Finite Group Databasebeta

← C2×#11731892 #13522158

Subgroups — C2×#11731892 #13522158

Order 1792.

3330 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6493C211yesmaximal, characteristic
2C22×#6455C211yesmaximal, characteristic, complemented
3C2×C7×#385C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
5C2×#89763C211yesmaximal, characteristic, complemented
6C2×#89762C211yesmaximal, characteristic, complemented
7C2×#89753C211yesmaximal, characteristic, complemented
8C2×#89728C211yesmaximal, characteristic, complemented
9C2×#89733C211yesmaximal, characteristic, complemented
10C2×#89733C211yesmaximal, characteristic, complemented
11C2×#89729C211yesmaximal, characteristic, complemented
12#11731892C2116yesmaximal, direct product factor
13C2×#89437C211yesmaximal, characteristic, complemented
14C2×#89433C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89441C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C2×#6493—28no—
29C2×#6493C2218yes—
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C22×C4⋊Dic7C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6455—28no—
47C2×#6455C2218yescomplemented
48C7×#385C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C4×C22⋊Dic7C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89763C2218yescomplemented
59#89762C2218yescomplemented
60#89753C2218yescomplemented
61#89733C2218yescomplemented
62#89733C2218yescomplemented
63#89729C2218yescomplemented
64#89728C2218yescomplemented
65#89442C2218yescomplemented
66#89441C2218yescomplemented
67#89437C2218yescomplemented
68#89433C2218yescomplemented
69C2×#2476—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7—24no—
74C23×C4×C7—24no—
75C23×C4×C7—42no—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2314yes—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C22×C22⋊D7—24no—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—24no—
87C22×C22⋊D7—42no—
88C22×C22⋊D7—42no—
89C22×C22⋊D7C2314yes—
90C22×C22⋊D7C2314yes—
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C22×D28—24no—
98C22×D28—24no—
99C22×D28—42no—
100C22×D28C2314yes—
101C22×C4×D7—24no—
102C22×C4×D7—24no—
103C22×C4×D7—24no—
104C22×C4×D7C2314yes—
105C2×C7×C4⋊C4—24no—
106C2×C7×C4⋊C4—24no—
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—42no—
111C2×C7×C22⋊C4C2314yes—
112C2×C7×C22⋊C4C2314yes—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117#6493—232no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—42no—
123C2×(C2×D7)⋊C4—42no—
124C2×(C2×D7)⋊C4—42no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4D418yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×C4⋊Dic7—24no—
137C2×C4⋊Dic7—24no—
138C2×C4⋊Dic7—42no—
139C2×C4⋊Dic7C2314yes—
140C2×C4⋊Dic7C2314yes—
141C2×C4⋊Dic7C2314yes—
142C2×Dic7⋊C4—42no—
143C2×Dic7⋊C4C2314yes—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—24no—
146C2×C4×Dic7—42no—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150#6455—232no—
151C7×#95C2314yes—
152C7×#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#121—71no—
160C22×#117—71no—
161#2476—716no—
162C2×#398—71no—
163C2×#394—71no—
164C2×#394—71no—
165C2×#394—71no—
166C2×#390—71no—
167C2×#388—71no—
168C2×#388—71no—
169C2×#388—71no—
170C2×#387—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×#385D711yescharacteristic, complemented
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#4114yes—
182C24×C7C2412yes—
183C24×C7C2411yescharacteristic
184C23×D7—22no—
185C23×D7—22no—
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7—22no—
190C23×D7—22no—
191C23×D7—22no—
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7—22no—
197C23×D7C2×D414yes—
198C23×D7C2412yes—
199C23×D7C2412yes—
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—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—22no—
214C22×C4×C7—22no—
215C22×C4×C7—28no—
216C22×C4×C7—28no—
217C22×C4×C7—44no—
218C22×C4×C7—416no—
219C22×C4×C7C2×D414yes—
220C22×C4×C7#4114yes—
221C22×C4×C7#4114yes—
222C22×C4×C7C2412yes—
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×Dic7C2×D414yes—
253C22×Dic7#4114yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C2×D28—28no—
261C2×D28—28no—
262C2×D28—44no—
263C2×D28—416no—
264C2×C4×D7—232no—
265C2×C4×D7—28no—
266C2×C4×D7—28no—
267C2×C4×D7—28no—
268C7×C4⋊C4—28no—
269C7×C4⋊C4—28no—
270C7×C22⋊C4—28no—
271C7×C22⋊C4—44no—
272C22⋊Dic7—28no—
273C22⋊Dic7—28no—
274(C2×D7)⋊C4—28no—
275(C2×D7)⋊C4—28no—
276(C2×D7)⋊C4—28no—
277(C2×D7)⋊C4—28no—
278(C2×D7)⋊C4—44no—
279(C2×D7)⋊C4—44no—
280(C2×D7)⋊C4—44no—
281(C2×D7)⋊C4—44no—
282(C2×D7)⋊C4C2×D4116yes—
283C4⋊Dic7—28no—
284C4⋊Dic7—28no—
285C4⋊Dic7—44no—
286Dic7⋊C4—44no—
287C4×Dic7—28no—
288C4×Dic7—28no—
289C4×Dic7—44no—
290C23×D4—71no—
291C23×D4—71no—
292C23×D4—71no—
293C24×C4—71no—
294C24×C4C2×D711yescharacteristic
295C2×#121—78no—
296C2×#121—148no—
297C2×#117—78no—
298C2×#117—148no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4C2×D711yescharacteristic
304C22×C4⋊C4C2×D711yescharacteristic
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⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321#398—78no—
322#394—78no—
323#394—78no—
324#394—78no—
325#390—78no—
326#388—78no—
327#388—78no—
328#388—78no—
329#387—78no—
330#386—78no—
331#386—78no—
332#385C2×D718yescomplemented
333C4×C22⋊C4—78no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95C2×D711yescharacteristic
341C2×#95C2×D711yescharacteristic
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—44no—
352C23×C7—44no—
353C23×C7—44no—
354C23×C7—44no—
355C23×C7C22×D412yes—
356C23×C7C2×#4112yes—
357C23×C7C2×#4112yes—
358C23×C7C2×#4114yes—
359C23×C7C2×#4112yes—
360C23×C7C2×#4112yes—
361C23×C7H(5,𝔽2)12yes—
362C23×C7H(5,𝔽2)12yes—
363C23×C7C2511yescharacteristic
364C22×D7—28no—
365C22×D7—28no—
366C22×D7—28no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—44no—
381C22×D7—44no—
382C22×D7—44no—
383C22×D7—44no—
384C22×D7—44no—
385C22×D7—44no—
386C22×D7—44no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7C22×D414yes—
392C2×C4×C7—28no—
393C2×C4×C7—28no—
394C2×C4×C7—28no—
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×C7C22×D414yes—
415C2×C4×C7C2×#4114yes—
416C2×C4×C7C2×#4114yes—
417C22⋊D7—416no—
418C22⋊D7—416no—
419C2×Dic7—28no—
420C2×Dic7—28no—
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—44no—
438C2×Dic7—44no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7C22×D414yes—
442C2×Dic7C2×#4114yes—
443D28—416no—
444C4×D7—232no—
445C25—71no—
446C25—71no—
447C25C22×D711yescharacteristic
448C22×D4—74no—
449C22×D4—74no—
450C22×D4—74no—
451C22×D4—144no—
452C22×D4—144no—
453C22×D4—144no—
454C22×D4—144no—
455C22×D4—144no—
456C22×D4—144no—
457C22×D4—282no—
458C22×D4—282no—
459C22×D4—282no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—42no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—74no—
470C23×C4—144no—
471C23×C4—144no—
472C23×C4—144no—
473C23×C4C22×D711yescharacteristic
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D714yes—
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480#121—1432no—
481#117—1432no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—144no—
489C2×C4⋊C4—144no—
490C2×C4⋊C4—282no—
491C2×C4⋊C4—282no—
492C2×C4⋊C4C22×D714yes—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—78no—
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—74no—
507C2×C22⋊C4—74no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4—282no—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42—144no—
525C2×C42—282no—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95C22×D714yes—
533#95C22×D714yes—
534C22×C7—24no—
535C22×C7—24no—
536C22×C7—24no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—416no—
542C22×C7#52514yes—
543C22×C7#52914yes—
544C22×C7#54014yes—
545C22×C7#54614yes—
546C22×C7#54614yes—
547C22×C7#55314yes—
548C22×C7#55514yes—
549C22×C7C23×D411yescharacteristic
550C22×C7C22×#4111yescharacteristic
551C22×C7C22×#4111yescharacteristic
552C22×C7C22×#4111yescharacteristic
553C22×C7C22×#4111yescharacteristic
554C22×C7C2×H(5,𝔽2)11yescharacteristic
555C22×C7C2×H(5,𝔽2)11yescharacteristic
556C2×D7—24no—
557C2×D7—24no—
558C2×D7—24no—
559C2×D7—42no—
560C2×D7—42no—
561C2×D7—42no—
562C2×D7—42no—
563C2×D7—416no—
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—88no—
572C4×C7—24no—
573C4×C7—24no—
574C4×C7—24no—
575C4×C7—42no—
576C4×C7—42no—
577C4×C7—42no—
578Dic7—24no—
579Dic7—24no—
580Dic7—42no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—74no—
591C24—72no—
592C24—72no—
593C24—142no—
594C24—142no—
595C24—142no—
596C24—142no—
597C24—142no—
598C24—142no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24—142no—
606C24#116114yes—
607C24C23×D712yes—
608C24C23×D711yescharacteristic
609C2×D4—148no—
610C2×D4—148no—
611C2×D4—148no—
612C2×D4—148no—
613C2×D4—148no—
614C2×D4—148no—
615C2×D4—284no—
616C2×D4—2816no—
617C2×D4—284no—
618C2×D4—284no—
619C2×D4—2816no—
620C2×D4—2816no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—28no—
637C22×C4—28no—
638C22×C4—44no—
639C22×C4—416no—
640C22×C4—74no—
641C22×C4—74no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—148no—
649C22×C4—148no—
650C22×C4—1432no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
654C22×C4—142no—
655C22×C4—148no—
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#115714yes—
669C22×C4D4×D714yes—
670C22×C4#115914yes—
671C22×C4C23×D712yes—
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C4⋊C4—28no—
678C4⋊C4—28no—
679C4⋊C4—148no—
680C4⋊C4—148no—
681C4⋊C4—284no—
682C4⋊C4—284no—
683C22⋊C4—28no—
684C22⋊C4—44no—
685C22⋊C4—716no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—284no—
693C22⋊C4—284no—
694C22⋊C4—284no—
695C22⋊C4—284no—
696C42—148no—
697C42—148no—
698C42—284no—
699C2×C7—44no—
700C2×C7#247618yescomplemented
701C2×C7C2×#52511yescharacteristic
702C2×C7C2×#52911yescharacteristic
703C2×C7C2×#54011yescharacteristic
704C2×C7C2×#54611yescharacteristic
705C2×C7C2×#54611yescharacteristic
706C2×C7C2×#55311yescharacteristic
707C2×C7C2×#55511yescharacteristic
708D7—44no—
709D7—82no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—74no—
724C23—148no—
725C23—148no—
726C23—148no—
727C23—142no—
728C23—142no—
729C23—142no—
730C23—142no—
731C23—142no—
732C23—142no—
733C23—142no—
734C23—142no—
735C23—142no—
736C23—142no—
737C23—142no—
738C23—142no—
739C23—142no—
740C23—284no—
741C23—284no—
742C23—284no—
743C23—284no—
744C23—284no—
745C23—284no—
746C23—284no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23—284no—
751C23C2×#115712yes—
752C23C2×D4×D712yes—
753C23C2×#115912yes—
754C23#654812yes—
755C23C2×#116114yes—
756C23C2×#116112yes—
757C23D7×#4112yes—
758C23#655312yes—
759C23C24×D711yescharacteristic
760D4—2816no—
761D4—2816no—
762D4—2816no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
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—416no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—74no—
786C2×C4—74no—
787C2×C4—1432no—
788C2×C4—148no—
789C2×C4—148no—
790C2×C4—142no—
791C2×C4—142no—
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—284no—
807C2×C4—284no—
808C2×C4—284no—
809C2×C4—284no—
810C2×C4C2×#115714yes—
811C2×C4C2×D4×D714yes—
812C2×C4C2×#115914yes—
813C7C2×#247611yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—416no—
822C22—144no—
823C22—144no—
824C22—144no—
825C22—282no—
826C22—282no—
827C22—282no—
828C22—282no—
829C22—2816no—
830C22—282no—
831C22—282no—
832C22—282no—
833C22—282no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—568no—
838C22#9020514yes—
839C22#9023814yes—
840C22#9025414yes—
841C22#9028214yes—
842C22#9031514yes—
843C22#9032114yes—
844C22#9035414yes—
845C22C22×#115711yescharacteristic
846C22C22×D4×D711yescharacteristic
847C22C22×#115911yescharacteristic
848C22C2×#654811yescharacteristic
849C22C22×#116111yescharacteristic
850C22C2×D7×#4111yescharacteristic
851C22C2×#655311yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—144no—
859C4—144no—
860C4—282no—
861C4—282no—
862C4—282no—
863C4—282no—
864C2—44no—
865C2—284no—
866C2—562no—
867C2#1173189218yesdirect product factor
868C2C2×#9020511yescharacteristic
869C2C2×#9025411yescharacteristic
870C2C2×#9023811yescharacteristic
871C2C2×#9028211yescharacteristic
872C2C2×#9031511yescharacteristic
873C2C2×#9032111yescharacteristic
874C2C2×#9035411yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#385C2
socleC24×C7C24
prime radicalC22×#6493C2
hypercenterC2×#385D7
hypocenterC7C2×#2476
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#6455C2semidirect
3. C2×C7×#385C2semidirect
4. C2×C4×C22⋊Dic7C2semidirect
5. C2×#89763C2semidirect
6. C2×#89762C2semidirect
7. C2×#89753C2semidirect
8. C2×#89728C2semidirect
9. C2×#89733C2semidirect
10. C2×#89733C2semidirect
11. C2×#89729C2semidirect
12. #11731892C2direct (N × H)
13. C2×#89437C2semidirect
14. C2×#89433C2semidirect
15. C2×#89442C2semidirect
16. C2×#89441C2semidirect
47. C2×#6455C22semidirect
48. C7×#385C22semidirect
51. C4×C22⋊Dic7C22semidirect
58. #89763C22semidirect
59. #89762C22semidirect
60. #89753C22semidirect
61. #89733C22semidirect
62. #89733C22semidirect
63. #89729C22semidirect
64. #89728C22semidirect
65. #89442C22semidirect
66. #89441C22semidirect
67. #89437C22semidirect
68. #89433C22semidirect
173. C2×#385D7semidirect
332. #385C2×D7semidirect
700. C2×C7#2476semidirect
813. C7C2×#2476semidirect
867. C2#11731892direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64932
C22×#64552
C2×C7×#3852
C2×C4×C22⋊Dic72
C2×#897632
C2×#897622
C2×#897532
C2×#897282
C2×#897332
C2×#897292
#117318922
C2×#894372
C2×#894332
C2×#894422
C2×#894412
C2×#24767