Finite Group Databasebeta

← #33093090

Subgroups — #33093090

Order 18688.

1060 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988902C211yesmaximal, characteristic
2#22612439C211yesmaximal, characteristic
3C4×C4⋊C4×D73C211yesmaximal, characteristic, complemented
4#22610552C211yesmaximal, characteristic, complemented
5#22610551C211yesmaximal, characteristic, complemented
6#22610499C211yesmaximal, characteristic, complemented
7#22610247C211yesmaximal, characteristic
8#22610120C211yesmaximal, characteristic, complemented
9#22610016C211yesmaximal, characteristic, complemented
10#107×Dic73C211yesmaximal, characteristic, complemented
11#22609823C211yesmaximal, characteristic, complemented
12#22609745C211yesmaximal, characteristic, complemented
13#22609745C211yesmaximal, characteristic, complemented
14#22609688C211yesmaximal, characteristic, complemented
15C73×#1918C211yesmaximal, characteristic, complemented
16C2×#14556566C2211yescharacteristic
17C2×#14556553—21no—
18C2×#14556553C2211yescharacteristic
19C2×C4⋊C4×D73C2211yescharacteristic
20C2×C4⋊C4×D73C2211yescharacteristic
21C2×C42×D73—21no—
22C2×C42×D73C2211yescharacteristic
23#17988902C418yescomplemented
24C2×#14556525C2211yescharacteristic
25C2×#14556524C2211yescharacteristic
26C2×#14556524C2211yescharacteristic
27C2×#14556513C2211yescharacteristic
28C2×#14556513C2211yescharacteristic
29C2×#14556511C2211yescharacteristic
30C2×#14556511C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34C2×C8×Dic73C2211yescharacteristic
35#17988489C2211yescharacteristic
36#17988477—21no—
37#17988465—21no—
38#17988444C2211yescharacteristic
39C4⋊C4×Dic73C2211yescharacteristic
40C4⋊C4×Dic73C2211yescharacteristic
41C4⋊C4×Dic73C2211yescharacteristic
42C4×#11924007—21no—
43C4×C4⋊Dic73C2211yescharacteristic
44#17988438—21no—
45#17988434—21no—
46#95×D73—21no—
47#17988350C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988342C2211yescharacteristic
53C2×#107×C73C2211yescharacteristic
54#389×C73C2211yescharacteristic
55C4×C4⋊C4×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C22×D292—21no—
61C22×D292C2311yescharacteristic
62C22×C4×D73—21no—
63C22×C4×D73—21no—
64C22×C4×D73—21no—
65C22×C4×D73D411yescharacteristic
66C22×C4×D73D411yescharacteristic
67C22×C4×D73C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70#14556566—22no—
71#14556566C2×C414yes—
72#14556553—22no—
73#14556553—22no—
74#14556553—44no—
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
78C2×#11924007—21no—
79C2×#11924007—21no—
80C4⋊C4×D73—22no—
81C4⋊C4×D73—22no—
82C4⋊C4×D73—22no—
83C4⋊C4×D73C2×C414yescomplemented
84C2×#11924005—21no—
85C2×#11924005—21no—
86C2×#11924005—21no—
87C2×#11924005—21no—
88C2×#11924005—21no—
89C2×C4×Dic73—21no—
90C2×C4×Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93C2×C4×Dic73D411yescharacteristic
94C2×C4×Dic73D411yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C42×D73—22no—
97C42×D73—22no—
98C42×D73—44no—
99#14556525—22no—
100#14556524—22no—
101#14556524C2×C414yescomplemented
102#14556513—22no—
103#14556513C2×C414yescomplemented
104#14556511—22no—
105#14556511C2×C414yescomplemented
106#14556503—22no—
107#14556503C2×C414yescomplemented
108C8×Dic73—22no—
109C8×Dic73—22no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498—21no—
114#14556498—21no—
115C22×C8×C73C2311yescharacteristic
116C22×C8×C73C2311yescharacteristic
117C2×C4⋊C4×C73—21no—
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C42×C73—21no—
123C2×C42×C73C2311yescharacteristic
124#107×C73C2×C414yescomplemented
125#95×C73—21no—
126#95×C73—21no—
127C23×D73—21no—
128C23×D73C2×D411yescharacteristic
129C2×D292—21no—
130C2×D292—21no—
131C2×D292—21no—
132C2×D292—21no—
133C2×D292—24no—
134C2×D292—21no—
135C2×D292—42no—
136C2×D292—42no—
137C2×D292C22×C412yes—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73C2×D411yescharacteristic
142C22×Dic73C2×D411yescharacteristic
143C22×Dic73C2×D411yescharacteristic
144C2×C4×D73—21no—
145C2×C4×D73—21no—
146C2×C4×D73—21no—
147C2×C4×D73—21no—
148C2×C4×D73—22no—
149C2×C4×D73—22no—
150C2×C4×D73—24no—
151C2×C4×D73—24no—
152C2×C4×D73—22no—
153C2×C4×D73—22no—
154C2×C4×D73—41no—
155C2×C4×D73—42no—
156C2×C4×D73—42no—
157C2×C4×D73—42no—
158C2×C4×D73—42no—
159C2×C4×D73—42no—
160C2×C4×D73—42no—
161C2×C4×D73—42no—
162C2×C4×D73D814yes—
163C2×C4×D73C22×C412yes—
164C2×C4×D73#4112yes—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831C22×C412yes—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73C22×C412yes—
176C4⋊Dic73#4112yes—
177#11924007—24no—
178#11924007—24no—
179#11924005—24no—
180#11924005—42no—
181#11924005—42no—
182#11924005—42no—
183#11924005—42no—
184C4×Dic73—22no—
185C4×Dic73—22no—
186C4×Dic73—42no—
187C4×Dic73—42no—
188C4×Dic73—42no—
189C4×Dic73—42no—
190C4×Dic73#4112yes—
191C4×Dic73#4112yes—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2411yescharacteristic
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73C22×C412yes—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—42no—
211C4⋊C4×C73C22×C412yes—
212C4⋊C4×C73C22×C412yes—
213C4⋊C4×C73#4112yes—
214C42×C73—21no—
215C42×C73—21no—
216C42×C73—42no—
217C23×C73C22×D411yescharacteristic
218C22×D73—21no—
219C22×D73—21no—
220C22×D73—21no—
221C22×D73—21no—
222C22×D73—22no—
223C22×D73—41no—
224C22×D73—41no—
225C22×D73—41no—
226C22×D73—41no—
227C22×D73—41no—
228C22×D73—41no—
229C22×D73C4×D412yes—
230C22×D73C2×D812yes—
231C22×D73#13512yes—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—22no—
235C2×C4×C73—22no—
236C2×C4×C73—21no—
237C2×C4×C73—22no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73C2×D812yes—
250C2×C4×C73C23×C411yescharacteristic
251C2×C4×C73C2×#4111yescharacteristic
252C2×C4×C73C2×#4111yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73C2×#4111yescharacteristic
255C2×C4×C73C2×#4111yescharacteristic
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—22no—
261C2×Dic73—22no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267C2×Dic73—41no—
268C2×Dic73—41no—
269C2×Dic73C4×D412yes—
270C2×Dic73#12312yes—
271C2×Dic73#12312yes—
272C2×Dic73C2×D812yes—
273C2×Dic73#13712yes—
274D292—22no—
275D292—22no—
276D292—48no—
277D292—41no—
278D292—41no—
279C4×D73—22no—
280C4×D73—22no—
281C4×D73—22no—
282C4×D73—22no—
283C4×D73—28no—
284C4×D73—44no—
285C4×D73—48no—
286C4×D73—48no—
287C4×D73—84no—
288C8×C73—22no—
289C8×C73—41no—
290#10596831—22no—
291#10596831—41no—
292C22×C73C2×C4×D411yescharacteristic
293C22×C73C2×#12311yescharacteristic
294C22×C73#52511yescharacteristic
295C22×C73C22×D811yescharacteristic
296C22×C73C2×#13511yescharacteristic
297C22×C73C2×#13711yescharacteristic
298C22×C73#57511yescharacteristic
299C2×D73—22no—
300C2×D73—22no—
301C2×D73—22no—
302C2×D73—22no—
303C2×D73—22no—
304C2×D73—22no—
305C2×D73—42no—
306C2×D73—42no—
307C2×D73—42no—
308C2×D73—81no—
309C2×D73—81no—
310C2×D73—81no—
311C2×D73—81no—
312C2×D73C4×D814yes—
313C4×C73—22no—
314C4×C73—41no—
315C4×C73—42no—
316C4×C73—42no—
317C4×C73—42no—
318C4×C73—81no—
319C4×C73C4×#4111yescharacteristic
320C4×C73C4×#4111yescharacteristic
321C4×C73#52911yescharacteristic
322C4×C73#52911yescharacteristic
323Dic73—22no—
324Dic73—22no—
325Dic73—42no—
326Dic73—42no—
327Dic73—81no—
328Dic73#48014yescomplemented
329C4×#480—731nomaximal, Sylow
330C2×C73C4×#12311yescharacteristic
331C2×C73C2×C4×D811yescharacteristic
332C2×C73C4×#13711yescharacteristic
333C2×C73C2×#48011yescharacteristic
334C2×C73#309111yescharacteristic
335C2×C73#310011yescharacteristic
336C2×C73#310811yescharacteristic
337D73—24no—
338D73—82no—
339C2×#480—731no—
340C4×#121—731no—
341C2×C4×C4⋊C4—731no—
342#1925—731no—
343#1925—731no—
344#1918—731no—
345#1918D7311yescharacteristic, complemented
346#1874—731no—
347#1852—731no—
348#1823—731no—
349C4×#107—731no—
350C4×#107—731no—
351C4×#102—731no—
352C4×#102—731no—
353C4×C22⋊C8—731no—
354C73C4×#48011yescharacteristic, complemented, Sylow
355C2×#121—731no—
356C2×C4×D4—731no—
357C2×C4×D4—1461no—
358C22×C4⋊C4—731no—
359C22×C4⋊C4—731no—
360C22×C42—731no—
361C22×C42—1461no—
362#480—738no—
363C2×#107—731no—
364C2×#107—731no—
365C2×#107—731no—
366C2×#107C2×D7311yescharacteristic
367C2×#102—731no—
368C2×#102—731no—
369C2×#102—731no—
370C2×#102—731no—
371C2×C22⋊C8—731no—
372C2×C22⋊C8—731no—
373C2×C4×C8—731no—
374C2×C4×C8—731no—
375#390—731no—
376#389C2×D7311yescharacteristic
377#388—1461no—
378#386—1461no—
379#380—731no—
380C4×C4⋊C4—731no—
381C4×C4⋊C4—731no—
382C4×C4⋊C4—731no—
383C4×C4⋊C4—731no—
384C4×C4⋊C4—1461no—
385C4×C4⋊C4—1461no—
386C4×C4⋊C4C2×D7311yescharacteristic
387C4×C22⋊C4—1461no—
388C2×#95—1461no—
389#340—731no—
390#340—731no—
391#340—731no—
392#340—731no—
393#340—731no—
394#340C2×D7311yescharacteristic
395#340C2×D7311yescharacteristic
396#340C2×D7311yescharacteristic
397#336—731no—
398#336C2×D7311yescharacteristic
399C22×D4—731no—
400C22×D4—1461no—
401C23×C4—731no—
402C23×C4—731no—
403C23×C4—731no—
404C23×C4—1461no—
405C23×C4—1461no—
406C23×C4—1461no—
407C22×C8—731no—
408C22×C8—731no—
409C22×C8C22×D7311yescharacteristic
410C22×C8C22×D7311yescharacteristic
411#121—734no—
412#121—1462no—
413C4×D4—2924no—
414C4×D4—1462no—
415C4×D4—1462no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—731no—
418C2×C4⋊C4—731no—
419C2×C4⋊C4—734no—
420C2×C4⋊C4—731no—
421C2×C4⋊C4—1462no—
422C2×C4⋊C4—1462no—
423C2×C4⋊C4—1461no—
424C2×C4⋊C4—1461no—
425C2×C4⋊C4—1462no—
426C2×C4⋊C4C22×D7311yescharacteristic
427C2×C4⋊C4C22×D7311yescharacteristic
428C2×C4⋊C4C22×D7311yescharacteristic
429C2×C4⋊C4C22×D7311yescharacteristic
430C2×C22⋊C4—1461no—
431C2×C22⋊C4—1461no—
432C2×C22⋊C4—1461no—
433C2×C22⋊C4—1461no—
434C2×C22⋊C4—1461no—
435C2×C42—21no—
436C2×C42—2924no—
437C2×C42—731no—
438C2×C42—731no—
439C2×C42—731no—
440C2×C42—1462no—
441C2×C42—1462no—
442C2×C42—1461no—
443C2×C42—1461no—
444C2×C42—1461no—
445C2×C42—1461no—
446C2×C42C22×D7311yescharacteristic
447#107—734no—
448#107—1462no—
449#107—1462no—
450#107C4×D7314yescomplemented
451#102—734no—
452#102—734no—
453#102—1462no—
454#102—1462no—
455C22⋊C8—734no—
456C22⋊C8—1462no—
457C4×C8—1462no—
458C4×C8—1462no—
459#95—21no—
460#95—21no—
461#95—1461no—
462#95—1461no—
463#95—1461no—
464#95—1461no—
465#95—1461no—
466C24—731no—
467C24—1461no—
468C2×D4—2922no—
469C2×D4—2922no—
470C2×D4—732no—
471C2×D4—1464no—
472C2×D4—1461no—
473C2×D4—1461no—
474C2×D4—1461no—
475C2×D4—1461no—
476C2×D4—1461no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—2921no—
482C22×C4—2922no—
483C22×C4—2922no—
484C22×C4—2922no—
485C22×C4—2922no—
486C22×C4—2922no—
487C22×C4—2922no—
488C22×C4—2922no—
489C22×C4—731no—
490C22×C4—731no—
491C22×C4—731no—
492C22×C4—734no—
493C22×C4—732no—
494C22×C4—732no—
495C22×C4—1462no—
496C22×C4—1464no—
497C22×C4—1462no—
498C22×C4—1464no—
499C22×C4—1462no—
500C22×C4—1462no—
501C22×C4—1461no—
502C22×C4—1461no—
503C22×C4—1461no—
504C22×C4—1461no—
505C22×C4—1461no—
506C22×C4—1461no—
507C22×C4—1461no—
508C22×C4D4×D7311yescharacteristic
509C22×C4D4×D7311yescharacteristic
510C22×C4C23×D7311yescharacteristic
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—732no—
517C2×C8—1461no—
518C2×C8—1461no—
519C2×C8—1461no—
520C2×C8—1461no—
521C2×C8—1461no—
522C2×C8C2×C4×D7312yes—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—732no—
530C4⋊C4—732no—
531C4⋊C4—1464no—
532C4⋊C4—1464no—
533C4⋊C4—1461no—
534C4⋊C4—1461no—
535C4⋊C4—1461no—
536C4⋊C4—1461no—
537C4⋊C4C2×C4×D7312yes—
538C4⋊C4C2×C4×D7312yes—
539C4⋊C4#1192402912yes—
540C22⋊C4—2922no—
541C22⋊C4—2922no—
542C22⋊C4—2922no—
543C22⋊C4—2922no—
544C22⋊C4—1464no—
545C42—21no—
546C42—21no—
547C42—42no—
548C42—2922no—
549C42—2922no—
550C42—2922no—
551C42—2922no—
552C42—732no—
553C42—732no—
554C42—1462no—
555C42—1462no—
556C23—2921no—
557C23—2921no—
558C23—2921no—
559C23—2921no—
560C23—2921no—
561C23—2921no—
562C23—732no—
563C23—732no—
564C23—732no—
565C23—1462no—
566C23—1461no—
567C23—1461no—
568C23—1461no—
569C23—1461no—
570C23C2×D4×D7311yescharacteristic
571D4—2928no—
572D4—2921no—
573D4—2921no—
574D4—1462no—
575D4—1462no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—2928no—
594C2×C4—2928no—
595C2×C4—2924no—
596C2×C4—2921no—
597C2×C4—2921no—
598C2×C4—2921no—
599C2×C4—2921no—
600C2×C4—2921no—
601C2×C4—2921no—
602C2×C4—2921no—
603C2×C4—5844no—
604C2×C4—732no—
605C2×C4—732no—
606C2×C4—732no—
607C2×C4—732no—
608C2×C4—732no—
609C2×C4—1468no—
610C2×C4—1462no—
611C2×C4—1462no—
612C2×C4—1461no—
613C2×C4—1461no—
614C2×C4—1461no—
615C2×C4—1461no—
616C2×C4—1462no—
617C2×C4—1462no—
618C2×C4—1462no—
619C2×C4—1462no—
620C2×C4D8×D7312yes—
621C2×C4C22×C4×D7311yescharacteristic
622C2×C4#41×D7311yescharacteristic
623C2×C4#41×D7311yescharacteristic
624C2×C4#41×D7311yescharacteristic
625C2×C4#41×D7311yescharacteristic
626C2×C4C2×#1192402911yescharacteristic
627C8—22no—
628C8—41no—
629C8—2921no—
630C8—1462no—
631C22—2922no—
632C22—2922no—
633C22—2922no—
634C22—5841no—
635C22—5841no—
636C22—5841no—
637C22—5841no—
638C22—734no—
639C22—1462no—
640C22—1462no—
641C22—1462no—
642C22—1462no—
643C22—1462no—
644C22—1462no—
645C22C4×D4×D7311yescharacteristic
646C22#123×D7311yescharacteristic
647C22#1798910011yescharacteristic
648C22C2×D8×D7311yescharacteristic
649C22#135×D7311yescharacteristic
650C22#137×D7311yescharacteristic
651C22#1798938611yescharacteristic
652C4—22no—
653C4—42no—
654C4—42no—
655C4—42no—
656C4—41no—
657C4—81no—
658C4—2922no—
659C4—2922no—
660C4—5841no—
661C4—734no—
662C4—1462no—
663C4—1462no—
664C4#1798905511yescharacteristic
665C4C4×#1192402911yescharacteristic
666C4#1798912011yescharacteristic
667C4#1798912211yescharacteristic
668C2—5842no—
669C2—1464no—
670C2#2261245211yescharacteristic
671C2C4×D8×D7311yescharacteristic
672C2#2261874711yescharacteristic
673C2#480×D7311yescharacteristic
674C2#2261984911yescharacteristic
675C2#2261993311yescharacteristic
676C2#2262001611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1918C2
socleC23×C73C22×D4
prime radicalC2×#14556566C22
cosocleC22×C4×C73C24
hypercenter#1918D73
hypocenterC73C4×#480
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
3. C4×C4⋊C4×D73C2semidirect
4. #22610552C2semidirect
5. #22610551C2semidirect
6. #22610499C2semidirect
8. #22610120C2semidirect
9. #22610016C2semidirect
10. #107×Dic73C2semidirect
11. #22609823C2semidirect
12. #22609745C2semidirect
13. #22609745C2semidirect
14. #22609688C2semidirect
15. C73×#1918C2semidirect
23. #17988902C4semidirect
83. C4⋊C4×D73C2×C4semidirect
101. #14556524C2×C4semidirect
103. #14556513C2×C4semidirect
105. #14556511C2×C4semidirect
107. #14556503C2×C4semidirect
124. #107×C73C2×C4semidirect
328. Dic73#480semidirect
345. #1918D73semidirect
354. C73C4×#480semidirect
450. #107C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179889022
#226124392
C4×C4⋊C4×D732
#226105522
#226105512
#226104992
#226102472
#226101202
#226100162
#107×Dic732
#226098232
#226097452
#226096882
C73×#19182
C4×#48073