Finite Group Databasebeta

← #13277281

Subgroups — #13277281

Order 1792.

2358 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#124C211yesmaximal, characteristic
2C22×Q8×Dic7C211yesmaximal, characteristic, complemented
3C2×#90002C211yesmaximal, characteristic, complemented
4C2×#89993C211yesmaximal, characteristic
5C2×#89993C211yesmaximal, characteristic
6#11729300C214yesmaximal, complemented
7#11729299C214yesmaximal, complemented
8#11729289C211yesmaximal, characteristic, complemented
9C4×C7⋊#95C211yesmaximal, characteristic, complemented
10C23×C7×Q8C2211yescharacteristic
11C23×C7×D4C2211yescharacteristic
12C2×C7×#124—24no—
13C2×C7×#124—24no—
14C2×C7×#124C418yescomplemented
15C22×C7×C22⋊C4C2214yes—
16C22×C42×C7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2214yes—
19C22×C22⋊Dic7C2212yes—
20C2×Q8×Dic7—24no—
21C2×Q8×Dic7—24no—
22C2×Q8×Dic7—24no—
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2212yes—
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2212yes—
28C22×C4×Dic7C2211yescharacteristic
29#90002—24no—
30#89993—24no—
31#89993—24no—
32C2×C7⋊#95C2214yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2214yes—
36#14026—71nomaximal, Sylow
37C25×C7C2312yes—
38C22×C7×Q8—22no—
39C22×C7×Q8—22no—
40C22×C7×Q8—22no—
41C22×C7×Q8—22no—
42C22×C7×Q8C2×C414yes—
43C22×C7×Q8D414yes—
44C22×C7×Q8D414yes—
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4C2×C414yes—
52C23×C4×C7C2312yes—
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C23×Dic7C2312yes—
56C23×Dic7C2311yescharacteristic
57C23×Dic7C2312yes—
58C23×Dic7C2312yes—
59C23×Dic7C2311yescharacteristic
60C7×#124—232no—
61C2×C7×C22⋊C4—28no—
62C2×C7×C22⋊C4—28no—
63C2×C7×C22⋊C4C2×C4116yes—
64C2×C42×C7—22no—
65C2×C42×C7—22no—
66C2×C42×C7C2×C414yes—
67C2×C22⋊Dic7—28no—
68C2×C22⋊Dic7—24no—
69C2×C22⋊Dic7—24no—
70C2×C22⋊Dic7—28no—
71C2×C22⋊Dic7—28no—
72C2×C22⋊Dic7—44no—
73C2×C22⋊Dic7—44no—
74Q8×Dic7—232no—
75C2×C4⋊Dic7—24no—
76C2×C4⋊Dic7—22no—
77C2×C4⋊Dic7—22no—
78C2×C4⋊Dic7—24no—
79C2×C4⋊Dic7—24no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7D414yes—
84C2×C4×Dic7—24no—
85C2×C4×Dic7—22no—
86C2×C4×Dic7—22no—
87C2×C4×Dic7—24no—
88C2×C4×Dic7—24no—
89C2×C4×Dic7—22no—
90C2×C4×Dic7—22no—
91C2×C4×Dic7—22no—
92C2×C4×Dic7D414yes—
93C7⋊#95—28no—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—44no—
97C22×#124D711yescharacteristic
98C22×C4×Q8—71no—
99C2×#391—71no—
100C2×#390—71no—
101C2×#390—71no—
102#1439—74no—
103#1437—74no—
104C4⋊#95—71no—
105C4×#95—71no—
106C24×C7—22no—
107C24×C7—22no—
108C24×C7—22no—
109C24×C7—22no—
110C24×C7—24no—
111C24×C7—24no—
112C24×C7—22no—
113C24×C7—22no—
114C24×C7—24no—
115C24×C7—24no—
116C24×C7C22×C414yes—
117C24×C7C2411yescharacteristic
118C2×C7×Q8—28no—
119C2×C7×Q8—28no—
120C2×C7×Q8—28no—
121C2×C7×Q8—28no—
122C2×C7×Q8—28no—
123C2×C7×Q8—28no—
124C2×C7×Q8C22⋊C4116yescomplemented
125C2×C7×D4—28no—
126C2×C7×D4—28no—
127C2×C7×D4—28no—
128C2×C7×D4—44no—
129C2×C7×D4—44no—
130C2×C7×D4—44no—
131C2×C7×D4—44no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7C22×C414yes—
143C22×C4×C7C22×C414yes—
144C22×C4×C7C22×C412yes—
145C22×C4×C7C2×D414yes—
146C22×C4×C7C2×D414yes—
147C22×C4×C7C2×D412yes—
148C22×C4×C7C2×D412yes—
149C22×C4×C7C2×D412yes—
150C22×C4×C7C2×D412yes—
151C22×C4×C7#4112yes—
152C22×C4×C7#4112yes—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—21no—
159C22×Dic7—22no—
160C22×Dic7—21no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—24no—
166C22×Dic7—24no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—24no—
174C22×Dic7—24no—
175C22×Dic7C2×D414yes—
176C22×Dic7C2×D412yes—
177C22×Dic7C2×D412yes—
178C22×Dic7#4114yes—
179C22×Dic7#4114yes—
180C7×C22⋊C4—232no—
181C42×C7—28no—
182C22⋊Dic7—416no—
183C22⋊Dic7—48no—
184C22⋊Dic7—48no—
185C4⋊Dic7—216no—
186C4⋊Dic7—28no—
187C4⋊Dic7—44no—
188C4×Dic7—216no—
189C4×Dic7—28no—
190C4×Dic7—44no—
191C23×Q8C2×D711yescharacteristic
192C23×D4C2×D711yescharacteristic
193C2×#124—24no—
194C2×#124—24no—
195C2×#124Dic718yescomplemented
196C2×C4×Q8—144no—
197C2×C4×Q8—144no—
198C2×C4×Q8—144no—
199C22×C4⋊C4—71no—
200C22×C4⋊C4—72no—
201C22×C4⋊C4—71no—
202C22×C22⋊C4—72no—
203C22×C22⋊C4—74no—
204C22×C22⋊C4—72no—
205C22×C22⋊C4C2×D714yes—
206C22×C42—71no—
207C22×C42—72no—
208C22×C42—71no—
209C22×C42C2×D711yescharacteristic
210#391—144no—
211#390—144no—
212#390—144no—
213C2×#95—72no—
214C2×#95—72no—
215C2×#95—74no—
216C2×#95—74no—
217C23×C7—24no—
218C23×C7—24no—
219C23×C7—24no—
220C23×C7—28no—
221C23×C7—28no—
222C23×C7—42no—
223C23×C7—42no—
224C23×C7—42no—
225C23×C7—42no—
226C23×C7—42no—
227C23×C7—44no—
228C23×C7—42no—
229C23×C7—42no—
230C23×C7—42no—
231C23×C7—44no—
232C23×C7—44no—
233C23×C7—44no—
234C23×C7—44no—
235C23×C7—44no—
236C23×C7—44no—
237C23×C7—44no—
238C23×C7—44no—
239C23×C7—44no—
240C23×C7C23×C411yescharacteristic
241C23×C7C22×D411yescharacteristic
242C23×C7C22×D411yescharacteristic
243C23×C7C22×D411yescharacteristic
244C23×C7C22×D411yescharacteristic
245C23×C7C2×#4111yescharacteristic
246C23×C7C2×#4111yescharacteristic
247C23×C7C2×#4112yes—
248C23×C7C2×#4112yes—
249C23×C7H(5,𝔽2)12yes—
250C23×C72−1+412yes—
251C7×Q8—232no—
252C7×D4—416no—
253C2×C4×C7—24no—
254C2×C4×C7—24no—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—24no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
261C2×C4×C7—24no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7C2×C22⋊C418yes—
267C2×C4×C7C2×C22⋊C414yes—
268C2×C4×C7C4×D414yes—
269C2×C4×C7C4×D414yes—
270C2×C4×C7#12014yes—
271C2×C4×C7#12114yes—
272C2×C4×C7#12114yes—
273C2×C4×C7#12314yes—
274C2×Dic7—22no—
275C2×Dic7—22no—
276C2×Dic7—24no—
277C2×Dic7—24no—
278C2×Dic7—24no—
279C2×Dic7—22no—
280C2×Dic7—24no—
281C2×Dic7—22no—
282C2×Dic7—22no—
283C2×Dic7—24no—
284C2×Dic7—28no—
285C2×Dic7—24no—
286C2×Dic7—42no—
287C2×Dic7—42no—
288C2×Dic7—42no—
289C2×Dic7—42no—
290C2×Dic7—42no—
291C2×Dic7—42no—
292C2×Dic7—42no—
293C2×Dic7—42no—
294C2×Dic7—44no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7—42no—
298C2×Dic7—44no—
299C2×Dic7—44no—
300C2×Dic7#12414yescomplemented
301C25C22×D712yes—
302C22×Q8—22no—
303C22×Q8—22no—
304C22×Q8—22no—
305C22×Q8—22no—
306C22×Q8C2×Dic714yes—
307C22×Q8C22⋊D714yes—
308C22×Q8C22⋊D714yes—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4C2×Dic714yes—
316C23×C4—71no—
317C23×C4—71no—
318C23×C4—72no—
319C23×C4—72no—
320C23×C4—72no—
321C23×C4C22×D712yes—
322C23×C4C22×D712yes—
323C23×C4C22×D711yescharacteristic
324#124—232no—
325C4×Q8—1432no—
326C2×C4⋊C4—74no—
327C2×C4⋊C4—144no—
328C2×C4⋊C4—144no—
329C2×C4⋊C4—142no—
330C2×C4⋊C4—144no—
331C2×C4⋊C4—142no—
332C2×C4⋊C4—142no—
333C2×C4⋊C4—142no—
334C2×C4⋊C4—142no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—148no—
338C2×C22⋊C4—148no—
339C2×C22⋊C4—144no—
340C2×C22⋊C4—148no—
341C2×C22⋊C4—144no—
342C2×C22⋊C4—284no—
343C2×C22⋊C4—284no—
344C2×C22⋊C4C2×Dic7116yes—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—74no—
348C2×C42—144no—
349C2×C42—144no—
350C2×C42—142no—
351C2×C42—144no—
352C2×C42—142no—
353C2×C42—142no—
354C2×C42—142no—
355C2×C42—142no—
356C2×C42C2×Dic714yes—
357#95—144no—
358#95—144no—
359#95—148no—
360#95—284no—
361C22×C7—44no—
362C22×C7—48no—
363C22×C7—48no—
364C22×C7—44no—
365C22×C7—44no—
366C22×C7—84no—
367C22×C7—82no—
368C22×C7—82no—
369C22×C7—84no—
370C22×C7—82no—
371C22×C7—82no—
372C22×C7C22×C22⋊C411yescharacteristic
373C22×C7C2×C4×D411yescharacteristic
374C22×C7C2×C4×D411yescharacteristic
375C22×C7C4×#4112yes—
376C22×C7#52012yes—
377C22×C7C2×#12011yescharacteristic
378C22×C7C2×#12111yescharacteristic
379C22×C7C2×#12111yescharacteristic
380C22×C7C2×#12311yescharacteristic
381C22×C7C2×#12411yescharacteristic
382C22×C7#52912yes—
383C22×C7#53211yescharacteristic
384C22×C7#53511yescharacteristic
385C22×C7#53611yescharacteristic
386C22×C7#54212yes—
387C22×C7#54612yes—
388C22×C7#54812yes—
389C22×C7#54812yes—
390C22×C7#54812yes—
391C22×C7#55012yes—
392C22×C7#55012yes—
393C22×C7#55612yes—
394C22×C7#55912yes—
395C4×C7—28no—
396C4×C7—44no—
397C4×C7#38618yes—
398Dic7—24no—
399Dic7—44no—
400Dic7—42no—
401Dic7—44no—
402Dic7—82no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—24no—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—22no—
412C24—22no—
413C24C22×Dic714yes—
414C24C23×D711yescharacteristic
415C2×Q8—28no—
416C2×Q8—28no—
417C2×Q8—28no—
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—28no—
421C2×Q8C22⋊Dic7116yescomplemented
422C2×D4—28no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—44no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—72no—
440C22×C4—74no—
441C22×C4—72no—
442C22×C4—74no—
443C22×C4—74no—
444C22×C4—141no—
445C22×C4—142no—
446C22×C4—141no—
447C22×C4—142no—
448C22×C4—142no—
449C22×C4—141no—
450C22×C4—142no—
451C22×C4—142no—
452C22×C4—142no—
453C22×C4—144no—
454C22×C4—144no—
455C22×C4—142no—
456C22×C4—142no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—141no—
461C22×C4—142no—
462C22×C4—142no—
463C22×C4—144no—
464C22×C4—144no—
465C22×C4—142no—
466C22×C4D4×D712yes—
467C22×C4D4×D712yes—
468C22×C4#115912yes—
469C22×C4#115912yes—
470C22×C4C22×Dic714yes—
471C22×C4C22×Dic714yes—
472C22×C4C22×Dic712yes—
473C22×C4C2×C22⋊D714yes—
474C22×C4C2×C22⋊D714yes—
475C22×C4C2×C22⋊D712yes—
476C22×C4C2×C22⋊D712yes—
477C4⋊C4—1416no—
478C4⋊C4—148no—
479C4⋊C4—284no—
480C22⋊C4—232no—
481C22⋊C4—288no—
482C22⋊C4—2816no—
483C22⋊C4—288no—
484C42—28no—
485C42—1416no—
486C42—148no—
487C42—284no—
488C2×C7—84no—
489C2×C7C2×#38611yescharacteristic
490C2×C7C4×#12411yescharacteristic
491C2×C7#232611yescharacteristic
492C2×C7#234112yes—
493C2×C7#236712yes—
494C2×C7#242612yes—
495C2×C7#243111yescharacteristic
496C2×C7#243611yescharacteristic
497C2×C7#244812yes—
498C2×C7#254511yescharacteristic
499C2×C7#254811yescharacteristic
500C23—24no—
501C23—24no—
502C23—28no—
503C23—28no—
504C23—24no—
505C23—44no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—44no—
514C23—44no—
515C23—44no—
516C23—44no—
517C23—42no—
518C23—44no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—44no—
523C23C2×D4×D711yescharacteristic
524C23C2×D4×D711yescharacteristic
525C23C2×#115911yescharacteristic
526C23C2×#115911yescharacteristic
527C23D7×#4112yes—
528C23D7×#4112yes—
529C23#655312yes—
530C23#655412yes—
531C23C23×Dic711yescharacteristic
532C23C22×C22⋊D711yescharacteristic
533C23C22×C22⋊D711yescharacteristic
534Q8—232no—
535D4—416no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—74no—
550C2×C4—144no—
551C2×C4—142no—
552C2×C4—144no—
553C2×C4—142no—
554C2×C4—144no—
555C2×C4—144no—
556C2×C4—142no—
557C2×C4—144no—
558C2×C4—142no—
559C2×C4—142no—
560C2×C4—144no—
561C2×C4—148no—
562C2×C4—282no—
563C2×C4—282no—
564C2×C4—282no—
565C2×C4—282no—
566C2×C4—282no—
567C2×C4—284no—
568C2×C4—282no—
569C2×C4—282no—
570C2×C4—282no—
571C2×C4—284no—
572C2×C4—282no—
573C2×C4—284no—
574C2×C4—282no—
575C2×C4—282no—
576C2×C4D4×Dic714yes—
577C2×C4D4×Dic714yes—
578C2×C4#649814yes—
579C2×C4#650014yes—
580C2×C4#650214yes—
581C2×C4#650214yes—
582C2×C4C2×C22⋊Dic718yes—
583C2×C4C2×C22⋊Dic714yes—
584C7#1402611yescharacteristic, complemented, Sylow
585C22—44no—
586C22—48no—
587C22—44no—
588C22—44no—
589C22—48no—
590C22—82no—
591C22—82no—
592C22—84no—
593C22—82no—
594C22—82no—
595C22—84no—
596C22#9035911yescharacteristic
597C22#9036212yes—
598C22D7×#12411yescharacteristic
599C22#9036511yescharacteristic
600C22#9036611yescharacteristic
601C22#9036712yes—
602C22#9036812yes—
603C22#9037112yes—
604C22#9037212yes—
605C22#9037312yes—
606C22C2×D4×Dic711yescharacteristic
607C22C2×D4×Dic711yescharacteristic
608C22C2×#649811yescharacteristic
609C22C2×#650011yescharacteristic
610C22C2×#650211yescharacteristic
611C22C2×#650211yescharacteristic
612C22#41×Dic712yes—
613C22#9051812yes—
614C22#9052212yes—
615C22#9052212yes—
616C22#9052512yes—
617C22#9052512yes—
618C22C22×C22⋊Dic711yescharacteristic
619C4—28no—
620C4—44no—
621C4—144no—
622C4—284no—
623C4—282no—
624C4—284no—
625C4—562no—
626C4#8999218yes—
627C2—84no—
628C2Dic7×#12411yescharacteristic
629C2#1174039811yescharacteristic
630C2#1174040012yes—
631C2#1174040311yescharacteristic
632C2#1174040611yescharacteristic
633C2#1174040812yes—
634C2#1174041711yescharacteristic
635C2#1174041911yescharacteristic
636C2#1174044012yes—
637C2C2×#8999211yescharacteristic
638C2#1174153412yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C7×#124C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC22×#124D7
hypocenterC7#14026
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic7C2semidirect
3. C2×#90002C2semidirect
6. #11729300C2semidirect
7. #11729299C2semidirect
8. #11729289C2semidirect
9. C4×C7⋊#95C2semidirect
14. C2×C7×#124C4semidirect
124. C2×C7×Q8C22⋊C4semidirect
195. C2×#124Dic7semidirect
300. C2×Dic7#124semidirect
421. C2×Q8C22⋊Dic7semidirect
584. C7#14026semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1242
C22×Q8×Dic72
C2×#900022
C2×#899932
#117293002
#117292992
#117292892
C4×C7⋊#952
#140267