Finite Group Databasebeta

← #13169259

Subgroups — #13169259

Order 1728.

1226 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊#6296C211yesmaximal, characteristic, complemented
2C4×#6291C211yesmaximal, characteristic
3#11723503C211yesmaximal, characteristic, complemented
4#11723456C211yesmaximal, characteristic, complemented
5C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63856C211yesmaximal, characteristic, complemented
7C3×#63843C211yesmaximal, characteristic, complemented
8#11723014C212yesmaximal, complemented
9#11722982C212yesmaximal, complemented
10#11722978C212yesmaximal, complemented
11#11722932C212yesmaximal
12#10595371—31nomaximal
13#10594991—31nomaximal
14#10594536—31nomaximal
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6296C2212yes—
19C2×#6291C2211yescharacteristic
20C2×#6289C2212yes—
21C2×C3×D3×Dic3C2212yes—
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4×C3⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26#88815C2212yes—
27#88807C2211yescharacteristic
28#88807C2212yes—
29#88806C2212yes—
30#88804C2212yes—
31#88804C2211yescharacteristic
32(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×Dic32C2212yes—
38#64155—31no—
39C4×#638—31no—
40C4⋊C4×C3⋊D3—31no—
41C3×#946—31no—
42C3×Q8×Dic3—31no—
43C2×C3×C4⋊Dic3—31no—
44C3×#924—31no—
45C3×D3×C4⋊C4—31no—
46C3×#887—31no—
47#63964—32no—
48#63952—32no—
49#63919—31no—
50#63918—31no—
51#63918—31no—
52C4×#626—31no—
53C4×#626—31no—
54C4×#626—32no—
55C4×#626—61no—
56#63900—31no—
57#63900—31no—
58#63900—61no—
59#63899—32no—
60#63895—32no—
61#63895—32no—
62D3×C4⋊Dic3D311yescharacteristic, complemented
63#63880—32no—
64#63871—31no—
65#63871—31no—
66#63871—61no—
67#63867—32no—
68#63867—32no—
69#63865—32no—
70#63856D311yescharacteristic, complemented
71#63851—32no—
72#63847—32no—
73#63843D311yescharacteristic, complemented
74C22×C3⋊(C3⋊D3)C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C4×C3⋊(C3⋊D3)—22no—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C32×C4×D3—22no—
87C32×Dic6—22no—
88#6296—42no—
89#6291Q814yescomplemented
90#6289—42no—
91C3×D3×Dic3—42no—
92#5635—91no—
93#5579—91no—
94#5511—91no—
95C2×C32×Q8—31no—
96C22×C32×C4—31no—
97C2×#638—31no—
98C2×C4×C3⋊D3—31no—
99C2×C4×C3⋊D3—31no—
100C2×C4×C3⋊D3—31no—
101C2×C4×C3⋊D3—32no—
102C2×C4×C3⋊D3—61no—
103C2×C4×C3⋊D3—61no—
104C2×C4×C3⋊D3—61no—
105C2×C4×C3⋊D3—121no—
106C22×C3×Dic3—32no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3C2×D311yescharacteristic
110C2×C3×C4×D3C2×D311yescharacteristic
111C2×C3×Dic6—21no—
112C2×C3×Dic6C2×D311yescharacteristic
113C2×C3×Dic6C2×D311yescharacteristic
114C2×#627—32no—
115C2×#627—32no—
116C2×#627—32no—
117C2×#626—31no—
118C2×#626—31no—
119C2×#626—61no—
120C2×#624—32no—
121C2×#624—32no—
122C2×#624—62no—
123C2×D3×Dic3C2×D312yes—
124C32×C4⋊C4—31no—
125#3757—31no—
126#3752—32no—
127#3752—31no—
128C4⋊(C3⋊Dic3)C2×D311yescharacteristic
129C4⋊(C3⋊Dic3)C2×D311yescharacteristic
130#3750—32no—
131#3750—31no—
132#3750—32no—
133C4×C3⋊Dic3C2×D311yescharacteristic
134C3×#217—32no—
135C3×(C2×D3)⋊C4—32no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—31no—
141C3×C4⋊Dic3—32no—
142C3×C4⋊Dic3—32no—
143C3×C4⋊Dic3—61no—
144C3×C4⋊Dic3—61no—
145C3×C4⋊Dic3C2×D311yescharacteristic
146C3×C4⋊Dic3C2×D311yescharacteristic
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—32no—
154C3×C4×Dic3—32no—
155C3×C4×Dic3—61no—
156#3724—32no—
157#3724—32no—
158#3724—32no—
159#3724—62no—
160#3724C2×D312yes—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—31no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—62no—
168Dic3⋊Dic3—61no—
169Dic3⋊Dic3C2×D312yes—
170Dic3⋊Dic3C2×D312yes—
171#3722—31no—
172#3722—32no—
173#3722—32no—
174#3722—31no—
175#3722—62no—
176#3722—61no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—31no—
179(C2×D3)⋊Dic3—61no—
180(C2×D3)⋊Dic3C2×D312yes—
181Dic32C2×D312yes—
182C22×C33C2411yescharacteristic
183C2×C3⋊(C3⋊D3)—21no—
184C2×C3⋊(C3⋊D3)—21no—
185C2×C3⋊(C3⋊D3)C2×Q812yes—
186C2×C32×D3—21no—
187C2×C32×D3—21no—
188C2×C32×D3C2×Q812yes—
189C33×C4#4112yes—
190C3⋊(C3⋊Dic3)—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—22no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3C2×Q812yes—
195C32×Dic3—22no—
196C32×Dic3—21no—
197C32×Dic3—22no—
198C3×C22⋊Q8—91no—
199C3×C4×Q8—91no—
200C2×C3×C4⋊C4—91no—
201#946—31no—
202#946—91no—
203#946—91no—
204#946—181no—
205Q8×Dic3—31no—
206C4×#67—92no—
207C4×#67—91no—
208C4×#67—91no—
209C4×#67—181no—
210C2×C4⋊Dic3—31no—
211#924—31no—
212#924—92no—
213#897—92no—
214#897—91no—
215#896—92no—
216#896—92no—
217#896—92no—
218D3×C4⋊C4—31no—
219D3×C4⋊C4—91no—
220D3×C4⋊C4—91no—
221D3×C4⋊C4—91no—
222D3×C4⋊C4—181no—
223#889—92no—
224#889—92no—
225#888—91no—
226#888—91no—
227#887—31no—
228#67⋊C4—92no—
229#878—92no—
230C4×D12—92no—
231C4×D12—91no—
232#870—92no—
233#869—91no—
234C23×C32—31no—
235C22×C3⋊D3—31no—
236C22×C3⋊D3—31no—
237C22×C3⋊D3—31no—
238C22×C3⋊D3—61no—
239C22×C3⋊D3—61no—
240C22×C3⋊D3—61no—
241C22×C3⋊D3—121no—
242C22×C3×D3—21no—
243C22×C3×D3C22×D311yescharacteristic
244C22×C3×D3C22×D311yescharacteristic
245C32×Q8—62no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—32no—
250C2×C32×C4—32no—
251C2×C32×C4—31no—
252C2×C32×C4—41no—
253C2×C32×C4—62no—
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257#638—34no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C2×C3⋊Dic3—61no—
262C2×C3⋊Dic3—61no—
263C2×C3⋊Dic3—61no—
264C2×C3⋊Dic3—121no—
265C2×C3⋊Dic3C22×D312yes—
266C2×C3⋊Dic3C22×D312yes—
267C2×C3⋊Dic3C22×D311yescharacteristic
268C2×C3⋊Dic3C22×D311yescharacteristic
269C4×C3⋊D3—62no—
270C4×C3⋊D3—64no—
271C4×C3⋊D3—62no—
272C4×C3⋊D3—62no—
273C4×C3⋊D3—122no—
274C4×C3⋊D3—122no—
275C4×C3⋊D3—124no—
276C4×C3⋊D3—122no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—62no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3—122no—
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C22×D312yes—
295C2×C3×Dic3C22×D312yes—
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D312yes—
299C3×C4×D3—22no—
300C3×C4×D3—22no—
301C3×C4×D3—42no—
302C3×C4×D3—122no—
303C3×Dic6—22no—
304C3×Dic6—22no—
305C3×Dic6—42no—
306#627—122no—
307#627—122no—
308#627—122no—
309#626—34no—
310#626—34no—
311#626—64no—
312#624—122no—
313#624—122no—
314#624—124no—
315D3×Dic3—42no—
316#554—271noSylow
317C2×C33C22×Q811yescharacteristic
318C2×C33C2×#4111yescharacteristic
319C2×C33H(5,𝔽2)11yescharacteristic
320C3⋊(C3⋊D3)—22no—
321C32×D3—22no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—61no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—61no—
328C22×C3×C4—92no—
329C2×#67—91no—
330C2×#67—91no—
331C2×#67—181no—
332C22×Dic3—32no—
333C2×D12—91no—
334C2×C4×D3—32no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—92no—
339C2×C4×D3—92no—
340C2×C4×D3—92no—
341C2×C4×D3—181no—
342C2×C4×D3—182no—
343C2×C4×D3—181no—
344C2×C4×D3—181no—
345C2×C4×D3—361no—
346C2×C4×D3D3211yescharacteristic
347C2×Dic6—92no—
348C2×Dic6—92no—
349C2×Dic6—92no—
350C2×Dic6D3211yescharacteristic
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—92no—
355C3×C4⋊C4—92no—
356C3×C4⋊C4—92no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4—91no—
359C3×C22⋊C4—92no—
360C3×C42—92no—
361C3×C42—91no—
362#217—32no—
363#217—91no—
364#217—91no—
365#217—181no—
366(C2×D3)⋊C4—32no—
367(C2×D3)⋊C4—92no—
368(C2×D3)⋊C4—92no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—92no—
374(C2×D3)⋊C4—181no—
375(C2×D3)⋊C4—182no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—32no—
381C4⋊Dic3—32no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—92no—
385C4⋊Dic3—91no—
386C4⋊Dic3—92no—
387C4⋊Dic3D3211yescharacteristic
388Dic3⋊C4—32no—
389Dic3⋊C4—32no—
390Dic3⋊C4—32no—
391Dic3⋊C4—32no—
392Dic3⋊C4—92no—
393Dic3⋊C4—92no—
394Dic3⋊C4—92no—
395Dic3⋊C4—92no—
396Dic3⋊C4—92no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—92no—
400Dic3⋊C4—92no—
401Dic3⋊C4—182no—
402Dic3⋊C4—181no—
403Dic3⋊C4—182no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—32no—
407C4×Dic3—32no—
408C4×Dic3—61no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—32no—
413C22×C32—41no—
414C22×C32—61no—
415C22×C32—61no—
416C22×C32C23×D311yescharacteristic
417C22×C32C23×D311yescharacteristic
418C22×C32C23×D311yescharacteristic
419C2×C3⋊D3—32no—
420C2×C3⋊D3—32no—
421C2×C3⋊D3—32no—
422C2×C3⋊D3—62no—
423C2×C3⋊D3—62no—
424C2×C3⋊D3—62no—
425C2×C3⋊D3—61no—
426C2×C3⋊D3—61no—
427C2×C3⋊D3—62no—
428C2×C3⋊D3—62no—
429C2×C3⋊D3—61no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—122no—
434C2×C3⋊D3—121no—
435C2×C3⋊D3—121no—
436C2×C3⋊D3—121no—
437C2×C3⋊D3—121no—
438C2×C3⋊D3—122no—
439C2×C3⋊D3—122no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C2×C3×D3—21no—
443C2×C3×D3—21no—
444C2×C3×D3—22no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3D3×Q812yes—
448C2×C3×D3D3×Q812yes—
449C32×C4—22no—
450C32×C4—22no—
451C32×C4—22no—
452C32×C4—42no—
453C32×C4—61no—
454C32×C4—62no—
455C32×C4—62no—
456C32×C4#23512yes—
457C32×C4#23512yes—
458C32×C4#23712yes—
459C3⋊Dic3—22no—
460C3⋊Dic3—21no—
461C3⋊Dic3—22no—
462C3⋊Dic3—61no—
463C3⋊Dic3—62no—
464C3⋊Dic3—61no—
465C3⋊Dic3—61no—
466C3⋊Dic3—121no—
467C3⋊Dic3—121no—
468C3⋊Dic3—122no—
469C3⋊Dic3D3×Q812yes—
470C3×Dic3—22no—
471C3×Dic3—21no—
472C3×Dic3—22no—
473C3×Dic3—21no—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3—32no—
477C3×Dic3—32no—
478C3×Dic3—42no—
479C3×Dic3—42no—
480C3×Dic3—41no—
481C3×Dic3—62no—
482C3×Dic3—62no—
483C3×Dic3—61no—
484C3×Dic3—62no—
485C3×Dic3—61no—
486C3×Dic3—62no—
487C3×Dic3—62no—
488C3×Dic3—122no—
489C3×Dic3—121no—
490C3×Dic3—122no—
491C4⋊Q8—271no—
492#125—272no—
493C22⋊Q8—91no—
494C22⋊Q8—272no—
495C22⋊Q8—272no—
496C22⋊Q8—271no—
497C4×Q8—91no—
498C4×D4—272no—
499C4×D4—271no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—271no—
502C33#55411yescharacteristic, complemented, Sylow
503C23×C3—31no—
504C23×C3—31no—
505C23×C3—61no—
506C22×D3—91no—
507C22×D3—91no—
508C22×D3—91no—
509C22×D3—181no—
510C22×D3—181no—
511C22×D3—181no—
512C22×D3—361no—
513C22×D3C2×D3211yescharacteristic
514C3×Q8—62no—
515C3×Q8—62no—
516C3×Q8—122no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—31no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—62no—
529C2×C3×C4—62no—
530C2×C3×C4—62no—
531C2×C3×C4—62no—
532C2×C3×C4—91no—
533C2×C3×C4—92no—
534C2×C3×C4—92no—
535C2×C3×C4—91no—
536C2×C3×C4—122no—
537C2×C3×C4—362no—
538C2×C3×C4C2×D3211yescharacteristic
539C2×C3×C4C2×D3211yescharacteristic
540C2×C3×C4C2×D3211yescharacteristic
541#67—94no—
542#67—94no—
543#67—184no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—32no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—62no—
555C2×Dic3—62no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—122no—
560C2×Dic3—181no—
561C2×Dic3—181no—
562C2×Dic3—181no—
563C2×Dic3—361no—
564C2×Dic3C2×D3212yes—
565C2×Dic3C2×D3212yes—
566C2×Dic3C2×D3211yescharacteristic
567D12—94no—
568C4×D3—22no—
569C4×D3—122no—
570C4×D3—184no—
571C4×D3—182no—
572C4×D3—182no—
573C4×D3—182no—
574C4×D3—362no—
575C4×D3—362no—
576C4×D3—364no—
577C4×D3—362no—
578C4×D3—362no—
579C4×D3—362no—
580C4×D3—364no—
581Dic6—22no—
582Dic6—362no—
583Dic6—362no—
584Dic6—362no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—21no—
591C2×C32—21no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—41no—
595C2×C32—41no—
596C2×C32—41no—
597C2×C32—62no—
598C2×C32C2×#23511yescharacteristic
599C2×C32C2×#23511yescharacteristic
600C2×C32C2×#23711yescharacteristic
601C2×C32#100411yescharacteristic
602C2×C32C2×D3×Q811yescharacteristic
603C2×C32C2×D3×Q811yescharacteristic
604C2×C32C2×D3×Q811yescharacteristic
605C2×C32#100911yescharacteristic
606C2×C32#100911yescharacteristic
607C3⋊D3—62no—
608C3⋊D3—64no—
609C3⋊D3—62no—
610C3⋊D3—62no—
611C3⋊D3—122no—
612C3⋊D3—122no—
613C3⋊D3—124no—
614C3×D3—22no—
615C3×D3—22no—
616C3×D3—42no—
617C2×Q8—31no—
618C2×Q8—272no—
619C2×D4—271no—
620C22×C4—31no—
621C22×C4—92no—
622C22×C4—272no—
623C22×C4—271no—
624C4⋊C4—31no—
625C4⋊C4—92no—
626C4⋊C4—92no—
627C4⋊C4—92no—
628C4⋊C4—91no—
629C4⋊C4—91no—
630C4⋊C4—272no—
631C4⋊C4—271no—
632C4⋊C4—272no—
633C4⋊C4—272no—
634C22⋊C4—92no—
635C22⋊C4—272no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C42—92no—
639C42—91no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—32no—
644C22×C3—32no—
645C22×C3—41no—
646C22×C3—62no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3C22×D3211yescharacteristic
654C22×C3C22×D3211yescharacteristic
655C22×C3C22×D3211yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—92no—
659C2×D3—92no—
660C2×D3—92no—
661C2×D3—182no—
662C2×D3—182no—
663C2×D3—182no—
664C2×D3—182no—
665C2×D3—182no—
666C2×D3—181no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—181no—
670C2×D3—181no—
671C2×D3—181no—
672C2×D3—362no—
673C2×D3—361no—
674C2×D3—361no—
675C2×D3—361no—
676C2×D3—361no—
677C2×D3—362no—
678C2×D3—362no—
679C2×D3#379712yes—
680C3×C4—22no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—42no—
684C3×C4—61no—
685C3×C4—62no—
686C3×C4—62no—
687C3×C4—62no—
688C3×C4—61no—
689C3×C4—62no—
690C3×C4—92no—
691C3×C4—122no—
692C3×C4—121no—
693C3×C4—122no—
694C3×C4—181no—
695C3×C4—182no—
696C3×C4—182no—
697C3×C4#379812yes—
698C3×C4#380412yes—
699C3×C4#380412yes—
700Dic3—22no—
701Dic3—22no—
702Dic3—21no—
703Dic3—32no—
704Dic3—32no—
705Dic3—62no—
706Dic3—62no—
707Dic3—62no—
708Dic3—61no—
709Dic3—62no—
710Dic3—61no—
711Dic3—62no—
712Dic3—122no—
713Dic3—122no—
714Dic3—121no—
715Dic3—182no—
716Dic3—181no—
717Dic3—181no—
718Dic3—181no—
719Dic3—361no—
720Dic3—361no—
721Dic3—362no—
722C32—21no—
723C32—21no—
724C32—21no—
725C32—41no—
726C32#551111yescharacteristic, complemented
727C32#557911yescharacteristic, complemented
728C32#563511yescharacteristic, complemented
729C23—31no—
730C23—271no—
731Q8—62no—
732Q8—1082no—
733D4—274no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—31no—
737C2×C4—62no—
738C2×C4—91no—
739C2×C4—91no—
740C2×C4—92no—
741C2×C4—92no—
742C2×C4—271no—
743C2×C4—362no—
744C2×C4—542no—
745C2×C4—1082no—
746C2×C4D3311yescharacteristic
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—41no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—62no—
760C2×C3—62no—
761C2×C3—122no—
762C2×C3C2×#379711yescharacteristic
763C2×C3C2×#379811yescharacteristic
764C2×C3#6430711yescharacteristic
765C2×C3#6431411yescharacteristic
766C2×C3D32×Q811yescharacteristic
767C2×C3D32×Q811yescharacteristic
768C2×C3#6432011yescharacteristic
769C2×C3C2×#380411yescharacteristic
770C2×C3C2×#380411yescharacteristic
771D3—22no—
772D3—184no—
773D3—182no—
774D3—182no—
775D3—182no—
776D3—362no—
777D3—362no—
778D3—364no—
779C22—32no—
780C22—61no—
781C22—61no—
782C22—272no—
783C22—541no—
784C22—541no—
785C22C2×D3311yescharacteristic
786C4—62no—
787C4—61no—
788C4—62no—
789C4—92no—
790C4—182no—
791C4—182no—
792C4—181no—
793C4—541no—
794C4#8895912yes—
795C3—21no—
796C3—21no—
797C3—21no—
798C3—41no—
799C3#1059453611yescharacteristic, complemented
800C3#1059499111yescharacteristic, complemented
801C3#1059537111yescharacteristic, complemented
802C2—62no—
803C2—542no—
804C2D3×#379711yescharacteristic
805C2#1172438511yescharacteristic
806C2C2×#8895911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6291C22
hypercenterC2×C4D33
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C4⋊#6296C2semidirect
3. #11723503C2semidirect
4. #11723456C2semidirect
5. C3×D3×C4⋊Dic3C2semidirect
6. C3×#63856C2semidirect
7. C3×#63843C2semidirect
8. #11723014C2semidirect
9. #11722982C2semidirect
10. #11722978C2semidirect
62. D3×C4⋊Dic3D3semidirect
70. #63856D3semidirect
73. #63843D3semidirect
89. #6291Q8semidirect
502. C33#554semidirect
726. C32#5511semidirect
727. C32#5579semidirect
728. C32#5635semidirect
799. C3#10594536semidirect
800. C3#10594991semidirect
801. C3#10595371semidirect

Maximal subgroups

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

subgroupindex
C4⋊#62962
C4×#62912
#117235032
#117234562
C3×D3×C4⋊Dic32
C3×#638562
C3×#638432
#117230142
#117229822
#117229782
#117229322
#105953713
#105949913
#105945363