Finite Group Databasebeta

← C2×#11732230 #13520230

Subgroups — C2×#11732230 #13520230

Order 1792.

3326 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6502C211yesmaximal, characteristic
2C22×#6441C211yesmaximal, characteristic, complemented
3C2×C7×#386C211yesmaximal, characteristic, complemented
4C2×#89992C211yesmaximal, characteristic, complemented
5C2×#89985C211yesmaximal, characteristic, complemented
6C22×C7⋊#95C211yesmaximal, characteristic, complemented
7C2×#89731C211yesmaximal, characteristic, complemented
8C2×#89724C211yesmaximal, characteristic, complemented
9C2×#89733C211yesmaximal, characteristic, complemented
10C2×#89719C211yesmaximal, characteristic, complemented
11C2×#89730C211yesmaximal, characteristic, complemented
12#11732230C2116yesmaximal, direct product factor
13C2×#89447C211yesmaximal, characteristic, complemented
14C2×#89445C211yesmaximal, characteristic, complemented
15C2×#89432C211yesmaximal, characteristic, complemented
16C2×#89430C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C24×Dic7C2211yescharacteristic
23C23×Dic14C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C2×#6502—28no—
32C2×#6502C2218yes—
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C2×#6441—28no—
43C2×#6441C2218yescomplemented
44C7×#386C2218yescomplemented
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47#89992C2218yescomplemented
48#89985C2218yescomplemented
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#89733C2218yescomplemented
61#89731C2218yescomplemented
62#89730C2218yescomplemented
63#89724C2218yescomplemented
64#89719C2218yescomplemented
65#89447C2218yescomplemented
66#89445C2218yescomplemented
67#89432C2218yescomplemented
68#89430C2218yescomplemented
69C2×#2639—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—24no—
76C22×C7×D4C2314yes—
77C23×C4×C7—24no—
78C23×C4×C7—42no—
79C23×C4×C7—42no—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2314yes—
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×Dic7—42no—
98C23×Dic7—42no—
99C23×Dic7D418yes—
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C23×Dic7C2314yes—
108C23×Dic7C2314yes—
109C22×Dic14—24no—
110C22×Dic14—42no—
111C22×Dic14—42no—
112C22×Dic14C2314yes—
113C2×C7×C22⋊C4—24no—
114C2×C7×C22⋊C4—42no—
115C2×C7×C22⋊C4—42no—
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2314yes—
118C2×C7×C22⋊C4C2314yes—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—42no—
122C2×C22⋊Dic7—42no—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127#6502—232no—
128C2×(C2×D7)⋊C4—24no—
129C2×(C2×D7)⋊C4—42no—
130C2×(C2×D7)⋊C4—42no—
131C2×(C2×D7)⋊C4—42no—
132C2×(C2×D7)⋊C4—42no—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×C4⋊Dic7—24no—
139C2×C4⋊Dic7C2314yes—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4—24no—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×Dic7⋊C4C2314yes—
146#6441—232no—
147C7×#95C2314yes—
148C7×#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×C22⋊Q8—71no—
160C22×#121—71no—
161#2639—716no—
162C2×#400—71no—
163C2×#400—71no—
164C2×#397—71no—
165C2×#397—71no—
166C2×#394—71no—
167C2×#394—71no—
168C2×#393—71no—
169C2×#393—71no—
170C2×#386—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×#386D711yescharacteristic, complemented
174C22×#95—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×C7C2×D414yes—
187C24×C7#4114yes—
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—28no—
203C2×C7×D4—416no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—28no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—44no—
221C22×C4×C7—44no—
222C22×C4×C7—416no—
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—28no—
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—22no—
255C22×Dic7—22no—
256C22×Dic7—416no—
257C22×Dic7—44no—
258C22×Dic7—44no—
259C22×Dic7—44no—
260C22×Dic7—44no—
261C22×Dic7—416no—
262C22×Dic7C2×D414yes—
263C22×Dic7C2×D414yes—
264C22×Dic7C2×D4116yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C2×Dic14—28no—
273C2×Dic14—44no—
274C2×Dic14—44no—
275C2×Dic14—416no—
276C7×C22⋊C4—28no—
277C7×C22⋊C4—44no—
278C7×C22⋊C4—44no—
279C22⋊Dic7—28no—
280C22⋊Dic7—28no—
281C22⋊Dic7—44no—
282C22⋊Dic7—44no—
283(C2×D7)⋊C4—28no—
284(C2×D7)⋊C4—44no—
285(C2×D7)⋊C4—44no—
286(C2×D7)⋊C4—44no—
287(C2×D7)⋊C4—44no—
288C4⋊Dic7—28no—
289Dic7⋊C4—28no—
290Dic7⋊C4—28no—
291Dic7⋊C4—28no—
292C23×Q8—71no—
293C23×D4—71no—
294C23×D4—71no—
295C23×D4C2×D711yescharacteristic
296C24×C4—71no—
297C24×C4—71no—
298C24×C4C2×D711yescharacteristic
299C2×C22⋊Q8—78no—
300C2×C22⋊Q8—148no—
301C2×#121—78no—
302C2×#121—148no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C4⋊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⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C22⋊C4C2×D711yescharacteristic
319#400—78no—
320#400—78no—
321#397—78no—
322#397—78no—
323#394—78no—
324#394—78no—
325#393—78no—
326#393—78no—
327#386—78no—
328#386—78no—
329#386—78no—
330#386C2×D718yescomplemented
331C2×#95—78no—
332C2×#95—71no—
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×#95C2×D711yescharacteristic
343C2×#95C2×D711yescharacteristic
344C23×C7—28no—
345C23×C7—28no—
346C23×C7—28no—
347C23×C7—28no—
348C23×C7—28no—
349C23×C7—28no—
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#124116yes—
369C23×C7C22×D414yes—
370C23×C7C22×D412yes—
371C23×C7C2×#4114yes—
372C23×C7C2×#4112yes—
373C23×C7C2×#4114yes—
374C23×C7C2×#4112yes—
375C23×C7H(5,𝔽2)12yes—
376C23×C7H(5,𝔽2)12yes—
377C23×C7H(5,𝔽2)12yes—
378C23×C72−1+412yes—
379C23×C7C2511yescharacteristic
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7—44no—
392C22×D7—44no—
393C22×D7—44no—
394C7×D4—416no—
395C2×C4×C7—22no—
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—22no—
410C2×C4×C7—416no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7—44no—
414C2×C4×C7—44no—
415C2×C4×C7—44no—
416C22⋊D7—416no—
417C22⋊D7—416no—
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—22no—
439C2×Dic7—416no—
440C2×Dic7—416no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7—44no—
444C2×Dic7—44no—
445C2×Dic7—44no—
446C2×Dic7C22×D414yes—
447C2×Dic7C22×D414yes—
448Dic14—416no—
449C25—71no—
450C25C22×D711yescharacteristic
451C25C22×D711yescharacteristic
452C22×Q8—74no—
453C22×Q8—144no—
454C22×Q8—282no—
455C22×Q8—282no—
456C22×D4—24no—
457C22×D4—24no—
458C22×D4—24no—
459C22×D4—74no—
460C22×D4—74no—
461C22×D4—144no—
462C22×D4—144no—
463C22×D4—144no—
464C22×D4—144no—
465C22×D4—282no—
466C22×D4—282no—
467C22×D4C22×D714yes—
468C23×C4—24no—
469C23×C4—42no—
470C23×C4—42no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—78no—
474C23×C4—74no—
475C23×C4—71no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—74no—
481C23×C4—144no—
482C23×C4—282no—
483C23×C4—282no—
484C23×C4—282no—
485C23×C4—282no—
486C23×C4C22×D711yescharacteristic
487C23×C4C22×D711yescharacteristic
488C23×C4C22×D711yescharacteristic
489C23×C4C22×D711yescharacteristic
490C23×C4C22×D711yescharacteristic
491C23×C4C22×D714yes—
492C22⋊Q8—1432no—
493#121—1432no—
494C2×C4⋊C4—74no—
495C2×C4⋊C4—74no—
496C2×C4⋊C4—74no—
497C2×C4⋊C4—74no—
498C2×C4⋊C4—144no—
499C2×C4⋊C4—144no—
500C2×C4⋊C4—144no—
501C2×C4⋊C4—144no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—74no—
507C2×C22⋊C4—74no—
508C2×C22⋊C4—74no—
509C2×C22⋊C4—74no—
510C2×C22⋊C4—74no—
511C2×C22⋊C4—74no—
512C2×C22⋊C4—74no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—144no—
515C2×C22⋊C4—144no—
516C2×C22⋊C4—144no—
517C2×C22⋊C4—282no—
518C2×C22⋊C4—282no—
519C2×C22⋊C4—282no—
520C2×C22⋊C4—282no—
521C2×C22⋊C4—282no—
522C2×C22⋊C4—282no—
523C2×C22⋊C4C22×D714yes—
524C2×C22⋊C4C22×D714yes—
525C2×C22⋊C4C22×D714yes—
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—
536#95C22×D714yes—
537#95C22×D714yes—
538C22×C7—232no—
539C22×C7—24no—
540C22×C7—24no—
541C22×C7—24no—
542C22×C7—24no—
543C22×C7—24no—
544C22×C7—24no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—88no—
553C22×C7C2×#12418yes—
554C22×C7C2×#12414yes—
555C22×C7#53414yes—
556C22×C7#53714yes—
557C22×C7#53814yes—
558C22×C7#53814yes—
559C22×C7#53914yes—
560C22×C7#53914yes—
561C22×C7C23×D411yescharacteristic
562C22×C7C22×#4111yescharacteristic
563C22×C7C22×#4111yescharacteristic
564C22×C7C2×H(5,𝔽2)11yescharacteristic
565C22×C7C2×H(5,𝔽2)11yescharacteristic
566C22×C7C2×H(5,𝔽2)11yescharacteristic
567C22×C7C2×2−1+411yescharacteristic
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—42no—
572C2×D7—42no—
573C2×D7—42no—
574C2×D7—42no—
575C2×D7—88no—
576C4×C7—42no—
577C4×C7—42no—
578C4×C7—42no—
579C4×C7—42no—
580C4×C7—42no—
581Dic7—24no—
582Dic7—24no—
583Dic7—42no—
584Dic7—42no—
585Dic7—42no—
586Dic7—42no—
587Dic7—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—72no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24—142no—
606C24—142no—
607C24#115714yes—
608C24D4×D714yes—
609C24#115914yes—
610C24C23×D712yes—
611C24C23×D712yes—
612C24C23×D711yescharacteristic
613C2×Q8—148no—
614C2×Q8—284no—
615C2×Q8—284no—
616C2×Q8—2816no—
617C2×D4—28no—
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—416no—
621C2×D4—148no—
622C2×D4—148no—
623C2×D4—148no—
624C2×D4—148no—
625C2×D4—284no—
626C2×D4—284no—
627C2×D4—2816no—
628C2×D4—2816no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—28no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—416no—
648C22×C4—74no—
649C22×C4—74no—
650C22×C4—72no—
651C22×C4—72no—
652C22×C4—716no—
653C22×C4—72no—
654C22×C4—72no—
655C22×C4—72no—
656C22×C4—72no—
657C22×C4—72no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—148no—
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—142no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—2816no—
679C22×C4—284no—
680C22×C4—284no—
681C22×C4—284no—
682C22×C4—284no—
683C22×C4—2816no—
684C22×C4C23×D712yes—
685C22×C4C23×D712yes—
686C22×C4C23×D712yes—
687C22×C4C23×D712yes—
688C22×C4C23×D712yes—
689C4⋊C4—148no—
690C4⋊C4—148no—
691C4⋊C4—148no—
692C4⋊C4—148no—
693C22⋊C4—28no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—148no—
697C22⋊C4—148no—
698C22⋊C4—148no—
699C22⋊C4—284no—
700C22⋊C4—284no—
701C22⋊C4—284no—
702C22⋊C4—284no—
703C22⋊C4—284no—
704C22⋊C4—284no—
705C2×C7—28no—
706C2×C7—82no—
707C2×C7#263918yescomplemented
708C2×C7C22×#12411yescharacteristic
709C2×C7C2×#53411yescharacteristic
710C2×C7C2×#53711yescharacteristic
711C2×C7C2×#53811yescharacteristic
712C2×C7C2×#53811yescharacteristic
713C2×C7C2×#53911yescharacteristic
714C2×C7C2×#53911yescharacteristic
715D7—82no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—22no—
722C23—22no—
723C23—28no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—142no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23—142no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23—284no—
751C23—284no—
752C23—284no—
753C23—284no—
754C23#6448116yes—
755C23C2×#115714yes—
756C23C2×#115712yes—
757C23C2×D4×D714yes—
758C23C2×D4×D712yes—
759C23C2×#115914yes—
760C23C2×#115912yes—
761C23#654812yes—
762C23#654812yes—
763C23#655312yes—
764C23#655412yes—
765C23C24×D711yescharacteristic
766Q8—2816no—
767D4—416no—
768D4—2816no—
769D4—2816no—
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—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—416no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—74no—
792C2×C4—74no—
793C2×C4—148no—
794C2×C4—148no—
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—142no—
811C2×C4—142no—
812C2×C4—142no—
813C2×C4—142no—
814C2×C4—2816no—
815C2×C4—2816no—
816C2×C4—284no—
817C2×C4—284no—
818C2×C4—284no—
819C2×C4—284no—
820C2×C4—284no—
821C7C2×#263911yescharacteristic, complemented, Sylow
822C22—24no—
823C22—232no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—88no—
837C22—282no—
838C22—282no—
839C22—282no—
840C22—282no—
841C22—282no—
842C22—282no—
843C22—282no—
844C22—568no—
845C22C2×#644818yes—
846C22C2×#644814yes—
847C22#9025114yes—
848C22#9025514yes—
849C22#9028414yes—
850C22#9028814yes—
851C22#9029614yes—
852C22#9035614yes—
853C22C22×#115711yescharacteristic
854C22C22×D4×D711yescharacteristic
855C22C22×#115911yescharacteristic
856C22C2×#654811yescharacteristic
857C22C2×#654811yescharacteristic
858C22C2×#655311yescharacteristic
859C22C2×#655411yescharacteristic
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—144no—
866C4—144no—
867C4—282no—
868C4—282no—
869C4—282no—
870C4—282no—
871C4—282no—
872C2—28no—
873C2—82no—
874C2—562no—
875C2#1173223018yesdirect product factor
876C2C22×#644811yescharacteristic
877C2C2×#9025511yescharacteristic
878C2C2×#9025111yescharacteristic
879C2C2×#9028411yescharacteristic
880C2C2×#9028811yescharacteristic
881C2C2×#9029611yescharacteristic
882C2C2×#9035611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC22×#6502C2
hypercenterC2×#386D7
hypocenterC7C2×#2639
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×#6441C2semidirect
3. C2×C7×#386C2semidirect
4. C2×#89992C2semidirect
5. C2×#89985C2semidirect
6. C22×C7⋊#95C2semidirect
7. C2×#89731C2semidirect
8. C2×#89724C2semidirect
9. C2×#89733C2semidirect
10. C2×#89719C2semidirect
11. C2×#89730C2semidirect
12. #11732230C2direct (N × H)
13. C2×#89447C2semidirect
14. C2×#89445C2semidirect
15. C2×#89432C2semidirect
16. C2×#89430C2semidirect
43. C2×#6441C22semidirect
44. C7×#386C22semidirect
47. #89992C22semidirect
48. #89985C22semidirect
59. C2×C7⋊#95C22semidirect
60. #89733C22semidirect
61. #89731C22semidirect
62. #89730C22semidirect
63. #89724C22semidirect
64. #89719C22semidirect
65. #89447C22semidirect
66. #89445C22semidirect
67. #89432C22semidirect
68. #89430C22semidirect
173. C2×#386D7semidirect
330. #386C2×D7semidirect
707. C2×C7#2639semidirect
821. C7C2×#2639semidirect
875. C2#11732230direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65022
C22×#64412
C2×C7×#3862
C2×#899922
C2×#899852
C22×C7⋊#952
C2×#897312
C2×#897242
C2×#897332
C2×#897192
C2×#897302
#117322302
C2×#894472
C2×#894452
C2×#894322
C2×#894302
C2×#26397