. C2×#67C2×C3⋊D3semidirect
364. #235C2×C3⋊D3direct (N × H)
371. C2×D12C2×C3⋊D3semidirect
386. C2×C4×D3C2×C3⋊D3semidirect
393. C2×Dic6C2×C3⋊D3semidirect
414. C2×C3⋊D3#235direct (N × H)
452. C33C22×#41semidirect
490. C2×C3×C4C2×D32semidirect
493. C2×C3×C4C22×C3⋊D3semidirect
501. #67C22×C3⋊D3semidirect
516. D12C22×C3⋊D3semidirect
528. C4×D3C22×C3⋊D3semidirect
534. Dic6C22×C3⋊D3semidirect
541. C2×C32C2×#235semidirect
542. C2×C32D3×#41semidirect
549. C3⋊D3C2×#235direct (N × H)
586. C22×C4D3×C3⋊D3semidirect
634. C32C22×#235semidirect
635. C32C2×D3×#41semidirect
671. C2×C4C2×D3×C3⋊D3semidirect
680. C2×C3D3×#235semidirect
681. C2×C3#41×C3⋊D3semidirect
710. C3C2×D3×#235semidirect
711. C3C2×#41×C3⋊D3semidirect
717. C2C3⋊D3×#235direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890762
C22×C3×C4×C3⋊D32
C2×C32×#2352
C2×C3⋊D3×#672
C2×#890282
C3⋊D3×#2352
C2×C3⋊D3×D122
C2×C4×D3×C3⋊D32
C2×#890202
C2×#890182
C2×C3⋊D3×Dic62
C2×#890142
C2×#41×C3⋊D33
C2×D3×#2353