Finite Group Databasebeta

← C3×#79299 #11870569

Subgroups — C3×#79299 #11870569

Order 1152.

851 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3C32×#431C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4845C211yesmaximal, characteristic, complemented
6C3×#4844C211yesmaximal, characteristic, complemented
7C3×#4829C211yesmaximal, characteristic, complemented
8C3×#4737C211yesmaximal, characteristic, complemented
9C3×#4734C211yesmaximal, characteristic
10C3×#4733C211yesmaximal, characteristic, complemented
11C3×#4723C211yesmaximal, characteristic, complemented
12C3×C4×Dic12C211yesmaximal, characteristic, complemented
13C3×C4×D24C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×C4×#204C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#79299C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C2×C32×C42C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C3×#929—21no—
22C3×C4×#67—21no—
23C3×C4×#67—21no—
24C3×C4×#67—21no—
25C3×#926C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic
28C2×C3×D24C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C3×#876—21no—
32C3×#875C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36C3×#872—21no—
37C3×#872—21no—
38C3×C42×D3—21no—
39C3×#870C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C32×C4×C8C2211yescharacteristic
48C32×C4×C8C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#818C2211yescharacteristic
54C3×#818C2211yescharacteristic
55C3×#817C2211yescharacteristic
56C3×#817C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×#816C2211yescharacteristic
59C3×#816C2211yescharacteristic
60C3×#816C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63#5479C2×C311yescharacteristic, complemented
64C4×#235C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#479—31no—
68C3×#478—31no—
69C3×#464—31no—
70C3×#463—31no—
71C3×#452—31no—
72C3×#449—31no—
73C3×C4×Q16—31no—
74C3×C4×SD16—31no—
75C3×C4×SD16—31no—
76C3×C4×D8—31no—
77C3×#431—21no—
78C3×#431D311yescharacteristic, complemented
79C3×#431C2×C311yescharacteristic, complemented
80#4847C2×C311yescharacteristic, complemented
81#4845C2×C311yescharacteristic, complemented
82#4844C2×C311yescharacteristic, complemented
83#4829C2×C311yescharacteristic, complemented
84#4737C2×C311yescharacteristic, complemented
85#4734C2×C311yescharacteristic
86#4733C2×C311yescharacteristic, complemented
87#4723C2×C311yescharacteristic, complemented
88C4×Dic12C2×C311yescharacteristic, complemented
89C4×D24C2×C311yescharacteristic, complemented
90C4×#204C2×C311yescharacteristic, complemented
91C4×#204C2×C311yescharacteristic, complemented
92C22×C32×C4D411yescharacteristic
93C22×C32×C4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C3×#235—22no—
98C3×#235—22no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C42D411yescharacteristic
112C32×C42D411yescharacteristic
113C32×C42C2311yescharacteristic
114C32×C42C2311yescharacteristic
115C3×#217—21no—
116C3×#217—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×Dic12—22no—
138C3×D24—22no—
139C3×#204—22no—
140C3×#204—22no—
141#3102—31noSylow
142C2×C3×#41—31no—
143C2×#235C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×D8—31no—
148C3×#126—61no—
149C3×#125—31no—
150C3×#124—31no—
151C3×#123—61no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C3×C4×D4—61no—
161C3×C4×D4—61no—
162C3×C4×D4—61no—
163C3×#117—31no—
164C3×#117—61no—
165C3×#117—61no—
166C2×C3×C42—21no—
167C2×C3×C42—61no—
168C2×C3×C42C2×D311yescharacteristic
169C2×C3×C42C22×C311yescharacteristic
170#930C22×C311yescharacteristic
171#929—21no—
172C4×#67—21no—
173C4×#67—21no—
174C4×#67—21no—
175#926C22×C311yescharacteristic
176#924C22×C311yescharacteristic
177C2×Dic12C22×C311yescharacteristic
178C2×D24C22×C311yescharacteristic
179C2×#204C22×C311yescharacteristic
180C2×#204C22×C311yescharacteristic
181#876—21no—
182#875C22×C311yescharacteristic
183C4×D12C22×C311yescharacteristic
184C4×D12C22×C311yescharacteristic
185C4×D12C22×C311yescharacteristic
186#872—21no—
187#872—21no—
188C42×D3—21no—
189#870C22×C311yescharacteristic
190C4×Dic6C22×C311yescharacteristic
191C4×Dic6C22×C311yescharacteristic
192C4×Dic6C22×C311yescharacteristic
193C3×#107—31no—
194C3×#107—31no—
195C3×#106—31no—
196C3×#106—31no—
197C3×C4⋊C8—21no—
198C3×C4⋊C8—21no—
199C3×C4⋊C8C2×D311yescharacteristic
200C3×C4⋊C8C2×D311yescharacteristic
201C3×C4⋊C8C22×C311yescharacteristic
202C3×C4⋊C8C22×C311yescharacteristic
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C22⋊C8—21no—
212C3×C22⋊C8—21no—
213C3×C22⋊C8C2×D311yescharacteristic
214C3×C22⋊C8C2×D311yescharacteristic
215C3×C22⋊C8C22×C311yescharacteristic
216C3×C22⋊C8C22×C311yescharacteristic
217C3×C4×C8—21no—
218C3×C4×C8—21no—
219C3×C4×C8C2×D311yescharacteristic
220C3×C4×C8C2×D311yescharacteristic
221C3×C4×C8C22×C311yescharacteristic
222C3×C4×C8C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224#821C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226#821C22×C311yescharacteristic
227#818C22×C311yescharacteristic
228#818C22×C311yescharacteristic
229#817C22×C311yescharacteristic
230#817C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C2×C32×C4—22no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—41no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C3×#67—24no—
249C3×#67—42no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12#4112yes—
260C3×C4×D3—24no—
261C3×C4×D3—42no—
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268C32×C8—21no—
269C32×C8—21no—
270C32×C8—21no—
271C32×C8—21no—
272#529—31no—
273C4×#41—31no—
274#485—31no—
275#482—31no—
276#479—31no—
277#478—31no—
278#464—31no—
279#463—31no—
280#452—31no—
281#449—31no—
282C4×Q16—31no—
283C4×SD16—31no—
284C4×SD16—31no—
285C4×D8—31no—
286#431C3×D311yescharacteristic, complemented
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×D4—31no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4D1211yescharacteristic
303C22×C3×C4D1211yescharacteristic
304C22×C3×C4C3×D411yescharacteristic
305C22×C3×C4C3×D411yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C23×C311yescharacteristic
308C2×#67—21no—
309C2×#67—21no—
310#235—22no—
311#235—22no—
312C2×D12C23×C311yescharacteristic
313C2×D12C23×C311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×Dic6C23×C311yescharacteristic
319C2×Dic6C23×C311yescharacteristic
320C3×Q16—62no—
321C3×SD16—62no—
322C3×SD16—62no—
323C3×D8—62no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C23×C311yescharacteristic
333C2×C3×C8C23×C311yescharacteristic
334C2×C3×C8C23×C311yescharacteristic
335C2×C3×C8C23×C311yescharacteristic
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—21no—
355C3×C42—21no—
356C3×C42—21no—
357C3×C42—21no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42—61no—
362C3×C42D1211yescharacteristic
363C3×C42D1211yescharacteristic
364C3×C42C3×D411yescharacteristic
365C3×C42C3×D411yescharacteristic
366C3×C42C22×D311yescharacteristic
367C3×C42C22×D311yescharacteristic
368C3×C42C23×C311yescharacteristic
369C3×C42C23×C311yescharacteristic
370#217—21no—
371#217—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378C4⋊Dic3C23×C311yescharacteristic
379C4⋊Dic3C23×C311yescharacteristic
380C4⋊Dic3C23×C311yescharacteristic
381C4⋊Dic3C23×C311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392Dic12—22no—
393D24—22no—
394#204—22no—
395#204—22no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—22no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4#13512yes—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3×Dic3—22no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C2×#41—31no—
420C2×Q16—31no—
421C2×SD16—31no—
422C2×SD16—31no—
423C2×D8—31no—
424#126—61no—
425#125—31no—
426#124—31no—
427#123—61no—
428C22⋊Q8—31no—
429#121—31no—
430C4×Q8—31no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×D4—31no—
434C4×D4—31no—
435C4×D4—31no—
436C4×D4—61no—
437C4×D4—61no—
438C4×D4—61no—
439#117—31no—
440#117—61no—
441#117—61no—
442C2×C42—61no—
443C2×C42C2×C3×D311yescharacteristic
444#107—31no—
445#107—31no—
446#106—31no—
447#106—31no—
448C4⋊C8C2×C3×D311yescharacteristic
449C4⋊C8C2×C3×D311yescharacteristic
450#103—31no—
451#103—31no—
452#103—31no—
453#103—31no—
454#102—31no—
455#102—31no—
456#102—31no—
457#102—31no—
458C22⋊C8C2×C3×D311yescharacteristic
459C22⋊C8C2×C3×D311yescharacteristic
460C4×C8C2×C3×D311yescharacteristic
461C4×C8C2×C3×D311yescharacteristic
462C23×C3—21no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3C2×D1211yescharacteristic
466C23×C3C2×C3×D411yescharacteristic
467C22×D3—21no—
468C22×D3—21no—
469C3×Q8—32no—
470C3×Q8—61no—
471C3×Q8—61no—
472C3×Q8—61no—
473C3×D4—32no—
474C3×D4—64no—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—61no—
478C3×D4—122no—
479C2×C3×C4—24no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—42no—
497C2×C3×C4—64no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—122no—
505C2×C3×C4—122no—
506C2×C3×C4—122no—
507C2×C3×C4C2×D1211yescharacteristic
508C2×C3×C4C2×D1211yescharacteristic
509C2×C3×C4C2×D1211yescharacteristic
510C2×C3×C4C2×D1211yescharacteristic
511C2×C3×C4C2×D1211yescharacteristic
512C2×C3×C4C2×C3×D411yescharacteristic
513C2×C3×C4C2×C3×D411yescharacteristic
514C2×C3×C4C2×C3×D411yescharacteristic
515C2×C3×C4C2×C3×D411yescharacteristic
516C2×C3×C4C2×C3×D411yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C24×C311yescharacteristic
519#67—24no—
520#67—42no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527D12—21no—
528D12—21no—
529D12—21no—
530D12C3×#4112yes—
531C4×D3—24no—
532C4×D3—42no—
533C4×D3—42no—
534C4×D3—42no—
535Dic6—21no—
536Dic6—21no—
537Dic6—21no—
538Dic6C3×#4112yes—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—21no—
543C3×C8—21no—
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—21no—
547C3×C8—41no—
548C3×C8—41no—
549C3×C8—41no—
550C3×C8—41no—
551C2×C32—41no—
552C2×C32#52511yescharacteristic
553C2×C32C2×#13511yescharacteristic
554C2×C32#57511yescharacteristic
555C3×D3—42no—
556C3×D3—81no—
557#41—62no—
558#41—62no—
559C2×Q8—31no—
560C2×Q8—31no—
561C2×D4—31no—
562C2×D4—31no—
563C2×D4—61no—
564C2×D4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4C3×D1211yescharacteristic
570C22×C4C3×D1211yescharacteristic
571C22×C4C22×C3×D311yescharacteristic
572Q16—62no—
573SD16—62no—
574SD16—62no—
575D8—62no—
576C2×C8C22×C3×D311yescharacteristic
577C2×C8C22×C3×D311yescharacteristic
578C2×C8C22×C3×D311yescharacteristic
579C2×C8C22×C3×D311yescharacteristic
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C42—61no—
599C42—61no—
600C42—61no—
601C42—61no—
602C42C3×D1211yescharacteristic
603C42C3×D1211yescharacteristic
604C42C22×C3×D311yescharacteristic
605C42C22×C3×D311yescharacteristic
606C22×C3—22no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—62no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3C22×D1211yescharacteristic
623C22×C3C22×C3×D411yescharacteristic
624C2×D3—22no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—41no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—22no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—62no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4#90412yes—
652C3×C4C3×#13512yes—
653C3×C4D3×#4111yescharacteristic
654C3×C4D3×#4111yescharacteristic
655C3×C4C2×C3×#4111yescharacteristic
656C3×C4C2×C3×#4111yescharacteristic
657Dic3—22no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663C32#310211yescharacteristic, complemented, Sylow
664C23—61no—
665C23—61no—
666C23C2×C3×D1211yescharacteristic
667Q8—32no—
668Q8—61no—
669Q8—61no—
670Q8—61no—
671D4—32no—
672D4—64no—
673D4—61no—
674D4—61no—
675D4—61no—
676D4—122no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—41no—
681C2×C4—64no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—122no—
689C2×C4—122no—
690C2×C4—122no—
691C2×C4C2×C3×D1211yescharacteristic
692C2×C4C2×C3×D1211yescharacteristic
693C2×C4C2×C3×D1211yescharacteristic
694C2×C4C2×C3×D1211yescharacteristic
695C2×C4C2×C3×D1211yescharacteristic
696C2×C4C23×C3×D311yescharacteristic
697C8—21no—
698C8—21no—
699C8—21no—
700C8—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—42no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—122no—
708C2×C3—241no—
709C2×C3#552411yescharacteristic
710C2×C3C2×#90411yescharacteristic
711C2×C3#574811yescharacteristic
712C2×C3C3×#52511yescharacteristic
713C2×C3C2×C3×#13511yescharacteristic
714C2×C3C3×#57511yescharacteristic
715D3—42no—
716D3—81no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—62no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22—121no—
725C22—121no—
726C22C22×C3×D1211yescharacteristic
727C4—21no—
728C4—21no—
729C4—21no—
730C4—21no—
731C4—62no—
732C4—121no—
733C4—121no—
734C4—121no—
735C4—121no—
736C4—121no—
737C4C3×#90412yes—
738C4C3×D3×#4111yescharacteristic
739C4C3×D3×#4111yescharacteristic
740C3—21no—
741C3#7929911yescharacteristic, direct product factor
742C3C3×#310211yescharacteristic, complemented
743C2—41no—
744C2—122no—
745C2—241no—
746C2C3×#552411yescharacteristic
747C2C2×C3×#90411yescharacteristic
748C2C3×#574811yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#431C2
socleC22×C32C22×D4
prime radicalC3×#4734C2
hypercenterC3×#431D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#431

Complements

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

NH ≅ G/Ntype
1. C3×#5479C2semidirect
2. C3×C4×#235C2semidirect
3. C32×#431C2semidirect
4. C3×#4847C2semidirect
5. C3×#4845C2semidirect
6. C3×#4844C2semidirect
7. C3×#4829C2semidirect
8. C3×#4737C2semidirect
10. C3×#4733C2semidirect
11. C3×#4723C2semidirect
12. C3×C4×Dic12C2semidirect
13. C3×C4×D24C2semidirect
14. C3×C4×#204C2semidirect
15. C3×C4×#204C2semidirect
17. #79299C3direct (N × H)
63. #5479C2×C3semidirect
64. C4×#235C2×C3semidirect
78. C3×#431D3semidirect
79. C3×#431C2×C3semidirect
80. #4847C2×C3semidirect
81. #4845C2×C3semidirect
82. #4844C2×C3semidirect
83. #4829C2×C3semidirect
84. #4737C2×C3semidirect
86. #4733C2×C3semidirect
87. #4723C2×C3semidirect
88. C4×Dic12C2×C3semidirect
89. C4×D24C2×C3semidirect
90. C4×#204C2×C3semidirect
91. C4×#204C2×C3semidirect
286. #431C3×D3semidirect
663. C32#3102semidirect
741. C3#79299direct (N × H)
742. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C3×C4×#2352
C32×#4312
C3×#48472
C3×#48452
C3×#48442
C3×#48292
C3×#47372
C3×#47342
C3×#47332
C3×#47232
C3×C4×Dic122
C3×C4×D242
C3×C4×#2042
C3×#31023
#792993