Finite Group Databasebeta

← #11878510

Subgroups — #11878510

Order 1152.

856 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5629C211yesmaximal, characteristic, complemented
2#10595044C211yesmaximal, characteristic, complemented
3#10592743C211yesmaximal, characteristic, complemented
4C3×#5047C211yesmaximal, characteristic, complemented
5#10591635C211yesmaximal, characteristic, complemented
6#10591597C211yesmaximal, characteristic, complemented
7#10591587C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10591161C211yesmaximal, characteristic, complemented
10#10591145C211yesmaximal, characteristic, complemented
11#10591094C211yesmaximal, characteristic, complemented
12#10590517C211yesmaximal, characteristic, complemented
13#10590515C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590498C211yesmaximal, characteristic, complemented
16#83426—31nomaximal
17#80239—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#930C2211yescharacteristic
27C3×#896—21no—
28C3×#895—21no—
29C3×#895C2211yescharacteristic
30C3×D3×C4⋊C4C2211yescharacteristic
31C3×#884—21no—
32C3×#884—21no—
33#63980—21no—
34#63980—21no—
35#63908—21no—
36#63908C2211yescharacteristic
37#63908C2211yescharacteristic
38#63856—21no—
39#63856C2211yescharacteristic
40#63856C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63657C2211yescharacteristic
48#63634C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63565C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#537—31no—
62#5833—31no—
63#5833—31no—
64#5629D311yescharacteristic, complemented
65C3×#452—31no—
66#5239—31no—
67#5238—31no—
68#5238—31no—
69#5234—31no—
70#5188—31no—
71#5187—31no—
72#5174—31no—
73#5172—31no—
74#5051—31no—
75#5049—31no—
76#5047D311yescharacteristic, complemented
77#5044—31no—
78#5044—31no—
79#5044—61no—
80#5042—31no—
81#5038—31no—
82#5037—31no—
83#5033—31no—
84#4970—31no—
85#4967—31no—
86#4812—31no—
87#4811—31no—
88#4775—31no—
89#4774—31no—
90#4736—31no—
91#4727—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C2×C3×#67D411yescharacteristic
99C3×#239—41no—
100C3×#239—41no—
101C3×#235—41no—
102C3×#235—41no—
103C3×#235—41no—
104C3×#235—41no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12D411yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6D411yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#625—21no—
118C2×#625—21no—
119C32×C4⋊C4—21no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C22⋊C4—21no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#216—41no—
128C3×#215—41no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138#3724—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3715—41no—
144#3713—41no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3203—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×C3×#41—31no—
151C2×#239C2×D311yescharacteristic
152C2×#235C2×D311yescharacteristic
153C2×#235C2×D311yescharacteristic
154C2×C3×Q16—31no—
155C2×C3×SD16—31no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8C2×D311yescharacteristic
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×#121—31no—
162C3×#121—31no—
163C3×#121—61no—
164C3×#121—61no—
165C3×#121—61no—
166C2×C3×C4⋊C4—31no—
167#946—31no—
168#946—31no—
169#946—61no—
170#946C2×D311yescharacteristic
171C2×#216C2×D311yescharacteristic
172C2×#215—31no—
173C2×#215C2×D311yescharacteristic
174#939—61no—
175#939—61no—
176#939—61no—
177#939—61no—
178#938—31no—
179#938—31no—
180#938—61no—
181C2×#214—31no—
182C2×#213—31no—
183C2×#213—31no—
184#930—31no—
185#930—31no—
186#930—61no—
187#930C2×D311yescharacteristic
188C2×C4⋊Dic3—31no—
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—61no—
191#924—31no—
192#924—31no—
193#924—61no—
194C2×#208—31no—
195C22×C3⋊C8—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×D3×C8—31no—
198#896—21no—
199#895—21no—
200#895C2×D311yescharacteristic
201D3×C4⋊C4C2×D311yescharacteristic
202#884—21no—
203#884—21no—
204C3×#103—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835—61no—
214#832—31no—
215#832—31no—
216#832—31no—
217#830—31no—
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222#830C2×D311yescharacteristic
223#821—31no—
224#821—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#818—31no—
228#818—31no—
229#810—31no—
230#810C2×D311yescharacteristic
231#809—31no—
232#809C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238#807—31no—
239#807—61no—
240#807—61no—
241C23×C32C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—81no—
257C3×#67—41no—
258C3×#67—41no—
259C3×#67—42no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—41no—
270C3×D12—42no—
271C3×D12—81no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—42no—
277C3×C4×D3—42no—
278C3×C4×D3—81no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3×Dic6—41no—
282#625—81no—
283#625—81no—
284C3⋊(C3⋊C8)—21no—
285C3⋊(C3⋊C8)—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—31no—
289#537—91no—
290#484—91no—
291#484—91no—
292#480—91no—
293#480—91no—
294#468—91no—
295#468—91no—
296#467—91no—
297#466—91no—
298#452—31no—
299#452—91no—
300#449—91no—
301#449—91no—
302#408—91no—
303C3×#41—121no—
304C3×#41—121no—
305C3×#41—121no—
306C3×#41—121no—
307C3×#41—121no—
308C3×#41—121no—
309C2×C3×Q8—21no—
310C2×C3×Q8—31no—
311C2×C3×Q8—31no—
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×Q8C22×D311yescharacteristic
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C22×C3×C4—21no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C2×#67—21no—
332C2×#67—21no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67#6711yescharacteristic
338C2×#67#6711yescharacteristic
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—121no—
342#239—41no—
343#239—41no—
344#235—41no—
345#235—41no—
346#235—41no—
347#235—41no—
348C2×D12—21no—
349C2×D12—21no—
350C2×D12#6711yescharacteristic
351C2×D12C22×D311yescharacteristic
352C2×D12C22×D311yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3C22×D311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6#6711yescharacteristic
359C2×Dic6C22×D311yescharacteristic
360C3×Q16—121no—
361C3×SD16—121no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—41no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—41no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379#217—61no—
380#217—61no—
381#217—61no—
382#217—61no—
383#216—41no—
384#215—41no—
385#215—121no—
386#214—121no—
387#213—121no—
388#213—121no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—121no—
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412#208—121no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—121no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422ΓL(1,𝔽25)—121no—
423D3×C8—121no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32C22×D411yescharacteristic
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C32×C4—21no—
441C32×C4—41no—
442C32×C4—41no—
443C32×C4H(5,𝔽2)11yescharacteristic
444C32×C4H(5,𝔽2)11yescharacteristic
445C3⋊Dic3—41no—
446C3⋊Dic3—41no—
447C3×Dic3—21no—
448C3×Dic3—21no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C2×#41—31no—
452C2×#41—31no—
453C2×#41—31no—
454C2×Q16—31no—
455C2×SD16—31no—
456C2×SD16—91no—
457C2×D8—91no—
458C2×M16—91no—
459C22×C8—91no—
460C22⋊Q8—31no—
461C22⋊Q8—61no—
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464C22⋊Q8—181no—
465C22⋊Q8D3211yescharacteristic
466#121—31no—
467#121—31no—
468#121—61no—
469#121—61no—
470#121—61no—
471#121—91no—
472#121—91no—
473#121—181no—
474#121—181no—
475#121—181no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—91no—
478#107—91no—
479#107—91no—
480#107—91no—
481#107—91no—
482#103—31no—
483#103—91no—
484#103—91no—
485#103—91no—
486#102—31no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—31no—
491C22⋊C8—91no—
492C22⋊C8—91no—
493C22⋊C8—91no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—31no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3D3×D411yescharacteristic
500C23×C3C2×#6711yescharacteristic
501C22×D3—21no—
502C22×D3—21no—
503C22×D3C2×#6711yescharacteristic
504C22×D3C2×#6711yescharacteristic
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×Q8—61no—
512C3×Q8—61no—
513C3×Q8—121no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—121no—
519C3×D4—122no—
520C3×D4—121no—
521C3×D4—121no—
522C3×D4—122no—
523C3×D4—241no—
524C3×D4—241no—
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—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—122no—
548C2×C3×C4—122no—
549C2×C3×C4—241no—
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554#67—41no—
555#67—41no—
556#67—42no—
557#67—81no—
558#67—241no—
559#67—241no—
560#67—241no—
561#67—241no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—121no—
569C2×Dic3—121no—
570C2×Dic3—241no—
571C2×Dic3—241no—
572C2×Dic3—242no—
573C2×Dic3C2×#6711yescharacteristic
574C2×Dic3C2×#6711yescharacteristic
575D12—21no—
576D12—21no—
577D12—21no—
578D12—21no—
579D12—41no—
580D12—42no—
581D12—81no—
582C4×D3—21no—
583C4×D3—21no—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—42no—
587C4×D3—42no—
588C4×D3—81no—
589Dic6—21no—
590Dic6—21no—
591Dic6—41no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—61no—
599C3⋊C8—61no—
600C3⋊C8—121no—
601C3⋊C8—121no—
602C2×C32—41no—
603C2×C32#53411yescharacteristic
604C2×C32#57611yescharacteristic
605C2×C32#57811yescharacteristic
606C3×D3—41no—
607C3×D3—41no—
608C3×D3—81no—
609C3×D3—81no—
610#41—121no—
611#41—121no—
612#41—121no—
613#41—121no—
614#41—121no—
615#41—121no—
616C2×Q8—31no—
617C2×Q8—31no—
618C2×Q8C2×D3211yescharacteristic
619C2×D4—31no—
620C2×D4—31no—
621C2×D4—31no—
622C2×D4—31no—
623C2×D4—31no—
624C2×D4—61no—
625C2×D4—61no—
626C2×D4—61no—
627C2×D4—61no—
628C2×D4—181no—
629C2×D4—181no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—181no—
636C22×C4C2×D3211yescharacteristic
637Q16—121no—
638SD16—121no—
639SD16—361no—
640D8—361no—
641M16—361no—
642C2×C8—31no—
643C2×C8—31no—
644C2×C8—91no—
645C2×C8—91no—
646C2×C8—361no—
647C4⋊C4—21no—
648C4⋊C4—31no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—91no—
652C4⋊C4—91no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4C2×D3211yescharacteristic
657C22⋊C4—21no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22×C3—22no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3C2×D3×D411yescharacteristic
688C22×C3C22×#6711yescharacteristic
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—41no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—81no—
713C3×C4—81no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4#100411yescharacteristic
717C3×C4#100411yescharacteristic
718C3×C4#100411yescharacteristic
719C3×C4#100411yescharacteristic
720Dic3—21no—
721Dic3—21no—
722Dic3—41no—
723Dic3—41no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—121no—
728Dic3—241no—
729Dic3—241no—
730C32#320311yescharacteristic, complemented, Sylow
731C23—31no—
732C23—31no—
733C23—61no—
734C23—61no—
735C23D3×#6711yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—61no—
739Q8—61no—
740Q8—121no—
741D4—61no—
742D4—61no—
743D4—61no—
744D4—61no—
745D4—121no—
746D4—122no—
747D4—121no—
748D4—121no—
749D4—122no—
750D4—241no—
751D4—241no—
752D4—721no—
753D4—721no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—181no—
769C2×C4—181no—
770C2×C4—241no—
771C2×C4—721no—
772C2×C4D3×#6711yescharacteristic
773C2×C4C22×D3211yescharacteristic
774C8—61no—
775C8—61no—
776C8—181no—
777C8—181no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—42no—
782C2×C3—41no—
783C2×C3—41no—
784C2×C3—121no—
785C2×C3—121no—
786C2×C3—241no—
787C2×C3—241no—
788C2×C3#558911yescharacteristic
789C2×C3#576911yescharacteristic
790C2×C3#577911yescharacteristic
791C2×C3#580411yescharacteristic
792C2×C3#583511yescharacteristic
793C2×C3#583811yescharacteristic
794D3—41no—
795D3—41no—
796D3—81no—
797D3—81no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—61no—
802C22—61no—
803C22—61no—
804C22—61no—
805C22—61no—
806C22—61no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22C2×D3×#6711yescharacteristic
814C4—21no—
815C4—41no—
816C4—41no—
817C4—61no—
818C4—61no—
819C4—121no—
820C4—121no—
821C4—361no—
822C4—361no—
823C4#6431311yescharacteristic
824C4#6431311yescharacteristic
825C3—21no—
826C3#8023911yescharacteristic, complemented
827C3#8342611yescharacteristic, complemented
828C2—41no—
829C2—121no—
830C2—121no—
831C2—241no—
832C2—241no—
833C2#1059523011yescharacteristic
834C2#1059532811yescharacteristic
835C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3203
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5629C2semidirect
2. #10595044C2semidirect
3. #10592743C2semidirect
4. C3×#5047C2semidirect
5. #10591635C2semidirect
6. #10591597C2semidirect
7. #10591587C2semidirect
8. #10591586C2semidirect
9. #10591161C2semidirect
10. #10591145C2semidirect
11. #10591094C2semidirect
12. #10590517C2semidirect
13. #10590515C2semidirect
14. #10590499C2semidirect
15. #10590498C2semidirect
64. #5629D3semidirect
76. #5047D3semidirect
730. C32#3203semidirect
826. C3#80239semidirect
827. C3#83426semidirect

Maximal subgroups

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

subgroupindex
C3×#56292
#105950442
#105927432
C3×#50472
#105916352
#105915972
#105915872
#105915862
#105911612
#105911452
#105910942
#105905172
#105905152
#105904992
#105904982
#834263
#802393