Finite Group Databasebeta

← C2×#11740307 #13523903

Subgroups — C2×#11740307 #13523903

Order 1792.

3330 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#123C211yesmaximal, characteristic, complemented
2C22×#6448C211yesmaximal, characteristic, complemented
3C2×#89995C211yesmaximal, characteristic
4C2×#89992C211yesmaximal, characteristic, complemented
5C2×#89985C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
7#11740307C2116yesmaximal, direct product factor
8C2×#89765C211yesmaximal, characteristic, complemented
9C2×#89746C211yesmaximal, characteristic, complemented
10C2×#89762C211yesmaximal, characteristic, complemented
11C2×#89750C211yesmaximal, characteristic, complemented
12C2×#89724C211yesmaximal, characteristic, complemented
13C2×#89719C211yesmaximal, characteristic, complemented
14C2×#89729C211yesmaximal, characteristic, complemented
15C2×#89730C211yesmaximal, characteristic, complemented
16C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×Dic14C2211yescharacteristic
23C2×C7×#123—28no—
24C2×C7×#123C2218yescomplemented
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6448—28no—
45C2×#6448C2218yescomplemented
46#89995C2218yes—
47#89992C2218yescomplemented
48#89985C2218yescomplemented
49C4×C22⋊Dic7C2218yescomplemented
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⋊#95C2211yescharacteristic
60#89765C2218yescomplemented
61#89762C2218yescomplemented
62#89750C2218yescomplemented
63#89746C2218yescomplemented
64#89730C2218yescomplemented
65#89729C2218yescomplemented
66#89724C2218yescomplemented
67#89719C2218yescomplemented
68C22⋊C4×Dic7C2218yescomplemented
69C2×#2557—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—42no—
76C22×C7×D4C2314yes—
77C23×C4×C7—24no—
78C23×C4×C7—24no—
79C23×C4×C7—42no—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2314yes—
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C22×C22⋊D7—24no—
87C22×C22⋊D7—24no—
88C22×C22⋊D7—24no—
89C22×C22⋊D7—24no—
90C22×C22⋊D7—42no—
91C22×C22⋊D7—42no—
92C22×C22⋊D7C2314yes—
93C22×C22⋊D7C2314yes—
94C23×Dic7—24no—
95C23×Dic7—42no—
96C23×Dic7—42no—
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2314yes—
105C22×Dic14—24no—
106C22×Dic14—24no—
107C22×Dic14—42no—
108C22×Dic14C2314yes—
109C7×#123—232no—
110C2×C7×C4⋊C4—24no—
111C2×C7×C4⋊C4—24no—
112C2×C7×C4⋊C4C2314yes—
113C2×C7×C4⋊C4C2314yes—
114C2×C7×C22⋊C4—24no—
115C2×C7×C22⋊C4—24no—
116C2×C7×C22⋊C4D418yescomplemented
117C2×C7×C22⋊C4C2314yes—
118C2×C7×C22⋊C4C2314yes—
119C2×C7×C22⋊C4C2314yes—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7—42no—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×(C2×D7)⋊C4—24no—
131C2×(C2×D7)⋊C4—24no—
132C2×(C2×D7)⋊C4—24no—
133C2×(C2×D7)⋊C4—42no—
134C2×(C2×D7)⋊C4—42no—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4C2314yes—
142C2×C4×Dic7—24no—
143C2×C4×Dic7—42no—
144C2×C4×Dic7—42no—
145C2×C4×Dic7C2314yes—
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148#6448—232no—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#124—71no—
160C22×#123D711yescharacteristic, complemented
161#2557—716no—
162C2×#397—71no—
163C2×#397—71no—
164C2×#393—71no—
165C2×#392—71no—
166C2×#391—71no—
167C2×#390—71no—
168C2×#388—71no—
169C2×#387—71no—
170C2×#386—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×C4×C22⋊C4—71no—
174C2×C4×C22⋊C4—71no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7C2×D414yes—
188C24×C7#4114yes—
189C24×C7C2412yes—
190C24×C7C2412yes—
191C24×C7C2411yescharacteristic
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7—22no—
197C23×D7—22no—
198C23×D7—22no—
199C23×D7C2412yes—
200C2×C7×D4—28no—
201C2×C7×D4—28no—
202C2×C7×D4—44no—
203C2×C7×D4—416no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—28no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—28no—
219C22×C4×C7—44no—
220C22×C4×C7—416no—
221C22×C4×C7C2×D414yes—
222C22×C4×C7C2×D414yes—
223C22×C4×C7C2412yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C2×C22⋊D7—28no—
229C2×C22⋊D7—28no—
230C2×C22⋊D7—28no—
231C2×C22⋊D7—28no—
232C2×C22⋊D7—44no—
233C2×C22⋊D7—44no—
234C2×C22⋊D7—416no—
235C2×C22⋊D7—416no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—28no—
255C22×Dic7—44no—
256C22×Dic7—44no—
257C22×Dic7—416no—
258C22×Dic7#4114yes—
259C22×Dic7#4114yes—
260C22×Dic7#4114yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C2×Dic14—28no—
269C2×Dic14—28no—
270C2×Dic14—44no—
271C2×Dic14—416no—
272C7×C4⋊C4—28no—
273C7×C4⋊C4—28no—
274C7×C22⋊C4—28no—
275C7×C22⋊C4—28no—
276C7×C22⋊C4C2×D4116yescomplemented
277C22⋊Dic7—28no—
278C22⋊Dic7—28no—
279C22⋊Dic7—28no—
280C22⋊Dic7—28no—
281C22⋊Dic7—44no—
282(C2×D7)⋊C4—28no—
283(C2×D7)⋊C4—28no—
284(C2×D7)⋊C4—28no—
285(C2×D7)⋊C4—44no—
286(C2×D7)⋊C4—44no—
287Dic7⋊C4—28no—
288C4×Dic7—28no—
289C4×Dic7—44no—
290C4×Dic7—44no—
291C23×Q8—71no—
292C23×D4—71no—
293C23×D4—71no—
294C23×D4C2×D711yescharacteristic
295C24×C4—71no—
296C24×C4C2×D711yescharacteristic
297C2×#124—78no—
298C2×#124—148no—
299C2×#123—28no—
300C2×#123C2×D718yescomplemented
301C22×C4⋊C4—71no—
302C22×C4⋊C4C2×D711yescharacteristic
303C22×C4⋊C4C2×D711yescharacteristic
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C42—71no—
318C22×C42—71no—
319C22×C42—71no—
320#397—78no—
321#397—78no—
322#393—78no—
323#392—78no—
324#391—78no—
325#390—78no—
326#388—78no—
327#387—78no—
328#386—78no—
329#386—78no—
330#386—78no—
331C4×C22⋊C4—78no—
332C4×C22⋊C4—78no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—28no—
346C23×C7—28no—
347C23×C7—28no—
348C23×C7—28no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—44no—
362C23×C7—44no—
363C23×C7—44no—
364C23×C7—44no—
365C23×C7—44no—
366C23×C7—44no—
367C23×C7—44no—
368C23×C7—44no—
369C23×C7C22×D414yes—
370C23×C7C22×D412yes—
371C23×C7C2×#4114yes—
372C23×C7C2×#4112yes—
373C23×C7C2×#4112yes—
374C23×C7C2×#4112yes—
375C23×C7C2×#4112yes—
376C23×C7H(5,𝔽2)12yes—
377C23×C7H(5,𝔽2)12yes—
378C23×C7C2511yescharacteristic
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—44no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7—44no—
392C22×D7—44no—
393C7×D4—416no—
394C2×C4×C7—28no—
395C2×C4×C7—28no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—416no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7C22×D414yes—
414C2×C4×C7C22×D414yes—
415C22⋊D7—416no—
416C22⋊D7—416no—
417C2×Dic7—28no—
418C2×Dic7—28no—
419C2×Dic7—28no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—416no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7C2×#4114yes—
444C2×Dic7C2×#4114yes—
445C2×Dic7C2×#4114yes—
446Dic14—416no—
447C25—71no—
448C25C22×D711yescharacteristic
449C25C22×D711yescharacteristic
450C22×Q8—74no—
451C22×Q8—144no—
452C22×Q8—144no—
453C22×Q8—282no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—42no—
457C22×D4—74no—
458C22×D4—74no—
459C22×D4—144no—
460C22×D4—144no—
461C22×D4—144no—
462C22×D4—144no—
463C22×D4—282no—
464C22×D4—282no—
465C22×D4C22×D714yes—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—42no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—71no—
474C23×C4—71no—
475C23×C4—71no—
476C23×C4—74no—
477C23×C4—144no—
478C23×C4—282no—
479C23×C4—282no—
480C23×C4C22×D711yescharacteristic
481C23×C4C22×D711yescharacteristic
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D714yes—
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486#124—1432no—
487#123—232no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—144no—
492C2×C4⋊C4C22×D714yes—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—74no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—74no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—144no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—282no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4C22⋊D718yescomplemented
517C2×C22⋊C4C22×D714yes—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42—282no—
525C2×C42—282no—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95—74no—
533#95—74no—
534#95—74no—
535#95—74no—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—24no—
541C22×C7—24no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—416no—
551C22×C7—416no—
552C22×C7#52914yes—
553C22×C7#53214yes—
554C22×C7#53814yes—
555C22×C7#54614yes—
556C22×C7#54614yes—
557C22×C7#55114yes—
558C22×C7#55914yes—
559C22×C7C23×D411yescharacteristic
560C22×C7C22×#4111yescharacteristic
561C22×C7C22×#4111yescharacteristic
562C22×C7C22×#4111yescharacteristic
563C22×C7C22×#4111yescharacteristic
564C22×C7C2×H(5,𝔽2)11yescharacteristic
565C22×C7C2×H(5,𝔽2)11yescharacteristic
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—42no—
572C2×D7—42no—
573C2×D7—88no—
574C4×C7—24no—
575C4×C7—24no—
576C4×C7—42no—
577C4×C7—42no—
578C4×C7—42no—
579Dic7—24no—
580Dic7—24no—
581Dic7—24no—
582Dic7—42no—
583Dic7—42no—
584Dic7—42no—
585Dic7—42no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—72no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24—142no—
606C24#115914yes—
607C24C2×C22⋊D714yes—
608C24C23×D712yes—
609C24C23×D712yes—
610C24C23×D711yescharacteristic
611C2×Q8—148no—
612C2×Q8—148no—
613C2×Q8—284no—
614C2×Q8—2816no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—44no—
618C2×D4—416no—
619C2×D4—148no—
620C2×D4—148no—
621C2×D4—148no—
622C2×D4—148no—
623C2×D4—284no—
624C2×D4—284no—
625C2×D4—2816no—
626C2×D4—2816no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—28no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—28no—
642C22×C4—44no—
643C22×C4—416no—
644C22×C4—74no—
645C22×C4—74no—
646C22×C4—74no—
647C22×C4—72no—
648C22×C4—72no—
649C22×C4—72no—
650C22×C4—72no—
651C22×C4—72no—
652C22×C4—72no—
653C22×C4—72no—
654C22×C4—148no—
655C22×C4—142no—
656C22×C4—142no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—142no—
664C22×C4—142no—
665C22×C4—142no—
666C22×C4—142no—
667C22×C4—142no—
668C22×C4—142no—
669C22×C4—142no—
670C22×C4—142no—
671C22×C4—142no—
672C22×C4—142no—
673C22×C4—284no—
674C22×C4—284no—
675C22×C4—2816no—
676C22×C4C2×C22⋊D714yes—
677C22×C4C2×C22⋊D714yes—
678C22×C4C23×D712yes—
679C22×C4C23×D712yes—
680C22×C4C23×D712yes—
681C22×C4C23×D712yes—
682C22×C4C23×D712yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—148no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—148no—
695C22⋊C4—284no—
696C22⋊C4—284no—
697C22⋊C4—284no—
698C22⋊C4C2×C22⋊D7116yescomplemented
699C42—148no—
700C42—284no—
701C42—284no—
702C2×C7—44no—
703C2×C7—44no—
704C2×C7#255718yescomplemented
705C2×C7C2×#52911yescharacteristic
706C2×C7C2×#53211yescharacteristic
707C2×C7C2×#53811yescharacteristic
708C2×C7C2×#54611yescharacteristic
709C2×C7C2×#54611yescharacteristic
710C2×C7C2×#55111yescharacteristic
711C2×C7C2×#55911yescharacteristic
712D7—82no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—142no—
740C23—142no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23—284no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23—284no—
751C23—284no—
752C23—284no—
753C23C2×#115914yes—
754C23C2×#115912yes—
755C23#654812yes—
756C23D7×#4112yes—
757C23D7×#4112yes—
758C23D7×#4112yes—
759C23#655312yes—
760C23C22×C22⋊D714yes—
761C23C22×C22⋊D712yes—
762C23C24×D711yescharacteristic
763Q8—2816no—
764D4—416no—
765D4—2816no—
766D4—2816no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—74no—
787C2×C4—74no—
788C2×C4—74no—
789C2×C4—148no—
790C2×C4—148no—
791C2×C4—148no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—142no—
808C2×C4—142no—
809C2×C4—142no—
810C2×C4—2816no—
811C2×C4—284no—
812C2×C4—284no—
813C2×C4—284no—
814C2×C4—284no—
815C2×C4C22×C22⋊D714yes—
816C2×C4C22×C22⋊D714yes—
817C7C2×#255711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—416no—
833C22—416no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—282no—
838C22—282no—
839C22—282no—
840C22—282no—
841C22—568no—
842C22#9034014yes—
843C22#9034814yes—
844C22#9034914yes—
845C22#9035514yes—
846C22#9049714yes—
847C22#9052014yes—
848C22#9052314yes—
849C22C22×#115911yescharacteristic
850C22C2×#654811yescharacteristic
851C22C2×D7×#4111yescharacteristic
852C22C2×D7×#4111yescharacteristic
853C22C2×D7×#4111yescharacteristic
854C22C2×#655311yescharacteristic
855C22C23×C22⋊D711yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—144no—
862C4—144no—
863C4—144no—
864C4—282no—
865C4—282no—
866C4—282no—
867C4—282no—
868C2—44no—
869C2—44no—
870C2—562no—
871C2#1174030718yesdirect product factor
872C2C2×#9034011yescharacteristic
873C2C2×#9035511yescharacteristic
874C2C2×#9034811yescharacteristic
875C2C2×#9034911yescharacteristic
876C2C2×#9049711yescharacteristic
877C2C2×#9052311yescharacteristic
878C2C2×#9052011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#123C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC22×#123D7
hypocenterC7C2×#2557
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C7×#123C2semidirect
2. C22×#6448C2semidirect
4. C2×#89992C2semidirect
5. C2×#89985C2semidirect
6. C2×C4×C22⋊Dic7C2semidirect
7. #11740307C2direct (N × H)
8. C2×#89765C2semidirect
9. C2×#89746C2semidirect
10. C2×#89762C2semidirect
11. C2×#89750C2semidirect
12. C2×#89724C2semidirect
13. C2×#89719C2semidirect
14. C2×#89729C2semidirect
15. C2×#89730C2semidirect
16. C2×C22⋊C4×Dic7C2semidirect
24. C2×C7×#123C22semidirect
45. C2×#6448C22semidirect
47. #89992C22semidirect
48. #89985C22semidirect
49. C4×C22⋊Dic7C22semidirect
60. #89765C22semidirect
61. #89762C22semidirect
62. #89750C22semidirect
63. #89746C22semidirect
64. #89730C22semidirect
65. #89729C22semidirect
66. #89724C22semidirect
67. #89719C22semidirect
68. C22⋊C4×Dic7C22semidirect
116. C2×C7×C22⋊C4D4semidirect
160. C22×#123D7semidirect
276. C7×C22⋊C4C2×D4semidirect
300. C2×#123C2×D7semidirect
516. C2×C22⋊C4C22⋊D7semidirect
698. C22⋊C4C2×C22⋊D7semidirect
704. C2×C7#2557semidirect
817. C7C2×#2557semidirect
871. C2#11740307direct (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×#64482
C2×#899952
C2×#899922
C2×#899852
C2×C4×C22⋊Dic72
#117403072
C2×#897652
C2×#897462
C2×#897622
C2×#897502
C2×#897242
C2×#897192
C2×#897292
C2×#897302
C2×C22⋊C4×Dic72
C2×#25577