Finite Group Databasebeta

← C3×#78759 #11887187

Subgroups — C3×#78759 #11887187

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic
2C3×#5513C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic, complemented
4C3×#5218C211yesmaximal, characteristic, complemented
5C3×#5116C211yesmaximal, characteristic, complemented
6C3×C8×#67C211yesmaximal, characteristic, complemented
7C3×#4971C211yesmaximal, characteristic, complemented
8C3×#4784C211yesmaximal, characteristic, complemented
9C3×#4783C211yesmaximal, characteristic, complemented
10C3×#4778C211yesmaximal, characteristic, complemented
11C3×#4772C211yesmaximal, characteristic, complemented
12C3×#4768C211yesmaximal, characteristic, complemented
13C3×#4767C211yesmaximal, characteristic, complemented
14C3×#4766C211yesmaximal, characteristic, complemented
15C3×#4758C211yesmaximal, characteristic, complemented
16C3×#3296—31nomaximal
17#78759C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C3×#953—21no—
23C2×C3×#217—21no—
24C3×#939—21no—
25C3×#938C2211yescharacteristic
26C3×#936C2211yescharacteristic
27C3×#935—21no—
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C3×#929—21no—
32C3×C4×#67C2211yescharacteristic
33C3×#926—21no—
34C3×#924C2211yescharacteristic
35C3×#924C2211yescharacteristic
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#898—21no—
39C3×#897C2211yescharacteristic, complemented
40C3×#892C2211yescharacteristic, complemented
41C3×#890C2211yescharacteristic, complemented
42C3×#889—21no—
43C3×#887C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59C3×#808C2211yescharacteristic, complemented
60C3×#808C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×#546—31no—
63#5806C2×C311yescharacteristic
64#5513C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#483—31no—
67C3×#482—31no—
68C3×#478—31no—
69C3×#467—31no—
70C3×#465—31no—
71C3×#464—31no—
72C3×#452—31no—
73C3×#450—31no—
74C3×C4×SD16—31no—
75C3×C8×D4—31no—
76C3×#416—31no—
77C2×C3×#102—21no—
78C2×C3×#102D311yescharacteristic, complemented
79C2×C3×#102C2×C311yescharacteristic, complemented
80#5218C2×C311yescharacteristic, complemented
81#5116C2×C311yescharacteristic, complemented
82C8×#67C2×C311yescharacteristic, complemented
83#4971C2×C311yescharacteristic, complemented
84#4784C2×C311yescharacteristic, complemented
85#4783C2×C311yescharacteristic, complemented
86#4778C2×C311yescharacteristic, complemented
87#4772C2×C311yescharacteristic, complemented
88#4768C2×C311yescharacteristic, complemented
89#4767C2×C311yescharacteristic, complemented
90#4766C2×C311yescharacteristic, complemented
91#4758C2×C311yescharacteristic, complemented
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—21no—
95C2×C32×D4—41no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C3×#237—22no—
106C3×#237—41no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×#214—22no—
124C3×#214—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×Dic12—41no—
143C3×D3×C8—41no—
144#3296—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—21no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C22×C311yescharacteristic
149C2×#237C22×C311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C2×C3×SD16—31no—
153C22×C3×C8—21no—
154C22×C3×C8—31no—
155C22×C3×C8C2×D311yescharacteristic
156C22×C3×C8C22×C311yescharacteristic
157C3×#126—61no—
158C3×#125—31no—
159C3×#125—61no—
160C3×#124—31no—
161C3×#123—61no—
162C3×#123—61no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×#121—31no—
167C3×#121—61no—
168C3×#120—61no—
169C3×C4×Q8—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×#117—31no—
173C3×#117—61no—
174C2×C3×C4⋊C4—21no—
175C2×C3×C4⋊C4C2×D311yescharacteristic
176C2×C3×C4⋊C4C22×C311yescharacteristic
177C2×C3×C22⋊C4—61no—
178#953—21no—
179C2×#217—21no—
180#939—21no—
181#938C22×C311yescharacteristic
182#936C22×C311yescharacteristic
183#935—21no—
184D4×Dic3C22×C311yescharacteristic
185C2×#214C22×C311yescharacteristic
186C2×#214C22×C311yescharacteristic
187#929—21no—
188C4×#67C22×C311yescharacteristic
189#926—21no—
190#924C22×C311yescharacteristic
191#924C22×C311yescharacteristic
192C2×Dic12C22×C311yescharacteristic, complemented
193C2×D3×C8C22×C311yescharacteristic, complemented
194#898—21no—
195#897C22×C311yescharacteristic, complemented
196#892C22×C311yescharacteristic, complemented
197#890C22×C311yescharacteristic, complemented
198#889—21no—
199#887C22×C311yescharacteristic, complemented
200C3×#107—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#102—21no—
209C3×#102—21no—
210C3×#102—21no—
211C3×#102—21no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic
215C3×#102C2×D311yescharacteristic
216C3×#102C2×D311yescharacteristic
217C3×#102C2×D311yescharacteristic
218C3×#102C22×C311yescharacteristic
219C3×#102C22×C311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×#102C22×C311yescharacteristic
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×C4×C8—31no—
225#832C22×C311yescharacteristic
226#832C22×C311yescharacteristic
227#830C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic, complemented
229#818C22×C311yescharacteristic, complemented
230#816C22×C311yescharacteristic, complemented
231#816C22×C311yescharacteristic, complemented
232Dic3⋊C8C22×C311yescharacteristic, complemented
233C8×Dic3C22×C311yescharacteristic, complemented
234#810C22×C311yescharacteristic, complemented
235#810C22×C311yescharacteristic, complemented
236#808C22×C311yescharacteristic, complemented
237#808C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—42no—
241C23×C32—42no—
242C23×C32—81no—
243C23×C32C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—42no—
249C32×D4#4112yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—42no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C3×#67—22no—
258C3×#67—42no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—31no—
281#488—31no—
282#483—31no—
283#482—31no—
284#478—31no—
285#467—31no—
286#465—31no—
287#464—31no—
288#452—31no—
289#450—31no—
290C4×SD16—31no—
291C8×D4—31no—
292#416—31no—
293C2×#102C3×D311yescharacteristic, complemented
294C24×C3—21no—
295C24×C3—21no—
296C24×C3—41no—
297C3×#41—62no—
298C3×#41—121no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×D4—24no—
302C2×C3×D4—22no—
303C2×C3×D4—22no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—41no—
310C2×C3×D4—41no—
311C2×C3×D4—41no—
312C2×C3×D4—42no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C23×C311yescharacteristic
318C2×C3×D4C23×C311yescharacteristic
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—41no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C23×C311yescharacteristic
328C2×#67—21no—
329C2×#67—21no—
330C2×#67C3×D411yescharacteristic
331C22×Dic3—21no—
332C22×Dic3—21no—
333#237—22no—
334#237—41no—
335C2×C4×D3C23×C311yescharacteristic
336C2×Dic6C23×C311yescharacteristic
337C2×Dic6C23×C311yescharacteristic
338C3×Q16—121no—
339C3×SD16—62no—
340C3×SD16—121no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—41no—
346C2×C3×C8—41no—
347C2×C3×C8—42no—
348C2×C3×C8—121no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C23×C311yescharacteristic
352C2×C3×C8C23×C311yescharacteristic
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—41no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C4⋊C4C23×C311yescharacteristic
370C3×C4⋊C4C23×C311yescharacteristic
371C3×C22⋊C4—31no—
372C3×C22⋊C4—31no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C42—31no—
382C3×C42—61no—
383C3×C42—61no—
384#217—21no—
385#217—21no—
386#217—21no—
387#217—21no—
388#217—21no—
389#217—21no—
390#217C3×D411yescharacteristic
391#214—22no—
392#214—41no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4C3×D411yescharacteristic
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3C23×C311yescharacteristic
399C4⋊Dic3C23×C311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4C3×D411yescharacteristic
405C4×Dic3—21no—
406C4×Dic3—21no—
407C4×Dic3C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410Dic12—41no—
411D3×C8—41no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—84no—
421C22×C32#13512yes—
422C22×C32C22×D411yescharacteristic
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—31no—
439C22×D4C2×C3×D311yescharacteristic
440C2×Q16—31no—
441C2×SD16—31no—
442C2×SD16—31no—
443C22×C8—31no—
444C22×C8C2×C3×D311yescharacteristic
445#126—61no—
446#125—31no—
447#125—61no—
448#124—31no—
449#123—61no—
450#123—61no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—31no—
454#121—31no—
455#121—61no—
456#120—61no—
457C4×Q8—31no—
458C4×D4—31no—
459C4×D4—31no—
460#117—31no—
461#117—61no—
462C2×C4⋊C4C2×C3×D311yescharacteristic
463C2×C22⋊C4—61no—
464#107—31no—
465#106—31no—
466#106—31no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#102—31no—
473#102—31no—
474#102C2×C3×D311yescharacteristic
475#102C2×C3×D311yescharacteristic
476#102C2×C3×D311yescharacteristic
477#102C2×C3×D311yescharacteristic
478C22⋊C8—31no—
479C22⋊C8—31no—
480C4×C8—31no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—42no—
490C23×C3—42no—
491C23×C3—44no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—82no—
495C23×C3—81no—
496C23×C3—81no—
497C23×C3—82no—
498C23×C3D3×D411yescharacteristic
499C23×C3C2×C3×D411yescharacteristic
500C22×D3C2×C3×D411yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—22no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—42no—
516C3×D4—42no—
517C3×D4—44no—
518C3×D4—62no—
519C3×D4—122no—
520C3×D4—241no—
521C3×D4#23512yes—
522C3×D4C3×#4112yes—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—42no—
541C2×C3×C4—42no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—82no—
549C2×C3×C4—122no—
550C2×C3×C4—241no—
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4C2×C3×D411yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C24×C311yescharacteristic
555#67—22no—
556#67—42no—
557#67—81no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—42no—
563C2×Dic3—81no—
564C2×Dic3C2×C3×D411yescharacteristic
565C2×Dic3C2×C3×D411yescharacteristic
566C2×Dic3C2×C3×D411yescharacteristic
567C4×D3—21no—
568C4×D3—21no—
569Dic6—21no—
570Dic6—21no—
571Dic6—21no—
572Dic6—21no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3×C8—41no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C2×C32—22no—
584C2×C32—42no—
585C2×C32—81no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57711yescharacteristic
589C3×D3—41no—
590C24—21no—
591#41—62no—
592#41—121no—
593C2×Q8—31no—
594C2×Q8—31no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—31no—
598C2×D4—41no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4C22×C3×D311yescharacteristic
602C2×D4C22×C3×D311yescharacteristic
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4C22×C3×D311yescharacteristic
608Q16—121no—
609SD16—62no—
610SD16—121no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—41no—
614C2×C8—121no—
615C2×C8C22×C3×D311yescharacteristic
616C2×C8C22×C3×D311yescharacteristic
617C4⋊C4—21no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4C22×C3×D311yescharacteristic
628C4⋊C4C22×C3×D311yescharacteristic
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C42—31no—
640C42—61no—
641C42—61no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—84no—
672C22×C3—84no—
673C22×C3—88no—
674C22×C3#91212yes—
675C22×C3C3×#13512yes—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C22×C3×D411yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—21no—
681C3×C4—22no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—81no—
694C3×C4—81no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4C2×#23511yescharacteristic
700C3×C4#100411yescharacteristic
701C3×C4C2×C3×#4111yescharacteristic
702C3×C4C3×H(5,𝔽2)11yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—21no—
706Dic3—41no—
707Dic3—41no—
708Dic3—41no—
709Dic3—41no—
710C32#329611yescharacteristic, complemented, Sylow
711C23—21no—
712C23—21no—
713C23—31no—
714C23—42no—
715C23—42no—
716C23—81no—
717C23C3×D3×D411yescharacteristic
718Q8—61no—
719Q8—61no—
720Q8—61no—
721Q8—61no—
722D4—21no—
723D4—21no—
724D4—21no—
725D4—42no—
726D4—62no—
727D4—122no—
728D4—241no—
729D4C3×#23512yes—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—42no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—122no—
745C2×C4—241no—
746C2×C4C3×D3×D411yescharacteristic
747C2×C4C23×C3×D311yescharacteristic
748C8—21no—
749C8—21no—
750C8—61no—
751C8—61no—
752C2×C3—24no—
753C2×C3—22no—
754C2×C3—22no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—42no—
759C2×C3—42no—
760C2×C3—82no—
761C2×C3—82no—
762C2×C3—81no—
763C2×C3—81no—
764C2×C3—121no—
765C2×C3#549011yescharacteristic
766C2×C3C2×#91211yescharacteristic
767C2×C3#576211yescharacteristic
768C2×C3C3×#54611yescharacteristic
769C2×C3C2×C3×#13511yescharacteristic
770C2×C3C3×#57711yescharacteristic
771D3—41no—
772C22—21no—
773C22—21no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—84no—
784C22C3×#91212yes—
785C22C2×C3×D3×D411yescharacteristic
786C4—21no—
787C4—41no—
788C4—41no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—121no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4C2×C3×#23511yescharacteristic
797C4C3×#100411yescharacteristic
798C3—21no—
799C3#7875911yescharacteristic, direct product factor
800C3C3×#329611yescharacteristic, complemented
801C2—22no—
802C2—42no—
803C2—81no—
804C2—121no—
805C2C3×#549011yescharacteristic
806C2C2×C3×#91211yescharacteristic
807C2C3×#576211yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#102C2
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC2×C3×#102D3
hypocenterC3C3×#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C3×#5513C2semidirect
3. C2×C32×#102C2semidirect
4. C3×#5218C2semidirect
5. C3×#5116C2semidirect
6. C3×C8×#67C2semidirect
7. C3×#4971C2semidirect
8. C3×#4784C2semidirect
9. C3×#4783C2semidirect
10. C3×#4778C2semidirect
11. C3×#4772C2semidirect
12. C3×#4768C2semidirect
13. C3×#4767C2semidirect
14. C3×#4766C2semidirect
15. C3×#4758C2semidirect
17. #78759C3direct (N × H)
36. C2×C3×Dic12C22semidirect
37. C2×C3×D3×C8C22semidirect
39. C3×#897C22semidirect
40. C3×#892C22semidirect
41. C3×#890C22semidirect
43. C3×#887C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#818C22semidirect
53. C3×#816C22semidirect
54. C3×#816C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×C8×Dic3C22semidirect
57. C3×#810C22semidirect
58. C3×#810C22semidirect
59. C3×#808C22semidirect
60. C3×#808C22semidirect
64. #5513C2×C3semidirect
78. C2×C3×#102D3semidirect
79. C2×C3×#102C2×C3semidirect
80. #5218C2×C3semidirect
81. #5116C2×C3semidirect
82. C8×#67C2×C3semidirect
83. #4971C2×C3semidirect
84. #4784C2×C3semidirect
85. #4783C2×C3semidirect
86. #4778C2×C3semidirect
87. #4772C2×C3semidirect
88. #4768C2×C3semidirect
89. #4767C2×C3semidirect
90. #4766C2×C3semidirect
91. #4758C2×C3semidirect
192. C2×Dic12C22×C3semidirect
193. C2×D3×C8C22×C3semidirect
195. #897C22×C3semidirect
196. #892C22×C3semidirect
197. #890C22×C3semidirect
199. #887C22×C3semidirect
228. (C2×D3)⋊C8C22×C3semidirect
229. #818C22×C3semidirect
230. #816C22×C3semidirect
231. #816C22×C3semidirect
232. Dic3⋊C8C22×C3semidirect
233. C8×Dic3C22×C3semidirect
234. #810C22×C3semidirect
235. #810C22×C3semidirect
236. #808C22×C3semidirect
237. #808C22×C3semidirect
293. C2×#102C3×D3semidirect
710. C32#3296semidirect
799. C3#78759direct (N × H)
800. C3C3×#3296semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
C3×#55132
C2×C32×#1022
C3×#52182
C3×#51162
C3×C8×#672
C3×#49712
C3×#47842
C3×#47832
C3×#47782
C3×#47722
C3×#47682
C3×#47672
C3×#47662
C3×#47582
C3×#32963
#787593