Finite Group Databasebeta

← C2×#11740302 #13522728

Subgroups — C2×#11740302 #13522728

Order 1792.

3114 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
1C22×C7×#123C211yesmaximal, characteristic
2C22×#6441C211yesmaximal, characteristic, complemented
3C2×#89992C211yesmaximal, characteristic
4C2×#89992C211yesmaximal, characteristic
5C2×#89983C211yesmaximal, characteristic, complemented
6C22×C7⋊#95C211yesmaximal, characteristic, complemented
7#11740302C2116yesmaximal, direct product factor
8C2×#89754C211yesmaximal, characteristic, complemented
9C2×#89754C211yesmaximal, characteristic, complemented
10C2×#89746C211yesmaximal, characteristic, complemented
11C2×#89749C211yesmaximal, characteristic, complemented
12C2×#89725C211yesmaximal, characteristic, complemented
13C2×#89719C211yesmaximal, characteristic, complemented
14C2×#89717C211yesmaximal, characteristic, complemented
15C2×#89717C211yesmaximal, characteristic, complemented
16C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C2×C7×#123—28no—
23C2×C7×#123C2218yes—
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C2×#6441—28no—
41C2×#6441C2218yescomplemented
42#89992C2218yes—
43#89992C2218yes—
44#89983C2218yescomplemented
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2218yescomplemented
60#89754C2218yescomplemented
61#89754C2218yescomplemented
62#89749C2218yescomplemented
63#89746C2218yescomplemented
64#89725C2218yescomplemented
65#89719C2218yescomplemented
66#89717C2218yescomplemented
67#89717C2218yescomplemented
68C22⋊C4×Dic7C2218yescomplemented
69C2×#2488—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C22×C7×D4—24no—
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4C2314yes—
76C23×C4×C7—24no—
77C23×C4×C7—24no—
78C23×C4×C7—24no—
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2314yes—
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×Dic7—24no—
86C23×Dic7—24no—
87C23×Dic7—24no—
88C23×Dic7—24no—
89C23×Dic7—42no—
90C23×Dic7—42no—
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2314yes—
98C23×Dic7C2314yes—
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C22×Dic14—24no—
102C22×Dic14—24no—
103C22×Dic14—42no—
104C22×Dic14C2314yes—
105C7×#123—232no—
106C2×C7×C4⋊C4—24no—
107C2×C7×C4⋊C4—24no—
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C4⋊C4C2314yes—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4D418yes—
113C2×C7×C22⋊C4C2314yes—
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C22⋊Dic7—24no—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7—24no—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—42no—
121C2×C22⋊Dic7—42no—
122C2×C22⋊Dic7C2314yes—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C4⋊Dic7—24no—
129C2×C4⋊Dic7C2314yes—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4C2314yes—
133C2×Dic7⋊C4C2314yes—
134C2×C4×Dic7—24no—
135C2×C4×Dic7—42no—
136C2×C4×Dic7C2314yes—
137C2×C4×Dic7C2314yes—
138#6441—232no—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#123D711yescharacteristic
154C22×C22⋊Q8—71no—
155#2488—716no—
156C2×#400—71no—
157C2×#400—71no—
158C2×#397—71no—
159C2×#393—71no—
160C2×#391—71no—
161C2×#388—71no—
162C2×#388—71no—
163C2×#386—71no—
164C2×#386—71no—
165C2×#382—71no—
166C2×#381—71no—
167C2×C4×C22⋊C4—71no—
168C22×#95—71no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7C2×D414yes—
181C24×C7#4114yes—
182C24×C7#4114yes—
183C24×C7C2412yes—
184C24×C7C2412yes—
185C24×C7C2411yescharacteristic
186C2×C7×D4—28no—
187C2×C7×D4—28no—
188C2×C7×D4—28no—
189C2×C7×D4—416no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—28no—
198C22×C4×C7—28no—
199C22×C4×C7—28no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—416no—
207C22×C4×C7C2×D414yes—
208C22×C4×C7C2×D414yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—28no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—28no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—28no—
239C22×Dic7—28no—
240C22×Dic7—44no—
241C22×Dic7—44no—
242C22×Dic7—416no—
243C22×Dic7—416no—
244C22×Dic7#4114yes—
245C22×Dic7#4114yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C2×Dic14—28no—
255C2×Dic14—28no—
256C2×Dic14—44no—
257C2×Dic14—416no—
258C7×C4⋊C4—28no—
259C7×C4⋊C4—28no—
260C7×C22⋊C4—28no—
261C7×C22⋊C4—28no—
262C7×C22⋊C4C2×D4116yes—
263C22⋊Dic7—28no—
264C22⋊Dic7—28no—
265C22⋊Dic7—28no—
266C22⋊Dic7—28no—
267C22⋊Dic7—44no—
268C22⋊Dic7—44no—
269C4⋊Dic7—28no—
270Dic7⋊C4—28no—
271Dic7⋊C4—28no—
272C4×Dic7—28no—
273C4×Dic7—44no—
274C23×Q8—71no—
275C23×D4C2×D711yescharacteristic
276C24×C4—71no—
277C24×C4—71no—
278C24×C4C2×D711yescharacteristic
279C2×#123—28no—
280C2×#123C2×D718yes—
281C2×C22⋊Q8—78no—
282C2×C22⋊Q8—148no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4C2×D711yescharacteristic
287C22×C4⋊C4C2×D711yescharacteristic
288C22×C22⋊C4—71no—
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4C2×D711yescharacteristic
295C22×C22⋊C4C2×D711yescharacteristic
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C42—71no—
298C22×C42—71no—
299#400—78no—
300#400—78no—
301#397—78no—
302#393—78no—
303#391—78no—
304#388—78no—
305#388—78no—
306#386—78no—
307#386—78no—
308#382—78no—
309#381—78no—
310C4×C22⋊C4—78no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—78no—
326C23×C7—28no—
327C23×C7—28no—
328C23×C7—28no—
329C23×C7—28no—
330C23×C7—28no—
331C23×C7—28no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—44no—
344C23×C7—44no—
345C23×C7—44no—
346C23×C7—44no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7#124116yes—
351C23×C7C22×D414yes—
352C23×C7C22×D412yes—
353C23×C7C2×#4114yes—
354C23×C7C2×#4114yes—
355C23×C7C2×#4112yes—
356C23×C7C2×#4112yes—
357C23×C7C2×#4112yes—
358C23×C7C2×#4112yes—
359C23×C7H(5,𝔽2)12yes—
360C23×C72−1+412yes—
361C23×C7C2511yescharacteristic
362C7×D4—416no—
363C2×C4×C7—28no—
364C2×C4×C7—28no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—416no—
379C2×C4×C7—44no—
380C2×C4×C7—44no—
381C2×C4×C7—44no—
382C2×C4×C7C22×D414yes—
383C2×C4×C7C22×D414yes—
384C2×Dic7—28no—
385C2×Dic7—28no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—416no—
409C2×Dic7—416no—
410C2×Dic7—44no—
411C2×Dic7—44no—
412C2×Dic7—44no—
413C2×Dic7—44no—
414C2×Dic7—44no—
415C2×Dic7—44no—
416C2×Dic7C2×#4114yes—
417C2×Dic7C2×#4114yes—
418Dic14—416no—
419C25C22×D711yescharacteristic
420C25C22×D711yescharacteristic
421C22×Q8—74no—
422C22×Q8—144no—
423C22×Q8—144no—
424C22×Q8—282no—
425C22×D4—24no—
426C22×D4—24no—
427C22×D4—24no—
428C22×D4C22×D714yes—
429C23×C4—24no—
430C23×C4—24no—
431C23×C4—24no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—71no—
437C23×C4—71no—
438C23×C4—71no—
439C23×C4—71no—
440C23×C4—74no—
441C23×C4—74no—
442C23×C4—144no—
443C23×C4—144no—
444C23×C4—144no—
445C23×C4—144no—
446C23×C4—282no—
447C23×C4—282no—
448C23×C4C22×D714yes—
449C23×C4C22×D711yescharacteristic
450C23×C4C22×D711yescharacteristic
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454#123—232no—
455C22⋊Q8—1432no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—144no—
462C2×C4⋊C4—144no—
463C2×C4⋊C4—144no—
464C2×C4⋊C4C22×D714yes—
465C2×C4⋊C4C22×D714yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—74no—
469C2×C22⋊C4—74no—
470C2×C22⋊C4—74no—
471C2×C22⋊C4—74no—
472C2×C22⋊C4—74no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—144no—
475C2×C22⋊C4—144no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—282no—
479C2×C22⋊C4—282no—
480C2×C22⋊C4C22⋊D718yes—
481C2×C22⋊C4C22×D714yes—
482C2×C22⋊C4C22×D714yes—
483C2×C22⋊C4C22×D714yes—
484C2×C42—74no—
485C2×C42—74no—
486C2×C42—144no—
487C2×C42—282no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95—74no—
495#95—74no—
496#95—74no—
497#95—74no—
498#95—74no—
499#95—74no—
500#95—74no—
501#95—74no—
502C22×C7—24no—
503C22×C7—24no—
504C22×C7—24no—
505C22×C7—24no—
506C22×C7—24no—
507C22×C7—24no—
508C22×C7—232no—
509C22×C7—42no—
510C22×C7—42no—
511C22×C7—42no—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—42no—
515C22×C7—42no—
516C22×C7—88no—
517C22×C7C2×#12418yes—
518C22×C7C2×#12414yes—
519C22×C7#52914yes—
520C22×C7#53914yes—
521C22×C7#54614yes—
522C22×C7#54714yes—
523C22×C7#55114yes—
524C22×C7#55214yes—
525C22×C7C23×D411yescharacteristic
526C22×C7C22×#4111yescharacteristic
527C22×C7C22×#4111yescharacteristic
528C22×C7C22×#4111yescharacteristic
529C22×C7C22×#4111yescharacteristic
530C22×C7C2×H(5,𝔽2)11yescharacteristic
531C22×C7C2×2−1+411yescharacteristic
532C4×C7—24no—
533C4×C7—24no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7—42no—
537Dic7—24no—
538Dic7—24no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24#115914yes—
557C24#115914yes—
558C24C2×C22⋊D714yes—
559C24C23×D712yes—
560C24C23×D712yes—
561C24C23×D711yescharacteristic
562C2×Q8—148no—
563C2×Q8—148no—
564C2×Q8—284no—
565C2×Q8—2816no—
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—416no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—416no—
587C22×C4—74no—
588C22×C4—74no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—72no—
593C22×C4—72no—
594C22×C4—72no—
595C22×C4—72no—
596C22×C4—72no—
597C22×C4—148no—
598C22×C4—148no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—148no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—148no—
623C22×C4—284no—
624C22×C4—284no—
625C22×C4—2816no—
626C22×C4—2816no—
627C22×C4C2×C22⋊D714yes—
628C22×C4C2×C22⋊D714yes—
629C22×C4C23×D712yes—
630C22×C4C23×D712yes—
631C22×C4C23×D712yes—
632C22×C4C23×D712yes—
633C22×C4C23×D712yes—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—148no—
637C4⋊C4—148no—
638C4⋊C4—148no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—148no—
642C22⋊C4—148no—
643C22⋊C4—148no—
644C22⋊C4—148no—
645C22⋊C4—284no—
646C22⋊C4—284no—
647C22⋊C4C2×C22⋊D7116yes—
648C42—148no—
649C42—284no—
650C2×C7—28no—
651C2×C7—82no—
652C2×C7#248818yescomplemented
653C2×C7C22×#12411yescharacteristic
654C2×C7C2×#52911yescharacteristic
655C2×C7C2×#53911yescharacteristic
656C2×C7C2×#54611yescharacteristic
657C2×C7C2×#54711yescharacteristic
658C2×C7C2×#55111yescharacteristic
659C2×C7C2×#55211yescharacteristic
660C23—28no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23#6499116yes—
685C23C2×#115914yes—
686C23C2×#115914yes—
687C23C2×#115912yes—
688C23C2×#115912yes—
689C23D7×#4112yes—
690C23D7×#4112yes—
691C23#655312yes—
692C23#655412yes—
693C23C22×C22⋊D714yes—
694C23C22×C22⋊D712yes—
695C23C24×D711yescharacteristic
696Q8—2816no—
697D4—416no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—416no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—74no—
718C2×C4—74no—
719C2×C4—148no—
720C2×C4—148no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—2816no—
744C2×C4—2816no—
745C2×C4—284no—
746C2×C4—284no—
747C2×C4—284no—
748C2×C4—284no—
749C2×C4—284no—
750C2×C4—284no—
751C2×C4C22×C22⋊D714yes—
752C2×C4C22×C22⋊D714yes—
753C7C2×#248811yescharacteristic, complemented, Sylow
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—232no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—88no—
769C22#9034014yes—
770C22#9034114yes—
771C22#9034914yes—
772C22#9035614yes—
773C22C2×#649918yes—
774C22C2×#649914yes—
775C22#9051514yes—
776C22#9052014yes—
777C22C22×#115911yescharacteristic
778C22C22×#115911yescharacteristic
779C22C2×D7×#4111yescharacteristic
780C22C2×D7×#4111yescharacteristic
781C22C2×#655311yescharacteristic
782C22C2×#655411yescharacteristic
783C22C23×C22⋊D711yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—144no—
790C4—144no—
791C4—282no—
792C4—282no—
793C4—282no—
794C4—282no—
795C4—282no—
796C4—282no—
797C2—28no—
798C2—82no—
799C2#1174030218yesdirect product factor
800C2C2×#9034011yescharacteristic
801C2C2×#9035611yescharacteristic
802C2C2×#9034111yescharacteristic
803C2C2×#9034911yescharacteristic
804C2C22×#649911yescharacteristic
805C2C2×#9051511yescharacteristic
806C2C2×#9052011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#123C2
socleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC22×#123D7
hypocenterC7C2×#2488
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
2. C22×#6441C2semidirect
5. C2×#89983C2semidirect
6. C22×C7⋊#95C2semidirect
7. #11740302C2direct (N × H)
8. C2×#89754C2semidirect
9. C2×#89754C2semidirect
10. C2×#89746C2semidirect
11. C2×#89749C2semidirect
12. C2×#89725C2semidirect
13. C2×#89719C2semidirect
14. C2×#89717C2semidirect
15. C2×#89717C2semidirect
16. C2×C22⋊C4×Dic7C2semidirect
41. C2×#6441C22semidirect
44. #89983C22semidirect
59. C2×C7⋊#95C22semidirect
60. #89754C22semidirect
61. #89754C22semidirect
62. #89749C22semidirect
63. #89746C22semidirect
64. #89725C22semidirect
65. #89719C22semidirect
66. #89717C22semidirect
67. #89717C22semidirect
68. C22⋊C4×Dic7C22semidirect
652. C2×C7#2488semidirect
753. C7C2×#2488semidirect
799. C2#11740302direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1232
C22×#64412
C2×#899922
C2×#899832
C22×C7⋊#952
#117403022
C2×#897542
C2×#897462
C2×#897492
C2×#897252
C2×#897192
C2×#897172
C2×C22⋊C4×Dic72
C2×#24887