Finite Group Databasebeta

← C2×#11732139 #13521501

Subgroups — C2×#11732139 #13521501

Order 1792.

3222 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×#6498C211yesmaximal, characteristic
2C22×D4×Dic7C211yesmaximal, characteristic
3C2×C7×#386C211yesmaximal, characteristic
4C2×#89984C211yesmaximal, characteristic, complemented
5C22×C7⋊#95C211yesmaximal, characteristic, complemented
6C2×#89725C211yesmaximal, characteristic, complemented
7C2×#89725C211yesmaximal, characteristic, complemented
8C2×#89722C211yesmaximal, characteristic, complemented
9C2×#89722C211yesmaximal, characteristic, complemented
10C2×#89715C211yesmaximal, characteristic, complemented
11C2×#89715C211yesmaximal, characteristic, complemented
12#11732139C2116yesmaximal, direct product factor
13C2×#89431C211yesmaximal, characteristic, complemented
14C2×#89433C211yesmaximal, characteristic, complemented
15C2×#89425C211yesmaximal, characteristic, complemented
16C2×#89425C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C2×#6498—28no—
31C2×#6498C2218yes—
32C2×D4×Dic7—28no—
33C2×D4×Dic7C2218yes—
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C7×#386C2218yes—
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45#89984C2218yescomplemented
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⋊#95C2218yescomplemented
59#89725C2218yescomplemented
60#89725C2218yescomplemented
61#89722C2218yescomplemented
62#89722C2218yescomplemented
63#89715C2218yescomplemented
64#89715C2218yescomplemented
65#89433C2218yescomplemented
66#89431C2218yescomplemented
67#89425C2218yescomplemented
68#89425C2218yescomplemented
69C2×#2419—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C22×C7×D4—24no—
73C22×C7×D4—24no—
74C22×C7×D4D418yes—
75C22×C7×D4C2314yes—
76C23×C4×C7—24no—
77C23×C4×C7—24no—
78C23×C4×C7—42no—
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—24no—
90C23×Dic7—24no—
91C23×Dic7—24no—
92C23×Dic7—42no—
93C23×Dic7—42no—
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2314yes—
102C23×Dic7C2314yes—
103C23×Dic7C2314yes—
104C23×Dic7C2311yescharacteristic
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4—42no—
108C2×C7×C22⋊C4C2314yes—
109C2×C7×C22⋊C4C2314yes—
110C2×C7×C22⋊C4C2314yes—
111C2×C22⋊Dic7—24no—
112C2×C22⋊Dic7—24no—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7—24no—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121#6498—232no—
122D4×Dic7—232no—
123C2×C4⋊Dic7—24no—
124C2×C4⋊Dic7—24no—
125C2×C4⋊Dic7—24no—
126C2×C4⋊Dic7—42no—
127C2×C4⋊Dic7—42no—
128C2×C4⋊Dic7C2314yes—
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131C2×C4⋊Dic7C2314yes—
132C2×C4⋊Dic7C2314yes—
133C2×Dic7⋊C4—24no—
134C2×Dic7⋊C4—24no—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×C4×Dic7—24no—
138C2×C4×Dic7C2314yes—
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×#123—71no—
154C22×C4×D4—71no—
155#2419—716no—
156C2×#400—71no—
157C2×#398—71no—
158C2×#397—71no—
159C2×#397—71no—
160C2×#387—71no—
161C2×#387—71no—
162C2×#386D711yescharacteristic
163C2×#385—71no—
164C2×#385—71no—
165C2×#381—71no—
166C2×#381—71no—
167C2×#380—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×C7C2×D414yes—
180C24×C7C2×D414yes—
181C24×C7#4114yes—
182C24×C7#4114yes—
183C24×C7C2412yes—
184C24×C7C2412yes—
185C24×C7C2411yescharacteristic
186C2×C7×D4—232no—
187C2×C7×D4—28no—
188C2×C7×D4—28no—
189C2×C7×D4C2×D4116yes—
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—22no—
198C22×C4×C7—28no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—28no—
205C22×C4×C7—44no—
206C22×C4×C7—416no—
207C22×C4×C7C2×D414yes—
208C22×C4×C7#4114yes—
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—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—28no—
224C22×Dic7—28no—
225C22×Dic7—28no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—28no—
230C22×Dic7—28no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—28no—
243C22×Dic7—28no—
244C22×Dic7—44no—
245C22×Dic7—44no—
246C22×Dic7—416no—
247C22×Dic7—416no—
248C22×Dic7—416no—
249C22×Dic7#4114yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C7×C22⋊C4—28no—
259C7×C22⋊C4—28no—
260C7×C22⋊C4—44no—
261C22⋊Dic7—28no—
262C22⋊Dic7—28no—
263C22⋊Dic7—28no—
264C22⋊Dic7—28no—
265C22⋊Dic7—28no—
266C4⋊Dic7—28no—
267C4⋊Dic7—28no—
268C4⋊Dic7—28no—
269C4⋊Dic7—44no—
270C4⋊Dic7—44no—
271Dic7⋊C4—28no—
272Dic7⋊C4—28no—
273C4×Dic7—28no—
274C23×D4C2×D711yescharacteristic
275C24×C4—71no—
276C24×C4—71no—
277C24×C4—71no—
278C24×C4C2×D711yescharacteristic
279C2×#123—78no—
280C2×#123—148no—
281C2×C4×D4—78no—
282C2×C4×D4—148no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4—71no—
289C22×C4⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4C2×D711yescharacteristic
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C22⋊C4C2×D711yescharacteristic
298C22×C42—71no—
299#400—78no—
300#398—78no—
301#397—78no—
302#397—78no—
303#387—78no—
304#387—78no—
305#386C2×D718yes—
306#385—78no—
307#385—78no—
308#381—78no—
309#381—78no—
310#380—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—78no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95C2×D711yescharacteristic
325C2×#95C2×D711yescharacteristic
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—28no—
337C23×C7—28no—
338C23×C7—28no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—44no—
346C23×C7—44no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7#123116yes—
350C23×C7C22×D414yes—
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—232no—
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×C7C2×#4114yes—
384C2×Dic7—28no—
385C2×Dic7—22no—
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—416no—
411C2×Dic7—44no—
412C2×Dic7—44no—
413C2×Dic7—44no—
414C2×Dic7—44no—
415C2×Dic7—44no—
416C2×Dic7—44no—
417C2×Dic7—44no—
418C2×Dic7C2×#4114yes—
419C25C22×D711yescharacteristic
420C25C22×D711yescharacteristic
421C22×D4—24no—
422C22×D4—24no—
423C22×D4D2818yes—
424C22×D4C22×D714yes—
425C23×C4—24no—
426C23×C4—24no—
427C23×C4—42no—
428C23×C4—71no—
429C23×C4—74no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—71no—
437C23×C4—74no—
438C23×C4—74no—
439C23×C4—144no—
440C23×C4—144no—
441C23×C4—144no—
442C23×C4—144no—
443C23×C4—144no—
444C23×C4—144no—
445C23×C4—144no—
446C23×C4—282no—
447C23×C4—282no—
448C23×C4C22×D711yescharacteristic
449C23×C4C22×D711yescharacteristic
450C23×C4C22×D711yescharacteristic
451C23×C4C22×D714yes—
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454#123—1432no—
455C4×D4—1432no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—144no—
464C2×C4⋊C4—144no—
465C2×C4⋊C4—144no—
466C2×C4⋊C4—144no—
467C2×C4⋊C4—144no—
468C2×C4⋊C4—282no—
469C2×C4⋊C4—282no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—74no—
475C2×C22⋊C4—74no—
476C2×C22⋊C4—74no—
477C2×C22⋊C4—74no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—144no—
480C2×C22⋊C4—144no—
481C2×C22⋊C4—144no—
482C2×C22⋊C4—144no—
483C2×C22⋊C4C22×D714yes—
484C2×C22⋊C4C22×D714yes—
485C2×C22⋊C4C22×D714yes—
486C2×C42—74no—
487C2×C42—144no—
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#95C22×D714yes—
501#95C22×D714yes—
502C22×C7—24no—
503C22×C7—232no—
504C22×C7—24no—
505C22×C7—24no—
506C22×C7—24no—
507C22×C7—24no—
508C22×C7—24no—
509C22×C7—24no—
510C22×C7—24no—
511C22×C7—24no—
512C22×C7—42no—
513C22×C7—416no—
514C22×C7—42no—
515C22×C7—42no—
516C22×C7—42no—
517C22×C7C2×#12318yes—
518C22×C7C2×#12314yes—
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—42no—
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—
555C24C2×D2814yes—
556C24C2×D2814yes—
557C24#115914yes—
558C24#115914yes—
559C24C23×D712yes—
560C24C23×D712yes—
561C24C23×D711yescharacteristic
562C2×D4—232no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4C2×D28116yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—44no—
582C22×C4—416no—
583C22×C4—74no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—148no—
593C22×C4—148no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—148no—
604C22×C4—148no—
605C22×C4—148no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—148no—
609C22×C4—148no—
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—284no—
623C22×C4—284no—
624C22×C4—2816no—
625C22×C4—2816no—
626C22×C4—2816no—
627C22×C4C2×D2814yes—
628C22×C4#115914yes—
629C22×C4C23×D712yes—
630C22×C4C23×D712yes—
631C22×C4C23×D712yes—
632C22×C4C23×D712yes—
633C22×C4C23×D712yes—
634C4⋊C4—148no—
635C4⋊C4—148no—
636C4⋊C4—148no—
637C4⋊C4—148no—
638C4⋊C4—148no—
639C4⋊C4—284no—
640C4⋊C4—284no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—44no—
644C22⋊C4—148no—
645C22⋊C4—148no—
646C22⋊C4—148no—
647C22⋊C4—148no—
648C22⋊C4—148no—
649C42—148no—
650C2×C7—28no—
651C2×C7—44no—
652C2×C7#241918yescomplemented
653C2×C7C22×#12311yescharacteristic
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—28no—
671C23—28no—
672C23—28no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23#6449116yes—
684C23C22×D2814yes—
685C23C22×D2814yes—
686C23C22×D2812yes—
687C23C2×#115914yes—
688C23C2×#115914yes—
689C23C2×#115912yes—
690C23C2×#115912yes—
691C23C2×#115912yes—
692C23#654812yes—
693C23D7×#4112yes—
694C23#655412yes—
695C23C24×D711yescharacteristic
696D4—232no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—22no—
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—416no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—74no—
717C2×C4—148no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
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—2816no—
742C2×C4—2816no—
743C2×C4—2816no—
744C2×C4—284no—
745C2×C4—284no—
746C2×C4—284no—
747C2×C4—284no—
748C2×C4—284no—
749C2×C4—284no—
750C2×C4—284no—
751C2×C4C22×D2814yes—
752C2×C4C2×#115914yes—
753C7C2×#241911yescharacteristic, complemented, Sylow
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—232no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—416no—
769C22C2×#644918yes—
770C22C2×#644914yes—
771C22#9024514yes—
772C22#9024614yes—
773C22#9027814yes—
774C22#9029114yes—
775C22#9029314yes—
776C22#9034114yes—
777C22C23×D2811yescharacteristic
778C22C22×#115911yescharacteristic
779C22C22×#115911yescharacteristic
780C22C22×#115911yescharacteristic
781C22C2×#654811yescharacteristic
782C22C2×D7×#4111yescharacteristic
783C22C2×#655411yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—144no—
790C4—282no—
791C4—282no—
792C4—282no—
793C4—282no—
794C4—282no—
795C4—282no—
796C4—282no—
797C2—28no—
798C2—44no—
799C2#1173213918yesdirect product factor
800C2C22×#644911yescharacteristic
801C2C2×#9024611yescharacteristic
802C2C2×#9024511yescharacteristic
803C2C2×#9027811yescharacteristic
804C2C2×#9029111yescharacteristic
805C2C2×#9029311yescharacteristic
806C2C2×#9034111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#386D7
hypocenterC7C2×#2419
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
4. C2×#89984C2semidirect
5. C22×C7⋊#95C2semidirect
6. C2×#89725C2semidirect
7. C2×#89725C2semidirect
8. C2×#89722C2semidirect
9. C2×#89722C2semidirect
10. C2×#89715C2semidirect
11. C2×#89715C2semidirect
12. #11732139C2direct (N × H)
13. C2×#89431C2semidirect
14. C2×#89433C2semidirect
15. C2×#89425C2semidirect
16. C2×#89425C2semidirect
45. #89984C22semidirect
58. C2×C7⋊#95C22semidirect
59. #89725C22semidirect
60. #89725C22semidirect
61. #89722C22semidirect
62. #89722C22semidirect
63. #89715C22semidirect
64. #89715C22semidirect
65. #89433C22semidirect
66. #89431C22semidirect
67. #89425C22semidirect
68. #89425C22semidirect
652. C2×C7#2419semidirect
753. C7C2×#2419semidirect
799. C2#11732139direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64982
C22×D4×Dic72
C2×C7×#3862
C2×#899842
C22×C7⋊#952
C2×#897252
C2×#897222
C2×#897152
#117321392
C2×#894312
C2×#894332
C2×#894252
C2×#24197