Finite Group Databasebeta

← C2×#11734379 #13523239

Subgroups — C2×#11734379 #13523239

Order 1792.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6502C211yesmaximal, characteristic
2C22×#6452C211yesmaximal, characteristic, complemented
3C2×C7×#394C211yesmaximal, characteristic, complemented
4C2×#89993C211yesmaximal, characteristic, complemented
5C2×#89762C211yesmaximal, characteristic, complemented
6C2×#89731C211yesmaximal, characteristic, complemented
7C2×#89724C211yesmaximal, characteristic, complemented
8C2×#89729C211yesmaximal, characteristic, complemented
9C2×#89729C211yesmaximal, characteristic, complemented
10C2×#89729C211yesmaximal, characteristic, complemented
11C2×#89716C211yesmaximal, characteristic, complemented
12C2×#89714C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
14#11734379C2116yesmaximal, direct product factor
15C2×#89446C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
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
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C2×#6452—28no—
49C2×#6452C2218yescomplemented
50C7×#394C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52#89993C2218yescomplemented
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89762C2218yescomplemented
59#89731C2218yescomplemented
60#89729C2218yescomplemented
61#89729C2218yescomplemented
62#89729C2218yescomplemented
63#89724C2218yescomplemented
64#89716C2218yescomplemented
65#89714C2218yescomplemented
66C22⋊C4×Dic7C2218yescomplemented
67#89446C2218yescomplemented
68#89421C2218yescomplemented
69C2×#2490—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×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—24no—
83C22×C22⋊D7—24no—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—24no—
87C22×C22⋊D7—42no—
88C22×C22⋊D7C2314yes—
89C22×C22⋊D7C2314yes—
90C23×Dic7—24no—
91C23×Dic7—24no—
92C23×Dic7—24no—
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2314yes—
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4C2314yes—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—42no—
105C2×C7×C22⋊C4—42no—
106C2×C7×C22⋊C4—42no—
107C2×C7×C22⋊C4C2314yes—
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—42no—
115C2×C22⋊Dic7—42no—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121#6502—232no—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4—24no—
124C2×(C2×D7)⋊C4—42no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4—42no—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×C4⋊Dic7—24no—
133C2×C4⋊Dic7C2314yes—
134C2×Dic7⋊C4—24no—
135C2×Dic7⋊C4—24no—
136C2×Dic7⋊C4—24no—
137C2×Dic7⋊C4—24no—
138C2×Dic7⋊C4D418yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—24no—
146C2×C4×Dic7—42no—
147C2×C4×Dic7—42no—
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150C2×C4×Dic7C2314yes—
151C2×C4×Dic7C2314yes—
152#6452—232no—
153C7×#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#125—71no—
160C22×#121—71no—
161#2490—716no—
162C2×#397—71no—
163C2×#397—71no—
164C2×#394—71no—
165C2×#394D711yescharacteristic, complemented
166C2×#390—71no—
167C2×#390—71no—
168C2×#390—71no—
169C2×#390—71no—
170C2×#388—71no—
171C2×#388—71no—
172C2×#380—71no—
173C2×C4×C4⋊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×C7—22no—
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—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7C2×D414yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C2×C22⋊D7—28no—
225C2×C22⋊D7—28no—
226C2×C22⋊D7—28no—
227C2×C22⋊D7—28no—
228C2×C22⋊D7—28no—
229C2×C22⋊D7—44no—
230C2×C22⋊D7—416no—
231C2×C22⋊D7—416no—
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—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—28no—
249C22×Dic7—28no—
250C22×Dic7—28no—
251C22×Dic7—416no—
252C22×Dic7C2×D414yes—
253C22×Dic7C2×D414yes—
254C22×Dic7#4114yes—
255C22×Dic7#4114yes—
256C22×Dic7#4114yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C7×C4⋊C4—28no—
265C7×C22⋊C4—28no—
266C7×C22⋊C4—44no—
267C7×C22⋊C4—44no—
268C7×C22⋊C4—44no—
269C22⋊Dic7—28no—
270C22⋊Dic7—28no—
271C22⋊Dic7—28no—
272C22⋊Dic7—44no—
273C22⋊Dic7—44no—
274(C2×D7)⋊C4—28no—
275(C2×D7)⋊C4—28no—
276(C2×D7)⋊C4—44no—
277(C2×D7)⋊C4—44no—
278(C2×D7)⋊C4—44no—
279C4⋊Dic7—28no—
280Dic7⋊C4—28no—
281Dic7⋊C4—28no—
282Dic7⋊C4—28no—
283Dic7⋊C4—28no—
284Dic7⋊C4C2×D4116yes—
285C4×Dic7—28no—
286C4×Dic7—28no—
287C4×Dic7—44no—
288C4×Dic7—44no—
289C23×D4—71no—
290C23×D4—71no—
291C23×D4C2×D711yescharacteristic
292C24×C4—71no—
293C2×#125—78no—
294C2×#125—148no—
295C2×#121—78no—
296C2×#121—148no—
297C22×C4⋊C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
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×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321C22×C42—71no—
322#397—78no—
323#397—78no—
324#394—78no—
325#394C2×D718yescomplemented
326#390—78no—
327#390—78no—
328#390—78no—
329#390—78no—
330#388—78no—
331#388—78no—
332#380—78no—
333C4×C4⋊C4—78no—
334C4×C22⋊C4—78no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95C2×D711yescharacteristic
341C23×C7—28no—
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
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—44no—
358C23×C7—44no—
359C23×C7—44no—
360C23×C7—44no—
361C23×C7—44no—
362C23×C7—44no—
363C23×C7—44no—
364C23×C7—44no—
365C23×C7—44no—
366C23×C7—44no—
367C23×C7—44no—
368C23×C7C22×D412yes—
369C23×C7C2×#4114yes—
370C23×C7C2×#4112yes—
371C23×C7C2×#4112yes—
372C23×C7C2×#4112yes—
373C23×C7C2×#4112yes—
374C23×C7H(5,𝔽2)12yes—
375C23×C7H(5,𝔽2)12yes—
376C23×C7C2511yescharacteristic
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—44no—
385C22×D7—44no—
386C22×D7—44no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C7×D4—416no—
392C2×C4×C7—28no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
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—44no—
408C2×C4×C7—44no—
409C2×C4×C7—44no—
410C2×C4×C7—44no—
411C2×C4×C7C22×D414yes—
412C22⋊D7—416no—
413C22⋊D7—416no—
414C2×Dic7—28no—
415C2×Dic7—28no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
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—44no—
433C2×Dic7—44no—
434C2×Dic7—44no—
435C2×Dic7—44no—
436C2×Dic7—416no—
437C2×Dic7#124116yes—
438C2×Dic7C22×D414yes—
439C2×Dic7C22×D414yes—
440C2×Dic7C2×#4114yes—
441C2×Dic7C2×#4114yes—
442C2×Dic7C2×#4114yes—
443C25—71no—
444C25C22×D711yescharacteristic
445C25C22×D711yescharacteristic
446C22×D4—24no—
447C22×D4—24no—
448C22×D4—42no—
449C22×D4—74no—
450C22×D4—74no—
451C22×D4—144no—
452C22×D4—144no—
453C22×D4—144no—
454C22×D4—144no—
455C22×D4—144no—
456C22×D4—282no—
457C22×D4C22×D714yes—
458C23×C4—71no—
459C23×C4—71no—
460C23×C4—71no—
461C23×C4—74no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—144no—
467C23×C4—144no—
468C23×C4—144no—
469C23×C4C22×D711yescharacteristic
470C23×C4C22×D711yescharacteristic
471C23×C4C22×D711yescharacteristic
472C23×C4C22×D711yescharacteristic
473C23×C4C22×D711yescharacteristic
474#125—1432no—
475#121—1432no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—78no—
478C2×C4⋊C4—74no—
479C2×C4⋊C4—74no—
480C2×C4⋊C4—74no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—144no—
485C2×C4⋊C4—144no—
486C2×C4⋊C4—144no—
487C2×C4⋊C4—144no—
488C2×C4⋊C4—144no—
489C2×C4⋊C4C22×D714yes—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—74no—
495C2×C22⋊C4—74no—
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—144no—
505C2×C22⋊C4—144no—
506C2×C22⋊C4—144no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—282no—
510C2×C22⋊C4—282no—
511C2×C22⋊C4—282no—
512C2×C22⋊C4—282no—
513C2×C22⋊C4—282no—
514C2×C22⋊C4C22×D714yes—
515C2×C22⋊C4C22×D714yes—
516C2×C22⋊C4C22×D714yes—
517C2×C22⋊C4C22×D714yes—
518C2×C42—74no—
519C2×C42—74no—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—144no—
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#95C22×D714yes—
532C22×C7—24no—
533C22×C7—24no—
534C22×C7—24no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—416no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—88no—
548C22×C7C2×#12414yes—
549C22×C7#52914yes—
550C22×C7#54014yes—
551C22×C7#54614yes—
552C22×C7#55014yes—
553C22×C7#55314yes—
554C22×C7#55314yes—
555C22×C7C23×D411yescharacteristic
556C22×C7C22×#4111yescharacteristic
557C22×C7C22×#4111yescharacteristic
558C22×C7C22×#4111yescharacteristic
559C22×C7C22×#4111yescharacteristic
560C22×C7C2×H(5,𝔽2)11yescharacteristic
561C22×C7C2×H(5,𝔽2)11yescharacteristic
562C2×D7—42no—
563C2×D7—42no—
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—88no—
570C4×C7—24no—
571C4×C7—42no—
572C4×C7—42no—
573C4×C7—42no—
574C4×C7—42no—
575Dic7—24no—
576Dic7—24no—
577Dic7—42no—
578Dic7—42no—
579Dic7—42no—
580Dic7—42no—
581Dic7C2×#12418yes—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—72no—
596C24—142no—
597C24—142no—
598C24—142no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24#115914yes—
604C24C23×D712yes—
605C24C23×D712yes—
606C24C23×D711yescharacteristic
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—44no—
610C2×D4—416no—
611C2×D4—148no—
612C2×D4—148no—
613C2×D4—148no—
614C2×D4—148no—
615C2×D4—148no—
616C2×D4—2816no—
617C2×D4—284no—
618C2×D4—2816no—
619C22×C4—22no—
620C22×C4—22no—
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—74no—
634C22×C4—74no—
635C22×C4—74no—
636C22×C4—72no—
637C22×C4—74no—
638C22×C4—74no—
639C22×C4—72no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—148no—
646C22×C4—148no—
647C22×C4—148no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
654C22×C4—142no—
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—2816no—
665C22×C4D4×D714yes—
666C22×C4C23×D712yes—
667C22×C4C23×D712yes—
668C22×C4C23×D712yes—
669C22×C4C23×D712yes—
670C22×C4C23×D712yes—
671C4⋊C4—28no—
672C4⋊C4—716no—
673C4⋊C4—148no—
674C4⋊C4—148no—
675C4⋊C4—148no—
676C4⋊C4—148no—
677C4⋊C4—148no—
678C22⋊C4—28no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—148no—
683C22⋊C4—148no—
684C22⋊C4—148no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—284no—
688C22⋊C4—284no—
689C22⋊C4—284no—
690C22⋊C4—284no—
691C22⋊C4—284no—
692C42—148no—
693C42—148no—
694C42—284no—
695C42—284no—
696C2×C7—44no—
697C2×C7—82no—
698C2×C7#249018yescomplemented
699C2×C7C22×#12411yescharacteristic
700C2×C7C2×#52911yescharacteristic
701C2×C7C2×#54011yescharacteristic
702C2×C7C2×#54611yescharacteristic
703C2×C7C2×#55011yescharacteristic
704C2×C7C2×#55311yescharacteristic
705C2×C7C2×#55311yescharacteristic
706D7—82no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—142no—
735C23—142no—
736C23—142no—
737C23—142no—
738C23—142no—
739C23—142no—
740C23—142no—
741C23—284no—
742C23—284no—
743C23—284no—
744C23—284no—
745C23—284no—
746C23—284no—
747C23—284no—
748C23C2×D4×D712yes—
749C23C2×#115914yes—
750C23C2×#115912yes—
751C23#654812yes—
752C23#654812yes—
753C23D7×#4112yes—
754C23D7×#4112yes—
755C23D7×#4112yes—
756C23C24×D711yescharacteristic
757D4—416no—
758D4—2816no—
759D4—2816no—
760C2×C4—28no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
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—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—74no—
780C2×C4—74no—
781C2×C4—74no—
782C2×C4—716no—
783C2×C4—74no—
784C2×C4—74no—
785C2×C4—148no—
786C2×C4—148no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
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—2816no—
804C2×C4—284no—
805C2×C4—284no—
806C2×C4—284no—
807C2×C4—284no—
808C2×C4C2×D4×D714yes—
809C7C2×#249011yescharacteristic, complemented, Sylow
810C22—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—416no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—88no—
826C22—282no—
827C22—282no—
828C22—282no—
829C22—282no—
830C22—282no—
831C22—282no—
832C22—282no—
833C22—568no—
834C22#9028214yes—
835C22#9029014yes—
836C22#9029214yes—
837C22#9030614yes—
838C22#9034014yes—
839C22#9035214yes—
840C22D7×#12414yes—
841C22C22×D4×D711yescharacteristic
842C22C22×#115911yescharacteristic
843C22C2×#654811yescharacteristic
844C22C2×#654811yescharacteristic
845C22C2×D7×#4111yescharacteristic
846C22C2×D7×#4111yescharacteristic
847C22C2×D7×#4111yescharacteristic
848C4—24no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—78no—
854C4—144no—
855C4—144no—
856C4—282no—
857C4—282no—
858C4—282no—
859C4—282no—
860C2—44no—
861C2—82no—
862C2—562no—
863C2#1173437918yesdirect product factor
864C2C2×#9028211yescharacteristic
865C2C2×#9030611yescharacteristic
866C2C2×#9029011yescharacteristic
867C2C2×#9029211yescharacteristic
868C2C2×#9034011yescharacteristic
869C2C2×#9035211yescharacteristic
870C2C2×D7×#12411yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC22×#6502C2
hypercenterC2×#394D7
hypocenterC7C2×#2490
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#6452C2semidirect
3. C2×C7×#394C2semidirect
4. C2×#89993C2semidirect
5. C2×#89762C2semidirect
6. C2×#89731C2semidirect
7. C2×#89724C2semidirect
8. C2×#89729C2semidirect
9. C2×#89729C2semidirect
10. C2×#89729C2semidirect
11. C2×#89716C2semidirect
12. C2×#89714C2semidirect
13. C2×C22⋊C4×Dic7C2semidirect
14. #11734379C2direct (N × H)
15. C2×#89446C2semidirect
16. C2×#89421C2semidirect
49. C2×#6452C22semidirect
50. C7×#394C22semidirect
52. #89993C22semidirect
58. #89762C22semidirect
59. #89731C22semidirect
60. #89729C22semidirect
61. #89729C22semidirect
62. #89729C22semidirect
63. #89724C22semidirect
64. #89716C22semidirect
65. #89714C22semidirect
66. C22⋊C4×Dic7C22semidirect
67. #89446C22semidirect
68. #89421C22semidirect
165. C2×#394D7semidirect
325. #394C2×D7semidirect
698. C2×C7#2490semidirect
809. C7C2×#2490semidirect
863. C2#11734379direct (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×#64522
C2×C7×#3942
C2×#899932
C2×#897622
C2×#897312
C2×#897242
C2×#897292
C2×#897162
C2×#897142
C2×C22⋊C4×Dic72
#117343792
C2×#894462
C2×#894212
C2×#24907